Answers
Answer:
Step-by-step explanation:
The sum of the measures of angles DAC and CAB must equal the measure of angle DAB, since they are adjacent angles that share a common vertex, A. Therefore, we have:
(DAC) + (CAB) = (DAB)
Substituting the given values, we get:
(2y - 7) + (3y + 2) = (DAB)
Simplifying and solving for y, we get:
5y - 5 = (DAB)
y = (DAB + 5) / 5
Now we can find the measure of angle CAB by substituting y back into the given expression for CAB:
<CAB = (3y + 2) = 3[(DAB + 5)/5] + 2 = (3DAB + 17)/5
Therefore, the measure of angle CAB is (3DAB + 17)/5 degrees.
Related Questions
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?
Answers
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
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−
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lim
x
→
2
(
x
+
2
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(
x
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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?
Answers
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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Check symbolically (using our new definition of inverse from 3.) that the
function you wrote down in (d) is, indeed, the inverse of ().
Answers
The definition of inverse states that if f(g(x)) = x, then g(x) is the inverse of f(x). We can substitute our functions in to check if this is true, and it is, so g(x) is the inverse of f(x).
Using our new definition of inverse from 3, we can symbolically verify that the function we wrote down in (d) is the inverse of (). To do this, we will substitute the function we wrote down in (d) into the definition of inverse, and we will substitute () into the definition as well. The definition of inverse states that if f(x) and g(x) are functions such that f(g(x)) = x, then g(x) is the inverse of f(x). We can substitute our functions in to check if this is true.If f(x) = 2x + 3 and g(x) = (x - 3) / 2, then f(g(x)) = ( (x - 3) / 2 + 3) = x. This satisfies the definition of inverse, so we can conclude that g(x) is the inverse of f(x).
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Check the equation in slope-intercept form to make sure it represents the graph. If it doesnt, cross out the answer and write the correct equation
PLSSSSS!!!!! help i need the answers FAST
Answers
The equation y = 2x + 4 is in slope-intercept form with m = 2 and b = 4. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 4).
Define the term equation?An equation is a statement that asserts the equality of two expressions or values, typically separated by an equal sign (=). The expressions or values on either side of the equal sign are called the "sides" of the equation.
Equations are used to represent mathematical relationships between variables and to solve problems involving those variables.
To check if an equation is in slope-intercept form, we need to ensure that it has the form:
y = mx + b
The equation y = 2x + 1/3 is also in slope-intercept form with m = 2 and b = 1/3. This means that the line has a slope of 2 and intersects the y-axis at the point (0, 1/3).
The equation y = 3x/2 + 1 is in slope-intercept form with m = 3/2 and b = 1. This means that the line has a slope of 3/2 and intersects the y-axis at the point (0, 1).
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What is the probability of Meikel wearing khakis and sandals
3/21
1/4
4/8
1/2
Answers
Answer:
Answer
Step-by-step explanation:
The probability of Meikel wearing khakis and sandals is
3 / 12 which will give us
1/4
Circles I and L are shown. Sector HIJ and sector KLM have the same area.
K
H
90°
J
4 units
K
What is the measure, in degrees, of angle KLM?
M
6 units
Answers
The measure of the sector angle KLM is equal to 40 degrees which makes the first option correct.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
Given that the areas of sectors HIJ and KLM are the same, then we have that;
(angle KLM/360°) × 22/7 × 6 × 6 = (90°/360°) × 22/7 × 4 × 4
(angle KLM/360°) × 22/7 × 36 = (1/4) × 22/7 × 16
(angle KLM/10) × 22/7 = 22/7 × 4
(angle KLM/10) × 22/7 = 22/7 × 4
angle KLM = 22/7 × 7/22 × 4 × 10
angle KLM = 40
Therefore, measure of the sector angle KLM is equal to 40 degrees which makes the first option correct.
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Find the inverse of the function.
Answers
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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What is the slope-intercept form of -6x+y=2?
Answers
Answer:
y = 6x + 2
Step-by-step explanation:
The slope-intercept form is y = mx + b
What is the slope-intercept form of -6x + y = 2?
-6x + y = 2
Add 6x to both sides
y = 6x + 2
So, the answer is y = 6x + 2
a job recruitment firm runs assessment days for their clients, where potential employees are given a series of tests. part of this assessment day is a multiple-choice exam on general knowledge. the firm is trying to determine if the time of day that the test is given is a factor in how well candidates perform. a study is done, in which three random samples of people are given the same test, with one sample given the test at 9:00 am, one sample given the test at midday, and the final sample given the test at 3:00 pm. each sample has 60 candidates.
A one-way ANOVA test is performed. The following table shows the relevant figures in the ANOVA test: Sum of squares Degrees of freedom Mean squares F P
Between groups 1,493.76 2 746.88 3.4842 0.0328 Within groups 37,941.72 177 214.36
Total 39,435.48 179 Calculate the coefficient of determination, R^2. Give your answer as a percentage to 2 decimal places. R^2 = _____ %
Answers
The coefficient of determination (R^2) is 3.78%.
To calculate the coefficient of determination (R^2), we need to first find the total sum of squares (SST) and the sum of squares error (SSE) from the given ANOVA table. SST is the variation between the observed values and the mean value of all observations. SSE is the variation between the observed values and the group means.
SST = Between groups + Within groups = 1,493.76 + 37,941.72 = 39,435.48
SSE = Within groups = 37,941.72
R^2 = (SST - SSE) / SST
Plugging in the values, we get:
R^2 = (39,435.48 - 37,941.72) / 39,435.48
R^2 = 0.0378
To convert this to a percentage, we multiply by 100 and round to two decimal places:
R^2 = 3.78% (rounded to 2 decimal places)
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Solve the system using the substitution
y = -2x + 20 
6x - 5y =12
The solution is _.
Answers
Answer:
x=7, y=6
Step-by-step explanation:
One of the ways we can find a value of a variable in a multiple part equation system is via substitution.
What is substitution?
Substitution works by making one equation equal to a variable with no coefficients (that is, a number without any action being done to the variable), then using this said equation and plugging it into the other equation to find the value of one variable. Then, using this value that was found can be plugged again to one of the two equations to find the other variable.
In our situation, one of the equations ([tex]y=-2x+20[/tex] ) is already equal to y; so we can use this equation to plug it in the second equation.
- Given: [tex]y=-2x+20\\6x-5y=12[/tex]
- Insert the first equation: [tex]6x-5(-2x+20)=12[/tex]
- Distribute the -5: [tex]6x+10x+-100=12[/tex]
- Combine like terms: [tex]16x-100=12[/tex]
- Isolate the variable x: [tex]16x-100=12\\~~~~~~+100+100\\16x=112\\\frac{16x}{16} =\frac{112}{16} \\x=7[/tex]
Now that we have the variable x=7, we can use this number to find the value of the variable y.
- Given: [tex]y=-2x+20[/tex]
- Plug in the known variable value: [tex]y=-2(7)+20\\[/tex]
- Solve: [tex]y=-14+20\\y=6[/tex]
Therefore, x=7, and y=6 is your final answer.
Additionally, we can cross reference this on a graphing calculator. Plug both of those formulas in as so, and the intersection between the two lines will be the answer of what x and y are equal to, (x,y).
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x=7 , y=6
_________________________
Substituting y = -2x + 20 =
6x - 5(-2x + 20) = 12
Simplifying =
6x + 10x - 100 = 12
Combining like terms =
16x - 100 = 12
we add 100 =
16x = 12 + 100
16x = 112
Divide both sides by 16 =
x = 112 / 16
x = 7
y = -2(7) + 20
y = -14 + 20
y = 6
x=7 , y=6
Which statements explain that the table does not
represent a probability distribution?
Select each correct answer.
The probabilities have different
denominators.
The results are all less than 0.
O The sum of the probabilities is 31
12'
The probability is greater than 1.
12
Result
-2
-4
-6
-8
C
Probability
A
23
1
12
53
L
Next
Answers
Answer: The correct statements that explain that the table does not represent a probability distribution are:
The results are all less than 0.
The probability is greater than 1.
The sum of the probabilities is 31/12.
A probability distribution must have probabilities between 0 and 1 (inclusive) and the sum of all probabilities must equal 1.
Step-by-step explanation:
Miranda orange $12 per hour at her job if she say 60% of her earnings for the computer, she’ll be able to buy the computer after working x hours at her job.
What is x?
Answers
Miranda needs to work 50 hours at her job in order to purchase the computer.
What is amount?Amount is a term generally used to refer to a numerical value which represents a quantity of something. It can be used to describe the size, magnitude, or total of an object, event, or concept. Amount is often used to refer to money, but it can also be used to refer to other elements such as time, energy, weight, and volume. Amount can also be used to refer to a certain degree or level, such as a certain amount of effort or a certain amount of progress.
To find the amount of hours Miranda needs to work in order to purchase the computer, the following equation can be used:
12 x = Computer Price x 0.6
Where 12 is the hourly wage Miranda earns, x is the amount of hours Miranda needs to work, and 0.6 is the percentage (60%) of Miranda’s earnings that will be used to purchase the computer.
The computer price is not given, so let’s assume it to be $1000. Plugging in the values, the equation becomes:
12 x = 1000 x 0.6
Simplifying the equation, we have:
12 x = 600
Dividing both sides by 12, we get:
x = 600/12
x = 50
Therefore, Miranda needs to work 50 hours at her job in order to purchase the computer.
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whats
6-789=v=c-78930+57y
Answers
Answer:
v = c - 78930 + 57y - 6
Step-by-step explanation:
The image point of A after a translation right 1 unit and down 3 units is the point B(5,-3). Determine the coordinates of the pre-image point A.
Answers
The coordinates of the pre-image point A given the transformation is (4, 0)
How to determine the coordinates of the pre-image point A.If the image point of A after a translation right 1 unit and down 3 units is the point B(5,-3), then we can find the pre-image point A by reversing the translation.
This means we need to move B back 1 unit to the left and up 3 units to get to A.
So, the x-coordinate of A is 5 - 1 = 4 (moved 1 unit to the left)
And, the y-coordinate of A is -3 + 3 = 0 (moved 3 units up)
Therefore, the coordinates of the pre-image point A are (4,0).
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HELP PLS !!!!!!!!!!!!!!!
Answers
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)
Answers
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)
mark -1/2 on a number line?
Answers
Answer: Answer is below <3
Step-by-step explanation:
It’s in-between zero and negative one because it’s a half number. (Not fully one yet)
Therefore, -1/2 would be in-between the number 0 and -1.
Answer:
-1/2 is "-0.5" in form of decimal
So,
the answer will come between 0 and -1
Kindly mark the answer brainliest
What is the missing denominator?
18
06
O 10
O 19
O24
Answers
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
Please help me i need it for today!
Answers
The solution to the problems are;
1. Area = 108 square feet
2. Area = 342 square feet
3. x = $1, 890, x = $1764
4. Cost, x = $151. 2, $117. 6
How to determine the valuesThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that;
l is the length of the rectangle.w is the width of the rectangle.From the diagram shown, we have that;
The deck is gray
The garden is white
1. The area of the garden in design A
Area = 9(12) = 108 square feet
2. The area of the deck in design A is;
Area = 18(25) = 450 square feet
The area of the deck without the garden = 450 - 108
Area = 342 square feet
3. If $4. 20 = 1 square feet in design A
Then, x = 450 square feet
x = $1, 890
Area of deck of design B = 21(20) = 420 square feet
cost = $1764
4. If $1. 40 = 1 square feet of garden A
Then, x = 108 square feet
Cost = $151. 2
For garden of design B
Area = 1/2 × (12)(14) = 84 square feet
Then, cost = $117. 6
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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.
Answers
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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Alyssa combines a 10.2 gram bag or pretzels and a 21.3 gram bag of snack mix. She puts an equal amount of the combined pretzel and snack mix into each of 3 snack bags. How many grams of mix does Alyssa put into each snack bag?
Answers
Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = [tex]\sqrt{1+6x^3[/tex] , 0 ≤ x ≤ 1
Answers
The estimated volume of the region obtained by rotating y = √(1 + 6x³) about the y-axis using the Midpoint Rule with n = 5 is 0.702 cubic units.
What is the volume using midpoint rule?To use the Midpoint Rule to estimate the volume V, we first need to divide the interval [0, 1] into n subintervals of equal width. In this case, n = 5, so we have:
Δx = (1 - 0)/5 = 0.2
Next, we need to find the midpoint of each subinterval. The midpoints are:
x₁ = 0.1
x₂ = 0.3
x₃ = 0.5
x₄ = 0.7
x₅ = 0.9
Now we can evaluate the function y = √(1 + 6x³) at each midpoint to get the heights of the cylinders that will make up the approximate volume V:
y₁ = √(1 + 6(0.1)³) ≈ 1.027
y₂ = √(1 + 6(0.3)³) ≈ 1.247
y₃ = √(1 + 6(0.5)³) ≈ 1.466
y₄ = √(1 + 6(0.7)³) ≈ 1.687
y₅ = √(1 + 6(0.9)³) ≈ 1.908
Finally, we can use these heights to calculate the volumes of the cylinders and add them up to get an estimate of V:
V ≈ π(Δx/2)²(y₁ + y₂ + y₃ + y₄ + y₅)
≈ π(0.1)²(1.027 + 1.247 + 1.466 + 1.687 + 1.908)
≈ 0.702
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The one-to-one functions g and h are defined as follows.
Answers
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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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?
Answers
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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There are four points $T,I,P,$ and $O$ in the plane. Suppose $\triangle TIP$ and $\triangle TOP$ are isosceles triangles. Also suppose that $TI=5,$ $PI=7,$ and $PO=11$.
What are all the possible lengths TP
Answers
The sum οf all pοssible lengths fοr TP is 12
What is triangle ?A triangle is a type οf pοlygοn with three sides; the pοint where the twο sides meet is knοwn as the vertex οf the triangle. Between twο sides, an angle is created. One οf geοmetry's key cοmpοnents is this.
Triangle prοperties are necessary fοr sοme fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry. Based οn its angles and sides, a triangle can be classified intο variοus types.
Given that triangle TIP and triangle TOP are isοsceles triangles with sides;
TI = 5, PI = 7, PO = 11
Therefοre, given that triangle TIP is an isοsceles triangle, the length οf segment TP will be equal either the length οf segment TI οr segment PI which give;
TP = TI 5 οr TP = PI = 7
The sum οf all pοssible lengths fοr TP is given by the sum οf the twο unequal sides οf triangle TIP which gives;
The sum οf all pοssible lengths fοr TP = 5 + 7 = 12.
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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?
Answers
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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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
Answers
Option B : The range of 45 is the most accurate measure of variability to use to represent the data.
The range is the difference between the highest and lowest values in a dataset. In this case, the highest donation was $55 and the lowest was $10, so the range is:
range = highest value - lowest value = $55 - $10 = $45
Since the range takes into account all the values in the dataset, it is an appropriate measure of variability for this skewed dataset. The IQR (interquartile range) would also be a valid measure of variability, but it is less appropriate for skewed data because it only takes into account the middle 50% of the data and is less affected by extreme values. In this case, the extreme values (the two $55 donations) have a large effect on the distribution of the data, so the range is a more appropriate measure of variability.
Therefore, the charity should use the range of $45 to represent the variability of their donations.
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Suppose on your 21st birthday you begin saving $500 quarterly into an account that pays 12% compounded quarterly. If you continue the savings until your 51st birthday (30 years), how much money will be in the account?
Answers
From your 21st to your 51st birthday, if you deposit $500 quarterly into an account that pays 12% compounded quarterly, you will have about $386,711.70 in the account.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
FV = $500 x [(1 + 0.03/4)²²(4*30) - 1] / (0.03/4)
FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075
FV = $500 x [6.3207 - 1] / 0.0075
FV = $500 x 773.4234
FV = $386,711.70
Hence, From your 21st to your 51st birthday, if you deposit $500 quarterly into an account that pays 12% compounded quarterly, you will have about $386,711.70 in the account.
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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.
Answers
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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Math tell me
division
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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: