Random samples of size
100
100 are taken from an infinite population whose population proportion is
0.2
0.2. What are the mean and standard deviation of the sample proportion?

Answer:

See answers and explanations below (along with a visual graph)

Step-by-step explanation:

For the function \(y=acos(b(x+c))+d\):

Amplitude: \(|a|\)

Period: \(\frac{2\pi}{|b|}\)

Phase shift: \(\frac{-c}{b}\)

Vertical shift: \(d\)

Therefore, for \(y=2cos(\frac{2}{3}(\theta+\pi))-1\):

Amplitude: \(|a|=|2|=2\), which is 2 units above and below the midline (see d)

Period: \(\frac{2\pi}{|b|}=\frac{2\pi}{|\frac{2}{3}|}=\frac{2\pi}{\frac{2}{3}}=3\pi\), so the cycle will repeat every 3π units

Phase shift: \(\frac{-c}{b}=\frac{-\frac{2\pi}{3} }{\frac{2}{3} }=-\pi\), or π units to the left

Vertical shift: \(d=-1\), or 1 unit down

Answer:

Yes

Step-by-step explanation:

Yes, the lines represented by the equations y=x-3 and x-y=8 are parallel. To see why, you can write both equations in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. For the equation y=x-3, the slope is 1 and the y-intercept is -3. For the equation x-y=8, you can solve for y to get y=x-8, so the slope is also 1 and the y-intercept is -8. Since the slopes are equal, the lines are parallel.

Given that the periodic function f(t) is explained with the alternative Fourier coefficients.  A1∠θ1= 3∠5°, A4∠θ4= 4∠4° and the frequency, ωo = 1000radHz.We know that a periodic function can be expressed as the sum of sine and cosine waves.

The Fourier series represents a periodic function as a sum of an infinite series of sines and cosines. This representation can be expressed mathematically as,

f(t) = a0 + Σ[an cos(nω0t) + bn sin(nω0t)]Here, ωo is the angular frequency of the waveform. a0, an, and bn are the Fourier coefficients and are expressed as follows; a0 = (1/T) ∫T₀f(t) dt an = (2/T) ∫T₀f(t)cos(nω₀t) dt bn = (2/T) ∫T₀f(t)sin(nω₀t) dt

where T₀ is the period of the waveform, and

T

= n T₀ is the interval over which the Fourier series is to be computed. In this case, the values of a1 and a4 have been given, A1∠θ1

= 3∠5° and

A4∠θ4

= 4∠4°. Hence the expression of the function is,  f(t)

=  a0 + 3cos(ω0t + 5°) + 4cos(4ω0t + 4°) where,

ω0 = 1000 rad/s. This is the required expression of the function f(t).

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Answer: 5

Step-by-step explanation:

Answer:

She needs to get 8 bags of spoon and 1 bag of fork

Step-by-step explanation:

Here in this question, we want to know the least number of spoons and the least number of bags to be bought so that there are same number of each.

Basically, to calculate this, we need the lowest common multiple of 16 and 2. The lowest common multiple of both is 16 (2 is a factor of 16)

So the lowest number of each she can buy to have the same number of pieces is 16.

Kindly recall that spoons come in bags of 2. So to achieve the 16, she needs 8 bags.

Since fork comes in bag of 16, to achieve 16, she only need a single bag of fork.

A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.

So we have to find 2.3% of 65,000 which is 1495

Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is

Answer : 76960

(Choice 1)

Answer:

its is A

Step-by-step explanation:

32.13 is 32 rounded to the nearest whole so then 32/4 and 4 represents events, so 32/4 is 8

Answer:

  {-4, -2, 2, 3}

Step-by-step explanation:

The domain is the set of first numbers in the pairs, so includes 2, -4, -2, 3, 2. When we write this as a set, we eliminate duplicates. Often, we list them in order: {-4, -2, 2, 3}

Answer:

The percentage discount for the cost of the guitar is 45%.

Step-by-step explanation:

First let's find the difference between the original price and the new price.

80 - 44 = 36

So the actual discount got the price down by $36.

To find the percentage discount we need to ask ourselves the question

36 is what percent of 80?

36 = X percent of 80

In math, of means multiply.

36 = X percent * 80

So to get the "X percent" part alone we divide by 80 on both sides.

36 divided by 80 = 0.45

36 is 45 percent of 80.

The percentage discount for the cost of the guitar is 45%.

Answer:

Step-by-step explanation:

0.03550295857

Given:

1 chocolate chip cookie recipe = 12 cup of chocolate chips per batch.

Alonzo wants to make 3 12 batches.

Lets's find the number of chocolate chips he will need.

Number of batches he wants to make is = 3 x 12 = 36 batches

SInce 1 chocolate chip cookie recipe calls for 12 cup of chocolate chips per batch, we have:

Answer:

1646

Step-by-step explanation:

2/3 of 2469 = 2/3 × 2469 = 2 × 2469/3 = 1646

Answer:

so 2469

Step-by-step explanation:

3973.5 i think

Answer:

Number of rooms reserved for the students are - 90 .

Step-by-step explanation:

Firstly ,

As we know 60% of the 600 students went on the trip,

Then ,

Number of students went on the trip = 60% of 600

                                                          = \(\frac{60}{100}\times600\)

                                                        = 360

Now ,

Given - One room is reserved  for 4 students ,

Therefore , Number of rooms for 360 students = \(\frac{360}{4}\)

                                                                             = 90

Hence , the answer is  90 rooms reserved for the students.

The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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The image of the square S under the given transformation is a parallelogram in the (x, y) plane, defined by the points (0, 0), (1, 0), (0, 1), and (1, 1).

To find the image of the set S under the given transformation, we substitute the coordinates of the points in S into the transformation equations. The set S is a square bounded by the lines u = 0, u = 1, v = 0, and v = 1.

Let's consider the four corners of the square:
Corner 1: (u, v) = (0, 0)
Corner 2: (u, v) = (0, 1)
Corner 3: (u, v) = (1, 0)
Corner 4: (u, v) = (1, 1)

For each corner, we apply the transformation:
Corner 1: (x, y) = (v, u(1 - v^2)) = (0, 0)
Corner 2: (x, y) = (v, u(1 - v^2)) = (1, 0)
Corner 3: (x, y) = (v, u(1 - v^2)) = (0, 1)
Corner 4: (x, y) = (v, u(1 - v^2)) = (1, 1)

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Answer:

this is a positive correlation

Step-by-step explanation:

it is going up so its positive

Answer:

It would be C i believe

Step-by-step explanation:

The normal sampling distribution cannot be used, according to the given sample statistics and claim about the population proportion. The correct answer is option A, "No, because np is less than 5."

To determine whether the normal sampling distribution can be used to test the given claim about the population proportion, we need to check whether the conditions for a normal approximation are met. There are three conditions that need to be satisfied:

The sample size should be large enough (n ≥ 30). However, in this case, the sample size is only 25, which is not large enough.

The expected number of successes (np) and the expected number of failures (nq) should both be greater than or equal to 5. In this case, np = (25)(0.11) = 2.75 and nq = (25)(0.89) = 22.25, so np is less than 5.

The sample is independent and random. There is no information given in the question to suggest that this condition is not met.

Therefore, the correct answer is option A, "No, because np is less than 5." Since np is less than 5, we cannot use the normal sampling distribution to test the claim about the population proportion p at the given level of significance α = 0.05 using the given sample statistics p = 0.08 and n = 25. Instead, we would need to use the binomial distribution to calculate the probability of obtaining a sample proportion of 0.08 or less assuming the null hypothesis is true.

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Answer:

5cd=157qr

1cd=157/55qr

or

qr=55/157cd

Step-by-step explanation:

1qr=30nc

55/157×cd=30nc

55/157×1/30×cd=1nc

1nc=0.011670cd

rs2870=0.01167×2870cd=33.49cd

₹2870 is equal to 33.49 CD.

Given that, 55 Canadian Dollars=157 Qatari Riyal and 1 Qatari Riyal=30NC.

We need to find how much the Canadian Dollar is equal to ₹2870.

The Canadian dollar is the currency of Canada. It is abbreviated with the dollar sign $, or sometimes CA$, Can$ or C$ to distinguish it from other dollar-denominated currencies. It is divided into 100 cents.

Converting the Canadian Dollar to rupees use 1 NC=0.011670 CD.

1 QR=30 NC

55/157 CD=30 NC

55/157×1/30×CD=1 NC

1 NC=0.011670CD

₹2870=0.01167×2870 CD=33.49 CD

Therefore, ₹2870 is equal to 33.49 CD.

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Answer:

250 g of water

Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is \(f(n)=rf(n-1), f(1)=a, n\geq 2\), then the explicit formula of that GP is:

\(f(n)=ar^{n-1}\)

Where, a is the first term and r is the common ratio.

The first recursive formula is:

\(f(1)=5\)

\(f(n)=3f(n-1)\) for \(n\geq 2\).

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

\(f(n)=5(3)^{n-1}\)

Therefore, the required explicit formula for the first recursive formula is \(f(n)=5(3)^{n-1}\).

If the recursive formula of an AP is \(f(n)=f(n-1)+d, f(1)=a, n\geq 2\), then the explicit formula of that AP is:

\(f(n)=a+(n-1)d\)

Where, a is the first term and d is the common difference.

The second recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+5\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

\(f(n)=5+(n-1)5\)

\(f(n)=5+5(n-1)\)

Therefore, the required explicit formula for the second recursive formula is \(f(n)=5+5(n-1)\).

The third recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+3\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

\(f(n)=5+(n-1)3\)

\(f(n)=5+3(n-1)\)

Therefore, the required explicit formula for the third recursive formula is \(f(n)=5+3(n-1)\).

The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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The red one is \(x +2y = 6\) and the blue one is \(2x -y = 4\)

The black points are the y-intercepts and and purple ones are the x-intercepts.

Expressions, equations, and inequalities are all mathematical sentence forms, but they differ in their structure, purpose, and meaning.

An expression is a mathematical phrase that combines numbers, variables, and operators but does not contain an equals sign. Expressions can be simplified by performing arithmetic operations, but they cannot be solved for a particular value. Examples of expressions include 2x + 5, 3y - 7, and 4z² - 6z + 9.

An equation is a mathematical sentence that states that two expressions are equal. Equations have an equals sign and are used to solve for a particular value of a variable. They can be solved by applying algebraic operations to both sides of the equation until the variable is isolated. Examples of equations include 2x + 5 = 11, 3y - 7 = 2y + 1, and 4z² - 6z + 9 = 0.

An inequality is a mathematical sentence that compares two expressions using inequality symbols such as <, >, ≤, or ≥. Inequalities can be used to represent relationships between quantities that are not necessarily equal. They are solved by isolating the variable on one side of the inequality symbol. Examples of inequalities include 2x + 5 < 11, 3y - 7 > 2y + 1, and 4z² - 6z + 9 ≤ 0.

In summary, expressions are mathematical phrases that cannot be solved for a particular value, equations are mathematical sentences that state that two expressions are equal and can be solved for a particular value, and inequalities are mathematical sentences that compare two expressions using inequality symbols and can be used to represent relationships between quantities that are not necessarily equal.

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To determine the value of c that allows a function to serve as a probability distribution for a discrete random variable X, we need to ensure that the function satisfies two properties: non-negativity and the sum of probabilities equals 1.

(a) For the function f(x) = \(c(x^2 + 4)\), we need to determine the value of c. To satisfy the properties of a probability distribution, we must ensure that f(x) is non-negative for all possible values of x and that the sum of probabilities equals 1.

The possible values of x are 0, 1, 2, and 3. We can evaluate f(x) for each value of x:

f(0) = c(0^2 + 4) = 4c

f(1) = c(1^2 + 4) = 5c

f(2) = c(2^2 + 4) = 8c

f(3) = c(3^2 + 4) = 13c

For f(x) to serve as a probability distribution, all values of f(x) must be non-negative. Therefore, we need to ensure that 4c, 5c, 8c, and 13c are all non-negative. This implies that c must be greater than or equal to 0.

f(0) + f(1) + f(2) + f(3) = 4c + 5c + 8c + 13c = 30c

For the sum of probabilities to equal 1, we must have:

30c = 1

Solving for c, we find c = 1/30.

(b) For the function f(x) = c^(2x)^(3(3-x)), we can follow a similar approach. We need to ensure that f(x) is non-negative for all possible values of x and that the sum of probabilities equals 1.

The possible values of x are 0, 1, and 2. Evaluating f(x) for each value:

f(0) = \(c^(2(0))^(3(3-0)) = c^0 = 1\)

f(1) = \(c^(2(1))^(3(3-1)) = c^2^6 = c^12\)

f(2) =\(c^(2(2))^(3(3-2)) = c^4^3 = c^12\)

To satisfy the non-negativity property, we need to ensure that c^12 is non-negative, which implies that c must be greater than or equal to 0.

To satisfy the sum of probabilities equaling 1, we sum up the probabilities:

\(f(0) + f(1) + f(2) = 1 + c^12 + c^12\)

However, since c must be greater than or equal to 0, we conclude that there is no valid value of c that allows the function f(x) = c^(2x)^(3(3-x)) to serve as a probability distribution.

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we don't have enough information to determine the exact lengths of the streamers or the distance from the center of the floor to where the second streamer is attached.

Sure, I'd be happy to help! Based on the information you provided, we know that Belle is hanging two streamers of different lengths at the peak of the ceiling for her brother's surprise birthday party. The center of the floor is directly underneath the ceiling peak.

We also know that the distance along the floor from the center of the room to where the first streamer is attached is 6 feet.

Since the second streamer is attached to the floor further from the center of the floor than the first streamer, we can infer that the second streamer is longer than the first streamer.
I hope this helps! Let me know if you have any other questions.

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The correct that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels

If 3 scoops of unpopped kernels produce 6 quarts of popcorn, we can find the rate of popcorn produced per scoop by dividing the total popcorn by the number of scoops:

6 quarts popcorn / 3 scoops = 2 quarts popcorn per scoop

We can use this rate to fill out the table for any number of scoops:

Number of scoops      Total amount of popcorn (in quarts)

1                                                             2

2                                                            4

3                                                            6

4                                                            8

5                                                            10

...                                                            ...

x                                                            2x

Therefore, the correct table that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels is:

Number of scoops    Total amount of popcorn (in quarts)

1                                                     2

2                                                    4

3                                                    6

4                                                    8

5                                                     10

...                                                     ...

x                                                      2x

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Answer:

Length = 36feet

Width = 64 feet

Area = 2304 ft²

Step-by-step explanation:

Complete Question

A contractor bought a rectangular piece of land that has a perimeter of 200 feet. The ratio of the land's length to width is 9 : 16. Find the area of the land

Perimeter of the land = 2(L+W)

L is the length

W is the width

Given

Perimeter = 200 feet

If the ratio of the land's length to width is 9 : 16, then;

L/W = 9/16

9W = 16L

W = 16/9 L

Substitute into the formula

P = 2(L + 16/9 L)

P = 2(25L/9)

P = 50L/9

200 = 50L/9

1800 = 50L

L = 180/5

L = 36

Since W = 16/9 L

W = 16/9 * 36

W = 16 * 4

W = 64 feet

The area of the land = Length * Width

The area of the land = 36*64

The area of the land = 2304ft²