Section 2-5 Three-Dimensional Figures • Classwork
Question 1 of 15
Question 1
Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
4.0 cm
2.4 cm
2.0 cm
3.2 cm

Answer:

the correct answer is option D

Answer:

(0, [tex]\frac{1}{2}[/tex] ) , (1, [tex]\frac{5}{4}[/tex] ) , (2, 2 )

Step-by-step explanation:

to determine which points are contained in the graph.

substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.

(0, [tex]\frac{1}{2}[/tex] )

y = [tex]\frac{3}{4}[/tex] (0) + [tex]\frac{1}{2}[/tex] = 0 + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] = y- coordinate ← contained in graph

(1, [tex]\frac{5}{4}[/tex] )

y = [tex]\frac{3}{4}[/tex] ( 1) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{5}{4}[/tex] = y- coordinate ← contained in graph

([tex]\frac{1}{2}[/tex], 0 )

y = [tex]\frac{3}{4}[/tex] ([tex]\frac{1}{2}[/tex] ) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{7}{8}[/tex] ≠ y- coordinate ← not contained in graph

(2, 2 )

y = [tex]\frac{3}{4}[/tex] (2) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 = y- coordinate ← contained in graph

If you buy a ticket, you can expect to make a profit of approximately $0.96 on average.

To calculate the expected profit, we need to consider the probability of winning each prize and the value of each prize.

The probability of winning each prize can be calculated by dividing the number of winning tickets by the total number of tickets. There is 1 winning ticket for each prize, so the probability of winning each prize is:

$240 prize: 1/250

$130 prize: 1/250

$120 prize: 1/250

$70 prize: 1/250

The value of each prize is already given, so we can multiply the probability of winning each prize by its value and sum the results to find the expected profit:

Expected profit = (1/250 x $240) + (1/250 x $130) + (1/250 x $120) + (1/250 x $70) - ($16)

Expected profit = $0.96

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Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

Matrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.

A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:

| a11 a12 a13 |

| a21 a22 a23 |

| a31 a32 a33 |

 Given matrix;

A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]

B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]

C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Solving the equation

(A-4B)X=C

[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]-  4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Taking the inverse and multiplying it with RHS,  we get

X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

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The value of  51. 2 divided by 6. 4 using long division is 8.0

To find the value of 512 divided by 64, we can use long division. We start by dividing 5 (the first digit of 512) by 6 (the first digit of 64). Since 5 is less than 6, we bring down the next digit (1) to form the new dividend, 51. We then add a decimal point to the quotient and bring down the next digit (2) to form 512.

We repeat the process of dividing 51 by 6, which gives us 8 with a remainder of 3. We write the quotient (8) above the next digit of the dividend (2) and bring down the next digit (0) to form the new dividend, 30. We continue this process until we have brought down all the digits of the dividend.

At the end of the process, we get a quotient of 8.0, which is the value of our original expression, 51.2 divided by 6.4.

Therefore, 512 divided by 64 is equal to 8.0.

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Answer:

To write the equation of a line parallel to AB through a given point, you need to follow these steps:

1. Find the slope of line AB using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the given ordered pairs A and B.

2. Since the line you want to find is parallel to AB, it will have the same slope as AB.

3. Use the point-slope form of a linear equation to write the equation of the line. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope you found in step 1, and (x1, y1) is the given point through which the line passes.

4. Simplify the equation by distributing the slope and combining like terms if necessary.

5. Your final equation should be in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

If the total trip takes 12 hours, the speed of the current is 1 mph.

The speed of an object is described as  the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.

The downstream trip:

distance = rate × time

96 = (18 + x) × t ( 18 + x)

The upstream trip:

distance = rate × time

96 = (18 - x) × (12 - t)

96 = (18 - x) × (12 - t)

8 = x - (x/6)t

We have two equations and two unknowns, so we can solve for x and t.

We solve for x by making t subject fomula and substituting into the equation.

Where x = 1

In conclusion, if the total trip takes 12 hours, the speed of the current is 1 mph.

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The solution for the given quadratic equation is √27.

What is a quadratic equation?

A quadratic equation is any algebraic equation that can be written in the standard form as where variable 'x' is an unknown number and where a, b, and c are known values, with a ≠ 0.

We are given a quadratic equation in variable 'w' as 3[tex]w^{2}[/tex] + 9 = 90.

Now, on solving the given equation , we get

⇒ 3[tex]w^{2}[/tex] + 9 = 90

⇒ 3[tex]w^{2}[/tex] = 81

⇒ [tex]w^{2}[/tex] = 27

⇒ w = √27

Hence, the solution for the given quadratic equation is √27.

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The complete question has been attached below.

Answer:

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

- 12e = 6q - 4 ( divide through by - 12 )

e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Answer:

C. 15 + 18x ≥ 95

Step-by-step explanation:

Given: She has $15 saved so far

She earns $18.00 for each lawn she mows (each lawn she mows = x)

The inequality has to be greater or equal to $95.00, so she can have enough to buy a pair of shoes.

15 + 18x ≥ 95

The simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

To solve the given expression, we can start by simplifying it using trigonometric identities.

Given expression: tanx / (1 + secx) + (1 + secx) / tanx

Step 1: Simplify denominators

We can rewrite secx as 1/cosx, and tanx as sinx/cosx. Using these identities, we get:

tanx / (1 + 1/cosx) + (1 + 1/cosx) / (sinx/cosx)

Step 2: Find the least common denominator (LCD)

The LCD is cosx, as it is the common denominator for both fractions.

Step 3: Combine the fractions

Using the LCD, we can combine the fractions:

[(tanx * cosx) + (1 + 1/cosx)(cosx)] / cosx

Step 4: Simplify the numerator

Multiplying through by cosx to simplify the numerator, we get:

[tanx * cosx + (cosx + 1)] / cosx

Step 5: Combine like terms

Combining like terms in the numerator, we get:

[tanx * cosx + cosx + 1] / cosx

Step 6: Factor out cosx

We can factor out cosx from the numerator:

cosx * (tanx + 1) + 1 / cosx

So, the simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

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QUESTION IS - simplify . tanx/1+secx  +  1+secx/tan x

The probability that the spinner lands on an even number or a number greater than 10 is 11/18.

There are two cases where the spinner can land on an even number or a number greater than 10:

Case 1: The spinner lands on an even number.

There are 9 even numbers on the spinner: 2, 4, 6, 8, 10, 12, 14, 16, and 18. The probability of the spinner landing on an even number is 9/18 = 1/2.

Case 2: The spinner lands on a number greater than 10.

There are 7 numbers greater than 10 on the spinner: 11, 12, 13, 14, 15, 16, and 18. The probability of the spinner landing on a number greater than 10 is 7/18.

To find the probability of either event occurring, we add the probabilities of the two cases and subtract the probability of both occurring simultaneously (since the numbers 12, 14, and 16 are even and greater than 10). Therefore, the probability of the spinner landing on an even number or a number greater than 10 is:

(1/2) + (7/18) - (3/18) = 11/18

Thus, the probability that the spinner lands on an even number or a number greater than 10 is 11/18.

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Answer:

[tex]S = \dfrac{v^2 - u^2}{2a}[/tex]

Step-by-step explanation:

We can solve for S using algebraic manipulation.

[tex]v^2 = u^2 + 2aS[/tex]

↓ subtract [tex]u^2[/tex] from both sides

[tex]v^2 - u^2 = 2aS[/tex]

↓ divide both sides by [tex]2a[/tex]

[tex]\dfrac{v^2 - u^2}{2a} = S[/tex]

[tex]\boxed{S = \dfrac{v^2 - u^2}{2a}}[/tex]

[tex]\sf \boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}[/tex]

[tex]\sf v^{2} =u^{2} +2aS[/tex]

[tex]\sf v^{2}-u^{2} =u^{2} +2aS-u^{2}\\ \\v^{2}-u^{2} =2aS[/tex]

[tex]\sf \dfrac{v^{2}-u^{2} }{2a} =\dfrac{2aS}{2a} \\ \\ \\\dfrac{v^{2}-u^{2} }{2a} =S\\ \\ \\\boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}.[/tex]

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Since h(-x) = -h(x), the function is odd.

The given function is h(x) = 2x³ + 9x.

To determine whether the function is even, odd, or neither, we need to analyze the behavior of the function when x is replaced by -x:

h(-x) = 2(-x)³ + 9(-x) = -2x³ - 9x.

Since h(-x) = -h(x), the function is odd.

Odd functions have origin symmetry, which means that if you rotate the graph 180 degrees around the origin, it remains unchanged. In other words, the graph has symmetry with respect to the origin, which occurs when the point (x, y) on the graph implies the point (-x, -y) is also on the graph.

So, the function h(x) is odd and has origin symmetry.

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If she will begin paying off the loan in 15 months, . The amount she will she owe when she begins making payments is: C. $12,496.52, since Alma is responsible for the interest on the loan that accrues before she starts making payments.

The formula to calculate the future value of a loan with monthly compounding interest is:

FV = PV * (1 + r/12)^n

where:

PV = present value of the loan

r = annual interest rate

n = number of months

Using this formula, we can calculate the amount that Alma will owe when she begins making payments:

PV = $10,925

r = 10.8% APR = 0.9% monthly interest rate

n = 15 months

FV = $10,925 * (1 + 0.009)^15 = $12,496.52

Therefore, the answer is C. Alma is responsible for the interest on the loan that accrues before she starts making payments, and she will owe $12,496.52 when she begins making payments.

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The 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

To determine how many yards deep the layer of snow would be if spread evenly over the rectangular football field, we need to know the volume of the snow and the area of the football field.

First, let's find the area of the football field. Assuming standard dimensions for a football field, we have:

Length = 120 yards

Width = 53.3 yards

Area = Length x Width

Area = 120 yards x 53.3 yards

Area = 6,396 square yards

Now, let's find the volume of the snow. We are given that 10,000 cubic yards of snow were removed from the downtown area, so the volume is:

Volume = 10,000 cubic yards

Finally, to find the depth of the layer of snow, we can divide the volume of the snow by the area of the football field:

Depth = Volume / Area

Depth = 10,000 cubic yards / 6,396 square yards

Depth ≈ 1.56 yards

Therefore, if the 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

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Answer:

x=162

Step-by-step explanation:

55+x-87+50=180

x+18=180

x=162

The quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

A quadrilateral known as a kite has four sides that may be grouped into two adjacent pairs of equal-length sides, and the diagonals cross each other at right angles. The quadrilateral is a polygon with four sides.

Thus, the quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

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Answer:Range, because it measures the difference between the highest and lowest values in a datase........

Step-by-step explanation:

The median should be used to determine which location typically has the cooler temperature, with Beach Town being the location with higher temperatures due to its skewed data.

The measure of center that should be used to determine which location typically has the cooler temperature is the Median, because Beach Town is skewed.

The median is a measure of center that represents the middle value of a data set when it is arranged in ascending or descending order. When comparing the two histograms, Sunny Town's data is symmetric, meaning that it has roughly equal frequencies on both sides of the center. In this case, the median could be a good representation of the typical temperature in Sunny Town.

However, Beach Town's data is skewed, meaning that it is not symmetrical and has a longer tail on one side of the center. This indicates that there are more occurrences of higher temperatures in Beach Town compared to Sunny Town. In skewed data, the mean can be affected by extreme values, making it less reliable as a measure of center. The median, on the other hand, is less influenced by extreme values and can give a better indication of the typical temperature in Beach Town.

Therefore, the median should be used to determine which location typically has the cooler temperature, with Beach Town being the location with higher temperatures due to its skewed data.

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In the above scenario, it can be estimated with 95% confidence that the true proportion of young adult novels that include a love triangle are between 0.6854 and 0.8890

First we compute the Point Estimate

PE = 59/75 = 0.7867

Next we compute the standard error

SE = √((- - hat x (1 - p- hat) )/n)

= √( (o.7867 x (1 - 0.7867 ))/ 75
= 0. 509

Since the expected confidence level is 95%,

Margin of error = t - critical x S E

= 1.99 x 0.0509
= 0.101291

Thus,

point estimate ± margin of error

0.7867  ±  0.1013

(0.6854, 0.8880)

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Answer:

58

Step-by-step explanation: You add them all together

If each row behind the "row-A" has 6 more seats than row immediately in front of it, then there are (b) 46 seats in "Row-G".

The number of seats in "Row A" is = 10 seats,

We know that, each row behind the "row-A" has 6-more seats than the row immediately in front of it.

So, Number of seats in "Row-B" are =  10 + 6 = 16 seats,

Number-of-seats in "Row-C" are = 16 + 6 = 22 seats,

Number of seats in "Row-D" are = 22 + 6 = 28 seats,

Number of seats in "Row-E" are = 28 + 6 = 34 seats,

Number of seats in "Row-F" are = 34 + 6 = 40 seats,

So, According to the pattern,

Number of seats in "Row-G" will be = 40 + 6 = 46 seats.

Therefore, there are 46 seats in "Row-G", Option (b) is correct.

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Answer: 2

Step-by-step explanation:  0 1 1 2 2 3 3  order

011 2 middle one  233

Answer:

Therefore, the answer is: The graph of the equation is a straight line passing through the points (0, -2), (7, 2), and (-7, -6).

Step-by-step explanation:

The given equation is y = (4/7)x - 2.

To graph this equation, we need to plot points on a coordinate plane. We can do this by choosing values of x and then finding the corresponding values of y using the equation.

Let's choose some values of x and find the corresponding values of y:

When x = 0, y = (4/7)(0) - 2 = -2

When x = 7, y = (4/7)(7) - 2 = 2

When x = -7, y = (4/7)(-7) - 2 = -6

We now have three points: (0, -2), (7, 2), and (-7, -6). We can plot these points on a coordinate plane and draw a line through them to get the graph of the equation.

The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.

In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.

Here,

Part A:

The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.

Part B:

To create a histogram of the given data, follow these steps:

Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.

Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.

Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.

Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.

Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.

Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.

Title: Grades on Recent 8th Grade Mathematics Exam

X-axis label: Grades

Y-axis label: Frequency

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Answer:

s=3

Step-by-step explanation:

Equation: s=(50-44)/2

First, do the operation(s) in parenthesis:

s=(50-44)/2

s=(6)/2

Next, do the division, since it's the last operation:

s=6/2

s=3

So, your answer is s=3

Answer:

Based on the information in the problem, you would have a total of 16 cards, with 6 being face cards, 1 being an ace, and 9 being numbered cards.

Step-by-step explanation:

According to the issue:

The deck contains 52 distinct cards.

There are 36 numbered cards ranging from 2 to 9.

There are four aces in the deck.

There are 12 face cards (including the jack, queen, and king).

If you draw half of the face cards, one ace, and one-fourth of the numbered cards, you will get the following:

Face cards in half: 1/2 * 12 = 6 face cards

1 ace: 1 ace

One-fourth of a deck of numbered cards: 1/4 * 36 = 9 decks of numbered cards

When you add these up, you get a total of 6 + 1 + 9 = 16 cards.

Based on the information in the problem, you would have a total of 16 cards, with 6 being face cards, 1 being an ace, and 9 being numbered cards.

By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.

Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.

For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.

The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.

The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:

P(A and B) equals P(A) times P(B|A)

where there are two events, A and B.

In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.

P(A) is known to equal 0.8. and P(B) = 0.4.

We also know that P(A or B) = 0.9.

Using the following equation to determine the likelihood of two events occurring together:

P(A or B) = P(A) + P(B) - P(A and B)

we can find P(A and B):

P(A and B)

           = 0.8 + 0.4 - 0.9

           = 0.3

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