Mathematics College

## Answers

**Answer 1**

The value of the **expression** one fifth times the quantity 3 times x plus 10 end quantity **minus** 11 over 15 times x is 2 - 2/15x.

How to illustrate the information?

It should be noted that **expressions** are simply used to show the relationship that exists between the **variables** that are given.

In this case, one fifth times the quantity 3 **times** x plus 10 end quantity **minus** 11 over 15 times x will be illustrated as:

= 1/5(3x + 10) - (11/15x)

= 3/5x + 2 - 11/15x

= 9/15x + 2 - 11/15x

= 2 - 2/15x

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## Related Questions

1. A triangle is rotated 90° about the origin. What is true about the relationship between the image and the

pre-image?

(1 point)

The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent.

The lengths of the sides are enlarged and measures of the angles are preserved, so the triangles are similar.

The lengths of the sides change and the measures of the angles change as well, so the triangles look nothing alike.

The lengths of the sides are reduced and measures of the angles are preserved, so one triangle is a reduction of the other.

### Answers

**Answer:**

the first answer option : all lengths and angles stay the same.

**Step-by-step explanation:**

imagine you have a piece of plastic or glass of a triangular shape on your table.

now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.

and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.

that finger is dragging the triangle along.

what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.

that is what a rotation is.

Find a function f whose graph is a parabola with the given vertex and that passes through the given point.

vertex (−1, 9); point (−2, −8)

### Answers

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]

The point (-2, 1) is on the graph of which of these functions?

A. y = -x² -1

B. y = -3x -5

C. y = x² + 3

D. Y = 1/2x

### Answers

Answer: B

-3(-2)-5=Y

6-5=1

Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?

### Answers

The plane containing point B and** parallel **to the **plane CDH** is plane ABF.

What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two **parallel planes** is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the **shortest distance** between them.

As, from the diagram we can see that there are two plane passing from point B;** plane ABF** and ABC.

But plane ABC is intersecting the given plane CDH, while plane ABF is not.

Thus, plane ABF is parallel to the **plane CDH**.

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A college professor hands out a list of 16 questions, 8 of which will appear on the final examination for the course. One of the students taking the course is pressed for time and can prepare for only 9 of the 16 questions on the list. Suppose the professor chooses the 8 questions at random from the 16. What is the probability that the student will be prepared for exactly 4 questions?

### Answers

The **probability** that the student will be prepared for exactly 4 questions is; 0.3427

How to solve Hypergeometric Probability distribution?

**Hypergeometric distribution** is defined as a discrete **probability distribution** that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.

The **probability mass function** of Hypergeometric distribution is given by the formula;

P(K = k) = KCk * N-KCn-k ]/NCn

Now, the probability that the student will be prepared for exactly 4 questions will be;

P(K = 4) where;

N = 16

K = 9

n = 8

Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427

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Select the correct answer.

How many solutions for x does the following equation have?

2(x+4) -1 = 2x + 7

O A. 1

О в. о

OC. 7

OD. infinite

### Answers

**Answer:**

D. infinite

**Step-by-step explanation:**

2(x+4) -1 = 2x + 7

**To solve for x**

Distribute

2x+8 -1 = 2x+7

Combine like terms

2x +7 = 2x + 7

Subtract 2x from each side

2x+7-2x = 2x+7-2x

7 = 7

This is always true, so there are infinite solutions

Does the table show a proportional relationship? If so, what is the value of y when x is 11?

x 4 5 6 10

y 64 125 216 1,000

### Answers

Yes. As each number in x is cubed to give y

Help Me Pleaseeeeeee.

### Answers

Based on the dimensions of the** right triangle**, the **equation **to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².

How to find a missing length on a right angled triangle?

To find the missing length of a** right-angled triangle,** you should use **Pythagoras theorem. **

This theorem allows you to find the dimensions of missing leg as:

hypotenuse² = Known leg² + Unknown leg²

When you solve for the **missing length**, the length is:

9² = 6² + Unknown leg²

81 = 36 + Unknown leg²

Unknown leg² = 81 - 36

Unknown leg = √(81 - 36)

Unknown leg = 6.7

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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the function with its inverse.

### Answers

The **correct pairs **of the **functions **and their **inverses **are given by the **image **at the end of the answer.

How to find the inverse function?

To find the inverse function, we **exchange **x and y in the original function, then **isolate **y.

The **first **function that we want to find the inverse is:

f(x) = (2x - 1)/(x + 2).

Hence:

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

(y + 2)x = 2y - 1

xy + 2x = 2y - 1

xy - 2y = -1 - 2x

y(x - 2) = -1 - 2x

y = (-1 - 2x)/(x - 2) (which is the **inverse **function).

The **second **function which we want to find the inverse is:

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

Then:

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

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

-2yx + x = y + 2

-2yx - y = 2 - x

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

y = (x - 2)/(2x + 1) (which is the **inverse **function).

The **third **function which we want to find the inverse is:

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

Then:

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

2yx + x = y - 1

2yx - y = -1 - x

y(2x - 1) = -1 - x

y = (-x - 1)/(2x - 1) (which is the **inverse **function).

The **fourth **function which we want to find the inverse is:

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

Then:

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

2yx - x = 2y + 1

2yx - 2y = 1 + x

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

y = (x + 1)/(2(x - 1)) (which is the **inverse **function).

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HURRY!!!!!!!1Solve the equation −112 = 8x for x. −14 14 −104 120

### Answers

The **solution** to the **equation**, −112 = 8x, is: x = -14.

How to Solve an Equation?

To find the value of the **variable** in an **equation**, means to **solve** the **equation**.

To **solve** any given **equation**, we are to apply all necessary properties of equality in other to isolate, as much as possible, the **variable** of the **equation** to one side of the **equation**. Th value of the **variable** is the solution to the **equation**.

Given the **equation**:

-112 = 8x

Divide both sides of the **equation** by 8:

-112/8 = 8x/8 [division property of equality]

-14 = x

x = -14

Check: Plug in x = -14 into the **equation**:

-112 = 8(-14)

-112 = -112 [true]

Thus, the **solution** to -112 = 8x is: x = -14.

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the equation of the regression line for the data in the table is y = 4.9 - 198 where x represents the height and y is the predicted walking speed

### Answers

The numerical value of 4.9 in the **equation** of the regression line

[y = (4.9x - 198)] determines "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

As per the question statement, the **equation** of the regression line goes as [y = (4.9x - 198)], where "x" represents the height and "y" is the predicted walking speed.

We are required to determine, what the numerical value of 4.9 expresses in the regression line.

To solve this question, first we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)], where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line, and compare this standard form to our question mentioned **equation,** to establish the numerical significance of 4.9.

Now, [y = (4.9x - 198)] can be written as [(y - 0) = 4.9(x - 40.41)], and comparing it to the standard point-slope form of a line, we get (m = 4.9), i.e., the slope of our concerned line of regression is 4.9.

Hence, 4.9 in 4.9x signifies "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

**Equation: **In mathematics, an **equation** is a statement that expresses the relation of equality between two or more separate expressions, by connecting them with the "equal to" sign.

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**Answer:**

For every 1 inch increase in height, walking speed increases by 4.9 m/min.

**Step-by-step explanation:**

Just took it, hope this helps.

The rooftop of a 5-story building is 50 feet above the ground.

How long does it take the water balloon dropped from the

rooftop to pass by a third-story window at 24 feet?

Using the model h(t) = h, 16², solve the equation

h(t) = 24. (When you reach the step at which you divide

both sides by -16, leave 16 in the denominator rather than

simplifying the fraction because you'll get a rational

denominator when you later use the quotient property.)

### Answers

With the help of the **quotient, **we know that the time the water balloon dropped from the rooftop is 1.3sec.

**What do we mean by Quotient?**In this example, the number divided by (15) is known as the **dividend**, and the number divided by (3 in this instance) is known as the **divisor**. The **quotient **is the outcome of the division.The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4. The quotient and divisor are always less than their dividend, as you can see.

So, h(t) = 24:

= 50

Then, calculate as follows:

h(t) = - 1624 = 50 - 1616 = 50 - 2416 = 26 = 26/16t = √26/16t = 1.3sec

Therefore, with the help of the **quotient, **we know that the time the water balloon dropped from the rooftop is 1.3sec.

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Find the value of x:

### Answers

**Answer:**

3

because 3 divided by one is 3 so then you would have to divide with nine which we know is 3

**Step-by-step explanation:**

**Have a great day!**

Use the definition of the derivative to find the derivative of the function with respect to the given variable.

Show steps

### Answers

The **derivative **of the given function [g(r) = -2r + 2] is d/dr (rⁿ) = nrⁿ⁻¹.

**What is derivative?**The **derivative **of a **function **of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative. In conclusion, the **tangent line's slope**, or instantaneous rate of change, at any point on the **curve **is essentially what the derivative is. When you take a function's derivative, you're left with a different function that gives you the slope of the original function.

So, g(r) = -2r + 2:

Differentiate with respect to r as follows:

g(r) = -2r + 2

Using Power rule:

d/dr (rⁿ) = nrⁿ⁻¹

Therefore, the **derivative **of the given function is d/dr (rⁿ) = nrⁿ⁻¹.

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Over the last three evenings, Amy received a total of 112 phone calls at the call center. The first evening, she received 7 more calls than the second evening. The third evening, she received 3 times as many calls as the second evening. How many phone calls did she receive each evening?

### Answers

Based on the relationship between the **number of phone calls **that **Amy **received for the three **evenings**, the number of phone calls received on each evening was:

First evening - 28 calls Second evening - 21 calls Third evening - 63 calls

How to find the number of phone calls received?

The first evening saw **Amy **receiving 7 more calls than the second evening while the third evening saw Amy receiving 3 times as many **calls **as the second evening.

Assuming the second evening is x, the relationship can be represented by the equation:

First evening calls + Second evening calls + Third evening calls = Total number of calls

(7 + x) + x + 3x = 112

Solving for the number of phone calls on the **second evening **gives:

(7 + x) + x + 3x = 112

7 + x + x + 3x = 112

7 + 5x = 112

5x = 112 - 7

x = 105 /5

= 21 calls

Number of calls on** first evening:**

= 21 + 7

= 28 calls

Number of calls on** third evening:**

= 21 x 3

= 63 calls

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Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.

### Answers

The result of the **synthetic division **of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:

2x³ - 4x² + 2x - 5.

How does synthetic division works?

In synthetic division, the **coefficients **of a polynomial are each divided by a value.This value is the **zero **of the divided polynomial, which goes into the far left box.

For this problem, the **polynomial **is given by:

2x^4 - 12x³ + 18x² - 13x + 20.

Hence the **coefficients **are:

2, -12, 18, -13, 20.

The **divisor **is:

x - 4.

Hence the **left **coefficient is:

4.

From the **image **at the end of the answer, the **resulting coefficients** are given as follows:

2, -4, 2, -5, with a remainder of 0.

Hence the **result **is:

2x³ - 4x² + 2x - 5.

For the **procedure**, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.

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Answer the following.

### Answers

To convert 2.21 x 10⁻⁶, place 6 zeros before 2.21 and move the decimal point to the left:

= 0.000021210

To convert 28,000 to scientific notation, write the non-zero digits, placing a decimal after the first non-zero digit: 2.8, then, multiply by 10 elevated to 4 (number of digits after 2):

28,000 = 2.8 x 10

nswer:

Can I get help please ?

### Answers

**SOLUTION:**

**Case: Pythagoras Triple**

**Method:**

The Pythagorean triple:

(8, 15, 17) can be formed with factor integers

8----> 4

15---->3.

**Final answer:**

**x=4, y= 3**

Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.

### Answers

Solution:

Given;

[tex]\mu=1160,\sigma=200[/tex]

The z-score is calculated using;

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{760-1160}{200}\text{ at }x=760 \\ \\ z=-2 \\ \\ z=\frac{1560-1160}{200}\text{ at }x=1560 \\ \\ z=2 \end{gathered}[/tex]

Thus;

[tex]P(-2**ANSWER: ****95%**

**(b) **The z-score of 99.7 probability is between -3 and 3. Thus;

[tex]\begin{gathered} -3=\frac{x_1-1160}{200} \\ \\ x_1=560 \\ \\ 3=\frac{x_2-1,160}{200} \\ \\ x_2=1760 \end{gathered}[/tex]

**ANSWER: ****Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc**

Tammy has 4 more then five times the amount of dimes than nickels in her pocket. She has total of $1.50 in her pocket. Write an equation that could be used to determine the number of nickels(x) she has in her pocket.

### Answers

In a case whereby Tammy has 4 more then five times the **amount** of dimes than nickels in her pocket and have total of $1.50 in her pocket the **equation** that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.

How can the number of nickels(x) she has in her pocket been determined?

The number of nickels(x) that can be found her pocket be determined by adding the the number of times the amount of dimes is than nickels, which can be expressed as :

let x will be number of dimes

let x+4 will be number of nickels

Therefore the number of **nickels(x)** that is required will be (0.10)X + (0.05)(X+3) = 1.50

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1.

find a

a =

21°

explain why using one of these

words: adjacent,

complementary, supplementary,

vertical

explanation goes here

add a pic of your work

(or just type it here)

to show HOW you got your

answer

pic (or typing) goes Hereford

### Answers

[tex]21+a=90 \implies a=69^{\circ} [/tex]

This is because the angles are complementary.

Determine the rate of this problem -> A 18-kg bag of cherries for $2.65 =_____per kg

### Answers

**Answer:**

$0.14 per kg

**Step-by-step explanation:**

A 18-kg bag of cherries for $2.65

for 1 kg

[tex] \frac{2.65}{18} = 0.14 \\ [/tex]

so, the answer is **$****0****.****1****4**

Kaj earns $35 for 2 hours of work. ￼If she makes a constant hourly wage, which table

represents the relationship between the number of hours she works and her total

earnings?

### Answers

The **table of values **of the relationship between time and earnings is a linear relation

How to determine the table of values that represents the earnings?

From the question, we have the following parameters:

Number of hours = 2 hours

Total earnings in this time = $35

Also from the question, we understand that:

She makes a **constant hourly wage**

A **constant hourly wage** implies that the table of values has a **linear relationship**

In this case, the **linear relationship **is represented as

A(t) = constant hourly wage * t

Where

A(t) represents the earnings

t represents the number of hours

So, we have

constant hourly wage * 2 = 35

Divide both sides of the **equation **by 2

So, we have

constant hourly wage = 17.5

Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t

A(t) = 17.5 * t

Evaluate

A(t) = 17.5t

Using the values of t as:

t = 0, 2, 4, 6

We have the following **table of values**

Number of hours (t) || Amount earned

0 0

2 35

4 70

6 105

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A particle moves along the r-axis so that its velocity vat any given time t, for 0 St $ 16, is given byW(0) =e»-1. At time r=0, the particle is at the origin. At what time does the particle's accelerationequal zero for the first time?Round to the nearest thousandth or write as a fraction

### Answers

Given: The velocity function of a moving particle as

[tex]V(t)=e^{2sint}-1[/tex]

To Determine: The time at which the acceleration equals to zero

Solution

Note that at time t=0, the particle is at origin, so

[tex]\begin{gathered} V(0)=e^{2sin0}-1 \\ V(0)=e^{2\times0}-1 \\ V(0)=e^0-1 \\ V(0)=1-1 \\ V(0)=0 \end{gathered}[/tex]

Determine the acceleration function

The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,

[tex]A(t)=\frac{dV(t)}{dt},or,A(t)=V^{\prime}(t)[/tex][tex]\begin{gathered} V(t)=e^{2sint}-1 \\ let:u=2sint:\frac{du}{dt}=2cost \\ V(t)=e^u \\ \frac{dV(t)}{du}=e^u=e^{2sint} \\ A(t)=\frac{dV(t)}{dt}=\frac{dV}{du}\times\frac{du}{dt} \\ A(t)=e^{2sint}\times2cost \\ A(t)=2e^{2sint}cost \end{gathered}[/tex]

When the acceleration is equal to zero, then we have

[tex]\begin{gathered} A(t)=0 \\ 2e^{2sint}cost=0 \end{gathered}[/tex]

Let us plot the graph of the acceleration function

The time for given interval for which the acceleration is zero are

[tex]t=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\frac{7\pi}{2},\frac{9\pi}{2}[/tex]

ence, thre first time the acceleration is zero is π/2 or **1.571**

#6 and #7 Axioms of Equality

### Answers

It is proved that ∠2 and ∠3 are **supplementary angles.**

**What are angles?**An **angle **is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and **vertex**, respectively. Angles created by two rays are in the plane where the **rays **are located. The meeting of two planes also creates angles. We refer to these as **dihedral angles.**

So, according to the given image below:

(A) m∠1 = m∠3 ⇒ **Alternate angles.**

(B) m∠1 + m∠2 = 180°

Reason:

R is a straight line through which line m asses making two angles m∠1 and m∠2.As we know a** straight line** has an angle of 180°.And since, line m divides the angle of 180° into two parts ∠1 and ∠2.So w ecam conclude that: m1 + m∠2 = 180°.

(C) m∠3 + m∠2 = 180° due to:** Linear Pair Axiom**.

(D) m∠2 and m∠3 are supplementary because: Since a linear pair of angles always results in a straight line, their sum is always 180°.

Therefore, it is proved that ∠2 and ∠3 are **supplementary angles.**

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1/4(n-6)=1/4n-3/2

Hint: undo the fraction

### Answers

The **solution **to 1/4(n - 6) = 1/4n - 3/2 is **infinite many **solutions

How to solve the equation?

The **equation **is given as

1/4(n - 6) = 1/4n - 3/2

Multiply through the **fraction equation **by 4

So, we have the following equation

4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2

Evaluate the products in the equation

So, we have the following equation

n - 6 = n - 6

Evaluate the like terms

0 = 0

The equation cannot be **solved further**

If the **solution **to an equation is 0 = 0, then the equation has **infinite many **solutions

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**Answer: infinite many answers **

**Step-by-step explanation:**

For a test whose scores are normally distributed, with mean 470 and standard deviation 52, what is the cutoff score separating the bottom 11% of the test scores from the rest (that is, the score so that 11% of all scores are below this score)?

### Answers

We will employ the z score table in this problem.

The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.

when we ahave a probability of 0.11 or 11%

This corresponds with a z-score of -1.225.

We then substitute into our z-score equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where

[tex]\begin{gathered} z=z\text{ score} \\ x=\text{cut off point} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation} \end{gathered}[/tex]

Therefore, we have

[tex]\begin{gathered} x=\sigma z+\mu \\ x=52(-1.225)+470 \\ x=406.3 \end{gathered}[/tex]

What is the value of 8 in 8.260

### Answers

**Answer:**

**Step-by-step explanation:**

The **value of 8 in 8.260** is **8 units.**

Where is the least common denominator of two fractions to product of the denominator￼?

### Answers

When two or more **fractions** are provided, the** least common denominator** is defined as the smallest **common multiple** of all the common multiples of the denominators.

What is the least common denominator?The smallest **number** that is a common denominator for a particular set of fractions is referred to as the **least common denominator (LCD)**. For fraction **addition** and **subtraction**, as well as comparing two or more fractions, the given fractions must have common denominators.

Let's assume we have to add the fractions: (2/9)+(3/4)

We need to determine a common** integer** that is a** **multiple of both denominators, which are 9 and 4.

This **common multiple** will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the **expression **can be written as follows:

(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36

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Determine if the sequence below is arithmetic or geometric and determine

the common difference / ratio in simplest form.

64, 16, 4, ...

### Answers

The **sequence** 64, 16, 4,. is **geometric **

What is an arithmetic sequence?

**Arithmetic** Sequence can simply be defined as a sequence in which the **difference** between successive or consecutive terms is known as a constant.

The sequence is in the form a, a + d, a + 2d, a + 3d, a + 4d

Where;

a is the first termd is the common difference of the sequence

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n – 1)d

What is a geometric sequence?

**Geometric sequence **can simply be defined as a sequence where the **ratio **of every two consecutive or successive terms is a known constant.

Given the sequence;

64, 16, 4, ...

We can see that the common ratio between the terms is 4 and hence a geometric sequence

Hence, it is a** geometric **sequence

Learn more about **geometric sequence **here:

https://brainly.com/question/1509142

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