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bulgar [2K]
3 years ago
9

The function f(x)=2x+1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of

the function at the right endpoint of the kth rectangle?

Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer:

  D.  5 +6k/n

Step-by-step explanation:

The width of the interval is (5 -2) = 3. The width of one of n parts of it will be ...

  3/n

Then the difference between the left end point of the interval and the value of  x at the right end of the k-th rectangle will be ...

  k·(3/n) = 3k/n

So, the value of x at that point is that difference added to the interval's left end:

  2 + 3k/n

The value of the function for this value of x is ...

  f(2 +3k/n) = 2(2 +3k/n) +1 = (4 +6k/n) +1

  = 5 +6k/n

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3 years ago
For a certain population of men, 8 percent carry a certain genetic trait. For a certain population of women, 0.5 percent carry t
slavikrds [6]

Answer:

C) 150 men and 100 women

D) 200 men and 2000 women

E) 1000 men and 1000 women

Step-by-step explanation:

Hello!

To compare the proportion of people that carry certain genetic trait in men and woman from a certain population two variables of study where determined:

X₁: Number of men that carry the genetic trait.

X₁~Bi(n₁;p₁)

X₂: Number of women that carry the genetic trait.

X₂~Bi(n₂;p₂)

The parameter of interest is the difference between the population proportion of men that carry the genetic trait and the population proportion of women that carry the genetic trait, symbolically: p₁-p₂

To be able to study the difference between the population proportions you have to apply the Central Limit Theorem to approximate the distribution of both sample proportions to normal.

<u><em>Reminder:</em></u>

Be a variable with binomial distribution X~Bi(n;p), if a sample of size n is taken from the population in the study. Then the distribution of the sample proportion tends to the normal distribution with mean p and variance (pq)/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

So for both populations in the study, the sample sizes should be

n₁ ≥ 30

n₂ ≥ 30

Also:

Both samples should be independent and include at least 10 successes and 10 failures.

Both populations should be at least 20 times bigger than the samples. (This last condition is to be assumed because without prior information about the populations is impossible to verify)

  • If everything checks out then (p'₁-p'₂)≈N(p₁-p₂; p(1/n₁+1/n₂))

<u>The options are:</u>

A) 30 men and 30 women

n₁ ≥ 30 and n₂ ≥ 30

Both samples are big enough and independent.

Population 1

Successes: x₁= n₁*p₁= 30*0.08= 2.4

Failures: y₁= n₁*q₁= 30*0.92= 27.6

Population 2

Successes: x₂= n₂*p₂= 30*0.5= 15

Failures: y₂= n₂*q₂= 30*0.5= 15

The second condition is not met.

B) 125 men and 20 women

n₁ ≥ 30 but n₂ < 30

Both samples are independent but n₂ is not big enough for the approximation.

C) 150 men and 100 women

n₁ ≥ 30 and n₂ ≥ 30

Both samples are big enough and independent.

Population 1

Successes: x₁= n₁*p₁= 150*0.08= 12

Failures: y₁= n₁*q₁= 150*0.92= 138

Population 2

Successes: x₂= n₂*p₂= 100*0.5= 50

Failures: y₂= n₂*q₂= 100*0.5= 50

All conditions are met, an approximation to normal is valid.

D) 200 men and 2000 women

n₁ ≥ 30 and n₂ ≥ 30

Both samples are big enough and independent.

Population 1

Successes: x₁= n₁*p₁= 200*0.08= 16

Failures: y₁= n₁*q₁= 200*0.92= 184

Population 2

Successes: x₂= n₂*p₂= 2000*0.5= 1000

Failures: y₂= n₂*q₂= 2000*0.5= 1000

All conditions are met, an approximation to normal is valid.

E) 1000 men and 1000 women

n₁ ≥ 30 and n₂ ≥ 30

Both samples are big enough and independent.

Population 1

Successes: x₁= n₁*p₁= 1000*0.08= 80

Failures: y₁= n₁*q₁= 1000*0.92= 920

Population 2

Successes: x₂= n₂*p₂= 1000*0.5= 500

Failures: y₂= n₂*q₂= 1000*0.5= 500

All conditions are met, an approximation to normal is valid.

I hope this helps!

6 0
3 years ago
A boat traveled 240 miles downstream and back. The trip downstream took 12 hours. The trip back took 24 hours. What is the speed
RoseWind [281]

Answer:

rate boat = 15 mph

rate current = 5 mph

explanation:

d = r * t

t = d/r

240 / (r_boat + current) = 12       Multiply both sides by r_boat + r_current.

240 = 12(r_boat + current)

240/ (r_boat - current) = 24       Multiply both sides by r_boat - r_current

240 = 24*(r_boat - current)    

Since the distances are the same in both equations, you can equate the right side of each.

12 (r_boat + current) = 24(r_boat - current)     Divide by 12

r_boat + current  = 2 (r_boat - current)             Remove the brackets.

r_boat  + current = 2*r_boat - 2* current          add 2 currents to both sides

r_boat  + 3currents = 2*r_boat                          Subtract r_boat both sides

3 currents = r_boat.

240 = 12*(r_boat + current.                               Divide by 12

20 = r_boat + current                                        Put 3 currents in for r_boat

20 = 3currents + 1 current                                Combine

20 = 4 currents                                                  Divide by 4

5 = current

The rate of the current = 5 miles / hour

3 currents = r_boat

3*5 = rate_boat

15 = rate of the boat

8 0
2 years ago
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