If a man was born in 1898 how old was he in 1945

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

The fraction of Earth that is not made up of ocean = 1/4.

The numbers we are familiar with are whole numbers, such as 1, 2, and so on.

Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.

In essence, a fraction explains how a portion of a group interacts with the entire group.

Given that-

The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water

The fraction of Earth that is not made up of ocean = 1 - 3/4

The fraction of Earth that is not made up of ocean = (4 - 3)/4

The fraction of Earth that is not made up of ocean = 1/4

Thus, the fraction of Earth that is not made up of ocean = 1/4.

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Complete question:

Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?​

Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

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Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

Step-by-step explanation:

the answer is 115 remainder 1

Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

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Answer: 104%

Step-by-step explanation: 26% times 4 years

Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.

The answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?

To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,

Z = (X - mean) / standard deviation

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.

(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?

We need to standardize the values of 16 and 18 using the mean and standard deviation provided.

Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.

(c) What is the age at which growth plates fuse for the top 5% of males?

We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).

Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.

Then, we can solve for X using the formula:

Z = (X - mean) / standard deviation

1.645 = (X - 18.8) / (15.1/12)

Simplifying the equation, we get:

X = 18.8 + (1.645)(15.1/12) = 20.24

Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.

(d) What percentage of males have growth plates that fuse before the age of 16?

We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).

Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.

Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.

hence, the answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

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Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776

Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

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

Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.

The three consecutive integers are 18, 19, and 20.

Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.

Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:

4x + (x+2) = 92

Simplifying this equation, we get:

5x + 2 = 92

Subtracting 2 from both sides, we get:

5x = 90

Dividing both sides by 5, we get:

x = 18

Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:

4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.

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Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.

The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.

Here,

According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.

This suggests that between 30% and 60% of people have brown eyes.

Let's figure out what proportion of the entire population is equal to 30% of 60%:

=> 30% of 60% = (30/100) * (60/100)

=>  0.3 * 0.6

=>  0.18 or 18%

Therefore, brown eyes are present in Math Town's overall population of 18%.

Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.

Therefore, D) 28% is the right response.

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The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

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Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer

Angle A equals 41.81°

c:

The type of the relation are

A linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.

In the given expressions:

Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".

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a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.

APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

= 6.18

Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

= 3.43

Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Answer:

[tex]25.5h = 153[/tex]

[tex]h = 6[/tex]

The height is 6 feet, so A is correct.

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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Answer:

Step-by-step explanation:

I think its 42 because 7/20ths of 120 is 42

7/20 x 120 =42

The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

(a) The total surface area of the triangular prism is 560 in².

(b) The surface area of the cuboid is 944 ft².

(c) The surface area of the cylinder is  678.58 in².

Cuboid;

The surface area of the cuboid is calculated as;

S.A = 2(12 x 16  +  12 x 10  + 16 x 10)

S.A = 944 ft²

Cylinder:

The surface area of the cylinder is calculated as follows;

S.A = 2π x 6 (6 + 12)

S.A = 678.58 in²

The surface area of a triangular prism can be calculated by summing the areas of its individual faces.

A triangular prism has three rectangular faces and two triangular faces.

The formula for the surface area of a triangular prism is:

Surface Area = Area of triangular faces + Area of rectangular faces

To calculate the area of a triangular face, we can use the formula for the area of a triangle:

Area of a triangle = (base × height) / 2

Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.

The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:

Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²

The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:

Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²

The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:

Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²

Now, let's calculate the area of the rectangular faces.

Area of rectangular face 1 = 18 in × 12 in = 216 in²

Area of rectangular face 2 = 18 in × 12 in = 216 in²

Finally, we can sum up all the areas to get the total surface area of the triangular prism:

Surface Area = Area of triangular faces + Area of rectangular faces

Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²

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The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

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The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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