Find the area of the rectangle recall that area and length width

Using p for price and q for quantity, the demand function is; q = -3/2p + 1590

Given that at;

The monthly demand at a price of $900 = 240

The monthly demand at a price of $850 = 315

We are told that the system is a linear function. Therefore demand function would be in the form of slope intercept form as;

q = mp + c

Where;

q = quantity demanded

p = price

m = slope

c = y-intercept

At a price of $900 with a monthly demand of 240 gives the equation;

240 = 900m + c  ---(1)

At a price of $850 with a monthly demand of 315 gives the equation;

315 = 850m+ c  ------(2)

Subtracting eqn 2 from 1 gives;

-75 = 50m

m = -75/50

m = -3/2

Substituting m = -3/2 into equation 1;

240= -3/2(900) + c

c = 240 + 3/2(900)

c = 1590

Therefore the demand function can be given as; substituting m and c into equation 5, we have; q = -3/2p + 1590

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Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

The answer is 20

Step-by-step explanation:

6 (20 - 8 ) = 72

Answer:

20

Step-by-step explanation:

edge 2021

Answer:

below

Step-by-step explanation:

Clare's mistake was the writing of 4000 in standard form

he wrote 4 ×10²

instead of 4 ×10³

Answer:

Step 1

Step-by-step explanation:

I believe Claire's mistake is when she tries to simplify 4000

She says that 4000 = 4 × 10²

4000 is actually equal to 4 ×10³

Answer:

ncx(2.718282)=18;c=456

ncx(2.718282)=18;c=456

Answer:

47.008

Step-by-step explanation:

Answer:  r = (2π/2)1/2 = 1 cm and h = 2 cm.

Step-by-step explanation:

The radius of the closed right circular cylindrical can of smallest surface area whose volume is 2π cm3 is 1 cm and the height is 2 cm. This can be computed by using the formula for the volume of a right circular cylinder, V = πr2h, and solving for the radius. The equation becomes r = (V/πh)1/2. When plugging in the given values, we find that r = (2π/2)1/2 = 1 cm and h = 2 cm.

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.

To find the value of S4, we substitute n = 4 into the expression and evaluate it.

♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)

Simplifying, we get:

♾️. 3 Σ 1/4(-1/3)

Since the term 1/4(-1/3) is constant, we can pull it out of the summation:

1/4(-1/3) ♾️. 3

Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:

1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12

Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

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The probable question could be:

What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?

A) 1/9

B) 7/54

C) 5/27

D) 10/27

The resulting equation is the x-coordinate of the point of local extrema of a quadratic function.

To find the local extrema of a polynomial function f(x), we apply the equation f'(x) = 0. We are given the basic form of a quadratic equation. The equation is given below.

f(x) = ax² + bx + c

We need to find the differentiation of the above equation.

f'(x) = 2ax + b

Now, we will equate the obtained equation to zero and solve for the value of the variable "x".

f'(x) = 0

2ax + b = 0

2ax = -b

x = -b/2a

This resulting equation is familiar from algebra/pre-calculus. This is the x-coordinate of the point of local extrema of a quadratic function.

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The correct answer is The mean price is 50.

The median price is 41.111.

The modal price is 52.857.

The standard deviation price is 22.271.

The data table represents the prices (in R) of 50 items purchased by a shopper is,

Price                       Frequency

0<20                            6

20<40                          0

40<60                          18

60<80                          13

80<100                         4

Explanation:

The mean of the data is the average of the given values.

The mean of the data is calculated as,

Price                   frequency (f)     Mid point (xi)                 f.xi

0-20                          6                         10                            60

20-40                        9                         30                           270

40-60                        18                        50                           900

60-80                        13                        70                           910

80-100                       4                         90                           360

Total                          50                       250                        2500

Mean = ∑fx1/N

Mean = 2500/50

Mean = 50

Price                   frequency (f)     cf

0-20                          6                  6      

20-40                        9                 15    

40-60                        18                33  

60-80                        13                46      

80-100                       4                 50  

Total                          50               150

The median class is 40 -60 as cf ≥ N/2

which is 33 ≥ 25

medain = 40 + |25-15|/18 ×20

medain = 40 + 200/18

median = 41.111

Mode = lower limit + f1-f0/2f1-f0-f2 × height

Here, f1 is the frequency of the modal class = 18.

f0 is the frequency of the preceding modal class = 9.

f2 is t/he frequency of the succeeding modal class = 13.

Mode = 40+ 18-9/2(18)-9-13

Mode = 52.857

Hence, the modal price is 52.857.

Price                   frequency (f)     Mid point (xi)                 f.(xi)^2

0-20                          6                         10                            600

20-40                        9                         30                           8100

40-60                        18                        50                           45000

60-80                        13                        70                           63700

80-100                       4                         90                           32400

Total                          50                                                       149800

The standard deviation of the data is calculated as,

SD = √(∑f(x1)^2)/N - (mean)^2

SD = √149800/50- (50)^2

SD = 22.271

Hence, the standard deviation of the data is 22.271.

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The key here is to not worry too much and just follow PEMDAS.

Here we have the expression \((5\cdot 7)^2\).  Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)

Hope this helps.

Answer:

$15348

Step-by-step explanation:

i = prt is the simple interest equation

i = 12,000(0.031) = 372

i = 372*9 = 3348

12000+3348 = $15348

Answer:

Step-by-step explanation:

I=PRT

I=12,000(3.1%)

I=12,000(0.031)=372

I=372*9=3348

The total interest paid is $3,348.

The number 2755 flights were scheduled.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Recently many airlines have had to cancel flights in a single day.

Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.

The number of flights scheduled,

= 416 x 100/ 15.1

= 41600/15.1

= 2754.96

≈ 2755

Therefore, 2755 flights were scheduled.

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Answer:

-7

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

|13-15|=|-2|=2

|-5|=5

2-5=-3

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

All the terms are alike.

Step-by-step explanation:

Answer:

its the 2nd one

Step-by-step explanation:

Hopefully this helped, if not HMU and I will get u a better answer.

-Have a great day! :)

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Generally, insurance helps the policyholder to transfer the A. Risk from their bank account to the insurance company.

Insurance risk refers to the exposure of a policyholder to financial loss and consequent inability to meet their liabilities.

Insurance risks are transferable to insurance companies who pool resources together from many policyholders to meet and spread the risks.

Insurance does not transfer money, insurance, or health to the insurance company, but it transfers risk.

Thus, the correct option is Option A.

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The maximum grazing area for the cow is approximately 53,343.08 square feet.

The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.

Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.

To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.

Area of circle = π(130)^2 square feet = 53,407.08 square feet

Area of barn = 64 square feet

Maximum grazing area = Area of circle - Area of barn

= 53,407.08 - 64

= 53,343.08 square feet (rounded to two decimal places)

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Answer:

-54 is a integer and rational number

Step-by-step explanation:

Assuming you mean isolate for x

Answer:

\(x=-1\)

Step-by-step explanation:

We can subtract \(4x\) from both sides to get \(3x-4x=4x-4x+1\).

That simplifies to \(-x=1\).

We can multiply by \(-1\) to get \(-x*-1=1*-1\).

That simplifies to \(x=-1\).

So, \(x=-1\) and we're done!

Answer:

8/27. Though the question is a bit confusing. If your asking which term describes it, its this a multiple choice question?

Step-by-step explanation:

8 /27

is already in the simplest form. It can be written as 0.296296 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions :

Find the GCD (or HCF) of numerator and denominator

GCD of 8 and 27 is 1

Divide both the numerator and denominator by the GCD

8 ÷ 1

27 ÷ 1

Reduced fraction:  

8 /27

Therefore, 8/27 simplified to lowest terms is 8/27.

Answer:

-8/27

Step-by-step explanation:

Answer:

x ≥ 88

Step-by-step explanation:

In order to have at least an average of 80 after 4 tests, the sum of her scores must be at least 80 * 4 = 320 so we can write the following inequality:

71 + 78 + 83 + x ≥ 320

232 + x ≥ 320

x ≥ 88

Answer:

Your correct answer to this problem is x ≥ 88

Step-by-step explanation:

71 + 78 + 83 + x ≥ 320

232 + x ≥ 320

= x ≥ 88

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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Answer:

Assuming order does not matter, the probability of selecting all midsize cars is 0.000277373, or \(\frac{4}{14421}\).

Step-by-step explanation:

First, we must find the n(Total arrangements of selections)=(8+15)C6

n(Total arrangements of selections)=23C6

n(Total arrangements of selections)=100,947

Second, we must find the n(Arrangements where all are midsize cars)=8C6

n(Arrangements where all are midsize cars)=28

To find the probability of selecting all midsize cars, we divide the n(Arrangements where all are midsize cars) by the n(Total arrangements of selections):

P(All midsize cars)= \(\frac{28}{100,947}\)

P(All midsize cars)= \(\frac{4}{14421}\)=0.000277373.

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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