At their​ family's pizzeria, Dave makes 6 pizzas in the first hour it is open and 3 pizzas each hour after that. Lauren makes 11 pizzas in the first hour and 3 pizzas each hour after that. If the pizzeria is open for 6​ hours, how many pizzas will they make in​ all?

Answer:

$134217728

Step-by-step explanation:

Day 1: $1

Day 2: $2

Day 3: $4

Day 4: $8

Day 5: $16

Day 6: $32

Day 7: $64

Day 8: $128

Day 9: $256

Day 10: $512

Day 11: $1024

Day 12: $2048

Day 13: $4096

Day 14: $8192

Day 15: $16384

Day 16: $32768

Day 17: $65536

Day 18: $131072

Day 19: $262144

Day 20: $524288

Day 21: $1048576

Day 22: $2097152

Day 23: $4194304

Day 24: $8388608

Day 25: $16777216

Day 26: $33554432

Day 27: $67108864

Day 28: $134217728

a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

To know more about substitution visit:

https://brainly.com/question/26094713

#SPJ11

The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

Answer:

30

Step-by-step explanation:

Because EF and BC are parallel, ΔEFD, and ΔBCD are similar. Because we know what CF and DF are, we can add their lengths together to get CD, which in this case is 44 units long. Then, we can divide the length of CD and DF to get the scale of ΔEFD, which is 6/11. Because ΔEFD and ΔBCD are similar, we can multiply the length of BD by 6/11 to get the length of ED, which turns out to be 30.

Answer:

30 is the correct answer/solution

Step-by-step explanation:

Answer:

the answer is 357

Step-by-step explanation:

350 + 440 + 400 = 1190

30% of 1190 = 357

May I have brainliest please? :)

Answer:

C then B

Step-by-step explanation:

If  2x > 50 , then x > 25.  Draw a circle at x=25 and then extend a ray in the positive x direction away from x = 25.

If x + 6 < 32, subtract 6 from both sides, obtaining x < 26.

    Draw a cirlce at x=26 and extend a ray from that x to the left.

Answer:

graph c is 2x> 50 and graph b is x+6<32

Step-by-step explanation:

For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.

For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is  all numbers less than 26.

By separating variables and assuming U(x, t) = X(x)T(t), we can solve the equation using separation of variables.  By substituting the solutions back into the original equation, we can verify that u = 4U satisfies the heat equation.

To solve the heat equation u = 4U, we can use separation of variables. We assume that the solution can be written as U(x, t) = X(x)T(t), where X(x) represents the spatial component and T(t) represents the temporal component.

By substituting U(x, t) = X(x)T(t) into the heat equation, we obtain X(x)T(t) = 4X(x)T(t). Dividing both sides by X(x)T(t), we have T(t)/T(t) = 4X(x)/X(x), which simplifies to T(t)/T(t) = 4 and X(x)/X(x) = 1.

Since the left side of the equation only depends on t and the right side only depends on x, they must be equal to a constant. Let's denote this constant as lambda, so we have T'(t)/T(t) = lambda and X''(x)/X(x) = lambda.

Solving the equation T'(t)/T(t) = lambda gives us T(t) = e^(lambda*t), where lambda can be any constant.

Solving the equation X''(x)/X(x) = lambda leads to X(x) = sin(sqrt(lambda)*x) or X(x) = cos(sqrt(lambda)*x), where sqrt(lambda) is the square root of lambda.

The constant lambda is determined by the boundary conditions of the system. By applying appropriate boundary conditions, we can find the specific values of lambda that satisfy the problem.

Finally, by substituting the solutions T(t) and X(x) back into U(x, t) = X(x)T(t), we can verify that u = 4U satisfies the heat equation.

To learn more about separation of variables click here, /brainly.com/question/30417970

#SPJ11

Answer:

first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1

Step-by-step explanation:

Answer:

Stop and save is the best

Step-by-step explanation:

I say this because your getting  the same apples for cheap not only are they cheap but your also getting more.

The median is greater than the mean. From the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean.

In the given chart we can deduce the following;

These numbers can be listed as follows;

5, 6, 7, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12

The median of these numbers is calculated as;

\(median = \frac{9+ 10}{2} = 9.5\)

The mean of these numbers is calculated as;

\(mean = \frac{5+6+7+8+9+9+9+10+10+10+10+11+11+12}{14} = 9.07\)

Thus, the median is greater than the mean.

Also, from the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean. But if the distribution is skewed to the right, the mean is always greater than the median.

Learn more here: https://brainly.com/question/24055593

Answer:

28800 square feet

Step-by-step explanation:

We solve this using the Heron's formula

Area of a Triangle = √s(s - a)(s - b)(s - c)

s = a + b + c/2

s = 100 + 580 + 600/2 = 640

Area of the land(Triangle) = √640 × (640 - 100)(640 - 580)(640 - 600)

= √640 × (540) ×( 60) × (40)

= √(829440000)

= 28800 square feet

Therefore, the approximate the area of the land is 28800 square feet.

the smallest of the three numbers is 14

Hi there !

three consecutive numbers a ; b ; c

b = a + 1

c = a + 2

a + b + c = 45

replace b ; c

a + (a + 1) + (a + 2) = 45

3a = 45 - 3

3a = 42

a = 42 : 3

a = 14

Good luck !

SOLUTION:

Step 1:

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

Step 2:

In this triangle PQR, where the angle under consideration is P,

the hypotenuse is 53, the opposite is 28 and the adjacent side is 45.

Step 3:

From the definition in step 1,

CONCLUSION:

The ratio that represents the cosecant of angle P is;

Answer:

0.1 > 10^-2

(I'm pretty sure I'm right. sorry if im wrong :(

The expression is given as,

The given expression is simplified as follows:

Thus the result of the given expression is,

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

x = \(\frac{a(k-r)}{7}\)

Step-by-step explanation:

Given

a = \(\frac{7x}{k-r}\) ( multiply both sides by (k - r) )

a(k - r) = 7x ( divide both sides by 7 )

\(\frac{a(k-r)}{7}\) = x

Answer:

27(2+1)

Step-by-step explanation:

Its 27(2+1) because 27 is the GCF and it  goes into 54 and 27 then you divide 54/27 and then 27/27, at that point you have the numbers 2 and 1 then you just put them into the equeation. And BOOM just like that your finished.

Using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, we know that:

Lemons required to make 16 cups of lemonade: 4 lemons

Then, the rate of lemons being used in lemonade per cup:

4/16

1/4

Therefore, using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ4

Answer:

its b

Step-by-step explanation:

The perimeter of the rectangular path is 64 ft

Rectangle is a type of quadrilateral that has its parallel sides equal to each other, opposite sides are equal to each other, and all the angle are equal to 90 degrees.

How to determine this

The perimeter of a Rectangle = 2 ( Length + Width)

Where the Width = 2 ft

Length = 28 ft longer than Width

i.e W + 28

Length = 2 + 28 = 30 ft

To calculate the perimeter if the path

Perimeter = 2( 30 + 2)

Perimeter = 2(32)

Perimeter = 64 ft

Therefore, the perimeter of the rectangular path is 64 ft

Read more about Rectangle

https://brainly.com/question/6320071

#SPJ1

Answer:

500

Step-by-step explanation:

Answer: No, they are not inverses of one another.

=======================================================

Explanation:

There are at least 3 methods we can use to prove the functions aren't inverses of each other.

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

Method 1

Let's say we plugged x = 0 into f(x).

\(f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\\)

The input x = 0 leads to the output y = 1.

Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.

\(g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\\)

If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.

This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.

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

Method 2

Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties

The left hand side of each equation involves the concept of "function composition".

Let's see what f(g(x)) is equal to in this case.

\(f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\\)

We do not get an output of simply x only, so this is another way to see how we don't have inverses.

Through similar steps, you should find that \(g(f(\text{x})) = -4\text{x}-3\) which is further confirmation that f(x) and g(x) are not inverses of each other.

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

Method 3

Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.

The process involves this basic outline:

So,

\(f(\text{x}) = 2\text{x}+1\\\\\text{y} = 2\text{x}+1\\\\\text{x} = 2\text{y}+1\\\\\text{x}-1 = 2\text{y}\\\\\text{y} = \frac{\text{x}-1}{2}\\\\f^{-1}(x) = \frac{\text{x}-1}{2}\\\\\)

Unfortunately we do not end up with -2x-1 as the actual inverse.

So if \(g(\text{x}) = \frac{\text{x}-1}{2}\) was the case, then f(x) and g(x) would be inverses of each other.

Through similar steps, the inverse of \(g(\text{x}) = -2\text{x}-1\\\\\) is \(g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\\)

The given formula for the car's value after n years since it was purchased is V(n) = 28000(0.875)^n. We are asked to find the amount of value the car loses in its fifth year.

To calculate the value lost in the fifth year, we need to find the difference between the value at the start of the fifth year (V(5)) and the value at the end of the fifth year (V(4)).

Using the formula, we can calculate V(5):

V(5) = 28000(0.875)^5

To find V(4), we substitute n = 4 into the formula:

V(4) = 28000(0.875)^4

To determine the value lost in the fifth year, we subtract V(4) from V(5):

Value lost in fifth year = V(5) - V(4)

Now, let's calculate the values:

V(5) = 28000(0.875)^5

V(5) ≈ 28000(0.610)

V(4) = 28000(0.875)^4

V(4) ≈ 28000(0.676)

Value lost in fifth year = V(5) - V(4)

≈ (28000)(0.610) - (28000)(0.676)

≈ 17080 - 18928

≈ -1850

The negative value indicates a loss in value. Therefore, the car loses approximately $1,850 in its fifth year.

To learn more about car - brainly.com/question/20842520

#SPJ11

We are asked to find the left and right hand limits of the given function.

1. Left-hand limit:

The numerator is negative when we substitute -1, so the absolute value will be evaluated as a negative expression.

Now, factor the numerator

So, the left-hand limit is equal to 7

2. Right-hand limit:

The numerator is positive when we substitute +1, so the absolute value will be evaluated as a positive expression.

Now, factor the numerator and the denominator.

So, the right-hand limit is equal to -7

Answer:

In the middle of 1 and 2

Step-by-step explanation:

1 1/2 is 1 and halfway to 2. Therefore it is the middle of 1 and 2.

The image of the number line is attached below, 1 1 / 2 can be written as 3 / 2 or 1.5.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged sequentially at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

Given:

1 1 / 2

Solve the above-mixed fraction to improper fraction as shown below,

1 1 / 2 = (2 × 1 + 1) / 2

1 1 / 2 = (2 + 1) / 2

1 1 / 2 = 3 / 2

Convert into decimal form as shown below,

1 1 / 2 = 1.5

To know more about number line:

https://brainly.com/question/557284

#SPJ2

Answer:

232.05 miles, no  Mr. Carson’s did not estimate reasonable

Step-by-step explanation:

The most famous version of the song was recorded by the Nitty Gritty Dirt Band. "Will the Circle Be Unbroken" is a traditional Christian hymn that has been recorded by many artists over the years.

However, the most famous version of the song was recorded by the Nitty Gritty Dirt Band in 1972 as a collaborative project that featured a wide variety of country, bluegrass, and folk musicians, including legends such as Mother Maybelle Carter, Earl Scruggs, and Doc Watson. The three-disc album was a critical and commercial success and helped to popularize traditional country and bluegrass music among a wider audience. The Nitty Gritty Dirt Band's rendition of "Will the Circle Be Unbroken" remains a beloved classic in the history of American music.

Find more about Nitty Gritty Dirt Band

brainly.com/question/6061970

#SPJ4