Mathematics High School

## Answers

**Answer 1**

The **volume **of the **cylindrical jar **be 1130.97 in³.

Also, 56 **whole marbles** can **fit** in the **jar**.

Given, a **cylindrical jar** has a **radius** of 6 inches and a **height** of 10 inches.

The **jar** is **filled** with **marbles** that have a **volume** of 20 in³.

(a) The **volume** of the** cylindrical jar** be,

Volume = πr²h

Volume = (3.14)(6)²(10)

Volume = 1130.97 in³

(b) Now, if each **marble** has the **volume** of 20 in³

then, the **number** of **marbles** that can be **fit** in the **jar** be,

The number of marbles = 1130.97/20

The number of marbles = 56.

Hence, the **volume **of the **cylindrical jar **be 1130.97 in³.

Also, 56 **whole marbles** can **fit** in the **jar**.

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## Related Questions

Express using exponents and simplify any numerical coefficients: w · w · w

### Answers

**Answer:**

w to the power of 3 or w^3

**Step-by-step explanation:**

For example, plug in a number for the variable given, and in this case, I used the number 2. When using the number 2, the question would become 2 * 2 * 2. It would be simplified as 2 to the power of 2 to the power of 3. That's how I got the answer of w to the power of 3.

This is confusing.

Gradient is???

### Answers

For the given **graph**, the **gradient** of the given blue line in the graph is equal to** 2.**

As given in the question,

For the given graph,

Consider two pairs of coordinates on the blue **line** of the given graph,

( x₁ , y₁ ) = ( 2, 2 )

( x₂ , y₂ ) = ( 3, 4 )

Gradient is nothing but slope of the line

Formula to calculate the gradient of the given blue line of the graph is given by:

**Gradient **= ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Gradient = ( 4 - 2 ) / ( 3 - 2 )

= 2 / 1

= 2

Therefore, for the given graph, the **gradient** of the given blue line in the graph is equal to 2.

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$1200, 3.5%, 2 years

### Answers

The** simple interest** would be $84.

**What is simple interest?**

Calculating the** interest** on a loan using **simple interest** is quick and simple. **Simple interest** is calculated by dividing the principle by the daily **interest** rate and the number of days between installments.

A quick and simple way to figure out **interest **on money is to use the **simple interest** technique, which adds **interest **at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us** interest **on our investment. One of the different types of **interest** charged by banks is **simple interest**.

**Interest** = (Principle x Rate x Time in years)/100

= (1200 x 3.5 x 2)/100

= 84

The **simple interest** would be $84.

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How much would you subtract from the grouping?

(4 – 2)4 – 42 × 4

### Answers

**Answer:**

-160 I think so

**Step-by-step explanation:**

(2)4-168

8-168

-160

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

### Answers

According to the **Pythagoras theorem,** the value of the other **leg **is, **15.7 cm**

**Pythagoras theorem:**

Pythagoras theorem defines that the square of the **hypotenuse **is equal to the sum of the **squares **of the other two **sides**.

Given,

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.

Here we need to find the measure of the other leg and round off it to nearest tenth.

Though the given question, we know that the value of

**Hypotenuse **= 16 cm

one leg = 3cm,

Then let us consider the length of the other leg as x.

So, according to the Pythagoras theorem,

It can be calculated as,

=> **hypotenuse² = one leg² + other leg²**

=> 16² = 3² + x²

=> 256 = 9 + x²

Here we need the value of x, so it can be rewritten as,

=> 247 = x²

=> x = √247

When we take **square **root for 247, then we get the value of x as,

=> x = 15.716

When we round off it to the **nearest **tenth then we get the value of another leg as 15.7 cm.

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Factor the expression in the image please

### Answers

To **factorize** this,the answer is [tex]\frac{1}{3} x^{4} y^{2} (\frac{1}{4} y^{} -\frac{1}{3} x)[/tex]

What is Factorization?

**Factorization** is when you break a number down into smaller numbers that, when multiplied together, give you that original **number**.

The expression above can only be determined by looking at the common **factors** and using it to answer the question. [tex]\frac{1}{12} x^{4}y^{3} -\frac{1}{9}x^{5}y^{2}[/tex]

To factorize the **fractions** by looking at the common **factor** between the both[tex]\frac{1}{3} (\frac{1}{4} -\frac{1}{3} )[/tex]To factorize the indices by looking at the common factor[tex]x^{4}y^{2} (y-x)[/tex]

So, to **factorize** the expression above[tex]\frac{1}{3} x^{4} y^{2}(\frac{1}{4} y-\frac{1}{3} x)[/tex]

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Please help F(-1/2)=1 and f(0)=-4

### Answers

Question:

Write a linear function f with f (- 1/2) = 1 and f (0) = -4

The** linear function** f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

**What is a linear equation?**

A linear** equation** is an equation in which each term has at max one degree. Linear equations in **variables** x and y can be written in the form

y = mx + c

Linear **equation** with two **variables**, when graphed on the **cartesian plane **with axes of those **variables**, give a straight line.

We are asked to write the **linear function **f with f (- 1/2) = 1 and f (0) = -4

Let the **equation** in **variables** x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c -----------eq 1

Also f (0) = -4

This gives -4 = c. --------------eq2

Now Putting the value of c in the **equation** in eq1 we get m=0.

So 1 = -1/2m+c

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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in september 2011, gallup surveyed 1,004 american adults and asked them whether they blamed barack obama a great deal, a moderate amount, not much, or not at all for u.s. economic problems. the results showed that 53% of respondents blamed barack obama a great deal or a moderate amount. using these data, we calculated a 99% confidence interval of (0.489, 0.571) for the proportion of all american adults who blame barack obama a great deal or a moderate amount. does the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems?

### Answers

The 99% **confidence interval** indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).

In the given question we have to find the **confidence interval** indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems.

Gallup surveyed 1,004 american adults.

So n=1004

The results showed that 53% of respondents blamed barack obama a great deal or a **moderate amount**.

So p=53% = 0.53

The 99% confidence interval for the** proportion** of all american adults who blame barack obama a great deal or a moderate amount for u.s. economic **problems** is

CI=p±z× √{p(1−p)}/n

Now finding the value of z for 99% confidence interval.

The **z critical value** at 99% confidence interval is 2.575.

Now putting the value

CI=0.53±2.575× √{0.53(1−0.53)}/1004

CI=0.53±2.575× √(0.53*0.47)/1004

CI=0.53±2.575× √0.2491/1004

CI=0.53±2.575× √0.00025

CI=0.53±2.575× 0.0158

CI=0.53±0.0407

CI=(0.53+0.0407, 0.53−0.0407)

CI=(0.571, 0.489)

Hence, the 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).

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9. If XYZ LMN, what is the length of XZ?

### Answers

**Answer:**

XZ = 21 cm

**Step-by-step explanation:**

since the triangles are congruent then corresponding sides are congruent, so

LN = XZ , that is

5x - 19 = 2x + 5 ( subtract 2x from both sides )

3x - 19 = 5 ( add 19 to both sides )

3x = 24 ( divide both sides by 3 )\

x = 8

then

XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm

A helicopter hovers 60 m above the ocean's surface. A submarine is resting 30 m

underwater, directly below the helicopter. What is the difference between the positions of these two objects?

### Answers

**Answer:**

90 m

**Step-by-step explanation:**

because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects

you send e-mails to tell your four friends about the school fair.Then those people send e-mails to four more people. Which formula can be used in this situation

### Answers

The formula used in the situation of **sending **the **emails **is distributive property of multiplication and simple **addition **formula

How to determine the formula to be used

information gotten from the question

you **send e-mails** to tell your four **friends **about the school fair

Then those people send e-mails to four more people

From the first statement the number of **emails **sent is 4

The second statement says that the 4 persons sent to 4 more people hence each person sent one email

The total number of email sent is solved by

= 4 emails sent by you + 1 email sent by each friend * 4 (**distributive property**)

= 4 emails sent by you + 4 emails sent by friends

= 8 emails

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8x + 5° + 3x + 8° =90

Solve for x pls <3

### Answers

**Answer: x=7°**

Combine like terms and divide.

8x+5°+3x+8°=90°

(8x+3x)+(5°+8°)=90°

11x+13°=90°

-13° -13°

11x=77°

[tex]\frac{11x}{11} =\frac{77}{11}[/tex]

x=7°

The lifetime (in hours) of an electronic component is a random variable with density function given by

\(f(y)=\left\{\begin{array}{ll}

\frac{1}{100} e^{-y / 100}, & y>0, \

0, & \text { elsewhere. }

\end{array}\right.

\)

Three of these components operate independently in a piece of equipment. The equipment fails if at least two of the components fail. Find the probability that the equipment will operate for at least 200 hours without failure.

### Answers

The **probability** that the equipment will operate for at least 200 **hours** without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

Given:

mean = 1/100

Let X = the number of** components **that fail before 200 hours . The X has a **binomial distribution** n = 3 and p = 1 – e^-2.

probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].

= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]

= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]

= [tex](1-e^{-2} )^2[2e^-2+1][/tex]

Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

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A bookstore had 150 copies of a magazine. Yesterday the bookstore sold 2/5 of these copies. How many copies were sold yesterday

### Answers

60 because 2/5 = x/150. 300 = 5x. 300/5 = 60

**Answer:**

Hi

**Step-by-step explanation:**

so the question is asking what is 2/5 of 150

if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.

does 150 split up into 5 even parts??

hmmm you probably are thinking, 15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30 :)

2 time 30 = 60

so there is how to figure out the answer and , the answer 60 :)

Select the correct answer from each drop-down menu.

For the diagram shown, complete a true statement.

A

B

G

DE is the ray with endpoint

D

E

GA and DF

intersect.

### Answers

The DE is the ray with **end point** E and the ray GA and ray DF will not **intersect**

From the given** diagram**

Consider the ray DE,

**The starting **point of the ray DE = D

Then the end point of the ray DE = E

The D is the starting point and E is the end point of the ray DE

Therefore DE is the ray with end point E

Consider the **ray GA and DF**, those rays are not in contact and going opposite direction, therefore it will not intersect

The GA and DF **will not intersect**

Hence, the DE is the ray with end point E and the ray GA and ray DF will not intersect

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month of the gym

membership?

5. A train travels 16 miles in

20 minutes. At this rate, how

many minutes will it take to

travel 12 miles?

### Answers

**Answer: 15 minutes**

**Step-by-step explanation:**

Let's make a proportion

16 miles - 20 minutes

12 miles - х minutes

Hence,

[tex]\displaystyle\\x=\frac{12(20)}{16} \\\\x=\frac{3(4)(4)(5)}{4(4)} \\\\x=3(5)\\\\x=15\ minutes[/tex]

Which two lines are perpendicular to each other?

Line A: 2y=8x+10

Line B: 6y+3x = 12

Line C: 8y = −2x − 16

### Answers

**Answer:**

Line A and C

**Step-by-step explanation:**

The perpendicular slope of another line is the negative reciprocal of the other slope.

For example, we have line [tex]x_{1}[/tex].

y = x

The line that is perpendicular to it is:

y= [tex]-\frac{1}{x}[/tex]

Lets tranform all of these equation to slope intercept form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Divide 2 on both sides to simplify line a into slope intercept form.

[tex]\frac{2y}{2} = \frac{8x+10}{2}[/tex]

Simplify.

y = 4x + 5

Now it is in slope-intercept form. Slope of 4 and y-intercept of 5.

Line B

Isolate y on both sides by subtracting 3x on both sides.

6y + 3x - 3x = 12 - 3x

6y = 12 - 3x

Divide 6 on both sides.

[tex]\frac{6y}{6} = \frac{-3x+12}{6}[/tex]

Simplify.

y = -1/2x + 2

Now it is in slope-intercept form. Slope of -1/2 and y-intercept of 2.

Line C

Divide both sides by 8.

[tex]\frac{8y}{8} = \frac{-2x-16}{8}[/tex]

Simplify.

y = -1/4x - 2

Line A has a slope of 4. Line C has a slope of -1/4x. Line C is the negative reciprocal of Line A as multiplying Line A by -1 and flipping the fraction simple gets you Line C. (and vice versa).

7x+y=5 equations answer

### Answers

**Answer:**[tex]x=\frac{5}{7} -\frac{y}{7}[/tex]

**Step-by-step explanation:**

You move all terms that dont contain **x **to the right side and solve.

Hope this helps! :))

The perimeter of a rectangle is 30 cm. Its width is 3 cm. Which equation can represent the perimeter of the rectangle if L= length? (please explain how you got the answer)

A.) 3 + L = 30

B.) 3L = 30

C.) 6 + 2L = 30

D.) 6L = 30

### Answers

The equation that can represent the perimeter of the given rectangle is

6 + 2L = 30, **option c **is correct.

Given,

**width** of rectangle = 3 cm

**length** of rectangle = L

**perimeter** of rectangle = 30 cm

**equation** of perimeter of rectangle = 2 × (L + W)

By substituting the values of width and perimeter we can get the equation,

perimeter = **2 × (L + W)**

=> 30 = 2 × (L + 3)

=> 30 = 2L + 6

=> 6 + 2L = 30

Therefore, the equation of the perimeter of a rectangle is** 6 + 2L = 30**.

Translate this sentence into an equation.

Six more than the quotient of a number and 7 is equal to 9.

### Answers

I believe it is (7 ÷ x) + 6 = 9

−2 1/4×(−1 1/3)[tex]−2 1/4×(−1 1/3)[/tex]

### Answers

The **value **after **multiplying **the given** mixed fractions** is 7/6 .

In the question ,

it is given that ,

the two** mixed fraction** are given as [tex]-2\frac{1}{4}[/tex] and [tex]-1\frac{1}{3}[/tex] ,

we need to find their **value **after **multiplication **.

we first convert the mixed fractions into **improper fraction** ,

So ,

[tex]-2\frac{1}{4}[/tex] = (-2×4+1)/4 = (-8+1)/4 = -7/4

and

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

So , the **product **of -7/4 and -2/3 is written as

= -7/4 × -2/3

= (-7 × -2)/(4 × 3)

= 14/12

after simplifying ,

= 7/6

Therefore , The **value **after **multiplying **the given** mixed fractions** is 7/6 .

The given question is incomplete , the complete question is

Find the value after multiplying the given mixed fraction [tex]-2\frac{1}{4} \times -1\frac{1}{3}[/tex] .

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Rain fell at a constant rate for 2 hours on Friday. During that time, the total amount of rain that fell was 3/4 inch. what is the rate, in inches per hour, at which rain fell during that time on Friday?

3 1/3

1 7/8

8/15

3/10

### Answers

The** rate**, in inches per hour, at which the rain fell during that time on Friday is 3/8 inches per hour.

**Time **for which the rain fell = 2 hours

The** **total amount of rain that fell = 3/4 inch

So, in 2 hours, the amount of rain that fell = 3/4

In 1 hour, the amount of rain that fell = 3/8 inches

Hence, The **rate**, in inches per hour, at which the rain fell during that time on Friday = 3/8 inches per hour.

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(a) 11³ x 11=11

11³

||³ + x = || 2

### Answers

**Step-by-step explanation:**

I suspect you mean

11³ × 11 = ?

11³ ÷ 11 = ?

11³ × 11 = 11⁴

11³ ÷ 11 = 11²

why ?

11³ = 11×11×11

11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴

11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²

Johnny has some nickels and dimes in his pocket, and the change is worth $0.75. He has twice as many dimes as nickels. How many of each type of coin does Johnny have?

| BTW this is a system of equations question

### Answers

The number of **dimes** and **nickels** that **Johnny** has are 6 and 3 respectively.

How to calculate the value?

The following should be noted:

**Nickel** = 5 cent = 0.05

**Dime** = 10 cents = 0.10

Let the number of **nickels** = n

Let the number of dimes = 2n

Total worth = $0.75

This will be illustrated as:

0.05(n) + 0.10(2n) = 0.75

0.05n + 0.20n = 0.75

0.25n = 0.75

**Divide**

n = 0.75/0.25

n = 3

Number of **nickels** = 3

Number of dimes = 2n

= 2 × 3

= 6

Number of **dimes** = 6

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4. Each year a certain amount of money is deposited in an account which pays an

annual interest rate of r so that at the end of each year the balance in the account is

multiplied by a growth factor of x = 1+r. $1,000 is deposited at the start of the first

year, an additional $300 is deposited at the start of the next year, and $500 at the

start of the following year.

a. Write an expression for the value of the account at the end of three years in

terms of the growth factor x.

b. Determine (to the nearest cent) the amount in the account at the end of three

years if the interest rate is 4%.

### Answers

a)An **expression** for the value of the **account** at the end of three years will be:

$1000[tex]x^3[/tex] +300[tex]x^2[/tex] + 500x

b) The **amount** in the account at the end of three years if the **interest** **rate** is 4% will be:

= 1000 × [tex]1.04^3[/tex] + 300 × [tex]1.04^2[/tex] + 500 × 1.04

= $ 1969.344

Given,

In the question:

A **growth** **factor** of x = 1+r. $1,000 is deposited at the start of the first year,

An additional $300 is deposited at the start of the next year, and $500 at the start of the following year.

To find the:

a) Write an expression for the value of the account at the end of three years in terms of the growth factor x.

b) Determine (to the nearest cent) the **amount** in the account at the end of three years if the interest rate is 4%.

Now, According to the question:

a) Growth factor x = 1 + r

Based on the given conditions:

An **expression** for the value of the **account** at the end of three years will be:

$1000[tex]x^3[/tex] +300[tex]x^2[/tex] + 500x

b) The amount in the account at the end of three years if the **interest** **rate** is 4% will be:

1 + 4% = 1 + 0.04 = 1.04

= 1000 × [tex]1.04^3[/tex] + 300 × [tex]1.04^2[/tex] + 500 × 1.04

= $ 1969.344

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What is the area of the base, B, of the prism?

### Answers

**Area** of the base 'B' of a given **rectangular prism** is equal to **12 ft².**

As given in the question,

For the given rectangular prism ,

Shape of the base is rectangle,

**Length** of the base of a rectangular prism = 4 ft

Width of the base of a rectangular prism = 3ft

**Area** of the base of a rectangular prism is given by

= ( length of the base ) × ( Width of the base)

Substitute the value of length and width of the base of the rectangular prism we get,

= ( 4 × 3 ) ft²

= 12 ft²

Therefore, **area** of the base 'B' of given rectangular prism is equal to 12 ft².

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**Answer:**

**Step-by-step explanation:**

Determine the new coordinate location after (-3,7) on the graph y=-x^2 has undergone the following transformation: A reflection in the x axis followed by a vertical translation of 4 units up. What is the new coordinate?

### Answers

Check the picture below.

notice the point, reflected over the x-axis and then shifted upwards, notice the parabola mentioned above, nowhere near it.

The number of books in Hannah's home library can be described by n(x) = 4x + 2, where x is the number of months that have passed since she began expanding her library. Describe how n(x) is related to its parent function and interpret the function in the context of the situation.

### Answers

n(x) is a **vertical dilation** of scale factor 4 followed by a **translation **of 2 units upwards of the **parent linear function.**

**How is n(x) related to the parent function?**

The** parent linear function **is:

f(x)= x

And the **function **n(x) is:

n(x) = 4x + 2

If first we apply a **vertical dilation** of scale factor 4 to the **parent linear function**, we will get:

n(x) = 4*f(x)

And if now we apply a **translation **of 2 units upwards, then we get:

n(x) =4*f(x) + 2

Replacing f(x) by x we get:

n(x) = 4*x + 2

And we returned to n(x), so these are the transformations that define our function in terms to the **parent function.**

And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.

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A group of friend wnat to go to the amuement park. They have no more than $110 to pend on parking and admiion. Parking i $8 and ticket cot $23 per peron including tax

### Answers

**Inequality**: 23x + $8 ≤ $110

Inequality:

$110 = Amount of money they have

$8 = Parking Cost

$23 = Cost of tickets per person

23x + $8 ≤ $110

23x=$110-8

23x=$102

In** mathematics**, a courting among expressions or values that aren't the same as every other is referred to as **'inequality**. This term is used to examine the significance, wide variety, and intensity of two values or expressions. **Equations** and inequalities are both mathematical sentences fashioned by using referring to two expressions for every difference. In an equation, the two expressions are **deemed** equal's shown with the aid of the symbol =.

whereas in inequality, the **two expressions **aren't necessarily the same that's indicated by means of the** symbols**: >, <, ≤ or ≥. Inequality is critical to poverty due to the fact the relative role of people or families in society is taken into consideration as a** crucial aspect** of their welfare.

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selecting a counter displays information about that counter's collected data as a chart type. which chart type displays the current value of each performance counter in decimal format? group of answer choices line histogram bar report stacked area

### Answers

**The Bar graph, Line graph and Report displays the counter in decimal format.**

Selecting a counter displays information about that counter's collected data as a chart type. The bar graph, line graph and report displays the current value of each performance counter in decimal format.

**Line graph**: - Line graph, also known as a l**ine chart **or **line plot**, is commonly drawn to show how something changes over a period of time. scientists and engineers use these graphs to understand and derive meaning from large chunks of data.

**Bar graph**: - This are the pictorial **representation **of **data**, in the form of vertical or horizontal rectangular bars, where the length of bars are proportional to the **measure of data.** They are mostly used in business and finance, but they can also be found in other contexts. This can be used to show the distribution of different heights of students in a class.

**Report: -** A **report** is a document that presents **information** in an organized format for a specific audience and purpose. All the skills and the knowledge of the professionals are communicated through reports. Reports help the top line in decision making. A rule and balanced report also helps in problem solving.

Learn more about **Measures of Data:**

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