A development economist is studying income growth in a rural area of a developing country. The last census of the population of this area, several years earlier, showed that mean household annual income was 425 dollars, and the variance of household income was 2500 (dollarssquared). A current random sample of 100 households yields a sample mean income of $433.75. Assume that household annual incomes are approximately normally distributed, and that the population variance is known still to be 2500. Test the null hypothesis that population mean income has not increased ( H0 : "m"(greek letter) greater than equal to< 425 ) against the alternative hypothesis that it has increased ( HA :"m"(greek letter > 425 ), at a 1% level of significance.
What is the form of the rejection region?
a. Reject H0 if x < cv
b. Reject H0 if x > cv
c. Reject H0 if x < cv or if x > cv
d. Reject H0 if x = cv 3
What is the critical value?
a. 436.63
b. 433.75
c. 425
d. 437.88
What is the conclusion of the hypothesis test?
a. Accept H0
b. Reject H0 in favor of HA

Solution :

Let x = number of coach class tickets sold per day on $ 10 reduced price

y = number of the business class tickets sold per day on $ 50 reduced per price.

Number of the coach class tickets sold = 20 per day at a price of $ 250

Number of the business class tickets sold = 10 per day at a price of $ 750

Decrease in the price of coach class tickets by $ 10 increases the number of tickets sold by 4 per day

Decrease in the price of business class tickets by $ 50 increases the number of tickets sold by 2 per day.

Therefore, the coach price, p(x) = 250 - 10x

Business class price, p(y) = 750 - 50y

Coach tickets, q(x) = 2 + 4x

Business class tickets, q(y) = 6 + 2y  

Revenue R(x, y) = p(x) q(x) + q(y) q(y)

R(x, y) = (250-10x)(20+4x)+(750-50y)(6+2y)

R(x) = (250-10x)(0.4)+(20+4x)(-10)+0 = 0

1000-40x-200-40x=0

80x = 800

x = 10

R(y) = 0 + (750 - 50y)(0.2) + (6+2y)(-50) = 0

1500 - 100y+(-300-100y) = 0

200 y = 1200

y = 6

P(x) = 250 - 10(10) = $ 150

P(y) = 780-50(6) = $450

q(x) = 20 + 4(10) = 60

q(y) = 6 + 2(6) = 18

Maximum revenue = 150 x 60 + 450 x 18

                              = 9000 + 8100

                              = $ 17100

Answer:

9' - 1.29"

Step-by-step explanation:

Total rise = 5' - 2"

Total run = 7' - 6"

1' = 12" = 1 feet = 12 inches

5' = 5 * 12 = 60"

3' = 7 * 12 = 84"

Total rise = 60" + 72" = 62"

Total run = 84" + 6" = 90"

Length of stringer = hypotenus

Hypotenus = √(total rise² + total run²)

Hypotenus = √(62² + 90²)

Hypotenus = 109.28860"

Convwrting back to feet and inches

= 9' - 1.29"

Answer:

Step-by-step explanation:

What is 20 as a decimal? To write 20 as a decimal you have to divide numerator by the denominator of the fraction. 20 is not a fraction so it is a decimal already. And finally we have: 20 as a decimal equals 20

Answer:

6 Months where she borrowed less than 10,

and he borrowed the most books in August.

Step-by-step explanation:

Answer:

y = (4/7)x + 3

Step-by-step explanation:

rise = 7 - 3 = 4

run = 7 - 0 = 7

slope = rise/run = 4/7

y-intercept = 3

---------------------

Slope intercept form is

y = mx + b

m is the slope = 4/7

b is the y-intercept  = 3

the equation is

y = (4/7)x + 3

Answer:

Step-by-step explanation:

c

Answer:

Their present ages are:

Step-by-step explanation:

Given that:

To Find:

Let us assume:

After 12 years:

Finding their present ages:

According to the question.

⇒ 3x + 12 = 2(x + 12)

⇒ 3x + 12 = 2x + 24

⇒ 3x - 2x = 24 - 12

⇒ x = 12

Their present ages:

Both a and b lie in the second quadrant, which means

π/2 < a < π

π/2 < b < π

for which we have both cos(a) and cos(b) negative, while both sin(a) and sin(b) are positive. We're also given that

cos(a) = -2/3

csc(b) = 2   =>   sin(b) = 1/2

Now, recall the following identities:

• sin^2(x) + cos^2(x) = 1

• sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

• cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

• tan(x) = sin(x)/cos(x)

Now,

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

… = √(1 - cos^2(a)) (-√(1 - sin^2(b))) + cos(a) sin(b)

* * where we take the negative square root because we expect cos(b) < 0 * *

… = - √(1 - (-2/3)^2) √(1 - (1/2)^2) + (-2/3) (1/2)

… = - √(1 - 4/9) √(1 - 1/4) - (2/3) (1/2)

… = - √(5/9) √(3/4) - 1/3

… = - (√5/3) (√3/2) - 1/3

… = -√15/6 - 1/3

… = -(√15 + 2) / 6

From the above, we know sin(a) = √5/3 and cos(b) = -√3/2. Then

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

… = (-2/3) (-√3/2) - (√5/3) (1/2)

… = √3/3 - √5/6

… = (2√3 - √5) / 6

and so it follows that

tan(a + b) = sin(a + b) / cos(a + b)

… = (-(√15 + 2) / 6) / ((2√3 - √5) / 6)

… = - (√15 + 2) / (2√3 - √5)

… = - (√15 + 2) (2√3 + √5) / ((2√3 - √5) (2√3 + √5))

… = - (2√45 + 4√3 + √75 + 2√5) / (12 - 5)

… = - (6√5 + 4√3 + 5√3 + 2√5) / 7

… = - (8√5 + 9√3) / 7

Answer:

Step-by-step explanation:

120/6=20

Answer:

20cm

Step-by-step explanation:

120/6 = 20

Answer:

I give the crown

if you do

Step-by-step explanation:

Answer:

what does that mean?

Step-by-step explanation:

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

The marked angles are "alternate interior" angles, so are congruent.

  (x° +20°) = (4x° -10°)

  30 = 3x . . . . . . . . . . . . . . . divide by °, add 10-x

  10 = x . . . . . . divide by 3

Answer: 3 or 9/12

Step-by-step explanation:

3/4 to 0.75

0.75 * 4 = 3

Answer:

$33000

Step-by-step explanation:

Given data

Principal= ​$22,000

Rate= 6%

Time= 25 years

The interest to be paid is

Simple interest= PRT/100

Simple interest= 22000*6*25/100

Simple interest=3300000/100

Simple interest=$33000

Hence the total simple interest paid is $33000

Answer:

80%, 41/50, 0.83

Step-by-step explanation:

80% = 0.80

41/50 = 0.82

0.83 = 0.83

Answer:

-30

Hope this helps!

i can't see the photo.

9514 1404 393

Answer:

  1/2

Step-by-step explanation:

The base of the exponent tells us the common ratio of this geometric series is 1/2. The start value of n=7 tells us the first term in the series we're evaluating is ...

  a1 = 2(1/2)^(7-4) = 2·(1/2)^3 = 2/8 = 1/4

The formula for the infinite sum of a geometric series is ...

  S = a1(1/(1-r))

Filling in the values we know, this is ...

  S = (1/4)(1/(1 -1/2)) = (1/4)(2) = 1/2

The infinite sum is 1/2.

Answer: See explanation

Step-by-step explanation:

Interest = Principal × Rate × Time

Interest = $1500 × 5.6% × 4

= $1500 × 0.056 × 4

= $336

The total amount that will be paid will be:

= Principal + Interest

= $1500 + $336

= $1836

Answer:

-3x + 6

Step-by-step explanation:

(gof) = -(3x-2)+4

= -3x + 2 + 4

= -3x + 6

Answer:

D: {all reals}

R: {-5}

Step-by-step explanation:

Answer:

I think it could be 28 because 28 minis 5 is 23

Answer:

3

Step-by-step explanation:

We can use the Pythagorean thorem to solve this question

leg = [tex]\sqrt{hypotenuse^2 - leg^2} = \sqrt{(3\sqrt{5})^2 - 6^2} = \sqrt{45 -36} = \sqrt{9} = 3[/tex]

Answer:

C.

Step-by-step explanation:

Most people do not want personal information about sensitive topics revealed about themselves, so Topic A requires anonymity.  

With non-sensitive topics, people are usually comfortable with revealing their identity, so Topic B doesn't require anonymity.

Answer:

43.98

Step-by-step explanation:

i was doing a problem like that on my math paper as well

Answer:

f(x) = -7x + 1

Step-by-step explanation:

Slope intercept form is

y = mx + b

m is slope

b is y-intercept

--------------------------

y decreases by 7 for each increase of 1 in x

slope = -7

to find "b" plug in one of the points and m = -7

using point (3, -20)

y = mx + b

-20 = -7(3) + b

-20 = -21 + b

b = 1

The equation is

f(x) = -7x + 1

Answer:

18%

Step-by-step explanation:

Hope this helps :))

Answer:

the answer is 18%

hope this helps