PLEASE HELP I NEED THIS ASAP ! 100 POINTS!!
A newspaper article about an opinion poll says that "53% of Americans approve of the president's overall job performance." The poll is based on online survey interviews with 1,350 adults randomly chosen from a numbered list of one million responses from around the United States, excluding Alaska and Hawaii.

Part A: What is the population and sample in this poll? (3 points)

Part B: What type of sampling is used? (3 points)

Part C: Are there any sources of bias present? Explain. (4 points)

There is a 21.5% chance that a point in a square with nine congruent circles drawn there won't be within one if it is chosen at random.

It is given to us that :

Nine congruent circles are inscribed in a square

The square has a side length of 126

We have to find out the probability that the point is not in a circle, if a point in the square is chosen at random.

It is known that the square has a side length of 126.

=> Area of the square = \((Length)^{2}\)

=> Area of the square = \(126^{2}\)

=> Area of the square = 15876 ------ (1)

It is also known to us that nine congruent circles are inscribed in the square that has a side length of 126.

=> Diameter of each circle = 126/3

=> Diameter of each circle = 42

=> Radius of each circle = 21  ------ (2)

We know that the area of a circle is given as -

Area of circle = \(\pi r^{2}\)  ------ (3)

where,

r = radius of the circle

Substituting the value of r from equation (2) in equation (1), we have

Area of circle = \(\pi r^{2}\)

=> Area of circle = \(\pi (21)^{2}\)

=> Area of circle = 1385.44

=> Area of 9 circles = 12468.96    ----- (4)

Now, we can say that -

Area not in a circle = Area of square - Area of 9 circles

=> Area not in a circle = 15876 - 12468.96 [From equation (1) and (4)]

=> Area not in a circle = 3407.04    ------ (5)

We know that the probability of a outcome is given as -

Probability = Number of favorable outcomes/Total number of outcomes

So, the probability that the point is not in a circle can be calculated as -

Probability = Area not in a circle/Area of square

=> Probability = 3407.04/15876

=> Probability = 0.215

=> Probability = 21.5%

Thus, if there are nine congruent circles inscribed in a square and a point in the square is chosen at random, the probability that the point is not in a circle is 21.5%.

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Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

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it can be 95% confident that the proportion of boys in all births in the state is between 0.455 and 0.537. The confidence interval calculated does include 0.513, so the sample results do not provide strong evidence against that belief.

\(CI = \hat{p} ± z_{\alpha/2} * \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)

Where,\(\hat{p}=\frac{x}{n}\) where n is the sample size, x is the number of boys in the sample, \(\hat{p}\) is the sample proportion, \(z_{\alpha/2}\) is the z-score corresponding to the desired level of confidence, and \(\alpha\) is the significance level. Sample size (n) = 863Number of boys (x) = 428.

Sample proportion

(\(\hat{p}\)) = \(\frac{428}{863}\)Z-score at 95% level of confidence = 1.96 calculate the 95% confidence interval:

\(CI = \hat{p} ± z_{\alpha/2} * \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)

\(CI = \frac{428}{863} ± 1.96 * \sqrt{\frac{\frac{428}{863} * \frac{435}{863}}{863}}\)

CI = 0.496 ± 1.96 * 0.021

CI = (0.455, 0.537)

Therefore, it can be 95% confident that the proportion of boys in all births in the state is between 0.455 and 0.537.The belief is that the proportion of boys in all births is 0.513.

The confidence interval calculated does include 0.513, so the sample results do not provide strong evidence against that belief.

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Ok, so

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.

Answer:

C. 80 ft

Step-by-step explanation:

Volume=width ×height ×length

5×2×8 = 80

Answer:

A (0, 0).

Step-by-step explanation:

y = x

y = -x

Therefore x = -x.

x + x = 0

x = 0

and y = x = 0.

Answer:

Which ordered pair is a solution to the following linear system?

y = x

y = –x

(1, 1)

(0, 1)

(1, 0)

Correct Answer

(0, 0)

Step-by-step explanation:

just did this on a test.

Answer:

3:1

Step-by-step explanation:

Answer: To determine if a set of dimensions is possible for the container, we need to check if it satisfies both the inequality h > 0.3r^2 and the two constraints.

A) radius = 21 inches, height = 21 inches:

The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 21^2).

The height must be no more than 15 inches greater than the radius (21 - 21 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 21^2 < 36pi).

So, option A is not a possible set of dimensions.

B) radius = 8 inches, height = 21 inches:

The inequality h > 0.3r^2 is satisfied (21 > 0.3 * 8^2).

The height must be no more than 15 inches greater than the radius (21 - 8 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is satisfied (pi * 8^2 >= 36pi).

So, option B is a possible set of dimensions.

C) radius = 7 inches, height = 23 inches:

The inequality h > 0.3r^2 is satisfied (23 > 0.3 * 7^2).

The height must be no more than 15 inches greater than the radius (23 - 7 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches (pi * r^2 >= 36pi), which is not satisfied (pi * 7^2 < 36pi).

So, option C is not a possible set of dimensions.

D) radius = 9 inches, height = 18 inches:

The inequality h > 0.3r^2 is not satisfied (18 <= 0.3 * 9^2).

The height must be no more than 15 inches greater than the radius (18 - 9 <= 15), which is not satisfied.

So, option D is not a possible set of dimensions.

Therefore, the only possible set of dimensions is B) radius = 8 inches, height = 21 inches.

Step-by-step explanation:

The probability of having at least one dog adopted is 0.6126

It is given that the probability to adopt a dog is 0.1

The adoption of the dog here clearly follows a Binomial distribution

ⁿCₓ  X  pˣ  X  (1 - p)ⁿ⁻ˣ

where,

n = no. os sample

p = probability of success

x = random variable.

Here the success would be the adoption of a dog, We are given here there were 9 visits

Hence,

n = 9

p = 0.1

1 - p = 0.9

we need to find the probability of the adoption of at least one dog

= P(X ≥ 1)

= 1 - P(X = 0)

Hence we get

P(X = 0)

= ⁹C₀  X  0.1⁰  X  0.9⁹

= 0.3874

Hence,

P(X ≥ 1)

= 1 - 0.3874

= 0.6126

Therefore the probability that at least one dog will be adopted is 0.6126

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Answer:

(-2,1)

Step-by-step explanation:

P' = (-5+3,2-1)

P' = (-2,1)

Answer:

7/6x3/7===21/42=== 1/2

Step-by-step explanation:

No, it is not possible that t is one-to-one if there is a nonzero vector x ∈ Rm such that t(x) = 0.

This is because a one-to-one transformation means that each input has a unique output. If t(x) = 0 for a nonzero vector x, then there must be another vector y such that t(y) = 0 as well, since the zero vector is always in the range of a transformation. This means that t is not one-to-one, as there are multiple inputs that have the same output.

For example, consider the transformation t(x) = Ax, where A = [[1, -1], [1, -1]]. Then, for the vector x = [1, 1], t(x) = [0, 0], and for the vector y = [2, 2], t(y) = [0, 0] as well. This shows that t is not one-to-one, as there are multiple vectors that have the same output.

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Answer:

B.× =158.11

IS THE ANSWER

x=158.11 is the solution to 24•log(2x) = 60, rounded to two decimal places

To test the null hypothesis that the daily average revenue was $675 for the coin-operated laundry, you should use a one-sample t-test.

1. State the null hypothesis (H0) and alternative hypothesis (H1):

H0: The daily average revenue is $675.

H1: The daily average revenue is not $675.

2. Determine the sample size (n), sample mean (x), and sample standard deviation (s):

n = 30 days, x = $625, and s = $75.

3. Calculate the t-score:

t = (x - μ) / (s / √n)

t = (625 - 675) / (75 / √30)

t ≈ -3.58

4. Determine the degrees of freedom (df):

df = n - 1 = 30 - 1 = 29

5. Find the critical t-value for a two-tailed test at a 0.05 significance level:

Using a t-distribution table, the critical t-value is approximately ±2.045.

6. Compare the calculated t-score to the critical t-value:

Since the calculated t-score of -3.58 is more extreme than the critical t-value of -2.045, you would reject the null hypothesis.

In conclusion, based on the one-sample t-test, there is evidence to suggest that the daily average revenue is not $675 as claimed by the current owner.

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The z score for the actor is -2.04, and the z score for the actress is 1.69. The actor had the more extreme age as their z score was further away from the mean compared to the actress.

z score for actor

z = (32 - 43.7) / 8.8 = -2.04

z score for actress

z = (53 - 34.5) / 11.2 = 1.69

Since the z score for the actor is more negative than the z score for the actress, the actor had the more extreme age.

The z score is a measure of how far a specific value is away from the mean, in terms of standard deviations. A negative z score indicates that the value is below the mean, while a positive z score indicates that the value is above the mean.

In this case, both the actor and the actress had ages that were below the mean for their respective genders. However, the actor's age was further below the mean than the actress's age. Therefore, the actor had the more extreme age.

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In completing the square method, considering the equation X^2 + 82x +  the number to be added should be 1681 to make it a perfect square

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 +82x

= (b / 2a)^2

= (82 / 2)^2

= (41)^2

= 1681

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The reciprocal of 6 and -12y -18x are:

\( \frac{1}{6} and \: \frac{1}{ - 12y - 18x} \)

Answer:

0.2 mi

Step-by-step explanation:

3 mi for 15 min

so divide 3 mi by 15 min = 0.2

Answer

The price of 1 snowdrop = $1

The price of 1 chocomalt = $2

Explanation

a) The cost of 1 snowdrop = x

The cost of 1 chocomalt = y

1 snowdrop and 2 chocomalts cost $5

x + 2y = 5

2 snowdrops and 3 chocomalts cost $8

2x + 3y = 8

The two equations brought together is

x + 2y = 5

2x + 3y = 8

To plot this graph, we use the red line to indicate x + 2y = 5 and the blue line for 2x + 3y = 8

b)

We can then see that the two lines intersect at the black point which is the purple point according to your question, where

x = 1 and y = 2

c) If we substitute this point of intersection into the equations, we should obtain the two sides of the equation being equal to each other because they would be solutions to the simultaneous expression.

d) x + 2y = 5

2x + 3y = 8

x = 1 and y = 2

x + 2y = 5

1 + 2(2) = 5

1 + 4 = 5

5 = 5

2x + 3y = 8

2(1) + 3(2) = 8

2 + 6 = 8

8 = 8

This indicates that these are the true solutions of this simultaneous equation.

Hope this Helps!!!

Answer:

b = y - mx

Step-by-step explanation:

Given

y = mx + b ( subtract mx from both sides )

y - mx = b

Answer:

if t is the total time in hours, 1 car takes 6hrs to assemble, and the number of cars assembled in t hours is y, then

y=t/6 if you get a decimal remove it

Answer:

y = x + 7

Step-by-step explanation:

If the slope is 1, the original equation is y = mx + b, with m being 1.

Now substitute -6 and 1 for x and y and solve for b

1 = 1(-6) + b

1 = -6 + b

7 = b

Put it all together:

y = x + 7

(a) Mean = 0; Variance = 0.333; Standard deviation = 0.577.
(b) x = 0.841.


(a) The mean of a continuous uniform distribution is the midpoint of the interval, which is (−1+1)/2=0. The variance is calculated as (1−(−1))^2/12=0.333, and the standard deviation is the square root of the variance, which is 0.577.
(b) We need to find the value of x such that the area to the left of −x is 0.25. Since the distribution is symmetric, the area to the right of x is also 0.25. Using the standard normal table, we find the z-score that corresponds to an area of 0.25 to be 0.674. Therefore, x = 0.674*0.577 = 0.841.

For a continuous uniform distribution over the interval [−1,1], the mean is 0, the variance is 0.333, and the standard deviation is 0.577. To find the value of x such that P(−x< X < x) = 0.5, we use the standard normal table to find the z-score and then multiply it by the standard deviation.

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Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

1 Ampere = 1 Coulomb of charge per second

2.5 A  =  2.5 C of charge per second

Time to deliver 3.5 C of charge = (3.5 C) / (2.5 C / sec)

Time = (3.5 / 2.5) (C / C-sec)

Time = 1.4 sec

A current of 2.5 A delivers 3.5 C of charge in 1.4 seconds.

Answer:

The answer would be 7.3x10^-12

Step-by-step explanation:

Fill in 7.3 then negative 12

The total price before the discount was $107.29.

In order to find the total price of the items before the discount, we need to use some basic math. We know that she saved $7.29 on her first purchase by using the credit card, which means that the discount was $7.29. We also know that the discount represents a percentage of the total price, but we don't know what that percentage is.

To find the total price before the discount, we can use the following formula:

Total Price = Discounted Price / (1 - Discount Percentage)

We know that the discounted price is the original price minus the discount, so we can write:

Total Price = (Original Price - Discount) / (1 - Discount Percentage)

Substituting the values we know, we get:

Total Price = (X - 7.29) / (1 - Discount Percentage)

We still don't know the discount percentage, but we can rearrange the formula to solve for it:

Discount Percentage = 1 - (X - 7.29) / Total Price

Now we can use the fact that the discount percentage is the percentage by which the total price was reduced, so it's equal to:

Discount Percentage = Discount / Total Price

Setting these two expressions for the discount percentage equal to each other, we get:

1 - (X - 7.29) / Total Price = 7.29 / Total Price

Solving for X, we get:

X = Total Price + 7.29

We can use this equation to find the total price before the discount. For example, if we know that the discounted price was $100, we can plug that in and get:

X = 100 + 7.29 = $107.29

Long Answer: To find the total price before the discount, we need to use the formula:

Total Price = Discounted Price / (1 - Discount Percentage)

We know that the discounted price is the original price minus the discount, so we can write:

Total Price = (Original Price - Discount) / (1 - Discount Percentage)

Substituting the values we know, we get:

Total Price = (X - 7.29) / (1 - Discount Percentage)

Now we need to find the discount percentage. We can do this by rearranging the formula to solve for it:

Discount Percentage = 1 - (X - 7.29) / Total Price

The discount percentage represents the percentage by which the total price was reduced. To see why, consider that if the total price was $100 and the discount was $10, the discounted price would be $90, which is a reduction of 10%. Therefore, the discount percentage is equal to:

Discount Percentage = Discount / Total Price

Setting these two expressions for the discount percentage equal to each other, we get:

1 - (X - 7.29) / Total Price = 7.29 / Total Price

Solving for X, we get:

X = Total Price + 7.29

We can use this equation to find the total price before the discount. For example, if we know that the discounted price was $100, we can plug that in and get:

X = 100 + 7.29 = $107.29

Therefore, the total price before the discount was $107.29.

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Answer:

Step-by-step explanation:

a) Out of 5, 1 only one is wrong. So number of questions answered correctly is (4/5)

To find the percentage, multiply (4/5) by 100

    \(\sf \dfrac{4}{5}*100 = 4* 20 = 80 \%\)

b) It is not possible to find the actual score because we don't know how many questions were there actually and the score for each question.

Answer:

jajajjajaja

Step-by-step explanation:

sdfgsdfgsdfg