The cylinder shown has a diameter of 20 in. and a height of 4 in.
20 in.
Use 3.14 for T.
What is the approximate volume of the cylinder?
OA. 251.2 in.3
OB. 502.4 in.³
OC. 879.2 in.3
OD. 1,256 in.3
OE. 5,024 in.3
4 in.

Answer:

a. vertical angles

b. supplementary angles

c. complementary angles

Answer:

10 inches

Step-by-step explanation:

If the original figure has a height of 25 inches and it was photocopied at a scale of 40%, we can find the new height of the figure by multiplying the original height by the scale factor:

new height = 25 inches x 0.4

new height = 10 inches

Therefore, the new height of the figure is 10 inches.

Answer:

Wassup

Step-by-step explanation:

By multiplying the initial height by the scale factor, which is 40% or 0.4 in decimal notation, the new height of the image can be calculated.

New height: 25 inches times 0.4 to equal 10 inches.

The figure's revised height is 10 inches as a result.

58 degrees at m24 as angles are congruent since they are vertical angles visible in the diagram.

In geometric, an angle is a figure made up of two rays that share a vertex and are referred to as the side of the angle. An angle's measurement is the degree of rotation required to turn a single rays around the vertex till it crosses the other ray. Angles are commonly expressed as degrees or radians.

given

Angles 24 and 25, which are congruent since they are vertical angles, are visible in the diagram. We know that: since angle 25 is marked as 58 degrees

m24=m25=58 degrees

The measurement of 24 is thus:

58 degrees at m24 as angles are congruent since they are vertical angles visible in the diagram.

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Answer:

perimeter = 96.8 m

Step-by-step explanation:

the sides of a square are congruent , then perimeter (P) is calculated as

P = 4s ( s is the side length )

the area (A ) of a square is calculated as

A = s²

given A = 585.64 , then

s² = 585.64 ( take square root of both sides )

s = [tex]\sqrt{585.64}[/tex] = 24.2

Then

P = 4 × 24.2 = 96.8 m

Answer:

= 96.8 m

Step-by-step explanation:

Area of a square = side²

Perimter of a square = 4*side

Then:

585.64 = side²

√585,64 = √side²

it is a geometric figure, therefore, only the positive value will be obtained

24.2m = side

Perimeter = 4*side

Perimeter = 4*24.2

Since the outputs of -5 and 1, and -1 and 7, are not equal, we can conclude that f is injective.

In mathematics, a function is a rule that assigns a unique output value to each input value in a given set. The input values are also known as the domain of the function, while the output values are known as the range. A function can be thought of as a machine that takes an input and produces an output. For example, a simple function could be doubling a number. In this case, the input is the number to be doubled, and the output is the result of doubling that number.

Here,

To determine if a function is injective, we need to check whether different inputs produce different outputs. In other words, if for any two distinct inputs x and y, f(x) is not equal to f(y), then the function is injective.

Let's examine the table of values for the function f:

× -5 -3 -1 0 3 5

f(×) 1 3 7 3 2 4

We can see that f(-5) = 1, f(-3) = 3, f(-1) = 7, f(0) = 3, f(3) = 2, and f(5) = 4.

Since the outputs of -5 and 1, and -1 and 7, are not equal, we can conclude that f is injective. Therefore, for this function, no two distinct inputs produce the same output.

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Complete question:

A function f is expressed through a table of values. Determine if f is injective:

× -5 -3 -1 0 3 5

f(×) 1 3 7 3 2 4

The volume of metal that we have in the hollow bar is 180 cubic inches.

For a prism of length L, width W, and height H, the volume is:

V = L*H*W

Here we need to take the volume of the larger prism, and subtract the volume of the hole, then the volume of metal that we have is:

Volume = 5in*6in*10in - 3in*4in*10in

Volume = 300in³ - 120in³

Volume = 180 in³

The bar has 180 cubic inches of metal.

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Answer:

length = 10 in

width = 8 in

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Then:

36 = 2(h + w)          Eq. 1

h = 2 + w                 Eq. 2

h = length

w = width

From Eq. 1

36/2 = h + w

18 = h + w              Eq. 3

Replacing Eq. 2 in Eq. 3

18 = (2+w) + w

18 = 2 + 2w

18 - 2 = 2w

16 = 2w

16/2 = w

w = 8

From Eq. 2

h = 2 + w

h = 2 + 8

h = 10

Check:

from Eq. 1:

36 = 2(h + w)

36 = 2(10 + 8)

36 = 2*18

Answer:

true

Step-by-step explanation:

3.5*2.5-6=2.75

2+0.75= 2.75

It is proven true.

Consider concert tickets as a long-term savings objective.Therefore, the answer is A.

Savings refers to anything that existing at any given moment, a stock variable, whereas saving refers to an action occurring over period, a flow variable. Even seasoned economists and financial experts frequently refer to "saving" for "savings" due to the widespread misunderstanding of this distinction.\

Saving for a concert is not a long-term savings goal because it is a short-term financial goal. Long-term savings goals typically involve saving money for events or expenses that will occur several years or even decades in the future, such as college, a down payment on a house, or retirement. Saving for a concert is unlikely to take more than a few months or a year, so it is not a long-term goal.

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Answer:    scalene triangle

Step-by-step explanation:

can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.

Answer:

scalene triangle is the triangle

Answer: Yes

Step-by-step explanation:

To determine if Mindy's estimate is reasonable, we need to consider the context of the movie theater and the audience it serves. Generally, movie theaters offer tickets to various categories of customers, such as adults, children, and seniors. Seniors usually receive discounted tickets to encourage their attendance.

Mindy estimates that out of 400 tickets sold on a Friday evening, about 100 of them will be senior tickets. This means that she is estimating that 25% of the tickets sold are senior tickets (100 senior tickets / 400 total tickets = 0.25 or 25%).

While it's difficult to know the exact proportions of ticket categories sold without more information, a 25% estimate for senior tickets may be reasonable if the movie theater attracts a diverse audience and offers films or events that appeal to seniors. The actual proportion of senior tickets might vary depending on the location of the theater, the movies being shown, and the demographics of the surrounding community.

It would be helpful to gather more data on the actual distribution of ticket sales across different categories or to compare Mindy's estimate with industry averages to determine if her estimate is reasonable.

Answer:

2⁵ / ( 2²)⁵

2⁵ / (2×2)⁵

2⁵ / ( 4 )⁵

2⁵ / 4⁵

32 / 1024

4 / 128

1 / 32

0.03125

The two pieces of information which are needed to determine the critical f-value are "degrees of freedom" and "alpha level".

The critical f-value is defined as the threshold or cutoff value used to determine whether an obtained F-value is statistically significant or not.

To determine the critical f-value, we need two pieces of information:

(i) The degrees-of-freedom for numerator and denominator of the F-distribution.

These are denoted as df₁ and df₂, respectively. The degrees of freedom depend on the sample sizes and the number of groups being compared.

(ii) The alpha-level : This is the probability of making a "Type I" error, or rejecting the null hypothesis when it is actually true.

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The constant percent rate of change in the exponential function [tex]f(x) = 2(3)^x[/tex] is 200%, indicating a doubling of the output value for each unit increase in the input value.

The equation [tex]f(x) = 2(3)^x[/tex] represents an exponential function. Exponential functions have a constant percent rate of change, which means that the percent change between any two points on the graph of the function is the same.

In this case, we can find the percent rate of change by calculating the ratio of the output values for any two input values that differ by 1. For example, if we compare the output value when x=1 to the output value when x=0, we get:

[tex]f(1) = 2(3)^1 = 6[/tex]

[tex]f(0) = 2(3)^0 = 2[/tex]

The percent change from x=0 to x=1 is:

percent change = (f(1) - f(0)) / f(0) x 100%

= (6 - 2) / 2 x 100%

= 200%

This means that the output value increased by 200% when the input value increased by 1. We can also express this as a constant percent rate of change by dividing the percent change by the change in input value:

constant percent rate of change = percent change / change in input value

= 200% / 1

= 200%

Therefore, the equation [tex]f(x) = 2(3)^x[/tex] has a constant percent rate of change of 200%.

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Answer:

------------------------

Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.

Total surface area includes a square base and four triangular faces and the measure of it is:

The matching choice is B.

We are given the system of equations:

p = d + 3 ----(1)

p + 2d = 10.50 ----(2)

We can use substitution to solve for the variables. From equation (1), we can see that p = d + 3. We can substitute this expression for p in equation (2) to get:

(d + 3) + 2d = 10.50

Simplifying this equation, we get:

3d + 3 = 10.50

Subtracting 3 from both sides, we get:

3d = 7.50

Dividing both sides by 3, we get:

d = 2.50

Now that we know the value of d, we can substitute this back into equation (1) to solve for p:

p = d + 3

p = 2.50 + 3

p = 5.50

Therefore, the solution to the system is p = 5.50 and d = 2.50.

In order to be certain that the probability of at least one occurrence of each of the six faces of the die is greater than 0.99, you would need to toss the die a minimum of[tex]6 x 5 x 4 x 3 x 2 = 720[/tex] times.

For example, if you tossed the die 6 times, the probability of at least one occurrence of each of the six faces is 0.54. This probability increases with each additional toss, reaching 0.99 after 720 tosses.

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The solution to the given inequality expression is: x ≥ -8 and it is shown on the number line attached

To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle. An open circle shows it does not include the value. A closed circle shows it does include the value.

We are given the inequality expression as:

8x - 4 ≥ -68

Add 4 to both sides to get:

8x ≥ -64

Divide both sides by 8 to get:

x ≥ -8

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The score obtained by Lara is less than the score obtained by Pei, which can be modeled by this inequality 30,065 < 30,408.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided about the scores (points) scored by Lara and Pei after playing the same game;

Lara = thirty thousand sixty five points = 30,065 points.

Pei = thirty thousand four hundred eight points = 30,408 points.

In conclusion, we can logically deduce that 30,408 points is greater than 30,065 points or 30,065 points is less than 30,408 points.

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The graph of each function from a to d are attached below

Graphs of nonlinear functions are graphs of functions that do not have a constant rate of change or a linear relationship between the input and output values. Nonlinear functions include quadratic, exponential, logarithmic, trigonometric, and many other types of functions.

The shape of the graph of a nonlinear function can vary greatly depending on the specific type of function. For example:

The graph of a quadratic function (y = ax^2 + bx + c) is a parabola, which is a symmetric U-shaped curve.

The graph of an exponential function (y = a^x) is a curve that increases or decreases rapidly, depending on whether the base a is greater than or less than 1.

The graph of a logarithmic function (y = log_a(x)) is a curve that approaches a vertical asymptote as x approaches zero.

The graph of a trigonometric function (y = sin(x) or y = cos(x)) is a periodic wave that oscillates between a maximum and minimum value.

Nonlinear functions can exhibit complex and interesting behaviors, such as multiple intercepts, asymptotes, and singularities. The graphs of these functions can be used to model a wide range of real-world phenomena, such as population growth, radioactive decay, and the motion of objects under the influence of gravity.

The graphs of the functions given are attached below

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Answer:

1) car speed = 1.05km/minute

2) 5.25 km in 5 minutes

Step-by-step explanation:

1) [tex]\frac{63km}{60minutes}=1.05km/minute\\[/tex]

2) 1.05 km × 5 minutes = 5.25 km

Answer:

Step-by-step explanation:

process =63/60=1.05m/min

Answer:

.............

Step-by-step explanation:

.............

Using division, we can find that he must sell 2123 pairs to get a profit of $69840.

One of the four fundamental operations in mathematics is division, along with addition, subtraction, and multiplication. The splitting of a large group into smaller groups so that each group contains an equal number of items is a straightforward definition of division. It is a mathematical process used for equitable grouping and distribution.

Here,

Profit by selling one pair of shoes = $80.

Now, expenses = $100,000

Total profit he wants = $69,840.

So, total revenue to be generated = 100000 + 69840

= $169840.

Let x be the total pairs sold.

So, x = 169840/80

= 2123.

Therefore, he must sell 2123 pairs to get a profit of $69840.

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The answer is , (a)  the length of AD is approximately 7.62 meters. (b) the size of angle DCB is approximately 59.04° degrees. 3. the angle of depression of the pedestrian from the man is approximately 38° degrees.

The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle (a triangle with one angle measuring 90 degrees), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. (a) To calculate the length of AD, we can use the Pythagorean theorem,

In triangle ABD, we have:

AB² + BD² = AD²

Substituting the given values, we get:

7² + 3² = AD²

49 + 9 = AD²

58 = AD²

Taking the square root of both sides, we get:

AD ≈ 7.62 m

Therefore, the length of AD is approximately 7.62 meters.

(b) To calculate the size of angle DCB, we can use the trigonometric function tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In triangle DBC, we have:

tan(DCB) = opposite/adjacent = BC/BD = 5/3

Using a calculator, we can find the inverse tangent of 5/3, which gives us:

DCB ≈ 59.04°

Therefore, the size of angle DCB is approximately 59.04° degrees.

3. Let's call the height of the building "h" and the angle of depression "θ".

From the man's point of view, we can draw a right triangle with the hypotenuse being the line of sight from the man to the pedestrian, and the opposite side being the height of the building "h". The adjacent side is the distance from the man to the pedestrian, which is 48 meters.

Similarly, we can draw another right triangle from the pedestrian's point of view, with the hypotenuse being the line of sight from the pedestrian to the top of the building, and the opposite side being the distance from the pedestrian to the foot of the building, which is 34.5 meters.

Now, we can use trigonometry to solve for the angle of depression "θ". We have:

tan(θ) = opposite/adjacent = h/48

tan(θ) = adjacent/opposite = 34.5/h

Solving for "h" in the second equation, we get:

h = 34.5/tan(θ)

Substituting this value of "h" in the first equation, we get:

tan(θ) = h/48 = 34.5/(48*tan(θ))

Simplifying this equation, we get:

tan²(θ) = 34.5/48

Taking the square root of both sides, we get:

tan(θ) = √(34.5/48) = 0.7975

Now, we can find the angle of depression "θ" by taking the inverse tangent (arctan) of this value:

θ = arctan(0.7975) = 38.3 degrees (rounded to the nearest degree)

Therefore, the angle of depression of the pedestrian from the man is approximately 38 degrees.

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(a) The standard error of the mean is 129. (b) The probability that the sample mean will be more than $27,175 is 0.50 (c) The probability that the sample mean will be within $1,000 of the population mean is 0.955. (d) The probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100 is 0.999.

(a) The standard error of the mean is the square root of the population standard deviation divided by the sample size, which in this case is 7,400/57 = 129.12. The value of the standard error of the mean is therefore 129 (rounded to the nearest whole number).

(b) To find the probability that the sample mean will be more than $27,175, you can use the Z-score formula. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175)/129 = 0. The probability that the sample mean will be more than $27,175 is 50%, since the probability of any Z-score of 0 is 0.50.

(c) To find the probability that the sample mean will be within $1,000 of the population mean, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/129 = ±7.8. The probability that the sample mean will be within $1,000 of the population mean is 95.5%, since the probability of any Z-score of ±7.8 is 0.955.

(d) To find the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/74 = ±13.5. The probability that the sample mean will be within $1,000 of the population mean is 99.9%, since the probability of any Z-score of ±13.5 is 0.999.

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The data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

The mean is a measure of central tendency that represents the average value of a set of numbers. There are different types of means, including the arithmetic mean , the geometric mean , and the harmonic mean.

The spread of data refers to the variability or dispersion of a set of values. It provides information about how spread out or clustered the data is. A set of data can have a high or low spread, depending on the range of values and how they are distributed.

In the given question,

The spread of a data set refers to how much the individual data points in the set vary from each other. There are several measures of spread that are commonly used, including the range, variance, and standard deviation.

To find the spread of the data set {4, 2, 6, 10, 8, 0}, we can calculate the range, which is the difference between the maximum and minimum values in the set. The maximum value in the set is 10, and the minimum value is 0, so the range is:

Range = maximum value - minimum value = 10 - 0 = 10

Therefore, the spread of the data set is 10.

In other words, the data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.

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Answer:

Its 6

Step-by-step explanation:

Did the test

Answer:

Whichever equation has a slope of 5/7.

Step-by-step explanation:

Parallel lines will always share the same slope. The slope is found by denoting where the variable m is at. It is noteworthy of the placement of m in the given slope equation:

y = mx + b

Therefore, whichever choice(s) have 5/7 as a slope would be your answer.

~

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The new number that was added to the set is 74 by using mean formula for some numbers.

Let's begin by determining the mean of a set of numbers using the following formula:

average = (sum of numbers) / (number of numbers)

We can write: since we know that the mean of 21 numbers is 30.

/ 21 = 30 = (sum of 21 numbers)

Multiply LHS and RHS by woth 10:

sum of 21 digits equals 630

The new mean will now be determined by adding a new number to the set. Let's call the new number x since we don't yet know its value. We can write: 32 = (sum of 21 numbers + x) / 22 since we also know the new mean is 32.

The result of adding the two sides together is: total of the 21 numbers plus x = 704

We may change the equation to read 630 + x = 704 as we already know the sum of the original 21 values is 630.

630 is subtracted from both sides, giving us:

x = 74

74 is the new number that was so added to the collection.

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