a weekly salary of $325 plus a 6.5% commission on sales at a store. How much would she make in a work week if she sold $4800 worth of merchandise?

Answer:

[tex]k=2[/tex]

Step-by-step explanation:

1) Rewriting:

[tex]f(x+k)=f(x)+2[/tex]

2) Suppose f(x)= ax (Linear function with b=0)

[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]

3) Check the graph below

The correct option is D) 2.

Step-by-step explanation:

Given :

f(x) +2 and f(x +k)

Solution :

let, [tex]f(x) = ax[/tex] (linear function with b = 0)

so,   [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]

Rewriting,

[tex]f(x+k)=f(x) + 2[/tex]

[tex]a(x + k) = ax +2[/tex]

[tex]k = 2 \;\;\;(at,\;a=1)[/tex]

Therefore, the correct option is D) 2.

For more information, refer the link given below

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Answer:

Step-by-step explanation:

So if p is the total amount paid, and h is the amount of time spent working, it'll be worked out something like this.

The amount of money she makes per hour   x    the amount of time spent working = the amount she is paid.

Thus making it...

8 x h = p

but in algebra expressions, we don't normally use arithmetic symbols. So if we get rid of that, we get the answer of 8h = p.

:)

A you earn 3 percent more money

Step-by-step explanation:

4-1

Answer:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

Step-by-step explanation:

If you are given a 4% raise and inflation is 1%, you are making 3% more.

[tex]4-1=3[/tex]

Or we can say you are making more money.

This is because you are given high percent of raise as compared to the low rate or percent of inflation, that shows you are on the positive side.

Answer:

480 pennies dated after 2000.

Step-by-step explanation:

1. Pennies dated before 1980 (x) - 25%,

All pennies (1,200) - 100%.

Then

[tex]\dfrac{x}{1,200}=\dfrac{25}{100},\\ \\100x=25\cdot 1,200,\\ \\x=25\cdot 12=300.[/tex]

2. Pennies dated from 1980 to 2000 (y) - 35%,

All pennies (1,200) - 100%.

Then

[tex]\dfrac{y}{1,200}=\dfrac{35}{100},\\ \\100y=35\cdot 1,200,\\ \\y=35\cdot 12=420.[/tex]

3. Rest pennies are dated after 2000, then

[tex]1,200-300-420=480.[/tex]

Answer:

480

Step-by-step explanation:

The surveyor is using a trigonometric method to calculate the distance between the two houses. They form a right triangle with points A, B and C, measure the length AC and the angle at point A or C, and then calculate the distance AB using trigonometric ratios.

In this scenario, the surveyor is using a method resembling triangle-based methods in Mathematics, which specifically relates to trigonometry. To determine the distance between points A (house on shore) and B (house on island), the surveyor measures line AC, forms a right triangle ABC, and uses an instrument (like a theodolite) to measure one of the corners (usually angle at point A or C). With the measured length and angle, the distance AB can be calculated using trigonometric ratios (like sine, cosine, or tangent), depending upon the given scenario. For instance, if the angle at point A and length AC are known, then the distance AB can be calculated as AB = AC / cos(A), where A is the angle at point A.

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Answer:

$206.54

Step-by-step explanation:

Divide the number of officials by the total days pay to get the pay for each official working the race

Answer:

The answer is 18 GB

Step-by-step explanation:

Okay to the breakdown:

This is a word problem that requires basic knowledge of equality.

So lets say that the total amount of data at the beginning of the cycle is equal to X.

We are told that the data has been used for 8 days at a daily rate of 1.5GB per day, so the total data already used will be "Days × Rate" => 8 × 1.5 = 12GB.

We are also made to know that after the 8 days we still have 6 GB left out of the initial amount X.

Let put all the above in an equation:

X - 12 = 6;

Using the approach of putting liked them together we will add 12 to both sides:

X -12 + 12 = 6 + 12 => X = 18;

So the amount at the beginning of the cycle is 18 GB.

Answer: 11(y+15)

Step-by-step explanation:

−

42

6

=

x

+

15

−

7

=

x

+

15

−

7

−

15

=

x

−

22

=

x

Easy, just do 60 seconds which equals a minute. Since we know that now simply use 60 minutes to get you to an hour. If your doing minutes to hours make sure there is a 0 at the end.

Answer:

the correct answer is 14.29%

Step-by-step explanation:

Answer:

If two events are mutually exclusive then they cannot occur at the same time.

Step-by-step explanation:

If two events are mutually exclusive then they cannot occur at the same time.

For example: If you take a coin, the two possible outcomes on flipping a coin will be mutually exclusive as when you flip a coin, it cannot give both heads and tails at the same time.

Hence, the two mutually exclusive events cannot occur at the same time.

Answer:

72,220 inches per  minute

Step-by-step explanation:

A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.

1 revolution = [tex]2\pi[/tex] radians

[tex]\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}[/tex]

Speed [tex]V= \frac{r*theta}{t}[/tex]

r is the radius , theta is the angle and t is the time

We know diameter = 23  , then radius = 23/2

Speed [tex]V= \frac{23}{2}*\frac{2000\pi}{1}[/tex]

Value of pi = 3.14

speed = 23000* 3.14= 72220 inches/ minute

Answer:

72,220 inches per minute

Step-by-step explanation:

Answer:

C) 4 : 2 Odds of rolling a number less than 5

Step-by-step explanation:

If there are 6 sides on the dice, 4 of the sides are going to be less than 5 and two of them are not.

Answer:

4:2 Odds of rolling a number less than 5.

Step-by-step explanation:

ODDS is defined as probability that event will occur divided by probability that event will not occur.

A six sided die has 6 numbers in total.

The odds of rolling a number LESS THAN 5 is therefore:

Odds = 4:2

Last answer choice is right.

Answer:

see below

Step-by-step explanation:

Let x = tootsie rolls

y = lollipops

Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.

3x+5y =30

To find the x intercept, set y=0 and solve for x

3x +0 = 30

3x = 30

Divide by 3

3x/3 = 30/3

x = 10

The x intercept is 10.  This means if you get no lollipops, you can have ten tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 30

5y = 30

Divide by 5

5y/5 = 30/5

x = 6

The y intercept is 6.  This means if you get no tootsie rolls you can have 6 lollipops.

To find the slope, solve the equation for y

3x+5y =30

Subtract 3x from each side

3x-3x+5y = -3x+30

5y = -3x+30

Divide by 5

y = -3/5 x +30/5

y = -3/5 x +6

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

If you have $45 dollars instead of 30,  this will change the x and y intercepts, but not the slope.  

3x+5y =45

To find the x intercept, set y=0 and solve for x

3x +0 = 45

3x = 45

Divide by 3

3x/3 = 45/3

x = 15

The x intercept is 15.  This means if you get no lollipops, you can have 15 tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 45

5y = 45

Divide by 5

5y/5 = 45/5

x = 9

The y intercept is 9.  This means if you get no tootsie rolls you can have 9 lollipops.

To find the slope, solve the equation for y

3x+5y =45

Subtract 3x from each side

3x-3x+5y = -3x+45

5y = -3x+45

Divide by 5

y = -3/5 x +45/5

y = -3/5 x +9

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: [tex]AB \cong BC[/tex]  and [tex]BC \cong EF[/tex]

By transitive property:  a = b  and b = c then, a =c

⇒[tex]AB \cong EF[/tex]

AB = EF                                [def of [tex]\cong[/tex] segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                     hence proved!

Since, in the fourth statement reason is:  It is an argument

Answer:

B, it is an argument

Step-by-step explanation:

ANSWER: Tim Carter's weekly pay was $282.25.

I will work on Tim Carter's weekly pay. Because he worked 50 hours, and there are 40 regular hours, he worked 10 overtime hours.

To find out his regular pay, we need to multiply his regular pay by his regular hours.

[tex]40 * 5.15 = 206[/tex]

Tim Carter makes $206 for his regular hours. To find out his overtime pay, we need to multiply his regular pay by his overtime hours, then multiply that product by 1.5.

[tex]10 * 5.15 = 51.5\\\\51.5 * 1.5 = 77.25[/tex]

Tim Carter makes $77.25 for his overtime hours. Lastly, add the regular pay and his overtime pay to get his weekly pay.

[tex]206 + 77.25 = 283.25[/tex]

Tim Carter's weekly pay was $283.25.

Answer:

Step-by-step explanation:

                               OT                                 Weekly Pay

Tim Carter:             10                 40x5.15= 206    5.15 x 1.5=7.725

                                                    7.725 x 10 =  77.25    206 + 77.25 = $283.25

Jesse Jones:         7.5               40x5.15= 206   5.15 x 1.5 = 7.725

                                                   7.725 x 7.5 = 57.9375 = 57.94

                                                   206 + 57.94 = $263.94

Barbara Burns:      4                  40x5.15= 206  5.15x1.5 = 7.725

                                                   7.725 x 4 = 30.90   206 + 30.90 = $236.90

Answer:

Step-by-step explanation:

Commutative property: 3x+12-2x = 3x-2x+12

Substitution property: 3x-2x+12 = x+12

x+12 = x+12

Subtraction property: x-x+12 = x-x+12

Substitution property: 12 = 12

Answer:

The bill total is $27.32

Step-by-step explanation:

how to figure out tax amount: 25.30 x .08 = $2.024

add tax to cost of meal : 25.30 + 2.024 = $27.32

To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.

The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.

First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:

$25.30 * 0.08 = $2.02

This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:

$25.30 + $2.02 = $27.32

So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.

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Answer:

The answer is B because the numbers in the geometric sequence are being multiplied by 2.

Answers:

right 1, down 3 (these two answers only)

Step-by-step explanation:

There are two transformations going on. The first of which is the horizontal or x translation (aka shifting) where the 'x' turns into 'x-1'. This moves the xy axis 1 spot to the left, giving the illusion that the graph moves 1 unit to the right.

The "-3" at the end shifts the graph down 3 units. If g(x) = f(x) - 3, then g(x) is the output of f(x) but 3 less than that, which is why it shifts down 3 units.

The function g(x) represents two transformations from its parent function f(x) = 1/x: a horizontal shift to the right by 1 unit and a vertical shift down by 3 units.

When comparing the graph of the function g(x) = (1)/(x-1) - 3 with its parent function f(x) = 1/x, the transformations undergone by g(x) include:

These transformations can be understood with the help of given examples. For instance, adding or subtracting a number to/from the independent variable x, like f(x+1), results in a horizontal shift of the graph. Multiplying the independent variable by a number, say 2 as in f(2x), would cause a horizontal compression of the graph. In our case, since the function g(x) includes x-1, it is indicating a horizontal shift to the right, and since the -3 is subtracted from the entire function, it denotes a vertical shift downward.

6(9)-8(-2)

6*9=54

8*(-2)=-16

54-16=38

38<-----

Answer:

70

Step-by-step explanation:

x=9 and y=−2, evaluate the following expression : 6x−8y

plug in

6(9) - 8(-2)

= 54 + 16

= 70

Answer:

1,500 rotations

Step-by-step explanation:

To answer this, divide 2.2 m into 3300 m.  This results in 1500.

The wheels made 1,500 rotations each.

Answer:

She has 11/20 yds left

Step-by-step explanation:

We take what she had and subtract what she gave away

9/10 - 7/20

We need to get a common denominator of 20

9/10 *2/2 - 7/20

18/20 - 7/20

11/20

She has 11/20 yds left

Answer:

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

Answer:

Question One: log_2(x - 6) = y

Question Two: First blank: 4 Second blank 0

Question Three: B

Step-by-step explanation:

f(x) = 2^x + 6

y = 2^x + 6                 Interchange the x and y

x = 2^y + 6                Subtract 6 from both sides

x - 6 = 2^y                 Take the log of both sides

log(x - 6) = log 2^y    The power can be multiplied by the log of 2

log(x - 6) = y log(2)    Divide by the log of 2

log(x - 6)/log(2) = y    This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos

The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.

log_2(x - 6) = y

Answer: D

Problem Two

You want the inverse of y = - 1/2 sqrt(x + 3)   x ≥ - 3

Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.

The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)

The range of f(x) is 0 <=y < - infinity

So the domain of f-1(x) <= 0

Answer: The first blank is 4 and the second one is 0

Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.

Problem Three

The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.

Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.

Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)

Answer: √(x^5) - 3√x^3 - 18√x

Answer: B

Answer:

The passengers paid approximately 162500

Step-by-step explanation:

We are find how much the passengers paid

657 passengers * 247 per passenger

Round 657 to 650

Round 247 to 250

650 * 250 = 162500

The passengers paid approximately 162500

We start from the third equation:

4z = 16     divide both sides by 4

Put the value of z to the second equation:

y + 4 = 5      subtract 4 from both sides

Put the values of y and z to the first equation:

3x + 2(1) - 4 = 4

3x + 2 - 4 = 4

3x - 2 = 4      add 2 to both sides

3x = 6      divide both sides by 3

[tex]25=12+r\\r=25-12\\r=13[/tex]

12 + r = 25      subtract 12 from both sides

12 - 12 + r = 25 - 12

Answer:

5 2/3 hours  

Step-by-step explanation:

We can use a ratio to solve this problem

hours over money

4.5 hours         x hours

-------------    =  ------------

27 dollars        34 dollars

Using cross products

4.5 * 34 = 27 * x

153 =27x

Divide each side by 27

153/27 = 27x/27

5.666666 hours