Resuelve los problemas de una bodega que exporta tomates al extranjero

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

Inessa [12570]

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

Step-by-step explanation:

Based on the provided information, we have

Sample size: n= 15

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

Sample standard deviation: s= $20

Since the population standard deviation is not known, we utilize a t-test.

For a significance level of 95% confidence: $\alpha=1-0.95=0.05$

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

The required 95% confidence interval yields:-

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

Thus, the sought-after 95% confidence interval for the mean amount spent by credit card customers during their initial visit to the new store in the mall, assuming normal distribution of the spending amounts, is:

$\$50\pm\$11.08$

5 0

2 months ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Inessa [12570]

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume ( $V$ ), measured in cubic centimeters, and surface area ( $A_{s}$ ), measured in square centimeters, for a box featuring a square base:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - The length of the base's side, in centimeters.

$h$ - The height of the box, in centimeters.

Using (2), we isolate $h$ in the formula:

$h = \frac{V}{l^{2}}$

Then, we substitute into (1) and simplify the outcome:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Next, we calculate the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find that the critical value for the base's side length is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Subsequently, we assess this outcome using the second derivative's expression:

$V'' = -600$

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The highest achievable volume for the box is 2000000 cubic meters.

4 0

2 months ago

A circle is centered at the point (-7, -1) and passes through the point (8, 7).The radius of the circle is____ units. The point

AnnZ [12381]

Part 1) The radius of the circle is r=17 units. Part 2) The points (-15,14) and (-15,-16) are situated on this circle. Step-by-step explanation: Step 1 Find the radius of the circle. We know that the distance from the center of the circle to any point on its circumference equals the radius of the circle. The formula to determine the distance between two points is equal to......we have (-7, -1) and (8, 7) substitute... Step 2 Determine the y-coordinate of point (-15,y). The standard form of the circle's equation is given by... where (h,k) represents the center, and r is the radius. Replace the values, substituting x=-15 in the equation... square root both sides... ultimately, we find two solutions: point (-15,14) and point (-15,-16) refer to the attached figure for a clearer understanding of the problem.

8 0

1 month ago

"There are 3 teams of 18 employees working today. Company policy says that we need to have 1 supervisor for every 8 employees on

tester [12383]

They require six supervisors.

8 0

3 months ago

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