Ollie earns a fixed amount of $2,700 per month and a commission of 12% on all of his sales for the month. To cover all of his expenses, he needs to earn at least $5,400 each month.

Part A

Write an inequality that will represent the amount of sales Ollie will need in order to cover his monthly expenses.

Part B

Find the solution and describe what the graph would look like on a number line. Show your work.

Answer:

$112.7

Step-by-step explanation:

15%=0.15

0.15*98=14.7

98+14.7=112.7

Answer: B. y = 3x - 26

Step-by-step explanation:

The equation of line in slope - intercept form is given as :

y = mx + c , where m is the slope and c is the y - intercept.

To write the given equation in this form , all we need do is to make y the subject of the formula.

y - 7 = 3 ( x - 11 )

y - 7 = 3x - 33

add 7 to both sides

y = 3x - 33 + 7

y = 3x -26

Answer:

Therefore the expression for y when x is 2 is

[tex]y=\dfrac{48}{6}\times 2[/tex]

Step-by-step explanation:

Given:

y varies directly as x, and y is 48 when x is 6

Means  Direct Variation.

Therefore,

[tex]y=kx[/tex]

Where,

k = Constant of Proportionality

To Find:

y when x = 2

Solution:

First step we need to Find Constant of Proportionality

So put y = 48 and x = 6

Substituting the values we get

[tex]48=k\times 6\\\\k=\dfrac{48}{6}[/tex]

Now When x = 2 and [tex]k=\dfrac{48}{6}[/tex] y will be

[tex]y=\dfrac{48}{6}\times 2[/tex]

Therefore the expression for y when x is 2 is

[tex]y=\dfrac{48}{6}\times 2[/tex]

n(D) = 4

Step-by-step explanation:

Given Data:

Set D = {4, 6, 8, 10}

The number of elements in a set is called the cardinal elements (or) cardinality of the sets. This is denoted by n(A).

Here it is denoted by n(D).

The number of elements in the set D is 4.

The cardinality of the set is 4.

Hence, n(D) = 4.

For the given set D; the number of elements in the set D as denoted by n(D) is; 4.

According to the question;

The number of elements in a set is given by the notation n(D).

On this note, the set given in this question;

Ultimately, n(D) = 4 elements.

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Answer:

56 grape

Step-by-step explanation:

160 fruit chews

25% are cherry, 40% are peach.....25 + 40 = 65%....so 65% of the fruit chews are NOT grape....meaning (100 - 65) = 35 % ARE grape.

so 35% of all the fruit chews are grape

35% of 160 = 0.35 * 160 = 56 are grape <===

The number of grape fruit chews in the display are 56.

To find the number of grape fruit chews in the display case:

Calculate the percentage of cherry and peach fruit chews: 25% cherry + 40% peach = 65% cherry and peach combined.

Subtract the combined percentage from 100% to find the percentage of grape fruit chews: 100% - 65% = 35% grape.

Calculate the number of grape fruit chews by finding 35% of 160 (total fruit chews): 35% of 160 = 0.35 x 160 = 56 grape fruit chews.

Answer:

6 shaded squares and 4 unshaded....shaded = 60%

Step-by-step explanation:

a grid with 100 squares, 6 are shaded....6/100 = 0.06 = 6%

a grid with 100 squares, 36 are shaded....36/100 = 0.36 = 36%

6 shaded squares and 4 unshaded...6:4...added = 10

shaded = 6/10 = 0.6 = 60% <====

4 shaded squares and 6 unshaded...4:6...added = 10

shaded = 4/10 = 0.4 = 40%

Answer: The answer is C

Answer:

B

Step-by-step explanation:

15% = 0.15

1 - 0.15 = 0.85

[Plug in the p and s]

Answer:

m > 124

Step-by-step explanation:

switch sides, add 91 to both sides then simplify :)

You need to isolate/get the variable "m" by itself on one side of the equation

33 < m - 91    Add 91 on both sides to get m by itself

33 + 91 < m - 91 + 91

124 < m    [124 is less than m]

Answer:

[tex]v = 15 \\ c = v \div 5[/tex]

Step-by-step explanation:

It could be this

Answer:

therefore the given equation is linear but it is not proportional.

Step-by-step explanation:

i) Is y = 4x - 5 proportional or non- proportional.

ii) therefore we can see that the equation is the same as the equation for a line, therefore the given equation is linear but it is not proportional.

Answer:

The answer is that 90 couples remain at the party after 11 pm

Step-by-step explanation:

Number of people who went to the couples only party at 9 pm = 250

Number of people who left the party at 11 pm = 70

How many couples remained at the party?

People that remained at the party = 250 - 70 = 180

Couples that remained at the party = 180/2 = 90

The answer is that 90 couples remained at the party after 11 pm

Answer:

y = abx. Where a ≠ 0, the base b ≠ 1 and x is any real number ... When given a percentage explanation:

Answer:

A system of equations is shown below: x + y = 3 2x − y = 6 The x-coordinate of the solution to this system of equations is _____. I'm thinking it could be X=3

Step-by-step explanation:

The value of the y-coordinate of the solution to the system of equations is; y = 1.

According to the question;

The equations given are;

By solving the pair of equations simultaneously; we have;

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Josh bought a total of 1,800 grams of fruit. This includes 1.5 kg of oranges (converted to 1,500 grams), 150 grams of grapes, and 15,000 centigrams of apples (converted to 150 grams). The weights were converted to grams to find the total weight.

The subject of the question you've asked pertains to Mathematics, specifically to the topic of weight measurement and addition. We have to convert different measurements to a uniform unit and then sum them up to find the total weight of all the fruits bought by Josh at the farmer's market.

To solve the problem presented in the question: Josh bought 1.5 kilograms of oranges, 150 grams of grapes, and 15,000 centigrams of apples. We want to find out the total weight of fruits in grams. First, we need to convert kilograms and centigrams to grams, since kilograms and centigrams are not directly compatible with grams. We know that 1 kilogram equals 1,000 grams, and 1 centigram equals 0.01 grams.

So, converting Josh's purchases to grams:

Oranges: 1.5 kg × 1,000 = 1,500 grams

Grapes: 150 grams (already in grams, no conversion necessary)

Apples: 15,000 cg × 0.01 = 150 grams

Now, we simply add all the weights in grams:

1,500 grams (oranges) + 150 grams (grapes) + 150 grams (apples) = 1,800 grams of fruit in total.

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Answer:

The value of the given expression -9w+9 when w=15 is -126

Step-by-step explanation:

Given expression is -9w+9

To find the given expression when w=15:

That is put w=15 in the given expression we get

-9w+9=-9(15)+9

=-135+9 ( adding the like terms )

=-126

Therefore the value of the given expression -9w+9 when w=15 is -126

First represent your 3 consecutive integers as follows.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since their sum is 84, our equation reads x + (x + 1) + (x + 2) = 84.

Simplifying on the left side we get 3x + 3 = 84.

Now subtract 3 from both sides to get 3x = 81.

Dividing both sides by 3, we find that x = 27.

Finally, make sure you list all your answers.

If x is 27 then x + 1 is 28 and x + 2 is 29.

Answer:

27 + 28 + 29 = 84

Step-by-step explanation:

Let the three consecutive integers be x +1, x+2 and x+3

Thus,

[tex](x + 1) + (x + 2) + (x + 3) = 84[/tex]

Remove the brackets

[tex]x + 1 + x + 2 + x + 3 = 84[/tex]

Group the like terms

[tex]x + x + x + 1 + 2 + 3 = 84[/tex]

[tex]3x + 6 = 84[/tex]

To make 3x subject of formula, subtract 6 from both sides of the equation thus,

[tex]3x + 6 - 6 = 84 - 6[/tex]

[tex]3x = 78[/tex]

Divide through by 3

[tex] \frac{3x}{3} = \frac{78}{3} [/tex]

[tex]x = 26[/tex]

Since x = 26

[tex]x + 1 = 26 + 1 = 27[/tex]

[tex]x + 2 = 26 + 2 = 28[/tex]

[tex]x + 3 = 26 + 3 = 29[/tex]

Therefore, the three consecutive integers are 27, 28 and 29

Check

[tex]27 + 28 + 29 = 84[/tex]

Answer:

x intercept is 6/13

y intercept is -6

Step-by-step explanation:

x intercepted when y is zero.

y intecepted when x is zero...

Answer:

Domain : {-2, -1, 0, 4}

Range: {-2, 2, 3, 4}

Answer:

b,c

Step-by-step explanation:

Answer:

Part 1)Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .  

If a consistent system has exactly one solution, it is independent .  

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

[tex]x+5y=-2[/tex]

[tex]x+5y=4[/tex]

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

[tex]y=3x+4[/tex]

[tex]-2x+y=4[/tex]

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes )m=3 and m=2)

so

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

[tex]3x+y=4[/tex] ----> equation A

[tex]-6x-2y=-8[/tex] ----> equation B

Multiply equation A by -2 both sides

[tex]-2(3x+y)=-2(4)[/tex]

[tex]-6x-2y=-8[/tex] ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

Answer: 25

Step-by-step explanation:

If two shapes are similar , then the ratio of their sides are also similar.

From the shapes given:

[tex]\frac{x}{50}[/tex] = [tex]\frac{20}{40}[/tex]

[tex]\frac{x}{50}[/tex] = [tex]\frac{1}{2}[/tex]

2x = 50

x = 25

Answer:

[tex]y = \frac{5}{2} + \frac{19}{2}[/tex]

Step-by-step explanation:

From the question;

We are required to determine the equation of a line that passes through points (-7,-8) and (-5,-3).

Note that we can get the equation of a line when;

Therefore, since we are given two points where the line is passing through we can get the equation;

First, we determine the slope of the line;

slope = change in y ÷ change in x

That is;

[tex]slope=\frac{(-3--8)}{(-5--7)}[/tex]

        [tex]=\frac{5}{2}[/tex]

Second, we take another point (x,y) and one of the points, in this case, we take (-5,-3).

Therefore;

[tex]\frac{y+3}{x+5}=\frac{5}{2}[/tex]

[tex]2(y+3)=5(x+5)\\2y + 6 = 5x +25\\2y= 5x + 19\\y = \frac{5}{2} + \frac{19}{2}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{2} + \frac{19}{2}[/tex]

Answer:

$ 1.10

Step-by-step explanation:

p + r = 1.45....p = 1.45 - r

2p + r = 1.80

2(1.45 - r) + r = 1.80

2.90 - 2r + r = 1.80

-2r + r = 1.80 - 2.90

-r = - 1.10

r = 1.10 <=== a ruler costs $ 1.10

p + r = 1.45

p + 1.10 = 1.45

p = 1.45 - 1.10

p = 0.35 .......a pencil will cost $ 0.35

By setting up simultaneous equations based on the purchases of Phoebe and Ioeh and solving them, we find that the cost of the ruler is £1.10.

To determine the cost of the ruler, we need to set up two equations based on the given information about Phoebe and Ioeh's purchases and use the method of simultaneous equations.

Let's assume 'R' represents the cost of the ruler and 'P' represents the cost of one pencil.

According to the question:

To find the cost of the ruler, we can solve these equations simultaneously. Subtract the first equation from the second to eliminate R and find P:

1. R + 2P = £1.80
2. R + P  = £1.45

Subtract equation 2 from equation 1:

2P - P = £1.80 - £1.45
P = £0.35

Now that we know one pencil costs £0.35, we can substitute P back into either equation to find R. Let's use the first equation:

R + P = £1.45
R + £0.35 = £1.45
R = £1.45 - £0.35
R = £1.10

Thus, the ruler costs £1.10.

A charter is to a city government as a state constitution is to a state government.

Answer: Option D

Explanation:

Apart from the national level constitution, in the United States of America, every state has its own constitution. They are more detailed when compared to the national constitution as they tend to have more words or content when compared to the national level constitution.

The shortest one belongs to Vermont and the longest one belongs to Alabama. These constitutions tell how the government of each state must function and carry out its day to day activities.

Answer:

Therefore  40 milliliter of 50% fungicide solution is required

Therfore  60 milliliter of 10% fungicide solution is required

Step-by-step explanation:

i) Let the 10% fungicide solution have x milliliter and the 50% fungicide solution have y milliliter.

ii) Therefore 10x + 50y = 26(x + y)

                      x + y = 100

iii) form the first equation in ii) we get

                   16 x  = 24 y   Therefore [tex]x = \frac{24}{16} y = \frac{3}{2} y[/tex]

iv) substituting the value obtained in iii) in the second equation in ii) we get

      [tex]\frac{3}{2} y + y = \frac{5}{2} y = 100[/tex]

  Therefore y = 100 ÷ 2.5 =  40 milliliter

   Therfore x = 100 - 40 = 60 milliliter

Answer:

Part A) Circumference

Part B) C=π D

Part C) The distance traveled in one rotation is 628.32 feet

Step-by-step explanation:

Part A) we know that

The distance around the circle is equal to the circumference.

The Ferris Wheel have a circular shape

so

To find out the distance around the Ferris Wheel you should use the circumference

Part B) What is the formula needed to solve this problem?

we know that

The circumference is equal to multiply the number π by the diameter of the circle

so

C=π D

Part C) What is the distance traveled in one rotation?

we know that

One rotation subtends a central angle of 360 degrees

The distance traveled in one rotation is the same that the circumference of the Ferris wheel

we have

[tex]D=200\ ft[/tex] ----> diameter of the Ferris wheel

substitute in the formula of circumference

[tex]C=\pi (200)\\C=200\pi\ ft[/tex]

assume

[tex]\pi=3.1416\\C=200(3.1416)=628.32\ ft[/tex]

therefore

The distance traveled in one rotation is 628.32 feet

Answer:

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

Step-by-step explanation:

i) the cost of an automobile is given by the equation is

 C(t) = [tex]28000\times(0.73)^{t}[/tex], where C(t) represents the cost and t represents the time in years

ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.

ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.

iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

Answer:

B

Step-by-step explanation:

You can solve this by using the vertical line test. When you do the vertical line test, the vertical line should only pass through one point on the function. That means that there can to be only one value of x for every y. Set B is the only set where the x value doesn't repeat.

In the provided sets of ordered pairs, B and D are considered functions. A function is a relation where each input corresponds to exactly one output, and in sets B and D, this requirement is met.

In mathematics, a relation is considered a function if and only if every input (also called the domain or the x-coordinate) corresponds to exactly one output (also called the range or the y-coordinate). In the language of ordered pairs, an ordered pair presents itself as (x, y). If x repeats with a different y in the set, then the relation is not a function.

So let's examine the sets of ordered pairs given:

Therefore, the set of ordered pairs which are functions are B and D.

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Answer:

Perimeter of triangle ABC = 5(3+13) = 5 x 16 = 80

Angle A = 30°, Angle B = 60°

Therefore Angle C = 90°

Pythagorean triplet = 40/3, 96/3, 104/3

Area of triangle ABC = 1/2 x b x h

= 1/2 x 40/3 x 96/3

= 1920/9

= 213.3 cm^2

Hope this helps!

The area of the triangle is found by recognizing that it is a special 30-60-90 triangle with sides in the ratio of 1: √3 : 2. The area, using these ratios and the given perimeter, is calculated as 25√3 square units.

This problem pertains to the area of a triangle. Because we know the two acute angles of triangle ABC, it is a 30-60-90 triangle. This is a special type of right triangle where the sides are in a particular ratio. In a 30-60-90 triangle, the sides across from the 30°, 60° and 90° angles are in the ratio of 1: √3 : 2.

Given that the perimeter is 5(3 + √13), we can set up the ratio for the sides as x, x√3, and 2x. Adding these together equals the perimeter: x + x√3 + 2x = 5(3 + √13). Solving this equation, we find x = 5.

The area of a triangle is calculated using the formula 1/2*base*height. Using the sides of the triangle, 5, 5√3, and 10, we will use the side across from the 90° angle (10) as the base and the side across from the 60° angle (5√3) as the height, giving us a triangle area of 1/2 * 10 * 5√3 = 25√3 square units.

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