f(x) = 3x + 1 and g(x) = x - 5find (f o g ) ( x )Which of the four options is it?

9514 1404 393

Answer:

  a. $297.50

  b. 150%

  c. 60%

  d. $14.88

Step-by-step explanation:

We are given that $100 of selling price breaks down to ...

  cost: $40

  operating profit: $100 -40 -45 - $5

  markup: $100 -40 = $60

__

a. The selling price is $100/$40 = 2.5 times the cost.

  selling price = 2.5 × $119 = $297.50

__

b. The ratio of markup to cost is ...

  markup/cost = $60/40 = 1.5 = 150%

__

c. The ratio of markup to selling price is ...

  markup/selling price = $60/$100 = 0.60 = 60%

__

d. The ratio of profit to cost is ...

  profit/cost = $5/$40 = 1/8

Then the operating profit on this item is ...

  $119 × 1/8 = $14.875 ≈ $14.88

Answer:

0 ≤ y ≤ 8

Step-by-step explanation:

DOMAIN is x values of a function/graph

RANGE is the y-values that a function can have .....

     this one goes from 0 to 8 inclusive

Answer:

F(-10)=186

Step-by-step explanation:

F(-10)=2(-10)^2+(-10)-4

F(-10)=2*100+(-14)

F(-10)=200-14

Therefore, F(-10)=186

Answer:

The answer is 186

Step-by-step explanation:

Answer:

\(3300cg = 330mg\) --- decimal

\(3300cg = 3.3 * 10^2mg\) --- scientific

Step-by-step explanation:

Given

3300 cg

Required

Convert to mg

cg to mg is gotten my multiplying cg by 100

So:

\(3300cg = 3300 * 0.1mg\)

\(3300cg = 330mg\) ---- decimal notation

Express 330 as 3.30 * 100

\(3300cg = 3.3 * 100mg\)

Express 100 at 10^2

\(3300cg = 3.3 * 10^2mg\)

By finding and solving a system of equations, we will see that after 2 hours they will drink the same amount of water.

For Elise, the number of cups consumed after the 10:00 am is:

y = 2*x + 4

Where x is the number of hours after 10:00 am.

For Jacob, the number is:

J = 3*x + 2

Then the system of equations is:

y = 2x + 4

y = 3x + 2

To solve it, we use the fact that the variable y is already isolated in both equations, so we can write:

2x + 4 = y = 3x + 2

2x + 4 = 3x + 2

Solving for x we get:

4 - 2 = 3x - 2x

2 = x

After 2 hours, Elise and Jacob drink the same amount of water.

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Answer:

3, -1

6,-3

2,0

5,2

Step-by-step explanation:

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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Answer:

The answer is 75.36......

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

12 3/5

Step-by-step explanation:

Answer:

12 3/5

Step-by-step explanation:

Got it right on my test.

Answer: I'm sorry, I am a text-based user and do not have the capability to drag tiles. However, I can provide you with a written proof of the statement "ABCD is a parallelogram" given the given information "AD = BC and AD || BC":

Statements:

AD = BC

AD || BC

Angles A and C are congruent

Angles B and D are congruent

Opposite sides are equal in length

Reasons:

Given

Given

If two lines are parallel, then the corresponding angles are congruent

If two lines are parallel, then the corresponding angles are congruent

If opposite angles of a quadrilateral are congruent, then the opposite sides are equal in length

Therefore, ABCD is a parallelogram.

Step-by-step explanation:

She needs to work a total of 60 hours including time-and-a-half pay hours.

What is time-and-a-half pay?

Time and a half pay is the overtime pay that non-exempt employees are entitled to when working more than 40 hours per week, as required by the Fair Labor Standards Act (FLSA). Time and a half pay are so-called because they equal an employee's hourly rate multiplied by 1.5 per hour of overtime.

Given, Hourly rate = $16 per hour

Angie regularly works a 40-hour week

Then, gross pay for 40-hour week = $16*40 = $640

Hourly overtime rate = $16 x 1.5 = $24

total pay = $1,120

Let x be the number of overtime hours, then

640 + 24x = 1120

or, 24x = 1120 - 640

or, 24x = 480

or, x = 20

Total hours = 40 + 20 = 60 hours

Hence, she needs to work 60 hours.

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Answer:

4.4 ounces/ 4 ounce (if rounded)

Step-by-step explanation:

There are 16 ounces in a pound, therefore the equation 12/16 will be useful since 16 ounces in a pound can be divided by 12, in conclusion 12/16=0.75 which is how much an ounce costs.

Then you will take $3.30 and divide it by 0.75 to get your answer for how many ounces you can buy for $3.30 which will equal 4.4 ounces but if you were to round it would be 4 ounces

Hope this helps!

Answer:

2.5 cm

Step-by-step explanation:

From the first 4 bounces, we find that the height of the lacrosse ball after each bounce is 1/4 the height that it was after the previous bounce. Therefore, since the 7th bounce is 6 bounces after the first bounce, we can set up an equation to find the balls height (y), after some number of bounces after the first one:

\(y=10240*(\frac{1}{4})^x\).

Plug-in 6 for x to get 2.5.

Hope this helps :)

Answer:

The change should Sara receive from the $10 bill is $3.56.

Step-by-step explanation:

Given:

The table shows the prices of some breakfast items at a restaurant.

Item                                      Price

One egg                               $1.69

Slice of bacon                      $1.49

Glass of orange juice          

$1.09

Sara ordered 2 eggs, a slice of bacon, and  a glass of orange juice for breakfast.

The sales tax for the order was $0.48.

She paid for her breakfast with a  $10 bill.

Now, to find the change should Sara receive from the $10 bill.

Bill for the Sara's breakfast:

2 eggs =

A slice of bacon = $1.49.

A glass of orange = $1.09.

The sales tax = $0.48.

Total bill =

Sara paid for the breakfast bill = $10.

Now, to get the change Sara should receive we subtract the amount of bill from the money Sara paid for the bill:

Therefore, the change should Sara receive from the $10 bill is $3.56.

Answer:

Her change would be 3 dollars and 56 cents

Step-by-step explanation:

1.69 times 2 because she ordered 2 eggs

1.49 for the bacon

1.09 for the orange juice

0.48 for the sales tax

add them all up

it would equal 6.44

then subtract 6.44 from 10 which would equal 3.56

Answer:

1, 3, 9, 27

Step-by-step explanation:

1 times 27 = 27

3 times 9 = 27

9 times 3 = 27

27 times 1 = 27

hope this helps!!!

Answer:

1, 3, 9, 27

Step-by-step explanation:

27 = 3³

The factors of 27 are:

1, 3, 9, 27

Answer:

GO SEARCH MATH_WAY its a math calculator gives you  

Step-by-step explanation:

Answer:

photo is not clear so i can't help u

Answer:

i cant really see the q so sorry but goodluck <3

Answer:

The stock price beyond which 0.05 of the distribution fall is $12.44.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of $8.52 with a standard deviation of $2.38

This means that \(\mu = 8.52, \sigma = 2.38\)

The stock price beyond which 0.05 of the distribution fall is

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 8.52}{2.38}\)

\(X - 8.52 = 1.645*2.38\)

\(X = 12.44\)

The stock price beyond which 0.05 of the distribution fall is $12.44.

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Answer:

5 units.

Explanation:

To find the distance between two points in the coordinate plane, use the distance formula below:

Substituting the points gives:

The distance from A to B ​is 5 units.

The man is in the south direction from the starting point.

Let's visualize the movements of the man step by step:

The man starts by going 10 meters north.

He then turns left (which means he is now facing west) and covers 6 meters in that direction.

Next, he turns left again (which means he is now facing south) and walks 5 meters.

To determine the final direction of the man from the starting point, we can consider the net effect of his movements.

Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by 180 degrees.

Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the starting point is "south."

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The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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Answer:

undoable

Step-by-step explanation:

theres no =

The coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.

A polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane.

We have an angle of 120 degree

θ = 120 degree

r = 1 unit

As we know, the coordinate in the polar form from the rectangular form is:

x = rcosθ = cos120 = -1/2

y = rsinθ = sin120 = √3/2

Thus, the coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.

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Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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