Consider the 1000 95% confidence intervals (CI) for that a statistical consultant will obtain for various clients.
Suppose the data sets on which the intervals are based are selected independently of one another.
How many of these 1000 intervals do you expect to capture the corresponding value of?
What is the probability that between 950 and 970 of these intervals contain the corresponding value of ? (Hint: Let Y = the number among the 1000 intervals that contain . What kind of random variable is Y?).
Note: use continuity correction.

Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.

Given data:

Perimeter = sum of all sides:

The shaded portion in the figure shows the left over rectangle:

Perimeter of EFCD = EF + FC + CD + DE

ED = FC = 16 - 7.3 = 8.7

P = 8.7 + 13 + 8.7 + 13

P = 43.4 cm.

Thus, the perimeter of the  left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.

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complete question:

The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the left shape.

The mean is 49 and the standard deviation is 5.33.

What is mean?

The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

We can use the empirical rule to solve these problems. According to the empirical rule:

About 68% of the data falls within one standard deviation of the mean.

About 95% of the data falls within two standard deviations of the mean.

About 99.7% of the data falls within three standard deviations of the mean.

a) To find the mean (u) and standard deviation (sigma) for each problem, we can use the following formulas:

u = (a + b) / 2

sigma = (b - a) / 6

where a and b are the lower and upper bounds for the data, respectively.

b) For each problem, we can use the given information to set up an equation and solve for either the mean or standard deviation.

If 68 percent of the data is between 42 and 58:

a) H: We are not given enough information to solve for the mean or standard deviation.

b) To find one of the missing values, we can use the formulas above and the given information. Since we are given that 68% of the data falls within one standard deviation of the mean, we know that:

(58 - u) / sigma = 1

Simplifying this equation, we get:

58 - u = sigma

We can also use the fact that the range of the data is 16 (from 42 to 58):

b - a = 16

58 - u - (42 - u) = 16

16 = 16u/16

Solving for the mean, we get:

u = (42 + 58) / 2

u = 50

Using the equation 58 - u = sigma, we can solve for the standard deviation:

sigma = 58 - u

sigma = 8

Therefore, the mean is 50 and the standard deviation is 8.

If 95 percent of the data is between 34 and 64:

a) u: We can find the mean using the formula:

u = (a + b) / 2

u = (34 + 64) / 2

u = 49

b) To find the standard deviation, we can use the formula:

sigma = (b - a) / 6

sigma = (64 - 34) / 6

sigma = 5.33

Therefore, the mean is 49 and the standard deviation is 5.33.

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The total area of the shaded portion is (x² - 16)(x²- 1) square meters.

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The area of the outer square is (x² - 8)², and the area of the inner square is x². Therefore, the area of the shaded region can be found by subtracting the area of the inner square from the area of the outer square:

Area of shaded region = Area of outer square - Area of inner square

= (x² - 8)² - x²

Expanding the first term using the formula for the square of a binomial, we get:

Area of shaded region = (x⁴ - 16x² + 64) - x²

= x⁴ - 17x² + 64

Therefore, the expression that represents the total area of the shaded figure is x⁴ - 17x² + 64, which can be simplified by factoring:

x⁴ - 17x² + 64 = (x² - 16)(x² - 1)

So the simplified expression for the total area of the shaded figure is (x² - 16)(x²- 1).

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473,615 rounded to the nearest hundred is D. 473,600.

Number rounding or approximation is the adjustment of the digits (up or down) to make rough calculations easier.

The result of number rounding is an estimated value rather than a precise one.

Number rounding or approximation are useful when the precise information is not required for decision-making.

473,615 = 473,600

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Answer:

Step-by-step explanation:

Each die can show one of the five possible numbers. So, the number of possible outcomes for rolling one die is 5.

Since there are three dice being rolled, the total number of possible outcomes is the product of the number of possible outcomes for each die. That is:

Number of possible outcomes = 5 x 5 x 5 = 125

Therefore, there are 125 different outcomes possible when rolling three distinct, five-sided dice.

Answer:

[tex]-\frac{5}{2}[/tex] or -2.5

Step-by-step explanation:

1) [tex]2y + 5 = 0[/tex]

2) Move 5 over to the other side by subtracting

[tex]2y = -5[/tex]

3) Divide both sides by 2 so y is alone

[tex]y = -\frac{5}{2}[/tex]

Step-by-step explanation:

Put both of the equations into   y = mx + b form to compare them

                   m = slope    if they have the same slope they are parallel and do not intersect

                    b = y axis intercept

                  if m and b are equal in each of the equations , they are the same line

2x+y = 0   ======>   y =  - 2x + 0

2y = -4x + 6  ====>   y =  - 2x + 3

The both have the same slope = -2   so they are parallel

   but they have different  b  values so they are not the same lines

No intersection means no solution :   parallel  lines do not intersect  

The container will be 7 meters high and 8 meters in diameter. Steel will be used to make the container (including its top and bottom). If a square meter of steel costs 29 dollars, the total cost of the steel will be $5,467.60.

The cylinder has a diameter of 8m and a height of 7m, which means the radius of the cylinder is 4m (half of the diameter).

The surface area of a cylinder is calculated as follows:

SA = 2πr² + 2πrh

where h is the cylinder's height and r is the radius.

Plugging in the values we get:

SA = 2 x 3.14 x 4² + 2 x 3.14 x 4 x 7

SA = 100.48 + 87.92

SA = 188.4 square meters

So, the surface area of the cylinder is 188.4 square meters.

If the steel costs $29 per square meter, then the cost of the steel for the cylinder would be:

Cost = 188.4 x $29

Cost = $5,467.60

Therefore, the cost of the steel for the cylinder would be $5,467.60.

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As a result, there is a 1/77 chance of choosing two Independents consecutively as probabilities in order to get the likelihood of choosing two Independents.

The chance of an event happening is gauged by probability. It is stated as a value between zero and 1, with 0 denoting that the occurrence is unlikely and 1 denoting that it is unavoidable. Typically, P stands for the likelihood of something happening A. (A). It is computed by dividing the number of positive outcomes but by total number of potential outcomes. For instance, if you flip a fair coin, the likelihood of receiving heads is 50% since there is only one positive result (heads) so out two possible possibilities (heads or tails).

given

The likelihood of choosing an Independent on the first draw is: There are 3 Independents out of a total of 10 Democrats, 9 Republicans, and 3 Independents.

P(Unrelated to the initial draw) = 3/22

P(Independent on First Draw and Second Draw) = 2/21

We must compound these probabilities in order to get the likelihood of choosing two Independents consecutively:

P(Choosing two Independents) = P(Independent on first draw) + P(Independent on second draw | Independent on first draw)

= (3/22) * (2/21)

= 6/462

= 1/77

As a result, there is a 1/77 chance of choosing two Independents consecutively as probabilities in order to get the likelihood of choosing two Independents.

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The total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².

The shape described in the problem is a trapezoid. The formula to calculate the area of a trapezoid is:

[tex]Area = (base1 + base2) x height / 2[/tex]

We are given the following measurements:

Base1 = 21.3 yards

Height = 12.8 yards

A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards, which is a part of the base2.

A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards, which is the remaining part of the base2.

To calculate the missing part of base2, we subtract the known parts of base2 from the total length of the top, which is:

21.3 - 6.4 - 14.9 = 0

This means that the missing part of base2 is zero, and the trapezoid becomes a rectangle. Therefore, the area of the trapezoid is equal to the area of the rectangle, which is:

Area = base x height

Area = 21.3 x 12.8

Area = 272.64 square yards

Therefore, the total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².

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The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.

The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.

So, we need to solve the inequality:

R(x) > C(x)

7x > 13x + 132

Subtracting 13x from both sides, we get:

-6x > 132

Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:

x < -22

Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

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The equation of the graph before it was shifted to the right one unit is given as follows:

B. G(x) = (x - 0.5)³ - (x - 0.5).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The function in this problem is defined as follows:

G(x) = (x - 1.5)³ - (x - 1.5).

To remove the effect of a shift right one unit, we must shift the graph left one unit, hence the original rule is given as follows:

G(x) = (x - 1.5 + 1)³ - (x - 1.5 + 1).

G(x) = (x - 0.5)³ - (x - 0.5).

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Answer:

its on quizzes

Step-by-step explanation:

To solve this problem, we can start by noticing that each round cuts the number of teams in half. Therefore, we can create a table to see how many teams are left after each round:

Round Number of Teams

1 32

2 16

3 8

4 4

5 2

6 1

We can see that there are 6 rounds in total, and that the number of games in each round is half the number of teams. So we can calculate the number of games for each round and add them up to get the total number of games:

Round Number of Teams Number of Games

1 32 16

2 16 8

3 8 4

4 4 2

5 2 1

6 1 0

Adding up the number of games for each round, we get:

16 + 8 + 4 + 2 + 1 + 0 = 31

Therefore, a total of 31 games were played in the tournament.

part1)Rounding to four decimal places, the test statistic is z = -1.7918.  part2) Rounding to four decimal places, the p-value is p = 0.0728.

what is decimal places ?

Decimal places refer to the number of digits to the right of the decimal point in a decimal number. For example, in the decimal number 3.14159, there are 5 decimal places, with the digit 1 being in the first decimal place, the digit 4 being in the second decimal place, and so on.

In the given question,

Part 1:

To calculate the test statistic, we use the formula:

z = (p - P) / √[(P(1-P))/n]

where p is the sample proportion (71/341 = 0.2082), P is the hypothesized proportion (0.227), n is the sample size (341).

z = (0.2082 - 0.227) / √[(0.227 * 0.773)/341]

z = -1.7918

Rounding to four decimal places, the test statistic is z = -1.7918.

Part 2:

To calculate the p-value, we use a standard normal distribution table or a calculator. Since this is a two-tailed test, we calculate the area in both tails of the distribution.

Using a calculator or a standard normal distribution table, we find that the area to the left of z = -1.7918 is 0.0364. Therefore, the area in the right tail is also 0.0364.

Thus, the p-value is 2*0.0364 = 0.0728.

Rounding to four decimal places, the p-value is p = 0.0728.

Therefore, we would fail to reject the null hypothesis at the 0.05 significance level since the p-value is greater than the level of significance. We do not have enough evidence to suggest that the percentage of children who develop asthma by age two for expectant mothers who smoke 20 cigarettes per day during pregnancy is lower in this other country compared to the US.

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(a) All values at which g has a local minimum: -2, 3

(b) All local minimum values of g: g(-2) ≈ -2.5, g(3) ≈ -1.5

What is the Graph?

The graph is a visual representation of the function g, which shows how the output of the function varies with the input. It plots the values of g(x) on the vertical axis against the values of x on the horizontal axis.

(a) All values at which g has a local minimum:

From the graph, it appears that there are two values at which g has a local minimum:

x = -2

x = 3

(b) All local minimum values of g:

From the graph, the local minimum value at x = -2 appears to be approximately -2.5, and the local minimum value at x = 3 appears to be approximately -1.5. So, the local minimum values of g are:

g(-2) ≈ -2.5

g(3) ≈ -1.5

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Convert 3% to a decimal by doing 3/100. You should get 0.03.

Now multiply 0.03 and 44.50, you will get 1.335.

Add 1.335 to 44.50 and you will get 45.835.

The new price of the item after it was marked up is $45.835

Answer:

B = 1/2

A = 1/3

D = 2/3

C = 5/6

Step-by-step explanation:

B = 3/6 = 1/2

A = 2/6 = 1/3

D = 4/6 = 2/3

C = 5/6

The estimated taxes for a taxable income of $63,700 using the 2020 Federal Tax Rates for Individuals is $9,804.00.

The estimated taxes for an individual with a taxable income of $63,700 for the fiscal year uses the progressive tax (graduated) system of the Federal Tax Rates for Individuals, as computed below.

Taxable Income for 2020 = $63,700

Tax rate  Taxable Income Bracket       Tax Payable

10%                $0 to $9875                       $987.50 ($9,875 x 10%)

12%                $9876 to $40,125           $3,630.00 ($30,250 x 12%)

22%               $40,126 to $85,525        $5,186.50 ($23,575 x 22%)

Estimated taxes                                   $9,804.00

Thus, an individual whose taxable income is $63,700 in 2020 is expected to pay taxes amounting to $9,804.00.

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The point estimate for the proportion parameter for this population is A)0.305.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.

From the given information then,

Sample size n = 892

No of favorable outcomes (i.e successes) x=272

We know ,

The point estimate for the population parameter [tex]\hat P[/tex]=x/n.

Where n=sample size , x=number of success.

Here x = 272 ,n=892 then

The point estimate for the proportion parameter for this population then,

=> [tex]\hat p[/tex] = 272/892 = 0.305.

Hence  the point estimate for the proportion parameter for this population is A)0.305.

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The values of the composite function are (f + g)(x) = 2x² + 3x - 2, (f - g)(x) = -2x² + 3x - 8, (f . g)(x) = 6x³ + 4x² - 15x - 15, (f o g)(x) = 6x² + 4, (g o f)(x) = 18x² - 60x + 53, (f o g)(3) = 58

To determine the values of the composite functions, we have to evaluate or simplify each as

7. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2

8. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8

9. (f . g)(x) = f(x) * g(x) = (3x - 5) * (2x² + 3) = 6x³ + 4x² - 15x - 15

10. (f o g)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4

11. (g o f)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53

12. (f o g)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58

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Answer:

13 inches

Step-by-step explanation:

17=85

1=85/17

1=5

Now

For 65 cents,

65=nx5

65/5=n

n=13 inches

Answer: 13 inches

Step-by-step explanation:

To solve this problem you would need to make a ratio.

A Ratio can be the symbol, : , / or the word to.

In this case you would need to do the problem as shown:

17/85 = x/65

First you would need to cross multiply, then flip the equation. And should end up with something like this:

85x =1105

Then Divide both sides by 85.

85x/85 = 1105/85

Answer:

X= 13

It might just be 536320

We can use the multiplication principle of counting to find the total number of possible outcomes.

Since there are 5 options on the first spinner, 6 options on the second die, and 3 options on the third spinner, there are a total of:

5 x 6 x 3 = 90

different possible outcomes.

Therefore, there are 90 different possible outcomes if Madelyn spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.

Answer:

what is biology and types

The experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%

The experimental probability of finding a card is 30%. The complete table is given below:

Trial  Numbers Generated Chairs Checked

1 6,5,1                        No Card, No Card, Card

2 8,1                                No Card, Card

3 10,1                                No Card, Card

4 7,8,4,1                        No Card, No Card, No Card, Card

5 9,3                                No Card, Card

6 5,4,2                        No Card, No Card, Card

7 3                                Card

8 9,5,8,2                        No Card, No Card, No Card, Card

9 7,3                                No Card, Card

10 9,6,8,4,7,3    No Card, No Card, No Card, No Card, No Card, Card

The probability that the first card he finds will be under the third chair that he checks is calculated by taking the total number of trials in which the third chair had a card (3) and dividing it by the total number of trials (10).

The table can be completed by generating 10 sets of random numbers from 1 to 10 and checking the first three numbers in each set. If the first number is between 1 and 3, then the first chair has a card. If the second number is between 1 and 3, then the second chair has a card. If the third number is between 1 and 3, then the third chair has a card. If none of the first three numbers are between 1 and 3, then there are no cards in the first three chairs

Out of the 10 trials, 4 have a card under the third chair. Therefore, the experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%.

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The expression is equivalent  to -4x²-3x-5

An equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value of the variable that make the equation true. For example, in the equation 2x + 5 = 11, the variable x is being multiplied by 2, added to 5, and then compared to the number 11. To solve for x, one must isolate the variable on one side of the equation by performing the same operation on both sides of the equation until the variable is alone on one side. The resulting value of x will make the equation true.

Given expression is:

-4x²+2x-5(1+x)

Solving the expression

-4x²+2x-5-5x

-4x²-3x-5

Hence, the expression is equivalent  to -4x²-3x-5.

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