Evaluate variable expressions for 1 and 2

The equation that represents the amount that Arian should save is S = P x 20 / 100, and she should save $12 in case of earning a $60 paycheck.

Given that Arian wants to save 20% of his paycheck is an a savings account, to determine A) an equation to represent the amount Arian should save, S, from a paycheck in the amount of P dollars; B) create a table of value with five different paycheck amounts; and D) find how much of a $60 paycheck Arian should put into his savings account; the following calculations must be made:

Therefore, the equation that represents the amount that Arian should save is S = P x 20 / 100, and she should save $12 in case of earning a $60 paycheck.

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Answer:

Please see the analysis

The p-value that would be associated with the two-tail hypothesis test is 0.03.

A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters.

The mean will be 2.587

The standard deviation will be 0.467

By two tail test,

The p-value is 0.03

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Answer:

x=29

Step-by-step explanation:

Just as simple as substitution:

We will substitute in 16 for y

So the equation will look like 16=x-13

Isolate x:

Add 13 to both sides isolate the variable

-13+13=0

16+13=29

The new equation:

29=x

29-13 is 16.

Answer:

See below for all the cube roots

Step-by-step explanation:

DeMoivre's Theorem

Let [tex]z=r(cos\theta+isin\theta)[/tex] be a complex number in polar form, where [tex]n[/tex] is an integer and [tex]n\geq1[/tex]. If [tex]z^n=r^n(cos\theta+isin\theta)^n[/tex], then [tex]z^n=r^n(cos(n\theta)+isin(n\theta))[/tex].

Nth Root of a Complex Number

If [tex]n[/tex] is any positive integer, the nth roots of [tex]z=rcis\theta[/tex] are given by [tex]\sqrt[n]{rcis\theta}=(rcis\theta)^{\frac{1}{n}}[/tex] where the nth roots are found with the formulas:

for  [tex]k=0,1,2,...\:,n-1[/tex]

Calculation

[tex]z=27(cos330^\circ+isin330^\circ)\\\\\sqrt[3]{z} =\sqrt[3]{27(cos330^\circ+isin330^\circ)}\\\\z^{\frac{1}{3}} =(27(cos330^\circ+isin330^\circ))^{\frac{1}{3}}\\\\z^{\frac{1}{3}} =27^{\frac{1}{3}}(cos(\frac{1}{3}\cdot330^\circ)+isin(\frac{1}{3}\cdot330^\circ))\\\\z^{\frac{1}{3}} =3(cos110^\circ+isin110^\circ)[/tex]

First cube root where k=2

[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(2)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+720^\circ}{3})\biggr]\\3\biggr[cis(\frac{1050^\circ}{3})\biggr]\\3\biggr[cis(350^\circ)\biggr]\\3\biggr[cos(350^\circ)+isin(350^\circ)\biggr][/tex]

Second cube root where k=1

[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(1)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+360^\circ}{3})\biggr]\\3\biggr[cis(\frac{690^\circ}{3})\biggr]\\3\biggr[cis(230^\circ)\biggr]\\3\biggr[cos(230^\circ)+isin(230^\circ)\biggr][/tex]

Third cube root where k=0

[tex]\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(0)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ}{3})\biggr]\\3\biggr[cis(110^\circ)\biggr]\\3\biggr[cos(110^\circ)+isin(110^\circ)\biggr][/tex]

Answer:

It would be m = -2

Step-by-step explanation:

For this line slope would be negative because it is going down. It is going 2 down 1 across. Since it is rise over run it would be -2/1.

Answer:

26 in. x 9 in.

Step-by-step explanation:

27 / 9 =

3

78 / 3 =

26

9 inches by 26 inches

Answer:

625

Step-by-step explanation:

so we do 500/ 0.6 = 625

Answer:

1 6611/12500

Step-by-step explanation:

1 is the whole number and 6611/12500 is in simplest form :)

It is used to analyze and verify materials for quality assurance.PMI is used to prevent potential product failure in manfunctioning.

Answer: 17,160 feet

Step-by-step explanation:

Because I mile = 5280 feet, 3 and 1/4 miles = 3.25 x 5280 = 17160 feet

Answer:

13 quarters must be tails.

Step-by-step explanation:

Number of quarters = 40% of 50 coins

Number of quarters = 40/100 * 50 = 20 coins which are quarters.

35% of these 20 quarters on heads. We can proceed in 2 ways from here.

We can actually find the number of quarters that are on heads.

35/100 * 20 = 7 quarters are showing heads.

Since the other quarters must be tails 20 - 7 = 13 quarters must be tails.

The other way to do it is to realize that if 35% of the coins are heads, 65% of the coins must be tails 20 * 65/100 = 13 which is a bit more direct.

Answer:

The revenue equation  is y=2.6x,

cost equation is y=x+2000

When the company makes profit only when  revenue > cost

Lets frame inequality using revenue > cost

Replace the revenue equation and cost equation

Now solve the inequality for x

Subtract 1x from both sides

Divide both sides by 1.6

The company makes profit when x is greater than 1250

Step-by-step explanation:

Answer:

Greater than 1250

x > 1250

Step-by-step explanation:

Base on  the revenue equation and cost equation , we can infer that the company make a profit when x > 1250

Important Given Information:

The revenue equation  is [tex]y=2.6x[/tex]

Cost equation is [tex]y = x+2000[/tex]

When the company makes profit only when: [tex]revenue > cost[/tex]

Let's frame inequality using: [tex]revenue > cost[/tex]

Replace the revenue equation and cost equation

[tex]Revenue > Cost: 2.6x > + 2000[/tex]

Now Let's solve the inequality for x

[tex]2.6x > 1x + 2000[/tex]

[tex]2.6x - 1x > 2000[/tex]        [tex][2.6x-1x=1.6x][/tex]

[tex]1.6x > 2000[/tex]

Divide both sides by 1.6 ( what you do on one side do to the other)

[tex]\frac{1.6x}{1.6}=\frac{2000}{1.6}[/tex]

[tex]x >1250[/tex]

Hence, the company makes profit when x is greater than 1250

[RevyBreeze]

Answer:

2/3

this question doesn't make sense

Answer:

4/5x + 7

Step-by-step explanation:

the slope-intercept form is y = ax+b

a is the slope, to figure it out the line is perpendicular to y = -5/4x+11/4

There is a rule said if two lines are perpendiculars, the multiplication of their slopes = -1, so -5/4 * a = 1, solve for a = 4/5

b is the intercept to get it use the point (0,7)

so y = 4/5x+b, 7 = 4/5 * 0 + b,  then b = 7

Answer:

p ( x ) = ( x- 6 ) ² - 256

Step-by-step explanation:

1- Add the same value to both sides

2- Add 36 to the expression

3- Add 36 to the left-hand  side

4- Factor the expression

5- Move the constant to the right

6- Calculate

The factors of the given polynomial is (x-10) (x+22) and the price of 5 kg papaya is 5x²-60x-1100.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

p(x) = x² – 12x – 220

i) These two terms are 22x and -11x.

p(x) = x²-12x-220

p(x) = x²+22x-10x-220

Taking x common from the first two terms and -10 from the last two terms,

x(x+22)-10(x+22)

(x-10) (x+22)

ii) We are given that the rate of papaya per kg is p(x) = x²-12x-220.

1 kg = x²-12x-220

5 kg = 5(x²-12x-220)

5 kg = 5x²-60x-1100

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Answer:

B

Step-by-step explanation:

First you put that then multiply inside of that then you cross over percent than boom there's your awnser your welcome

The inequality that represents all values of x for which the product  is defined is x ≥ 0

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Given is an expression, we need to determine the all values of x for which the product is defined,

The product is √4x · √x+2

We must meet both conditions:

(4x) ≥ 0 and (x+2) ≥ 0

So, 4x ≥ 0

x ≥ 0

And,   x ≥ -2 [subtract 2 from both sides.]

So, we can say the condition should be x ≥ 0

Hence, the inequality that represents all values of x for which the product  is defined is x ≥ 0

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Answer:

(x+3)

2

=43

BY TAKING SQUARE ROOT ON BOTH SIDES

x + 3 = \sqrt{43}x+3=

43

OR

x + 3 = - \sqrt{43}x+3=−

43

THUS

x = \sqrt{43} - 3x=

43

−3

OR

x = - \sqrt{43} - 3x=−

43

−3

THIS QUADRATIC EQUATION HAS 2 SOLUTIONS SINCE √43 CAN BE A POSITIVE OR A NEGATIVE INTEGER. FOR EXAMPLE, 2^2=4

BUT, (-2)^2=4 Thus. √4=2 or (-2)

After this. Simply shifting the 3 on the LHS to keep 'x' on one side to find its value.

Taking the square root of both sides of the equation (x + 3)² = 43 will result in two solutions for x.

The correct option is C.

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

When taking the square root of both sides of the equation (x + 3)² = 43, we get:

x + 3 = ±√43

To solve for x, we can subtract 3 from both sides:

x = -3 ±√43

So there are two solutions for x:

x = -3 + √43

x = -3 - √43

Therefore, the solutions are x = -3 + √43 and x = -3 - √43.

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Answer:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

x−4y=−45x−4y=12x-4y=-45x-4y=12

Her annual property insurance premium is $673.50.

Option A is the correct answer.

Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.

here,

We have,

To calculate Sheila annual property insurance premium, we need to determine the appropriate rating based on the type of house and the area where it is located. Aida's house is a brick house in the country,

So we need to use the "Brick" and "Rural" ratings from the table.

The rating for the building is 0.6 per $100 of coverage, so for a value of $95,000, the premium for the building is:

0.6 x $950 = $570

The rating for the contents is 0.69 per $100 of coverage, so for a value of $15,000, the premium for the contents is:

0.69 x $150 = $103.50

The total annual premium is:

$570 + $103.50 = $673.50

Thus,

Her annual property insurance premium is $673.50.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &4 \end{cases} \\\\\\ I=(500)(0.02)(4)\implies I=40[/tex]

Answer:

How to find the area in terms of pi?

Answer: First divide the circumference by Pi to give the diameter of the circle (27 divided by 3.14 = 8.59...). Now halve the diameter to give the radius (8.59 divided by 2 is 4.29...). Now use Pi*r^2 to find the area of the circle (Pi times 4.29^2 = 58.0 cm^2 to 1 decimal place)

Step-by-step explanation:

Answer:

10 centimeters, I think.

Step-by-step explanation:

Answer:

C. No solution.

Step-by-step explanation:

Due to the y-intercepts (When the equation is in slope-intercept form: 1.5, and 3.5) we can identify that the equations are parallel from each other.

The slopes are the same, but the y-intercepts are different, the equations will be 2 (y) apart since each will intersect at different values. This means that both equations can't intersect with each other, making it impossible to find a solution.

[tex]\\ \tt\longrightarrow y+2>5[/tex]

[tex]\\ \tt\longrightarrow y>5-2[/tex]

[tex]\\ \tt\longrightarrow y>3[/tex]

[tex]\\ \tt\longrightarrow y\in (3,\infty)[/tex]

Graph attached

Answer:

see attached diagram

Step-by-step explanation:

y + 2 > 5

Subtract 2 from both sides:

⇒ y > 3

Graphing inequalities

< or > : dashed line to show that the line is not included in the region.

≤ or ≥ : solid line to show that the line is included in the region.

Draw a horizontal dashed line at y = 3 and shade above the line.

Number line

≤ or ≥ : closed circle

< or > : open circle

Draw an open circle at 3 and shade to the right.

The sum of the lengths of the tables and the total length of overhang

give the length of fabric that Devon needs.

Response:

The given parameters are;

Length of the small tables = 6 feet

Length of the long tables = 10 feet

Length of overhang on each end = 8 inches

Number of small tables = 12

Number of long tables = 2 × 12 = 24

Required:

The yards of fabric needed to make the table runners.

Solution;

The total number of tables = 12 + 24 = 36

Length of overhang for each table = 8 inches + 8 inches = 16 inches

Sum of the length of the overhang = 36 × 16 inches = 576 inches

From the given unit conversion factors, we have;

Sum of the length of overhang = 576 inches ÷ 12 inch/feet = 48 feet

Length of the tables = 12 × 6 feet + 24 × 10 feet = 312 feet

Total length of table runner = 312 feet + 48 feet = 360 feet

Length of table runner needed = 360 feet ÷ 3 feet/yd = 120 yd.

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Answer: The slope would be 2/3. The parallel slope would be 2/3. the parallel intercept is -4

Step-by-step explanation: I how this helps!

Answer:

527 cubic meters

Step-by-step explanation:

The area of the cube would be 7.5^3 and the area of the rectangular prism would be 3.75*3.75*7.5. Then it would be 421.9 + 105.5 and rounded to the whole number the answer would be 527