Mathematics College

## Answers

**Answer 1**

The amount of substance present determines the extent of the properties. **Extensive properties** include **volume**, **size**, **mass**, **length**, and **weight.**

An** extensive property **is one that is influenced by the quantity of** matter** in a test. The vastness of a system is determined by its scale or the volume of materials contained within it. Extensive properties are those in which the value of a system's property equals the sum of the importance of its constituents.

The extent of a** system** is determined by its size or the amount of matter in it. The value of a system's property is said to be extensive if it equals the sum of the values of the system's parts.

There are properties of matter that are affected by the **quantity **or size of the matter, such as length, mass, volume, weight, and so on; these are known as extensive properties of matter, and their **value** changes as the size or quantity of matter changes.

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## Related Questions

A force of 40 pounds, exerted at an angle of 10° with the horizontal, is required to slide a desk across a floor. Determine the work done in sliding the desk 12 feet. (Round your answer to one decimal place.)

### Answers

The **work done** in sliding the desk 12 feet is 479.04 foot-pounds.

How to calculate the work done?

The **work** **done** in sliding the desk is given by the equation:

work = force x distance x cos(θ)

In this case, the **force** is 40 pounds, the **distance** is 12 feet, and the angle is 10°.

Converting the angle to **radians**:

angle (radians) = 10° x (π / 180°) = 0.174 radians

Next, we can calculate the **cosine** of the angle:

cos(θ) = cos(0.174) = 0.9848

Finally, we can calculate the **work** **done**:

work = 40 pounds x 12 feet x 0.9848 = 479.04 foot-pounds (rounded to one **decimal** place)

So, the work done in sliding the desk 12 feet is 479.04 foot pounds.

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(2x-21)+x=180 Find the value of x with a 180 degree line

### Answers

**Answer:**

x = 67

**Step-by-step explanation:**

2x - 21 + x = 180 Add like terms

3x - 21 = 180 Add 21 to both sides

3x - 21 + 21 = 180 + 21

3x = 201 Divide by 3

x = 67

**Answer:**

x=67

**Step-by-step explanation:**

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Use the number line to answer the following 2 questions. how many groups of 5/3 are in 1?

### Answers

Rounding up, 3/5 is approximately **equal **to 1. So there is one group of **fraction **5/3 in 1.

What is a number line?

In basic mathematics, a **number line** is an image of a magnitude line that serves as a visual representation of real numbers. Each point on the number line corresponds to a **real number**, and each real number is assumed to correspond to a point. To find the number of 5/3 groups in 1, you can divide 1 by 5/3. The result shows how many 5/3 groups fit in 1.

1 / (5/3) = 3/5

So 1 has 3/5 of the 5/3 groups. To convert this to an **integer**, you can round the result to the nearest integer.

Rounding up, 3/5 is approximately equal to 1. So there is one group of 5/3 in 1.

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Find (f • g)(4) for the functions

f(x) and g(x) given below.

f(x) = x² + 1 and g(x)=x-4

(f.g)(4) = [?]

### Answers

The value of the **required **function f.g for x=4 is 0

What are functions?

Function, in **mathematics**, is an expression, rule, or law that defines a relationship between one **variable **(the independent variable) and another **variable **(the dependent variable).

Given here: Two **functions **f(x)=x²+1 and g(x)=x-4

thus f(x).g(x)=(x²+1).(x-4)

=x³+x-4x²-4

(f.g)(4)=4³+4-4×4²-4

= 64+4-64-4

=0

Thus the **value **of (f.g)(4) =0

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give an example of three linearly dependent vectors in r3 such that none of the three is a multiple of another.

### Answers

x (-2) + 2x1 - 3x2 + X3 = 0 is an **example** of three linearly **dependent** **vectors** in R³.

A set of vectors is said to be** linearly dependent** in the theory of vector spaces if there is no nontrivial linear combination of the vectors that equals the zero vector. The vectors are referred to as being linearly dependent if such a linear combination is **present**.

A plane's three vectors can rely on each other linearly. They are not **scalar multiples** if there are no parallel pairs. So, using (1,0,0),(0,1,0), and(1,1,0) as our three vectors, we can see that they are linearly dependent by noting that (1,0,0)+(0,1,0)+(1)(1,1,0)=(0,0,0).

According to this,

x (-2) + 2x1 - 3x2 + X3 = 0 is an **example** of three linearly dependent vectors in R³.

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aved Data concerning Follick Corporation's single product appear below Selling price per unit variable expense per unit Fixed expense per month s 180.00 68.40 $130,200 The break-even in monthly dollar sales is closest to: (Round your intermediate calculations to 2 decimal places.) Multiple Choice $210,000 $289,800 $130,200 $420,000 Cubie Corporation has provided the following data concerning its only product Selling price Current sales Break-even sales s 111 per unit 9,500 units 8,170 units What is the margin of safety in dollars? Multiple Choice $1,054,500 $147630 $906,870 $779,908 Serfass Corporation's contribution format income statement for July appears below: Sales Variable expenses Contribution margin Fixed expenses Net operating income $106,560 $320,000 176,000 144,000 37,440 The degree of operating leverage is closest to: Multiple Choice 0.33 0.74 2.22 1.35

### Answers

The break-even in monthly dollar sales is **closest **to $789,216, the margin of safety in **dollars **is $147,630 and the degree of operating **leverage **is 4.71, which is closest to 2.22.

A. The **break-even** in monthly dollar sales for Follick Corporation is calculated as follows:

*Fixed expenses ÷ (Selling price per unit - Variable expense per unit) = Break-even point in units*

$130,200 ÷ ($180 - $68.40) = 4,378 units

*Break-even point in dollar sales = Break-even point in units × Selling price per unit*

$130,200 ÷ ($180 - $68.40) × $180 = $789,216

The break-even in monthly dollar sales is **closest **to $789,216, which is between $130,200 and $789,216, so the answer is $789,216.

B. The **margin **of safety in dollars is calculated as follows:

*The margin of safety in units = Current sales - Break-even sales*

9,500 units - 8,170 units = 1,330 units

*The margin of safety in dollars = Margin of safety in units × Selling price per unit*

1,330 units × $111 = $147,630

The margin of **safety **in dollars is $147,630.

C. The degree of **operating leverage** is calculated as follows:

*Degree of operating leverage = Contribution margin ÷ Net operating income*

$176,000 ÷ $37,440 = 4.71

The degree of operating leverage is 4.71, which is closest to 2.22.

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Besides choosing a phone plan; relate this overall activity to a real-life application when you can use patterning and expressions to make an informed decision about real life

### Answers

**Answer:**

You use probability in daily life to make decisions when you don't know for sure what the outcome will be.

A fair die is rolled twelve times, and X is the number of composite numbers that result.

Find the mean of X.

Find the variance and standard deviation of X.

### Answers

The mean of X is 6, the **variance** of X is 3, and the standard deviation of X is 1.732.

What is Probability?

It is a branch of mathematics that deals with the **occurrence** of a random event.

A composite number is a positive integer **greater than** 1 that is not prime.

The** prime numbers **on a die are 2, 3, and 5, and the composite numbers are 4, 6, and 1.

The probability of rolling a **composite** number on one roll of the die is therefore 1/2.

Since each roll is independent, X follows a **binomial** **distribution** with n=12 trials and p=1/2 probability of success.

The **mean** of X is given by μ = np = 12(1/2) = 6.

The variance of X is given by σ²= np(1-p) = 12(1/2)(1/2) = 3.

The** standard deviation** of X is the square root of the variance, i.e., σ = √3 = 1.732.

Therefore, the mean of X is 6, the **variance** of X is 3, and the standard deviation of X is 1.732.

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The population of a town was 4800 last year. And the population decreased by 5% this year what was the population of the town this year?

### Answers

Using **percentage**, The **population **of town during this year was **4560.**

Before figuring out the **percentage **drop, figure out the difference (reduction) between the two numbers you are comparing. Divide the decrease by the starting number, and then **multiply **the result by **100.**

What is the percentage reduction?

The **percentage decline **is the difference between the starting and ending statistics. Regardless of the units, it shows a % decline in value relative to the starting point. The amount of decrease is the difference between the beginning and **final values**.

How are percentage gains and declines determined?

Determine the difference between the two numbers you are comparing first (rise). Next, divide the **increase **by the **original amount **and multiply the result by 100: increase = 100 times the initial number. If the response you give is a negative number.

Given,

**Population **of town=**4800**

Population **decreased **by=**5%**

**New population **this year=4800-(5/100)x4800=4800-240=**4560**

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A manufacturing company has 5 vice presidents: Andrew, Beth, Charles, Diane, and Eric.

Their regional responsibilities are shown in the table.

Vice President Regional Responsibility

Andrew East

Beth East

Charles East

Diane West

Eric West

The president of the company wants to select 2 of the 5 vice presidents to send to a conference. The 10 possible samples of size 2 that can be selected from this population without replacement are (Andrew, Beth), (Andrew, Charles), (Andrew, Diane), (Andrew, Eric), (Beth, Charles), (Beth, Diane), (Beth, Eric), (Charles, Diane), (Charles, Eric), and (Diane, Eric).

Which of the following gives the sampling distribution of the sample proportion of east regional responsibility for all possible samples of size 2 from this population?

### Answers

The **sample proportion** of east regional responsibility for all possible **samples** of size 2 from this population is given by option 1.

What is sampling distribution?

The **probability distribution** of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a given population.

A population is the total group from which a **statistical sample** is taken in statistics. An entire group of individuals, things, occasions, medical visits, or measurements can all be referred to as a population. Therefore, a population can be defined as an overall observation of persons clustered together by a shared characteristic.

From all the given combinations we have:

(Andrew, Beth) = 1

(Andrew, Charles) = 1

(Andrew, Diane) = 0.5

(Andrew, Eric) = 0.5

(Beth, Charles) = 1

(Beth, Diane) = 0.5

(Beth, Eric) = 0.5

(Charles, Diane) = 0.5

(Charles, Eric) = 0.5

(Diane, Eric) = 0

Hence, the sample proportion of east regional responsibility for all possible samples of size 2 from this population is given by option 1.

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The correct question is:

What’s the value for y?

### Answers

**Answer:**

y = 18.75

**Step-by-step explanation:**

Because of the parallel segments, triangles JKL and JMN are similar.

JK/JM = KL/MN

9/(9 + 13.5) = 7.5/y

9/22.5 = 7.5/y

9y = 22.5 × 7.5

y = 18.75

Graph the rational function . Both branches of the rational function pass through which quadrant?

### Answers

The graph of the **rational function **given as** **y=x/x²+2x+1 has been attached below. Both the branches of the** rational function** pass through the **third quadrant**.

**What is a rational function?**

A **rational function** is the ratio of two polynomial functions with a non-zero denominator polynomial. **R(x) = P(x)/Q(x)**, where P(x) and Q(x) are **polynomial functions**, is the standard representation of this relationship.

We are given a **rational function **as y=x/x²+2x+1.

The graph for the same has been attached below.

From the graph, it can be observed that both branches of the** rational function** pass through the **third quadrant**.

Hence, both branches of the** rational function** pass through the **third quadrant**.

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Question:

Graph the rational function y=x/x²+2x+1. Both branches of the rational function pass through which quadrant?

Problem of the Week: -1-30-2023 Walking Rate Table Ben uses different modes of transportation. The table shows the relationship between the number of blocks walked and the number of minutes spent walking. Part A Number of Minutes Walking, x 5 7 12 16 24 Strate Walking Rate Number of Blocks, y 2 4.8 6.4 8 9.6

### Answers

The **relationship **between the number of blocks walked and the number of minutes spent walking is y = 6/11 x + 8/11.

**What is a relationship?**

A collection of ordered pairs containing one item from each set makes up a relation between two sets. If the **ordered pair** (x,y) is present in the relationship and the **objects** x and y come from different sets, then the objects are said to be related. One kind of relationship is a function.

Given **table** is

x 5 7 12 16 24

y 2 4.8 6.4 8 9.6

Assume the relationship is y = mx +c

Putting x = 5 and y = 2 in the **equation** y = mx +c:

2 = 5m + c .....(i)

Putting x = 16 and y = 8 in the equation y = mx +c:

8 = 16m + c .....(ii)

**Subtract **equation (i) from (ii)

11m = 6

m = 6/11

Putting m = 6/11 in equation (i)

2 = 5(6/11) + c

c = 2 - 30/11

c = 8/11

The **relation **is y = 6/11 x + 8/11

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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 71 kilograms. A delivery of 6 large boxes and 2 small boxes has a total weight of 92 kilograms. How much does each type of box weigh?

### Answers

The **solution **is, each type of box **weigh** is large box 13.25 kg & small box 6.25 kg.

What is equation?

An **equation** is a mathematical statement that is made up of two **expressions** connected by an equal sign. In its simplest form in algebra, the definition of an** equation** is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an **equation,** in which 3x + 5 and 14 are two **expressions **separated by an 'equal' sign.

here, we have,

A delivery of 3 large **boxe**s and 5 small boxes has a total weight of 71 kilograms.

A delivery of 6** large **boxes and 2 small boxes has a total weight of 92 kilograms.

let, large box **weight** = x

small box weight = y

then, we have,

3x+5y= 71

6x+2y= 92

solving we get,

x= 53/4

y=25/4

Hence, The **solution **is, each type of box **weigh** is large box 13.25 kg & small box 6.25 kg.

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Sally's mother said Sally can spend, at most, $25.00

on books and magazines. Books cost $3.00 each, and

magazines cost $1.60 each. Which inequality represents the

number of books, b, and magazines, m, Sally may purchase?

A)4.6bm > 25

B)4.6bm ≤ 25

C)3b+ 1.6m < 25

D)3b + 1.6m ≥ 25

### Answers

The **inequality **of the given expression is; 3b + 1.6m ≤ 25

How to solve Inequality Word Problems?

The parameters for the **inequality expression **are given as;

**Maximum amount** to be spent on books and magazines = $25

Cost of each book = $3

Cost of each magazine = $1.6

If number of books is b, and magazines is m, then we have;

3b + 1.6m ≤ 25

Thus, we conclude that is the **inequality** that is required.

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Determine what number should be added to complete the square of the expression

x^2-x. Express the answer as a decimal number.

### Answers

0.25 should be added to complete the square of the expression[tex]x^2-x.[/tex]The solution has been obtained by using **algebraic** identities.

What are algebraic identities?

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Moreover, they are employed in the factorization of **polynomials**. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

We are given an expression as x² - x.

We know that identity for (a - b)² = a² + b² - 2ab

Here, we have a = x and 2ab = x

This means that 2xb = x

So, x = 0.5

x² = 0.5 * 0.5 = 0.25

Hence, 0.25 should be added to complete the square of the **expression** [tex]x^2-x.[/tex]

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Given any two real numbersÂÂa andÂb, there is a real numberÂcÂsuch thatÂÂis _____ .

(A) betweenÂaÂandÂb

(B) betweenÂaÂandÂc

(C) betweenÂcÂandÂb

(D) betweenÂcÂandÂa

### Answers

Given any two** real **numbers a and b, there is a real number c such that c is between a and b. So, the answer is (A) between a and b.

This is because the real **numbers** form a continuous, ordered set, which means that there is** another** real number between any two real numbers.

In mathematics, if a b, then for any c such that a c b, where c is a real number between a and b. Option (A) "between a and b" is the **correct **answer in this context.

Option (B) "between a and c" is not a **valid** option because c is already defined as being between a and b. Option (C) "between c and b" is also **ruled **out because c is defined as being between a and b, not c and b. Option (D) "between c and a" is ruled out because c is **defined** as being between a and b, not between c and a.

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50 + 30h = 35h what is h ?

### Answers

**Answer: h=10**

**Step-by-step explanation:**

**50 + 30h = 35h**

**50 = 5h (subtract 30h from both sides)**

**h = 10 (divide each side by 5)**

**Final Answer: h = 10**

**Answer:**

h=10

Subtract 35h from both sides.

Combine 30h and −35h to get −5h.

Subtract 50 from both sides. Anything subtracted from zero gives its negation.

Divide both sides by −5.

Divide −50 by −5 to get 10.

**Step-by-step explanation:**

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The numeric components of the electric field in a region of space can be calculated using the equations Ex=6xy and Ey= -5? Which of the following expressions vields the potentia difference between the points (0, Y) and (X,Y)

### Answers

- [6xy × (3x'X - 3rY) - 5 × (3rY - 3x'X)] is the expression for the **potential difference** between the two points.

The potential difference between two points in an **electric field** can be calculated using the equation ΔV = - ∫Edl, where Edl is the dot product of the electric field vector and the displacement vector between the two points. In this case, we have the components of the electric field, Ex and Ey. To calculate the potential difference, we need to find the displacement **vector** between the two points.

The given points are ~3rY and 3x'X, so the **displacement** vector can be expressed as dl = (3x'X - 3rY)i + (3rY - 3x'X)j. Substituting this into the equation for ΔV, we get:

ΔV = - ∫ (Exi + Eyj) . (dl)

= - ∫ [6xy × (3x'X - 3rY) - 5 × (3rY - 3x'X)]

= - [6xy × (3x'X - 3rY) - 5 × (3rY - 3x'X)]

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The question is -

The numeric components of the electric field in a region of space can be calculated using the equations Ex=6xy and Ey= -5. Which of the following expressions fields the potential difference between the points ~3rY 3x'X 3X'X - 5

Will award brainliest I need help

### Answers

**Answer:**

38

**Step-by-step explanation:**

If F is midpoint of EG, then EF = FG

=> 4a + 6 = 7a

7a - 4a = 6

3a = 6

a = 6/3 = 2

EF = 4a + 6 = 4(2) + 6 = 14

FG = 7a = 7(2) = 14

GH = 5a = 5(2) = 10

EH = EF + FG + GH = 14 + 14 + 10 = 38

The **length **of the **segment **EG will be 16a + 6.

What is a line segment?

A **line **segment in geometry is a **section **of a line that has two clearly defined endpoints and **contains **every point on the **line **that lies within its confines.

Given that the segment EG is divided into three parts,

EF = 4a + 6

FG = 7a

GH = 5a

The length of the line segment EG will be,

EG = EF + FG + GH

EG = 4a + 6 + 7a + 5a

EG = 16a + 6

Therefore, the** length **of **segment **EG will be 16a + 6.

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How does the current real value of the investment compare to the current real value of the $2,000 after 19 years if

the father had put it in a coffee can?

A. It is approximately $4,000 more

B. It is approximately $950 more

C. It is approximately $600 less

### Answers

**Answer:**

B

**Step-by-step explanation:**

Find the height of the cylinder. Round your answer to the nearest tenth.

### Answers

The** height** of this** cylinder** is equal to 7.00 inches.

How to calculate the height of a cylinder?

Mathematically, the** volume** of a cylinder can be calculated by using this formula:

V = πr²h

Where:

V represents the** volume** of a cylinder.h represents the height of a cylinder.r represents the **radius **of a cylinder.

**Radius **= diameter/2 = 10/2 = 5 in.

Making h the subject of formula, we have the following:

Height, h = V/πr²

Height, h = 550/(3.14 × 5²)

Height, h = 550/(3.14 × 25)

Height, h = 7.00 in.

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Write an Algebraic equation that matches the value shown in the table

### Answers

An **algebraic equation** that matches the value shown in the table is y = 9x + 5.

The **y-values** are increasing by 9 each time x increases by 1. So, use 9 as a factor for x. Since 9 ·x is always 5 less than y, add 5 to the product.

What is the point-slope form?

Mathematically, the **point-slope** form of a straight** line** can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.x and y are the points.

Based on the information provided in the table (see attachment), we can logically deduce the following **data points** on the line:

Points on x-axis = (1, 2).

Points on y-axis = (14, 23).

At **data points** (1, 14), a linear equation of this line in slope-intercept form can be calculated by using the **point-slope** form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 14 = (23 - 14)/(2 - 1)(x - 1)

y - 14 = 9(x - 1)

y = 9x + 14 - 9

y = 9x + 5

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Prepare general journal entries to record the transactions below for Spade Company by using the following accounts: Cash; Accounts Receivable; Office Supplies; Office Equipment; Accounts Payable; Common Stock; Dividends; Fees Earned; and Rent Expense. Use the letters beside each transaction to identify entries. After recording the transactions, post them to T-accounts, which serves as the general ledger for this assignment. Determine the ending balance of each T-account.

a. Kacy Spade, owner, invested $100,750 cash in the company in exchange for common stock.

b. The company purchased office supplies for $1,250 cash.

c. The company purchased $10,050 of office equipment on credit.

d. The company received $15,500 cash as fees for services provided to a customer.

e. The company paid $10,050 cash to settle the payable for the office equipment purchased in transaction c.

f. The company billed a customer $2,700 as fees for services provided.

g. The company paid $1,225 cash for the monthly rent.

h. The company collected $1,125 cash as partial payment for the account receivable created in transaction f.

i. The company paid $10,000 cash in dividends to the owner (sole shareholder).

Journal and General Ledger Entries:

Accounting entries begin in the general Journal where each event is recorded as they occur. Each entry in the Journal is made using the double entry system of bookkeeping where each event/transaction affects two (2) accounts with equal and opposing entries (a debit and a credit). Entries are later posted to the General Ledger from which the financial statements evolve.

### Answers

**Journal** is the collection of **raw** **data** regarding transactions in **accounting**. **T** **account** means visual representation of thus created journals. T account gives insight about balance in each account.

Here there are 9 accounts used for **transaction** in Spade company. **Credit** and **debit** accounting is done to see the inflow and outflow of Cash. Credit is the cash paid or where cash flow out of the business. Debit is the cash received or **cash** **flow** into the **business**. Debit value increase the assets while credit value increase liabilities.

The first image is journal entry in chronological order. The second one is the T- accounts where the cash flow is categorized and visualized. The balance after transactions in each account is mentioned in it.

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1.16 convert the following binary numbers to decimal numbers, show the steps of your work. a) 1110, b) 100100, c) 11010111, d) 011101010100100

### Answers

A: 1110 represents the **decimal number **14; B: 100100 represents the decimal number 36; C: 11010111 represents the decimal number **215**; D: **011101010100100 **represents the decimal number 98164.

a) 1110 in binary represents the decimal number 14. To convert, we can use the formula:

**decimal **= 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 = 8 + 4 + 2 + 0 = 14

b) 100100 in binary represents the decimal number 36. To convert, we can use the formula:

decimal = 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 0 * 2^0 = 32 + 4 + 0 + 0 + 0 + 0 = **36**

c) 11010111 in binary represents the decimal number 215. To convert, we can use the formula:

decimal = 1 * 2^7 + 1 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 0 + 16 + 0 + 4 + 2 + 1 = 215

d) 011101010100100 in binary represents the decimal number 98164. To convert, we can use the formula:

**decimal **= 0 * 2^13 + 1 * 2^12 + 1 * 2^11 + 1 * 2^10 + 0 * 2^9 + 1 * 2^8 + 0 * 2^7 + 1 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 4096 + 2048 + 1024 + 0 + 256 + 0 + 64 + 0 + 16 + 0 + 0 + 2 + 0 = 98164

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A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 90 cubic feet. Rectangular prism B has a length of 7 feet and a width of 4 feet. The total volume of the solid figure is 230 cubic feet. What is the height of rectangular prism B? Show your work.

### Answers

The **height** of **rectangular** prism B is 5 feet.

**What is volume ?**

Volume is the amount of three-dimensional space that an object occupies or the total **amount** of space enclosed by a **three**-**dimensional** object. It is usually measured in cubic units, such as cubic feet, cubic meters

Let the **height** of rectangular prism B be h. Then, the volume of rectangular prism B can be **expressed** as:

**V(B) = length * width * height**

V(B) = 7 * 4 * h

**V(B) = 28h**

We know that the **total** volume of the solid figure is 230 cubic feet, so we can set up the following equation:

**V(A) + V(B) = 230**

**Substituting** the given values for V(A) and V(B), we get:

90 + 28h = 230

Solving for h, we can isolate the variable term by subtracting 90 from both sides:

28h = 230 - 90

**28h = 140**

Then, dividing both sides by 28, we get:

**h = 5**

Therefore, the height of rectangular prism B is **5 feet.**

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What is this in mixed number

4 1/2 - 2 2/3

### Answers

Therefore , the solution of the given problem of** fraction** comes out to be 1 5/6.

Fraction : What is it ?

An whole can be represented by any set of related sums or fractions. In standard English, a **percentage** is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the** ratio **of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction.

Here,

To subtract mixed numbers, we first subtract the whole numbers and then subtract the fractions separately.

4 1/2 - 2 2/3

Subtracting the whole numbers:

4 - 2 = 2

Now, let's subtract the fractions.

1/2 - 2/3

To subtract fractions, we need to have a common denominator. In this case, the least common multiple of 2 and 3 is 6.

1/2 = 3/6

2/3 = 4/6

Now we can subtract:

3/6 - 4/6 = -1/6

Putting it all together:

4 1/2 - 2 2/3 = 2 - 1/6

The answer in mixed number form is:

1 5/6

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A marble is selected from a bag containing eight marbles numbered 1 to 8. The number on the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has a number from 2 to 5. Event B: The marble selected has an odd number. Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. Event "A or B": {[]} X $ ? Event "A and B": {0} The complement of the event A: } Check Explanation

### Answers

(a) The outcomes for events "A or B" are 2, 4, 6, 3, 4, 5, 6. (b) The outcome for Events "4 and B" is just 4, and (c) The **complement of event** B is 1, 2, 7, and 8.

(a) Event "A or B" is the **union** of events A and B. This means the outcome is any marble that is either even numbered or has a number from 3 to 6. The outcomes in this event would be 2, 4, 6, 3, 4, 5, 6.

(b) Event "4 and B" is the** intersection** of events A and B. This means the outcome is only a marble that is both even-numbered and has a number from 3 to 6. The only outcome in this event would be 4.

(c) The complement of event B is all the **outcomes** that are not in event B. The outcomes in this event would be 1, 2, 7, and 8.

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--The given question is incorrect; the correct question is

"A marble is selected from a bag containing eight marbles numbered 1 to 8.

The number of marble selected will be recorded as the outcome.

Consider the following events.

Event A: The marble selected has an even number.

Event B: The marble selected has a number from 3 to 6.

Give the outcomes for each of the following events.

If there is more than one element in the set, separate them with commas.

(a) Event "A or B":

(b) Event "4 and B":

(c) The complement of the event B:"--

Pleas help me (image attached)

8th grade math. Please check if the graphs correct. Please explain.

### Answers

The correct **graph **of each situation is,

⇒ You gradually increase your **speed**, then ride at a constant speed along a bike path. You then slow down until you reach your friends house, shown in graph C.

⇒ You gradually increase your speed, then g down a **hill**. You then quickly come to stop at an intersection, shown in graph D.

⇒ You gradually increase your speed and then stop at the 7 - 11 for a **couple **of minutes, you then continue to ride, gradually *increase *your speed is shown in graph B.

⇒ You ride at a **constant speed **and then go up a hill. Once on top of hill, you gradually increase your speed is shown in graph A.

**What is an expression?**

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let the **speed **is represent on y - axis and time is represent on x - axis.

Hence, We get;

The correct graph of each situation is,

⇒ You gradually **increase **your speed, then ride at a constant speed along a bike path. You then slow down until you reach your friends house, shown in graph C.

⇒ You gradually increase your speed, then g down a hill. You then quickly come to stop at an **intersection**, shown in graph D.

⇒ You gradually increase your speed and then stop at the 7 - 11 for a couple of minutes, you then continue to ride, gradually increase your speed is shown in graph B.

⇒ You ride at a constant speed and then go up a hill. Once on top of hill, you gradually increase your **speed **is shown in graph A.

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which o fthe following represents the magnitude of the electric field e and the potential v as functions of r the distance from he center of the sphere when r

### Answers

The electric field (E) and potential (V) are related concepts in **electromagnetism**. The electric field at a point in space represents the force that would be experienced by a unit positive test charge placed at that point. The potential at a point in space is the energy per unit charge required to move a test charge from a reference point to that point in the electric field.

The magnitude of the **electric** field E and the **potential** V as functions of the distance r from the center of a sphere can be described as follows:

[tex]E(r) = kQ/r^2[/tex]

where k is **Coulomb's** constant and Q is the charge of the sphere.

[tex]V(r) = kQ/r[/tex],

where k is Coulomb's constant and Q is the charge of the sphere.

Note: These equations are valid only for a **uniformly** charged spherical shell. If the sphere has a non-uniform charge distribution, then the electric field and potential would need to be calculated using more complex methods.

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