A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost. (Let x represent the length of the sides of the square base and let y represent the height. Round your answers to two decimal places.) x

Answer:

d. normal if the population is normally distributed

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Sample size less than 30, so only will be normal if the population is normally distribution, and thus the correct answer is given by option d.

Answer:72 [tex]cm^{2}[/tex]

Solution 1:

Step 1: Find EF use Pythagorean theorem

[tex]EF^{2} = EB^{2} + BF^{2}[/tex]

[tex]EF^{2} = 6^{2} + 6^{2}[/tex]

EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm

Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72

Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD

The area of ABCD = 12x12 = 144

Thus, the area of EFGH = 144: 2 = 72:)

Have a nice day!

Answer:

Option C

Step-by-step explanation:

Suppose that we have a given proposition p

We define the complement as:

"NOT p" or ¬p

So, if p is:

the dog is red

the complement is

the dog is NOT red.

The principal rule to work with this is:

if p is true, then ¬p is false

if p is false, then ¬p is true.

Here the proposition is:

p = "When 100 engines are shipped, all of them are free of defects."

When this is this is true, ¬p must be false.

when this is false, ¬p must be true.

Let's analyze the given options, first the incorrect ones:

A: "At most one of the engines is defective."

here if we have for example, two defective engines, then this proposition and the original proposition are false.

B: " All of the engines are defective."

Here if there is one defective engine, then this is false, and also is the original proposition.

D: "None of the engines are defective"

When the original proposition is true "When 100 engines are shipped, all of them are free of defects.", this proposition is also true (because none of the engines are defective)

Finally, the corrrect one

C "At least one of the engines is defective"

When the original proposition is true, there are no defective engines, so this is false.

While, if this is true, there is at least one defective engine, so the original proposition is false.

Then this is the correct option:

¬p = "At least one of the engines is defective"

9514 1404 393

Answer:

  False

Step-by-step explanation:

f(-2) = (1/2)(-2) -3 = -1 -3 = -4

g(-2) = -2(-2) +2 = 4 +2 = 6

The function values are not the same at x=-2, so the graphs do not intersect there.

__

The graphs intersect at x=2.

Answer:

the total square footage = 194

1.88 x 194 = 364.72

Step-by-step explanation:

Area for triangle ends.

A = [tex]\frac{2.5 (8)}{2}[/tex]   (Times two, because there are two ends.)

Base of prism = 8 x 10 = 80

Sides of prism = 2(10 x 4.7 ) = 94  (What's the 2?  There's two of them)

Add all together : 10 + 10 + 80 + 94 = 194

1.88 x 194 = 364.72

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

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Answer:

  (c)

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]

Answer:

sorry i dont know this answer

Answer:

I belive it has no x intercepts

it looks weird, but it can be a function. the x-intercept and the y-intercept can also be found in the table above.

to draw a line that can represent a function with these point, we would need to cross y=0 multiple times, so it will have more then one x-intercept.

option A

key takeaway: just draw stuff you find complicated:)

Answer:

0.0158 = 1.58% probability that all of them are under 18.

Step-by-step explanation:

Probability of independent events:

If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]

The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.

This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]

If one person is selected from each city, what is the probability that all of them are under 18?

Since the three people are independent:

[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]

0.0158 = 1.58% probability that all of them are under 18.

Answer:

Nathan's because his sample was more random  

Step-by-step explanation:

Nathan's survey could be described as a Systematic random sampling technique whereby every 5th observation taken as a sample from the population. With these technique we have a more random observation than with.

Answer:

C

Step-by-step explanation:

Answer:

-  [tex]\frac{4}{\sqrt{29} }[/tex]

Step-by-step explanation:

The equations for the 1st object :

x₁ = 10 cos(2t),  and  y₁ = 6 sin(2t)

2nd object :

x₂ = 4 cos(t), y₂ = 4 sin(t)

Determine rate at which distance between objects will continue to change

solution Attached below

Distance( D )  = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]

hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]

Answer:

x=-2

Step-by-step explanation:

3x-1=8x+8+1

3x-1 = 8x+9

3x-1+1=8x+9+1

3x= 8x+10

3x-8x=8x+10-8x

-5x=10

-5x ÷-5

10 ÷-5

x=-2

Answer:

(–1,4)

Step-by-step explanation:

x – y = –5

3x + y = 1

You omit Ys due to their positive and negative signs and you got

4x = –4===> x= –1

and now place –1 inside the upper linear equation and there you have the Y, look

–1 – Y= –5===> –Y= –4===> Y = 4

(–1,4)

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Answer:

  blue

Step-by-step explanation:

If two red marbles are removed, 1 red is returned. The number of reds is reduced by 1, and the number of blues is unchanged.

If two blue marbles are removed, 1 red is returned. The number of reds is increased by 1, and the number of blues is decreased by 2.

If one of each is removed, one blue is returned. The number of reds is reduced by 1, and the number of blues is unchanged.

So, at each step, the number of blue marbles is unchanged or reduced by 2. That is, it only changes by an even number. The number of blues is initially odd, so can never reach zero.

The last marble in the bag is blue.

Answer: i need the formula and i got you.

Step-by-step explanation:

Answer:

25 boxes could be stacked safely on the pallet.

Step-by-step explanation:

To determine how many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box is 1 x 1 and the maximum safe stacking height is 5 boxes, the following calculation should be performed:

Pallet = 5 x 5 = 25 square feet

Box = 1 x 1 = 1 square foot

25/1 = 25

Therefore, 25 boxes could be stacked safely on the pallet.

Answer:

hi

Step-by-step explanation:

Answer: 5

Step-by-step explanation: I think it is 5

Answer:

Variables are used to represent an unknown quantity in a mathematical expression.

Step-by-step explanation:

Answer:

he found y value

Step-by-step explanation:

y value would be 8 3/4 + (-4) which is equivalent to 8 3/4 - 4 = 4 3/4

Answer:

standard deviation

Step-by-step explanation:

Answer:

[tex]x < 4368 \frac{8}{19} [/tex]

Step-by-step explanation:

[tex]28x < 83000 + 9x[/tex]

[tex]28x - 9x < 83000[/tex]

[tex]19x < 83000[/tex]

[tex]x < 4368 \frac{8}{19} [/tex]

Answer:

Hence the total number of possible options available to a person who calls the 800 number is 216.

Step-by-step explanation:

Given that the caller 10 800 telephone system has six options. For each of these four options, three more options are available. For each of these three options, another three options are presented.

Hence the total number of possible options available to a person who calls the 800 number = [tex]6 \times 4 \times 3 \times 3 = 216[/tex].

Answer:

False

Step-by-step explanation:

To show that this is false, all we have to do is find one example.

9 is an odd number less than 15

9 is composite

9 =3*3

Step-by-step explanation:

here is the answer to your question

Answer:

"0.0808" is the appropriate response.

Step-by-step explanation:

Given:

n = 524

[tex]\hat{P}[/tex] = 41%

or,

   = 0.41

[tex]1-\hat{P}=1-0.41[/tex]

         [tex]=0.59[/tex]

[tex]\mu \hat{P}=\hat{P}[/tex]

     [tex]=0.41[/tex]

Now,

⇒ [tex]6 \hat{P}=\sqrt{\frac{\hat {P}(1-\hat{P})}{n} }[/tex]

         [tex]=\sqrt{\frac{0.41\times 0.59}{524} }[/tex]

         [tex]=0.0215[/tex]

[tex]P(\hat {P}>44 \ percent)[/tex]

or,

[tex]P(\hat{P}>0.44)[/tex]

          [tex]=1-P(\hat{P}<0.44)[/tex]

          [tex]=1-P(\frac{\hat{P}-\mu \hat{P}}{6 \hat{P}} <\frac{0.44-0.41}{0.0215} )[/tex]

          [tex]=1-P(z<1.40)[/tex]

By using the standard normal table, we get

          [tex]=1-0.9192[/tex]

          [tex]=0.0808[/tex]    

Answer:189.75

Step-by-step explanation:

The lateral area of the cone for the height of 11 cm and diameter 10 cm is given by option D. 189.75 cm²

To calculate the lateral area of a cone,  find the curved surface area.

The lateral area of a cone can be calculated using the formula:

Lateral Area = π × r × l

where:

π is the mathematical constant pi (approximately 3.14159)

r is the radius of the base of the cone

l is the slant height of the cone

Height (h) = 11 cm

Diameter (d) = 10 cm

First, we need to find the radius (r) and the slant height (l).

The radius (r) is half of the diameter:

r

= d / 2

= 10 cm / 2

= 5 cm

The slant height (l) can be found using the Pythagorean theorem:

l² = r² + h²

l² = 5² + 11²

l² = 25 + 121

l² = 146

l = √146

 ≈ 12.083 cm

Now, calculate the lateral area:

Lateral Area = π × r × l

Lateral Area = 3.14159 × 5 cm × 12.083 cm

Lateral Area ≈ 189.75 cm²

Therefore, the lateral area of the cone is approximately 189.75 cm². The correct answer is C) 189.75 cm²

learn more about  lateral area here

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