A publishing company sells 100,000 copies of certain books each year. It costs the company $1 to store each book for a year. Each time it must print additional​ copies, it costs the company $500 to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup​ costs?

Answer:

See below.

Step-by-step explanation:

Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]

We know that the diameter is 14, so the radius is 7.

Plug it into the equation:

[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]

Answer:

1/4

Step-by-step explanation:

There are 36 possible combinations.  Of those 36, the ones that add up to either 6 or 9 are:

1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3

There are 9 combinations that add up to either 6 or 9.  So the probability is 9/36, or 1/4.

The probability that the sum of the numbers rolled is either 6 or 9 is   [tex]\frac{1}{4}[/tex] . In rounded to the nearest millionth, the probability is 0.25.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Possible outcomes are

1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3.

The number of possible outcomes is 9.

Each dice has 6 possible outcomes.

Total number of outcomes = 6 × 6 =36

The probability is the ratio of total number of outcomes to possible outcomes.

The probability is 9/ 36 = 1/4 = 0.25

Hence, required probability is 1/4 or 0.25.

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Answer:

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]\sigma = 1.27, n = 85[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 2.575*\frac{1.27}{\sqrt{85}}[/tex]

[tex]M = 0.3547[/tex]

The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547

I would use a chart to solve this problem.

This is a good wya to organize your information.

Down the left side, list the people involved.

I put Bob first and the mom second but the order doesn't matter.

Since Bob's mom is 3 times older than Bob, we can represent

Bob's age now as x and Bob's mom's age now as 3x.

Bob's age in 12 years will be x + 12 and Bob's mom's

age in 12 years will simply be 3x + 12.

Since the second sentence starts with in 12 years,

we will be using the information from our second column.

In 12 years, Bob's mom's age, 3x + 12, will be,

equals, twice of her son's age, 2(x + 12).

Solving from here, we find that x = 12.

This means that Bob's age now is 12 and his mom is 36.

The chart is attached below.

Answer:

12 and 36 = bob is 12 and bob's mother is 36

Answer:

the answer for the question is b.because calculated statistic less than critical t,value we reject the null hypothesis. Therefore, Wilson Community Pool cannot conclude............

The Conclusion of the Hypothesis is; D. Because the t calculated is less than the critical t, we fail to reject the null hypothesis.

From the given question, we see that;

Population Mean; μ = 7.2

Sample Mean; x⁻ = 7.02

Significance level; α = 0.05

Now, in hypothesis, If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis whereas if the absolute value of the t-value is greater than the critical value, you reject the null hypothesis.

Thus, the conclusion is that d. Because the t calculated is less than the critical t, we fail to reject the null hypothesis. Therefore, Wilson Community Pool conclude that the pH value is equal to 7.2. Based on this sample, no corrective action is needed.

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Answer:

x + (4x-85) = 90

Step-by-step explanation:

The two angles are complementary which means they add to 90 degrees

x + (4x-85) = 90

Answer: A

Step-by-step explanation:

Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.

Answer:

100

Step-by-step explanation:

The Volume of the Rectangular prism on the left is 60

The Volume of the Rectangular prism on the right is 40

Answer:

Your correct answer is 40

Step-by-step explanation:

Multiply 8 x 5.

8 x 5 = 40

MUltiply 40 x 1.

40 x 1 = 40

So, it stays the same. Anything multiplied by 1 stays the same.

Therefore, your correct answer is 40.

Answer:

x=4/3

Step-by-step explanation:

By using the formula =

MQ/QP=MN/NO

4/x=6/2

Cross multiply

6x=8

x=4/3

Answer:

$14.034

Step-by-step explanation:

40/10 means that the price has a 40% discount and then, a 10% discount from what is left. To calculate the net price, first you have to calculate the price with the 40% discount:

25.99*(1-0.4)= 15.594

Then, you have to calculate the price with the 10% discount:

15.594*(1-0.1)= 14.034

According to this, the net price is $14.034.

Answer:

82 miles

Step-by-step explanation:

Since Nathan only needs the car for a day and he has 75$ then we can set that as are maximum to build the equation to find the amount of miles he can drive.

75 = 29.5 + 0.55x

45.5 = 0.55x

x = 82.73

The problem states that partial miles will count as full miles, so Nathan can only afford to drive 82 miles on the rental car.

Cheers.

Nathan can drive a number of miles would be 82.73 the without exceeding his budget.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given that Nathan only needs the car for a day and has $75, we can use it as the maximum to develop the equation to determine how many kilometers he can drive.

⇒ 75 = 29.5 + 0.55x

⇒ 45.5 = 0.55x

⇒ x = 82.73

Thus, the partial miles are counted as full miles, Nathan can only afford to travel 82 miles in the rented car.

Therefore, he can drive a number of miles would be 82.73 the without exceeding his budget.

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Answer:

72 : 108

Step-by-step explanation:

180/(total parts)

180/(2+3)

180/5

= 36

Find the ratio:

2 : 3

2 × 36 : 3 × 36

72 : 108

Answer:

72:108

Step-by-step explanation:

180 dived by 5 = 36

36 times 2 = 72

36 times 3 = 108

72:108

hope this helps ; )

Answer:

[tex] \angle B[/tex]

Step-by-step explanation:

[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,

Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

Answer:

Given,

CB=X

CD=3

CA=3+7=10

HERE,

[tex] {(cb)}^{2} = cd \times ca \\ {x}^{2} = 3 \times 10 \\ {x}^{2} = 30 \\ x = \sqrt{30} [/tex]

Hope this helps...

Good luck on your assignment..

The value of x is: x= √30.

Here, we have,

from the given figure, we get,

let, angle C = Ф

then, from triangle BCD,

cos Ф = 3/x

and, from triangle ABC,

cos Ф = x/10

so, we have,

3/x = x/10

=> x² = 10×3

=> x² = 30

=> x= √30

Hence, The value of x is: x= √30.

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Answer:

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Step-by-step explanation:

Let the hotel charge in the first city be x and in the second city be y.

Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:

[tex]y - x = \$1500[/tex] ...[1]

The tax in the first city was 5 %, and the tax in the second city was 8.5 %.

The total hotel tax paid for the two cities was $ 836.25

5% of x + 8.5% of y = $836.25

[tex]0.05x+0.085y=\$836.25[/tex]...[2]

Now putting value of y from [1] in to [2]:

[tex]y = \$1500+x[/tex]

[tex]0.05x+0.085\times (\$1500+x)=\$836.25[/tex]

On solving we get :

x = $5,250

Using vakue of x in [1] to find y:

[tex]y=\$1500+\$5,250=\$ 6,750[/tex]

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Work Shown:

A = area of bottom rectangular face = 10*5 = 50

B = area of back rectangular face = 12*10 = 120

C = area of slanted front rectangular face = 13*10 = 130

D = area of left triangle = 0.5*base*height = 0.5*5*12 = 30

E = area of triangle on right = 0.5*base*height = 0.5*5*12 = 30

S = total surface area

S = A+B+C+D+E

S = 50+120+130+30+30

S = 360

Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates:

[tex]m = \frac{10-(-4)}{6-2}[/tex]

Simplify:

[tex]m= \frac{14}{4}[/tex]

[tex]m = \frac{7}{2}[/tex]

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

[tex]

6+5\sqrt{249}-2x=7 \\

-2x=7-6-5\sqrt{249} \\

-2x\approx-77.9 \\

x\approx\frac{-77.9}{2}\approx38.95

[/tex]

Hope this helps.

Answer:

The answer is

Step-by-step explanation:

Usng the formula

[tex]A(n) = 3(2) ^{n - 1} [/tex]

Where n is the number of terms

For the first term

[tex]A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3[/tex]

For the fourth term

[tex]A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24[/tex]

For the eighth term

[tex]A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384[/tex]

Hope this helps you

Answer: –3; –24; –384

Step-by-step explanation:

Answer:

1) Radius of the cone = 9.5 cm

2) BA = 90.25 π cm²

3) SA = 384.7 π cm²

Step-by-step explanation:

1) Radius of the cone = 9.5 cm

2) Base Area of the cone = [tex]\pi r^2[/tex]

BA = (π)(9.5)²

BA = 90.25 π cm²

3) Surface Area of Cone = [tex]\pi r(r+\sqrt{h^2+r^2)}[/tex]

SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)

SA = 9.5π(9.5 + 31)

SA = 9.5π(40.5)

SA = 384.7 π cm²

Answer:

Option (2)

Step-by-step explanation:

In the figure attached,

ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.

Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.

Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]

                    = [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]

                    = [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]

                    = [tex]\frac{(6+12)}{6}[/tex]

                    = 3

Therefore, scale factor is 3 when center of dilation is B.

Option (2) will be the answer.

Answer:

B. 65°

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 130 = 50

Angles in a triangle add up to 180 degrees.

y + y + 50 = 180

2y + 50 = 180

2y = 180 -50

2y = 130

y = 130/2

y = 65

Answer:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

Step-by-step explanation:

For this case we know that the random variable follows a binomial distribution given by:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

Answer and Step-by-step explanation:

The computation is shown below:

Let us assume that

Spam Email be S

And, test spam positive be T

Given that

P(S) = 0.3

[tex]P(\frac{T}{S}) = 0.95[/tex]

[tex]P(\frac{T}{S^c}) = 0.05[/tex]

Now based on the above information, the probabilities are as follows

i. P(Spam Email) is

= P(S)

= 0.3

[tex]P(S^c) = 1 - P(S)[/tex]

= 1 - 0.3

= 0.7

ii. [tex]P(\frac{S}{T}) = \frac{P(S\cap\ T}{P(T)}[/tex]

[tex]= \frac{P(\frac{T}{S}) . P(S) }{P(\frac{T}{S}) . P(S) + P(\frac{T}{S^c}) . P(S^c) }[/tex]

[tex]= \frac{0.95 \times 0.3}{0.95 \times 0.3 + 0.05 \times 0.7}[/tex]

= 0.8906

iii. [tex]P(\frac{S}{T^c}) = \frac{P(S\cap\ T^c}{P(T^c)}[/tex]

[tex]= \frac{P(\frac{T^c}{S}) . P(S) }{P(\frac{T^c}{S}) . P(S) + P(\frac{T^c}{S^c}) . P(S^c) }[/tex]

[tex]= \frac{(1 - 0.95)\times 0.3}{ (1 -0.95)0.95 \times 0.3 + (1 - 0.05) \times 0.7}[/tex]

= 0.0221

We simply applied the above formulas so that the each part could come

Answer:

0.0221

Step-by-step explanation:

Answer:

The answer is 0.9726

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

W is the vertex, you can see the letter above the angle

Answer:

W

Step-by-step explanation:

The vertex is where the 2 rays meet, or the corner of the angle

The vertex is W

Answer:

$25.00 + $10x = $115.00

Step-by-step explanation:

We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.

Answer: $824.73

Step-by-step explanation:

The 5.5% payment will be divided between the interest payment and a principal deduction to reduce the debt balance.

APR = 26.2%/12 = 0.0218

Month 1

Payment =  5.5% * 943.85 = $51.91

Interest = 0.0218 * 943.85 = $20.61

Balance after Principal Deduction = 943.85 - ( 51.91 - 20.61)

= $912.55

Month 2

Payment =  5.5% *912.55  = $50.19

Interest = 0.0218 * 912.55 = $19.92

Balance after Principal Deduction = 912.55 - ( 50.19 - 19.92)

= $882.28

Month 3

Payment =  5.5% *882.28  = $48.53

Interest = 0.0218 * 882.28 = $19.26

Balance after Principal Deduction = 882.28 - ( 48.53 - 19.26)

= $853.02

Month 4

Payment =  5.5% * 853.02  = $46.92

Interest = 0.0218 *853.02 = $18.62

Balance after Principal Deduction = 853.02 - ( 46.92 - 18.62)

= $824.73

Balance at end of month 4 is beginning balance for month 5.

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × b × h

69.3 = 8.4 × h

h = 69.3 / 8.4

h = 8.25 mm

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Answer:

16.5mm

Step-by-step explanation:

1. 69.3 x 2

2. 138.6 divided by 8.4

3. solve which equals 16.5mm

Hope this helps you:)

Answer:

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.

Step-by-step explanation:

The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:

[tex]P(t) = 9t^{2} + 34[/tex]

Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.

This is P(10).

[tex]P(t) = 9t^{2} + 34[/tex]

[tex]P(10) = 9*(10)^{2} + 34 = 934[/tex]

The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.