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Nina [5.8K]
2 years ago
15

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) a

nd evaluating the function at the right-hand endpoints of the subintervals. (See Example 1.)
f(x) = 9 − x2 from x = 1 to x = 3; 4 subintervals
Mathematics
1 answer:
RideAnS [48]2 years ago
5 0

Split up [1, 3] into 4 subintervals:

[1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]

each with length (3 - 1)/2 = 1/2.

The right endpoints r_i are {3/2, 2, 5/2, 3}, which we can index by the sequence

r_i=1+\dfrac i2

with 1\le i\le4.

Evaluating the function at the right endpoints gives the sampling points f(r_i), {27/4, 5, 11/4, 0}.

Then the area is approximated by

\displaystyle\int_1^3f(x)\,\mathrm dx\approx\frac12\sum_{i=1}^4f(r_i)=\frac12\left(\frac{27}4+5+\frac{11}4+0\right)=\boxed{\frac{29}4}

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The mean finish time for a yearly amateur auto race was 186.32 minutes with a standard deviation of 0.305 minute. The winning​ c
uranmaximum [27]

Complete Question

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

Find their respective z-scores.

 Who had the more convincing victory?

A. Roger​ had a more convincing victory because of a higher z-score.

B. Karen a more convincing victory because of a higher z-score.

C. Roger had a more convincing victory, because of a lower z-score.

D. Karen a more convincing victory because of a lower z-score.

Answer:

The correct option is  D

Step-by-step explanation:

From the question we are told that

  The mean of the current year  is  \mu_c =  186.32 \  minutes

   The standard deviation is  \sigma_c  =  0.305 \  minutes

   The time taken by  the winning car for the current year  is  x =  185.85 \ minutes

  The mean of the previous  year  is  \mu_p =  110.7 \  minutes

   The standard deviation the previous  year  is  \sigma_p  = 0.115  \  minutes

 The time taken by  the winning car for the previous year  is  y =   110.48 \ minutes    

Generally the z-score for current year is mathematically evaluated as

     z_c  =  \frac{x- \mu_c}{\sigma_c }

=>     z_c  =  \frac{ 185.85- 186.32}{0.305 }

=> z_c  = -1.536

Generally the z-score for previous year is mathematically evaluated as

     z_p  =  \frac{y- \mu_p}{\sigma_p }

=>     z_p  =  \frac{ 110.48-110.7}{0.115  }

=> z_p  = -1.913

From the value obtained we see that  z_p  <  z_c , Hence  Karen had a more convincing victory because of the lower z -score.

5 0
2 years ago
Drake knows that the ratio of eggs to cups of milk in his favorite pancake recipe is 3:5. He finds four pancake recipes for larg
ruslelena [56]

Answer:

Ratios are proportional when the numbers in the ratio are multiply or divide by the same number. Ex. 3:5 = 6:10 = 12:20 = 9:15 (cross multiply the fractions and the results are the same 3/5 = 6/10)

Step-by-step explanation:

6 0
2 years ago
What is the point slope and slope intercept form of 6,1 and 5,4
Keith_Richards [23]
M= -3
b= 19

y= -3x +19 

please crown me brainliest

5 0
3 years ago
Find two consecutive integers whose product is 24 more than three times the first integer
gregori [183]
X= first integer
x+1= second consecutive integer

Product means multiply, so we'll multiply x by x+1. More than means to add and 3 times is multiplication.

x(x + 1)= 3x + 24
use distributive property to multiply x by everything in parentheses
(x*x) + (x*1)= 3x + 24
x^2 + x= 3x + 24
subtract 3x from both sides
x^2 - 2x= 24
subtract 24 from both sides
x^2 - 2x - 24= 0
factor the expression
(x-6)(x+4)= 0
x-6=0
x=6

x+4=0
x=-4

If x= 6 is the first integer, x+1= 7 is the second integer

If x= -4 is the first integer, x+1= -3 is the second integer


Hope this helps! :)
7 0
3 years ago
Question 1: Which equation shows p(x)=x^6−1 factored completely over the integers? (Hint: You will need to use more than one met
kodGreya [7K]

Answer:

Question #1:  Option C, (x - 1)(x^2 + x + 1)(x + 1)(x^2 - x + 1)

Question #2:  Option C, 8x^3−56x^2+12x−84

Step-by-step explanation:

Question #1

<u>Step 1:  Factor</u>

p(x) = x^6 - 1

<em>p(x) = (x + 1)(x - 1)(x^2 + x + 1)(x^2 - x + 1)</em>

<em />

Answer:  Option C, (x - 1)(x^2 + x + 1)(x + 1)(x^2 - x + 1)

Question #2

<u>Step 1:  Expand</u>

p(x) = 4(x - 7)(2x^2 + 3)

p(x) = (4x - 28)(2x^2 + 3)

p(x) = 8x^3 + 12x - 56x^2 - 84

<em>p(x) = 8x^3 - 56x^2 + 12x - 84</em>

<em />

Answer:  Option C, 8x^3−56x^2+12x−84

8 0
3 years ago
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