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The statistical measures for the data-set are given as follows:

From the stem plot, the observations of the data-set are given as follows:

45, 46, 48, 74, 74, 75, 76, 93, 95.

The mean is given by the sum of all observations divided by the number of observations, hence:

Mean = (45 + 46 + 48 + 74 + 74 + 75 + 76 + 93 + 95)/9 = 69.6

The median is the middle element of the data-set. The data-set has 9 elements, hence the median is the 5th element, which is of 74.

The mode is the element that appears the most times in the data-set, which is also 74.

The first quartile is the median of the first half of the distribution, which is  the median of the first four elements, hence:

Q1 = (46 + 48)/2 = 47.

The third quartile is the median of the last four elements, hence:

Q3 = (76 + 93)/2 = 84.5.

Then the midrange is given as the difference of the quartiles, as follows:

IQR = Q3 - Q1 = 84.5 - 47 = 37.5.

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Answer:

The annual interest rate is 0.018, or 1.8%.

Step-by-step explanation:

Let r be the annual interest rate, t be the number of years the money was in the account, and I be the amount of interest earned. Since the interest is simple interest, the amount of interest earned is given by the formula I = Prt, where P is the principal, or initial amount deposited. In this case, we know that P = $3000, t = 3.5 years, and I = $262.50. Substituting these values into the formula, we get:

262.50 = 3000r * 3.5

r = 0.018

Thus, the annual interest rate is 0.018, or 1.8%.

The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).

A random sample of 1000 people was condidered for testing.

Number of people in sample favoured candidate

= 450

So, sample proportion, p = 450/1000 = 0.45

Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..

Confidence interval formula,

CL = p ± Z× √(p×(1-p)/n)

Lower bound of interval is ,

=0.45 - 1.96× √(0.45× (1-0.45)/1000)

= 0.45 - 1.96× √(0.45× 0.55/1000)

= 0.45 - 1.96× √(0.0002475)

=0.419165~ 0.419

So the Upper bound is

= p + Z×√(p×(1-p)/n)

= 0.45 + 1.96× √(0.45× (1-0.45)/1000)

= 0.45 + 1.96× √(0.0002475)

= 0.480835 ~0.481

Hence, the required confidence interval is (0.419,0.481).

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Answer:

c. 3 [tex]\leq[/tex] y [tex]\leq[/tex] 5

Step-by-step explanation:

Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.

Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.  

So, the range of this relation is 3 ≤ y ≤ 5.

Answer:

c

Step-by-step explanation:

the maximum of y is 5 the minimum of y is 3

The average rate of change of the function at the interval x = 5 and x = 7 is 22.5

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The interval is given as

x = 5 and x = 7

This can be represented as

5 ≤ x ≤ 7

On the graph, we have

x = 5 and y = 3

x = 7 and y = 48

This means that

f(5) = 3 and f(7) = 48

The average rate of change is then calculated as

Average rate of change = [f(7) - f(5)]/[7 - 5]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[2]

Evaluate the expression

Average rate of change = 22.5

Hence, the rate is 22.5

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Complete question

The function y=f(x) is graphed below. Plot a line segment connecting the the points on f where x=5 and x=7. Use the line segment to determine the average rate of change of the function f(x) on the interval 0≤x≤ 4.

See attachment for graph

Answer:

Step-by-step explanation:

f x = (4x/9)

so it will be x into 4x = 9/f

so 4x square = 9/f

The difference between a line and a line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.

Lines are the geometrical picture with non-terminating ends. A line runs in two opposite directions with endless. Both the points of a line can be extended to infinity.

The line is non-ending but it can be fractionally divided into different segments. These segments are known as the line segment which has two endpoints.

Difference between line and line segment:

A line segment can be taken as the shortest distance between two endpoints and they are the distance between two defined endpoints.

A line segment can be measured in length as it has two fixed endpoints, which are denoted by ‘_’ or \overline{xy}

A line extends up to infinity as it does not have any starting or endpoint, Which can be measured as it has no end and extends up to infinity, and is denoted by any two points lying on the line.

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one cyclist travels faster than the other. Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).

Let x = the rate of the faster cyclist, and y = the rate of the slower cyclist.

We can set up the equation:

x + y = (distance between towns) / (time they met)

x + y = (distance between towns) / (hours)

We can solve for x and y:

x = (distance between towns) / (2 * hours)

y = (distance between towns) / (2 * hours)

Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).

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Answer:

-1.8f-19

Step-by-step explanation:

2.5f-0.7f=1.8 and 16+3=19

make both negative

By solving the inequality we get that the cheapest ticket is $29.

Here given,

If x is the number of $2 dollar increases required to meet her goal, then the minimum number of increases required is:

-100x² + 15,750x + 212,500 ≥ 243,600

- 100x² + 15,750x - 31,100 ≥ 0

x² - 157.5x + 311 ≥ 0

x = (157.5 ± [tex]\sqrt{157.5^{2} - (4*1*311 }[/tex] ) / 2

x1 = 2

x2 = 155.5

The only conceivable value is x = 2 $2 increases

If the original cost was $25, the new rice needed to meet Amy's goal is:

P = 25 + 2 x 2

P = $29

The cheapest ticket is $29.

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Answer: 7,176 inches

Step-by-step explanation:

Areas equation is Length times width so applying that we have 78 times 92 giving you the answer of 7,176

How to solve a system of equations by elimination.

How to solve a system of equations by Substitution.

Let us take an example :

y = 3x - 4

2y = -x + 6

Order of Operations: BPEMDAS

Step 1: Define Systems

y = 3x - 4

2y = -x + 6

Step 2: Solve for x

Substitution

Step 3: Solve for y

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18 inches is not a possible length for the thrid side of a triangle.

A triangle is a polygon with the 3edges and 3 vertices. It  is 1 of the basic shaped on geometry. A triangle with vertices A, B, and C is denoted ∆ ABC. In Euclidean geometry, any 3 points, when non-colli early, determined a uniquely ∆ and simultaneously, to unique plane.

As we know in a ∆ if the measurement of two sides are given than the sum of these 2 sides.

Otherwise buliding of a triangle is never possible.

Here two side are 10 and 8 inches.

So, 3rd side of the triangle should be less than

10+8 = 18

Third sides=

2<x<18

Now we have to calculate the range of 3rd sides

2<x<18

Thus,3rd side of the measurement with 18 inches is not possible.

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The area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in²,  16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given

A company makes different-sized shoeboxes in the shape of rectangular prisms.

We have to match the area of the material needed to make each box to the box’s dimensions.

S₁ = 12in× 5in× 6in

S₁ = (12×5+12×6+6×6)×2

S₁ = 162×2

S₁ = 324in²

S₂ = 10in× 6in ×6in

S₂ = (10×6+10×6+6×6)×2

S₂ = 156×2

S₂ = 312in²

S₃ = 16in× 6in× 4in

S₃  = (16×6+16×4+6×4)×2

S₃  = 184×2

S₃  = 368in²

S₄ = 14in× 5in× 5in

S₄ = (14×5×2+5×5)×2

S₄ = 165×2

S₄ = 330in²

Hence, the area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in²,  16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².

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Answer:

The discount on the barbecue grills is 75.11%.

Step-by-step explanation:

To calculate the discount as a percentage, we first need to find the total discount amount by subtracting the new price of the barbecue grills from the old price. This gives us $844 - $211 = $633.

To find the discount as a percentage, we divide the discount amount by the old price and multiply the result by 100%. This gives us $633 / $844 * 100% = 75.11%.

Therefore, the discount on the barbecue grills is 75.11%.

Answer: y=7

Step-by-step explanation:

Slope intercept form

y=mx+b

m=slope

b= y-intercept

find the slope with the slope formula

y2-y1/x2-x1

7-7/6-(-1)

0/7

the slope is 0, meaning this is a horizontal line.

Find the y-intercept

7=0(-1)+b

b=7

y=7

The value of y is 9 in the graph where y is 3x.

We must use the equation y = 3x.

To locate the point on the graph that represents the price of three pounds of meat

As a result, when x = 3,

y = 3 × 3

i.e. y = 9

So, the price of 3 pounds of meat is represented by the following point on the graph is point B

The graph in the question is attached below.

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Step-by-step explanation:

a)Perimeter of a Rectangle = [tex]2 (l+w)=2(24+15)=78[/tex]

Circumference of a circle = [tex]\frac{\pi d}{2}[/tex]

= [tex]\frac{3.14X24}{2} \\= \frac{75.36}{2} \\= 37.68[/tex]

Perimeter of the whole figure = [tex]15 + 15 + 24 + 37.68= 91.68cm[/tex]

b) Area of the rectangle =[tex]wl=15X24=360[/tex]

Area of a semi circle = [tex]\frac{\pi }{2} Xr^{2}[/tex]

= [tex]1.57[/tex] x [tex]12X12[/tex]

=[tex]226.08[/tex]

Area of the whole figure = [tex]360 + 226.08[/tex]

= [tex]586.08[/tex][tex]cm^{2}[/tex]

Hope it helps

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The properties of the angles and sides of a triangle are as follows:

1. The sum of the three angles of any triangle is 180°

2. The longest side of a triangle is opposite the largest angle and the smallest side is opposite the smallest angle.

3. The sum of any two sides of a triangle is always greater than the third side.

These properties can be used to solve problems involving triangles by working out the angles or lengths of sides. For example, let's say we have a triangle with two sides of length 5 and 8, and we need to find the length of the third side. Using the third property listed above, we can set up the following equation:

5 + 8 > x

13 > x

Therefore, the length of the third side is greater than 13.

A triangle (of any kind) has a total angle of 180°. A triangle's two sides add up to a length bigger than its third side. In the same way, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."

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To determine the minimum number of subjects needed for a z-test with a power of at least 80% and a type 1 error rate of 0.05, you can use a sample size calculator or perform the calculations manually.

Assuming that the population of differences is approximately normal, the z-test is appropriate to use. The z-test allows you to test whether the mean of a population differs significantly from a specified value (the null hypothesis) based on a sample taken from the population.

To perform the calculations manually, you will need to know the following:

Once you have this information, you can use the following formula to calculate the minimum sample size:

n = (Z_alpha/2 + Z_beta)^2 * (SD / effect size)^2

where:

For example, let's say the desired power of the test is 80%, the type 1 error rate is 0.05, the effect size is 0.5, and the standard deviation of the population is 1. Using the formula above, we can calculate the minimum sample size as follows:n = (1.96 + 0.84)^2 * (1 / 0.5)^2

= 3.8236^2 * 2^2

= 14.52 * 4

= 58.08

Therefore, the minimum sample size needed for this test would be 59 subjects.

It's important to note that this is just a rough estimate, and the actual sample size may need to be adjusted based on the specific characteristics of the population and the research question being addressed.

Answer:  The first bolt he bought is 7/8 inches long. The second bolt he bought is 5/8 inches long.

Step-by-step explanation:

The bolt he already has: 3/4 inches, or this can be written as 6/8 inches.

Since the the first bolt he bought was 1/8 inches longer than the original one, we can do 1/8 + 3/4 (6/8) and we get the sum of 7/8.

The first bolt he bought is 7/8 inches long.

The second bolt he bought was 1/8 inch shorter than the first one, so we just take 1/8 from 3/4,

==> 6/8 - 1/8 = 5/8

The second bolt he bought was 5/8 inches long.

Hope this helped, have a good day :D

According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

The standard deviation and the mean of the provided data must first be determined.

Below are the standard deviation and mean

Mean = (50 + 46 + 54 + 51 + 29 + 52+ 48 + 54 + 47 + 48)/10

Mean x = 47.9

Standard deviation: √∑(x - x')²/(n - 1)

s = √(50 -  47.9)² + (46 -  47.9)² + (51 -  47.9)² + .....+ (48 -  47.9)²)/(9)

s = 7.20

We possess:

x' ± s = (47.9 ± 7.2)

x' ± s = (40.7, 55.1)

The proportion of values that are within 1 standard deviation of that mean is thus:

9/10 * 100 = 90%.

According to the normal distribution, 68% of values should fall in one standard deviation from the mean.

As a result, the percentage of values seen to be within 1 standard deviation of a mean is significantly larger than the percentage a normal distribution would predict.

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Answer: 0.159

Step-by-step explanation:

0.159

The value of a percentage between 11% and 17% is,

⇒ 0.14

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

To find value of a percentage between 11% and 17%.

Now, We can formulate;

The value of a percentage between 11% and 17% is,

⇒ (11% + 17%) /2

⇒ 28% / 2

⇒ 14%

⇒ 0.14

Thus, The value of a percentage between 11% and 17% is,

⇒ 0.14

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Answer:

it will be 37.8 cm tall

Answer: y=-5x+6

Step-by-step explanation:

The percentile rank of a score of 71 on this test will be 33.33% and the score of the 60th percentile will be 84.

Percentile is the amount to measure the rank of a student in respect to the other students.

For example, the 90 percentile score means that there is 10 percent of members higher than you.

As per the given test scores,

The score of 71 from left to is at the 5th number.

Percentile = 5/15 x 100 = 33.33%

If the percentile is 60%.

x/15 = 60/100

x = 9

The 9th from left to is 84

Hence "On this test, a score of 71 will yield a percentile rank of 33.33%, while an outcome of 84 will represent the 60th percentile.".

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The number of elements of set (XUY) = 8

A set is simply an organized collection of distinct objects forming a group and can be expressed in set-builder form or roaster form.

Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). .

Means write all the elements in X and Y, then

X = {x|x is a whole number less than 10}

Means write the common elements in X and Y

Y= {-3, -2, 1, 3, 5, 7, 20).

Since there are no common elements in X and Y, then

(XUY) is null set.

The number of elements in (XUY)  is 4 + 4 = 8 elements

Then (XUY) = 8

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Answer: i say 36.2 mph but this is my option i could be wrong :)

Step-by-step explanation: