The volume of a rectangular prism can be calculated with the following formula:

[tex]V=lwh[/tex]Where "l" is the length, "w" is the width and "h" is the height.

In this case, you can set up that:

[tex]undefined[/tex]$4500 is deposited for 4.5 years in an account that pays 4.5% interest compounded monthly. What is the value of the account when the customer takes the money at the end of the 4.5 years?

**Answer:**

$5507.98

**Explanation:**

To find the value of the account, we use the compound interest formula below:

[tex]Amount\: at\: Compound\: Interest,A=P(1+\frac{r}{n})^{nt}[/tex]From the given information:

• Principal,P=$4500

,• Interest Rate, r=4.5%=0.045

,• Number of compounding periods, n=12 (Monthly)

,• Time, t=4.5 years

Substituting the given values, we have:

[tex]\begin{gathered} A=4500(1+\frac{0.045}{12})^{12\times4.5} \\ =4500(1+0.00375)^{54} \\ =4500(1.00375)^{54} \\ =\$5507.98 \end{gathered}[/tex]**The value of the account when the customer takes the money at the end of the 4.5 years is $5507.98.**

Graph the line with slope 2/3

passing through the point (3,-1).

The **graph** of the line with **slope** 2/3 and passing through the **point** (3,-1) is given by

**What is an equation of the line?**

An **equation** of the line is a way of representing the set points which form a line in **coordinates** **system**. A basic **equation** of line is y=mx+c

We are given the **slope** of line as 2/3 and the line passes through the **point** (3,-1)

We substitute the values in **slope intercept form** we get

[tex]-1=\frac{2}{3}*3 +c\\c=-1-2\\c=-3[/tex]

Substituting the value of c in the original **equation** we get

y=2/3x-3

Hence the plot the **graph** of the above **equation**

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Solve for x:

X=

76⁰

9x+1

40°

7 is the value of x, and** 64°** is the measure of the **unknown angle.**

**Triangle angles **of 76°, (9x+1)°, and 40° are provided.

According to the triangle's "**angle sum property**," a triangle's angles add up to **180 degrees**. Three sides and three angles, one at each vertex, make up a triangle. The sum of the **interior angles** in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the **unknown angles** are calculated using this **attribute.**

Now, the total of a triangle's **three angles** equals

76°+(9x+1)°+40°= 180°

⇒ 116+9x+1 = 180

⇒ 9x + 117 = 180

⇒ 9x = 63

⇒** x = 7**

So, **9x+1=64°**

As a result, **x is equal to 7** and the **unmeasured angle is 64°.**

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What value does the 4 represent in the number 347, 490

A.40

**Explanation**

Step 1 (with number 347 and 490)

347

the digit** 7** is at one's place

digit** 4 **is at ten's place

and digit **3** is at hundred's place

then

[tex]347=(3\cdot100)+(4\cdot10)+(7\cdot1)[/tex]the value 4 represents is

[tex]\begin{gathered} \text{value}=4\cdot10=40 \\ \\ \text{value =40} \end{gathered}[/tex]

**Answer: 40,000**

**Step-by-step explanation:**

347800:three hundered and forty-seven thousand. Big chunugess

s

Simplify √50 over √2

In order to simplify this expression, we need to use the following property:

[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So we have that:

[tex]\frac{\sqrt[]{50}}{\sqrt[]{2}}=\sqrt[]{\frac{50}{2}}=\sqrt[]{25}=5[/tex]So the answer is **5.**

2. Technology required.

X

2.3

2.8

3.1

3

3.5

3.8

y

6.2

5.7

4.7

3.2

3

2.8

a. What is the equation of the line of best fit? Round

numbers to 2 decimal places.

b. What does the equation estimate for y when x is 2.3?

Round to 3 decimal places.

c. How does the estimated value compare to the actual value

from the table when x is 2.3?

The line of best fit using Desmos has the equation y = approximately **y=-2.45x+11.82**.When** **x = 2.3 y = 6.18.The **residual **is thus 0.02.

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Analyze the solution. If there is an error, circle the error and show the correct solution

Notice that on the second step, we have the following:

[tex]\begin{gathered} -2(x-7)=6 \\ +2\text{ +2} \end{gathered}[/tex]in this case, the -2 is multiplying x-7, then to eliminate it, we have to divide by 2 both sides of the equation.

if we divide by -2, we have the following:

[tex]\begin{gathered} -2(x-7)=6 \\ \Rightarrow x-7=\frac{6}{-2}=-3 \\ \Rightarrow x-7=-3 \end{gathered}[/tex]finally, if we add7 on both sides, we get:

[tex]\begin{gathered} x-7+7=-3+7 \\ \Rightarrow x=4 \end{gathered}[/tex]**therefore, x = 4**

Question 4Scott is constructing a taste of values that satisfies the definition of function.InpertOutput20320O16Which number could be placed in the empty cell so that the table of values satisfies the definition of afunction?

Remember that

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

so

in this problem

the input value must be 3

answer is option CHow many books must the publisher produce and sell so that the production cost will equal the money from sales

**Step by step explanation:**

Assuming x as the number of books, the function of production cost is:

[tex]C(x)=45240+9.25x[/tex]And the selling price function would be:

[tex]S(x)=25.5x[/tex]For rhe production cost to be equal to the money from sales we have:

[tex]\begin{gathered} 25.5x=45240+9.25x \\ 25.5x-9.25x=45240 \\ 16.25x=45240 \\ x=\frac{45240}{16.25} \\ x=2784 \end{gathered}[/tex]**Answer:**

The publisher must produce **2784 **books

What is the slope of a line perpendicular to the line whose equation is 6x+8y=−128. Fully simplify your answer.

The** slope of a line **perpendicular to the line 6x + 8y = -128 is 4/3.

Given,

The equation of a line = 6x + 8y = -128

We have to convert this into standard form of **linear equation, **y = mx + b :

So,

6x + 8y = -128

Add -6x to both sides,

6x + 8y - 6x = -6x - 128

Now,

8y = -6x - 128

Divide 8 on both sides

8y/8 = (-6x - 128) / 8

We get,

y = -6/8x - 16

Here, this is in **standard form** of linear equation.

Here slope of line, m₁ = -6/8

We have to find the slope of line(m₂) which is perpendicular to the given line.

If the line is perpendicular, the slope(m₂) will be the** negative reciprocal** of the slope(m₁) of the given line.

That is,

Slope of line, (m₂)= -(m₁) = - (-8/6) = 8/6 = 4/3

That is, the **slope of the line** which is perpendicular to the given line is 4/3.

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Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget

So to create this inequality, we will set the number of gigabytes as x, seeing as it is the unknown variable. 58+3x<70

Can someone please help me graph this? It’s due in 5 minutes

An order relationship with **greater than**, greater than or equal to, **less than**, or less than or equal to between two algebraic expressions. The solution of **inequality** -3x+4≥10 is x≤-2

An order relationship with **greater than**, greater than or equal to, **less than**, or less than or equal to between two algebraic expressions.

The given **inequality** is

-3x+4≥10.

To solve the above inequality

**Subtract** -4 from both sides.

-3x+4-4≥10-4

+4 and -4 we get **zero.**

-3x≥6

**Divide** by 3 on both sides

-x≥2

When negative sign is **multiplied **on both sides, the **greater than or equal to** symbol changes to lesser than or equal to.

x≤-2

Hence x≤-2 is **solution **for -3x+4≥10.

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HELP ASP show your work please

**Answer: 8 days**

**Step-by-step explanation:**

**1) Set up an equation. Let x be the day**

3,500 >= 2(816) + x(100+95)

The 816 is just two times (Plane ticket back and forth) so it doesn't go into the x. 100 and 95 do as it is one day.

**2) Solve the equation**

3,500 >= 2(816) + x(100+95)

1868 >= 195x

9.57 >= x

**3) Rounding**

Since the x has to be less than 9.57, our next option is **8**

WILL GIVE BRAINLIEST

please solve using order of elimination and show work pleasse

**Answer:**

c. no solution

d. x = 11, y = -5

**Step-by-step explanation:**

c.

3x - y = 7----->3x - (3x - 2) = 7

y = 3x - 2 3x - 3x + 2 = 7

2 = 7, so no solution

d.

x + 2y = 1 ----> 3x + 6y = 3

3x + 5y = 8----> 3x + 5y = 8

-----------------

y = -5

x + 2(-5) = 1

x - 10 = 1

x = 11

The following table shows the rental charge of a room in a lodge for different number of days. Find the rate of change.

**Rate of change** is $35.

The momentum of a variable is represented by the **rate** **of** **change**, which is used to mathematically express the percentage change in value over a specified period of time. Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change. The rate of change is expressed by a line's slope. It is frequently used while discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.

Given,

Table shows the rental charge of a room in a lodge for different **number** of days.

y₂ = 245

y₁ = 105

x₂ = 7

x₁ = 3

**Rate** **of** **change** = [tex]\frac{y_{2}-y_{2} }{x_{2}-x_{1} }[/tex]

Rate of change = [tex]\frac{245-105}{7 -3}[/tex]

Rate of change = 35

Rate of change is $35.

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Which equation is equivalent to

5x - 2(7x + 1) = 14x?

A. -9x - 2 = 14x

B. -9x + 1 = 14x

C. -9x + 2 = 14x

D. 12x 1 = 14x

Option A, -9x - 2 = 14x is the required **equivalent equation** for the equation 5x - 2(7x + 1) = 14x.

**What are equivalent equations?**

**Equations **with the same answer or solution are said to be **equivalent**. Comparisons between linear equations are common. When graphed, linear equations result in straight lines with a slope and a y-intercept. The characteristics that make a linear equation linear are crucial in establishing if two linear equations are **equivalent**. Although it may not seem like it at first, there are mathematical procedures to determine whether the **equivalent equations** will have the same solution.

To get** equivalent equation** of the given equation, we need to simplify it.

So, given equation

5x - 2(7x + 1) = 14x

Lets multiply -2 with 7x+1, we get

5x-14x-2=14x

it can be written as:

-9x - 2 = 14x

This is required **equivalent equation**.

Therefore, option A is correct answer

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Which of the following is NOT Linear/does not increase at a constant rate?

**Answer: The one that starts with (-4,10)**

**Step-by-step explanation:**

Linear means that the numbers are going up at a constant rate. It means, that the y will go up corrosponding x.

**1) Linear**

X goes up 2 per 4 y

**2) Linear**

X goes up 1 per 3y

**3) Linear**

X goes up 2 per 4y

**4) Not Linear**

X goes up 2 per Unequal growth y.

You can tell because it goes up by +5 until the last where it goes up +7

￼A recipe Carmen is

making calls for 4 cups of milk. She has 1 liter of milk.

Her sister says she has enough milk. Is her sister

correct? Explain.

**Answer:**

**Step-by-step explanation:**

Yes, Carmen's sister is correct because 1 liter equals 4.227 (rounded) so yes carmen would have enough milk!

A doctor visits her patients during morning rounds. In how many ways can the doctor visit 5 patients during the morning rounds?

5 patients

5 times 5 = 25

She can visit the 5 patients in 25 different ways

5 times 5 = 25

She can visit the 5 patients in 25 different ways

HELP

PLEAE I NEED HELP EPKPELPELPEL

**Answer:**

[tex]\sqrt{89}[/tex] cm

**Step-by-step explanation:**

use the pythagorean theorem

[tex]5^{2} +8^{2} =x^{2}[/tex]

25+64=[tex]x^{2}[/tex]

89=[tex]x^{2}[/tex]

[tex]\sqrt{89} =x[/tex]

Arturo asked all of his classmates if they prefer soccer or football. He found that 16 students prefer football while 20 prefer soccer. Which ratio represents the number of students who prefer soccer to the total number of students in Arturo's class? 5 4 4 Mark this and return Save and Exit Next Submit J ContentViewers/AssessmentViewer/Activity#

The number of students who prefer soccer to the total number of students in Arturo's class is represented by:

16:20

Dividing by 4 on each side of the proportion we have

4:5

Final answer is: 4:5

Marcus just got a summer job as acashier making $8.50 an hour andhas already saved $50. If he wantsto earn at least $475 for a newcomputer, how many hours musthe work? Write an inequality andsolve.

Marcus's hourly income = $8.50

Amount that has already been saved by Marcus = $50

If Marcus wants to earn at least $475 for a new computer:

Let the amount of hours he will work to earn $475 = t

Since he earns $8.50 hourly and he already saved $475, the inequality will be of the form:

50 + 8.50t ≥ 475

8.50t ≥ 475 - 50

8.50t ≥ 425

t ≥ 425 / 8.50

t ≥ 50

**Marcus must work for at least 50 hours**

I NEED HELP PLEASE!

The answer is Its 1.112

On a horizontal number lime, -6 is located to the left of -1. Enter an inequality that represents this statment.

the expression "-6 is located to the left of -1" can be written as follow:

**-6 < - 1**

where the < symbol means "lower than", that is, you have "-6 is lower than -1".

6. The net profit margin ratio for two companies is modelled by

by

8x

3x - 1

for company B where x is the number of items sold in thousands. Sam is trying

5x

2x - 3

for company A and

to decide in which company he should buy stock so he is going to compare the ratios. He

has researched both companies and he knows that each produces over 25 000 items per

month.

(C: 25)

a) He wants to find out if theywould ever have the same ratio and if so when. How would

you tell him how to find this mathematically? What should he have found as his answer

to the question?

b) Which company has a higher ratio for 30 000 items sold? What is that ratio to the

nearest thousand for both companies?

We deduce that the **ratios **would be the same for 2111 sales.

Consequently, it is obvious that firm B has a **better **ratio for 30000 sales.

Majority of the explanations for **ratio** and **proportion** use **fractions**. A ratio is a **fraction** that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of** ratio and proportion.**

if A = B then

5x/(3x-3) = 8x/(3x-1)

24x^2 - 24x = 15x^2 - 5x

9x^2 - 19x = 0

x(9x - 19) = 0

x = 0 , not possible because zero number of sales is not possible

or

x = 19/9 thousands = approximately 2111

Therefore, we conclude 2111 sales, the** ratios** would be the same.

For the second part :

we substitute the value of x as 30000 in the** equations** to see which ratio is bigger

8*30000/3*30000-1=2.666 or 2.7

5*30000/2*30000-3=2.5

Therefore we can clearly see that the company b has a** higher ratio** for 30000 sales.

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Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q′, and R′. Then sketch ΔP′Q′R′.

**In case it is a 270º ****Counter-clockwise ****rotation:**

**P'(3,-3), Q'(5,-5), R'(6,-3)**

**In case it is a 270º ****Clockwise**** rotation:**

**P'(-3, 3), Q'(-5,5), R'(-6,3)**

1) Since in this case, there is a 270º rotation about the origin then we can write out the following:

As there is no mention of the direction then we'll do it for both cases.

**2)** For** a 270º**** Counter-Clockwise ****rotation**

Pre-image rule Image

P(3,3) (x,y)=(y,-x) P'(3,-3)

Q(5,5) Q'(5,-5)

R(3,6) R'(6,-3)

3) **For a Clockwise Direction**

Pre-image rule Image

P(3,3) (x,y)=(-y,x) P'(-3, 3)

Q(5,5) Q'(-5,5)

R(3,6) R'(-6,3)

Find the distance between the two points rounding to the nearest tenth.

(1,-3) and (-7,2)

**Answer:**

Length between two points is given as √(x1-x2)²+(y1-y2)², where x and y are the coordinates of the points.

Distance = √(1-(-7))²+(-3-2)²

= √8²+(-5)²

= √64+25

= √89

= 9.43

= 9.4 (nearest tenth)

The table on the right gives the annual income for eight families, in thousands of dollars.Find the mean and standard deviation for family incomo.Family A B C D E F G HIncome 47 42 44 45 43 45 48 46The mean of the data set is thousand dollars. (Round to three decimal places as needed)

We can compute the mean by;

[tex]\operatorname{mean}=\frac{47+42+44+45+43+45+48+46}{8}=45[/tex]and the standard deviation by;

[tex]\frac{\sum ^{}_{}(x-\operatorname{mean})^2}{\sum ^{}_{}f}=\frac{28}{8}=3.5[/tex]**So the mean of the data set is 45.**

**The standard deviation is 3.5**

Rachel and Nicole are training to run a half-marathon. Rachel begins by running 30 minutes on the first day of training. Each day she increases the time she runs by 3 minutes. Nicole’s training follows the function f(x)=5x+30, where x is the number of days since the training began, and f(x) is the time in minutes she runs each day. What is the rate of change in minutes per day for the training program that has the slowest rate of change?

............ minutes per day

The slowest **rate of change** that is the slowest for the training program is: 3 minutes per day.

In a given **function** that is expressed in slope-intercept form as .f(x) = mx + b, the **rate of change** of the **function** is represented as "m", while the starting or initial value is represented as "b" in the equation.

Given that Rachel increases the time she runs by 3 minutes for each day, then, the **rate of change** per day for the training program or Rachel is 3.

Given that the **function** .f(x) = 5x + 30 represents the minutes Nicole runs per day in the training program, then the **rate of change** is represented as "5" in the equation. This means that each day, Nicole increases her time of running by 5 minutes as compared to 3 minutes per day that Rachel increases her daily runs.

3 minutes per day is slower than 5 minutes per day, in order words, the slowest **rate of change** is therefore: 3 minutes per day.

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What whole number n makes 6/78<1/n<5/55 true?

the expression is,

[tex]\frac{6}{78}<\frac{1}{n}<\frac{5}{55}[/tex][tex]\begin{gathered} \frac{6}{78}<\frac{1}{n} \\ n<\frac{78}{6} \\ n<13 \end{gathered}[/tex]Now,

[tex]\begin{gathered} \frac{1}{n}<\frac{5}{55} \\ \frac{1}{n}<\frac{1}{11} \\ n>11 \end{gathered}[/tex]so the number n is between 11 and 13

**that is n = 12**

**thus, the answer is n = 12**

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ce products manufactures and markets a product called grow tall. ace claims in its advertising that grow tall will make its users grow a minimum of six inches taller than their current height. the federal trade commission (ftc) will likely find that the ad is:
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