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2 years ago

The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by

Mathematics

2 answers:

Firdavs [7]2 years ago

3 0

Answer:

(k-h)(x) = 4x - 8

Step-by-step explanation:

We know Profit = Revenue - Cost

Basically we gotta subtract cost function from revenue function and get the profit function.

The cost function is h(x) = 5x + 6

The revenue function is k(x) = 9x - 2

Hence, Profit is:

(k-h)(x) = (9x - 2) - (5x + 6)

(k-h)(x) = 9x -2 - 5x - 6

(k-h)(x) = 4x - 8

goldenfox [79]2 years ago

3 0

Answer:

Step-by-step explanation:

The complete question is

The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?

A. 14x – 8

B. 14x + 4

C. 4x – 8

D. 4x + 4

The expresison that represents the profit is $(k-h)(x)$ . Which means the profit is the difference between the revenue function and the cost functions, that is

$(k-h)(x)=k(x)-h(x)=9x-2-(5x+6)=9x-2-5x-6=4x-8$

Therefore, the expression that represents profit is 4x-8, whcih is choice C.

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The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the

Harman [31]

THE QUESTION IS NOT PROPERLY WRITTEN

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard. If t1 is the time (in seconds) it takes for the object to strike the water, then t1 obeys the equation s = 16t1², where s is the distance (in feet) Solving for t1, we have t1 = √s/4. Let t2 be the time it takes for the sound of the impact to reach your ears. Since sound waves travel at a speed of approximately 1100 feet per second, the time to travel the distance s is t2 = s/1100. Now t1 +t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation; Total elapsed time √s/4 + s/1100.

Find the distance to the water’s surface if the total time elapsed from dropping a rock to hearing it hit water is 4 seconds.

Answer:

229.94 feet

Step-by-step explanation:

Given

t1 = √s/4

t2 = s/1100

From the question, we understand that

t1 + t2 = 4 seconds

Let y = √s

So,

t1 + t2 = 4 becomes

√s/4 + s/1100 = 4

y/4 + y²/1100 = 4 ------ Solve the fractions

(275y + y²)/1100 = 4

275y + y² = 4 * 1100

275y + y² = 4400 ------- Rearrange

y² + 275y - 4400 = 0 (Quadratic Equation)

The standard form of a quadratic equation is ax² + bx + c = 0

Where x =

frac{-b+-\sqrt{bx^{2} - 4ac } }{2a}

Here a = 1, b = 275 and c = -4400

So,

y = (-275+- √(275² - 4*1*-4400))/2

y = (-275+- √75625 + 17600))/2

y = (-275+- √(93225))/2

y = (-275 +- 305.328)/2

y = (-275 + 305.328)/2 or (-275-305.328)/2

y = 30.328/2 or -580.328/2

y = 15.164 or -290.164 -------Negative is not applicable

So, y = 15.164

But y = √s

So, s = y²

S = 15.164²

s = 229.94 ft

6 0

2 years ago

If a plant grows 1/4 cm every day for 21 days, what is the total amount of growth?

Naddika [18.5K]

I think it’s 5.25 cm but you might want to double check.

5 0

2 years ago

Read 2 more answers

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

Firdavs [7]

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

7 0

2 years ago

A certain article indicates that in a sample of 1,000 dog owners, 610 said that they take more pictures of their dog than of the

lbvjy [14]

Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

Step-by-step explanation:

(a)

Let X = number of dog owners who take more pictures of their dog than of their significant others or friends.

Given:

X = 610

n = 1000

Confidence level = 90%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{610}{1000}=0.61$

The critical value of z for a 90% confidence level is:

$z_{\alpha/2}=z_{0.10/2}=z_[0.05}=1.645$

Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)$

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

Interpretation:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

(b)

Let X = number of dog owners who are more likely to complain to their dog than to a friend.

Given:

X = 440

n = 1000

Confidence level = 95%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{440}{1000}=0.44$

The critical value of z for a 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)$

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend is (0.42, 0.46).

Interpretation:

There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

The confidence level
Sample size
Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of z in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

4 0

1 year ago

The Bakhshali Manuscript shows that another method for calculating nonperfect squares was being used in India by 400 CE. Use thi

vovikov84 [41]

The nearest perfect square that is less than 22 is 16, whose square root is 4.

Add the square root from step 1 to 3/4 to get 4.75.

Calculate the quantity one-half times the square of divided by the value found in step 2, or 4.75. (1/2 * (3/4)^2) ÷ 4.75 = 0.06.

Subtract the value found in step 3 from the value found in step 2, or 4.75.
The approximate value of √22 is 4.69.

7 0

2 years ago

Read 2 more answers