For each of the figures write an absolute value equation that has the following solution set.
Answers
The absolute value equation that has the solution set with digits -18, 0, and X on a number line is :
|X| = X if X ≥ 0
|X| = -X if X < 0
What do you mean by term Equation?An equation is a mathematical statement that shows the equality of two expressions. It typically includes one or more variables (represented by letters) and may also include constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
If the solution set for the absolute value equation has digits -18, 0, and X on a number line, then the equation must have two separate cases: one where X is positive and one where X is negative. We can write the absolute value equation as:
|X| = X for X ≥ 0
|X| = -X for X < 0
To include the values -18 and 0 in the solution set, we need to check each case separately:
|X| = X if X is greater than 0 or zero. The equation X = a must therefore be resolved, where an is either -18 or 0. As X 0 is satisfied by only one value in the solution set, the case's solution is X = 0.
Example 2: X < 0
When X is negative, |X| equals -X. So, we must find a, where an is either -18 or 0, to solve the equation -X = a. This case's solution is X = 18, as it is the only value in the solution set that satisfies the condition X 0.
As a result, the absolute value equation whose answer is represented by the numbers -18, 0 and X on a number line is:
|X| = X if X ≥ 0
|X| = -X if X < 0
or
|X| = 0 if X = 0
|X| = 18 if X < 0
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Related Questions
At a coffee shop, the first 100 customers'
orders were as follows.
Hot
Cold
Small Medium Large
5
48
22
8
12
5
Find the probability a customer ordered a
medium, given that they ordered a hot drink.
P(B|A) =
P(medium | hot) = [? ]
P(ANB)
P(A)
Answers
P(medium | hot) = P(hot | medium) * P(medium) / P(hot)
We can find the values we need from the table:
P(hot) = (5+48+22)/100 = 0.75
P(medium) = (8+12)/100 = 0.2
P(hot | medium) = 12/20 = 0.6
Now we can substitute these values into the formula:
P(medium | hot) = 0.6 * 0.2 / 0.75 = 0.16
Therefore, the probability that a customer ordered a medium given that they ordered a hot drink is 0.16.
Empirical Rule Khan Academy; all, if not most, of the answers.
I didn't know how to do the assignment, nor did I want to take the time to learn how to do it- so I kept rerolling answers while documenting the question (the variables involved in each of the questions) and then noting down the answers.
Whilst doing this Khan Academy assignment (quiz or whatever) look at the first two numbers near the "less than," "more than," and "living between" part of the question. Proceed to align the next numbers to whichever ones I have on the pdf.
- The answers will be under the numbers that have "and" or "&." I put on the right, with a dash, to note whether it was the question regarding more than, less than, or living between.
This took me a while to do (I was going for 4 stars on Khan). I thought it was worth sharing. Goodluck, folks.
Answers
Answer:
dont no ok i dont konow ask an easy one
#
Jeff is purchasing a car for $28,175 that will depreciate in value 8.5% each year.
Write a function to model the value of p of the car after t years.
If he decides to sell the car after 6 years, what will be the value of his car? Express your answer as a decimal rounded to the nearest hundredth.
Answers
The function to model the value of p of the car after t years can be expressed as:
p(t) = 28,175 * (1 - 0.085)^t
where 0.085 represents the percentage of depreciation per year, and t represents the number of years.
To find the value of the car after 6 years, we substitute t = 6 into the function:
p(6) = 28,175 * (1 - 0.085)^6
p(6) = 28,175 * 0.5386
p(6) ≈ 15,199.35
Therefore, the value of Jeff's car after 6 years will be approximately $15,199.35.
y=log(2x+c) for what values of x will the log be positive
Answers
For the logarithm to be positive, the argument of the logarithm (i.e., 2x+c) must be greater than zero.
Solve the inequality 2x+c > 0 for x:
2x > -c
x > -c/2
Therefore, for x > -c/2, the logarithm Y=log(2x+c) will be positive.
two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. what is the probability that after they are painted, the cubes can be rotated to be identical in appearance?(2020amc12b problem 20) (a) 64 9 (b) 2048 289 (c) 512 73 (d) 1024 147 (e) 4096
Answers
Step-by-step explanation:
with 2 cubes we have 12 faces to paint.
each face has 2 options (black or white).
so, we have a total of 2¹² possible outcomes.
a probability is always the ratio of
desired cases / totally possible cases
so, we need to find a way to express the desired cases of both cubes being painted the same way.
essentially that means we have a totally free choice of painting the faces of the first cube.
that is 2⁶ possible outcomes.
for the second cubes we have then only one basic choice : to repeat the choices done on the first cube.
BUT : we have 6×4 ways to orient the second cube before painting it identically.
6 ways to pick e.g. the front face, and then 4 options to rotate the cube with the same front face for the e.g. top face.
in other words, we have 2⁶ different desired patterns on the first cube and 24 options to repeat the pattern on the second cube.
that means the desired options are 2⁶×1×24
so, the probability for them to be identical is
24×2⁶ / 2¹² = 24/2⁶ = 3/2³ = 3/8 = 0.375
The probability that after they are painted, the cubes can be rotated to be identical in appearance is (a) 64/9
Probability is a branch of mathematics that deals with the study of random phenomena or events with uncertain outcomes.
Let's start by assuming that one of the cubes has the black face facing up. The other cube can be painted in any of the possible ways.
Let's list all the possible configurations for the second cube.
There are six faces, and each can be painted either black or white. Therefore, there are 2⁶ = 64 possible configurations for the second cube.
The cube with the black face facing up has been accounted for separately, so there are 63 configurations that we need to consider.
If the second cube is painted all black or all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the black or white face is facing up.
There are two such configurations. If the second cube has exactly one white face and five black faces, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube has two white faces and four black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has three white faces and three black faces, there are eight ways to position it so that the cubes look identical. There are eight such configurations.
If the second cube has four white faces and two black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has five white faces and one black face, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube is painted all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the white face is facing up. There are two such configurations.
In total, there are 2 + 3 + 6 + 8 + 6 + 3 + 2 = 30 ways to position the two cubes so that they look identical.
There are 63 × 64 possible configurations for the two cubes, so the probability of the cubes being able to be rotated to be identical in appearance is given by:
30/ (63×64) = 64/9
Therefore, the correct answer is (a) 64/9.
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rico's mixing water and milk in the ratio 20 : 1
Answers
The total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1 is 21 liters.
When a ratio of 20:1 is given for milk and water, it means that for every 20 parts of milk, there is 1 part of water. Therefore, the total number of parts in the mixture is 20 + 1 = 21.
We know that Rico mixed 20 liters of milk, which represents 20 parts of the mixture. To find the corresponding volume of water, we can use the ratio given.
The ratio of milk to water is 20:1, which means that for every 20 parts of milk, there is 1 part of water. Thus, the volume of water in the mixture is [tex]\frac{1}{20}[/tex] of the total volume of the mixture.
Volume of water = [tex]\frac{1}{20}[/tex] x Total volume of the mixture
Since we know that the volume of milk is 20 liters, we can substitute that value in the equation to solve for the total volume of the mixture:
20 = ([tex]\frac{20}{21}[/tex]) x Total volume of the mixture
Total volume of the mixture = (20 × 21) ÷ 20
= 420 ÷ 20
= 21 liters
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The complete question is:
What is the total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1?
if lines ax-2y=5 and 2x-by =8 intersect at point (11,3), find the value of a and b
Answers
Answer:
To find the values of a and b, we need to substitute the coordinates of the given point (11,3) into both equations and solve for a and b.
Substituting (11,3) into the first equation ax-2y=5:
a(11)-2(3)=5
11a-6=5
11a=11
a=1
Substituting (11,3) into the second equation 2x-by =8:
2(11)-b(3)=8
22-3b=8
-3b=-14
b=14/3
Therefore, a=1 and b=14/3.
Answer:
a = 1
b = 4.67 OR 14/3
Step-by-step explanation:
ax - 2y = 5
a(11) - 2(3) = 5
11a - 6 = 5
11a = 11
a = 1
2x - by = 8
2(11) - b(3) = 8
22 - 3b = 8
3b = 14
b = 4.67 OR 14/3
Find the answer and explain
Answers
Answer:
660cm^2
Step-by-step explanation:
area of 2 triangle= 10×12
= 120cm^2
area of 3 rectangles= (13×15×2)+(10×15)
= 390+150
= 540cm^2
surface area of triangular prism
= 540+120
= 660cm^2
i need help to solve these questions step by step, PLEASEEE THIS DUES TODAY
Answers
10. x(3x+4) (2x-3
11. 8mn^2 (m-n) (m - 3n)
12. 3(5x - 2y)(2x + y)
13. x(2x - 1)(x + 3
hope this helps
6x^3 - x^2 -12x
Let’s go ahead and factor out an x:
x ( 6x^2 - x - 12)
Rewrite the 1st degree x as a difference of two values that have similar factors to 6 and 12:
x ( 6x^2 + 8x - 9x - 12 )
Factor out 2x from ( 6x^2 + 8x ):
x ( 2x ( 3x + 4) (-9x - 12) )
Factor out -3 from ( -9x - 12 ) to get the same:
x ( 2x ( 3x + 4 ) - 3 ( 3x + 4) )
Group these for your final factored form:
x (2x -3) (3x+4)
11.
Right off the bat, 8 is a factor of both 32 and 24, so divide these leading coefficients by 8:
8m^3n^2 - 32m^2n^3 + 24mn^4
m^3n^2 - 4m^2n^3 + 3mn^4
Factor out one m:
m ( m^2n^2 - 4mn^3 + 3n^4)
Now factor out an n^2:
mn^2 ( m^2 - 4mn + 3n^2)
This is the final factored form.
13.
Factor out an x:
x (2x^2 + 5x - 3)
Rewrite 5x as a difference of two terms that will factor well with 2 and 3:
x ( 2x^2 + 6x - x - 3)
Now factor out a 2x:
x ( 2x ( x + 3 ) - x - 3 )
Now factor the other part so that what’s left matches the previous factor:
x ( 2x (x + 3) -1 (x +3) )
Now group these for the final factored form:
x ( 2x - 1 ) ( x + 3 )
a forecast is defined as a(n) . a. quantitative method used when historical data on the variable of interest are either unavailable or not applicable b. prediction of future values of a time series c. outcome of a random experiment
Answers
A forecast is defined as a(n) prediction of future values of a time series which is option B.
Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Companies use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Often, this is based on the anticipated demand for the provided goods and services.
Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.
To predict how trends, like as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts utilise forecasting. Lastly, statisticians may examine the probable effects of a change in business operations via forecasting. Data may be gathered, for example, on how altering company hours affects consumer happiness or how changing particular work conditions affects staff productivity.
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Lily makes $8.25 an hour at her job. She has been offered a different job that pays $10.40 hour. What is the percent increase in her pay?
Answers
The percent increase in her pay is by 26.06% if she takes the new job.
What is percentage increase?A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.
Given that, the pat increases from $8.25 an hour to $8.25 an hour.
percent increase = [(new value - old value) / old value] x 100%
Substituting the values we have:
percent increase = [(10.40 - 8.25) / 8.25] x 100%
percent increase = 26.06%
Therefore, Lily's pay would increase by 26.06% if she takes the new job.
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Savannah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 5
Bass 12
Drums 14
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 12
Bass 5
Drums 10
Keyboard 8
Based on these results, express the probability that a student chosen at random will play the drums as a percent to the nearest whole number.
Answers
The probability that a student chosen at random plays the drums is approximately 34%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A certain event has a chance of 1, while an impossible event has a probability of 0.
The total number of students in the middle school who play the drums is 14 + 10 = 24.
The total number of students in the middle school is:
5 + 12 + 14 + 4 + 12 + 5 + 10 + 8 = 70
The probability of selecting a student who plays the drums at random is:
24/70 = 0.34285714285714286
To express this probability as a percentage, we multiply by 100 and round to the nearest whole number:
0.34285714285714286 * 100 ≈ 34
Therefore, the probability that a student chosen at random plays the drums is approximately 34%.
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NEED HELP ASAP!!! Q) A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, A) if two cards are randomly selected with replacement.
one third
one ninth
two thirds
two sixths
Answers
The prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .
What is Prοbability?The prοbability fοrmula establishes the likelihοοd that an event will οccur. It is the prοpοrtiοn οf favοurite websites tο all favοurite websites. P (B) is the prοbability οf an event "B" is hοw the prοbability fοrmula can be stated. The number "n" (B) represents the favοurite mοments οf an event "B."
There are three cards, each labelled with the letter A οr D. Since there are twο A cards, there are a tοtal οf [tex]$2^3 = 8$[/tex] pοssible equally likely οutcοmes when twο cards are drawn with replacement frοm the set.
The pοssible οutcοmes are: AA, AD, DA, DD, AA, AD, DA, DD.
Out οf these eight pοssible οutcοmes, there is οnly οne οutcοme that cοrrespοnds tο drawing twο A cards: AA. Therefοre, the prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .
In οther wοrds,
[tex]$P(A,A) = \boxed{\frac{1}{8}}$[/tex].
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The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 510 and a standard deviation of 270. If a college requires a student to be in the top 30 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
answer:(round to the nearest integer)
Answers
The minimum score that a student must obtain to be in the top 30% of students taking the national standardized examination for college admission is approximately 658.4.
To find the minimum score that a student must obtain to be in the top 30% of students taking the test, we need to find the score that corresponds to the 70th percentile of the distribution.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 70th percentile is approximately 0.52.
We can use the formula for transforming a score from a normal distribution to a standard normal distribution to find the corresponding score in the original distribution:
z = (x - mu) / sigma
where z is the z-score, x is the score in the original distribution, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.
Rearranging this formula, we get:
x = mu + z * sigma
Substituting the values we have, we get:
x = 510 + 0.52 * 270
x = 658.4
Therefore, to be among the top 30% of test-takers and be eligible for admission to the college, a student must score at least 658.4 on the exam.
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Mrs. Morales wrote a test with 18 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100. Write an equation in slope-intercept form to represent the total number of points on the test. If necessary, write any fraction in decimal form. (Please help ASAP its due tmrw)
Answers
By answering the presented question, we may conclude that As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an that the equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.
Let x denote the number of spelling and y the number of vocabulary questions. Because there are a total of 18 questions, we know:
x + y = 18
5x + 10y = 15 points
We must solve for y 5x + 10y = 100 to put this equation in slope-intercept form.
10y = -5x + 100
y = (-1/2)x + 10
As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
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as shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. what is the distance, in feet, between the centers of the two wheels?
Answers
The distance between the centers of the two wheels is approximately 11.86 feet.
The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.
Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula
C = πd
Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:
C = πd = π(0.5) = 1.57 feet (approx.)
The length of the conveyor belt is given as 15 feet. So we can write
2C + d = 15
Substituting the value of C, we get
2(1.57) + d = 15
3.14 + d = 15
d = 11.86 feet
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Room and board charged for on-campus students at the local college have increased 3.15 each year since 2000. In 2000, students paid 4,291 for room and board.
Write a function to model the cost of C after t years since 2000
If the trend continues, how much would a student expect to pay for room and board in 2017? Express your answer as a decimal rounded to the nearest hundredth
Answers
1) A function to model the cost of C after t years since 2000 is [tex]C = 4,291(1 + 0.0315)^t[/tex]
2)If the trend continues, a student expect to pay for room and board in 2017 is $7862.35 .
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here we need to use exponential function formula to find the cost function . Then,
=> [tex]f(x)=a(1+r)^t[/tex]
Where a is cost for room in 2000 and r is rate of change.
Then model the cost of room and board C after t years since 2000, we can use the formula:
=> [tex]C = 4,291(1 + 0.0315)^t[/tex]
where 0.0315 represents the annual increase of 3.15% expressed as a decimal.
Now we have to find the cost of room and board in 2017, we need to substitute t = 17 (since 2017 is 17 years after 2000) into the function and round the result to the nearest hundredth.
So,[tex]C = 4,291\times(1 + 0.0315)^{17}[/tex]
=>C = 7,862.35
Therefore, a student would expect to pay approximately $7862.35 for room and board in 2017 if the trend continued.
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2plus 2 is 4 everybody knows that
Answers
The circle graph represents the jobs at a digital animation company with1,620 employees. How many more story artists are there than ?
Answers
263 more story artists are there than interns.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number
In actual values
Number of story artists = 1620 x 20% = 1620 x 20/100 = 324
Number of interns = 1620 x 5% = 1620 x 5/100 = 81
Difference = 324 - 81 = 263
Hence, 263 more story artists are there than interns.
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Complete question:
The circle graph represents the jobs at a digital animation company with 1,620 employees. How many more story artists are there than interns?
See the image attached.
A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
Answers
The final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
The initial balance of the checking account is $350.
If the customer makes two withdrawals, one $50 more than the other, let's assume the smaller withdrawal amount is x. Then, the larger withdrawal amount will be x + $50.
So, the new balance of the checking account after these two withdrawals would be:
$350 - x - (x + $50) = $350 - 2x - $50 = $300 - 2x
After this, the customer makes a deposit of $75, which would increase the balance of the checking account to:
$300 - 2x + $75 = $375 - 2x
Therefore, the final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
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Complete question:
Write an expression for the new balance using as few terms as possible. A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
the null hypothesis is (typically) rejected, when select one: a. the p-value is less than or equal to .5. b. the p-value is less than or equal to .05. c. the p-value exceeds .05. d. the p-value exceeds .5.
Answers
The null hypothesis is (typically) rejected, when (b) the p-value is less than or equal to .05.
In hypothesis testing, the Null-Hypothesis represents the default assumption,
whereas the alternative hypothesis represents the claim made by the researcher.
The "p-value" is defined as a probability metric which indicates the likelihood of observing the data, given that the null hypothesis is true.
If the p-value is small (less than or equal to .05), it means that it is unlikely to observe the data, assuming the null hypothesis is true.
Therefore, a p-value less than or equal to .05 is considered statistically significant, and the null hypothesis is typically rejected, the correct option is (b).
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The given question is incomplete, the complete question is
The null hypothesis is (typically) rejected, when select one:
(a) the p-value is less than or equal to .5
(b) the p-value is less than or equal to .05
(c) the p-value exceeds .05
(d) the p-value exceeds .5
there are 25 people competing in a rubber duck regatta. each person is allowed only one entry. if there are no ties, how many ways are there to have the first, second, and third place winners?
Answers
There are 13,800 different ways to have the first, second, and third place winners without any ties.
In a rubber duck regatta with 25 people competing and each person having only one entry, we can determine the number of ways to have the first, second, and third place winners by using permutations.
Step 1: Calculate the number of options for the first place winner.
There are 25 contestants, so there are 25 options for the first place.
Step 2: Calculate the number of options for the second place winner.
Since the first place winner has been determined, there are 24 remaining contestants to choose from for the second place.
Step 3: Calculate the number of options for the third place winner.
After determining the first and second place winners, there are 23 remaining contestants to choose from for the third place.
Step 4: Multiply the number of options for each place to get the total number of possible outcomes.
25 options (first place) × 24 options (second place) × 23 options (third place) = 13,800 possible outcomes.
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I need help please thank y’all
Answers
Solving the given inequality, we get the value of x to be,
x ≥ 16.
What is an inequality?In a mathematical equation with an inequality, both sides must be equal. In inequality, we don't use equations but rather compare two values. The signs greater than (or greater than or equal to), less than (or less than or equal to), or not equal to are used in place of the equal sign.
Here in the question, we have the inequality:
x - 4 ≥ 12
Now to simplify this we will add 4 on both sides,
⇒ x - 4 + 4 ≥ 12 + 4
⇒ x ≥ 16
So, this implies that the value of x is greater than or equal to 16.
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What is the value of x? sin64°=cosx enter your answer in the box. x = °
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Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°
So, if we have given cos64° = cosx and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.
The answer is: x = 26°
Step-by-step explanation:
quartile and decile for ungrouped data
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A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7
B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17
C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98
D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98
E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147
F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848
What is number?Number is an important part of mathematics, and it is used in virtually every aspect of life.
A) First, we need to arrange the data in order:
[1,1,2,2,2,2,2,3,3,3,3,4,5,6,6,7,7,7,7,9,9]
The median is the middle value of the data set. Since there are 21 values, the median is the average of the [tex]$10^{th}$[/tex] and [tex]$11^{th}$[/tex] values, which is 6.
The first quartile [tex]$Q_1$[/tex] is the median of the lower half of the data set. The lower half of the data set is [1,1,2,2,2,2,2,3,3,3], which has 10 values. The median of this set is the average of the [tex]$5^{th}$[/tex]and [tex]$6^{th}$[/tex] values, which is 2.
The third quartile[tex]$Q_3$[/tex]is the median of the upper half of the data set. The upper half of the data set is [4,5,6,6,7,7,7,7,9,9], which also has 10 values. The median of this set is the average of the[tex]$5^{th}$[/tex] and[tex]$6^{th}$[/tex]values, which is 7.
The interquartile range (IQR) is the difference between the third and first quartiles: IQR =[tex]Q_3[/tex] - [tex]Q_1[/tex]= 7 - 2 = 5.
To find the deciles, we need to divide the data into $10$ equal parts. Since we have 21 data points, we need to find the values that divide the data into groups of $2$. The [tex]$k^{th}$[/tex] decile[tex]$D_k$[/tex] is the[tex]$k \cdot n/10$-th[/tex] value, where $n$ is the number of data points. The deciles are:
$D_1 = 1, D_2 = 2, D_3 = 2, D_4 = 2, D_5 = 3,$
$D_6 = 6, D_7 = 7, D_8 = 7, D_9 = 9$
B) Again, we need to arrange the data in order:
$10,11,12,12,14,14,14,15,15,15,15,16,16,16,17,17,14,14$
The median is the average of the[tex]$9^{th}$[/tex] and[tex]$10^{th}$[/tex] values, which is $15$.
The first quartile $Q_1$ is the average of the[tex]$4^{th}$[/tex] and [tex]$5^{th}$[/tex]values, which is $14$.
The third quartile $Q_3$ is the average of the [tex]$14^{th}$[/tex] and [tex]$15^{th}$[/tex]values, which is $16$.
The interquartile range (IQR) is [[tex]Q_3[/tex] - [tex]Q_1[/tex]= 16 - 14 = 2].
To find the deciles, we need to divide the data into [10] equal parts. Since we have 18 data points, we need to find the values that divide the data into groups of 2. The deciles are:
[[tex]D_1[/tex]= 10, D_2 = 12, D_3 = 14, D_4 = 14, D_5 = 14,]
[[tex]D_6[/tex]= 15, D_7 = 15, D_8 = 16, D_9 = 17]
From the above calculation, it can be seen that the quartiles and deciles of each set of data differ.
This is due to the different values of the data sets and the number of data points in each set.
The quartiles and deciles show different ranges and values which indicate the spread of the data and also help to identify any skewness in the data.
Summarizing, the quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.
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Trapezoid ABCD is formed when right triangle EAB is cut by line DC such that DC || AB. Find the volume of the solid generated when the trapezoid is rotated about side DA. Round your answers to the nearest tenth if necessary.
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The volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).
What is volume?A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
According to the given information:Given:
DC = 7
DA = 6
DE = 6
AB = 14
Height of the trapezoid:
ED = (DC/AB) * EA = (7/14) * EA = 0.5 * EA
Height = EA - ED = EA - 0.5 * EA = 0.5 * EA
Circumference of the cylindrical shell:
Circumference = 2 * π * AB = 2 * π * 14
Thickness of the cylindrical shell:
Since the trapezoid is being rotated about side DA, the thickness (Δx) will vary along DA. We'll integrate with respect to x from 0 to 6 (the length of DA).
Volume of the solid generated:
Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * EA * Δx]
Substituting EA = DE + DA = 6 + 6 = 12Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * 12 * Δx]
Integrating:
Volume = 2 * π * 14 * 0.5 * 12 * [x] from 0 to 6
Volume = 2 * π * 14 * 0.5 * 12 * (6 - 0)
Volume = 504 * π
Approximating to the nearest tenth:
Volume ≈ 504 * 3.14 ≈ 1586.6 cubic units (rounded to the nearest tenth)
Therefore, the volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).
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14. assuming p-value is 0.03, what is the conclusion of testing at the 0.10 level of significance whether the fruit drink distributor should sell this drink? a. based on the sample data, there isn't sufficient evidence to conclude that the average rating is more than 4.75. b. based on the sample data, there isn't sufficient evidence to conclude that the average rating is no more than 4.75. c. based on the sample data, there is sufficient evidence to conclude that the average rating is no more than 4.75. d. based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75. e. none of the above.
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Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.
If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.
Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.
Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.
Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
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What is the increasing and decreasing?!?!?!?!?!?!?!??!?!?!?!?!?!
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Answer:
Function decreasing: where x is (-4; 0) and (2; 4)
Function increasing: where x is (0; 2)
Step-by-step explanation:
Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.
Please help with finding the answer
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The two missing points on the line are:
(0, -1)
(-5, 0)
And the slope, using these points, is a = -1/5
How to find the missing y-values and the slope?Remember that a general linear equation is:
y = ax + b
Where a is the slope and b is the y-intercept.
If that line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can look at line e and find the two missing y-values, for the first point we have:
(0, -1)
For the second point we have:
(-5, 0)
Using these two, we will get the slope:
a = (0 + 1)/(-5 - 0) = -1/5
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approximately how many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein?
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Answer:
Therefore, there are approximately 102 kilocalories in the snack bar.
Step-by-step explanation:
One gram of fat provides 9 kilocalories (kcal), while one gram of carbohydrate and protein provide 4 kcal each. So, to find the total number of kilocalories in the snack bar, we can use the following formula:
Total kcal = (grams of fat * 9) + (grams of carbohydrate * 4) + (grams of protein * 4)
Plugging in the values, we get:
Total kcal = (6 * 9) + (10 * 4) + (2 * 4)
Total kcal = 54 + 40 + 8
Total kcal = 102
Therefore, there are approximately 102 kilocalories in the snack bar.
The answer is approximately 120 kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein.
What are kilocalories? Kilocalories, also known as calories, are a unit of energy used to calculate the amount of energy in food. The number of kilocalories in food is calculated based on the number of grams of protein, carbohydrate, and fat it contains. Kilocalories are used by the body to fuel its processes and maintain its vital functions. The energy in food is released when it is digested, absorbed, and transported to the cells where it is used to produce ATP, the body's primary source of energy. ATP is used to power cellular processes such as metabolism, respiration, and movement. How many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein? To calculate the number of kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein, we need to know the number of kilocalories per gram of each macronutrient. Protein and carbohydrates each contain 4 kilocalories per gram, while fat contains 9 kilocalories per gram. To calculate the number of kilocalories in the snack bar, we multiply the number of grams of each macronutrient by the number of kilocalories per gram and then add them together. Here is the calculation:6 grams of fat x 9 kilocalories per gram of fat = 54 kilocalories10 grams of carbohydrate x 4 kilocalories per gram of carbohydrate = 40 kilocalories2 grams of protein x 4 kilocalories per gram of protein = 8 kilocalories. Total kilocalories = 54 + 40 + 8 = 102Therefore, a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories.
A snack bar with 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories. This is calculated as follows: (6 grams fat x 9 kcal/g) + (10 grams carbohydrate x 4 kcal/g) + (2 grams protein x 4 kcal/g).
Therefore, answer is 120 kilocalories.
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