(25 points) A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 0.40M + 15.75, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I = 0.25M + 3.90.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

C =

Answer:

-5n+9.1

Step-by-step explanation:

- - = +

Answer:

60bracelets

Step-by-step explanation:

To solve this problem, we need to find her rate. This is the number of jewelries she makes per unit of time;

         Rate  = [tex]\frac{number of jewelries}{time taken }[/tex]

 Number of jewelries  = 12 bracelets

  time  = 4hrs

     Input the parameters:

           Rate  = [tex]\frac{12}{4}[/tex]   = 3bracelets/hr

She works 5hrs for 4 Thursdays;

   Number of hours worked  = 5 x 4 = 20hrs

Now, working at a rate of 3bracelets/hr for 20hrs, the number of bracelets she will produce is given as;

  Number of bracelets  = number of hours x rate

                                       = 20 x 3

                                       = 60bracelets

Answer:

130 earrings

Step-by-step explanation:

P=450

450=5n-200

+200     +200

650=5n

/5      /5

n= 130

She would have to sell 130 earrings in order to earn a profit of $450.

Profit is the money earned by a business when its total revenue exceeds its total expenses.

Given is Lena who sells earrings from a booth at the arts fair. She pays $200 to rent the booth. She makes $5 from each pair of earrings she sells. Her profit [P] can be found using the following equation (where n is the number of pairs of earrings sold) → P = 5n - 200.

Now, we have the following equation -

P = 5n - 200.

Now, for a profit of $450, substitute [P] by 450 as -

450 = 5n - 200

5n = 450 + 200

5n = 650

n = 130

Therefore, she would have to sell 130 earrings in order to earn a profit of $450.

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Answer:

A; (X=5)

Step-by-step explanation:

Move the constants and variable terms to one side:

3x-5= -2x+10

-5+10= -2x+ 3x

Combine like terms:

5=x or x=5

Answer:

The answer is C

Step-by-step explanation:

If you take the equation and simplify it.

3x-5=-2x+10

You would minus 3x from both sides, leaving the equation like

-5=-5x+10

Then you would minus 10 from both sides, leaving the equation like

-15=-5x

If you wanted to go further you could divide both sides by -1 and get rid of the negatives. Leaving the equation like

15=5x

Then to put it into the simpleist   form you would divide both sides by 5, leaving the equation like

3=x

I hope this helps.

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Principal = $20000

Interest rate = 5.5% = 0.055 compounded daily

Time = 16years =(360 * 16) = 5760

n = number of times interest is applied per period

Amount of money in account after 16 years :

A = p(1 + r/n)^nt

A = total amount

A = 20000(1 + 0.055/360)^(360*16)

A = 20000(1 + 0.0001527)^5760

A = 20000(1.0001527)^5760

A = 48193.1611

Interest on principal :

$48193.1611 - $20000

= $28193.1611

Answer:

The least common denominator is 77 so the fractions would become 63/77 and 66/77.

Analysing the Question:

We are given the following equations:

x - y = 4

x + y = 9

writing these equations in slope-intercept form

y = x - 4

y = -x + 9

the general form of the slope-intercept equation is :   y = mx + b (where m is the slope and b is the y-intercept)

Hence, we can say that the for Equation 1:

Slope  = 1

y-intercept = -4

For equation 2:

Slope = -1

y-intercept = 9

Finding if the lines are Perpendicular, parallel or neither

If the slope of the lines is equal, the lines are parallel

If the slope of the lines is the additive inverse (negative) of each other, the lines are perpendicular

Since the slopes of the 2 lines are the additive inverse (negative) of each other, the lines are perpendicular     [slope 1 = 1    , slope 2 = -1]

Answer:

The answer is B.

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer:

12-7=5

Step-by-step explanation: if you u need a equation for how much he has there u go

Answer:

Step-by-step explanation:

A...................................

∠MIH and ∠IHS are same side interior angles and sum up to 180° as per property, therefore

B...................................

∠AVM and ∠VAS are same side interior angles

and ∠VAS and ∠LAH are vertical angles, which are equal as per property of vertical angles, so:

C...................................

Obtuse angle at the intersection of AV and HI, if name the intersection point O:

It could be either.

1 + 1 + 1 = 3, which is prime

2 + 2 + 2 = 6, which is composite

Answer:

Yes please i really need it

Step-by-step explanation:

Answer:-1

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

Answer:

B. Insurance

Step-by-step explanation:

Answer:

3 over 100

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

86.4÷9=9.6

183.6 - 86.4=97.2

97.2 ÷ 9.6=10.8

10.8x9=97.2

97.2+86.4=183.6

Answer:

12 ounces for $1.47.

Step-by-step explanation:

:) ello

Answer:

50 mins

hope this helped :)

Answer:

1.2

Step-by-step explanation:

Just divide

Answer:

1.2

Step-by-step explanation:

Divide 18 by 15 and get the answer.

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

[tex]f(x) = x^{3}-9\cdot x^{2}+ 3[/tex], [tex]2 \leq x \leq 12[/tex]

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

[tex]f'(x) = 3\cdot x^{2}-18\cdot x[/tex]

[tex]3\cdot x^{2}-18\cdot x = 0[/tex]

[tex]3\cdot x \cdot (x-6) = 0[/tex] (Eq. 1)

As we can see, only a solution is a valid critical value. That is: [tex]x = 6[/tex]

Second, we determine the second derivative formula and evaluate it at the only critical point:

[tex]f''(x) = 6\cdot x -18[/tex] (Eq. 2)

x = 6

[tex]f''(6) = 6\cdot (6)-18[/tex]

[tex]f''(6) =18[/tex] (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

[tex]f(2) = 2^{3}-9\cdot (2)^{2}+3[/tex]

[tex]f(2) = -25[/tex]

x = 6

[tex]f(6) = 6^{3}-9\cdot (6)^{2}+3[/tex]

[tex]f(6) = -105[/tex]

x = 12

[tex]f(12) = 12^{3}-9\cdot (12)^{2}+3[/tex]

[tex]f(12) = 435[/tex]

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Answer:

Her new position is 37 feet below the cave entrance

Step-by-step explanation:

Let us solve the question

∵ The cave entrance is the zero position

∵ Anna is in 42 feet below the cave entrance

→ Below zero means negative

∴ Anna is in -42 feet

∵ She descends 10 feet

→ Descend means negative

∴ She is in -42 + -10 = -52 feet

∵ She ascends 15 feet

→ Ascend means positive

∴ She is in -52 + 15 = -37 feet

→ -37 means she is in below the cave entrance by 37 feet

∴ Her new position is 37 feet below the cave entrance

Answer:

1) 8,388,608 grains of wheat.

2) 16,777,215 grains of wheat.

3) 239,674.5 pounds.

Step-by-step explanation:

Question 1)

We know that on the first square, there is 1 grain of wheat.

On the second, 2 grains of wheat.

On the third, 4 grains of wheat.

And on the fourth, 8 grains of wheat.

Therefore, we have a geometrically increasing sequence. It looks like:

1, 2, 4, 8...

Therefore, to find the number of grains on the 24th square, we can write an explicit formula.

The standard form for the explicit formula for a geometric sequence is:

[tex]x_n=a(r)^{n-1}[/tex]

Where a is the initial amount, r is the common ratio, and n is the nth term (starting from 1).

We know that the initial term a is 1 because there’s one grain of wheat on the first square.

And the common ratio will be 2 because each square has double the amount of the previous square.

So, substitute 1 for a and 2 for r. This yields:

[tex]x_n=1(2)^{n-1}\\[/tex]

We can simplify this:

[tex]x_n=2^{n-1}[/tex]

So, to find the amount of wheat on the 24th square, we simply need to substitute 24 for n and evaluate. So:

[tex]x_{24}=2^{24-1}=2^{23}[/tex]

Evaluate. Use a calculator:

[tex]x_{24}=8,388,608[/tex]

Therefore, on the 24th square, there are 8,388,608 grains of wheat.

Question 2.1)

We want to find the total number of grains of wheat on the board at this time.

In other words, we want to find the sum of our geometric sequence when n is 24.

The formula for the sum of a geometric series is:

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

Where rⁿ is the value of the number of terms n, r is the common ratio, and a is the initial term.

We want to find the sum after 24 times. So, n is 24.

So, substitute 24 for n, 2 for r, and 1 for a. This yields:

[tex]S_{24}=\frac{(1)(2^{24}-1)}{2-1}[/tex]

Evaluate. Use a calculator:

[tex]S_{24}=16, 777, 215[/tex]

Therefore, the total sum of the number of grains of wheat at the board at the 24th square is 16,777,215.

Question 2.2)

And to find the weight, we will just have to multiply our total amount by 1/7000. So:

[tex]W=16777215(\frac{1}{70})[/tex]

Use a calculator:

[tex]W=239,674.5\text{ lbs}[/tex]

So, the total weight is 239,674.5 pounds.

Answer:

a. s = [tex]\frac{d}{t}[/tex]

b. 9600 ft

Step-by-step explanation:

In the given question, the motion of the bee involves speed (s), distance (d) and its time of flight (t).

a. The equation required to determine the distance of the flowerbed from the hive/ hive to flowerbed is;

speed = [tex]\frac{distance}{time}[/tex]

i.e s = [tex]\frac{d}{t}[/tex]

b. Given that: the bee flies back at 8 feet per second, and in 20 minutes (1200 seconds);

s = [tex]\frac{d}{t}[/tex]

⇒ d = s x t

       = 8 ft/s x 1200 s

       = 9600 ft

The flowerbed is 9600 feet from the hive.

Answer:

18 min

Step-by-step explanation:

Answer:

1x = 3x

Step-by-step explanation:

This is could be wrong not sure.