Mathematics College

## Answers

**Answer 1**

it will take 120 minutes or 2 hours to sell 200 cups of coffee

## Related Questions

Please help find the value of x and y

(picture included) please show work

### Answers

Applying the **classification angles**, the **values **of **x= 29°** and **y=8.5°**.

Classification Angles

They are a lot of **classifications **for **angles **like complementary angles, supplementary angles, right angles, and others. See below:

**complementary **angles - two angles whose sum is equal to 90°. **supplementary **angles - two angles whose sum is equal to 180°. **right **angles - angles whose measure is 90°.**alternate **angles - angles on opposite sides of the transversal line. They are congruent.

From the figure, it is possible to see that:

The angles (6x-36) and 138 are **alternate **angles. Because of this, they are congruent. Then,

6x-36=138

6x=138+36

6x=174

x=174/6

x=29°

The angles (4y+8) and 138 are **supplementary **angles. Because of this, the sum of these angles is equal to 180°. Then,

4y+8+138=180

4y=180-138-8

4y=180-146

4y=34

y=34/4

y=8.5°

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The buckingham fountain holds 725 gallons of water. due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour. let y represent the amount of water in gallons after x hours of leaking

### Answers

An **equation** represent the given scenario is 725=y-12.5x.

What is an equation?

In mathematics, an equation is a **formula** that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the Buckingham fountain holds 725 gallons of water.

Due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour.

Let y represent the amount of water in gallons after x hours of leaking.

Now, equation is 725=y-12.5x

Therefore, an **equation** is 725=y-12.5x.

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8 ft

10 ft

Find the perimeter of this figure to

the nearest hundredth.

Use 3.14 to approximate .

P = [?] ft

Notice that only half of the circle is included in the figure!

### Answers

The **perimeter** of the figure is 4(π + 9)ft.

What is perimeter?

A **perimeter** is a closed path that encompasses, surrounds, or outlines either a **two dimensional** shape or a **one-dimensional** length.

Given is a **2 - D figure **as shown in the figure attached.

We can write the **perimeter** as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P = (4π) + (36)

P = 4(π + 9)

Therefore, the **perimeter** of the figure is 4(π + 9)ft.

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Consider the system of linear equations y=ax+4 and y=bx-2, where a and b are real numbers. Determine whether each statement is always, sometimes, or never true.

### Answers

The system can never have infinitely many **solutions**.

What is a linear system of equations?

A system of **linear** **equations** consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The equation y=ax+4 is in the slope-intercept form.

Therefore, the **slope** m=a and the y−intercept b=4

The equation y=bx−2 is in the slope-intercept form.

Therefore, the slope m=b and the y−intercept b=−2

Since the two lines have different y−intercept, they can never be the same for any values of a and b.

Therefore, the system can never have infinitely many **solutions**.

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Please help, I'm stuck in this math problem

### Answers

The **quotient** is 32 and the **remainder** is 6.

i.e,

32 R6

Option A is the correct answer.

What is an expression?

An **expression** isa way of writing a statement with more than two variables or numbers with **operations** such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

774 ÷ 24

24 ) 774 ( 32

768

6

The **quotient** is 32 and the **remainder** is 6.

Now,

We can write in this form,

(**Quotient**) R(**remainder**)

Thus,

The **quotient** is 32 and the **remainder** is 6.

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Pierre is 3 years older than his brother, Claude. 1. Write an equation that represents how old Pierre is (p) when Claude is c years old.

### Answers

The **equation **which is used to represent the ages of Pierre and Claude is given by p =** c + 3.**

The question can be formulated in the form of Linear equation in two variables.

**Linear equation** in two variables can be written in the form of ax + by = c where a, b and c are constant terms and x, y are independent and dependent variables respectively. Here in this question the age of Pierre is represented as p and the age of Claude is represented as c. Since, Pierre is **3 years older** than Claude then the equation representing their age can be formulated as:

**p = c + 3 where p** is Pierre's age and c is Claude's age and this represents that Pierre's age will be given when we will add 3 years more in the age of Claude.

Thus, the equation representing the age of Pierre is p = **c + 3.**

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Answer:

p=c+3

20 years old

Step-by-step explanation:

based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). which of the following statements is true?

### Answers

90% of all **random **samples of 50 students obtained at this high school would result in a 90% confidence **interval **that contains the true mean amount of money students spend on lunch. Hence, the **correct **statement is **option **(d).

A confidence interval is a range of values that are expected to contain the true **population **parameter with a certain degree of **confidence**, usually expressed as a **percentage**. Here, a 90% confidence interval means that if we were to repeatedly take random samples of 50 students and compute a 90% confidence **interval **for each sample, we would expect that 90% of these intervals would contain the true **mean **amount of money that all students spend on lunch at this high school.

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The complete question is -

Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?

(a) 90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.

(b) 90% of all students spend between $3.45 and $4.15 on lunch at this high school.

(c) 90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.

(d) 90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.

At noon, the temperature in Hampstead, Virginia was 50℉

. By midnight, the temperature had fallen to 10℉

. What was the change in temperature over the 12-hour period?

### Answers

The change in temperature over the 12-hour period was 50℉ - 10℉ = 40℉.

Find the greatest common factor for the list of the terms. 70x² , 30x³ , 60x⁸

### Answers

10x^2 because 10 is the biggest number that they are divisible by and they all have x^2

**Answer: 70x²= 1 30x ALSO= 1 60x⁸= 1 again**

**Step-by-step explanation: To find the Greatest Common Factor of these three terms you must first factor each term separately:**

A glass contains 320 cm³ of orange juice. The mass of the juice

is 370 g.

Calculate the density of the juice in kilograms per cubic metre

(kg/m³).

Give your answer to the nearest integer.

### Answers

Therefore , the solution of the given problem of** volume** comes out to be density 1.15625 g/ cm³.

Describe volume.

The volume of a three-dimensional item, which is measured in **cubic** units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The** amount** of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,

Given:

Density = mass /volume

mass = 370 gm

volume = 320 cm³

Density = 370/320

=>Density = 1.15625 g/ cm³

thus , density 1.15625 g/ cm³

Therefore , the solution of the given problem of volume comes out to be density 1.15625 g/ cm³.

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10. Here are five shape

Four of the shapes are squares and one of the shapes is a circle.

One square is black. Three squares are white.

The circle is black. The five shapes are put in a bag.

(a) Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time.

Work out an estimate for the number of times she will take a white square.

(3)

(b) Alec takes a shape at random from the bag and does not replace it. Bashir then takes a shape at random from the bag.

Work out the probability that

(i) they both take a square,

(ii) they take shapes

### Answers

The **probability** that they both take shapes 3 / 8.

What is Probability?

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

Given that there are five **shapes**, Four of the shapes are squares and one of the shapes is a circle, One square is black, three **squares** are white, circle is black.

Jasmine takes a shape at **random** from the bag 150 times

3 / 5 ×150 = 90 times.

If Alec takes a shape at random from the bag and does not replace it, there are now 4 shapes **left** in the bag.

The probability that they both take a square is 3 / 4 × 3 / 3 = 3 / 4.

The **probability** that Bashir takes a square is 2 / 4 = 1 / 2.

If Alec takes a circle, the probability that Bashir takes a square is 3 / 4. The overall probability that they both take **shapes**

(3 / 4) × (1 / 2) + (1 / 4)× (3 / 4) = 3 / 8.

Hence, the **probability** that they both take shapes 3 / 8.

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Solve the system by substitution

Y= 8

-3x-y=1

### Answers

**Answer:**

x = -3

**Step-by-step explanation:**

-3x - 8 = 1

-3x = 9

3x = -9

x = -9/3

**x = -3**

since we know that by theorem, if a is a prime number and if a divides p2, then a divides p, where a is a positive integer)

### Answers

This is referred to **Fermat's Little Theorem,** which states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p).

In other words, if we raise a to the **power** of p-1 and divide by p, the remainder will always be 1. This theorem can be used to efficiently test the primality of a number or to find modular inverses in modular arithmetic.

Fermat's Little Theorem is a fundamental result in number theory and has important applications in **cryptography **and **computer science**. The theorem states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p). This can be expressed as:

a^(p-1) = 1 + kp where k is an integer.

This theorem is a direct consequence of the fact that the set of integers from 1 to p-1 (mod p) form a group under multiplication (mod p). This group is known as the group of units modulo p, and the order of this group is p-1. Hence, a^(p-1) must be congruent to 1 (mod p) since it is the product of all elements in the group.

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A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 550 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.

### Answers

**Answer:**

The width of the walkway is 5ft long

please help

after putting the first 2 terms together and the second 2 terms together, what needs to be in the middle

1. an equal sign

2. a plus sign

3. perenthatesis around all 4 terms

4. nothing

### Answers

After putting the first 2 **terms together** and the second 2 terms together, what needs to be in the middle is; Parenthesis around all 4 terms

How to factor Algebraic Expressions by grouping?

**Factorization** by **grouping** in algebra simply means that we need to group the terms with **common factors** before factoring.

Now, some of the steps to take in this regards are;

- From the groups of the given expression a factor can be taken out from each group.

-** Factorize** each group

- Now take out the factor common to group formed.

Thus, from the above after **grouping** the terms together, the next thing to be in the middle is to put parentheses around the 4 terms.

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A cell phone is plugged in to be charged. The table shows the percent of battery power at some times after it was plugged in.

### Answers

The **equation** representing the table is y = 0.9x + 6 and at 104.44 minutes the phone will be fully charged.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

**y = mx + b**.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Let, The x coordinate represents time in minutes and the y coordinate represents battery percentage.

So, The **ordered** **pairs **are, (0, 6), (10, 15).

Slope(m) = (15 - 6)/(10 - 0).

Slope(m) = 9/10 = 0.9.

y = 0.9x + b.

6 = 0.9(0) + b.

b = 6.

**y = 0.9x + 6**.

When it is fully charged it is,

**100 **= 0.9x + 6.

0.9x = 94.

x = 94/0.9.

x = 104.44 minutes or 104 minutes and 26 seconds.

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Write an equation of the line with the given slip and y-intercept slope is 3 y intercept is -9

### Answers

y=3x-9 is the equation of the line with the given slip and** y-intercept slope** is 3 y intercept is -9

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the **steepness** of line in the coordinate plane.

The** slope intercept form** of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two **points** (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the **equation** of the line with the given slip and y-intercept slope is 3 y intercept is -9

m=3 and **y intercept** is -9

y=3x-9

Hence, y=3x-9 is the **equation** of the line with the given slip and y-intercept **slope** is 3 y intercept is -9

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Help! I hate algebra

### Answers

**Answer: 77**

**Step-by-step explanation:**

Prove the following vector identities which, among other ideas, extend the chain rule to vector operations. Use index notation. a(x), b(x)-vector functions of position x; ф(x) - scalar function of position NOTE: Begin with the expression on the left and derive the expression on the right. Try not to simply expand both sides and show that they are identical (iii) V - (V xa)-0 (vii) V ab (V aba (Vb)

### Answers

Vector identities can be derived using **index notation**. The following vector identities are to be proved: (iii) V - (V xa) = 0, (vii) V ab = (V a)b + a(V b).

Starting with the left-hand side:

V - (V x a) = V + (a x V) (by definition of** cross product**)

Using the vector triple product, a x (b x c) = (a . c) b - (a . b) c, we get:

V + (a x V) = V + (V . a) a - (V . a) a

= V (since the second **term cancels **out with the first term)

Thus, V - (V x a) = 0.

(vii) V ab = (V x (b x a))

Starting with the **left-hand side:**

V ab = V (ab)

Using the **scalar triple** product, a . (b x c) = (a x b) . c, we get:

V (ab) = (V x b) . (a x a)

= (V x (b x a)) (since a x a = 0)

Thus, V ab = (V x (b x a)).

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What is the equation of the line that passes through the point (6, -3) and has a

slope of -?

### Answers

The **equation** of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

**y **=** - kx + (6k - 3)**.

What is the equation of a straight line?

The general equation of a **straight line** is -

y = mx + c

where -

{m} → slope

{c} → y - intercept

Given is the line that passes through the point **(6, -3)** and has a slope of **{m} = - k**.

We can write the general equation as -

y = mx + c

Now -

**{m} **=** - k ** .... Eq { 1 }

We can write -

y = - kx + c

For the point (6, - 3), we can write -

- 3 = - 6k + c

**{c} **=** 6k - 3 ** .... Eq { 2 }

We can write the equation of the line as -

y = - kx + (6k - 3)

Therefore, the **equation** of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

**y **=** - kx + (6k - 3)**.

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given a standard deck of cards find the probability of randomly drawingan ace of hearts from the deck

### Answers

**Answer:**

Since there are 54 cards in a standard deck, and only 1 ace of hearts:

**You would have 1/54 of a chance of drawing the ace of hearts.**

**You would also have 1.85% of a chance drawing the ace of hearts.**

**Step-by-step explanation:**

Hope it helps! =D

HELP PLEASE I DONT UNDERSTAND!!!!!!!! McLaughlin High School is selling 1,000 tickets for $10 each to raise funds for its arts programs. One ticket will be drawn, and the person who bought it will win a $1,000 prize. What do think of such a system for raising funds? Would you buy a ticket? Why or why not?

In general, what is your personal view of games of chance, such as a raffle? Do you participate in such games? Do you have particular feelings about people who do or about those who offer them?

Now that you have explored probability and its related concepts in this unit, do you have a different perspective on games of chance than you used to? Is fairness or lack of fairness an issue for you regarding such games? Explain

### Answers

**Answer: i wouldnt**

**Step-by-step explanation: while its a good way to get funds since you'd get 10x the amount the people came. But if you were the person buying the ticket you'd have 1 in a thousand chance. Unless less people came but still -**

**so no.**

question which statement best describes a graph of paired points that form a proportional relationship? responses a straight line can be drawn through all the points, and the line passes through the point (3,0). a straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . a straight line cannot be drawn through all the points, but the line passes through the point (0,0). a straight line cannot be drawn through all the points, but the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . a straight line can be drawn through all the points, and the line passes through the point (0,0). a straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . a straight line can be drawn through all the points, and the line passes through the point (0,3).

### Answers

A statement which best describes a graph of paired **points** that form a proportional relationship include the following: F. a **straight line** can be drawn through all the points, and the line passes through the **point**, begin ordered pair 0 comma 0 end ordered pair.

What is a proportional relationship?

In Mathematics, a **proportional relationship** is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

k is the constant of proportionality.y and x represent the variables in a **proportional relationship**.

Generally speaking, the **graph** of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).

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Simplify

5x^2 - x + 9= [?]

x=3

### Answers

[tex]5x^2-x+9[/tex] when x is equal to 3

Substitute for x with the given value(3):

[tex]5(3)^2-3+9[/tex]

[tex]5(9)-3+9[/tex]

[tex]45-3+9[/tex]

[tex]=\boxed{51}[/tex]

**Answer:**

it equals 231

**Step-by-step explanation:**

5x3 is 1515x15 is 225225-3= 222222+9=231

8 less than y times 28

### Answers

The mathematical **expression**, for the given mathematical phrase, 8 less than y times 28, is 8-28y

What is expression?

**Expressions **in math are mathematical statements that have a minimum of two terms containing numbers or **variables**, or both, connected by an **operator **in between.

Given that, a mathematical phrase, 8 less than y times 28,

Converting it into a mathematical **expression**,

8-28y

Hence, the mathematical **expression**, for the given mathematical phrase, 8 less than y times 28, is 8-28y

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Help please which graph shows…. Look at image

### Answers

The correct **graph** is "**Option 3**". The solution is −11 < x < − 4 or x > 2.

Which graph shows the solution set of [tex]\frac{ x^{2}+9x-22}{x+4} \geq 0[/tex]?

Let's work through your **inequality **piece by piece.

[tex]\frac{x^2+9x-22}{x+4} > 0[/tex]

Let's locate the **inequality's** crucial **points**.

[tex]\frac{x^2+9x-22}{x+4} = 0[/tex]

[tex]x^2+9x-22=0[/tex]

(**Add x+4** to both sides)

(x−2)(x+11)=0

(Left side of the **equation** **factor**)

x−2=0 or x+11=0

(Set all **variables** to 0)

x=2 or x=−11

Verify any **potential** weak **points**.

x=2(Works in original **equation**) (Works in original equation)

x=−11(Works in **original **equation) (Works in original equation)

Important points:

**x=2 or x=−11**

(Equalizes both sides)

x=−4

(Sets the left **denominator** to 0)

Check the gaps between important points. Test the interval values to see if they are effective.

(Works incorrectly in the **original** **inequality**) [tex]x < -11[/tex]

(Works in original inequality)[tex]-11 < x < -4[/tex]

(Not applicable to the original inequality) x > 2 (Works in original inequality)

The **answer **is [tex]-11 < x < -4 $ or $ x > 2~[/tex]

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Laura and Sean find the product of 3x4 using different methods.

Laura: It's 2 thirds of 4.

²×4 = 3 +

Use words, pictures, or numbers to compare their methods in the space below.

Sean: It's 4 groups of 2 thirds.

2|3

+

= 4x

8

83 this is also worth 100 points

### Answers

Both Laura and Sean arrive at the same answer of 8/3 by using different methods.

Laura starts by multiplying 2/3 by 4 to find the total amount of 2/3 in 4 units.

Sean starts by finding the total amount of 2/3 in one group and then multiplying that amount by the number of groups, 4.

Both methods lead to the same answer, so it doesn't matter which method is used. The important thing is that the answer is correct.

Three softball players discussed their batting averages after a game.

Probability

Player 1 seven elevenths

Player 2 six ninths

Player 3 five sevenths

Compare the probabilities and interpret the likelihood. Which statement is true?

Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)

Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)

Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)

### Answers

The correct statement regarding the **probabilities **is given as follows:

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).

How to obtain a probability?

A probability is obtained with the **division **of the number of **desired **outcomes by the number of **total **outcomes in the context of a problem.

The **probabilities **for each player are given as follows:

Player 1: 7/11 = 0.636 (converting to decimal).Player 2: 6/9 = 0.6667.7Player 3: 5/7 = 0.714.

Hence the correct statement is given by the **last option **among those presented in this problem.

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erify that the following function is a probability mass function, and determine the requested probabilities. [give exact answers in form of fraction.]

### Answers

The **probability** of x = 1 is 0.2,x = 2 is 0.3, x = 3 is** 0.5**

Let X be a** random variable** with the following probability mass function:

f(x) =

x = 1: 0.2

x = 2: 0.3

x = 3: 0.5

This is indeed a **probability** mass function because the values of f(x) are all greater than or equal to 0, and the sum of the values of f(x) is equal to

To calculate the probability of x = 1, we can use the formula for probability mass functions: P(X = x) = f(x).

Therefore, the probability of x = 1 is 0.2.

To calculate the probability of x = 2, we can use the **same formula**: P(X = x) = f(x).

Therefore, the probability of x = 2 is 0.3.

To **calculate** the probability of x = 3, we can use the same formula: P(X = x) = f(x).

Therefore, the probability of x = 3 is 0.5.

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complete question

What is the probability of x = 1, x = 2, and x = 3?

Each statement describes a transformation of the graph of f(s)=s. Which

statement correctly describes the graph of y=f(x-7)+3?

A. It is the graph of ftranslated 3 units up and 7 units to the left.

B. It is the graph of ftranslated 7 units down and 3 units to the right.

C. It is the graph of ftranslated 7 units up and 3 units to the right.

D. It is the graph of ftranslated 3 units up and 7 units to the right.

### Answers

The **Transformation **is graph of f is translated 3 units **up **and 7 units to the **right**.

What is Transformation?

A point, line, or geometric figure can be **transformed **in one of four ways, each of which affects the **shape **and/or **location** of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given: y=f(x-7) + 3.

As, from the **Rule **the f(x, y) --> f(x-c, y) shows the **horizontal shift **on **right **side.

So, the function is shifted 7 **units **to the right.

Now, the rule f(x)--> f(x) + c shows the **vertical** **translation** **up **by c units.

So, the function is translated 3 **units up**.

Learn more about **Transformation **here:

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