Given 8x-3y=-21, 3x+y=-10; Prove x=-3

Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 1960 − 70 p where n is the number

alexandr402 [8]

Answer:

$14

Step-by-step explanation:

The revenue from sales of fans is the product of the number of fans sold and the price at which they are sold:

R(p) = n·p = (1960-70p)p

R(p) = 70(28 -p)p

This equation describes a parabola that opens downward and has zeros at p=0 and p=28. The axis of symmetry is halfway between those zeros, at p=14. It goes through the vertex or point of maximum revenue.

The price for maximum revenue is p = 14 dollars.

7 0

2 years ago

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit

viva [34]

Answer: D) $\$50\pm\$11.08$

Step-by-step explanation:

As per given , we have

Sample size : n= 15

sample mean : $\overline{x}=\$50.50$

Sample standard deviation: s= $20

Since population standard deviation is unknown , so we use t-test.

Significance level for 95% confidence : $\alpha=1-0.95=0.05$

Critical t-value : $t_{n-1, \alpha/2}=t_{014,0.025}=2.145$ [Using students' t-value table]

Required 95% Confidence interval :-

$\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}\\\\ =\$50.50\pm(2.145)\dfrac{\$20}{\sqrt{15}}\\\\\approx \$50\pm\$11.08$

Hence, the required 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.:

$\$50\pm\$11.08$

5 0

2 years ago

Dingane has \$8.00$8.00dollar sign, 8, point, 00, and exactly 30\%30%30, percent of that money is from 555‑cent coins. How many

Ipatiy [6.2K]

<span>If Dingane has $8.00, and thirty percent of that money is from five cent coins, then 8 x 0.3 = $2.40 of Dingane's money is made of five cent coins. In this case the number of five cent coins is the number of cents divided by five: 240/5 = 48. Therefore, Dingane has forty-eight five-cent coins.</span>

6 0

2 years ago

Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

Pavel [41]

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)}$

$t = \frac{32 \pm 30.98}{2}$

$t_1 = \frac{32 + 30.98}{2}$

$t_1 = 31.49$

$t_2 = \frac{32 - 30.98}{2}$

$t_2 = 0.51$

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

4 0

2 years ago

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Thrifty Supply Store normally sells candy bars for $0.59. Today they are running a special 2 candy bars for $0.99. How much woul

yaroslaw [1]

At regular price the 10 candy bars would cost $5.90 (0.59×10=5.90). At the sale price the 10 candy bars cost $4.95 (0.99×5 = 4.95). So you would save $0.95 (as 5.90-4.95 =0.95).

7 0

2 years ago

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