Today, everything at the store is on sale. the store offers a 20% discount.

a.what percentage will you pay when a store offers a 20% discount?


b.if the regular price of a t-shirt is $18. what is the discount price?


c.if the regular price of a gaming system is $360. what is the sale price?
show what you typed into the calculator:


d.the discount price of a hat is $18. what’s the regular price (price before the coupon)?

The amount of money earned over a period of time is called 3. Income

Income refers to the money you receive from various sources such as salary, wages, investments, or any other means during a specific period of time.

Income is a fundamental concept in finance and accounting. It represents the inflow of money or economic benefits received by an individual, household, or organization.

It is typically measured and reported on a periodic basis, such as monthly, quarterly, or annually. Income can be derived from various sources, including salaries and wages, interest and dividends, rental income, profits from business activities, and capital gains.

It is an essential component in assessing an individual's or organization's financial health and is often used to calculate taxes, budgeting, and determining net worth. Understanding and effectively managing income is crucial for individuals and businesses to meet their financial goals and sustain their economic well-being.

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The value of ∠APB = 180°. It is a straight line.

Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.

Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.

Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,

∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.

So, we have shown that ∠APB is a straight line.

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If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793

To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.

Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.

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A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.

Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.

Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.

However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.

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Full Question: What is a collection of information such as number measurement or observation called?

The estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.

a. To find the linear approximation of f(x,y) at the point (3,-3), we need to find the gradient of the function at that point.

∇f(x,y) = [-8x, 4y]

So, at the point (3,-3), the gradient is ∇f(3,-3) = [-24, -12].

The linear approximation is given by:

L(x,y) = f(3,-3) + ∇f(3,-3)·(x-3,y+3)

Plugging in the values, we get:

L(x,y) = -4(3)^2 + 2(-3)^2 - 24(x-3) - 12(y+3)

Simplifying, we get:

L(x,y) = -12x - 4y - 36

b. To estimate f(3.1, -3.01) using the linear approximation, we plug in the values into the equation we found in part (a):

L(3.1, -3.01) = -12(3.1) - 4(-3.01) - 36

L(3.1, -3.01) ≈ -54.28

Therefore, the estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.

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we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.

To find the first eight terms of the sequence of partial sums for the series sin(n), we will calculate the sum of the series for each term up to n=8, and then determine whether the series appears to be convergent or divergent.

1. sin(1)

2. sin(1) + sin(2)

3. sin(1) + sin(2) + sin(3)

4. sin(1) + sin(2) + sin(3) + sin(4)

5. sin(1) + sin(2) + sin(3) + sin(4) + sin(5)

6. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6)

7. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7)

8. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7) + sin(8)

Now, let's calculate these sums up to four decimal places:

1. 0.8415

2. 0.8415 + 0.9093 = 1.7508

3. 1.7508 + 0.1411 = 1.8919

4. 1.8919 - 0.7568 = 1.1351

5. 1.1351 - 0.9589 = 0.1762

6. 0.1762 - 0.2794 = -0.1032

7. -0.1032 + 0.6569 = 0.5537

8. 0.5537 + 0.9894 = 1.5431

Now that we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.

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Answer:

1/3

Step-by-step explanation:

It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3

All of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

To calculate the speed of the model airplane, we need to use the formula:

Speed = Distance / Time

Given that the distance covered by the model airplane is 330 feet, and the time taken is 15 seconds, we can substitute these values in the above formula to get:

Speed = 330 feet / 15 seconds

Simplifying this, we get:

Speed = 22 feet per second

To convert this unit rate to other equivalent unit rates, we need to use conversion factors. For example, to convert feet per second to feet per minute, we can multiply the unit rate by 60 (since there are 60 seconds in a minute):

22 feet per second x 60 seconds per minute = 1320 feet per minute

Similarly, to convert feet per minute to miles per minute, we can use the conversion factor 1 mile = 5280 feet:

1320 feet per minute / 5280 feet per mile = 0.25 miles per minute

Therefore, all of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.

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4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°

We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)

Substituting the values

Area = 1/2 × 3.4 × 6.9 × sin(21°)

Area = 11.73 × sin(21°)

Area = 11.73 ×  0.3583

Area = 4.2016

Rounding to the nearest 10th of a square centimeter .

Area = 4.20 cm²

Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.

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The amount of popcorn the bigger box holds than the smaller box depends on the dimensions of the two containers, so it cannot be determined without additional information.

The difference in the amount of popcorn the two containers hold depends on the volume of each container. Let's assume the volume of Amanda's popcorn container is V1 and the volume of Mary's popcorn container is V2.

If we know the dimensions of both containers, we can calculate their volumes using the formula V = l × w × h, where l is the length, w is the width, and h is the height of the container. Then, we can find the difference in the volumes of the two containers by subtracting V1 from V2.

However, the question does not provide any information about the dimensions of the two containers, so we cannot determine the difference in their volumes. Therefore, the main answer is that the amount of popcorn the bigger box holds than the smaller box cannot be determined without additional information.

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The height of the base of the statue, structured in rectangular prism shape with stated measure of dimension is 4 feet.

The volume of the rectangular prism will be given by the formula -

Volume = length × width × height

Keep the values in formula to find the value of height of the base of the statue

60 = 5 × 3 × height

Rearranging the equation in terms of height

Height = 60 × (5 × 3)

Multiplying the denominator on Right Hand Side

Height = 60/15

Divide the values

Height = 4

Hence the height is 4 feet.

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The formula to calculate surface area is 2(Length × Width) + 2(Length × Height) + 2(Width × Height) and the length, width, and height of the sandbox is required to calculate rectangular area.

To determine how much sand your cousin will need to fill the rectangular prism-shaped sandbox, we first need to calculate its volume. To do this, we need the dimensions of the sandbox (length, width, and height). The formula for the volume of a rectangular prism is:

Volume = Length × Width × Height

Once we have the volume, we can determine the amount of sand needed to fill the sandbox in cubic units.

To find out how much paint is needed to paint all six surfaces of the sandbox, we need to calculate its surface area. The formula for the surface area of a rectangular prism is:

Surface Area = 2(Length × Width) + 2(Length × Height) + 2(Width × Height)

Once we have the surface area, we can determine the amount of paint required, usually measured in square units. Note that the amount of paint needed also depends on the coverage rate of the paint, which is typically listed on the paint container.

Please provide the dimensions of the sandbox (length, width, and height) so I can provide specific calculations for the sand and paint required.

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Answer:

x = 13

Step-by-step explanation:

We Know

(5x - 6) + (8x + 17) must equal 180°

Find the value of x.

Let's solve

5x - 6 + 8x + 17 = 180

13x + 11 = 180

13x = 169

x = 13

So, the value of x is 13.

The closest amount to the total balance is option B, 695.00.

For Account A, the interest earned after 2 years is:

Interest = Principal * Rate * Time = 400 * 0.035 * 2 = 28

So the total balance in Account A after 2 years is:

Total A = Principal + Interest = 400 + 28 = 428

For Account B, the interest earned after 2 years is:

Interest = Principal * (1 + Rate/100)^Time - Principal = 250 * (1 + 3.25/100)^2 - 250 = 25.95

The total balance in Account B after 2 years is:

Total B = Principal + Interest = 250 + 25.95 = 275.95

The total balance in both accounts after 2 years is:

Total Balance = Total A + Total B = 428 + 275.95 = 703.95

The closest amount to the total balance is option B, 695.00.

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The expected population proportion,  with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:

Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%

Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

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Volumes of the cylinder are given by:

(A) (1) Volume = 2486.88 cubic in.

(2) Volume = 108518.4 cubic ft.

(3) Volume = 47608.68 cubic yd.

(B) (4) Volume = 508.68 cubic ft.

(5) Volume = 8490.56 cubic yd.

(6) Volume = 43407.36 cubic in.

(7) Volume = 9420 cubic ft.

(8) Volume of cylindrical flower vase = 1105.28 cubic in.

Surface Area of the Cylinder are given by:

(1) Surface Area = 113.04 square in.

(2) Surface Area = 1444.4 square ft.

(3) Surface Area = 678.24 square yd.

(4) Surface Area = 1130.4 square yd.

(5) Surface Area = 602.88 square in.

(6) Surface Area = 1055.04 square ft.

(7) Surface Area = 1570 square ft.

(8) Surface Area = 791.28 square yd.

(9) Surface Area = 326.56 square in.

We know that the volume of a cylinder with radius 'r' and height 'h' is given by,

V = 2πr²h

(A) (1) From the figure, radius = 6 in and height = 11 in.

So the volume = 2π(6)²*11 = 2486.88 cubic in.

(2) Radius = 24 ft. and height = 30 ft.

Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.

(3) Radius = 19 yd. and height = 21 yd.

Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.

(B) (4) Radius = 3 ft. and height = 9 ft.

Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.

(5) Radius = 13 yd. and height = 8 yd.

Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.

(6) Radius = 16 in. and height = 27 in.

Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.

(7) Radius = 10 ft. and height = 15 ft.

Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.

(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.

The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.

   Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,

S = 2πrh + 2πr²

(1) Radius = 2 in. and Height = 7 in.

Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.

(2) Radius = 10 ft. and Height = 13 ft.

Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.

(3) Radius = 6 yd. and Height = 12 yd.

Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.

(4) Radius = 9 yd. and Height = 11 yd.

Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.

(5) Radius = 6 in. and Height = 10 in.

Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.

(6) Radius = 8 ft. and Height = 13 ft.

Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.

(7) Radius = 10 ft. and Height = 15 ft.

Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.

(8) Radius = 6 yd. and Height = 15 yd.

Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.

(9) Radius = 4 in. and Height = 9 in.

Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.

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The quadratics that would not have 5 and -7 as zeros are (1) and (3)

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

Zeros: 5 and -7

This means that

x = 5 and x = -7

Rewrite as

x - 5 = 0 and x + 7 = 0

Multiply both equation

This gives

(x - 5)(x + 7) = 0

Rewrite as

f(x) = (x - 5)(x + 7)

When expanded, we have

f(x) = x² + 2x - 35

So, we have

(2) f(x) = x² + 2x - 35

(4) f(x) = 2(x + 7)(x - 5)

Hence, the quadratics that would not have 5 and -7 as zeros are (1) and (3)

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Answer:

X = 2² * 3² * 5³ * 7.

Step-by-step explanation:

140 = 2*2*5*7

15^2 = 3*5*3*5

So X = 2² * 3² * 5³ * 7

To find the prime factorization of X, we first need to simplify the expression.

Now, we can factor 140 and 225 into their prime factors:

So,

We can now use the distributive property to multiply these factors together:

Therefore, the prime factorization of X is:

The expression that shows how many beads are on the necklace in all is:

b + 12.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.

In the given question,

To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:

Start with the initial number of beads on the necklace, which is 12.

To this, add the number of beads Josie added, which is b.

Combine the two terms to form the final expression: 12 + b.

Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.

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To determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd, we need to check if it satisfies the properties of even and odd functions.

An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the y-axis, we get the same graph.

An odd function is a function that satisfies the property f(x) = -f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the origin (both x and y-axis), we get the same graph.

Let's start by checking whether f(x) is even:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with f(x), we can see that f(-x) = -f(x) only when sin(x) = 0.

This means that f(x) is an even function only when sin(x) = 0, which occurs when x = nπ (where n is an integer).

Now, let's check whether f(x) is odd:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with -f(x), we can see that f(-x) = -f(x) only when a^x = -a^x, which is not possible for any real value of a.

Therefore, f(x) is neither an even nor an odd function.
To determine whether the function f(x) = a^x - a^(-x) + sin(x) is even or odd, we can evaluate f(-x) and compare it to f(x).

An even function satisfies the condition f(-x) = f(x), while an odd function satisfies the condition f(-x) = -f(x).

Let's evaluate f(-x):
f(-x) = a^(-x) - a^(-(-x)) + sin(-x)
f(-x) = a^(-x) - a^x - sin(x)

Now, let's compare f(-x) to f(x):
f(-x) ≠ f(x) because f(x) = a^x - a^(-x) + sin(x)
f(-x) ≠ -f(x) because -f(x) = -a^x + a^(-x) - sin(x)

Since f(-x) is neither equal to f(x) nor -f(x), the function f(x) = a^x - a^(-x) + sin(x) is neither even nor odd.

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The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

Where every student offer at least one of the subjects, there are 4 students who offer all three subjects.

To find the number of students who offer only one subject, we can use the formula:

number of students offering only one subject = total number of students offering the subject - number of students offering both subjects

For math, there are 22 students offering math and 5 offering both math and biology, so the number of students offering math only is:

22 - 5 = 17

Similarly, for physics and biology, the numbers of students offering the subjects only are:

14 - 7 = 7 (physics)
16 - 5 = 11 (biology)

To find the number of students offering all three subjects, we can use the formula:

number of students offering all three subjects = total number of students offering at least one subject - number of students offering only one subject in each subject + number of students offering no subject

We know that there are 7 students offering at least one subject. To find the number of students offering no subject, we can subtract this from the total number of students:

39 - 7 = 32

Now we can plug in the numbers:

number of students offering all three subjects = 7 - 17 - 7 - 11 + 32
= 4

Therefore, there are 4 students who offer all three subjects.

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Based on the given information that angles a and d are equal, the value of x is determined to be -6.

To find the value of x in the given scenario, we can equate the measures of the angles using the given information:

m< a = 3x

m< d = 4x + 6

Since angles a and d are stated to be equal, we can set up the equation:

3x = 4x + 6

To solve for x, we subtract 3x from both sides:

0 = x + 6

Next, we subtract 6 from both sides:

-6 = x

Therefore, the value of x is -6.

In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.

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Let's denote the total distance traveled by the object as `d` and time as `t`.

We can use the given information to set up a system of equations:

When t = 10.0 seconds, d = 50.0 meters

50.0 = a(10.0)^2 + b(10.0) + c         (Equation 1)

When t = 20.0 seconds, d = 200.0 meters

200.0 = a(20.0)^2 + b(20.0) + c          (Equation 2)

When t = 0 seconds, d = 0 meters

0 = a(0)^2 + b(0) + c           (Equation 3)

Simplifying Equation 3, we get c = 0.

Substituting c = 0 in Equations 1 and 2, we get:

50.0 = 100a + 10b               (Equation 4)

200.0 = 400a + 20b              (Equation 5)

We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:

From Equation 4, we get:

10b = 50 - 100a

b = 5 - 10a

Substituting this value of `b` in Equation 5, we get:

200.0 = 400a + 20(5 - 10a)

200.0 = 400a + 100 - 200a

200.0 = 200a + 100

100.0 = 200a

a = 0.5

Substituting this value of `a` in Equation 4, we get:

50.0 = 100(0.5) + 10b

50.0 = 50 + 10b

b = 0

Therefore, the quadratic function that models the total distance traveled by the object is:

[tex]d = 0.5t^2[/tex]

To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:

[tex]d = 0.5(30.0)^2[/tex]

d = 450.0 meters

Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.

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The average amount of books read per student according to the histogram is given as follows:

1.27 books.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The histogram shows the number of times for each observation, hence:

Hence the mean is calculated as follows:

M = (7 x 0 + 9 x 1 + 6 x 2 + 4 x 3)/(7 + 9 + 6 + 4) = 1.27 books.

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Answer:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the present balance ($1430.00)

r = the annual interest rate (2% or 0.02)

n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)

t = the number of years (8 years in this case)

Plugging in the values into the formula:

A = 1430(1 + 0.02/1)^(1*8)

Simplifying the equation:

A = 1430(1.02)^8

Using a calculator or performing the calculations manually:

A ≈ 1430(1.171661)

A ≈ 1674.02

the balance after 8 years will be approximately $1674.02.

The equation of the line that passes through (1, 2) and (a) having a slope of 2/3 is y = (2/3)x + 4/3, (b) Having an undefined slope is x = 1, (c) having slope m = 0 is y = 2 (d) point (2, 3) also lies on the line is y = x + 1.

a) To find the equation of a line with slope 2/3 passing through (1,2), we can use the point-slope formula:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (2/3)(x - 1)
Expanding and simplifying:
y = (2/3)x + 4/3
So the equation of the line is y = (2/3)x + 4/3.

b) To find the equation of a line with an undefined slope passing through (1,2), we know that this line must be vertical. The equation of a vertical line passing through (1,2) can be written as:
x = 1

So the equation of the line is x = 1.

c) To find the equation of a line with slope m=0 passing through (1,2), we know that this line must be horizontal. The equation of a horizontal line passing through (1,2) can be written as:
y = 2
So the equation of the line is y = 2.

d) To find the equation of a line passing through (1,2) and (2,3), we can use the point-slope formula again:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (3 - 2)/(2 - 1)(x - 1)
Simplifying:
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x + 1
So the equation of the line is y = x + 1.

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A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:

(x, y)                               →            (-y, x)

Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)

Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)

Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)

Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)

Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)

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