Answer:
The values in the table suggest that there is a mathematical relationship between the two variables X and Y. Upon inspection, we can observe that Y is increasing with respect to X, and the increase seems to be non-linear. Specifically, as X increases by a factor of 2, Y increases by a factor of approximately 1.5 to 2.
Based on these observations, it seems that the relationship between X and Y may be an exponential one. To confirm this, we can plot the data points on a graph and see if they form a curve that resembles an exponential function.
Alternatively, we can calculate the ratio of Y to X and see if it remains approximately constant. This can be done by dividing each value of Y by its corresponding value of X:
1/5 = 0.2
2/10 = 0.2
3/15 = 0.2
5/25 = 0.2
8/40 = 0.2
The ratio remains constant at approximately 0.2, suggesting that the relationship between X and Y may be a proportional one, with a constant of proportionality equal to 0.2.
Therefore, the table represents a proportional relationship between X and Y, where Y is proportional to X with a constant of proportionality equal to 0.2.
Step-by-step explanation:
Here's a step-by-step explanation of how to evaluate the table:
1. Identify the variables: The table contains two variables, X and Y, which are listed in two separate columns.
2. Examine the values: Look at the values in the table for both X and Y. Notice that as X increases, so does Y.
3. Determine the pattern: To determine the pattern between the two variables, calculate the ratio of Y to X. If the ratio is constant, then the relationship is proportional. If the ratio changes, then the relationship is nonlinear.
4. Calculate the ratio: To calculate the ratio, divide each value of Y by its corresponding value of X. For example, to find the ratio for the first row, divide 1 by 5: 1/5 = 0.2. Continue calculating the ratios for each row.
5. Analyze the ratio: If the ratios are approximately constant, then the relationship is proportional. In this case, we see that the ratios are all approximately 0.2, so we can conclude that the relationship is proportional.
6. Determine the constant of proportionality: To determine the constant of proportionality, simply use any one of the rows in the table. For example, let's use the first row, where X = 5 and Y = 1. The ratio of Y to X is 0.2, so we can write the relationship as Y = 0.2X. This means that for every increase of 1 unit in X, Y increases by 0.2 units.
7. Summarize the result: Based on the analysis, we can say that the table represents a proportional relationship between X and Y, with a constant of proportionality equal to 0.2.
Given
X 5 10 15 25 40
Y 1 2 3 5 8
5 / 40 = 0.2
y=0.2x
Malcolm and Peiling each have some $50, $10 and $2-notes. The total number of notes they have is the same. The number of $2-notes Peiling has is of the 1 2 4 number of $2-notes Malcolm has. The number of $10-notes Peiling has is the number of $10-notes Malcolm has. Peiling has 8 more $50-notes than Malcolm. The total number of $2 and $10-notes they have is 42. (a) Who has more money? (b) of How many $2-notes do they have altogether?
In the above word problem,
a) Peiling has more money than Malcolm.b) They (both Peiling and Malcom) have a total of M2 + P2 = 12 + 3 = 15 $2-notes altogether.What is the explanation for the above solution?
Let's denote the number of $50 notes that Malcolm and Peiling have as M50 and P50 respectively. Similarly, we'll denote the number of $10 notes as M10 and P10 and the number of $2 notes as M2 and P2.
From the problem statement we have the following information:
1. The total number of notes they have is the same: M50 + M10 + M2 = P50 + P10 + P2
2. The number of $2-notes Peiling has is 1/4 of the number of $2-notes Malcolm has: P2 = (1/4)M2
3. The number of $10-notes Peiling has is twice the number of $10-notes Malcolm has: P10 = 2M10
4. Peiling has 8 more $50-notes than Malcolm: P50 = M50 + 8
5. The total number of $2 and $10-notes they have is 42: M10 + M2 + P10 + P2 = 42
Substituting equations (2), (3) and (4) into equation (1) we get:
M50 + M10 + M2 = (M50+8) + 2M10 +(1/4)M2
Solving for M50 we get:
M50 = 8 + 2M10 - (3/4)M2
Substituting equations (2), (3), and (4) into equation (5) we get:
M10 + M2 + 2M10 + (1/4)M2 = 42
Solving for M10 we get:
M10 = 14 - (1/12)M2
Substituting this value of M10 into the equation for M50 we get:
M50 = 8 + 28 - M2/6 - (3/4)M2
Solving for M50 we get:
M50 = 36 - (11/6)M2
Since the number of notes must be a positive integer, the smallest possible value for M50 is when M2=6. This gives us a value of M50=35.
Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=43 $50 notes, P10=28 $10 notes and P2=1.5 $2 notes. However, since the number of notes must be a positive integer, this solution is not valid.
The next smallest possible value for M50 is when M2=12. This gives us a value of M50=34. Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=42 $50 notes, P10=28 $10 notes and P2=3 $2 notes.
Now we can calculate the total amount of money each person has:
Malcolm: 34 * 50 + 14 * 10 + 12 * 2 = $1,864
Peiling: 42 * 50 + 28 * 10 + 3 * 2 = $2,386
So to answer part (a) of the question: Peiling has more money than Malcolm.
To answer part (b) of the question: They have a total of M2 + P2 = 12 + 3 = 15 $2-notes altogether.
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Math tell me
division
Answer:
Arithmetic operationsvteAddition (+)Subtraction (−)Multiplication (×)Division (÷)Exponentiation (^)nth root (√)Logarithm (log)vteDivision is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. 7 This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples .
Step-by-step explanation:
The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16.
a. What proportion or percentage of children has an MDI of at least 120?
b. What proportion or percentage of children has an MDI of at least 80?
c. Find the MDI score that is the 99th percentile.
d. Find the MDI score such that only 1% of the population has an MDI score below it.
e. Recall what percentages that Q1 and Q3 represent. Find the scores for the lower quartile and upper quartile of the MDI and state them in a descriptive sentence describing what the scores represent.
f. Find the interquartile range (IQR) of the MDI scores.
g. Find the upper and lower limits and state the intervals of MDI scores that would be considered potential outliers.
a. The proportion or percentage of children with an MDI score of at least 120 is 10.56%.
b. The proportion or percentage of children with an MDI score of at least 80 is also 10.56%.
c. The MDI score that corresponds to the 99th percentile is approximately 137.
d. The MDI score such that only 1% of the population has an MDI score below it is approximately 63.
e. The lower quartile (Q1) of MDI scores is 89.28, and the upper quartile (Q3) is 110.72. These scores represent the range below which 25% of the population falls and the range above which 25% of the population falls, respectively.
f. The interquartile range (IQR) is 21.44.
g. The upper limit for potential outliers is 142.88, and the lower limit is 57.12. Any MDI scores outside this range would be considered potential outliers.
a. To find the proportion of children with an MDI score of at least 120, we need to calculate the z-score and use the standard normal distribution table. The z-score for an MDI score of 120 is (120-100)/16 = 1.25. Using the standard normal distribution table, the proportion of children with an MDI score of at least 120 is 0.1056 or 10.56%.
b. Similarly, to find the proportion of children with an MDI score of at least 80, we need to calculate the z-score for an MDI score of 80, which is (80-100)/16 = -1.25. Using the standard normal distribution table, the proportion of children with an MDI score of at least 80 is 0.1056 or 10.56%.
c. To find the MDI score that corresponds to the 99th percentile, we need to find the z-score that corresponds to the 99th percentile using the standard normal distribution table. The z-score is approximately 2.33. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI score that corresponds to the 99th percentile: x = zσ + μ = 2.33 * 16 + 100 = 136.88. Therefore, the MDI score that corresponds to the 99th percentile is approximately 137.
d. To find the MDI score such that only 1% of the population has an MDI score below it, we need to find the z-score that corresponds to the 1st percentile using the standard normal distribution table. The z-score is approximately -2.33. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI score that corresponds to the 1st percentile: x = zσ + μ = -2.33 * 16 + 100 = 63.12.
Therefore, the MDI score such that only 1% of the population has an MDI score below it is approximately 63.
e. The lower quartile (Q1) represents the 25th percentile, and the upper quartile (Q3) represents the 75th percentile. Using the standard normal distribution table, the z-score for the 25th percentile is approximately -0.67, and the z-score for the 75th percentile is approximately 0.67. Using the formula z = (x - μ)/σ, we can solve for x to find the MDI scores that correspond to Q1 and Q3: Q1 = -0.67 * 16 + 100 = 89.28, and Q3 = 0.67 * 16 + 100 = 110.72.
Therefore, the lower quartile of the MDI scores represents the scores below which 25% of the population falls, and the upper quartile represents the scores above which 25% of the population falls.
f. The interquartile range (IQR) is the difference between Q3 and Q1. Therefore, IQR = Q3 - Q1 = 110.72 - 89.28 = 21.44.
g. To find the upper and lower limits for potential outliers, we need to use the formula:
Upper limit = Q3 + 1.5IQR
Lower limit = Q1 - 1.5IQR
Substituting the values we have found, we get:
Upper limit = 110.72 + 1.521.44 = 142.88
Lower limit = 89.28 - 1.521.
The upper limit for potential outliers is 142.88, and the lower limit is 57.12. Any MDI scores outside this range would be considered potential outliers.
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before a visit to the vet, Bridget used a bathroom scale to weigh her cat, muffin. the bathroom scale said muffin weighed 8 pounds. the scale at the vet's office was more precise, and it showed muffins weight as 8.2 pounds. what is the percent error for the bathroom scales measurement
if necessary round your answer to the nearest tenth of a percent.
In Bridget's bathroom, the scale indicated the muffin weighed 8 pounds. The more accurate scale at the veterinarian's office indicated that the muffins weighed 8.2 pounds. The bathroom scales' measurement error is 2.4% percent.
To find the percent error, we need to compare the difference between the two measurements (the actual weight and the weight measured by the bathroom scale) with the actual weight, and express it as a percentage.
The actual weight of muffin is 8.2 pounds. The weight measured by the bathroom scale is 8 pounds.
The difference between the two measurements is:
8.2 - 8 = 0.2 pounds
To calculate the percent error, we divide the difference by the actual weight, and multiply by 100:
percent error = (difference / actual weight) x 100
percent error = (0.2 / 8.2) x 100
percent error = 0.0244 x 100
percent error = 2.44
To the nearest tenth of a percent, we round and obtain:
percent error ≈ 2.4%
Therefore, the percent error for the bathroom scale's measurement is approximately 2.4%.
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3y² +5y=12
Solve each equation by completing the square. If necessary, round to the nearest hundredth
By answering the presented question, we may conclude that Therefore, the solutions to the equation 3y² + 5y = 12 are y = -2/3 or y = 1, rounded to the nearest hundredth.
What is equation?A statement proving the equality of two expressions is known as an equation. It can include variables, integers, and mathematical operations like addition, subtraction, multiplication, and division. It also incorporates mathematical symbols. In mathematics and science, equations are frequently used to illustrate connections between quantities. The equals sign (=) is typically used in equations to denote that the expressions on each side of the sign have the same value. For instance, the formula 2 + 3 = 5 demonstrates that the total of 2 and 3 equals 5. Equations can be solved to determine a variable's value or to determine if a certain value meets the connection that the equation describes.
3y² + 5y = 12
3y² + 5y - 12 = 0
y² + (5/3)y - 4 = 0
y² + (5/3)y + 25/36 - 25/36 - 4 = 0
(y + 5/6)² - 49/36 = 0
(y + 5/6)² = 49/36
y + 5/6 = ±(7/6)
y = (-5 ± 7)/6
y = -2/3 or y = 1
Therefore, the solutions to the equation 3y² + 5y = 12 are y = -2/3 or y = 1, rounded to the nearest hundredth.
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1000 mg of vancomycin diluted in 250 ml D5W is to be infused for over 2 hours. In a gravity infusion with a Macro tubing of 15 gtt/ml. what is the drip rate?
The drip rate for the gravity infusion of 1000 mg of vancomycin diluted in 250 ml D5W over 2 hours with a Macro tubing of 15 gtt/ml is approximately 26 gtt/min.
What is drip rate?Drip rate, also known as infusion rate or flow rate, is the speed at which a solution is infused or delivered to a patient over a certain period of time. Drip rate is typically measured in drops per minute (gtt/min) for gravity infusions or milliliters per hour (ml/hr) for infusion pumps.
In a gravity infusion, the drip rate is calculated by dividing the volume of the solution to be infused by the time of the infusion, and then multiplying by the drop factor of the IV administration set. The resulting number is the number of drops that need to be delivered per minute to the patient.
To calculate the drip rate for a gravity infusion, we can use the formula:
Drip rate = (Volume to be infused × Drop factor) ÷ Time of infusion
where:
Volume to be infused = 250 ml (given)
Drop factor = 15 gtt/ml (given)
Time of infusion = 2 hours = 120 minutes (since the infusion is to be given over 2 hours)
To use this formula, we need to first convert the volume of vancomycin from milligrams (mg) to milliliters (ml), since the volume to be infused is given in ml. The concentration of the vancomycin solution is 1000 mg/250 ml = 4 mg/ml. Therefore, the volume of vancomycin to be infused is:
Volume of vancomycin = 1000 mg ÷ 4 mg/ml = 250 ml
Now we can replace in the values into the formula:
Drip rate = (250 ml × 15 gtt/ml) ÷ 120 minutes
Drip rate = 3125 gtt ÷ 120 minutes
Drip rate ≈ 26 gtt/min
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HELP PLS !!!!!!!!!!!!!!!
Please help!!!!!!!!!!!
Using rules of exponents,
Miguel:
Law-1: Rule of the product of powers: When multiplying like bases, add the powers together.
Law-2: Power of powers rule: When increasing a power by another exponent, multiply all the powers together.
Gia:
Law-1: Power of powers rule: When increasing a power by another exponent, multiply all the powers together.
Law-2: Rule of the product of powers: When multiplying like bases, add the powers together.
Define the rule of exponents?The work of simplifying exponent-based assertions is made easier by exponent rules, often known as the "laws of exponents" or "properties of exponents." These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
Here in the question:
We can see that in case of Miguel,
He first added the powers as the bases are same. Then he multiplied the powers together.
In case of Gia, it is vice versa:
Gia first multiplied the powers of the individual components and raised the powers accordingly.
Then further she added the powers of the like bases.
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Solve the following inequalities, giving your answer in interval notation and sketch the solution:
i. 3≤2(−5)<7
ii. −14<−7(3+2)<1
I. From 2(-5), we obtain -10. Next, we have: 3 -10 7
This cannot be true because -10 is not between 3 and 7. there is no solution to this inequality.
What three steps are involved in resolving an inequality?Make use of the following steps to solve an inequality:
Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator.
Step 2 Combine like terms on both sides of the inequality to simplify.
Step 3 Get the unknown on one side and the integers on the other by adding or subtracting quantities.
ii. To begin, we must use the following set of operations to simplify -7(3+2):
-7(3+2) = -7(5) = -35
We now have:
-14 < -35 < 1
This is accurate since -35 is less than both -14 and 1, as well as less than 1. As a result, the interval is the answer to this inequality: (-35, 1)
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please help me i really need help
Answer: 40%
Step-by-step explanation:
STEP 1: Start by adding all the data to get a total; 36 + 54 + 60 [150]
STEP 2: Divide the number of people that voted for Candidate B by the total number of voters; 60/150 [0.4]
STEP 3: Convert the decimal to percent; 0.4 x 100 [40]
Therefore, the answer to this problem is 40%.
marking as brainlist!! PLEASE HELP
Answer:
b = 93°
Step-by-step explanation:
We Know
A triangle sum is 180°.
We know two angles, one is 21.5° and the other is 65.5°.
Find angle b
We take
180 - (21.5 + 65.5) = 93°
So, b = 93°
Find the area of a segment by a chord 8 long in a circle with radius of 8
The area of the segment is 5.76 in²
What is a Segment of a Chord?A segment of a chord refers to a portion of a chord that lies between two points on the circumference of a circle. In other words, a chord is a line segment that connects two points on a circle, and a segment of a chord is any part of that chord that lies between the two endpoints.
For example, if we have a circle with points A and B on its circumference, and a chord that connects these two points, then any portion of the chord that lies between A and B is a segment of the chord.
How to solve
If a chord is 8`` long then α = 60° = π/3 ( the angle between the line segments connecting the ends of the chord and the center of the circle).
A = 1/2 r² ( α - sin α ) = 1/2 · 8² ( π/3 - sin π/3 ) =
= 1/2 · 64 ( 1.046 - 0.866 ) = 5.76 in²
Answer: The area of a segment is 5.76 in²
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Find the surface area of the triangular prism using the net.
Answer:
Step-by-step explanation:
Answer = 50.8 in^2 for surface area of the triangular prism
Step by step
A “net” is the figure laid out so you can see it broke down into smaller shape
Starting from the left we have 3 rectangles and two triangles
Area of rectangles = L x W
Area of triangles = 1/2bh
Solve
Rectangle #1 = 2 x 5 = 10 in^2
Rectangle #2 = 2 x 4 = 8 in^2
Rectangle #3 = 2 x 6.4 = 12.8 in^2
Triangle #1 = (1/2) (4) (5) = 10 in^2
Triangle #2 = (1/2) (4) (5) = 10 in^2
Add your figures together
10 + 8 + 12.8 + 10 + 10 = 50.8 in^2
see attachment for breakdown
Exercise 5:
You conduct a study to determine the impact that varying the amount of noise in an
office has on worker productivity. You obtain the following productivity scores.
Condition 1:
Low Noise
15
19
13
13
Condition 2:
Medium Noise
13
11
14
10
Condition 3:
Loud Noise
2978
a. Assuming that productivity scores are normally distributed ratio scores, compute
the summaries of this experiment.
b. Draw the appropriate graph for these data.
c. Assuming that the data are representative, draw how we would envision the
populations produced by this experiment.
d. What conclusions should you draw from this experiment?
The answers for the following questions are mentioned below respectively.
Define statistics?The branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.
a. To compute the summaries of this experiment, we need to calculate the mean and standard deviation of each condition.
Condition 1: Low Noise
Mean = (15 + 19 + 13 + 13) / 4 = 15
Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1)) = 2.58
Condition 2: Medium Noise
Mean = (13 + 11 + 14 + 10) / 4 = 12
Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1)) = 1.87
Condition 3: Loud Noise
Mean = 2978
Standard deviation = undefined, as there is only one observation.
b. The appropriate graph for these data is a histogram, with each condition represented by a different color or pattern. The x-axis represents the productivity scores, and the y-axis represents the frequency or percentage of observations in each condition.
c. Assuming that the data are representative, we would envision the populations produced by this experiment as three different normal distributions, each with its own mean and standard deviation. The population distribution for the low noise condition would be centered around a mean of 15, with most scores falling within 2.58 points of this mean. The population distribution for the medium noise condition would be centered around a mean of 12, with most scores falling within 1.87 points of this mean. The population distribution for the loud noise condition is unknown, as we only have one observation.
d. The conclusions that can be drawn from this experiment depend on the research question and hypothesis being tested. However, based on the information given, we can conclude that there is a difference in productivity scores across the three conditions, with the lowest scores occurring in the medium noise condition. However, we cannot draw any conclusions about the effect of noise on productivity without further analysis or experimental manipulation.
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We must determine the means and standard deviation of each circumstance.
Standard deviation = 1.87
Mean = 2978
Define statistics?The area of mathematics concerned with the gathering, examination, interpretation, display, and arrangement of data.
a). We must compute the means and standard deviations of each condition in order to compute the summaries for this exercise.
Condition 1: Low Noise
Mean = (15 + 19 + 13 + 13) / 4
= 15
Standard deviation = √([(15-15)²+ (19-15)² + (13-15)² + (13-15)²] / (4-1))
= 2.58
Condition 2: Medium Noise
Mean = (13 + 11 + 14 + 10) / 4
= 12
Standard deviation = √([(13-12)²+ (11-12)² + (14-12)² + (10-12)²] / (4-1))
= 1.87
Condition 3: Loud Noise
Mean = 2978
Standard deviation = undefined, as there is only one observation.
b). The suitable graph for these data is a histogram, where the x-axis represents productivity scores and the y-axis represents the frequency or percentage of observations in each condition, with each condition represented by a different color or pattern.
c). We would picture the populations generated by this experiment as three distinct normal distributions, each with its own mean and standard deviation, assuming that the data are representative. Most scores would lie within 2.58 points of the mean for the low noise condition, which would have a population distribution centered around a mean of 15. Most scores would lie within 1.87 points of the mean for the medium noise condition, which would have a population distribution centered around a mean of 12. We only have one observation, so we don't know the population distribution for the loud noise situation.
d). The study query and tested hypothesis determine the conclusions that can be drawn from this experiment. However, based on the available data, we can infer that there is a difference in output scores between the three conditions, with the medium noise condition recording the lowest scores. However, without additional investigation or experimental manipulation, we are unable to make any judgments about how noise affects output.
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The temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with a mean of 900 and a standard deviation of 50 degrees.
If bricks are fired at a temperature above 1100, they will crack and must be disposed of. If the bricks are placed randomly throughout the kiln, the proportion of bricks that crack during the firing process is closest to ______.
Answer:
Step-by-step explanation:
.................... ...............................................
In a survey of college students, each of the following was found. Of these students, 359 owned a tablet, 294 owned a laptop, 284 owned a gaming system, 195 owned a tablet and a laptop, 200 owned a tablet and a gaming system, 140 owned a laptop and a gaming system, 68 owned a tablet, a laptop, and a gaming system, and 26 owned none of these devices. Complete parts a) through e) below.
a) How many college students were surveyed?
b) Of the college students surveyed, how many owned a tablet and a gaming system, but not a laptop?
c) Of the college students surveyed, how many owned a laptop, but neither a tablet nor a gaming system?
d) Of the college students surveyed, how many owned exactly two of these devices?
e) Of the college students surveyed, how many owned at least one of these devices?
There were 850 college students surveyed. 132 students owned a tablet and a gaming system, but not a laptop. There seems to be an error in the data or the calculations for part c. 467 students owned exactly two of these devices. 824 students owned at least one of these devices.
What is probability?Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
According to the given information:a) To find the total number of college students surveyed, we can start by adding the number of students who own a tablet, a laptop, or a gaming system:
359 (tablet) + 294 (laptop) + 284 (gaming system) = 937
However, this includes some students who own more than one device. We need to adjust for the overlap:
195 own a tablet and a laptop
200 own a tablet and a gaming system
140 own a laptop and a gaming system
68 own all three devices
To get the total number of unique students who own at least one device, we can subtract the overlap from the initial sum:
937 - (195 + 200 + 140 - 68) = 850
Therefore, 850 college students were surveyed.
b) From the given information, we know that 200 students own a tablet and a gaming system, and 68 own all three devices. Therefore, the number of students who own a tablet and a gaming system, but not a laptop, is:
200 - 68 = 132
Therefore, 132 college students own a tablet and a gaming system, but not a laptop.
c) To find the number of students who own a laptop, but neither a tablet nor a gaming system, we can start by adding the number of students who own a laptop and then subtract the overlap:
294 (laptop) - 195 (tablet and laptop) - 140 (laptop and gaming system) - 68 (all three) = -9
This suggests that there is an error in the data or the calculations, since we cannot have negative students. It is possible that there was a typo or mistake in the original problem.
d) To find the number of students who own exactly two devices, we can add up the number of students who own each pair of devices and subtract the overlap:
195 own a tablet and a laptop
200 own a tablet and a gaming system
140 own a laptop and a gaming system
68 own all three devices
195 + 200 + 140 - 68 = 467
Therefore, 467 college students own exactly two of these devices.
e) To find the number of students who own at least one of these devices, we can simply subtract the number of students who own none of these devices from the total number of students surveyed:
850 - 26 = 824
Therefore, 824 college students surveyed own at least one of these devices.
Therefore,There were 850 college students surveyed. 132 students owned a tablet and a gaming system, but not a laptop. There seems to be an error in the data or the calculations for part c. 467 students owned exactly two of these devices. 824 students owned at least one of these devices.
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How many pets does Stella have in total
if all except two are dogs, all except two
are cats, and all except two are rabbits?
You have three pets.
If there were more to each "all" than one, those pets would have to be dogs AND cats AND rabbits.
trevon invests $7 246 in savings account with a fixed annual interest rate of 3.20 compounded monthly how long will it take for the account balance to reach $9,974.42?
Hence the Travon account balance reach 9974.42 in 10 years.
The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.
If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.
Traven invest $7246 in a saving account with a fixed annual interest rate of 3.20 compounded monthly, find the time for the account balance to reach $9974.42,
We know that the formula for compounded interest is-
[tex]A=p(1-\frac{r}{100})^n[/tex],
A=9974.42
p=7246
r=3.2
put all the values in the formula,
[tex]9974.42=7246(1-0.032)^n\\\\1.3765=(0.968)^n\\[/tex]
n=10 year
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OKL and OMN are sectors of two different circles. The central angle of both circles is 114 degrees. Work out perimeter of the shaded shape KLNM. Give answer to 2dp. (See picture)
The perimeter of the shaded shape KLNM is approximately 11.44 cm to 2 decimal places.
What is a circle?
A circle is a closed two-dimensional shape consisting of all the points that are equidistant from a given point called the center. The distance between the center and any point on the circle is called the radius.
We know that the central angle of both circles is 114 degrees, so the angle at the center of each circle is 114 degrees.
The angle formed by lines KL and KM is half of the central angle, which is 57 degrees. Similarly, the angle formed by lines NL and NM is also 57 degrees.
We can use the Law of Cosines to find the length of KL and NM:
KL² = OK² + OL² - 2(OK)(OL)cos(57°)
NM² = ON² + OM² - 2(ON)(OM)cos(57°)
We know that OK = OL = 5 cm and ON = OM = 6 cm. Plugging these values into the equations above, we get:
KL² = 50 - 50cos(57°) ≈ 26.96
NM² = 72 - 72cos(57°) ≈ 39.04
Taking the square root of both sides, we get:
KL ≈ 5.19 cm
NM ≈ 6.25 cm
The perimeter of the shaded shape KLNM is KL + LM + MN + NK. We can find LM and NK by subtracting KL and NM from the diameter of each circle, which is 10 cm:
LM = 10 - 2(OL) = 10 - 10 = 0
NK = 10 - 2(OM) = 10 - 12 = -2
Since NK is negative, we can ignore it for the perimeter calculation. Therefore, the perimeter of the shaded shape is:
KL + LM + MN + NK ≈ 5.19 + 0 + 6.25 + 0 = 11.44 cm
So, the perimeter of the shaded shape KLNM is approximately 11.44 cm to 2 decimal places.
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Answer:
83.62
Step-by-step explanation:
1. work out the circumference (2x pie x radius)
circumference of KOL= 42 pie
circumference of MON= 32 pie
2. Work out arch length ({114÷360} x circumference)
KL= (114÷360) x 42 pie = 133/10 pie
MN= (114÷360) x 32 pie = 152/15 pie
3. Add both lengths ( KL + MN)
= 41.78318229 + 31.83480556 = 73.61798785
4. Add sides (21-16=5, 5x2= 10)
73.61798785+10= 83.61798785
answer= 83.62 (2dp)
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs: (10,F1) , (−25,F2) Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equation.
The missing y value for the ordered pair (-25, F2) is F2 = -2343.
What is the ordered pair?
An ordered pair is a pair of numbers that are written in a specific order, typically separated by a comma and enclosed in parentheses.
The first number in the ordered pair represents the x-coordinate, and the second number represents the y-coordinate.
To compute the missing y values for each ordered pair, we need to substitute the given value of C into the equation and solve for F.
For the ordered pair (10, F1), we have C = 10 and F = F1. Substituting these values into the equation, we get:
F1 = 95(10) + 32
F1 = 950 + 32
F1 = 982
Therefore, the missing y value for the ordered pair (10, F1) is F1 = 982.
For the ordered pair (-25, F2), we have C = -25 and F = F2. Substituting these values into the equation, we get:
F2 = 95(-25) + 32
F2 = -2375 + 32
F2 = -2343
Therefore, the missing y value for the ordered pair (-25, F2) is F2 = -2343.
Hence, the missing y values for the ordered pairs
(10, F1) is F1 = 982.
(-25, F2) is F2 = -2343.
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The one-to-one functions g and h are defined as follows.
The inverse function of g(x) is g⁻¹(x) = x - 4/5
(g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.
h⁻¹(0) = 8.
What is the inverse function?
An inverse function is a function that undoes the action of another function. In other words, if a function f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes the output y and produces the input x.
To find g⁻¹(x), we need to solve for x in terms of g(x).
g(x) = x + 4/5
Let y = g(x), then we have:
y = x + 4/5
Subtracting 4/5 from both sides, we get:
y - 4/5 = x
Therefore, the inverse function of g(x) is:
g⁻¹(x) = x - 4/5
To find (g⁻¹ * g)(1), we need to evaluate g⁻¹(g(1)).
g(1) = 1 + 4/5 = 9/5
g⁻¹(9/5) = 9/5 - 4/5 = 5/5 = 1
Therefore, (g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.
To find h⁻¹(0), we need to find the element in h whose second coordinate is 0, and then take the first coordinate of that element as the output of h⁻¹(0).
From h, we see that the element with second coordinate 0 is (8,0). Therefore,
h⁻¹(0) = 8.
Therefore, the inverse function of g(x) is g⁻¹(x) = x - 4/5
(g⁻¹ * g)(1) = g⁻¹(g(1)) = g⁻¹(9/5) = 1.
h⁻¹(0) = 8.
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The cost of 6 pairs of shorts and 2 T-shirts is $240. The cost of 4 pairs of shorts and 3 T-shirts is $185.
Enter the cost of one pair of shorts and one T-shirt in the response boxes below.
Answer: Shorts 35 dollars. The T-shirts are 15 dollars.
Step-by-step explanation:
6x+2y=240
4x+3y=185
isolate one variable and use the substitution method.
2y=240-6x
y=120-3x
4x+3(120-3x)=185
4x+360-9x=185
-5x=-175
x=35
plug 35 in for x on one of the equation to get y as 15.
Sal's pizzeria charges $414 for 23 pizzas what does the pizzeria charge for one pizza
Answer: $18
Step-by-step explanation:
414 divided by 23 = 18
So, 18 is your answer
Answer:
Cost of 1 pizza = $18
Step-by-step explanation:
Given information,
→ 23 pizzas = $414
Now we have to,
→ Find the required cost of 1 pizza.
Let us assume that,
→ 1 pizza's cost = p
Forming the equation,
→ 23 pizzas × p = $414
Then the value of p will be,
→ 23 × p = 414
→ p = 414 ÷ 23
→ [ p = $18 ]
Hence, the value of p is 18.
Find A + F elements of a matrix
The answer is { 7,2,9
-7,3,1}
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X
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Suppose you have $150.00 with which to start a business. You have Exactly the skills
and training you have right now. What business will you start? How will you spend the money?
What will you do to make sure your business works? How would you advertise?
Therefore , the solution of the given problem of equation comes out to be company can be difficult, but with dedication and persistence, you can make your hobby a lucrative endeavor.
An unifying method is what?The task may be completed using this generally accepted ease, preexisting variables, as well as any essential components from the original Diocesan customizable query. As a result, you might get another opportunity to use the object. If not, significant effects on algorithmic data will disappear.
Here,
Here are some actions you might consider to launch a business with a $150 budget:
Pick a venture that appeals to your passions and complements your education and experience. Starting a small online business or providing freelance services in your field of expertise are both examples of this.
Describe your objectives, target market, pricing strategy, and marketing strategy in a company plan. This will assist you in maintaining organization and focus as you launch your company.
Spend your money sensibly by making purchases of the startup necessities. For instance, you might need to invest in website storage and a domain name if you're opening an online store. Or,
If you're a freelancer, you might need to spend money on promotional items or a website to display your work.
Maintain organization and keep close tabs on your money. Be sure to remain within your budget by keeping track of all your income and expenses. This will support you in making wise choices as your company expands.
Keep in mind that starting a company can be difficult, but with dedication and persistence, you can make your hobby a lucrative endeavor.
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20. An airplane is coming in for a landing. It is currently 80000 feet horizontally away from where it will eventually come to a stop. Its radar indicates that the plane is at an altitude of 60000 feet.
a) At what angle of depression is the plane flying as it lands?
b) In a direct line, how far from its landing destination is the plane?
Please help I will mark you brainless
Answer:
a.) 36.87 degrees
b.) 100000 feet
Step-by-step explanation:
First, we solve for the direct distance from destination, which is the slope of the triangle. We can use the formula a^2 + b^2 = c^2 for this. Then, by using the trig functions, we can determine the angle of depression by using the inverse of sine of 3/5. This leads to 36.87 degrees.
The point (0, ?) lies on the line y = 5x - 7?
Answer:
?= -7
its the y intercept
Step-by-step explanation:
What is the missing denominator?
18
06
O 10
O 19
O24
The missing denominator is 24.
Option D is the correct answer.
What is the missing denominator?To find the missing denominator, we can use the property of equality that states that if we multiply or divide both sides of an equation by the same number, the equation remains true.
Starting with:
3/4 = 18/d
We can cross-multiply to eliminate the fractions:
3d = 4 x 18
3d = 72
Finally, we can solve for d by dividing both sides by 3:
d = 24
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The complete question is below:
What is the missing denominator?
3/4 = 18/d
A. 6
B. 10
C. 19
D. 24
if the limit of f(x) as x approaches 2 is equal to 4, what is the limit of (f(x) -4)/(x-2) as x approaches 2?
Answer: lim
x
→
2
x
2
−
4
x
−
2
=
4
Step-by-step explanation: If we look at the graph of
y
=
x
2
−
4
x
−
2
we can see that it is clear that the limit exists, and is approximately
4
graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}
The numerator is the difference of two squares, and as such we can factorise using it as
A
2
−
B
2
≡
(
A
+
B
)
(
A
−
B
)
Se we can factorise as follows:
lim
x
→
2
x
2
−
4
x
−
2
=
lim
x
→
2
x
2
−
2
2
x
−
2
=
lim
x
→
2
(
x
+
2
)
(
x
−
2
)
x
−
2
=
lim
x
→
2
(
x
+
2
)
x
−
2
x
−
2
=
lim
x
→
2
(
x
+
2
)
=
(
2
+
2
)
=
4
Find the inverse of the function.
The correct option is (a) i.e. the inverse of the given function is [tex]F^{-1}(x) = \sqrt{x-5} + 19, x \geq 19[/tex]
What is inverse function ?
An inverse function undoes the effect of another function. Given a function f(x), an inverse function g(x) will return the original input value x when the output of f(x) is given as input to g(x). In other words, if y = f(x), then x = g(y)
To find the inverse of the function F(x), we first replace F(x) with y, and then interchange x and y to obtain an expression for x in terms of y. That is:
[tex]y = (x - 19)^{2} + 5[/tex]
Interchanging x and y gives:
[tex]x = (y - 19)^{2} + 5[/tex]
Now, we solve for y in terms of x:
[tex]x = (y - 19)^{2} + 5[/tex]
[tex]x - 5 = (y - 19)^{2}[/tex]
±[tex]\sqrt{x-5} = y - 19[/tex]
y = ±[tex]\sqrt{x-5} +19[/tex]
However, since the original function is defined only for x ≥ 19, we must consider only the positive square root, and obtain:
[tex]y=\sqrt{x-5} +19, x\geq 19[/tex]
Therefore, the inverse of the function F(x) is:
[tex]F^{-1}(x) = \sqrt{x-5} + 19, x \geq 19[/tex]
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