MODELING REAL LIFE The volume of the largest of the six pyramids constructed by the Norte Chico people in Caral, Peru, is about 4,500,000 cubic feet. What is the height of the pyramid? A pyramid with the height h feet. Length of 8 h minus 30 feet. Width of 8 h plus 20 feet. Height: ft

Answers

Answer 1

The height of the pyramid whose volume is already given would be = 1,440,000 ft

How to calculate the height of the given pyramid?

To calculate the height of the pyramid, the formula of the Volume of the pyramid should be used.

Volume = 1/3lwh

where l = base length = 8h-30 ft= 3.75 ft

w = base width= 8h+20 ft = -2.5 ft

h = h ft

The volume of the pyramid = 4,500,000 cubic feet

4,500,000 = 1/3 × (3.75)(-2.5)h

Make h the subject of formula;

h = 4500000×3/3.75×(-2.5)

h = 13500000/9.375

h = 1,440,000 ft.

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Related Questions

The equation ( x + 6)^2 + ( y + 4) ^2 = 36 models the position and range of the source of a radio signal.

1. Where is the signal located?

2. What is the range of the signal? Only enter numerical values. ​

Answers

1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).

What is the range of the signal?

2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).

To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.

In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.

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A local charity held a crafts fair selling donated, handmade items. Total proceeds from the sale were $1,950. A total of 150 items were sold, some at $5 each and the rest at $25 each.


How many items were sold at $25 ?

Answers

By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.

In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:

x + y = 150 (Equation 1)

5x + 25y = 1950 (Equation 2)

Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.

Let's rearrange Equation 2 to solve for y:

5x + 25y = 1950

25y = 1950 - 5x

y = (1950 - 5x)/25

Now, we can substitute this expression for y into Equation 1:

x + (1950 - 5x)/25 = 150

Simplifying this equation, we get:

25x + 1950 - 5x = 3750

20x = 1800

x = 90

Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:

y = 150 - x

y = 150 - 90

y = 60

Hence, 60 items were sold at $25 each.

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HLEP me please with math

Answers

For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

Explain about the scale factor:

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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Solve for X, please write an explanation.

Answers

Step-by-step explanation:

2x+20  and 2x-4  are supplementary angles...they form a straight line and thus = 180 degrees when added together

2x+20      +    2x-4     = 180          simplify

4x + 16 = 180                               subtract 16 from both sides

4x  = 164                                     divide both sides by 4

x = 41 degrees

Alfred buys a car for £13960 which depreciates in value at a rate of 0.75% per year.

Work out how much Alfred's car will be worth in 12 years.

Answers

Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

unit 7: geometry homework 3: angle relationship and algebra

Answers

Angle relationship and algebra are closely related in geometry, as we often use algebraic expressions to represent angle measures and their ratios.

How to express the relationship between angular relations and algebra?

For example, if we are given that angle A and angle B are complementary (meaning that their sum is 90 degrees), we can write an algebraic equation:

A + B = 90

Similarly, if we know that angle A is three times larger than angle B, we can write:

A = 3B

We can use algebraic equations to solve for unknown angle measures or to find relationships between angles.

For example, let's say we are given that angle A is complementary to angle B, and that angle B is twice as large as angle C. We can write:

A + B = 90B = 2C

We can substitute the second equation into the first equation to get:

A + 2C = 90

This equation relates the three angles A, B, and C. We can use algebra to solve for any of the unknown angles, given the measures of the others.

Therefore, algebraic equations and expressions are an important tool in understanding and analyzing angle relationships in geometry.

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Which statement about statistical questions is TRUE?

The answer must be a word.
The answer must be a number.
The answers will vary from person to person.
The answers will be the same no matter who you ask.

Answers

The answer is: The answers will vary from person to person.

Which statement about statistical questions is TRUE?

The statement that is true about statistical questions is that the answers will vary from person to person. Statistical questions are questions that can be answered using data and statistics. These questions involve gathering information from a population or a sample of that population, analyzing the data, and making conclusions based on the results. Since different people may have different data and different ways of analyzing that data, the answers to statistical questions can vary. This is why it is important to consider the sample size, the sample method, and the statistical methods used to analyze the data when interpreting the results of statistical questions. A well-designed study can help minimize variability and improve the accuracy of the results, but some degree of variability is still expected due to natural differences in the data collected by different individuals or groups

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what minus 1 1/2 equals 3 3/4

Answers

Answer:

5 1/4

Step-by-step explanation:

please help me question 3&4​

Answers

3. The area of the shaded region is 5x² + 2x - 3

4. The area of the shaded region is 18x² + 21x + 6

Calculating Area of Shaded part

From the question, we are to determine the area of the shaded region in the given diagrams.

3.

Area of the shaded region = {[(x - 1) + (2x - 1)] × [(x + 1) + (x + 1)]} - (x + 1)(x - 1)

Area of the shaded region = [(x - 1 + 2x - 1) × (x + 1 + x + 1)] - (x + 1)(x - 1)

Area of the shaded region = [(3x - 2) × (2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = [(3x - 2)(2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = (6x² + 6x - 4x - 4) - (x² - x + x -1)

Area of the shaded region = 6x² + 6x - 4x - 4 - x² + x - x + 1

Area of the shaded region = 6x² + 2x - 4 - x² + 1

Area of the shaded region = 6x² - x² + 2x - 4  + 1

Area of the shaded region = 5x² + 2x - 3

4.

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2(1/2(6x +4) × (4x + 2))]

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2((3x + 2)(4x + 2))]

Area of the shaded region = [24x² + 12x + 16x + 8] - [1/2(12x² + 6x + 8x + 4)]

Area of the shaded region = (24x² + 12x + 16x + 8) - (6x² + 3x + 4x + 2)

Area of the shaded region = (24x² + 28x + 8) - (6x² + 7x + 2)

Area of the shaded region = 24x² + 28x + 8 - 6x² - 7x - 2

Area of the shaded region = 24x² - 6x² + 28x - 7x + 8 - 2

Area of the shaded region = 18x² + 21x + 6

Hence, the area is 18x² + 21x + 6

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Select the correct answer. Sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each. Which expression shows the total area of these five rooms? A. (3 × 14^2) + (2 × 17^2) B. (2 × 14^3) + (2 × 17^2) C. (3 × 17^2) + (2 × 14^2) D. (3 × 14^2) × (2 × 17^2) Reset Next

Answers

The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.

What is expression?

An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.

In the given question,

C. (3 × 17²) + (2 × 14²)

To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.

For the three rooms with sides of 14 feet each, the area of each room is:

14^2 = 196 square feet

So the total area of these three rooms is:

3 × 196 = 588 square feet

For the two rooms with sides of 17 feet each, the area of each room is:

17^2 = 289 square feet

So the total area of these two rooms is:

2 × 289 = 578 square feet

Therefore, the total area of all five rooms is:

588 + 578 = 1166 square feet

Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.

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Can someone help me with this, please?

Learning Task 2: Try to solve the following problem. Use the block model

to help you. Write your answer in your notebook.


1) Ruben can paint square meters per hour. At the same rate, how

many square meters can he paint in an hour.


1

2 6


1

2 2


2) The lot has a length of meters and a width of meters. The

piece of lot per square unit is ₱ 850. 0. What is the total value of the lot?

Answers

Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.

Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour

help please without guessing ?//

Answers

Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

April is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her balloon payment at the end
of 7 years?
OA. $173,819.97
OB. $170,118.49
OC. $225,368.29
OD. $170,245.98
SUBMIT

Answers

The balloon payment at the end of 7 years would be $173,819.97, which is option A.

How to find the balloon payment at the end of 7 years

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV is the present value of the loan (the loan amount)n is the total number of paymentsr is the monthly interest rate

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

B is the remaining balancePV is the initial loan amount r is the monthly interest rateP is the monthly payment t is the number of payments made

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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a scientist claims that the mean gestation period for a fox is more than 48.9 weeks. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g

Answers

The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.

If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.

The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.

Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.

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the average car can go 25 miles on one gallon of gas. You can write an equation to show the relationship between the amount of gas you buy and how far you can travel

Answers

Answer:

Step-by-step explanation:

the inword

what is the range and domain of y = 3x^2 + 2?

Answers

The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

Define range!

In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).

According to question:

The given function is y = 3x² + 2.

The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.

Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.

The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).

Since the minimum value of the function is 2, the range of the function is [2, ∞).

Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

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PLEASE HELP!! ITS TIMED! WILL GIVE BRAINIEST TO THE FIRST CORRECT ANSWER!


Elijah bought earrings to give to his mother for her birthday. The earrings are in a case
shaped like a rectangular prism that is 2 inches long, 1½ inches wide, and 1 inches tall. He
doesn't want his mother to guess what the gift is, so he put the case in a larger, cube-shaped
gift box. The gift box is 4 inches along each edge.
What is the volume of the extra space left in the gift?

Answers

Answer:

The answer is 59 ½

Step-by-step explanation:

4×4×4-2×1 ½×1 ½

= 64 - 2× 3/2 × 3/2

= 64 - 9/2

= 128/2 - 9/2

= 119/2

= 59 ½ in3

Hope this helped :)

a quiz has 20 multiple choice questions. each question has four possible choices. if a student makes a random guess on each question, what is the expected number of correct answers?

Answers

If a quiz has 20 multiple choice questions, then the expected number of correct answers is 5.

For each question, there are 4 possible choices, and only 1 of them is correct.

So, the probability of randomly guessing the "correct-answer" for any  question is = 1/4 = 0.25,

Each question is an independent event, we use the concept of linearity of expectation to calculate the expected number of correct answers for all 20 questions.

The "Expected" number of correct answers for a "single-question" is  probability of guessing it correctly, which is 0.25,

The "Expected-Number" of correct answers for 20 questions is the sum of the expected number of correct answers for each question,

⇒ Expected number of correct answers = (Probability of guessing a single question correctly) × (Number of questions),

Substituting the values,

We get,

⇒ Expected number of correct answers = 0.25 × 20,

⇒ Expected number of correct answers = 5

Therefore, the expected number of correct answers when making "random-guesses" on all 20 multiple choice questions is 5.

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PLEASE HELP AND SHOW YOUR WORK! ALSO EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!

Answers

Answer:3.6

Step-by-step explanation:

Step 1: Calculate

We calculate the square root of 13

√13 = 3.60555127546399

Step 2: simplify

Reduce the tail of the answer above to two numbers after the decimal point which is :

3.60

Step 3: Round

Round 3.60 so you only have one digit after the decimal point to get the answer:

3.6

The square root of 13 to the nearest tenth is 3.6

Explanation: By calculating the square root of 13 in a calculator the answer is 3.60555127546. The tenth in this number is 6 so you look to the number beside 6 and it is 0. Therefore the answer to this problem is 3.6

every morning, laura practices shooting basketball free throws. she doesn't shoot a fixed amount, instead she keeps shooting free throws until she makes 12. suppose laura is an 82% free throw shooter. let x be how many free throws laura will miss tomorrow morning. then x has a negative binomial distribution. what is a trial? [ select ] what is a success? [ select ] how many successes are required? r

Answers

The probability of Laura missing 3 free throws before making 12 is approximately 0.0037 or 0.37%.
The basketball free throw.

A success would be considered when Laura makes a free throw.

A failure would be when Laura misses a free throw.
The negative binomial distribution is a probability distribution that calculates the probability of obtaining a certain number of failures before a specified number of successes occur.

The specified number of successes is 12, and the number of failures is represented by the variable x.
To calculate the probability of x failures, we need to know the probability of a single failure.

Since Laura is an 82% free throw shooter, the probability of her missing a free throw is 18%.
We can use the formula for negative binomial distribution to determine how many failures are required before 12 successes are achieved.

The formula is:
[tex]P(X = x) = (r+x-1)C(x) \times p^r \times (1-p)^x[/tex]
Where:
P(X = x) is the probability of having x failures before achieving 12 successes
r is the number of successes required (in this case, 12)
p is the probability of a single success (in this case, 0.82)

[tex](r+x-1)C(x)[/tex]is the combination of r+x-1 choose x

For example, if we want to find the probability of Laura missing 3 free throws before making 12, we will plug in x = 3, r = 12, p = 0.82 into the formula:

[tex]P(X = 3) = (12+3-1)C(3) \times 0.82^1^2\times (1-0.82)^3[/tex]
[tex]P(X = 3) = 14C3 \times 0.082^1^2 \times 0.18^3[/tex]
[tex]P(X = 3) = 364 \times 0.000018 \times 0.005832[/tex]
P(X = 3) = 0.000037
Overall, the trial in this scenario is each individual attempt at a free throw, the success is making a free throw, and 12 successes are required before the shooting session is considered complete.

The negative binomial distribution is used to calculate the probability of obtaining a certain number of failures before achieving the specified number of successes.

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'x' follows a negative binomial distribution with 'r' being 12 successes.

In this scenario, a trial refers to each individual attempt at shooting a free throw. A success is when Laura successfully makes a free throw. To achieve her goal of making 12 free throws, she needs to have 11 successes (since she will miss on the final attempt). Therefore, r = 11.

In this context, a "trial" refers to each individual attempt Laura makes to shoot a basketball free throw. A "success" is when Laura makes a free throw (hits the basket), while a "failure" (not mentioned in the question) would be when Laura misses a free throw. Since Laura keeps shooting free throws until she makes 12, the number of successes required, denoted as 'r', is 12.

Therefore, 'x' follows a negative binomial distribution with 'r' being 12 successes.

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Need help ASAP

there are 600 poetry books at the library.Of the poetry books,8 1/2% are for children.How many poetry books at the library are for children

Answers

The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

What is number?

Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.

8 1/2% is equal to 0.04.

To calculate the number of poetry books for children, multiply 0.04 by 600.

0.04 x 600 = 24

To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.

In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.

To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.

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answer the following ​

Answers

Answer:

6 inches

Step-by-step explanation:

Baseball Field Problem
Find the amount of fencing, dirt, and sod needed to rebuild the baseball field.
380 to the fence
G'
is
Grass
87
Cr=10
Gras
Grass
Note: Not drown to sale
Fence
Dut
IS'

Answers

The amount of fencing, dirt and sod for the baseball field are;

Length of fencing ≈ 1410.5 feet

Area of the sod ≈ 118017.13 ft²

Area of of the field covered with dirt ≈ 7,049.6 ft²

What part is the fencing of a baseball field?

The fencing of a baseball field is the outer enclosure of the field, which typically, is located along the outfield boundary.

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Area of a circle = π × r²

Circumference of a circle = 2 × π × r

Where r is the radius of the circle

The area of a quarter of a circle is therefore; Area of a circle ÷ 4

The perimeter of a quarter of a circle is; The perimeter of a circle ÷ 4

Fencing = (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

The fencing ≈ 1410.5 feet

Grass = π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

The area covered by the sod is about 118017.13 square feet

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

The area occupied by the dirt is about 7049.6 square feet

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Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.

Answers

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

What is the equation?

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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Determine the density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm3.

Answers

The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.

What do you mean by the density of an object?

Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.

Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:

Density = Mass/Volume

Substituting the given values, we get:

Density = 6 grams/12 cm³

Density = 0.5 grams/cm³

Therefore, the density of the sample is 0.5 grams/cm³.

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Amy is sewing some pants for herself. This is the rule for how much fabric she needs to buy. • Measure from your waist to the finished length of thepants • Double this measurement • Add 8inches 1. Amy’s measurement from her waist to the finished length of the pants is 35inches. How many inches of fabric does sheneed?

Answers

Amy needs 78 inches of fabric for her pants if she follows the given rule.

Define inches ?

An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.

To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.

Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.

Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.

Therefore, Amy needs 78 inches of fabric for her pants.

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Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.)
(a)
3/4

Answers

The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

What is coterminal angles ?

Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).

To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).

One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:

3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π

Simplifying, we get:

3/4 + 2π = (3π + 4)/4

Therefore, one positive coterminal angle is (3π + 4)/4 radians.

One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:

3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π

Simplifying, we get:

3/4 - 2π = (-5π + 4)/4

Therefore, one negative coterminal angle is (-5π + 4)/4 radians.

Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

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write an integral that quantifies the change in the area of the surface of a cube when its side length quadruples from s unit to 4s units.

Answers

Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3

Graph Y = 1/2x - 4 on the coordinate plane

Answers

The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Describe Coordinate Plane?

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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Find the radius of convergence, R, of the series. [infinity]

n = 2
(x + 8)n
8n ln(n)

Answers

The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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