a random sample of 245 students showed that 189 of them liked listening to music while studying. find the 90% confidence interval for the proportion of students that like listening to music while studying. what is the se (standard error) for this sample? do not round

(a) It will take Marti 38 spins to win by placing a $1 bet on number 15.

(b) The standard deviation of 37.36 means that there's a considerable variation in the number of spins it might take Marti to win her $1 bet on number 15.

We'll be discussing the mean and standard deviation of Y, where Y is the number of spins it takes for Marti to win by betting $1 on number 15 in roulette.

(a) The mean of Y can be calculated using the expected value formula for a geometric distribution: E(Y) = 1/p, where p is the probability of success. In this case, p = 1/38. Therefore, the mean of Y is:
E(Y) = 1 / (1/38) = 38
This means that on average, it will take Marti 38 spins to win by placing a $1 bet on number 15.

(b) The standard deviation of Y can be calculated using the formula for the standard deviation of a geometric distribution: SD(Y) = √[(1-p)/p^2].

Plugging in our values, we get:
SD(Y) = √[(1 - 1/38) / (1/38)^2] ≈ 37.36

The standard deviation of Y, approximately 37.36, indicates the average variation in the number of spins it takes for Marti to win. A higher standard deviation would suggest a wider range of spins needed to win, while a lower standard deviation indicates a more consistent number of spins.

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Surface area of a square pyramid:

To find the surface area of the given pyramid as you don't have the length of the slant height, use the height of the pyramid and the radius of the base to form a right triangle and find the slant height:

Pythagorean theorem for the right triangle above:

Perimeter of the base is:

Area of the square base:

Then, the surface area of the given pyramid is

Answer: G

Step-by-step explanation:

because I would be 15 and not 20

Answer: It is linear

Step-by-step explanation:

When you graph the equation, it is a straight line, meaning it is linear.

If you graphed the equation and it wasn't a straight line, it would be nonlinear.

Given the inverse demand function p = 100 - 20q for toasters and a price of $35, we can find the consumer surplus.

First, we'll find the quantity demanded at the given price:

35 = 100 - 20q
20q = 100 - 35
q = (100 - 35) / 20
q = 65 / 20
q = 3.25

Now, to find the consumer surplus, we'll use the formula:

Consumer Surplus = (1/2) × Base × Height

The base represents the quantity (q = 3.25) and the height is the difference between the maximum willingness to pay (p = 100) and the actual price (p = 35).

Consumer Surplus = (1/2) × 3.25 × (100 - 35)
Consumer Surplus = 0.5 × 3.25 × 65
Consumer Surplus = 105.625

So, the consumer surplus is $105.63 when rounded to two decimal places.

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Answer:

A

Step-by-step explanation:

use the quadratic formula and you should end up with this

d=1/32 (33+\(\sqrt{1217}\))=2.121

The domain is [0,2.121...].

x = -b / 2a = -3.3/(-3.2) = 1.031

max=1.902

so its A

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The cost of goods completed and transferred out, given 16,000 units completed and 1,600 units in ending inventory, is $104,000. This is calculated by multiplying the number of completed units by the weighted-average cost per equivalent unit for direct materials and conversion.

In this scenario, 16,000 units are completed and 1,600 units are in ending inventory. The weighted-average cost per equivalent unit for direct materials is $3.00, and for conversion, it is $3.50.

To calculate the cost of goods completed and transferred out, we can use the following formula:

Cost of goods completed and transferred out = (Number of completed units * Weighted-average cost per equivalent unit for direct materials) + (Number of completed units * Weighted-average cost per equivalent unit for conversion)

Substituting the given values:

Cost of goods completed and transferred out = (16,000 * $3.00) + (16,000 * $3.50)

                                            = $48,000 + $56,000

                                            = $104,000

Therefore, the cost of goods completed and transferred out is $104,000.

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The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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Answer:

\(x\leq -2\)

Step-by-step explanation:

Solve for x:

\(-4x+20\geq 28\)

Subtract 20 on both sides

\(-4x\geq 8\)

Flip the sign and multiply both sides by -4

\(16x\leq -32\)

Divide by 16

\(x\leq -2\)

The 48th percentile for weight means that the 16-year-old girl's weight falls within the range of weights that 48% of girls her age typically weigh.

The 78th percentile for height means that her height falls within the range of heights that 78% of girls her age typically have.

Percentiles are used in growth charts to compare an individual's height or weight to a reference population. The percentile values indicate the percentage of people in that population who have a lower measurement.

For example, a girl at the 48th percentile for weight means that 48% of girls her age weigh less than her, while 52% weigh more. Similarly, being at the 78th percentile for height means that 78% of girls her age are shorter than her, while 22% are taller.

In plain English, the girl's weight is considered to be in the middle range, as she is at the 48th percentile. However, her height is above average, as she is at the 78th percentile.

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Answer:

\(6x - 2x - 24 = - 52 \\ 4x = - 52 + 24 \\ 4x = 28 \\ x = \frac{-28}{4} = -7\)

Answer:

x = -7

Step-by-step explanation:

6x – 2(x + 12) = -52

6x - 2x - 24 = -52

4x - 24 = -52

    +24    +24

--------------------

4x = -28

/4      /4

--------------------

x = -7

Answer:

87.29,,,,,,,,

Step-by-step explanation:

87290 mm =87.29m

Answer:

5.04

Step-by-step explanation:

The largest interval of x-values where the function is increasing is (-1, 1)

The table of values is added as an attachment

From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2

So, we make use of the intervals

x = -1, 0 and 1

From the table,

From x = -1 to 0, the change is 3

From x =  0 to 1, the change is 3

From x =  -1 to 1, the change is 6

Using the above highlights, the largest increasing interval is (-1, 1)

Hence, the largest interval of x-values where the function is increasing is (-1, 1)

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Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

Given,

Making an interval estimate for the population mean requires making the following assumptions about the population:

a. The population is thought to have a normal distribution.

b. The central limit theorem is presumptively true.

The distribution of a variable's values is described by a normal distribution. There are 50% of the data to the left and 50% to the right of the mean in this probability distribution, which is symmetrical about the mean. The majority of the data are centered around the mean, meaning that they are more likely to occur or be located close to the mean than distant from it. A bell curve will represent the normal distribution's graph form. Mean = mode = median describes a normal distribution.

According to the Central Limit Theorem, when a variable does not follow a normal distribution, repeated random samples from the population will result in sample means that are normally distributed, regardless of the underlying distribution of the sample. This indicates that as the sample size increases, the sampling distribution of the sample means moves closer to a normal distribution.

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Step 1: Distribute:

3(x+2) + 5(x+4) = 3•(x+2) + 5•(x+4)

                        = 3•x + 3•2  +  5•x + 5•4

                        = 3x + 6  +  5x + 20

Step 2: Combine Like terms

                        = 8x + 26

The word that best fits the definition of identifying which books have romantic or heroic themes is "genre."

In literature, the term "genre" refers to a category or classification of literary works based on their content, style, and themes. It helps to categorize books into different types or groups, making it easier for readers to find the kind of books they enjoy. One such genre that encompasses romantic or heroic themes is "romance" or "adventure."

Romance novels typically revolve around romantic relationships and often feature passionate love stories. These books explore themes of love, desire, and emotional connections between characters. On the other hand, adventure novels often involve daring and heroic actions, with protagonists embarking on thrilling quests or facing challenges that require bravery and determination. These books often highlight themes of heroism, courage, and the triumph of good over evil.

By identifying the genre of a book as romance or adventure, readers can easily find and select books that align with their preference for stories with romantic or heroic themes

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Answer:

13 over 22

Step-by-step explanation:

because you want to change the denominator to where they can match. So 22 is where 11 and 2 can match. then you want to multiply the amount you multiplied with the denominator so 1 over 11 would be 2 over 22. And 1 over 2 would be 11 over 22. and then you can add. 11 plus 2 is 13 and you can keep the denominator the same. Therefore, the answer would be 13 over 22

hope i helped.

Answer:

Step-by-step explanation:

The shaded area is the difference of the large and small squares.

Area of large square:

Area of small square:

Shaded area:

The solutions to the system of equations are (-2,-6) and (4,6)

We have:

-2x + y = -2

\(y = -\frac12x^2 + 3x + 2\)

Next, we plot the graph of both functions.

From the attached graph, the equations intersect at (-2,-6) and (4,6)

Hence, the solutions to the system of equations are (-2,-6) and (4,6)

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The radius of convergence of the given series is infinity.

To find the radius of convergence, we use the ratio test, which involves computing the limit of the ratio of successive terms. Applying the ratio test to the given series, we get:

limit as n approaches infinity of [((n+1)!)^k/(k(n+1))!][k!/(n!)^k][x^(n+1)][(kn)!/k!][n!/(kn)!]*[x^n]

Simplifying the expression, we get:

limit as n approaches infinity of [(n+1)/(kx)]*|x|

Since the limit is infinity, the radius of convergence is infinity. This means that the series converges for all values of x.

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Answer: 58 books

Step-by-step explanation:

There are 35 English books on the shelf and this constitutes 60% of the total number of books on the shelf.

Denoting the total number as x, the total number is:

35 = 60% * x

x = 35 / 60%

= 58 books

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = \(a^x\)

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

The examples of exponential functions are:

f(x) = \(2^x\)

f(x) = 1/ \(2^x\) = \(2^-x\)

f(x) =\(2^(x+3)\)

f(x) = \(0.5^x\)

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Answer:

Because if you give the power of 2 to all of them you get a different number

1. 20 squared+ 21 squared = 841

Answer to number 1

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

We have the following information available from the question is:

An odd integer is an integer that can be expressed as 2k+1 , where k is an integer.

An even integer is an integer that can be expressed as 2k , where k is an integer.

Now, According to the question:

To prove the each statement:

a. The sum of an odd and an even integer is odd:

Let the odd integer = 3

Let the even integer = 2

Adding the both odd and even integers.

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

Let the first odd integer = 3

Let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

Let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

Let the first odd integer = 3

Let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

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The given question is incomplete, complete question is:

About Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1 , where k is an integer. An even integer is an integer that can be expressed as 2k , where k is an integer. Prove each of the following statements using a direct proof.

a. The sum of an odd and an even integer is odd.

b. The sum of two odd integers is an even integer.

c. The square of an odd integer is an odd integer.

d. The product of two odd integers is an odd integer.