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Gre4nikov [31]
3 years ago
5

Land's Bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the intern

et. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 11 sales receipts for mail-order sales results in a mean sale amount of $79.00 with a standard deviation of $18.25. A random sample of 18 sales receipts for internet sales results in a mean sale amount of $96.70 with a standard deviation of $20.25. Using this data, find the 98% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
Mathematics
1 answer:
nata0808 [166]3 years ago
3 0

Answer:

−35.713332 ; 0.313332

Step-by-step explanation:

Given that:

Sample size, n1 = 11

Sample mean, x1 = 79

Standard deviation, s1 = 18.25

Sample size, n2 = 18

Sample mean, x2 = 96.70

Standard deviation, s2 = 20.25

df = n1 + n2 - 2 ; 11 + 18 - 2 = 27

Tcritical = T0.01, 27 = 2.473

S = sqrt[(s1²/n1) + (s2²/n2)]

S = sqrt[(18.25^2 / 11) + (20.25^2 / 18)]

S = 7.284

(μ1 - μ2) = (x1 - x2) ± Tcritical * S

(μ1 - μ2) = (79 - 96.70) ± 2.473*7.284

(μ1 - μ2) = - 17.7 ± 18.013332

-17.7 - 18.013332 ; - 17.7 + 18.013332

−35.713332 ; 0.313332

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Find the interval in which f(x)=sinx−cosx is increasing or decreasing?
alisha [4.7K]

Answer:

There is no short answer.

Step-by-step explanation:

To find to intervals which f(x) increases or decreases, we first need to find it's derivative.

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The function is increasing when it's value is  > 0 and decreasing when it's value is < 0.

If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.

I hope this answer helps.

3 0
3 years ago
Layla, Eliana and Nature each carried 10 pound bag of soil into the backyard. After putting soil in the first flower bed, Layla'
Ivanshal [37]

Answer: 17.75 pounds

Step-by-step explanation:

After putting soil in the first flower bed, Layla's bag was ⅝ full. The pound of soil will be: = 5/8 × 10 = 6.25 pounds

Eliana's bag was ⅖ full. The pound of soil will be: = 2/5 × 10 = 4 pounds

Nature's bag was ¾ full. The pound of soil will be: = 3/4 × 10 = 30/4 = 7.5 pounds

The number of pounds of soil that they put in the first flower bed altogether will be:

= 6.25 + 4 + 7.5

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8 0
3 years ago
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
seropon [69]

Answer:

h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}

Step-by-step explanation:

1) The Fundamental Theorem of Calculus in its first part, shows us a reciprocal relationship between Derivatives and Integration

g(x)=\int_{a}^{x}f(t)dt \:\:a\leqslant x\leqslant b

2) In this case, we'll need to find the derivative applying the chain rule. As it follows:

h(x)=\int_{a}^{x^{2}}\sqrt{5+r^{3}}\therefore h'(x)=\frac{\mathrm{d} }{\mathrm{d} x}\left (\int_{a}^{x^{2}}\sqrt{5+r^{3}}\right )\\h'(x)=\sqrt{5+r^{3}}\\Chain\:Rule:\\F'(x)=f'(g(x))*g'(x)\\h'=\sqrt{5+r^{3}}\Rightarrow h'(x)=\frac{1}{2}*(r^{3}+5)^{-\frac{1}{2}}*(3r^{2}+0)\Rightarrow h'(x)=\frac{3r^{2}}{2\sqrt{r^3+5}}

3) To test it, just integrate:

\int \frac{3r^{2}}{2\sqrt{r^3+5}}dr=\sqrt{r^{3}+5}+C

5 0
3 years ago
If the area of a square is 25/36 the side length would be ____?
Zielflug [23.3K]
<h3>Answer:  5/6</h3>

Apply the square root to 25/36, which is the same as square rooting each piece of the fraction

sqrt(25) = 5

sqrt(36) = 6

Put another way, you can think of it in reverse:

(5/6)^2 = (5/6)*(5/6) = (5*5)/(6*6) = (5^2)/(6^2) = 25/36

6 0
3 years ago
Read 2 more answers
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