Bruce has been offered a position selling bungee seat belts to sports car manufacturers. He was given a choice of receiving a monthly salary of $500 plus a bonus of 25% of his monthly sales or a $2,000 monthly salary with a 5% bonus on sales. How much would Bruce have to sell to make the same amount of money from each?

The number of installations in September were forty that lead to John and Wesley earning same amount of money.

Let the number of installations be x. The equation of be formed for each paycheck will be -

Total paycheck = base pay + number of installations × comission on each installation

The total paycheck and number of installations is same. So equating the equations by keeping x.

2000 + 65.25x = 380 + 105.75x

Rewriting the equation -

105.75x - 65.25x = 2000 - 380

Performing subtraction on each side of the equation

40.5x = 1620

x = 1620/40.5

Performing division on Right Hand Side of the equation

x = 40

There were 40 installations.

Learn more about telephone problems -

https://brainly.com/question/28709868

#SPJ4

The length of the cuboid is 56 cm.

The breadth of the cuboid is 40 cm.

The height of the cuboid is 16 cm.

A cuboid is a three-dimensional shape where the volume is given by

Length x width x height.

We have,

Volume of a cuboid = 35840 cm³

The ratio of length, breadth, and height of the cuboid = 7:5:2

This means,

Length = 7x

Breadth = 5x

Height = 2x

Now,

(7x)(5x)(2x) = 35840

70x³ = 35840

x³ = 512

x = ∛512

x = 8

Now,

Length = 7x = 7 x 8 = 56 cm

Breadth = 5x = 5 x 8 = 40 cm

Height = 2x = 2 x 8 = 16 cm

Thus,

The length, breadth, and height of the cuboid are 56cm, 40cm, and 16 cm.

Learn more about cuboid here:

https://brainly.com/question/19754639

#SPJ1

The expected number of ball pens of a student is 2.4.

What is the expected number?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.

The weight for each group is the percentage of students that are in that group.

So, we can calculate the expected number of ball pens of a student by:

(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)

0.7 + 0.9 + 0.8 + 0.2

The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.

Here, the outcome is the number of ball pens.

Hence, the expected number of ball pens of a student is 2.4.

To learn more about the expected number visit,

https://brainly.com/question/10675141

#SPJ1

The measure of ∠Z is 165 degrees to the nearest degree.

In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.

Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.

∠Z = 180 - (x+y)

∠Z = 180 - (5.2+9.8)

∠Z = 180 - 15

∠Z = 165

So the measure of ∠Z is 165 degrees to the nearest degree.

Therefore, The measure of ∠Z is 165 degrees to the nearest degree.

To learn more about Triangle Sum Theorem,

Visit; brainly.com/question/2995226

#SPJ4

Using the slope of the least-squares regression line, the interpretation will be: C) The slope is 0. 50, which means for each additional pound in weight, the child’s height will increase by 0. 5 inches.

A linear approach is linear regression, which is used to represent the relationship between a scalar answer and one or more explanatory factors in statistics. When there are many explanatory factors, multiple linear regression is employed; otherwise, simple linear regression is utilised. It is possible to predict the value of one variable using linear regression analysis and the value of another variable.

Predicting the dependent variable is what you want to do. The variable you are using to anticipate the value of the other variable is the one you are utilising as an independent variable. Lines of best fit are another name for regression lines. To demonstrate how several graph points might be connected, a line of best fit is used.

To learn more about regression line: https://brainly.com/question/17004137

#SPJ4

Bar charts display categorical variables, whereas histograms display numerical or quantitative data.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.

Therefore, the correct answer is option C. 6 or fewer.

To learn more about histogram refer to;

https://brainly.com/question/28164315

#SPJ1

After 0.6412 years the average for mobile device and television usage will coincide.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here the equations as  y=-9.11x+280x and  y=12.34x + 169.9 the period for which the averages are equal will be given by

9.11x+280x=12.34x + 169.9

       x   = 0.6412 years

Again, after 7 years in 2021 the respective averages will be                  9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes

Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.

Learn more about functions here:

https://brainly.com/question/28303908

#SPJ1

The third side of the triangle will be less than 35.

A polygon with three angles, sides and angles is called a triangle.

Given that, Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than

We know that, triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, length of the third side < 15+20 < 35

Hence, the third side of the triangle will be less than 35.

Learn more about triangles, click;

https://brainly.com/question/2773823

#SPJ1

Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative

Step-by-step explanation:

The two sets A and B triangle must have identical items, but this does not require that they be put in the same order for the sets to be equal.

A triangle is a 2D shape with three vertices, three straight edges, and three straight edges. A key feature of these shapes is that each type of triangle has three inner angles that add up to 180° in these designs. during their math lectures about these angles and how to use this quality to spot missing values.

Here,

Triangle 1 in this instance has two angles, one of 34 degrees and the other of 48 degrees.

The third angle is therefore 180-34- 48=98.

The angles in Triangle 2 are 34 and a, where an is 48, respectively.

In other words, the third angle is 180−34−a=146−a≠146−48=98.

Jennifer claims that given the information at hand, triangles 1 and 2 cannot be compared.

If 34,98,48=34,a,146a., they are equivalent.

How many degrees will Jennifer's claim be ruled untrue? To compare the triangles, use the formula a.

It is crucial to understand that while components in two sets A and B must match, the sets are not always equal if they are not listed in the same order.

To know more about triangle , visit

brainly.com/question/2773823

#SPJ1

On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y = 7x - 17

at x= 0

y = -17

and m = -17

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

To simplify the expression 20-10y-7y + 9, we can combine like terms.

Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.

We can start by combining the like terms:

20 - 10y - 7y + 9

= 20 + (-10y - 7y) + 9

= 20 + (-17y) + 9

Next, we can combine the constants:

20 + (-17y) + 9

= (20 + 9) + (-17y)

= 29 + (-17y)

The simplified expression is: 29 + (-17y)

[tex]20-10y-7y + 9[/tex]

Combine Like Terms:

[tex](-10y+-7y)+(20+9)[/tex]

[tex]-17y+29[/tex]

[tex]\fbox{Option E}[/tex]

The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.

Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.

Given that:

A = $10,000

r = 4% = 0.04

t = 5 years

n = 12 (since the compounding is monthly)

P = ?

The compound interest is given as follows:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Substituting the values in the formula we have:

[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]

Learn more about compound interest here:

brainly.com/question/14295570

#SPJ4

The positive value of the distance between the two objects

is  [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.

The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]

[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].

learn more about gravitational force here :

brainly.com/question/12528243

#SPJ1

The x-coordinate of the solution of the system of equations is x = 20/3

Here we have a system of equations below:

3x - y = 6

3x + y = 34

And we want to find the x-cordinate of the solution, so we need to solve this for x.

We can use the elimination method, you can see that if we add both equations we will get:

(3x - y) + (3x + y) = 6 + 34

6x = 40

x = 40/6

We can simplify that fraction to get:

x = 20/3

That is the x-coordinate of the solution.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

The smallest number with the factors 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24 is 232792560.

To learn more about the smallest number with the factors refer to:

https://brainly.com/question/15296258

#SPJ4

The evaluation of the expression a + 4 when a = 7 is 11

From the question, we have the following parameters that can be used in our computation:

Expression: a + 4

Value a = 7

Substitute the known values in the above equation, so, we have the following representation

a + 4 = 7 + 4

Evaluate the like terms in the equation

So, we have the following representation

a + 4 = 11

Using the above as a guide, we have the following:

The solution is 11

Read more about equation at

https://brainly.com/question/2476251

#SPJ1

Answer:

28

Step-by-step explanation:

1 + 2 + 3 + 4 + 5 + 6 + 7

The gradient of the linear equation 2x + 3y + 6 is (3/2).

The gradient of a linear equation in the form of y = mx + c is m, which represents the slope of the line. The slope is defined as the ratio of the change in y to the change in x. It represents the steepness of the line.

The equation 2x + 3y + 6 is not in the form of y = mx + c. It is in the form of Ax + By + C = 0, which is the general form of a linear equation. To find the gradient of such an equation we need to divide -A/B. In this case, the gradient of the line is -2/3.

The gradient of a line gives us the direction of the line, it is the slope of the line. It tells us how steep the line is and if it is going up or down. A positive gradient means the line is going up and a negative gradient means the line is going down.

Learn more about Gradient here:

https://brainly.com/question/23016580

#SPJ4

The given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
Given expression,
an=19-7(n-1)

The above-given expression is an explicit formula for the arithmetic progression,

Comparing the given expression with general expression an = a + d[n-1]

From the above comparison, we
first term,a = 19 and
the common difference, d = -7

Thus, the given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.

Learn more about arithmetic progression here: https://brainly.com/question/20334860

#SPJ1

Answer:

A - $360

Step-by-step explanation:

Length times width equals area.

12 × 10 = 120

His office has 120 sq ft of space. If each sq ft costs $3

120 × 3 = $360

A

Answer:

A ($360)

Step-by-step explanation:

imagine a rectangle with one side 12ft and one side 10ft

multiply the length and the width to find the square footage:

12*10=120ft^2

each square foot is $3 so multiply 3 by 120

$3*120ft^2= $360

oops didn't realize someone already answered sorry

The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

Learn more work and force at: https://brainly.com/question/28039239

#SPJ4

Answer:

ye

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

A perfect square is a number from a number system that can be shown as the square of the number in the given number system. 4 can be written as 2 x 2 Making 4 a perfect square. In other words, if a number can be multiplied by its self and equal the number you are trying to square, then it is a perfect square.

The potential instances of sample distribution are options C and E.

Option E. Average male height based on samples of size 30.

Option C. Mean trout lengths based on samples of size 5.

The sampling distribution of the mean is the distribution of the variable x (all feasible sample means of size n) for a variable x and a given sample size n.

The mean is the most typical kind of sample distribution. Plotting the data points and computing the means of each sample group drawn from the population are its main goals.

This idea, which is a form of the probability distribution, is frequently used to gather precise data from a sizable population that is divided into a number of randomly chosen samples. This idea is further divided into three categories: T-Sampling, proportional sampling, and the sampling distribution of the mean.

For more questions on probability Distribution

#SPJ4

The correct questions should be like this:

Which of the following are possible examples of sampling distributions? (Select all that apply.) average SAT score of a sample of high school students

all mean trout lengths in a sampled lake

mean trout lengths based on samples of size 5

heights of college students at a sampled university

average male height based on samples of size 30

The probability of h that can be found using the discrete model but not the normal model is 0.03.

A discrete probability distribution or DPD (also known as a discrete probability model) records all possible values of a discrete random variable and gives their probabilities.

The normal probability model involves when the distribution of the continuous outcome conforms reasonably well to a normal or Gaussian distribution, which resembles a bell-shaped curve.

H represents the height of women

Determine P ( H < 60 ) using either a discrete or normal model

using discrete model

P ( H < 60 ) = ∑ relative frequencies of the women with height < 60 inches

P ( H < 60 ) = 0.01 + 0.02 = 0.03

To know more about Gaussian distribution, here

https://brainly.com/question/29734279

#SPJ4

The Filling time is After 25 minutes, both Aquariums will contain same amount of water.

you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.

Calculate the Filling Time of the aquarium Explanation

Given,

Water in Aquarium A = 4.6 gallons

Water in Aquarium B = 54.6 gallons

Filling rate = 1.2 gallons per minute.

Draining rate = 0.8 gallons per minute.

Let,

x represents the minutes.

A(x) = 4.6 + 1.2x

(Because Luis is adding water in the tank.)

B(x) = 54.6 - 0.8x

(Isacc is draining water from the tank.)

For same amount of water;

A(x) = B(x)

4.6+1.2x=54.6-0.8x

1.2x+0.8x=54.6-4.6

2x=50

Dividing both sides by 2

2x/2=50/2

x=25

Therefore, After 25 minutes, both Aquariums will contain same amount of water.

To learn more about the Filling Time of the aquarium visit:

brainly.com/question/28351464

#SPJ4

The light cream milk product have approximately 15.36 grams of milk fat in an 80-gram serving.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Let n be the percentage of milk product to have approximately 15.36 grams of milk fat in an 80-gram serving.

Using percentage formula,

15.36 = n x 80 / 100

n = 1536 / 80

n = 19.2%

Therefore, the product is light cream milk.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Answer:

3.5. 2.2.

x 4. x 1 1

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

14.0. 22

220

24.2

Step-by-step explanation:

answer for me is 38.2

are you sure ur math is right?