10. Johnny is looking at a map and measures the distance between Chattanooga and Nashville to be 3.5 inches. He wants to know the actual distance between the two cities. According to the scale on the map, 1 inch = 38 miles. How many miles is there between Chattanooga and Nashville?​

Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

The area of the irregular polygon is equal to 30.5 square units.

In this problem we find the representation of an irregular pentagon, that is, a polygon of five sides of different length. Whose area can be found by adding the areas of rectangles and triangles:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the irregular polygon:

A = 0.5 · 1 · 4 + 0.5 · 3 · 2 + 2 · 4 + 0.5 · 3 · 2 + 3 · 4 + 0.5 · 5 · 1

A = 2 + 3 + 8 + 3 + 12 + 2.5

A = 30.5

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The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.

In 2011, the total number of cars produced in the world was 59.9 million.

In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.

Let us say in 2016 the total number of cars produced in the world was N million.

Therefore, by expressing the given problem in a linear equation we get,

Total number produced in 2016, N = 59.9 + (21% of 59.9 )     in millions

⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex]     ( in millions )

= 59.9 + 12.579    ( in millions )

= 72.479  ( in millions )

= 72 millions ( rounded to the nearest whole number)

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The simplified form of the expression (8h + 7) - (7h + 6) is h + 1. We subtract this by using the distributive law.

An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.) that represents a mathematical quantity or value. Expressions can be simple, consisting of just a single number or variable, or they can be complex, involving multiple numbers, variables, and operations.

The distributive law, also known as the distributive property or distributive property of multiplication over addition, is a fundamental property of arithmetic and algebra that allows the distribution of a multiplication operation over an addition or subtraction operation.

The distributive law states that for any three numbers a, b, and c:

a × (b + c) = (a × b) + (a × c)

According to the given information:

To subtract (8h + 7) - (7h + 6), we can use the distributive property of multiplication over addition to simplify the expression.

(8h + 7) - (7h + 6)

= 8h + 7 - 7h - 6 (Applying the distributive property)

Now, we can combine like terms by adding or subtracting coefficients of the same variable:

= (8h - 7h) + (7 - 6) (Grouping-like terms)

= h + 1 (Simplifying)

So, the simplified form of the expression (8h + 7) - (7h + 6) is h + 1.

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The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.

We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= 0.94 * 0.08 + 0.09 * 0.92

= 0.0976

where P(not A) = 1 - P(A) = 0.92.

Substituting the values we have:

P(A|B) = 0.94 * 0.08 / 0.0976

= 0.763

Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

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The values of the exponential function are calculated below and as x increases, the exponential function increases.

In the table of function given, we can calculate the value of f(x) as it relates to x.

The given exponential function is ;

f(x) = 2ˣ

Substituting the values;

f(-4) = 2⁻⁴ = 1/2⁴ = 1/16

f(-3) = 2⁻³ = 1/2³ = 1/8

f(-2) = 2⁻² = 1/2² = 1/4

f(-1) = 2⁻¹ = 1/2

f(0) = 2⁻⁰ = 1/2⁰ = 1

As the value of x increases, the exponential function increases.

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The area of the circle rounded of to the nearest tenth having radius 9 inches is 254.3 square inches.

Hence option d is the correct answer.

The radius of a circle is, say r = 9 inches

The formula of calculating area of a circle is,

Area = πr² (square units)

= π(9)² square inches

= 81π square inches

Let us take π= 3.14 (approximated up to two decimal places).

Thus, area of the circle = 81(3.14) square inches = 254.34 square inches

Rounding of a number is a process of approximating the original number to some decimal points resulting the original number to shorten up for more explicit representation.

Rounding of a number to its nearest tenth gives the original number to round of to one decimal place.

Here Area =  254.34 square inches is rounded of to the nearest tenth is 254.3 square  inches, since the digit after the first decimal place of the original number is lesser than 5 then we round down the number by decreasing the previous place value digit by 1.

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Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.

In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.

To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:

Linearity: The relationship between the dependent variable and the independent variables must be linear.

Independence: The observations must be independent of each other.

Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.

Normality: The residuals should be normally distributed.

No multicollinearity: The independent variables should not be highly correlated with each other.

If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.

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To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms

2. Use the given information

3. Determine when the object is stopped

4. Calculate the distance traveled

Identify the terms:

For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:

Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:

To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.

Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:

Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.

We can use the equation s = ut + 0.5at²,

where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.

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Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.

In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:

l + 2x = 3w

In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:

l = 2(w + x)

We now have two equations with two unknowns, l and w:

l + 2x = 3w

l = 2(w + x)

Substituting the second equation into the first, we get:

2(w + x) + 2x = 3w

4x = w

Substituting this value of w into the second equation, we get:

l = 2(4x) = 8x

So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.

To find the value of x, we use the measurements given in the diagram:

l + 2x = 60

l = 36

Substituting into the equation l = 2(w + x), we get:

36 = 2(4x + x)

36 = 10x

x = 3.6

So the side length of the square rug is 3.6 feet.

Step-by-step explanation:

The average discount that is obtained by spinning the spinner is 17.7%.

Let, the probability of landing on an even number is denoted by P(E) and the probability of landing on an odd number is denoted by P(O).

We have that the pointer lands on an even number 135 times out of 250 spins.

So, the probability that is of landing on an even number is:

P(E) = Number of times the pointer lands on an even number / Total number of spins

P(E) = 135 / 250

Since, we have the sum of probabilities of all possible outcomes must be 1, we can find the probability of landing on an odd number as follows:

P(O) = 1 - P(E)

P(O) = 1 - (135 / 250)

Now, we know that even numbers get 20% off, and odd numbers get 15% off.

We find the average discount considering these probabilities:

Average Discount = (P(E) * 20%) + (P(O) * 15%)

Average Discount = (135 / 250) * 20% + [1 - (135 / 250)] * 15%

Now, let's perform the calculations:

Average Discount = (135 / 250) * 0.20 + [1 - (135 / 250)] * 0.15

Average Discount = 0.108 + (1 - 0.54) * 0.15

Average Discount = 0.108 + 0.46 * 0.15

Average Discount = 0.108 + 0.069

Average Discount = 0.177

So, the average discount that is obtained by spinning the spinner is 17.7%.

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complete question:

A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins. find the average discount obtained by spinning the spinner?

A blocked design compares different independent variable levels by using homogeneous groups of experimental units.

In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.

By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.

In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.

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Answer:

Plot (-3, -6). From this point, go up 4 units, then right 5 units, to (2, -2). Plot (2, -2), and then draw a line that goes through these two points.

Answer: 100 times

Step-by-step explanation:

The cube is numbered 1 to 6. That is, 1, 2, 3, 4, 5, 6. That means there are 6 possible outcomes for each toss. But there are 2 outcomes we want, 5 and 6 (greater than 4).

So, for each toss, there is a probability of 2/6 = 1/3 that this will occur.

With 300 tosses, we can say that this will probably happen 300 times. This means that it will happen

1/3 * 300 times = 100 times.

Therefore, we can predict we will get a 5 or 6 about 100 times.

The surface area of cylinder M is approximately 184.85 square feet, and the surface area of cylinder N is approximately 401.92 square feet.

Let r_N and h_N be the radius and height of cylinder N, and r_M and h_M be the radius and height of cylinder M. We are given that the radius of cylinder N is equal to its height (rN = hN), and the ratio of the height of cylinder N to the height of cylinder M is 5 : 3.

So, we can write:

hN = rN

hN / hM = 5 / 3

The surface area formulas for cylinders M and N:

Surface Area (M) = 2πr_MhM + 2πr_M^2

Surface Area (N) = 2πrNhN + 2πrN^2

If Surface Area (N) = Surface Area (M) + 256

∴ 2πrNhN + 2πrN^2 = 2πrMhM + 2πrM^2 + 256

Combine like terms:

4πrN^2 = 2πrMhM + 2πrM^2 + 256

Divide both sides by 2π:

2rN^2 = rMhM + rM^2 + 128/π

Since hN = rN, we can write:

hM = (3/5)rN

Now substitute hM into equation

2rN^2 = rM((3/5)rN) + rM^2 + 128/π

2rN^2 = (3/5)rN x ((3/5)rN) + ((3/5)rN)^2 + 128/π

= 2rN^2 = (9/25)rN^2 + (9/25)rN^2 + 128/π

= 2rN^2 = (18/25)rN^2 + 128/π

rN = 5.64, hN = 5.64,

rM = 5.64 x (3/5) = 3.38

rM = 3.38.

let's calculate the surface areas:

Surface Area (M) = 2π(3.38)(3.38) + 2π(3.38)^2 ≈ 71.15 + 113.70 ≈ 184.85 square feet

Surface Area (N) = 2π(5.64)(5.64) + 2π(5.64)^2 ≈ 200.96 + 200.96 ≈ 401.92 square feet

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The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

In mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.

To translate the triangle by a vector (x, y), we use the following transformation matrix:

|1 0 x|

|0 1 y|

|0 0 1|

For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:

|1 0 -2|

|0 1 4 |

|0 0 1 |

To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:

| -1 | | 1 0 -2 | | -3 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

| 0 | | 1 0 -2 | | -2 |

| -4 | -> | 0 1 4 | = | 0 |

| 1 | | 0 0 1 | | 1 |

| 3 | | 1 0 -2 | | 1 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

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Cash paid for interest during 2014 was $12,750. Based on the provided Phoenix Corp. information, the question requires you to calculate the cash paid for interest throughout the 2014 calendar year.

Also provided are the amounts for the year's interest expenditure and the balance of interest payable as of December 31, 2013 and 2014.

These are the formulas that can be used to determine the cash paid in interest in 2014:

Interest paid in 2014 minus any increases in interest due equals the cash paid in interest.

The difference between the balance of interest payable as of December 31, 2014, and as of December 31, 2013, can be used to compute the increase in interest payable:

Interest payable at December 31, 2014 minus interest payable at December 31, 2013 equals $6,200 minus $5,700, which equals $500 in

additional interest.

This signifies that the corporation incurred more interest expense than it paid during the year Since the balance of interest payable increased from 2013 to 2014, the corporation incurred more interest expense than it paid in that period. As a result, the money used to pay interest in 2014 is:

Interest paid in 2014 plus the increase in interest due is $12,250 plus $500.= $12,750

Thus, $12,750 is the correct response (D).

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Answer:

10

Step-by-step explanation:

Area of rectangle = 50 [tex]unit^2[/tex].

Perimeter of rectangle =30 unit.

Area of dilated rectangle = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle = 150 unit.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here the given rectangle length l = 10 unit and width = 5 unit.

Now using formulas,

Area of rectangle = lw square unit.

=> A = 10*5 = 50 [tex]unit^2[/tex].

Perimeter of rectangle = 2(l+w) unit

=> P =2(10+5) = 2(15) = 30 unit.

Here scale factor= 5

The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and

width [tex]w_1 = 5\times5 = 25[/tex] unit

Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.

=>  [tex]A_1[/tex]= 50*25 = 1250  [tex]unit^2[/tex].

Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.

=>  [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.

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The total cost of sending 97 text messages is $9.70

A unit cost is defined as the total expenditure incurred by a specific company to produce, store, and sell one unit of a specific product or service. Unit costs are also synonymous with cost of goods sold (COGS). This accounting measure also involves all of the fixed and variable costs associated with the production of a good or service.

Now, we are told that It cost Chile 17.70$ to send 177 text messages. Thus:

Unit cost of message = 17.70/177 = $0.1 per message

Thus:

Cost of 97 text messages = 97 * 0.1 = $9.7

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Her current checking account balance is $2,641.50.

To find Carrington's current checking account balance, we need to add up all the deposits and subtract all the withdrawals from her starting balance.

Starting balance = $800

Deposits = $2,800

Withdrawals = $310 + $88 + $35.50 + $150 + $375 = $958.50

Therefore, Carrington's current checking account balance is:

$800 + $2,800 - $958.50 = $2,641.50

Her current checking account balance is $2,641.50.

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The composite function g(h(8)) when evaluated is 94.

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

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.

given

a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.

The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:

[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]

The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.

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The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs

The histogram is not given and the data represented on the histogram are not properly presented

This means that the histogram cannot be interpreted

Here, we have

Ketchup = 63

Mustard = 27

Chili = 60

So, we have

Mustard = 27/(63 + 27 + 60) * 5000

Evaluate

Mustard = 900

This means that 900 people prefer mustard

Given that

Data = Milligrams of Vitamin C from 100 different gummy vitamins sold

This data can be represented using a box plot because the five-summary data can be easily identified from the dataset

From the five-summary, the median can be derived

In this case, the graph to use is a circle graph

This is so because the circle graph would show the proportion of the student's preferences

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Answer: 22,050.

Step-by-step explanation: The number of individuals who went on Summer Visit B is given within the moment push of lattice S as 150.

The fetched per individual for Summer Tour B is given within the moment push of matrix T as $145.

Hence, the whole income created from Summer Visit B is:

150 individuals × $145 per individual = $21,750

Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.

To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.

1 liter = 1000 milliliters

Therefore, Ann drinks 1000 milliliters of water in total for the day.

To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.

1000 milliliters / 8 hours = 125 milliliters per hour

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Answer:

[tex].28(22) + 3 = 9.16[/tex]

The predicted width of a foot with a length of 22 centimeters is 9.16 centimeters.

Answer:

Y= (x+4)(x+4)-21

Step-by-step explanation:

If you are factoring It out:

Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21

Let me know if it is incorrect!

-a friendly 8th grader