we would need at least 678 freshmen to make purchases to estimate the average amount spent on books in their first year with a 90% confidence interval and a margin of error of $2, assuming the estimated standard deviation of the amount spent is $30 based on last year's book sales.
To calculate the number of observations required to achieve a 90% confidence interval with a margin of error of $2 and an estimated standard deviation of $30, we can use the following formula:
n = (z * σ / E)^2
Where n is the number of observations required, z is the z-score for the desired confidence level (in this case, 90%, which corresponds to a z-score of 1.645), σ is the estimated standard deviation ($30 in this case), E is the desired margin of error ($2 in this case).
Substituting the values given:
n = (1.645 * 30 / 2)^2 = 677.89
Rounding up to the nearest integer, the number of observations required is 678.
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A parking lot was full of different colored cars. There were 12 red cars, 15 blue cars, and 3 green cars. At this rate, how many blue cars will there be if there were 120 total cars?
find the simple interest. round to the nearest cent
principal = $600
rate = 2%
time in years = 2
Answer:
To find the simple interest on a principal of $600 at a rate of 2% for a time period of 2 years, we can use the formula:
Simple Interest = (Principal * Rate * Time)
where Rate is the annual interest rate as a decimal, and Time is the time period in years.
In this case, we have:
Principal = $600
Rate = 0.02 (2% expressed as a decimal)
Time = 2 years
So, the formula becomes:
Simple Interest = ($600 * 0.02 * 2)
= $24
Therefore, the simple interest on a principal of $600 at a rate of 2% for 2 years is $24.
Shakita buys an apple tree and a cherry tree and measures them at the end of every
year for 5 years. After 1 year, the apple tree is 14 feet tall. After 5 years, it is 22 feet
tall. The cherry tree's height is represented by y = 3x + 8.
If both trees grew at a constant rate, which tree was taller when they were planted,
and which grew more quickly?
OA. The cherry tree was taller when the trees were planted, and it also grew
more quickly.
OB. The apple tree was taller when they were planted, but the cherry tree
grew more quickly.
OC. The cherry tree was taller when the trees were planted, but the apple tree
grew more quickly.
D. The apple tree was taller when the trees were planted, and it also grew
more quickly.
PRE
< PREVIOUS
2 of 2
Answer: B
Step-by-step explanation:
because I did it and it was right lol
one-tailed two-tailed a) a pharmacist wants to test whether the effect of a placebo is different from zero. b) holdem motors wants to test whether the mean time to assemble a car is less than 24 hours. c) ihi insurance wants to test whether the mean time to process a claim is less than 7 days
The appropriate type of test for each scenario is a) a two-tailed test, b) a one-tailed test, and c) a one-tailed test.
a) This would be a two-tailed test as the pharmacist is testing for a difference, rather than a specific direction of effect.
b) This would be a one-tailed test as Holdem Motors is specifically testing whether the mean time to assemble a car is less than 24 hours, rather than testing for a difference in either direction.
c) This would be a one-tailed test as IHI Insurance is specifically testing whether the mean time to process a claim is less than 7 days, rather than testing for a difference in either direction.
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Which of the following statements is true of the Comprehensive Environmental Response, Compensation, and Liability Act?
Cleanups may be carried out by the Environmental Protection Agency or private parties.
The statement "Cleanups may be carried out by the Environmental Protection Agency or private parties" is true of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), also known as Superfund.
What is the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA)?
The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, is a United States federal law aimed at cleaning up sites contaminated with hazardous substances as well as preventing future hazardous waste site contamination.
CERCLA was passed by the United States Congress in December 1980 as a means of counteracting the increasing risk of hazardous waste sites in the United States.
What does CERCLA cover?
CERCLA was enacted to offer a federal "Superfund" to clean up uncontrolled or abandoned hazardous waste sites, as well as responding to oil spills, chemical disasters, and other emergencies that present a threat to the public health and the environment.
Cleanups may be carried out by the Environmental Protection Agency or private parties.
When it comes to financing these cleanups, the law mandates that those responsible for the contamination pay for the cleanup or those who do not take responsibility for the pollution.
The legislation was enacted to provide for the cleanup of the country's most hazardous waste sites and to ensure that businesses that generate hazardous waste are held responsible for their toxic contributions to the environment.
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mrs. takac throws a ball upward from atop a 506 foot tall building and the ball's height, h, in feet after t seconds is given by the equation: the ball lands on a balcony that is 218 feet above the ground. how many seconds was it in the air?
The number of seconds that the ball was in the air is approximately 5.11 seconds
To find the time the ball was in the air, we need to find the time when the ball hits the balcony, which is located 218 feet above the ground.
Let's set h = 218 in the equation h = -16t^2 + 48t + 506 and solve for t
218 = -16t^2 + 48t + 506
Simplifying, we get
16t^2 - 48t - 288 = 0
Dividing both sides by 16, we get
t^2 - 3t - 18 = 0
Using the quadratic formula, we can solve for t:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = -18
t = (3 ± sqrt(3^2 - 4(1)(-18))) / 2(1)
t = (3 ± sqrt(105)) / 2
We can ignore the negative solution because time cannot be negative. Therefore, we have
t = (3 + sqrt(105)) / 2
t ≈ 5.11 seconds
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The given question is incomplete, the complete question is:
A person throws a ball upward from a 506 foot tall building the balls height h in feet after t seconds is given by the equation h= -16t^2+48t+506 the ball lands on a balcony that is 218 feet above the ground how many seconds was it in the air
a number is five times a smaller number. find the larger number of their difference is 52
The larger number if the difference of the numbers is 52 is 65.
How to find the larger number?A number is five times a smaller number. Let's find the larger number when their difference is 52.
Therefore,
let
x = smaller number
larger number = 5x
There difference is 52. Hence,
5x - x = 52
4x = 52
divide both sides of the equation by 4
x = 52 / 4
x = 13
Therefore,
larger number = 5(13) = 65
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Show how to change 9^8/7 into a radical expression
Answer:
Rewrite the expression using the negative exponent rule b−n=1bn b - n = 1 b n . 1y98 1 y 9 8.
Step-by-step explanation:
Which expression is equivalent to 0.75a + 10b + a – 2b?
Answer:
1.75a + 8b
Step-by-step explanation:
0.75a + 10b + a - 2b ← collect like terms
= (0.75 + 1a) + (10b - 2b)
= 1.75a + 8b
Answer:
1.75a+8b
Step-by-step explanation:
Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b
=1.75a+8b
Hence, The required equivalent expression is 1.75a+8b
alison has five different hats, six different bracelets, and seven cats. she wants to take a selfie with a hat, a bracelet, and two cats. how many different selfies can she take?
Answer:
The answer is 60
Step-by-step explanation:
2x5x6
rearrange by the commutative property
(2x5)x6
Calculate
10x6
calculate the product or quotient to 60
hence the answer is 60
Hoped this helped:D
Alison has five different hats, six different bracelets, and seven cats. She wants to take a selfie with a hat, a bracelet, and two cats. So she can take 630 different selfies.
She wants to take selfies with what she has, and the question asks how many different selfies can she take.
Let's solve the question below:
The total number of selfies Alison can take is 5 × 6 × ( ₇C₂ )
As Alison wants to take a selfie with a hat, a bracelet, and two cats, there are 5 hats and 6 bracelets she can select from, and she needs to select 2 cats out of 7 available cats.
We can use the combination formula to calculate the total number of ways:
₇C₂ = [tex](7 * 6)/2[/tex]
= 21
Hence, Alison can take [tex]5 * 6 * 21[/tex] = 630 different selfies with a hat, a bracelet, and two cats.
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tycho plans his running training. each week he wants to go for a run on the same weekdays. he never wants to go for a run on two consecutive days. but he wants to go for a run two days a week. how many different weekly plans meet those conditions?
There are 4 different weekly plans that meet the condition
If Tycho wants to go for a run on the same weekdays every week, there are 7 choices for the first day of the week, 6 choices for the second day of the week, and 5 choices for the third day of the week (since he can't run on two consecutive days).
However, we have to be careful not to overcount the number of plans that meet the conditions. For example, if Tycho chooses Monday and Tuesday as his running days, that's the same as choosing Tuesday and Monday.
To avoid overcounting, let's first count the total number of possible plans, regardless of whether they meet the conditions or not. We can choose any two days of the week for Tycho to run, which can be done in 7 choose 2 ways (or C(7,2) ways), since order doesn't matter.
C(7,2) = 7!/(2!(7-2)!) = 21
So there are 21 possible plans, regardless of whether they meet the conditions or not.
Now let's count the number of plans that meet the conditions. Since Tycho wants to run on two days a week and not on consecutive days, there are only two possible patterns: (1) run on Monday and Thursday, or (2) run on Tuesday and Friday.
Each pattern can be done in 2 ways: either run on Monday and Thursday, or run on Thursday and Monday. Similarly, either run on Tuesday and Friday, or run on Friday and Tuesday.
So there are 4 plans that meet the conditions: (Monday, Thursday), (Thursday, Monday), (Tuesday, Friday), and (Friday, Tuesday).
Therefore, there are 4 different weekly plans that meet the condition
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After Simon fully charges his electric car, he can drive for up to 350 miles before it runs out of battery. Simon's car was fully charged this morning, and he has driven 140 miles since then.
Let x represent how many more miles Simon can drive without running out of battery. Which inequality describes the problem?
the inequality that describes the problem is x ≤ 210, meaning that Simon can drive at most 210 more miles before his electric car runs out of battery.
If Simon has driven 140 miles since fully charging his car, then the amount of charge remaining in the battery can power the car for x miles. We can set up the following inequality to represent this situation:
x ≤ 350 - 140
The amount of charge left in the battery is shown on the right-hand side of the inequality and is equal to the maximum amount of charge the battery can store (350 miles) minus the amount of charge that has already been utilised (140 miles). The left-hand side of the inequality displays the number of miles Simon can travel until his battery runs out, which is either less than or equal to the battery's remaining charge.
Simplifying the inequality, we get:
x ≤ 210
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PLEASE HELP ME & FAST !!!
The percentage of 65 out of 140 will be 46.428%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
[tex]\text{Percentage (P) = [Final value - Initial value] / Initial value x 100}[/tex]
The whole numbers are 65 and 140.
Then the percentage is written as,
[tex]P = (65 \div 140) \times 100[/tex]
[tex]P=0.46428 \times 100[/tex]
[tex]P=46.428\%[/tex]
The percentage of 65 out of 140 will be 46.428%.
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what is the probability that the person selected will be someone whose response is never and who is a woman?
The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
The probability that the person selected will be someone whose response is never and who is a woman can be found by using conditional probability.What is conditional probability?Conditional probability is the likelihood of an event occurring given that another event has already occurred. The probability of event A happening given that event B has already occurred is known as conditional probability.Mathematically, the formula for conditional probability is:P(A|B) = P(A ∩ B) / P(B)Where,P(A|B) represents the probability of event A given that event B has already occurred.P(A ∩ B) represents the probability of both A and B occurring.P(B) represents the probability of event B occurring.The given scenario states that the person selected should have two attributes: the response never and the gender woman. Let A be the event that the person selected has a response never and B be the event that the person selected is a woman. Therefore, we need to find the probability of event A given event B.P(A|B) = P(A ∩ B) / P(B)Therefore, we need to find the probability of both A and B occurring and the probability of event B occurring.P(B) = 70/120P(B) = 7/12There are 50 women in the group. The number of women who have never responded is 30. Therefore,P(A ∩ B) = 30/120P(A ∩ B) = 1/4Therefore,P(A|B) = P(A ∩ B) / P(B)P(A|B) = 1/4 / 7/12P(A|B) = 3/7The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
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Answer these for points
6. f(x)g(x)+h(x) = 20x3-4x. This answer is arrived at by using the rules of algebra and the values of the given functions.
7. f(x)g(x) = -15x2 - 18x - 15
What are polynomials?Polynomials are algebraic expressions consisting of variables and coefficients that are combined through addition, subtraction, multiplication and division operations. For example, the polynomial 4x² + 3x - 5 can be written as the sum of 4x², 3x and -5.
6. In order to calculate f(x) g(x)+h(x), it is necessary to first multiply f(x) and g(x). Since f(x)=4x and g(x) = 5x2-4, it follows that f(x)g(x)=20x3-4x. Next, it is necessary to add h(x) to this product. Since h(x) = 9x, it follows that f(x)g(x)+h(x) = 20x3-4x+9x = 20x3-4x. Since each coefficient is correctly represented in the answer, it follows that the correct answer is 20x3-4x.
Multiplying f(x) and g(x) gives the product of 20x3-4x, and adding h(x) to this product gives the sum of 20x3-4x. As each coefficient is correctly represented in the answer, the correct answer is 20x3-4x.
7. The product of two polynomials is found by multiplying each term of one polynomial by each term of the other polynomial. This is known as the FOIL method (First, Outer, Inner, Last).
The first term is the product of the first terms of each polynomial, which is 3x x 4x = 12x2.
The second term is the product of the outer terms, which is 3x x -5x = -15x2.
The third term is the product of the inner terms, which is 5 x -5x = -25x.
Finally, the fourth term is the product of the last terms of each polynomial, which is 5 x -3 = -15.
We can now combine the terms to get the product of the two polynomials, which is:
f(x)g(x) = -15x2 - 18x - 15.
Therefore, the correct coefficient for each term is -15x2 for the first term, -18x for the second term, and -15 for the third term.
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which of the following best describes the chord of a circle? a chord is any segment in which the end points are found on the arc of the circle. a chord is a triangle inside of a circle. a chord is the arc formed from the segment. a chord is a square inside of a circle.
The statement that best describes the chord of a circle is a chord is any segment in which the end points are found on the arc of the circle. (option a).
A chord of a circle is a line segment that connects two points on the circle. The two endpoints of the chord are called the endpoints of the chord, and they lie on the circumference of the circle.
Therefore, option (a) that states that a chord is any segment in which the endpoints are found on the arc of the circle is the correct answer.
It is important to note that a chord does not have to pass through the center of the circle. If a chord passes through the center of the circle, it is called a diameter. A diameter is the longest chord of a circle, and it divides the circle into two equal parts called semicircles.
The correct answer to the question is option (a), which states that a chord is any segment in which the endpoints are found on the arc of the circle.
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Complete Question:
which of the following best describes the chord of a circle?
a) a chord is any segment in which the endpoints are found on the arc of the circle.
b) a chord is a triangle inside of a circle.
c) a chord is the arc formed from the segment.
d) a chord is a square inside of a circle.
Diego used unit cubes to make a rectangular prism what is the volume of the prism
can we see a picture or equation
Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.
a. x^2+5/6x+___=(x+___)^2
b. x^2-11x+___=(x-__)^2
ANSWERS:
A ) x^2 + 5/6x + 25/144 = (x + 5/12)^2
B ) x^2 - 11x + 121/4 = (x - 11/2)^2
EXPLANATION:
a. To complete the square for the equation x^2 + 5/6x + ___,
first divide the coefficient of the linear term (5/6) by 2,
which gives you 5/12.
Then, square the result:
(5/12)^2 = 25/144.
So, the equation becomes:
x^2 + 5/6x + 25/144 = (x + 5/12)^2
b. To complete the square for the equation x^2 - 11x + ___,
first divide the coefficient of the linear term (-11) by 2,
which gives you -11/2.
Then, square the result:
(-11/2)^2 = 121/4.
So, the equation becomes:
x^2 - 11x + 121/4 = (x - 11/2)^2
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8. how many cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3 ounce serving and each can weighs 5 pounds 10 oz ( 9 ounces of that as liquid which you will discard)?
8 Cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving and each can weights 5 pounds 10 oz (9 ounces of that as liquid which you will discard).
Given that each can of mandarin oranges weighs 5 pounds 10 oz (9 ounces of that as liquid which you will discard).We are to find out how many cans of mandarin oranges are needed to serve a part of 200 people if each person is to receive a 3-ounce serving.
Convert 3 ounces into pounds and ounces
3 ounces = 3/16 pound (1 pound = 16 ounces)
Amount of mandarin oranges required by one person = 3/16 pound
Amount of mandarin oranges required by 200 people = 200 * (3/16) pound
Amount of mandarin oranges required by 200 people = 37.5 pound
Convert the amount of mandarin oranges required into cans
Weight of one can of mandarin oranges = 5 pounds 10 oz = (5*16 + 10) ounce = 90 ounce
Weight of mandarin oranges only in one can = 90 ounce - 9 ounce = 81 ounce (9 ounce is liquid which you will discard)
Number of cans required = (total weight required) / (weight of one can)Number of cans required = (37.5 * 16) / 81 Number of cans required = 7.4 cans
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studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]
Where:
[tex]\(\lambda\)[/tex] is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
[tex]\(\lambda = 5\)[/tex]
[tex]\(k = 0\)[/tex], back to the formula as
[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]
Calculating the probability as
[tex]\[ P(X = 0) = e^{-5}[/tex]
[tex]= 0.0067379[/tex]
Therefore, the probability is 0.0067379 or 0.67%.
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Evaluate q2 + (r5 -10) if q = 5 and R = 2
Answer:
q=5,R=2
Step-by-step explanation:
=5×2+(2×5-10)
=10+(10-10)
=10+0
=10
-5,-7-9-11-13 what is the 2nd term in this linear sequence
The 2nd term in this given linear sequence {-5, -7, -9, -11, -13} is -7. So the correct answer is -7.
A linear sequence repeatedly increases or decreases by the same amount. The number added (or subtracted) at each stage of the linear sequence remains the same.
A linear sequence goes from one term to the next by always adding (or subtracting) the same value. The number added (or subtracted) at each stage of the linear sequence is called the common difference.
Examples of linear sequences occur when things change by the same amount each time.
Here is the linear sequence: 8, 11, 14, 17...
To find the next term in this sequence we calculate the common difference.
In this example the common difference is +3.
8 (+3) 11 (+3) 14 (+3) 17 (+3) …
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What is mutiplied by 6m-7 so that the produvct is 6m2-7m'
From the given information provided, m is multiplied by 6m-7 so that the product is 6m²-7m.
To find what is multiplied by 6m-7 so that the product is 6m²-7m, we can use polynomial long division or factorization. Here's how to do it using factorization:
We need to find two numbers that multiply to give 6m²-7m and add up to -7. We can factor the expression 6m²-7m as:
6m² - 7m = m(6m - 7)
So, we see that 6m-7 is a factor of 6m²-7m. Therefore, to find what is multiplied by 6m-7 to get 6m²-7m, we just need to divide 6m²-7m by 6m-7:
(6m² - 7m) / (6m - 7) = m
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Which inequality does this graph show?
We found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A is -2y + 2x ≥ 7x + y + 5.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the correct inequality, we need to find the equation of the line that passes through the points (-1, 0) and (0, -1.5).
The slope of the line can be calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (-1.5 - 0) / (0 - (-1))
m = -1.5
The y-intercept of the line can be found by substituting one of the points and the slope into the point-slope form of a line:
y - y1 = m(x - x1)
y - 0 = -1.5(x - (-1))
y + 1.5 = -1.5x - 1.5
y = -1.5x - 3
Now we can rewrite the inequality in the form y <= mx + b, where m is the slope and b is the y-intercept.
-2y + 2x >= 7x + y + 5 can be simplified to:
-3y >= 5x + 5
Dividing both sides by -3, we get:
y <= (-5/3)x - 5/3
Comparing this to the equation we found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A:
-2y + 2x ≥ 7x + y + 5
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what is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
Option B, The fact that this survey question is a double-barreled question makes it problematic.
A survey question known as a double-barreled question has two questions inside one, making it challenging for respondents to give truthful and insightful responses.
The offered inquiry, in this instance, combines two distinct inquiries: if the phone was acquired within the last two years and whether it has recently had an upgrade.
Inconsistent answers might result from a person who bought their phone more than two years ago but only recently upgraded it, or vice versa. In order to prevent double-barreled questions and guarantee that responders can give precise and complete replies, each question should be isolated and posed independently.
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The question is -
What is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
a. It is a leading question
b. It involves negative wording
c. It is a double-barreled question
d. It is not on a Likert Scale
.. Sasha Abbott earns $62,550.00 in taxable income each year. The tax rate is 3.6%, and she takes zero deductions. How much tax does her employer withhold each year? A $2,380.50 B $2,251.80 C $2,500.40 D $1,823.20
Answer: B $2,251.80
Step-by-step explanation:
:)
Enlarge shape A by scale factor 1. 5 with centre of enlargement (0, 0)
To enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.
Enlargement of Shape A
Enlargement of a shape is when it is either stretched or shrunk in one or both directions. The original shape is called the pre-image, while the new shape is called the image. What is the centre of enlargement?
The center of an enlargement is the point about which all of the points of the pre-image are scaled to obtain the image. When the scale factor is greater than 1, the image of the pre-image is an enlargement. When the scale factor is between 0 and 1, the image of the pre-image is a reduction.In an enlargement, each point on the pre-image is mapped onto a corresponding point on the image along a straight line which goes through the centre of enlargement.
The new shape has a larger size than the original shape. To expand shape A by a scale factor of 1.5, you need to multiply each length by 1.5. You have to create new points. It's easy to use a scale ruler to make sure each length is multiplied by 1.5.
A Centre of enlargement is a point in the coordinate plane that enlarges or shrinks a figure by some scale factor. In the problem, the center of enlargement is (0, 0).
Thus, we have to extend every length of Shape A by 1.5, and our scale factor is 1.5. We get Shape B by doing so. Now, we can conclude that to enlarge Shape A by a scale factor of 1.5 with the center of enlargement (0, 0), we have to multiply every length by 1.5.
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A random group of adults was asked to complete a survey regarding the number of pets in their households. No two adults sur came from the same household. The number of households, , with no pets is one fourth of the number of households with multip Which of the following equations represents this situation if of the households have a single pet?
The equation representing the situation is 4x = y - 1, where x is the number of households with one pet and y is the total number of households. This can be answered by the concept of Simple equation.
Let's assume that there are x households with a single pet. The number of households with no pets is given as one-fourth of the number of households with multiple pets, which means there are 4 times as many households with multiple pets as there are households with no pets. Let's represent the total number of households as y.
Therefore, we can say that the number of households with no pets is (y - x)/4, and the number of households with multiple pets is 3(y - x)/4 since there are 4 times as many households with multiple pets as there are households with no pets.
Now, we can use the given information that the number of households with no pets is one-fourth of the number of households with multiple pets to write the equation:
(y - x)/4 = x/3
Solving for y, we get:
y = 4x + 3x/4 = 16x/4 + 3x/4 = 19x/4
But we are given that the total number of households y includes the households with one pet, so we can write:
y = x + (y - x)/4 + 3(y - x)/4 = x + y/4
Substituting the value of y from the previous equation, we get:
19x/4 = x + 19x/16
Solving for x, we get:
x = 16/3
Therefore, the equation representing the situation is 4x = y - 1, where x = 16/3 and y = 19x/4, which simplifies to:
4(16/3) = y - 1
y = 21
Therefore, there are 16 households with one pet and 5 households without any pets.
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the survey of 72 students about their favourite fruit apple banana guava grapes 12 18 6 36. draw a circle and divide it into 12 parts and represent the data given as a pie chart .
The slice for apple will have an angle of 60 degrees, the slice for banana will have an angle of 90 degrees, the slice for guava will have an angle of 30 degrees, and the slice for grapes will have an angle of 180 degrees.
What is pie chart?A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Pie charts are commonly used in business, media, and other fields to represent percentages, ratios, and proportions. They are useful for quickly understanding the relative sizes of different categories or groups in a dataset.
Here,
To create a pie chart from the given data, we first need to calculate the angle of each slice of the pie chart. To do this, we use the following formula:
Angle for a slice = (Frequency of the category ÷ Total frequency) × 360°
Using the given data, we can calculate the angle of each slice as follows:
Angle for apple = (12 ÷ 72) × 360° = 60°
Angle for banana = (18 ÷ 72) × 360° = 90°
Angle for guava = (6 ÷ 72) × 360° = 30°
Angle for grapes = (36 ÷ 72) × 360° = 180°
Now, we can draw a circle and divide it into 12 parts (each representing 30 degrees). Then, we can draw the slices of the pie chart using the angles we calculated above.
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3.- cual es la máxima distancia que pueden recorrer sin cambiar de dirección en una pista de patinaje en forma de rombo, si cada lado mide 26 mts y ka diagonal menor 40 mts ?
Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.
what is perimeter ?The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.
given
The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.
Given that the sides are each 26 metres long, the rhombus's perimeter would be:
Perimeter: (4 x 26) = 104 metres
But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.
Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.
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The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?