The length of a rectangle is equal to
three times its width. If the perimeter of
the shape is equal to 56 feet, what is the
length and what is the width?

In a right triangle, the sum of the measures of the two acute angles is always 90 degrees. So if ∠J and ∠K are acute angles in a right triangle, then we have:

m∠J + m∠K = 90°

Since m∠J is less than 60°, it follows that m∠K is greater than 30°, because their sum is 90°.

Now, let's consider the cosine of ∠J and ∠K. By definition, the cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. So we have:

cos(J) = adjacent side to ∠J / hypotenuse

cos(K) = adjacent side to ∠K / hypotenuse

Since ∠J and ∠K are acute angles in a right triangle, they each have a unique adjacent side. Since the triangle is a right triangle, the hypotenuse is always the same, regardless of which angle is being considered.

Therefore, in general, it is not true that cos(J) = cos(K) for all right triangles with acute angles ∠J and ∠K, where m∠J is less than 60°. It depends on the specific values of the adjacent sides.

Answer:

3 and 1/2

Step-by-step explanation:

7 and 1/2 - 4

In the random sample of 17 students in this group, the probability of the average height being 73-75 inches is about 0.014, or 1.4%.  

Let the heights be normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

If we sample 17 students from this group, the distribution of the sample mean will also be approximately normal, with a mean of 70 inches and a standard deviation of 3/sqrt(17) inches (according to the central limit theorem).

This sample average interval can be normalized by the following formula:

z = (x - μ) / (σ / sqrt(n))

where x =sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

For the lower bound of 73 inches, the standardized values ​​are:

z1 = (73 - 70) / (3 / sqrt(17)) ≈ 2.25

For the upper limit of 75 inches, the standardized values ​​are:

z2 = (75 - 70) / (3 / sqrt(17)) ≈ 3.87

Find the probability that the sample mean is between these two values. This probability can be found by finding the area under the standard normal curve between z1 and z2 using a standard normal distribution table or calculator.

P(2.25 < z < 3.87) ≈ 0.014

So, in her random sample of 17 students in this group, the probability of the average height being 73-75 inches is about 0.014, or 1.4%.  

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The measure of angle 14 is 83° in the parallel line t and s and transversal n.

Parallel lines are a pair of lines in a two-dimensional plane that never intersect or cross each other, regardless of how far they are extended in either direction. Parallel lines have the same slope, which determines their steepness or inclination, and they maintain the same slope throughout their length.

A transversal is a line that intersects two or more other lines in a plane at distinct points. Specifically, if two or more lines in a plane are intersected by a third line, that third line is called a transversal. The lines being intersected are referred to as the "transversed lines".

According to the given information:

Given the parallel lines are t and s, the transversal are line m and n

the given angles are ∠2 = 97° and ∠6 = 83°

In the parallel lines t and s , line n is transversal

By the property that "corresponding angles are equal"

we can say that ∠5 =∠13, ∠7 =∠15, ∠6= ∠14, ∠8=∠16

given ∠6 = 83°, We know that ∠6= ∠14

∠14 = 83°       (Corresponding angles are equal)

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Answer:151

Step-by-step explanation:

Addition of 107 and 44

The value of the angle m∠EFG is 151.

We have,

From  the figure,

m∠EFG = m∠EFH + m∠HFG

Now,

Substituting the values in the angle.

m∠EFG

= m∠EFH + m∠HFG

= 44 + 107

= 151

Thus,

The value of the angle m∠EFG is 151.

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Answer: The angle elevation is 34.6 9 degree.

Step-by-step explanation:

Brainliest pls:)

The total surface area of the tower, including the bottom base, is [tex]3600+400\sqrt{2}[/tex] square meters.

The surface area of the tower can be found by calculating the surface area of the prism and the surface area of the pyramid separately, and then adding them together.

The surface area of the square base of the prism is [tex]20^2 = 400[/tex] square meters.

The lateral surface area of the prism is the product of the perimeter of the base and the height, which is [tex]4*(20)*40 = 3200[/tex] square meters.

The surface area of the pyramid is given by the formula:

base area + 1/2(perimeter of base)(slant height)

The base area of the pyramid is [tex]20^2 = 400[/tex] square meters. The perimeter of the base is 4(20) = 80 meters. Therefore, the surface area of the pyramid is:

[tex]400 + [(\frac{1}{2})*(80)(10\sqrt{2})] = 400 + 400\sqrt{2}[/tex] square meters.

The total surface area of the tower is the sum of the surface area of the prism and the surface area of the pyramid, which is:

[tex]3200 + 400 + 400\sqrt{2} = 3600 + 400\sqrt{2}[/tex] square meters.

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Hue is arranging chair, She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs. There are 7 chairs in that row length.

A row is anything that is arranged in a series, such as a sequence of figures on a worksheet or stitches on a knitting needle. A row is anything that is arranged in a straight line, such as a line of penguins at the zoo, tulips in a yard, or tuba players moving in your town's Fourth of July procession.

Suppose the number of chairs in a row is 'x' and total number of chairs are 'y'.

Given:

Hue can form 6 rows of a given length with 3 chairs left over.

From that we get

y=6x+3 ………… (1)

Or she can form 8 rows of that same length if she gets 11 more chairs.

We get

y=8x-11 …………(2)

We can put the value of y from the equation 1 in equation 2

6x+3=8x-11

Or, 2x=14

Or, x=7

X is the number of chairs present in a row length. So that is 7.

Hence there are 7 chairs in that row length

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The slope of a line segment represent in the context of this situation is the total wages for the week.

We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the

x-coordinate are denoted by y and x, respectively.

Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is

[tex]m=\frac{y}{x} =\frac{change \ in \ y}{change\ in\ x}[/tex]

You are a crew at a Convenience store that pays an hourly wage $ 7 and 1.5 times the hours wage for the extra hours if you work for more than 40 hours a week. Write a piecewise function that gives the weekly pay P in term of the number of hours h your work.

→ wages for 1 hours = $ 7

So,

we can say that, wages for 40 hours, = 7 x 40 = 280 .

Therefore,

→ Total wages of week is = 280.

Piecewise function is :-

P(h) = 280 , where h ≤ 40.

Now, we have given that, store gives 1.5 times the hours wage for the extra hours if you work for more than

40 hours a week.

So,

→ wages per hour now = 1.5 x 7 = 10.5 .

Therefore,

→ Total wages of week

= 280 + 10.5(h - 40)

= 280 + 10.5h - 420

= 10.5h - 140.

and,

Piecewise function that gives the weekly pay P in term of the number of hours h your work is:

P(h) = 280 + 10.5(h - 40), where [h > 40].

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By answering the presented question, we may conclude that Hence, the probability answer is that they are dependant since P(M) P(H) does not hold.

Probability theory is an area of mathematics that determines the likelihood that an event will occur or that a proposition is true. A probability is a number between 0 and 1, where 1 represents certainty and 0 represents how likely an event is to occur. A probability is a numerical expression for the chance or likelihood that a given event will occur. Probabilities may either be stated as percentages ranging from 0% to 100% or as numbers ranging from 0 to 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all conceivable outcomes.

To see if the two occurrences are independent, we may look at whether the likelihood of one event is changed by the occurrence of the other.

Let M represent a passing mathematics class and H represent a passing history class. The probability may therefore be stated as follows:

P(M) = 0.85 P(H) = 0.70 P(M H) = 0.50 (where signifies the "and" or intersection operation)

We may use the following formula to test for independence:

If M and H are independent, then P(M H) = P(M) P(H).

When we substitute the provided probabilities, we get:

0.50 = 0.85 × 0.70

0.50 ≠ 0.595

As a result, the equation is invalid, and the events are interdependent.

Hence, the answer is that they are dependant since P(M) P(H) does not hold.

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Answer: First section: (x³+x²-x-1); Second section: (2x³-6x+4); Total volume: (3x³+x²-7x+3)

Step-by-step explanation:

The picture I attached was the lines I drew to make finding the volume easier.

To find the second upper side I subtracted x+1 from 2x+3, which came to x+2.

This is why I scrapped out the 2x+3 in the bottom to make it less confusing.

Now you should be able to separate the two prisms.

For the first section, multiply (x+1)(x+1)(x-1). I'll do the right two first because it's easier.

(x+1)(x²-1x+1x-1)  -1x and 1x cancel out. So now it's (x+1)(x²-1).

The volume of the first section is (x³+x²-x-1).

For the second section, multiply (x+2)(2x-2)(x-1).

The first two turn out as (2x²-2x+4x-4), which is (2x²+2x-4). Then, multiply all that by (x-1): (2x²+2x-4)(x-1).

You should get (2x³-2x²+2x²-2x-4x+4), which is then (2x³-6x+4).

So the volume of the second section is (2x³-6x+4).

Then it asks you to find the total volume, so just add the two volumes: (x³+x²-x-1) + (2x³-6x+4). Then add like-terms.

(3x³+x²-7x+3) should be the total volume.

For the explaining part (being pretty vague), just say how the volumes for both sections were added by like-terms to sum up to the total volume of the plant stand.

Hope that had helped (or at least worked) :p

If the weight of coal in 43 cars selected at random had an average (x) of less than 61.5 tons, it might make you suspect that the loader had slipped out of adjustment.

Here's why:
Compare the average weight with the expected weight
First, you need to know the expected average weight of coal in the cars when the loader is functioning correctly. If the expected average is significantly higher than 61.5 tons, it could indicate an issue with the loader.
Assess the sample size
A sample size of 43 cars is relatively large, which gives you more confidence in the accuracy of the calculated average weight. If the sample size were smaller, it would be more likely that the result is due to random chance.
Evaluate the deviation from the expected weight
If the average weight is much lower than the expected weight, it would be more likely that the loader is out of adjustment. A small deviation could still be due to random chance or other factors, but a large deviation would suggest a potential issue with the loader.
Consider other factors
Before concluding that the loader is out of adjustment, it's essential to consider other factors that may have caused the lower average weight, such as changes in the type of coal, variations in car sizes, or even human error in weighing the coal.
Investigate further
If the deviation from the expected weight is significant and you cannot identify any other factors that might have caused the lower average weight, it would be reasonable to suspect that the loader may have slipped out of adjustment. In this case, you should conduct a thorough investigation, including inspecting the loader and checking its settings to determine if an adjustment is needed.

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The zeros of the quadratic function  [tex]f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.[/tex]

A quadratic function is a mathematical function of the form:

[tex]f(x) = ax^2 + bx + c[/tex]

where a, b, and c are constants, and x is the variable. The highest power of the variable x in a quadratic function is 2, which means it is a second-degree polynomial.

In a quadratic function, the graph is a parabola, which can open up or down depending on the sign of the leading coefficient a. If a > 0, the parabola opens up, and if a < 0, the parabola opens down. The vertex of the parabola represents the minimum or maximum value of the function, depending on the direction of the parabola.

To find the zeros of the quadratic function:

[tex]f(x) = 2x^2 - 5x + 2[/tex]

We need to solve the equation:

[tex]2x^2 - 5x + 2 = 0[/tex]

We can factor this quadratic equation as follows:

[tex]2x^2 - 4x - x + 2 = 02x(x - 2) - 1(x - 2) = 0(2x - 1)(x - 2) = 0[/tex]

So the zeros of the quadratic function are:

x = 1/2 or x = 2.

Therefore, the zeros of the quadratic function is:[tex]f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.[/tex]

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We know that the line passes through the origin, which means that the coordinates of the point on the line are (0,0). We also know that the line has a slope of 2. Therefore, we can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. Plugging in the values we know, we get:

y - 0 = 2(x - 0)

which simplifies to:

y = 2x

Thus, the equation of the line containing the origin and with a slope of 2 is y = 2x.

The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.

In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.

A. There is no one optimum approach to determine if an equation indicates a proportionate connection. One popular method is to test if the equation can be stated in the form y = kx, where k is a constant. A proportional connection is represented by an equation that may be expressed in this format.

A. Because it can be expressed as y = kx with k = 2, the equation y = 2x represents a proportional connection. As a result, D is the right answer: just y = 2x.

The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.

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The statement that best describes the 50% rule is: C. Individuals should spend up to only 50% of their medium-term savings then build savings back up.

The 50% rule is a personal finance guideline that suggests individuals should spend no more than 50% of their after-tax income on necessities, such as housing, food, transportation, and utilities.

The 50% rule is a personal finance guideline that suggests individuals should spend no more than 50% of their after-tax income on necessities, such as housing, food, transportation, and utilities. The other 50% should be split between savings and discretionary spending, such as entertainment and travel.

Therefore, the statement that best describes the 50% rule is:

C. Individuals should spend up to only 50% of their medium-term savings then build savings back up.

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Therefore , the solution of the given problem of average comes out to be  96% confidence interval is ($52,791.38, $53,086.62).

The result of a collection, also known as the arithmetic mean, is the sum of all values split by all of the values. One of the most commonly used primary trend indicators, it is frequently referred to as "mean." Multiply the total number of numbers in the collection by each value to get the result. Calculations can be performed using either the raw data or data that has been merged into frequency charts.

Here,

The error margin (E) is equal to z* (standard deviation / sqrt(n)).

Interval of confidence equals sample mean  E

Where n is the sample size, z* is the critical value for the required confidence level, and s is the population standard deviation.

We can enter the provided values into the margin of error formula as follows:

=> E = 2.05 * (1227 / sqrt(227))

=>  E ≈ 147.62

Therefore, the error range is roughly $147.62.

Next, we can create the confidence interval using the group mean and margin of error:

Interval of confidence equals sample mean  E

=>  Confidence range is between $52,939 and $147.62.

=>  Interval of confidence = ($52,791.38, $53,086.62)

Therefore, the range of the typical household income in Martin County within the 96% confidence interval is ($52,791.38, $53,086.62).

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Required true statements are B, C, D, G, H, I, L, M.

What is factor?

In mathematics, factors refer to the numbers that can be multiplied together to obtain a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Based on the given factors, we can conclude that:

f(x) has a factor of 3, which means that 3 is a root/solution of f(x).

f(x) has a factor of (2x-1), which means that 2x-1=0 or x=1/2 is a root/solution of f(x).

f(x) has a factor of (x+5), which means that x+5=0 or x=-5 is a root/solution of f(x).

Using these facts, we can determine which statements are true:

A) -1/2 is not a root/solution of f(x). (False)

B) We can check if this expression is equivalent to f(x) by factoring it:

6x² - 33x - 15 = 3(2x² - 11x - 5) = 3(x - 5)(2x + 1).

This shows that f(x) has factors of 3, (2x-1) and (x+5), so this statement is true.

C) -5 is a root/solution of f(x). (True)

D) 3 is a root/solution of f(x). (True)

E) We can check if this expression is equivalent to f(x) by factoring it:

2x²+9x-5 = (2x - 1)(x + 5), which is not the same as the factors given for f(x), so this statement is false.

F) 0 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at 0. (False)

G) We can check if this expression is equivalent to f(x) by factoring it:

6x²+27x-15 = 3(2x²+9x-5) = 3(2x-1)(x+5), which shows that f(x) has the same factors as this expression, so this statement is true.

H) 1/2 is a root/solution of f(x). (True)

I) 5 is a root/solution of f(x). (True)

J) We can check if this expression is equivalent to f(x) by factoring it:

2x²-9x-5 = (2x + 1)(x - 5), which is not the same as the factors given for f(x), so this statement is false.

K) -3 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at -3. (False)

L) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:

f(x) = 3(x + 5)(2x - 1) = 0

This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0). So, this statement is true.

M) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:

f(x) = 3(x + 5)(2x - 1) = 0

This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0).

So, this statement is true.

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If  x is the unknown number and Nineteen more than a number. Thus, Translation is 19 units on the right to get x + 19.

Each point in a figure is moved the same distance in a single direction using a type of transformation known as translation.

In geometry, a function that transfers an object a specific distance is referred to as translation. Nothing else is done to change the object. It is not scaled, reflected, rotated, or refracted.

Give that:

x is the unknown number and Nineteen more than a number.

Then, there is a shift of 19 units on the right of x. add 19 to unknown number x to get the translation.

x + 19

Thus, Translation is 19 units on the right to get x + 19.

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The value of k given the system of equations is 2

Given that

x + y + 3z = 10

4x + 2y + 5z = 7

kx + z = 3

Eliminate y in the first two equations

So, we have

2x + 2y - 6z = 20

4x + 2y + 5z = 7

kx + z = 3

Subtract the first two equations

So, we have

2x + z = -13

kx + z = 3

When it has no solution, we have

kx + z = 2x + z

Evaluate

k = 2

Hence, the value of k is 2

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The probability that owners ranked Subaru third is 2/6, which reduces to 1/3. Therefore, the correct answer is 1/3.

To find the probability that owners ranked Subaru third, we need to find out the total number of possible rankings for

the three dealers: Subaru, Honda, and Buick.

There are three possible rankings for the first choice, two for the second choice, and one for the third choice.

Therefore, there are 3 x 2 x 1 = 6 possible rankings for the dealers.

Since each of the possible rankings is equally likely, the probability that owners ranked Subaru third is the number of

ways to rank Subaru third divided by the total number of possible rankings.

Subaru can be ranked third in two out of the six possible rankings:

Subaru, Honda, Buick Honda, Buick, Subaru

Therefore, the probability that owners ranked Subaru third is 2/6, which reduces to 1/3.

Therefore, the correct answer is 1/3.

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115.

The point estimate for the average IQ score of the population of 3000 college students based on a simple random sample of 150 students with an average IQ score of 115 and a standard deviation of 10 is 115.

Therefore, the correct option is 115.

A point estimate is an estimate of a population parameter based on a single value or point. It is obtained by using statistics collected from a sample to infer population values. It can be a single value or a range of values that best represents the unknown population parameter.

Based on the given information, a simple random sample of 150 students is drawn from a population of 3000 college students.

Among sampled students, the average IQ score is 115 with a standard deviation of 10. The point estimate, in this case, is the average IQ score of the population, which is estimated to be 115 based on the sample data.

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The correct answer to the given question about equation of Candice taking a hike is option D)  0.38x + 13 = 87

The cost for Candice to enter the park is a fixed fee of $13.00, and the additional cost for the tour group to hike is $0.38 per mile. If Candice has $87.00 to spend, we can use the following equation to determine how many miles she can hike:

0.38x + 13 = 87

Here, x represents the number of miles Candice can hike.

The left-hand side of the equation represents the total cost, which includes the fixed entrance fee of $13.00 plus the variable cost of $0.38 per mile multiplied by the number of miles hiked, represented by 0.38x.

The right-hand side of the equation represents the total amount Candice can spend, which is $87.00.

By solving for x, we can find the number of miles Candice can hike within her budget.

Therefore, the correct answer is D. 0.38x + 13 = 87

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If you roll a four-sided pyramid-shaped die three times, there are 64 possible outcomes that could occur.

If you roll a four-sided pyramid-shaped die three times, there are 64 possible outcomes that could occur.

A four-sided die in the shape of a pyramid is also called a tetrahedral die, and it has four triangular faces, each with a different number on it.

When rolling this die once, there are four possible outcomes since there are four faces and each face has a different number.

When rolling the die three times, we can use the multiplication principle to find the total number of possible outcomes. According to this principle, the total number of outcomes is equal to the product of the number of outcomes for each roll.

Therefore, the total number of possible outcomes when rolling a tetrahedral die three times is:

4 x 4 x 4 = 64

A pyramid-shaped four-sided die can be rolled three times for a total of 64 potential results.

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Answer:

x = 3

Step-by-step explanation:

5(x + 2)- 12 = 3x + 4

5x + 10 - 12 = 3x + 4

5x - 3x = 4 - 10 + 12

2x = 6

x = 3

Answer:

x=3

Step-by-step explanation:

5(x+2)-12= 3x +4

5x + 10 -12= 3x + 4

10-12= -2x + 4

6-12= -2x

-6= -2x

-6/ -2= 3

We should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.

In statistics, a confidence interval is a range of values that is used to estimate an unknown population parameter with a certain degree of confidence or probability. It is a statistical measure that indicates the level of uncertainty or variation associated with a particular estimate or sample.

A confidence interval is typically expressed as a range of values, along with a level of confidence, such as 95% or 99%. This means that if the same study were to be repeated many times, the calculated confidence interval would contain the true population parameter for the given confidence level in a specified proportion of the repetitions. For example, a 95% confidence interval means that if the same study were repeated many times, the interval would contain the true population parameter 95% of the time.

We can use the formula for the margin of error of a confidence interval to solve this problem:

Margin of error = z*(sigma/√(n))

where:

z = the z-score associated with the desired level of confidence (in this case, 1.96 for 95% confidence)

sigma = the population standard deviation (15 days)

n = the sample size we want to find

We want the margin of error to be no more than 7 days, so we can set up the following inequality:

7 <= 1.96*(15/√(n))

Solving for n, we get:

n >= (1.96*15/7)²

n >= 12.36²

n >= 152.7

Therefore, we should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.

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Answer:

Step-by-step explanation:

Refers to the attachment given below!

Answer:

3

Step-by-step explanation:

A sample of 719 times bigger would be needed to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.68.

It is given to us that an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California and that he believes that the mean income is $21.2, and the standard deviation is known to be $9.3,

Therefore, here we can make out that:

Number of samples required (n) is given by:

n = (Z²α/2) × б²/e²

It is given to us that, α = 0.05

Therefore, from data provided to us we can get to know that the critical values of Z = ± 1.96

б = 9.3

e = 0.68

when we substitute these values in the above equation, we get:

n = 1.96² × 9.3²/0.68² = 719

Therefore, a sample of 719 times bigger would be needed to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.68.

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Answer:

Length is 7 units

Step by Step explanation:

Assuming you mean the Area is 28 square units

Then

L = w + 3

A = w(w + 3)

28 = w2 + 3w

We can subtract 28 from both sides of the equation to obtain the Quadratic

w2 + 3w - 28 = 0

Factoring to give

(w + 7)(w - 4) = 0

The width cannot be -7

w = 4

L = w + 3

L = 4 + 3 = 7

The width of the rectangle is 4 units and the length of the rectangle is 7 unites.