Let f be a continuous function on the closed
interval [0, 2] . If 2 (less than ir equal to) f(x) (less than or equal to) 4, then the greatest
possible value of (integral from 0 to 2)f(x)dx is

a. 0
b. 2
c. 4
d. 8
e. 16

Let F Be A Continuous Function On The Closedinterval [0, 2] . If 2 (less Than Ir Equal To) F(x) (less

Answers

Answer 1

Answer:

D) 8

Step-by-step explanation:

We are given a continuous function f on the closed interval [0, 2].

Where:

[tex]2\leq f(x)\leq 4[/tex]

And we want to find the greatest possible value of:

[tex]\displaystyle \int_0^2f(x)\,d x[/tex]

The range restriction tells us that even if f(x) = 2 for all x in the interval [0, 2], the smallest area possible will be 4, since that is the area of the rectangle.

Then in that case, the maximum possible value of the integral must be 8. f(x) cannot exceed 4, and the length of the interval is two units. Thus, the greatest possible value of the integral is 8. This will only occur if f(x) is a horizontal line at y = 4 from x = 0 to x = 2.


Related Questions

A line goes through the points (−7,−8) and (7,8). Find its slope.

Answers

Answer:slope = "rise over run"  (the change in y coordinates divided by the change in x coordinates) =

(8--7)/(3-7) = 15/-4 = -15/4

Step-by-step explanation: have a nice day

frank has a board that is 5/8 yards long he cuts off a piece that is 3/5 the length of the board how long is the piece of the board frank cutt off?​

Answers

Answer:

Step-by-step explanation:

If the board is 5/8 of a yard, then it is 5/8 of 36 inches (a yard is 36 inches).

5/8 * 36 = 22.5 inches.

Frank now cut's 3/5 of the length of the board. So he is going to cut off 3/5 of 22.5 inches.

(3/5) * 22.5 = 67.5 / 5 = 13.5 inches.

You don't specify what the units should be. I translate this into yards, but I think if you want something else, leave a comment.

13.5 /36 = 0.375 = 3/8 of a yard.

Connie is packing for a trip. She has 17 pairs of jeans. If she has room to pack 6 pairs how many ways can she choose which jeans to take

Answers

Answer:12,376

Step-by-step explanation:

Given

Connie has 17 Pairs of jeans

She has to choose 6 pairs out of 17

We know, no of ways to pick r items out of n items is [tex]^nC_r[/tex]

[tex]\therefore \text{No of ways is =}^{17}C_6\\\\\Rightarrow \dfrac{17!}{(17-6)!6!}=12,376\ \text{ways}[/tex]

Mrs. Spina bought 4 boxes of 8 pork chops. She set aside 12 and separated the rest into packs of4 to freeze. How many packs of chops did Mrs. Spina freeze

Answers

Answer:

5

Step-by-step explanation:

she brought 4 boxes of 8 therefore

4 × 8 = 32 she brought 32 pork chop

she put 12 aside

32- 12= 20 and pack the remaining 20 into pack of 4, 20÷4 =5.

therefore she had 5 freeze pack of pork chops

brainliest is appreciated

The length of a rectangle is twice its width.
If the perimeter of the rectangle is 60 m, find its length and width.

Answers

Answer:

120 m

Step-by-step explanation:

.

Answer:

length = 20m

width = 10m

Step-by-step explanation:

perimeter = 2 (length + width)

length = 2 * width = 2w

perimeter = 2 (2w +w)

perimeter = 2(3w)

60m = 6w

(divide both sides by 6)

60/6 = w

width = 10m

length = 2w

so length = 2 * 10 = 20m

34. Find each of the following probabilities when n indepen- dent Bernoulli trials are carried out with probability of success p. a) the probability of no successes b) the probability of at least one success c) the probability of at most one success d) the probability of at least two successes

Answers

Answer:

A.) (1 - p)^n

B.) 1 - (1 - p)^n

C.) (1 - p)^n + np*(1-p)^(n-1)

D.) 1 - (1 - p)^n - np*(1-p)^(n-1)

Step-by-step explanation:

General form of a binomial probability :

P(x = x) = nCx * p^x * q^(n-x)

q = 1 - p ; n = number of trials ; x = number of successes ; p = probability of success

A.) probability of no successes ;

P(x = 0) = nC0 * p^0 * (1 - p)^(n-0)

P(x = 0) = 1 * 1 * (1 - p)^n

P(x = 0) = (1 - p)^n

Probability of atleast one success = 1 - P(no success)

P(x ≥ 1) = 1 - P(x = 0)

P(x = 0) = (1 - p)^n

P(x ≥ 1) = 1 - P(x = 0) = 1 - (1 - p)^n

Probability of at most one success

P(x ≤ 1) = p(x = 0) + p(x = 1)

P(x = 0) = (1 - p)^n

P(x = 1) = nC1 * p^1 * (1 - p)^(n-1)

P(x = 1) = n * p * (1 - p)^(n-1) = np*(1-p)^(n-1)

P(x ≤ 1) = (1 - p)^n + np*(1-p)^(n-1)

Probability of atleast two successes:

(1 - probability of at most 2 successes)

P(x ≥ 2) = 1 - P(x ≤ 1)

P(x ≥ 2) = 1 - (p(x = 0) + p(x = 1))

P(x ≥ 2) = 1 - p(x = 0) - p(x = 1))

P(x ≥ 2) = 1 - (1 - p)^n - np*(1-p)^(n-1)

A company's sales in Seattle were $330,000 in 2012, while their sales in Portland were $235,000 for the same year. Complete the following statements: a. Seattle's sales were % larger than Portland's. b. Portland sales were % smaller than Seattle's. c. Portland sales were % of Seattle's. Give answers accurate to at least one decimal place.

Answers

Answer:

A) Seattle's sales were 40.42% larger than Portland's.

B) Portland sales were 28.79% smaller than Seattle's.

C)  Portland sales were 71.21% of Seattle's.

Step-by-step explanation:

Since a company's sales in Seattle were $ 330,000 in 2012, while their sales in Portland were $ 235,000 for the same year, the following calculations must be performed to complete the sentences:

A)

235,000 = 100

330,000 = X

330,000 x 100 / 235,000 = X

33,000,000 / 235,000 = X

140.42 = X

Seattle's sales were 40.42% larger than Portland's.

B)

330,000 = 100

235,000 = X

235,000 x 100 / 330,000 = X

23,500,000 / 330,000 = X

71.21 = X

100 - 71.21 = 28.79

Portland sales were 28.79% smaller than Seattle's.

C)

330,000 = 100

235,000 = X

235,000 x 100 / 330,000 = X

23,500,000 / 330,000 = X

71.21 = X

Portland sales were 71.21% of Seattle's.

what is the mean,median,mode and range or the data set 4, 7, 3, 7, 7, 12,

Answers

Answer:

the mean is6.7 the mode is 7 and the range is 9

Step-by-step explanation:

Antoinette buys 6 pounds of
tangerines. She pays with a $10 bill.
How much did she spend?

Answers

Answer:

10 = 6 pounds

1.67 = 1 pound

Step-by-step explanation:

Answer:

$1.67

Step-by-step explanation:

Hope its correct have a great day!

the perimeter of a rectangle is 18 inches. the length is 5 inches. find the width of the rectangle.

i will give brainliest <3

Answers

Answer:

4 inches

Step-by-step explanation:

33 is less than or equal to x


Question options:

33 < x

33 > x

33 ≥ x

33 ≤ x

Please explain please also, thanks! :)

Answers

Answer:

33 ≤ x

Step-by-step explanation:

≤  means less than or equal to, you can see < showing less than, and the _ meaning equal to.

Answer is the last one
33 ≤ x

33< means 33 is less than
And the _ underneath means equal to

An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.19 kgf/cm2 for the modified mortar (m = 42) and y = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let m1 and m2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that ?1 = 1.6 and ?2 = 1.3, testH0: m1 ? m2 = 0versus Ha: m1 ? m2 > 0 at level 0.01.State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.)
z ?
z ?
Compute the test statistic value. (Round your answer to two decimal places.)
z =
State the conclusion in the problem context.
Reject H0. The data does not suggest that the difference in average tension bond strengths exceeds 0.
Fail to reject H0. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
Fail to reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
Reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
(b) Compute the probability of a type II error for the test of part (a) when m1 ? m2 = 1.(Round your answer to four decimal places.)
(c) Suppose the investigator decided to use a level 0.05 test and wished ? = 0.10 when m1 ? m2 = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.)
n =
(d) How would the analysis and conclusion of part (a) change if ?1 and ?2 were unknown but s1 = 1.6 and s2 = 1.3?
Since n = 32 is not a large sample, it would no longer be appropriate to use the large sample test. A small sample t procedure should be used, and the appropriate conclusion would follow.
Since n = 32 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow. Since n = 32 is a large sample, it would no longer be appropriate to use the large sample test. Any other test can be used, and the conclusions would stay the same.
Since n = 32 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same.

Answers

how can i send it to u


Trying to prepare a budget Grant has done research and found that he spends an average of $178 on his phone/internet/cable service, $203 on his electric bill, and
$320 on his health insurance premium. If he earns $3200 per month, estimate the amount of money he will have after paying these bills each month.

Answers

Answer:

$2,499

Step-by-step explanation:

3200 - (178 + 203 + 320)

3200 - 701

2499

Grant will have $2,499 after paying these bills each month

Answer:  2,499

Step-by-step explanation:  Subtract expenditures from earnings...

3,200-178-203-320=2,499

so he makes 3,200 and spends 701 each month leaving 2,499

What’s the least common factor of two and six

Answers

Answer:

6

Step-by-step explanation:

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Answer: 6

Explanation: least common multiple

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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What is the mean of the data set that is represented by this data plot?

Answers

Answer:

90

Step-by-step explanation:

Answer:

[tex]\huge\blue{90}[/tex]

90 is the mean of the data set that is represented by this data plot

The smith family took a 2-day road trip.on the second day,they drove 3/4 the distance they traveled on the first day. What is possible distance they could have traveled over the 2 days ? Is there more than one possible distance? Justify your response

Answers

Answer:

1 1/4

Step-by-step explanation:

use mixed number calcator!

The total distance traveled by the Smith family for 2 days is given by the equation A = ( 7/4 )d , where d is the distance traveled on first day

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The distance traveled by the Smith family on first day = d miles

The distance traveled by the Smith family on second day = ( 3/4 ) of the distance of first day

On simplifying the equation , we get

The distance traveled by the Smith family on second day = ( 3/4 ) d

And , the total distance traveled A = d + ( 3/4 )d

The total distance traveled A = ( 7/4 )d

The total distance traveled A = 1.75d

Hence , the equation is A = 1.75d

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ3

y=(x+1)^2+2

plot five points​

Answers

Answer:

(−3,6)

(−2,3)

(−1.2)

(0,3)

(1,6)

Step-by-step explanation:

Answer the following questions

Answers

Answer:

Question 1 : -8/3

Question 2  : 7.62 or unrounded 7.615773106.

Step-by-step explanation:

Question 1:

( 2 , 4 ) ( 5 , -4)

^      ^     ^     ^

x1    y1    x2  y2

Equation : y2 -y1 / x2 - x1

-4-4/5-2 = -8/3

Question 2 :

Equation : a^2 + b^2 = c^2

3^2 + 7^2 = c^2

3^2 = 9

7^2 = 49

9 + 49 = 58

Square root of 58 = 7.615773106.

Which is the better deal? *

5 gallons of gas for $15.70
11 gallons of gas for $42.00

Answers

Answer:

5 gallons of gas for 15.70

Step-by-step explanation:

15.70 divided by 5 is 3.14 while 42 divided by 11 is 3.8

The product of 8 and four more than a number
The algebraic expression is:

Answers

Answer:

8(n+4)

Step-by-step explanation:

I need this ASAP!
Solve:

Answers

Ok the answer would be x=11

The pool table has a height of 7ft. Side one is 18ft and side two is 17 ft. What is the area and perimeter?

Answers

Answer:  

area = 2,142

perimeter = 70

Step-by-step explanation:

area = length x width x height

a=18 x 17 x 7

perimeter = all sides added together and assuming it is a rectangle...

p=18 + 18 + 17 + 17

Need help please show ur work

Answers

Use distributive property
5(4x + 3) - 2x
20x + 15 - 2x
Simplify by liked terms
18x + 15
The solution is A

An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, one-third are cats. Three-fourths of the remaining animals are dogs. How many of the animals are rabbits?

Answers

Answer:

21

Step-by-step explanation:

126/3=42

126-42=84

84/4=21

63 are dogs

42 are cats

and 21 are rabbits

Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a
15% alcohol solution.
Which equation can Bruce use to determine how much of the 10% alcohol solution he should use?

Answers

Answer:

20 ml of 15% alcohol and 30 ml of 10% alcohol should be used to create a 12% alcohol solution.

Step-by-step explanation:

Since Bruce wants to make 50 ml of an alcohol solution with a 12% concentration, and he has a 10% alcohol solution and a 15% alcohol solution, to determine how much of the 10% alcohol solution he should make the following calculations:

0.9 x 15 + 0.1 x 10 = 14.5

0.7 x 15 + 0.3 x 10 = 13.5

0.5 x 15 + 0.5 x 10 = 12.5

0.4 x 15 + 0.6 x 10 = 12

50 x 0.4 = 20

Therefore, 20 ml of 15% alcohol and 30 ml of 10% alcohol should be used to create a 12% alcohol solution.

If $40 U.S. dollars are equivalent to 20.3765 British pounds then how many British pounds are equivalent to $1 U.S. dollar? Round your answer to the nearest thousandths.

Answers

50 cents and some extra hope this helps

Find the approximate length of the bolded arc.

Answers

Answer:

Step-by-step explanation:

the figure below is a net for a triangular prism (Help)

Answers

Answer:

368 in²

Step-by-step explanation:

Surface area of the triangular prism is the sum of the area of each net = 2(area of two triangle) + 2(area of two similar rectangles) + area of rectangle

= 2(½*bh) + 2(L*W) + (L*W)

Surface area = 2(½*5*7) + 2(15*8.6) + (15*5)

= 35 + 258 + 75

= 368 in²

what is the center of dilation ?

Answers

Answer:

A fixed point on a plane.

Step-by-step explanation:

It is the starting point from which we measure distances in a dilation.

A T is the center of dilation cuz

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Answers

Answer:

12

Step-by-step explanation:

a² + b² = c²

a² + 9² = 15²

a² + 81 = 225

a² = 225 - 81

a² = 144

[tex]\sqrt{a^2} =\sqrt{144}[/tex]

a = 12

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