Few people who receive questionnaires in the mail actually fill them out and return them - often fewer than 10%! One researcher thinks he can improve the response rate by including a coupon good for a free pint of ice cream along with the questionnaire. The researcher believes that people will want the ice cream, and feel guilty if they don't return the questionnaire. To test this conjecture he mails questionnaires with ice cream coupons to 150 randomly selected people. After two weeks 41 of the surveys have been returned. a) Create a 95% confidence interval for the relurn rate. 1-Z proportion Interval b) Encouraged by this response rate this researcher now plans to replicate the study in hopes of estimating the return rate this strategy might achieve to within 5%. How many new questionnaires must he mail out?

Answer:

Step-by-step explanation:

Carry out indicated operations to see if they are equal

2(6-3x)+x=2(3x)+x+12

2(6)+2(-3x)+x=6x+x+12

12-6x+x=6x+x+12 combine like terms on both sides

12-5x=12+7x (we can see here they are unequal but we can continue) subtract 12 from both sides

-5x=7x divide both sides by x

-5=7

7 is not equal to -5 so the original expressions aren’t equivalent.

The equivalent value of the length MN is 52/3 units long.

Given is that LN = 6x - 5 , LM = 7 and MN = 3x + 20.

Now , we can write -

LM = LN + NM

(6x - 5) + (3x + 20) = 7

6x + 3x - 5 + 20 = 7

9x + 15 = 7

9x = 7 - 15

9x = - 8

x = -8/9

So -

MN = 3x + 20 = 3 x (-8/9) + 20

MN = 20 - 8/3

MN = (60 - 8)/3

MN = 52/3

Therefore, the equivalent value of the length MN is 52/3 units long.

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The expected number of defective toys when 2 toys are selected at random is 0.077 (rounded to three decimal places).

To find the expected number of defective toys when 2 toys are selected at random, we first need to find the probability of selecting a defective toy on each pick.

On the first pick, the probability of selecting a defective toy is 4/13 since there are 4 defective toys out of 13 total. On the second pick, the probability of selecting a defective toy depends on whether or not a defective toy was selected on the first pick.

If a defective toy was selected on the first pick, then there are only 3 defective toys left out of 12 total toys remaining. So the probability of selecting a defective toy on the second pick would be 3/12 or 1/4.

If a non-defective toy was selected on the first pick, then there are still 4 defective toys left out of 12 total toys remaining. So the probability of selecting a defective toy on the second pick would be 4/12 or 1/3.

To find the expected number of defective toys, we need to multiply the probabilities of each scenario and add them together:

Expected number of defective toys = (4/13 x 3/12) + ((9/13) x 4/12)

Simplifying this equation gives us:

Expected number of defective toys = 1/13

Therefore, the expected number of defective toys when 2 toys are selected at random is 0.077 (rounded to three decimal places).

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Answer:

This is your answer ☺️☺️

Answer:

- 7x + y = -30

2x - 5 = y

=> -7x + 2x - 5 = -30

2x - 5 = y

<=> -5x = -25

2x - 5 = y

<=> x = 5

y = 2.5 - 5 = 5

=> (x,y) = (5;5)

Answer:

y=7x-30

2x-5=7x-30

30-5=7x-2x

25=5x

x=5

if x = 5 substitute in any of the equations

y= 2*5 -5

y=5

Answer:

False

Step-by-step explanation:

12+9<20

21≮20

False

Answer:

{x|x is a rational non-integer}

Step-by-step explanation:

Plot of function g(n), g(-n), and g(2-n) for -5 ≤ n ≤ 5: g(n) is -2 for n < -4, n for -4 ≤ n < 1, and 4/n for n ≥ 1.

The function g(n) is defined piecewise. Let's break down the function and plot g(n), g(-n), and g(2-n) for the given range of -5 ≤ n ≤ 5.

For n < -4, g(n) = -2. This means that for n values less than -4, the function g(n) is a constant value of -2. Therefore, the plot of g(n) in this range will be a horizontal line at y = -2.

For -4 ≤ n < 1, g(n) = n. In this range, the function g(n) takes the same value as the input n. As n increases from -4 to 0, g(n) will increase linearly, resulting in a diagonal line with a positive slope.

For n ≥ 1, g(n) = 4/n. In this range, the function g(n) is defined as the reciprocal of n multiplied by 4. As n increases beyond 1, g(n) will decrease inversely, resulting in a curve that approaches but never reaches the x-axis.

To plot g(-n), we substitute -n for n in the original function. This essentially reflects the plot of g(n) across the y-axis. So, the plots of g(n) and g(-n) will be symmetric with respect to the y-axis.

To plot g(2-n), we substitute 2-n for n in the original function. This shifts the plot of g(n) horizontally to the right by 2 units. The overall shape of the plot remains the same, but it is shifted to the right.

Therefore, the final plot will consist of a horizontal line at y = -2 for n < -4, a diagonal line with a positive slope for -4 ≤ n < 1, a decreasing curve for n ≥ 1, and their respective symmetric and shifted versions for g(-n) and g(2-n).

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Answer:

y = 3x + 4

Step-by-step explanation:

slope is 9/3 simplified to 3

y intercept is 4

Answer:

oh did you just take your 7 grade MATH BENCHMARK

picked d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Remark

The trick is to solve the inequality. The last step is very tricky. Be careful with it.

Equation

15≤ -3x + 6                     Subtract 6 from both sides

15-6 ≤ - 3x + 6 - 6            Combine

9 ≤  -3x                           Divide by - 3

9/-3 ≥ -3x/-3                   Notice what happened to the less than or equal to

-3  ≥ x

Now there are 2 problems remaining.

1) why did the inequality turn around?

It turned around because when you divide by a number less than 0, the inequality turns around because the negative numbers work opposite to the positive numbers .

18 > 6

-18 < - 6

2) So which graph is correct.

The largest number that is possible is -3 The arrowhead should be pointing left.

In addition, the circle should be blacked in.

The answer is as you have marked it: A

ooo among us!! i was just looking at some fan art of it.. also love your pfp! who is it? if u don't mind me asking I would love to watch the show if it.. or at least know the person :D

anyway.. happy day/night ~

Answer:  approximately 24 square units in the shaded areas

Step-by-step explanation:  

The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:

16π + 9π = 25π   Half that times value for pi

≈ 39.2699  is the area of the dark semicircles. Round to 39.27

Now the fun! Find the area of the parts subtracted by the light semicircle:

The area of the entire circle is 25π  or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48.  Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27

Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

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Considering the graph the domain and range are

The domain refers to the possible values of the input variables which is in the x coordinate

Looking at the graph image attached, the values starts from -3 to 1 this is written as

The range refers to the values of the output functions. From the graph the range is 4 to 5

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The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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Answer:

y = 6x - 4

Step-by-step explanation:

Slope formula: y = mx + b

m = slope, found by figuring out the change in y over the change in x. A fancy way to say find the simplest rate of how far up it goes over how far right it goes. In this case, the line goes up 6 for every time it goes right one; 6/1. This can be simplified as 6.

b = y-intercept, meaning where the line crosses the y line. In this line, you can see that it crosses at -4.

Hope this helps!

Answer:

B or (-1)(1/2)(-1)(1)

Step-by-step explanation:

-4/5 is closest to (-1)

3/5 is closest to 1/2

-6/7 is closest to (-1)

5/6 is closest to 1

hope this helps

Answer: B

Step-by-step explanation:

I did the test on edge...

The dilated triangle R'S'T' has the following vertices R' (0, 6), S' (6, 3) and T' (3, 3)

The scale factor for dilation is 3/4

The new coordinates of the vertices after dilation:

Vertex R: (0, 8)

New coordinates:

x-coordinate: (3/4)× 0 = 0

y-coordinate: (3/4) × 8 = 6

So, the new coordinates for vertex R after dilation are (0, 6).

Vertex S: (8, 4)

New coordinates:

x-coordinate: (3/4) × 8 = 6

y-coordinate: (3/4) ×4 = 3

So, the new coordinates for vertex S after dilation are (6, 3).

Vertex T: (4, 4)

New coordinates:

x-coordinate: (3/4) ×4 = 3

y-coordinate: (3/4) ×4 = 3

So, the new coordinates for vertex T after dilation are (3, 3).

Hence, the dilated triangle R'S'T' has the following vertices R' (0, 6), S' (6, 3) and T' (3, 3)

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods. In this scenario, the utility function given is a(f, g) = 2√f + g

The price of good f is 2 and the price of good g is 1.

The consumer's income is 3/4 and 1/4 respectively. Using these, we can solve for the optimal consumption bundle for the consumer using the utility function.

a) To calculate the optimal consumption bundle when the income is 3/4, we can use the following method:

Let the optimal consumption bundle be represented as (x, y).

Here, x represents the quantity of good f consumed, and y represents the quantity of good g consumed.

The consumer's budget constraint can be given as follows:

2x + y = 3/4

The consumer's goal is to maximize their utility, which can be represented as:

a(f, g) = 2√f + g = 2√x + y

The consumer's optimization problem can be represented as follows:

Maximize 2√x + y subject to 2x + y = 3/4

To solve this optimization problem, we can use the Lagrangian function:

L(x, y, λ) = 2√x + y - λ(2x + y - 3/4)

To find the optimal consumption bundle, we must solve for the following set of equations:

∂L/∂x = 0,

∂L/∂y = 0, and

∂L/∂λ = 0

Solving for the first two equations yields the following:

x/√x = λ2y - λ

= 1

The third equation can be used to solve for λ:

2x + y - 3/4 = 0

Solving for x and y using the first two equations and the value of λ yields:

x = 1/2 and y = 1/4

Therefore, the optimal consumption bundle is (1/2, 1/4)

b) To calculate the optimal consumption bundle when the income is 1/4, we can use a similar method to the one used in part a.

Using the same budget constraint of 2x + y = 1/4 and the same utility function of 2√x + y, we can solve for the optimal consumption bundle by using the Lagrangian function L(x, y, λ) = 2√x + y - λ(2x + y - 1/4).

Solving for the same set of equations, we get:

x = 1/8 and y = 0

Therefore, the optimal consumption bundle is (1/8, 0)

Utility functions are mathematical representations of the satisfaction a consumer derives from consuming goods and services. A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.In this question, we were given a specific utility function and the prices of two goods. We used this information to solve for the optimal consumption bundle when the consumer's income was 3/4 and 1/4 respectively.To solve for the optimal consumption bundle, we used the Lagrangian method to optimize the consumer's utility function subject to their budget constraint. The Lagrangian method involves creating a Lagrangian function that includes the consumer's utility function and their budget constraint. We then solve for the first-order conditions of the Lagrangian function, which are a set of equations that yield the optimal values of the goods consumed.This method is useful for solving for optimal consumption bundles because it takes into account both the consumer's preferences and their budget constraint. By solving for the optimal consumption bundle, we can determine how much of each good the consumer should consume to maximize their satisfaction given their budget constraint

Utility functions and optimal consumption bundles are important concepts in microeconomics. They allow us to understand how consumers make choices and how they allocate their resources. By solving for the optimal consumption bundle, we can determine the best combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.

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Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Answer:

open up and have a minimum

Step-by-step explanation:

Since its positive it will open up since its positive it should have a minimum since it opens up

The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.

The Remainder is the extra part of a number that restricts the number to be divided completely.

a)

(19² mod 41) mod 9

Let us determine 361 mod 41

a=361 = 328+33= 8*41+33 =8d+33

The remainder is the constant in the final expression: 361 mod 41=33

33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)

b)

(32³ mod 13)² mod 11

Let us determine 32 mod 13

a=32=26+6=2*13+6+2d+6

The remainder is the constant in the final expression: 32 mod 13=6

\((6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11\)

Let us determine 216 mod 13

a= 216= 208+8=16*13+8 = 16d+8

The remainder is the constant in the final expression: 216 mod 13=8

\(8^{2} mod 11\\64 mod 11\) = 9 (since, 64= 55+9= 11*5+6= 11d+6)

c)

(7³ mod 23)² mod 31

\((343mod23)^{2} mod 31\\\)

Let us determine 343 mod 23

a=343=322+21=14*23+21=14d+21

The remainder is the constant in the final expression: 343 mod 23= 21

\(21^{2} mod 31 = 441 mod 31=7\) (since a = 441=434+7=14*31+7=14d+7)

d)

(21² mod 15)³ mod 22

\((441mod15)^{3} mod 22\)

Let us determine 441 mod 15

a=441 = 435+6= 29*15+6= 29d+6

The remainder is the constant in the final expression: 441 mod 15= 6

\(6^{2} mod 22=36mod22= 14\) (since a = 36= 22+14= 1*22+14= d+14)

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One of the most popular dance types of the sixteenth century was the pavane, another one are galliard and allemande.

Instruments in math are tools or processes used to perform mathematical operations and calculations. Examples of instruments in math include calculators, rulers, compasses, protractors, and computers. These instruments can be used to solve problems, analyze data, and understand mathematical concepts. Additionally, instruments in math can be used to teach students about problem-solving and allow them to gain a deeper understanding of mathematics.

This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The pavane was often used as a ceremonial dance in courts and was usually performed by couples.

Another popular dance type of the sixteenth century was the galliard. This was a lively, energetic dance, usually in triple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The galliard was often used as a dance for entertainment and was usually performed by couples.

The third popular dance type of the sixteenth century was the allemande. This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The allemande was often used as a ceremonial dance and was usually performed by couples. It was usually danced in a line or circle formation, with each dancer taking the lead in turn.

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The null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup is Divorce Opinions and Gender I.

We introduce the results of a

May 2010 Gallup poll of 1029 US adults. When asked if they view divorce as “morally acceptable”,

71% of the men and 67% of the women in the sample responded yes. In the test for a difference in

proportions, a randomization distribution gives a p-value of 0.165. Does this indicate a significant

Solution

If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not

reject H0 : pf = pm. This means the data do not show significant evidence of a difference in the

proportions of men and women that view divorce as “morally acceptable”

Solution

(a) The p-value (0.003) is small so the decision is to reject H0 and conclude that the mean recall

for sleep (¯xs = 15.25) is different from the mean recall for caffeine (¯xc = 12.25). Since the mean

for the sleep group is higher than the mean for the caffeine group, we have sufficient evidence to

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Answer:

x = 72

Step-by-step explanation:

36 - x = -36

*subtract 36 from both sides*

-x = -72

*divide by -1*

x = 72

Answer:

0 is the answer of the equation