Mathematics College

## Answers

**Answer 1**

Answer:

9495.221

Step-by-step explanation:

16000=Pe^(0.11x5)

## Related Questions

Which ordered pair, when graphed, would be on the same line as (1, -2) and (-2, 4)?

OA) (-2, 6)

OB) (3, 6)

OC) (3,-6)

OD) (1, 2)

### Answers

**Ordered pair**, when **graphed**, would be on the same line as (1, -2) and

(-2, 4) are** (3,-6)**.

As given in the question,

Equation of the line passes through the point (1.-2) and (-2,4) when **graphed **is :

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

⇒y +2 = -2(x -1)

⇒y =-2x

**Ordered pair **satisfied the equation of the line passes through the point (1.-2) and (-2,4) when graphed is :

A. (-2,6)

x=-2 ⇒y=4

Not satisfied.

B. (3,6)

x=3⇒y=-6

Not satisfied.

C.(3,-6)

x=3⇒y=-6

Satisfied.

D. (1,2)

x=1⇒y=-2

Not satisfied.

Therefore, **ordered pair**, when graphed, would be on the same line as (1, -2) and (-2, 4) are (3,-6).

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help meeee

11 Answer:

A box of rice is 19 centimeters long, 12 centimeters wide, and 3.5

centimeters deep. The volume of the box is the product of its length,

width, and height. What is the volume of the box?

20 Answer:

Write the verbal sentence as an equation or an inequality:

The sum of three and x is ten.

### Answers

**Answer:**

798

**Step-by-step explanation:**

11. v = l x w x h

19 x 12 x 3.5 = 798

20. 3+x=10

A state's recidivism rate is 22%. This means about 22% of released prisoners end up back in prison (within three years). Suppose two randomly selected prisoners who have been released are studied. What is the probability that both of them go back to prison?

### Answers

The **probability **that both of them go back to prison is 4.48%.

**What is probability?****Probability **is a measure of the likelihood of an event occurring. Many events cannot be predicted with total **certainty**. We can predict only the **chance **of an event to occur i.e., how likely they are going to happen, using it.The probability of an event is a number **between **0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

The state recidivism rate is given by 22%.

So, the probability that both of the prisoners will go back to prison will be:

= 22% × 22%= 0.22 × 0.22= 4.84%

Hence, the **probability **that both of them go back to prison is 4.48%.

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Simplify the fraction

315

405

as much as possible.

7

9

35

45

3

4

### Answers

**Answer:**

7/9

*Hope this helps!*

* Have a good day :)*

**Answer:**

7/9

**Step-by-step explanation:**

I took the quiz

An artist uses different types of paper to create her masterpieces. She has shiny metallic paper and pink glittery paper. The shiny paper comes in lengths of 24 inches and the glitter paper in lengths of 36 inches. She wants to make sure she can cut her paper into equal sizes but doesn’t want them to be too small. What’s the largest size she can cut them into without any waste?

### Answers

An artist can cut the **metallic paper** and pink glittery paper of the** largest size** of 12 inches without any waste.

What is defined as the term highest common factor?The greatest common factor is the largest number that is a factor of two numbers or more (GCF). The largest number (factor) divides them, yielding a Natural number. Once all of the number's factors have been identified, there are a few that are shared by both.

The length of the** metallic paper** is 24 inches.

The length of the** pink glittery** paper is 36 inches.

To find the largest size, find the HCF of both number.

First find the factors using prime factorisation;

24 = 2×2×2×3

36 = 2×2×3×3

Find the common term,

**HCF** (24, 36) = 2×2×3

HCF (24, 36) = 12

Thus, an artist can cut the metallic paper and pink glittery paper of the** largest size** of 12 inches without any waste.

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Write 9⁴ as a power of 3.

### Answers

**Answer:**

3^8

**Step-by-step explanation:**

9^4 = 9*9*9*9

9 = 3*3

9^4 = (3*3)*(3*3)*(3*3)*(3*3)

9^4 = 3*3*3*3*3*3*3*3 = 3^8

or, more simply

9 = 3^2

9^4 = (3^2)^4

we use (x^y)^z = x^(y*z)

(3^2)^4 = 3^(2*4) = 3^8

Runners at a cross-country meet run 3 miles north and then 5 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line.

square root of 8 miles

4 miles

square root of 34 miles

8 miles

### Answers

The **shortest straight **path they must run back to the **starting line **is the square root of 34 miles.

What is the shortest straight path?

The distance run by the **runners **forms a **right triangle. **A **right triangle **is a polygon that has three sides. The length, base and the hypotenuse. The hypotenuse is the longest side of the **right triangle. **

The miles run **north **is the length, the miles run **west **is the base and the shortest straight path to the **starting line **is the hypotenuse.

In order to determine the hypotenuse, the **Pythagoras theorem **would be used.

The **Pythagoras theorem**: a² + b² = c²

where a = length

b = base

c = hypotenuse

3² + 5²

= 9 + 25

= 34

c = √34

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Can you solve this please.

### Answers

1) simplify the expression using the rule of exponent

y^12 * y^5

y^17

Answer

y^17

Answer: y^17 have a good day

. Mandy and 6 of her teammates each sold an equal number of

shirts to raise money for their tennis team. If a total of 56 shirts

were sold, how many shirts did each person sell? Explain.

### Answers

**Answer:**

8

**Step-by-step explanation:**

56 shirts were sold, and including Mandy, 7 people sold them.

7 * x = 56

(7x)/7=56/7 (canceling out the 7 to get x alone)

x=8

So basically just 56 divided by 7

In Mr. Stowe's math class, Katherine earned an 88 in the 1st quarter and a 94 in the end quarter. What is the percentage of increase?

### Answers

The **percentage **of **increase **in her score is 6.82%

What is the percentage of increase?

Here we will define her **first score**, 88, as the 100%.

So we can write the **relation**:

88 = 100%.

Her next score is 94, this will be a **percentage **X, then we can write:

94 = X

Taking the quotient between the two equations:

94/88 = X/100%

Solving this for X we get:

(94/88)*100% = X = 106.82%

The difference between the **percentages **gives the increase:

106.82% - 100% = 6.82%

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An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)

R(x) =

### Answers

The equation of the **function** of the agency revenus in terms of x is R(x) = (50 + x) * (100 - 3x)

What are quadratic equations?

**Quadratic equations **are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

How to determine the agency's revenue R as a function of x?

From the question, the given parameters are given as

Number of people = 50

Amount charged per person = $100

The above means that the **total charges **is

Total = Number of person * Amount charged per person

Rewrite as

Revenue = Number of person * Amount charged per person

From the question, we have

The charges for each traveller **reduces **by $3 for each additional person

Let the number of **added person **be x

So, we have

Revenue = (Number of person + x) * (Amount charged per person - 3x)

Substitute the known values in the above equation

So, we have

R(x) = (50 + x) * (100 - 3x)

Hence, the agency's **revenue **R as a **function** of x is R(x) = (50 + x) * (100 - 3x)

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The table represents a quadratic function. Write an equation of the function in standard form.

-9-7-5-3

0 8 8

X

y

y=0

Previous

1 2

0

30

4

32

5

6

7

10

Next

### Answers

Answer:

Step-by-step explanation:

Given M(-2, 1) is the midpoint on AB and point A has coordinates (-8, -3), find:

Point B

### Answers

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -8}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(-2~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -8}{2}=-2\implies x-8=-4\implies \boxed{x=4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}=1\implies y-3=2\implies \boxed{y=5}[/tex]

Select all the correct answers.

Which functions have a range of {ye R |-∞0 < y < ∞0}?

F(x)=x^2+7x-9

F(x)=-4x+11

F(x)=2/3X-8

F(x)=2^x+3

F(x)=-(x+1)^2-4

### Answers

For all the given** functions,** the range lies between {y ∈ R |-∞ < y < ∞} as non of the function has **imaginary **number.

What is meant by the **imaginary **number?When imaginary numbers are squared, they produce a negative number. They can also be expressed as the **square root** of a negative number. An imaginary number is created by multiplying a** non-zero **real number by the imaginary unit I (also recognized as "iota"), where √(-1) = i (or) i² = -1. These are a type of complex number, which is the sum of a real number as well as an imaginary number. A complex number has the formula a + ib, where 'a' and 'b' are both real numbers and bi is just an **imaginary number**.

For all the given **functions;**

F(x)=x^2+7x-9F(x)=-4x+11F(x)=2/3X-8F(x)=2^x+3F(x)=-(x+1)^2-4

For any value of x ∈ R (**real number**), the value of y of f(x) will lie in the given range.

Thus, all the given function have the** range **of {y ∈ R |-∞ < y < ∞}.

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2x-3>7 i kinda need help can i get the answer

### Answers

**Answer:**

x>5

**Step-by-step explanation:**

2x>10

x>5

6 is added to the product of 7 and a number

### Answers

55

(7*7)+6=49+6=55

I solved it

The **value **of the **expression **will be equal to 55.

What is an expression?

The **mathematical **expression combines **numerical **variables and operations **denoted **by addition, **subtraction**, multiplication, and division signs.

Mathematical **symbols **can be used to **represent **numbers (constants), variables, operations, functions, **brackets**, punctuation, and grouping. They can also **denote **the logical syntax's **operation **order and other properties.

Given that 6 is **added **to the **product **of 7 and a number 7. The **expression **will be written as,

E = 7 x 7 + 6

E = 49 + 6

E = 55

Therefore, the **value **of the **expression **will be equal to 55.

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What would I set the scales to and where is the roots ,vertex and two other points

### Answers

**SOLUTION**

**Write out the equation **

[tex]y=x^2+4x-12[/tex]

The root of the equation is

[tex]\begin{gathered} x^2+4x-12=0 \\ x^2+6x-2x-12=0 \\ x(x+6)-2(x+6)=0 \\ (x+6)(x-2)=0 \end{gathered}[/tex]

Equate the factors to zero

[tex]\begin{gathered} x+6=0,x-2=0 \\ x=-6,x=2 \end{gathered}[/tex]

Hence, the root of the equation is

**(-6,0) and (2,0)**

**The vertex of the equation will be obtained using**

[tex]\begin{gathered} u\sin g\text{ the genera form of a quadractic equation } \\ ax^2+bx+c=0,\text{ tye vertex is given by } \\ \: x_v=-\frac{b}{2a} \\ \text{where } \\ a=1,b=4,c=-12\text{ from the given equation } \end{gathered}[/tex]

** Then **

[tex]\begin{gathered} x=-\frac{4}{2\times1}=-\frac{4}{2}=-2 \\ \text{Then} \\ y=x^2+4x-12,\text{ where x=-2} \\ y=^{}(-2)^2+4(-2)-12=4-8-12=-16 \\ \text{Vertex (-2,-16)} \end{gathered}[/tex]

Then

[tex]\begin{gathered} \text{The other two point could be } \\ x=0,y=0^2+4(0)-12=0+0-12=-12\text{ } \\ (0,-12) \\ x=2,y=2^2+4(2)-12=4+8-12=0 \\ (2,0) \end{gathered}[/tex]

Plotting this point using **the scale 2unit on both axes**, the image of the graph will be

Given m || n, find the value of x and y.

45°

२०

yº

m

n

### Answers

I believe that y = 45 degrees; x = 135 degrees. The entire line adds up to 180 degrees, so you can use opposite angles and subtract 45 from 180 to get the remaining angle (y).

What's the answer to this equation? Please include steps

6(915 - x) = 100 + x

### Answers

**Answer:**

x = 770

**Step-by-step explanation:**

You want the **solution** to the equation **6(915 - x) = 100 + x**.

Solution

It often works well to simplify the equation first. Here, that means eliminating parentheses using the distributive property:

6(915) -6(x) = 100 +x

5490 -6x = 100 +x . . . . . . . . carry out the multiplication

5490 -6x +6x = 100 +x +6x . . . . . add 6x to both sides

5490 = 100 +7x . . . . . . . . . . collect terms

5490 -100 = 100 +7x -100 . . . . . . subtract 100 from both sides

5390 = 7x . . . . . . . . . . . . . . collect terms

5390/7 = (7x)/7 . . . . . . . . . . . . . . . . divide both sides by 7

770 = x . . . . . . . . . . . . . . . . carry out the division

**The solution to the equation is x = 770**.

__

*Check*

6(915 -770) = 100 +770 . . . . use the value of x in the equation

6(145) = 870 . . . . true

__

*Additional comment*

After eliminating parentheses, this is a 3-step linear equation, so is solved in the usual way. First, the variable terms are collected on one side of the equal sign. Then the constant terms are collected on the other side of the equal sign. Finally, the equation is divided by the coefficient of the variable.

Elzabeth brought a box of donuts to share There are two dozen (24) donuts in the box, all identical in size shape and color Two are jelly, 10 are lemon filled, and 12 are custard-filled. You randomly select one donut eat it and select another donut. Find the probability

of selecting a lemon-filled donut followed by a jelly-filled donut.

### Answers

The **probability** of selecting a lemon-filled donut followed by a jelly-filled donut is [tex]\frac{5}{138}[/tex]

What is probability ?

**Probability** is the** potential** for something to happen. In this area of mathematics, **random events** are studied. The range from 0 to 1 is used to express the value. To forecast the **possibility of events**, probability has been included into mathematics. The degree of likelihood that something will happen is basically how probability is defined. This fundamental theory of probability, which also applies to the probability distribution, can be used to estimate the likelihood of results in a** random experiment.**

The **distribution **of donuts is given as:

jelly = 2

lemon = 10

custard = 12

Total = 24

Eating a chosen donut without replacing it is an example of a selection.

So, the probability of selecting one lemon-filled donuts and one jelly filled donut is:

P = [tex]\frac{lemon}{Total}[/tex]×[tex]\frac{jelly}{total - 1}[/tex]

Substitute known values

P = [tex]\frac{10}{24}[/tex]×[tex]\frac{2}{23}[/tex]

Simplify

P = [tex]\frac{5}{138}[/tex]

Hence, the probability is [tex]\frac{5}{138}[/tex]

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In the figure below, circle O has a central angle of 120°.

What is the area of the shaded sector of circle O in terms of r, the radius? Leave your answer in terms of pi.

### Answers

The** area **of the shaded section, in terms of the **radius** R, is:

A = 0.67*R^2

**How to get the area of the shaded part?**

On the image we can see a circle where a section with an angle of 120° is not shaded and the rest is shaded.

Remember that the **area **of a circle of **radius **R is:

A = pi*R^2

Where pi = 3.14

Particularly, for a section defined by an angle x the **area **is:

A = (x/360°)*pi*R^2

In this case we have:

x = 360° - 120° = 240°

Then the **area**, in terms of the **radius**, is:

A = (240°/360°)*3.14*R^2 = 0.67*R^2

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18% of students use books

164 students use tablet

How many students are in sixth grade?

### Answers

Total students in sixth grade **200students**

**What is Percentage?**

A **percentage **in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the **percent **symbol, "**%**," is most frequently employed. A **% **has no dimensions and no associated unit of measurement.

Given,

No. of students using Tablet = 164

No. of students using book = 18%

The students in sixth grade either use book or tablet

When 164 student use tablet then remaining use tablet, that is 18%

Then, the remaining **percent **would be the students using tablet:

100% - 18% = 82%

converting 82% into decimal we get,

82 /100

i.e, 0.82

Number of students in sixth grade = 164/0.82

= 200 students

Hence, **200 students** are in sixth grade

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Find the value of x

x=

112°

(3x + 11)°

### Answers

I think this should help you

4. E is between D and F. If DE = 3x + 2, EF = 18, and DF = 5x, find the value of x.

### Answers

The **value **of **x** is 10.

What are expressions in math?

A **mathematical expression** consists of a statement, at least one **arithmetic operation**, and at least two **integers** or **variables**. With this mathematical operation, you can multiply, divide, add, or subtract.

Given:

E is between D and F.

DE = 3x + 2

EF = 18

DF = 5x

We need to determine the value of x which is a **variable**, whose value is unknown to us and can take any value.

So, DF = DE + EF

Substituting the given values, we get

5x = 3x + 2 + 18

5x - 3x = 20

2x = 20

x = 20/2

x = 10

Therefore, the **value **of x is 10.

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Two cars leave an intersection. One car travels north; the other east.

When the car traveling north had gone 12 mi, the distance between

the cars was 4 mi more than the distance traveled by the car

heading east. How far had the east bound car traveled?

### Answers

The **distance** travelled by the **east bound** car is 8 mi.

What is defined as the distance?Distance is defined as an object's total movement without regard for **direction. **Distance can be defined as how much floor an object has covered regardless of its starting as well as ending point.Distance and** displacement** have been two quantities that appear to mean the same thing but have very different definitions and meanings. Distance is defined as "how much earth an object has contained during its motion," whereas displacement is defined as how far of place an object is."

The distance travelled by the **north car **is 12 mi.

Let the distance covered by south car is x.

The** distance **travelled by the north car is 4 mi more than the distance traveled by the car heading east.

Thus,

x + 4 = 12

x = 12 - 4

x = 8

Thus, the distance travelled by the **east bound** car is 8 mi.

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A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.

c. What is the probability that at least 12 sales will result from mailing to the 30 prospects?

### Answers

Using the **normal **approximation to the binomial distribution, there is a **0.0060 = 0.60% probability** that at least 12 sales will result from mailing to the 30 prospects.

Normal Probability Distribution

The **z-score** of a **measure X** of a normally distributed variable that has **mean **given by [tex]\mu[/tex] and **standard deviation** represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It **measures **how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the** p-value **associated with the z-score is found, which represents the **percentile **of the measure X.The **binomial **distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be **approximated **to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].

The **parameters **for the **binomial **distribution in the context of this problem are given as follows:

n = 30, p = 0.2.

Hence the **mean **and the **standard deviation** for the approximation are given as follows:

[tex]\mu = np = 30 \times 0.2 = 6[/tex].[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{30 \times 0.2 \times 0.8} = 2.19[/tex]

Using continuity correction, the **probability **that **at least 12** sales will result from mailing to the 30 prospects is **P(X > 11.5)**, which is one subtracted by the p-value of Z when X = 11.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (11.5 - 6)/2.19

Z = 2.51

Z = 2.51 has a p-value of 0.9940.

1 - 0.9940 = 0.0060.

Hence the **probability **is of **0.0060 = 0.60%.**

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Government agencies keep data about the income distribution of the population. The Moore family and Kelly family live in a county with 11,000 families.

Moore family's income is at the 24th percentile. The Kelly family's income is at the 77th percentile.

(If necessary, consult a list of formulas.)

(a) Which of the following must be true about the Moore family's and the Kelly

family's incomes?

The Kelly family earns more than the Moore family.

Both the Moore family and the Kelly family earn more than the median

income.

O The Kelly family earns $53,000 more than the Moore family.

The Moore family and the Kelly family both have incomes in the bottom half

of incomes in their county.

(b) Which of the following must be true about the Moore family's income?

O The Moore family earns more than about 76% of families in their county.

About 76% of the families in their county earn more than the Moore family.

O The Moore family earns about 24% of the highest income in their county.

The Moore family earns about 76% of the highest income in their county.

5

### Answers

(a) (c) The Kelly family earns **more than** the Moore family.

(b) (a) The Kelly family earns **more than** the Moore family.

What is Percentile ?

Each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable is called **percentile**.

Percentile is computed using the following formula,

P = n/N X 100

Where, n =ordinal rank of a given value

N = number of values in the data set,

P = Percentile

In (a) part , Kelly family's percentile is 77th percentile and Moore family's percentile is 24th percentile.

therefore option (c) i.e. The Kelly family earns **more than** the Moore family is correct .

In (b) part , Moore family's income is less than Kelly's family income.

therefore option (a) i.e. The Kelly family earns **more than** the Moore family is correct.

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I will give brainliest, like and rating if u solve this right

6) TRUE OR FALSE?

### Answers

**Answer: True**

**Step-by-step explanation:**

( Which table of values will generate this graph? 5 3 2 1 2 3 4 5 TT 1919 х 4 1 2

### Answers

To identify the data corresponding to the points in the plane:

In x you count the units of distance from 0 to the point: from left (negative x) or right (positive x).

In y you count the units of distance from 0 to the point: down (negative y) or upwards (positive y)

Then, in coordinates (x,y) you have the next:

Corresponding to the table:

I

2. Which is the more economical purchase: a 20-ounce box of cereal for $4.23 or an 18-ounce box for

$3.75? Justify your answer

### Answers

20 ounce because at the end of the day I’d you add the amount needed to the 16 one for it to be 20 is going to be more than $4.23