Use Mathematical Induction to prove that 3+11+19+···+(8n−5) = 4n^2 −n, for all n ∈ N (elements of Natural numbers)

Answer:

a is an even number and b is an odd number

Step-by-step explanation:

if a is even and b is even then the sum would be even ex.10+6=16. I'd a and b are both odd the sum would be even ex. 13+9=22. one has to be odd and one has to be even for the sum to be odd ex. 5+4=9

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:option A

(4.2✖️10^3)(2.6✖️10^4)

4.2✖️2.6✖️10^3✖️10^4

10.92✖️10^3+4

10.92✖️10^7

10.92✖️10✖️10^6

1.092✖️10^6

Step-by-step explanation:

I hope this will help you:)

Answer:

1.092 x 10^8

Step-by-step explanation:

(4.2 x 10^3)(2.6 x 10^4)

Multiply the numbers

4.2* 2.6 =10.92

Add the exponents

10^3 * 10 ^4 = 10 ^(3+4) = 10^7

10.92 * 10^7

But this is not scientific notation, there can only be one digit in front of the decimal

Move the decimal one place to the left and add one to the exponent

1.092 * 10 ^(7+1)

1.092 x 10^8

​

Therefore, the original purchased price of the medium pizza without a coupon is $10.31.

A coupon is a ticket or document that may be used in marketing to obtain a financial discount or refund when making a purchase of a good.  Customers receive a discount on their initial purchase thanks to the First Order Coupon. The first order coupon sales rule may be configured by admin in the admin area.

It aids in improving conversion rates. Frequently, yearly percentages are used to describe coupon payments. For instance, a bond with a $1,000 face value and an annual payment of $30 is said to have a 3% coupon. If the friend purchased a medium pizza for $10.31 with a 30% off coupon, then the price of the pizza after the discount is:

= 10.31 - 0.30(10.31)

= 10.31 - 3.09

= $7.22

So the price of the medium pizza without a coupon is $7.22 / (1 - 0.30) = $10.31.

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To maximize the revenue store should charge rental fee of $7 for a movie .

Let x be the number of $1 increases in the rental fee

Let p(x) be the price of renting a movie after x increases,

And let q(x) be the quantity of movies rented per week after x increases.

The rental fee is $3, we have q(0) = 55.

For each additional $1 increase in the rental fee, the store loses 11 rentals per week.

This means that,

q(x) = q(0) - 11x

The revenue generated from renting movies per week is equal to the price per movie times the number of movies rented,

R(x) = p(x)q(x)

Maximize the revenue with respect to x.

Express R(x) in terms of p(x),

Take the derivative with respect to p(x),

R(x) = p(x)q(x)

      = p(x)(55 - 11x)

      = 55p(x) - 11x p(x)

Taking the derivative with respect to p(x), we get,

d(R)/d(p(x)) = 55 - 11x

Setting this equal to zero, we get,

⇒55 - 11x = 0

⇒x = 5

Store should increase the rental fee by $5.

The new rental fee would be,

p(5) = $3 + $5

       = $8

And the quantity of movies rented per week would be,

q(5) = 55 - 11(5)

       = 0

Since the quantity of movies rented per week would be zero.

If the rental fee is increased by $5,

⇒ store should not increase the rental fee by that much.

Instead, the store should increase the rental fee by $4,

so the new rental fee would be,

p(4) = $3 + $4

      = $7

And the quantity of movies rented per week would be,

q(4) = 55 - 11(4)

       = 11

Therefore, the store should charge $7 per movie to maximize their revenue.

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The student would need to accumulate at least 7 more hours of instrument time, either actual or simulated, to fulfill the total instrument time requirement for an instrument rating.

To determine how many additional total instrument hours the student needs to meet the requirement for an instrument rating, we need to calculate the total instrument time she currently has and compare it to the minimum requirements.

Based on the given information, let's break down the student's experience:

1. 35 hours of PIC XC (cross-country) time: This type of flight time is not directly applicable to instrument rating requirements. Therefore, we won't consider these hours for the instrument rating.

2. 50 hours of PIC time: Similar to the previous case, this PIC time is not specific to instrument flying and won't be considered for the instrument rating.

3. 8 hours of instrument time with a CFII (Certified Flight Instructor - Instrument): This counts as actual instrument flight time and can be considered towards the instrument rating requirement.

4. 25 hours of simulated instrument time with a safety pilot: Simulated instrument time, where the student is wearing a view-limiting device (such as a hood or foggles) and a safety pilot is acting as a lookout, can also be considered towards the instrument rating requirement.

So, the total instrument time the student currently has is 8 hours (actual instrument time with a CFII) + 25 hours (simulated instrument time with a safety pilot) = 33 hours.

To obtain an instrument rating, the Federal Aviation Administration (FAA) requires a minimum of 40 hours of actual or simulated instrument time. Therefore, the student needs an additional 40 - 33 = 7 hours of instrument time to meet the requirement.

The student would need to accumulate at least 7 more hours of instrument time, either actual or simulated, to fulfill the total instrument time requirement for an instrument rating.

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Step-by-step explanation:

No because he had 14 and needs 16

Answer:

187.5mph

Step-by-step explanation:

If 1 hour= 75mph

what about 2.5 hours

you cross multiply

In this case, the monthly payment for the car loan would be approximately $1,299.13.

To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.

Here's how to do it:

1. Open Excel and create a new spreadsheet.

2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).

3. In cell A2, enter the annual interest rate: 9%.

4. In cell A3, enter the loan duration in years: 3.

5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).

6. The result in cell A4 will be the monthly payment.

So, in this case, the monthly payment for the car loan would be approximately $1,299.13.

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Answer:

x< 5

Step-by-step explanation:

See the graph below

She needs 15 minutes to complete 2 miles, thus completing 4 miles at the same rate will take her 4 hours and 15 minutes.

The average number of points received by students in one math class at the conclusion of the term, for instance, is an example of a statistic since it represents the population of all math classes, if we view that class as a sample. Because it integrates arithmetic ideas to create an analysis of a data set that may be used to comprehend an association in the data, statistics has earned a reputation for being an extremely challenging course, especially when studied in college (whoo that was a mouthful).

given

The unit rate for the ratio of 150 minutes to every 20 miles is obtained by dividing 150 by 20.

150÷20=7.5

Thus, the runner is covering one mile in 7.5 minutes. This unit rate can be multiplied by the number of miles:

6 miles in 7.5 minutes equals 45 minutes.

At this speed, she can complete 6 miles in 45 minutes.

If she runs 6 miles in 45 minutes, she will run 2 miles at the same pace in 453=15 minutes.

She needs 15 minutes to complete 2 miles, thus completing 4 miles at the same rate will take her 4 hours and 15 minutes. She is moving at a speed of 8 miles per hour since 60 minutes equal 1 hour.

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Answer:

Jim ran 60 miles

Step-by-step explanation:

T (Toby) - 5 miles

K (Katie) - 4T , 4(5), 20

J (Jim) - 3K, 3(20), 60

Answer:

Jim ran 60 miles.

Step-by-step explanation:

First off I would take note of the information given.

Toby = t

Kate = k

Jim = j___________________________________________

j = 3k

t = 5

4t = k  

Since we already know Tim ran 5 miles we multiply 5 x4 to get 20. So Kate ran 20 miles.

3 times Kate's amount is Jim's. So 20 x 3 = 60.

Hope that helps and have a great day!

Hi!

I can help you with joy!

We are given 2 points: (-2, 3) and (5, 4), so we can easily calculate the slope of this line using this formula:

\(\displaystyle\frac{y2-y1}{x2-x1}\)

\(\displaystyle\frac{4-(-3)}{5-(-2)}\)

\(\displaystyle\frac{4+3}{5+2}\)

\(\displaystyle\frac{7}{7}\)

\(1\) (Answer)

I hope it helps!

Ask if you have any queries.

~Misty~

\(\bf{GracefulTeen\)

Enjoy your day!

Answer:

37 dimes and 10 nickels

Step-by-step explanation:

let d = # dimes

let n = # nickels

we can set up a system of equations:

n + d = 47

.05n + .10d = 4.2

if we solve the first equation for 'n' we get:  

n = 47-d

now we can substitute this in for 'n' in the second equation:

.05(47-d) + .10d = 4.2

2.35 - .05d + .10d = 4.2

2.35 + .05d = 4.2

subtract 2.35 from each side to get:

.05d = 1.85

d = 1.85÷.05

d = 37

if d+n = 47 and d=37 then n = 10

Check:

.05(10) + .1(37) should equal 4.2

.50 + 3.7 = 4.2  [It Checks Out]

To fully describe the single transformation that maps shape a onto shape b, it is important to consider the different possible transformations. These include translation, rotation, reflection, dilation, and shear.

In order to determine which transformation is required to map shape a onto shape b, we need to analyze the specific characteristics of both shapes. For instance, if shape a is a rectangle and shape b is a square, we may need to use dilation to adjust the size of the rectangle to match that of the square. Once we have identified the appropriate transformation, we need to determine the specific parameters required to carry out that transformation. For example, if we need to perform a rotation, we need to know the angle of rotation and the point around which the rotation will occur.

It is also important to note that the transformation must be applied consistently to all points in shape a in order to accurately map it onto shape b.  Overall, fully describing the single transformation that maps shape a onto shape b requires a long answer as it involves carefully analyzing the characteristics of both shapes and applying the appropriate transformation consistently to all parts of shape a.

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P(x) = -2x² + 130x - 2000 when x is the price of each game to make the game profitable, the price should be at least $ 25 and no more than $ 40.

Quadratic equations are polynomial equations of degree 2 in one variable of the form f(x) = ax2 + bx + c = 0, where a, b, c, R, and a 0 are all zeros. It is the generic form of a quadratic equation in which 'a' is referred to as the leading coefficient and 'c' is referred to as the absolute term of f. (x). The roots of the quadratic equation (,) are the values of x that fulfil the quadratic equation.

There will always be two roots to the quadratic equation. Roots might be real or fictitious in nature.

p(x) = -2x² + 130x - 2000

The game will be profitable if P (x) > 0.

-2x² + 130x - 2000 > 0

-x² + 65x - 1000 > 0

x² - 65x + 1000 > 0

x(x-25) - 40(x -25) > 0

x>25 x < 40.

Therefore, price should be at least $ 25 and no more than $ 40.

The values of variables that satisfy the given quadratic equation are referred to as its roots. In other words, if f() = 0, x = is a root of the quadratic equation f(x).

The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

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Answer:

=use your sense

Step-by-step explanation:

if I teach you give me your sister number

Answer:

$787.5

Step-by-step explanation:

first, you have to find how much ginny makes in a week w/o her raise\

17.5*40=700

then, you have to raise it by 12.5%, so her new salary is 112.5% of 17.5

112.5% = 1.125

700*1.125=787.5

Answer:

Step-by-step explanation:

if the faster hose is ten minutes faster and both together only takes 12 minutes then the secound one by it self should take 22 mins. i think im not sure tho

Answer:

\(c = -P + R\)

Step-by-step explanation:

Answer:

it would be 19/15k

Step-by-step explanation:

Answer:

Hi! I think it's 15/8t and 19/15k

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

(x+4)²-2

Step-by-step explanation:

The lowest point of the curve is -2 at x=(-4)

=> The vertex of the upwards facing parabola is (-4,-2)

So, the vertex has shifted from (0,0) (vertex of x²) to (-4, -2)

Using function transformation (translation),

f(x) = (x+4)²-2

Answer: 12.25

Step-by-step explanation:

Every day the bag of bird food decreases by 1 3/4 or 1.75.

It decreases for 7 days, so the amount decreased for a week would be 1.75(7) which is 12.25.

Answer:

23.3

Step-by-step explanation:

Answer:

hello your answer will be 9/2

Answer:

the second one  

Step-by-step explanation:

Answer: x= 9,-8

Step-by-step explanation:

The area of the rectangular lot with the dimension of 10 dm by 15 dm is 1,500 m2.

The area of a rectangular lot can be calculated by multiplying the length (L) and the width (W) of the lot. The formula for calculating the area of a rectangular lot is: Area = L x W. In this case, the length of the lot is 10 dm (decimeters) and the width is 15 dm, so the area is 10 dm x 15 dm = 150 dm2. To convert this to square meters (m2), we need to divide 150 dm2 by 10,000, since there are 10,000 dm2 in 1 m2. Therefore, 150 dm2 = 1,500 m2. So, the area of the rectangular lot with the dimension of 10 dm by 15 dm is 1,500 m2.

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