The marketing research department of a computer company used a large city to test market the​ firm's new laptop. The department found the relationship between price p​ (dollars per​ unit) and the demand x​ (units per​ week) was given approximately by the following equation.

p= 1275 = 0.17x^2 0 < x < 80

So, weekly revenue can be approximated by the following equation.

R(x)= rp = 1275x- 0.17x^3 0 < x <80

Required:
a. Find the local extrema for the revenue function. What is/are the local maximum/a?
b. On which intervals is the graph of the revenue function concave upward?
c. On which intervals is the graph of the revenue function concave downward?

Answers

Answer 1

Answer:

a. Local maximum = 50 units per week.

b. The graph is never concave upward.

c. (0, 80)

Step-by-step explanation:

a. The revenue function is:

[tex]R(x) = 1275x-0.17x^3[/tex]

The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:

[tex]R'(x) =0= 1275-0.51x^2\\x=\sqrt{2,500}\\x=50[/tex]

The second derivate of the revenue function determines if x =50 is local maximum or minimum:

[tex]R''(x) = -1.02x\\R''(50) = -1.02*50=-51\\[/tex]

Since the second derivate yields a negative value, x = 50 units per week is a local maximum.

b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.

c. Since there is only one local maximum  in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)


Related Questions

If 10 is added to the maximum value and 10 is subtracted from the minimum value of a set of ages of citizens waiting in line to vote, which of the following is true? a-The mean age and median age are unchanged. b-The mean age changes but the median age does not change. c- The median age changes but the mean age does not change. d-The effect on the mean and median cannot be determined without knowing the other ages. e-None of these.

Answers

Answer:

a-The mean age and median age are unchanged.

Step-by-step explanation:

By adding the same you are subtracting, the sum of the ages remains the same. Therefore, the mean remains the same since you are dividing the same total of ages by the same number of people.

The middle number continues to be the middle number, so the median also does not change.

Try an example.

The ages are 30, 40, 50, 60, 70

Mean = (30 + 40 + 50 + 60 + 70)/5 = 250/5 = 50

Median: 50

Now add 10 to the greatest value and subtract 10 from the least value.

The ages now are 20, 40, 50, 60, 80

Mean = (20 + 40 + 50 + 60 + 80)/5 = 250/5 = 50

Median: 50

As you can see, both the mean and the median did not change.

Answer: a-The mean age and median age are unchanged.

Answer:

The mean age and median age are unchanged

Step-by-step explanation:

The median will not change when we alter the lowest and highest values so we can eliminate the answers that say the median changes

The mean is found by adding the values together and dividing by the number of values

If we add 10 and subtract 10, we have not changed the total value before dividing, so the mean does not change

What is the circumference of the circle below? (Round your answer to the nearest tenth.)

Answers

Hey there! :)

Answer:

75.4 cm.

Step-by-step explanation:

Formula for the circumference of a circle:

C = 2rπ

Given:

r = 12 cm

Plug this value of r into the equation:

C = 2(12)π

C = 24π

Multiply by π (3.14)

24 × 3.14 = 75.36 cm

Round to nearest tenth:

75.36 ≈ 75.4 cm.

Answer: B

Step-by Step: C=2n

r= 2•n•12= 75.39822

You round it to the nearest tenth, it would be 75.4

At an international conference, flags from 8 different countries will be displayed. Of these flags, 4 are from the continent of Africa and 4 flags are from the continent of Europe. The flags will be displayed in a row, alternating between continents. A flag from Africa will be in the first position. In how many ways can the flags be displayed?

Answers

Answer:

96 ways

Step-by-step explanation:

Let´s call flags of countries from Africa as  A₁,  A₂, A₃, A₄, and from Europe as  E₁, E₂, E₃ and E₄

We have to display the flags always beginning with one flag from Africa let´s take A₁

For that flag, we have 4! possibilities Then 4! is:

4*3*2*1  = 24

As we have 4 different Flags from Africa, we will have

4*24 = 96  possibilities

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.

Answers

The dimensions of the Norman window that admit the greatest possible amount of light are approximately:

Width (w) ≈ 11.72 ft

Height (h) ≈ 2.91 ft

To find the dimensions of the Norman window that admit the greatest possible amount of light, we need to maximize the area of the window. The window consists of a rectangle and a semicircle, so the area is the sum of the areas of both shapes.

Let's assume the width of the rectangle is "w" and the radius of the semicircle is "r".

Since the diameter of the semicircle is equal to the width of the rectangle, the radius "r" is half of "w".

Area of the rectangle = w * h, where h is the height of the rectangle.

Area of the semicircle = (1/2) * π * r²

The perimeter of the window is given as 30 ft, which can be written as:

Perimeter = 2 * (w + h) + π * r + w

Since r = w/2, we can rewrite the perimeter equation as:

Perimeter = 2 * (w + h) + (π/2) * w + w

Perimeter = 2w + 2h + (π/2 + 1) * w

Given that the perimeter is 30 ft, we have:

30 = 2w + 2h + (π/2 + 1) * w

Now, we can express "h" in terms of "w" using the perimeter equation:

h = (30 - 2w - (π/2 + 1) * w) / 2

Next, let's express the area "A" of the window in terms of "w" using the formulas for the area of the rectangle and the semicircle:

Area (A) = Area of rectangle + Area of semicircle

A = w * h + (1/2) * π * r²

A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w/2)²

A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w² / 4)

Now, we want to maximize the area "A."

To find the maximum value, we take the derivative of "A" with respect to "w" and set it equal to zero:

dA/dw = (30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0

Solving for "w":

(30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0

(30 - 2w - (π/2 + 1) * w) + (π/2) * w = 0

(30 - (2 + π/2) * w) + (π/2) * w = 0

30 - (2 + π/2) * w + (π/2) * w = 0

(30 - 2w) + (π/2 - π/4) * w = 0

30 - 2w + (π/4) * w = 0

(π/4) * w - 2w = -30

w ((π/4) - 2) = -30

w = -30 / ((π/4) - 2)

w ≈ 11.72 ft

Now that we have the value of "w," we can find the value of "h" using the perimeter equation:

Perimeter = 2w + 2h + (π/2 + 1) * w

30 = 2(11.72) + 2h + (π/2 + 1) * (11.72)

30 = 23.44 + 2h + (π/2 + 1) * 11.72

2h = 30 - 23.44 - (π/2 + 1) * 11.72

2h = 6.56 - (π/2 + 1) * 11.72

h = (6.56 - (π/2 + 1) * 11.72) / 2

h ≈ 2.91 ft

So, the dimensions of the Norman window that admit the greatest possible amount of light are approximately:

Width (w) ≈ 11.72 ft

Height (h) ≈ 2.91 ft.

To learn more on derivative click:

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The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis
Foundation. This foundation was created to help ease the pain of HIV/AIDS in Africa Lewis, a Canadian
works for the United Nations trying to determine ways to stop the spread of this deadly disease from crippling
an entire continent
a. Choose a variable to represent the money earned during fundraising activities and the revenue generated
for the foundation
b. Use these variables to create an equation that will determine the amount of money the foundation will
receive
c. In their latest bake sale, the club raised $72. Calculate the amount the foundation will receive
d. At the end of the year, the World Issues Club mailed a cheque to the foundation for $850. How much
money did they fundraise in total?​

Answers

Answer:

a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.

b. [tex]M =0.60x[/tex]

c. $43.2

d. $1416.67

Step-by-step explanation:

Given that:

The World Issues club donates 60% of the total of their fundraising activities.

Answer a.

Let us choose the variable [tex]x[/tex] to represent the money earned during fundraising activities and [tex]M[/tex] for the revenue generated for foundation.

Answer b.

Foundation will receive 60% of the total of the fundraising activities.

Equation to determine the money that will be received by foundation:

[tex]M = 60\%\ of\ x\\OR\\M = 0.6x[/tex]

Answer c.

Given that x = $72, M = ?

Putting the value of x in the equation above:

[tex]M = 0.6 \times 72\\\Rightarrow \$43.2[/tex]

Answer d.

Given that M = $850, x = ?

Putting the value of M in the equation above to find x:

[tex]850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67[/tex]

So, the answers are:

a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.

b. [tex]M =0.60x[/tex]

c. $43.2

d. $1416.67

Someone help me please pls pls pls ​

Answers

Answer:

There is 9 on each pace and 3 on a row

Step-by-step explanation:

54/6=9

if there is 9 on each side and the same on each side, then it has to be 3 in each row and column. Also, this is a Rubix cube

Please give me brainliest, it really helps! :)

Have a good day!

Which graph represents the function?

Answers

the answer is the bottom left option

find the value of x given the shape

Answers

Answer:

x = 5

Step-by-step explanation:

Note: I'm assuming this shape is a trapezoid, so I'm basing a theorem of that fact. Tell me if it's not a trapezoid.

    1. Identify the theorem:

          There is a theorem you can use for this problem that states that the length of the meadian of a trapezoid is equal to the average of the lengths of the bases of the trapezoid.

      So what I mean is:

    (Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid

     2. Identify:

             Base 1:  FC = 6x-6

             Base 2:  AD = 38

             Median:  EB = 7x-4

     

      3. Substitute:

  (Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid

              (FC + AD)/2 = EB    

              (6x-6 + 38)/2 = 7x-4

       4. Solve for x:

                x = 5  

     

What is the greatest common factor of the polynomial below 12x^2-9x

Answers

Answer:

the greatest common factor of this is 3

What is the interquartile range of this data set? 2,5,9,11,18,30,42,55,58,73,81

Answers

Answer:

I think it's 49 I'm sry if I'm wrong hope you luck

Step-by-step explanation:

Answer: 49

Step-by-step explanation: Apex said so

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.6 sine (3520 pi t). What is the frequency of the tuning fork?

Answers

Answer:

The frequency of the tuning fork is 1760 Hz.

Step-by-step explanation:

Suppose we have a sine function in the following format:

[tex]y = A\sin{Bx + C}[/tex]

The period is:

[tex]T = \frac{2\pi}{B}{/tex]

The frequency, in Hz, is:

[tex]F = \frac{1}{T}[/tex]

In this question:

[tex]d = 0.6\sin{3520\pi t}[/tex]

So

[tex]B = 3520\pi, T = \frac{2\pi}{3520} = \frac{2}{3520}, F = \frac{1}{T} = \frac{1}{\frac{2}{3520}} = \frac{3520}{2} = 1760[/tex]

The frequency of the tuning fork is 1760 Hz.

Answer:

its C. 1760 Hz

on edge2020

The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.Private Colleges 52.8 30.6 43.2 45.8 45.0 37.8 33.3 50.5 44.0 42.0 Public Colleges 20.3 22.8 22.0 25.8 28.2 18.5 15.6 25.6 24.1 14.4 28.5 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.
S1 =
S2 =
b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place.
Interpret this value in terms of the annual cost of attending private and public colleges.$
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges.

Answers

Answer:

Step-by-step explanation:

a) For private colleges,

Mean = (52.8 + 30.6 + 43.2 + 45.8 + 45.0 + 37.8 + 33.3 + 50.5 + 44.0 + 42.0)/10 = 42.5

x1 = 42.5 × 1000 = 42500

Standard deviation = √(summation(x - mean)²/n

n = 10

Summation(x - mean)² = (52.8 - 42.5)^2 + (30.6 - 42.5)^2 + (43.2 - 42.5)^2 + (45.8 - 42.5)^2 + (45.0 - 52.5)^2 + (37.8 - 42.5)^2 + (33.3 - 42.5)^2 + (50.5 - 42.5)^2 + (44.0 - 42.5)^2 + (42.0 - 52.5)^2 = 598.56

standard deviation = √(598.56/10 = 7.74

s1 = 7.74 × 1000 = 7740

For public colleges,

Mean = (20.3 + 22.8 + 22.0 + 25.8 + 28.2 + 18.5 + 15.6 + 25.6 + 24.1 + 14.4 28.5 + 21.8)/12 = 22.3

x2 = 22.3 × 1000 = 22300

n2 = 12

Summation(x - mean)² = (20.3 - 22.3)^2 + (22.8 - 22.3)^2 + (22 - 22.3)^2 + (25.8 - 22.3)^2 + (28.2 - 22.3)^2 + (18.5 - 22.3)^2 + (15.6 - 22.3)^2 + (25.6 - 22.3)^2 + (24.1 - 22.3)^2 + (14.4 - 22.3)^2 + (28.5 - 22.3)^2 + (21.8 - 22.3)^2 = 225.96

standard deviation = √(225.96/12 = 4.34

s2 = 4.34 × 1000 = 4340

b) The point estimate is the difference between the sample means

Point estimate = 42500 - 22300 = 20200

The best guess for the difference in population mean annual cost of attending private and public colleges is $20200. The range of the value is determined by the margin of error.

c) Confidence interval = point estimate ± margin of error

Margin of error = z√(s²/n1 + s2²/n2)

Where z is the test score for 95% confidence level from the t distribution table. To find the test score, we would first find degree of freedom, df

df = (n1 - 1) + (n2 - 1) = (10 - 1) + (12 - 1) = 20

From the t distribution table,

z = 2.086

Margin of error = 2.086√(7.74²/10 + 4.34²/12) = 4.84

4.84 × 1000 = 4840

Confidence interval = 20200 ± 4840

The number of bacteria, B(h), in a certain population increases according to the following
function, where time, h, is measured in hours:
B(h) = 1425 e ^0.15h
How many hours will it take for the bacteria to reach 3300?
Round your answer to the nearest tenth, and do not round any intermediate
computations.


Please helpppp!!!

Answers

Answer:

It will take 5.6 hours to get the given population (3300) of the bacteria.

Step-by-step explanation:

A function that defines the population increase of a bacteria is,

B(h) = [tex]1425e^{0.15h}[/tex]

where h = duration or number of hours for bacterial growth

B(h) = Final population

If the final bacterial population is 3300,

3300 = [tex]1425e^{0.15h}[/tex]

By taking log on both the sides of the equation,

ln(3300) = [tex]ln(1425e^{0.15h})[/tex]

8.10168 = ln(1425) + [tex]ln(e^{0.15h})[/tex]

8.10168 = 7.261927 + 0.15h

h = [tex]\frac{8.10168-7.261927}{0.15}[/tex]

h = 5.5983

h ≈ 5.6 hours

Therefore, it will take 5.6 hours to get the given population (3300) of the bacteria.

Please answer this correctly

Answers

Answer:

9/49

Step-by-step explanation:

The probability of landing on an even number is 3/7.

Because there are only 3 numbers even out of 7 total numbers.

[tex]3/7 \times 3/7[/tex]

[tex]= 9/49[/tex]

Consider a normal population with the mean of 40 and standard deviation of 10. A random sample of was selected: 39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0. What is the bias of this the estimated mean for this sample

Answers

Answer:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X= 38.91[/tex]

And we can find the bias with this formula:

[tex] Bias= \bar X -\mu[/tex]

And replacing we got:

[tex] Bias = 38.91 -40 = -1.09[/tex]

Step-by-step explanation:

For this problem we know that the random variable of interest follows this distribution:

[tex]X \sim N(\mu =40, \sigma= 10)[/tex]

And we have the following random sample given:

39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0

And we can calculate the sample mean with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X= 38.91[/tex]

And we can find the bias with this formula:

[tex] Bias= \bar X -\mu[/tex]

And replacing we got:

[tex] Bias = 38.91 -40 = -1.09[/tex]

The prize in a raffle is a flat-screen TV valued at $350, and 1,000 tickets are sold for a dollar each. Let’s find the expected value if you buy 1 ticket. Find the expected value. Round your answer to two decimal places. Remember a gain would be posit

Answers

Answer:

the expected value EV = −$0.65

Step-by-step explanation:

Expected value EV = expected gain - expected loss

Given;

Cost of a ticket L = $1

Probability of losing the ticket P(L)= 999/1000 = 0.999

Cost of a flat screen TV = $350

Expected gain G = $350 - $1 = $349

Probability of winning the TV P(G) = 1/1000 = 0.001

EV = G × P(G) - L × P(L)

Substituting the values;

EV = $349 × 0.001 - $1 × 0.999

EV = −$0.65

the expected value EV = −$0.65

Please help me!!!!!!!!

Answers

Step-by-step explanation:

might be option c is a correct answer of your given question

Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by commas. isn't the answer just ±4?

Answers

Answer:

0, 4, -4 and they may want you to mention formally all the kt multiples of [tex]\pi[/tex].

Step-by-step explanation:

Let's do the second derivative of the function: [tex]y(t)=sin(k\,t)[/tex]

[tex]y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)[/tex]

So now we want:

[tex]y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\[/tex]

Then we have to include the zeros of the binomial ([tex]16-k^2[/tex]) which as you say are +4 and -4, and also the zeros of [tex]sin(kt)[/tex], which include all those values of

[tex]kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.[/tex]

So an extra one that they may want you to include is k = 0

How long will it take 3800 to grow into 5700 if it’s invested at 6% interest compounded continuously?

Answers

Answer:

1234567891234567890

Answer: 25 years

Step-by-step explanation:

t = I / Pr

t = 5700 / ( 3800 × 0.06 ) = 25

t = 25 years

Emily and George had a farm with a new barn.
True
False

Answers

Answer:

true

Step-by-step explanation:

it is so because they are brother and sister

And in the chapter there is that they had farm with a new barn

if in your book lesson there is that they had no farm with a new barn then there will be false

Now did you understood?

Answer:

True

Step-by-step explanation:

About 16.6% of Americans can speak Spanish. We obtain a random sample of seventy-five Americans and determine the proportion in the sample who speak Spanish. Find the probability that 25% or more in the sample speak Spanish.

Answers

Answer:

The probability that 25% or more in the sample speak Spanish is 76%.

Step-by-step explanation:

Sample of 75 Americans

If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.

The proportion of those who do not speak Spanish is 18 (24% of 75)

Therefore, the proportion of those who speak Spanish is 57 (75 - 19)

This implies that 57/75 x 100 = 76% of the sample speak Spanish.

This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.

Probability is the chance that an event may occur from many other events that could have occurred.  It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.

a bag contains 6 cherry 3 orange and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability of all lemons

Answers

Answer:

0.181818

Step-by-step explanation:

There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818

John multiplied 400,000 by 7,800 on his calculator. He got the result shown on his calculator display. What is this number in standard form? A calculator screen that shows 3 point 1 2 E 9. A 0.00000000312 B 0.000000312 C 312,000,000 D 3,120,000,000

Answers

Answer:

D

Step-by-step explanation:

jtrsytexjgfcgvhjbkjnhgfdsasdfghjhgrertyu

Answer:

Correct answer is D

Step-by-step explanation:

In a random sample of 964 young adults aged 18-29, it was found that 196 of them were married. Construct a 99% confidence interval for the proportion of married young adults aged 18-29.

Answers

Answer:

99% confidence interval for the proportion of married young adults aged 18-29.

(0.1779 , 0.2287)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 964

Given data a random sample of 964 young adults aged 18-29, it was found that 196 of them were married

sample proportion

                           [tex]p^{-} = \frac{196}{964} = 0.2033[/tex]

Step(ii):-

99% confidence interval for the proportion of married young adults aged 18-29.

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} } ,p^{-} +Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} })[/tex]

[tex](0.2033 -1.96 \sqrt{\frac{0.2033(1-0.2033 ) }{964} } ,0.2033 +1.96\sqrt{\frac{0.2033(1-0.2033 ) }{964} })[/tex]

(0.2033 -  0.02540 , 0.2033 +0.02540)

(0.1779 , 0.2287)

Conclusion:-

99% confidence interval for the proportion of married young adults aged 18-29.

(0.1779 , 0.2287)

(1 point) A vendor sells ice cream from a cart on the boardwalk. He offers vanilla, chocolate, strawberry, blueberry, and pistachio ice cream, served on either a waffle, sugar, or plain cone. How many different single-scoop ice-cream cones can you buy from this vendor

Answers

Answer:

six single scoops icecream cones

What is PI times 4? HELP ASAP

Answers

12.5663706144 is the answer

Answer:

12.566370614359172953850573533118

Step-by-step explanation:

Find the value of x for which
A.31
B.43
C.121
D.47

Answers

Answer:

The value of x is 31°

Step-by-step explanation:

As we can see, the two angles at the bottom of the shape are base angles. These angles both form right angles which means they both have a measurement of 90°. Knowing this information, we can set up an equation to solve for x.

47 + (x + 12) = 90

47 + x + 12 = 90

Add 12 to 47.

59 + x = 90

Subtract 59 on both sides of the equation.

x = 31

The value of x is equal to 31.

Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2

Answers

Answer:

correct answer is 456 sq units.

Step-by-step explanation:

Let us have a look at the formula for Surface Area of a prism:

[tex]A =p \times h+2 \times B[/tex]

Where p is the perimeter of base

h is the height of prism

and B is the base area of prism.

Given that:

h = 7.5 units

Hypotenuse of prism's base = 20 units

One of the Other sides = 12  units

Pythagorean theorem can be used to find the 3rd side of right angled base.

Square of hypotenuse = Sum of squares of other two sides

[tex]20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units[/tex]

Area of base = area of right angled triangle:

[tex]B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units[/tex]

Perimeter [tex]\times[/tex] height = (12+20+16) [tex]\times[/tex] 7.5 = (48) [tex]\times[/tex] 7.5 = 360 sq units

Now putting the values in formula:

Surface area, A = 360+96 = 456 sq units

So, correct answer is 456 sq units.

Example of a 3rd degree polynomial in standard form?

Answers

Answer:

4x^3 + 2x^2 +8x -9

Step-by-step explanation:

A third degree polynomial is a  is a polynomial whose highest power of x is to the power of three.  Standard form is

Ax^3 + Bx^2 + Cx + D where A is non zero

An example would be

4x^3 + 2x^2 +8x -9

what is Divide −240 by 8

Answers

Answer:

-30

Explanation:

1. A negative divided by a positive = a negative

2. 8•-30=-240

I hope this helps you!!

The division -240 by 8 gives the quotient is -30.

What is Division?

The division is one of the four introductory fine operations, the other three being addition, deduction, and addition. In simple words, division can be defined as the splitting of a large group into lower groups similar that every group will have an equal number of particulars. It's an operation used for equal grouping and equal sharing in calculation.

We have to divide -240 by 8.

So, the division is

                              8 | -240 | 30

                                     24

                                    ____

                                      00

Thus, the quotient is -30.

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