QUESTION 5 of 10: To keep your start-up costs low, you decide to hire two salespeople on commission. They have a base salary of $30,000
and receive 6% of all sales in commission. If first year sales are $500,000, what is your total cost for the two salespeople?
a) $80,000
b) $90,000
c) $100,000
d) $110,000
Submit

Answer:

-6a-48

Step-by-step explanation:

-6(a+8)

=(-6)(a + 8)

=(-6)(a) + (-6)(8)

=-6a-48

The value of x in the proportion is x = 39/8

The proportion is given as:

3/8 =x/13

Cross multiply

8 * x = 3 * 13

Evaluate

8x = 39

Divide by 8

x = 39/8

Hence, the value of x in the proportion is x = 39/8

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Answer:

Equation::2n-4=18::N=11

Step-by-step explanation:

    2.Then divide 22 by 2 and get n=11

    3.So, N=11

Answer:

a³ + 1

Step-by-step explanation:

Step 1: Factor out -3a

\(\frac{-3a(a^3+1)}{-3a}\)

Step 2: Remove -3a

a³ + 1

Answer:

Range: 28

Mean: 12

Step-by-step explanation:

First line the numbers from small to big: 4, 6, 8, 8, 14, 32

Range is biggest minus smallest number

Mean is just the average: all the numbers' sum divided by the number of numbers

Hope this helps! ;)

Answer:

y=60

Step-by-step explanation:

1) Find x

All the interior angles of a triangle add up to 180 degrees. Knowing this, we can construct the following equation:

\(180=x+35+25\\180=x+60\)

Subtract 60 from both sides

\(180-60=x+60-60\\120=x\)

2) Find y

A straight line has an angle measure of 180 degrees as well. Knowing this, we can construct the following equation:

\(180=x+y\\180=120+y\)

Subtract 120 from both sides of the equation

\(180-120=y+120-120\\60=y\)

There is also a second way to solve for y: An exterior angle of a triangle is equal to the sum of the opposite interior angles. y, in this case, would be the exterior angle and 35 and 25 degrees would measure the opposite interior angles. To solve for y, we just add 35 and 25, getting us 60 degrees.

I hope this helps!

Answer:

Where is the table?

Step-by-step explanation:

Answer:

63 miles       x miles

----------- = -------------

3 gallons    7 gallons

Step-by-step explanation:

We will use proportions.  the number of miles over the gallons of gas

63 miles       x miles

----------- = -------------

3 gallons    7 gallons

Answer: 147 miles

Step-by-step explanation:

On 3 gallons, he travelled 63 miles

On 7 gallons, he travels

7/3 x 63 = 147 miles

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

Answer:

The shortest piece is the first piece and it is 14 cm long.

Step-by-step explanation:

We have three unknowns so we need 3 equations.

Let x = the length of the first piece

Let y = the length of the second piece

Let z = the length of the third piece.

x + y + z = 74            y = 2x          z = y + 4

There are a number of ways to solve this.  I am going to plug in 2x for y into the first and the third equation to get:

x + y + z = 74

x + 2x + z = 74 Combine the x terms

3x + z = 74

Next, I am going to substitute 2x in for y in the third equation above.

z = y + 4

z = 2x + 4  I am going to put both variable on the left side of the equation

z - 2x = 4

I can know take the two bold equations that I have above and solve for the either x or z.  I am going to solve for z.  I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out.  I am going to multiple z - 2x = 4 all the way through by -1 to get:

z - 2x = 4

-1(z - 2x) = 4(-1)

-z +2x = -4  

I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4

z + 3x = 74

-z + 2x = -4

      5x = 70 divide both sides by 5

x = 14  This is the length of the first piece.

y = 2x

y = 2(14) = 28

y = 28 This is the length of the second piece.

z = y+4

z = 28 + 4 = 32

or

x + y + z = 74

14 + 28 + z = 74

42 + z = 74  Subtract 42 from both sides.

z = 32

Answer:

189 components must be sampled.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

Assume that component lifetimes are normally distributed with population standard deviation of 16 hours.

This means that \(\sigma = 16\)

How many components must be sampled so that a 99% confidence interval will have margin of error of 3 hours?

n components must be sampled.

n is found when M = 3. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(3 = 2.575\frac{16}{\sqrt{n}}\)

\(3\sqrt{n} = 2.575*16\)

\(\sqrt{n} = \frac{2.575*16}{3}\)

\((\sqrt{n})^2 = (\frac{2.575*16}{3})^2\)

\(n = 188.6\)

Rounding up:

189 components must be sampled.

Answer:

0.56

Step-by-step explanation:

Since 1/10 is 0.1 as a decimal you will then change it to 5.6 x 0.1 which would equal 0.56

Hope this helps :)

Answer:

5.6×1/10=0.56

Hope that helps

Have a good day :)

Step-by-step explanation:

gradient=1

gradient of parallel lines is equal.

y1-y2/x1-x2=1

complete the rest

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

The equation of the plane passing through the point (-8,3,7) and parallel to the given plane will be 4x + 8y - 2z = -22.

The given equation of the plane is 4x + 8y - 2z = 45.

To find the equation of the plane which passes through the point (-8,3,7) and is parallel to the given plane, we need to calculate the values of x, y and z in the given equation.

We have x = -8, y = 3 and z = 7 in the given point.

Substituting these values in the given equation, we get

4(-8) + 8(3) - 2(7) = 45

-32 + 24 - 14 = 45

-22 = 45

This is not possible.

Hence, the equation of the plane passing through the point (-8,3,7) and parallel to the given plane will be 4x + 8y - 2z = -22.

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The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a 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,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Hey there! I'm happy to help!

We'll call our weeks w and call our total savings s.

We have an initial $85 and then we add 7 every week. This means that we will be adding 7 for every week, so we will put this in our equation as 7w.

Therefore, our equation would be s=7w+85

Now, we plug in 8 for our w value to see how much money she will have after 8 weeks.

s=7(8)+85

s=56+85

s=141

Therefore, Aubrey will have saved $141 after 8 weeks.

I hope that this helps! Have a wonderful day! :D

Answer:

Find a polynomial function whose graph passes through (6,13), (9,-11), (0,5)

1 Answers

Assuming a quadratic, we have that

y = ax^2 + bx + c

Since (0,5) is on the graph, c =5

And we have the remaining system

a(9)^2 + b(9) + 5 = -11

a(6)^2 + b(6) + 5 = 13 simplify

81a + 9b = -16 multiply through by 6 ⇒ 486a + 54b = - 96 (1)

36a + 6b = 8 multiply through by -9 ⇒ -324a -54b = -72 (2)

Add (1) and (2)

162a = -168

a = -28/27

To find b we have

36 (-28/27) + 6b = 8

-112/3 + 6b = 8

⇒ b = 68/9

The function is

y = - (28/27)x^2 + (68/9)x + 5

Answer:

See below

Step-by-step explanation:

Let the function be quadratic as the given points are not collinear, not a linear function

Standard form of quadratic equation:

Substituting the coordinates, we get:

From equation 3 we get c = 5, considering this in the other equations and simplifying:

Subtract 3 times the second equation from 2 times the first:

Finding the value of b:

The quadratic function is:

So the graph of any polynomial function:

will pass through the given 3 points

The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8)(attached)

The 180-degree rotation, whether clockwise and anticlockwise, is one of the most basic and frequent geometric transformations. The coordinates of B (x, y) after the rotation will only have the opposite signs of the initial values if B (x, y) is a point that needs to be rotated 180 degrees the about origin.

The camera may move wherever on its side in accordance with the 180-degree rule, but it must not cross the axis. The performers maintain the same left/right interaction with one another while the camera is on one side of the 180-degree line.

It is demonstrated to rotate 180 degrees around the origin.

From the question:

The coordinates of B are - B(1, -8).

Thus, the formula is (x,y)→(−x,−y)  for a 180° rotation of the origin.

B' - (-1 ,-(- 8))

B' - (-1, 8)

The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8): . (attached)

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Answer:b

Step-by-step explanation:

Answer:

Test 1

1. 15.09, 15.90, 15.009, 15.909

ans) 15.009, 15.09, 15.90, 15.909

2. 26.006, 26.606, 2.606, 26.060

ans) 2.606, 26.006, 26.060, 26.606

3. 404.40, 40.404,4.404,404.4

ans) 4.404, 40.404, 404.4, 404.40

4. 54.06,54.6,54.64,54.61

ans) 54.06, 54.6, 54.61, 54.64

5. 3.87,3.087,3.875,3.807

ans) 3.87, 3.087, 3.807, 3.875

Test 2

1. 21.216, 21.612, 21.162, 21.621

ans) 21.162, 21.216, 21.612, 21.621

2. 435.9, 453.9, 45.93, 94.35

ans) 45.93, 94.35, 435.9, 453.9

3. 3.224, 2.432, 3.422, 4.322

ans) 2.432, 3.224, 3.422, 4.322

4. 80.17, 80.02, 80.3, 80.63

ans) 80.02, 80.17, 80.3, 80.63

5. 5.463,5.036,5.36,5.003​

ans) 5.003, 5.036, 5.36, 5.463

I hope it helps.

Answer:

2 x 5 x 5 x 5

= 2 x \(5^{3}\)

maybe they want the answer in index notation

The function represents the area of the walkway along the width of the flower patch.

Rule, or law that establishes the link between an independent variable and a dependent variable is known as function.

Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.

The total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width represents  the area of the walkway along the width of the flower patch.

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Answer:

C

Step-by-step explanation:

The augmented matrix representing the system of equations is given as follows:

[1 1 175]

[2.5 0.75 262.5].

The amounts sold were of:

The amounts are obtained via a system of equations, for which the variables are given as follows:

A total of 175 transactions were made, hence:

x + y = 175

y = 175 - x.

They totaled earnings of $262.5, hence:

2.5x + 0.75y = 262.50.

The augmented matrix is:

[1 1 175]

[2.5 0.75 262.5].

Replacing the first equation into the second, the value of x is given as follows:

2.5x + 0.75(175 - x) = 262.5

1.75x = 131.25

x = 131.25/1.75

x = 75.

Then the value of y is given as follows:

y = 175 - 75

y = 100.

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Answer:

3 n 2/3

Step-by-step explanation:

i just used a calculator bro

Answer:

Step-by-step explanation: