Mathematics College

## Answers

**Answer 1**

The **point **should be withdrawn from the **data set **to contain a diagram illustrating the **function **will be (3, 1) or (3, 3).

What is a function?

Functions may be encountered throughout **mathematics **and are vital for the evolution of meaningful **connections**.

If the number of values of the variable 'y' is **more **than **one **for a given value of 'x', then it is **not **a **function**.

For a function, the **number **of values of 'y' should be **one **for each value of 'x'.

From the **graph**, at x = 3, the value of 'y' will be 1 and 3. Then the **coordinates **are (3, 1) and (3, 3).

The **point **should be withdrawn from the **data set **to contain a diagram illustrating the **function **will be (3, 1) or (3, 3).

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## Related Questions

pleaseeeeeeeeee 3 4/7 -2 1/5 rounded to the nearest half

### Answers

3 4/7 -2 1/5 **rounded **to the **nearest half** is simplified as: 1½

How to Round to the Nearest Half?

To **round **3 and 4/7 - 2 and 1/5 to the **nearest half**, we first need to convert the mixed numbers to improper **fractions**:

3 and 4/7 = (3 x 7 + 4)/7 = 25/7

2 and 1/5 = (2 x 5 + 1)/5 = 11/5

So the expression becomes:

25/7 - 11/5

To simplify this, we need to find a common denominator. The least common multiple of 7 and 5 is 35:

(25/7) x (5/5) = 125/35

(11/5) x (7/7) = 77/35

So the expression becomes:

125/35 - 77/35 = 48/35

To round to the **nearest half**, we need to look at the **fraction **in terms of eighths. To do this, we multiply both the numerator and denominator by 8:

(48/35) x (8/8) = 384/280

Next, we divide the numerator by the denominator and get:

384 ÷ 280 = 1 and 104/280

To **round **to the **nearest half**, we look at the **fraction **104/280 in terms of halves, which is:

(104/280) x (2/2) = 208/560

We can simplify this to:

208/560 = 13/35

Since 13/35 is more than half of a whole (which is 1/2), we **round up **to the **nearest half**. Therefore:

3 and 4/7 - 2 and 1/5 **rounded **to the **nearest half **is 1 and 1/2.

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g problems 25, 26, and 27 of the rhind papyrus are as follows: problem 25. a quantity and its 1 2 added together become 16. what is the quantity? problem 26. a quantity and its 1 4 added together become 15. what is the quantity? problem 27. a quantity and its 1 5 added together become 21. what is the quantity? solve each of these problems by false position, expressing the answers in unit fractions.

### Answers

After solving each of these problems by **false position**, the quantities of problems 25, 26, and 27 are 122/15, 3/20, and 91/20.

Problem 25: Let x be the quantity. Then we have:

x + 1/2 = 16

To solve this equation by false position, we start with a guess of x = 16/2 = 8, since the **quantity **is likely to be close to half of the **sum**. We substitute this value into the equation and find the error:

8 + 1/2 = 8.5

16 - 8.5 = 7.5

Since the error is **negative**, we need to increase our guess by adding a **unit fraction**. The unit fraction that we add is 1/7.5 = 2/15 since the error is 2/15 of the quantity. Thus, our new guess is:

x = 8 + 2/15 = 122/15

We can check that this value satisfies the original equation:

122/15 + 1/2 = 16

Problem 26: Let x be the quantity. Then we have:

x + 1/4 = 15

To solve this equation by false position, we start with a guess of x = 15 - 1/4 = 59/4, since the quantity is likely to be close to the **difference**. We substitute this value into the equation and find the error:

59/4 + 1/4 = 15

15 - 59/4 = -1/4

Since the error is negative, we need to **increase **our guess by adding a unit fraction. The unit fraction that we add is 1/(-1/4) = -4, since the error is 4 times the quantity. Thus, our new guess is:

x = 59/4 - 4 = -5/4

This value is negative, which means that our **initial **guess was too large. We need to decrease our guess by subtracting a unit fraction. The unit fraction that we **subtract **is -1/(-5/4) = 4/5, since the error is 4/5 of the quantity. Thus, our new guess is:

x = -5/4 + 4/5 = 3/20

We can check that this value satisfies the original equation:

3/20 + 1/4 = 15

Problem 27: Let x be the quantity. Then we have:

x + 1/5 = 21

To solve this equation by false position, we start with a guess of x = 21 - 1/5 = 104/5, since the quantity is likely to be close to the difference. We substitute this value into the equation and find the **error**:

104/5 + 1/5 = 21

21 - 104/5 = -4/5

Since the error is negative, we need to increase our guess by adding a unit fraction. The unit fraction that we **add **is 1/(-4/5) = -5/4 since the error is 5/4 of the quantity. Thus, our new **guess **is:

x = 104/5 - 5/4 = 91/20

We can check that this value satisfies the original equation:

91/20 + 1/5 = 21.

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The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.025 failure per hour.(a) What is the probability that the instrument does not fail in an 8-hour shift?(b) What is the probability of at least one failure in a 24-hour day?Round your answers to four decimal places (e.g. 98.7654).

### Answers

(a) The **probability** that the instrument does not** fail** in an **8-hour shift** is 0.7183 or 71.83%.

(b) The **probability** of at least one **failure** in a **24-hour day** is 0.999 or 99.9%.

Poisson Distribution: Failure Probability

The number of failures of a **testing instrument** in a given time period is modeled by a **Poisson** distribution with a rate parameter equal to the mean number of failures per unit time.

(a) To find the probability that the** instrument **does not fail in an 8-hour shift, we can use the **cumulative distribution function** (CDF) of the Poisson distribution. The CDF gives the probability that the number of failures is less than or equal to a given value. In this case, we want to find the probability that there are 0 failures in an **8-hour shift**, so the CDF can be expressed as:

P(X ≤ 0) = e^(-0.025 * 8) = 0.7183

So, the **probability** that the instrument does **not fail **in an 8-hour shift is 0.7183 or 71.83%.

(b) To find the **probability** of at least** one failure **in a 24-hour day, we can subtract the probability of 0 failures from 1. That is,

P(X ≥ 1) = 1 - P(X ≤ 0) = 1 - e^(-0.025 * 24) = 0.999

So, the probability of at least one failure in a 24-hour day is 0.999 or 99.9%.

Note: In these calculations, we use the formula for the cumulative **distribution function** of the Poisson distribution, which is:

P(X ≤ k) = e^(-lambda) * (lambda^k / k!)

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What is 6 times 2 in multiplication

### Answers

**Answer: 12**

**Step-by-step explanation:**

2+2+2+2+2+2= 2*6= 12

12 because skip count 6,12 see u skipped counted 2 times I learned this

A line has a slope of 7 and passes through the point (-1, -8). Write its equation in slope- intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

### Answers

y = 7x + 15 is the equivalent equation of the line in slope intercept form.

Equation of a line in slope-intercept form

The equation of a line in** slope intercept form** is expressed according to the equation below:

y = mx + b

where:

m is the slope

b is the intercept

Given that **slope** is a 7 with the point (-1, 8), the equation is;

y - 8 = 7(x+1)

In **slope intercept **form:

y - 8 = 7x + 7

y = 7x + 7 + 8

y = 7x + 15

Hence the **equatio**n in **slope- intercept** form is y = 7x + 15

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please answer part a and b

### Answers

**a) At least 75%** of the home buyers' age is between 25 years old and 69 years old.

**b) At least 84% **of the home buyer's age are between 19.5 years old and 74.5 years old.

What does Chebyshev’s Theorem state?

When the distribution is **not normal,** Chebyshev's Theorem is used. It states that:

**At least 75% **of the measures are within 2 standard deviations of the mean.**At least 84.5% **of the measures are within 2.5 standard deviations of the mean.**At least 89%** of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures** within k** standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].

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There are 15,000 average passengers on domestic flights daily.

1/20 of the passengers are tourists and 1/15 of the tourists are travel

bloggers. How many tourist passengers on domestic flights are

travel bloggers?

### Answers

The number of **travel** **bloggers** is 1000.

What is a fraction?

A **fraction** is written in the form of a **numerator** and a **denominator** where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of **passengers** = 15,000

The number of **travel** **bloggers**.

= 1/15 of 15,000

= 1/15 x 15,000

= 1,000

Thus,

1000 are **travel** **bloggers**.

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A basketball player makes an annual of $2,300,000. A charitable organization states that it can feed 1 child in a developing country for 43¢ per day. The basketball player donates 10% of his annual salary to this organization. How many children will his donation feed for 1 day?

### Answers

By donating** 10% **of the salary a basketball player donates money that can** **feed **534883 children **per day.

**What is percentage?**

A value or **ratio** that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a **percentage** of a number, we should divide it by its entirety and then multiply it by 100. The **proportion** therefore refers to a component per hundred.

The annual income of basketball player is $2,300,000.

The cost to feed 1 child is 43 cents per day.

The basket ball player donates 10% of his annual salary.

Calculate the **percentage** of salary donated by using the formula -

Amount Donated = 10% of Annual income

Plug in the values in the** equation** -

Amount Donated = 10/100 × 2,300,000

Amount Donated = $2,300,00

The amount donated is $2,300,00.

**Convert **dollar to cents -

$1 is equivalent to 100 cents

$2,300,00 is equivalent to 2,300,00 × 100 = 2,300,0000 cents

The number of children that can be fed -

Number of children = Amount donated / Amount needed for 1 child

Substitute the values in the **equation **-

Number of children = 2,300,0000 / 43

Number of children = 534883.721 ≈ 534883 children

Therefore, 534883 children can be fed.

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10. Select all expressions equivalent to 11 11. 11.

113

D 35.36

E 11¹ 11²

B 311

11¹. 11³

.

### Answers

The **expressions **that are **equivalent **are 11³, 11¹. 11². Options A and E

What are index forms?

**Index forms **are defined as mathematical forms of writing numbers that are two large or small in simpler forms.

They are also called standard forms or **scientific notation**.

It is also described as the exponent or power that is raised to a number or a variable.

Examples of index forma are;

2³ representing 2 in three places

3² representing 3 in two places

5³ representing 5 in three places

From the information given, we have that;

11 11. 11,

Hence, it is number 11 in three places 11³

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y=1/4x+1, y=-1/4x+1, y=-1/4-1

graph them on a picture

### Answers

The **solution** for the given equations is (0, 1) and the graph for the given equations is plotted below.

What is the graph?

**Graph** is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given **equations** are y=1/4 x+1 and y= -1/4 x+1.

Substitute x= 0, 1, 2, 3, 4,....in the equation y=1/4 x+1 , we get

y=1, 1.25, 1.5, 1.75, 2,....

So, the coordinate points are (0, 1), (1, 1.25), (2, 1.5), (3, 1.75) and (4, 2)

Substitute x= 0, 1, 2, 3, 4,....in the equation y= -1/4 x+1 , we get

y= 1, 0.75, 0.50, 0.25, 0

So, the **coordinate** points are (0, 1), (1, 0.75), (2, 0.50), (3, 0.25) and (4, 0)

So, the solution for the equations is (0, 1)

Therefore, the **solution** for the given equations is (0, 1) and the graph for the given equations is plotted below.

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Figure B is a scaled copy of Figure A.

What is the scale factor from Figure A to Figure B?

### Answers

From **Figure **A to Figure B, there will be a 1/3 **scale factor**.

What is dilation?

**Dilation **is the process of increasing the size of an item without affecting its form. Depending on the **scale factor**, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Figure B is a **scaled **copy of Figure A.

The **scale factor **from Figure A to Figure B is given as,

Scale factor = 3 / 9

Scale factor = 1/3

The **scale factor **from Figure A to **Figure **B will be 1/3.

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Answer these inter-related questions. Give only the numbers.

A) What is 145% of 600? Answer:

B) A town had a population of 600 two decades ago. Since then, there has

been a 45% increase. What is the population now? Answer:

C) A town has a population of 870, which is 145% of its population from 2

decades ago. What was the population then? Answer:

D) A town has 870 people. This is after a 45% increase since 2 decades ago.

What was the population before this change? Answer:

### Answers

A) 145% of 600 would be, 870

B) **Population **would be 870.

C)** **The population from two **decades **ago was 600.

D) The population before the change was 600

**What is Percentage?**

To compute a **percentage**, divide the value by the entire **amount **and multiply the result by 100. A **percentage **is a quantity or **ratio **that is stated as a **fraction **of one hundred. The percent **sign**, "%," is **frequently **used to represent it.

A) 145% of 600 is equal to 870. You can **calculate **this by multiplying 600 by 1.45:

600 * 1.45 = 870

B) If there was a 45% **increase **in the **population **since two decades ago, the current population would be, 600 * 1.45 = 870.

C) If the **current population **of a town is 870, which is 145% of its population from two decades ago, we can find the population from two decades ago by dividing 870 by 1.45:

870 / 1.45 = 600

So, the **population **from two **decades **ago was **600.**

D) If the **current population **of a town is 870 and it has gone through a 45% **increase **since two decades ago, we can find the population before this **change **by dividing 870 by 1 + 0.45 = 1.45:

870 / 1.45 = 600

So, the **population before **the **change **was 600.

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Suppose the data below represent, in thousands, the type of health insurance coverage of people by age. Determine and . Are the events "18 years old" and "no health insurance" independent?

### Answers

**Answer:ans A**

**Step-by-step explanation:**

please help i might give brainlist

### Answers

The **conversion factor** for liters to **gallons** is 1 gallon / 3.8 liters

What is an equation?

An equation is an expression that shows the **relationship** between two or more numbers and variables using **mathematical operations**. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

1 gallon = 3.8 liters

**Conversion factor **for liters to gallons = 1 gallon / 3.8 liters

The **conversion factor** is 1 gallon / 3.8 liters

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Please help!! Domain: -3 5 3 -5

Range: 6 -2 1

### Answers

The **ordered pair **is not a function

How to complete the statement

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

**Domain**: -3 5 3 -5Range: 6 -2 1

From the figure, we can see that

The **x values **-3 and 5 have the same value of 6

This means that the **relation** is no a function

This is so because for a relation to be a function, the **output values** must be unique

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labor (l) total product (tp) 0 0 1 150 2 320 3 510 4 660 5 800 using the data in the table, the marginal product of labor is highest if the number of workers is closest to but not more than:

### Answers

The number of **workers **that is closest to but not more than the point of **highest **MPL is 3. and the number of workers resulting in the highest level of average product of labor is also closest to 3.

To find the **marginal **product of labor, we need to calculate the additional output produced by each additional unit of labor.

We can calculate this by finding the **change **in the total product (TP) for each additional unit of labor. The table gives us the following information:

When there are 0 workers, TP = 0

When there is 1 worker, TP = 150

When there are 2 workers, TP = 320

When there are 3 workers, TP = 510

When there are 4 workers, TP = 660

When there are 5 workers, TP = 800

Using this information, we can calculate the marginal **product **of labor (MPL) as follows:

MPL of the 1st worker = TP of 1 worker - TP of 0 workers = 150 - 0 = 150

MPL of the 2nd worker = TP of 2 workers - TP of 1 worker = 320 - 150 = 170

MPL of the 3rd worker = TP of 3 workers - TP of 2 workers = 510 - 320 = 190

MPL of the 4th worker = TP of 4 workers - TP of 3 workers = 660 - 510 = 150

MPL of the 5th worker = TP of 5 workers - TP of 4 workers = 800 - 660 = 140

We can see that the highest marginal product of labor is 190, which **occurs **when there are **3 workers**. Therefore, the number of workers that is **closest **to but not more than the **point **of highest MPL is 3.

complete question:

1. Using the data in the table, the number of workers resulting in the highest level of average product of labor is closest to:

Group of answer choices

3

4

5

Cannot be determined from the information given.

2. Using the data in the table, the marginal product of labor is highest if the number of workers is closest to but not more than:

Group of answer choices

3

4

2

Cannot be determined from the information given.

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Part C

Why is it useful to factor polynomial expressions for a given scenario?

### Answers

The reason why it is **useful **to** factor polynomial expressions** for a given scenario is to solve or simplify the equation.

Why are polynomial expressions factorized ?

**Factoring polynomial expressions** is **useful **in a variety of mathematical scenarios because it can simplify complex expressions and make them easier to work with. By factoring polynomials, you can find the roots of an equation, which are the values that make the equation equal to zero.

In conclusion, factoring polynomial expressions can be a powerful tool in simplifying complex **mathematical expressions**, solving equations, understanding relationships between expressions, and finding common solutions.

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Use the information given in the figure to find the length EC. If applicable, round your answer to the nearest whole number.

The lengths on the figure are not drawn accurately.

### Answers

The value of the **length** of EC to the nearest **whole number** is 78 units.

What is Pythagoras Theorem?

According to Pythagoras's Theorem, the square of the **hypotenuse** side in a right-angled triangle is equal to the sum of the squares of the other two sides. **Perpendicular**, Base, and Hypotenuse are the names of this triangle's three sides. The hypotenuse in this case is the longest side since it forms the reverse of a 90° angle. When a right triangle's sides (let's say, a, b, and c) positive integer values are squared, they are used to create an equation known as a Pythagorean triple.

The given figure has right-triangles formed by the diagonals of the polygon.

We use the Pythagoras Theorem to find the value of EC.

The Pythagoras Theorem is given as:

c² = a² + b²

For the first triangle:

(73)² = a² + (55)²

a = 48

Now for the adjacent triangle with hypotenuse = 60.

(60)² = (48)² + (b)²

b = 36

Triangle with hypotenuse = 86:

(86)² = (a)² + (36)²

a = 78.10

Hence, the value of the length of EC to the nearest whole number is 78 units.

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I really need help please

### Answers

**Answer:**

3.5 feet

**Step-by-step explanation:**

You want to know the **tail length** of an **alligator** whose **body length is 7.7 feet**, if tail length is **proportional to body length**, and an alligator with a **body** length of **4.4 feet** has a **2 ft tail**.

Proportion

The proportion can be written ...

tail/body = x/(7.7 ft) = (2 ft)/(4.4 ft)

Multiplying by 7.7 ft gives ...

x = (7.7 ft)(2/4.4) = 7/2 ft = 3.5 ft

**The tail length is 3.5 feet**.

Can someone explain how to get these 3 questions

### Answers

**Answer:**

**1. Multiply each expression by a number to make a variable cancel out. The numbers can be different:**

**1(2x + 5y = 10)**

**5(x-y = -9)**

**Use the distributive property, then add the expressions together.**

**2x + 5y = 10**

**5x - 5y = -45**

**7x = -35**

**x = -5**

**2. Solve the inequality as if there was an equal sign.**

**-9x -6 < 3 - 2x**

**-7x < 9**

**Flip the inequality sign around if you have to multiply/divide by a negative number.**

**x > -1.2857...**

**3. Find the y-intercept and slope of each line. If the line is shaded below, it is <. If it is shaded above, it is >.**

**blue line: y < -0.5x - 3**

**red line: y > -1.5x -5**

module five problem set this document is proprietary to southern new hampshire university. it and the problems within may not be posted on any non-snhu website.

### Answers

Module Five in a course is generally focused on providing the student with the** knowledge and skills **needed to apply the concepts learned in the course. For this** problem set**, it is important to read the instructions thoroughly and understand the concepts discussed in the module material.

Additionally, be sure to support your answer with evidence from the **module material** and **external sources**, if applicable. It is important to keep in mind that the goal of the problem set is to demonstrate your understanding of the module material** **and how to apply it to **real-world situations. **

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PLEASE HELP

Evaluate the integral [x√1-x dx

### Answers

The **value **of the integral is [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex].

What is Integration?

Integration simply can be defined as the **method **of finding the whole by adding up the parts.

This is actually the reverse process of **differentiation**.

The given integral is, ∫[tex]x\sqrt{1-x}[/tex] dx

**Integration by parts **in an integral is defined as.

∫f(x) g(x) dx = f(x) ∫g(x) - ∫[f'(x)∫g(x)] dx

Let f(x) = x and g(x) = [tex]\sqrt{1-x}[/tex]

Integral is,

∫[tex]x\sqrt{1-x}[/tex] dx = [x ∫[tex]\sqrt{1-x}[/tex] dx] - ∫[d/dx (x) ∫[tex]\sqrt{1-x}[/tex]] dx

First let's find the following integral.

∫[tex]\sqrt{1-x}[/tex] dx = ∫[tex](1-x)^\frac{1}{2}[/tex] dx = [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]

Substituting in the main **equation**,

∫[tex]x\sqrt{1-x}[/tex] dx = [x [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]] - ∫ [ [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]]

= [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{5}[/tex] [tex](1-x)^\frac{5}{2}[/tex]

= [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex]

Hence the integration of the given **function **gives [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex].

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find the present value of $70,000 due in 2 years at the given rate of interest. (use a 365-day year. round your answer to the nearest cent.) 4%/year compounded monthly

### Answers

The present value of $70,000 payed in two years is $64,136.87 at a monthly compound **interest rate** of 4%.

Using the formula below, it is possible to determine the **present value** of $70,000 payable in two years at a 4% rate of interest compounded monthly:

PV = FV / (1 + r/n)^(nt)

such that:

Present Value, or PV, is the term.

FV stands for **future **value.

The annual number of **compounding **periods is n, and the interest rate is r.

The **number of years** is t.

To solve this problem, we have:

FV = $70,000

r = 4% = 0.04

n = 12 (as **compounding **is done monthly)

t = 2

Adding these **values **to the formula provides the following results:

PV = $70,000 / (1 + 0.04/12)^(12 × 2)

PV = $70,000 / (1.003333)^24

PV = $70,000 / 1.090777

PV = $64,136.87

We get: to the nearest cent

PV = $64,136.87 ≈ $64,136.87

As a result, $64,136.87 is the present value of **$70,000** that is due in two years at a 4% **annual **interest rate.

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What is the measurement of angle C?

### Answers

Angle c is 84 degrees

Angle c is 84 degrees

1. Which two numbers will have a negative sum?

A. -0.5 and 4/5

B. -0.6 and 7/10

C.-0.9 and ³/2

D. -2 2/3 and 2.2

### Answers

The two numbers that have a **negative sum** are the ones in option D.

-(2+ 2/3) and 2.2

Which two numbers will have a negative sum?

Two numbers have a **negative sum** if:

Both numbers are negative.The absolute value of the negative number is larger than the absolute value of the other one.

Here we need to look at the last option, we have the two numbers:

-(2 + 2/3) and 2.2

If we write the mixed number as a decimal, we will get:

2 + 2/3 = 2 + 0.66 = 2.66

Then:

-(2 + 2/3) = -2.66

Now we can add the two numbers to get:

-2.66 + 2.2 = -0.46

The sum is negative.

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The wholesale price of a pen is $0.60. In the city store, the pen is sold for 40% more.

The school library has decided to sell those kinds of pens too, and they buy it from the city store. The price of the pen is then marked up 25% more than its price in the city store.

What is the price of the pen if you buy it from the school library?

### Answers

$.6 x 40% = $.24

City store price is $.24+$.60=$.84

Library price is ($.84x25%)+$.84=$1.05

If the diameter of a circle with a circumference of 22.50 inches is reduced by three, what would be the circumference of the new circle?

### Answers

**Answer:**

**Step-by-step explanation:**

D = 6.2-3 = 3.2 inches.

Estimate the measure of angle 1.

### Answers

According to the **image**, the missing **angle** is 100°.

How to calculate the angle of a triangle?

When we want to calculate an **angle** of a **triangle** we must take into account the following information:

If we know the value of two **angles **(angles 2 and 3) of the triangle we must add the measure of the two angles we know.

55° (angle 2) + 25° (angle 3) = 80°

Now we must subtract the sum total of the two known **angles** from 180°.

180° - 80° = 100° (angle 1)

So the value of angle 1 would be 100°. Additionally, 180° is a rule that we must follow, because the **angles** of a **triangle** must always add up to 180°.

**Note**: This question is incomplete. Here is the complete information:

Image attached

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Hd+4Md=g^3

solve for d

### Answers

The **equation **is **solved **for d as d = g³/ H + 4M

How to determine the subject of formula

It is important to note that the **subject of formula** is the variable that is being worked out in an equation.

It is also described as the variable that is allowed to stand alone on one end of the equality sign.

From the information given, we have the equation;

Hd+4Md=g^3

To make 'd' the subject of formula, factorize the equation, we get;

d(H + 4M) = g³

Divide the the both sides by the coefficient of the variable, d, we have;

d = g³/ H + 4M

Hence, the **equation **is d = g³/ H + 4M

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Suppose you pay $0.90 to roll a fair 12-sided die with the understanding that you will get $2.10 back for rolling a 1, 2, 3, 4, or 5. Otherwise, you get no money back. What is your expected value of gain or loss?

### Answers

**Answer:**

-$0.025

**Step-by-step explanation:**

p(win) = 5/12

p(loss) = 7/12

expected value of a win: (2.10 - 0.90)(5/12)

expected value of a loss: (-0.90)(7/12)

overall expected value:

(2.10 - 0.90)(5/12) + (-0.90)(7/12) =

= 1.2 × 5/12 - 0.9 × 7/12

= -0.025