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Answer: Given

room height is x feet

room length is 3x feet

room width is 3x feet

a door 3 ft wide by 7 ft tall

Find

The net area of the wall, excluding the door

Solution

The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.

... gross wall area = (3x +3x +3x +3x)·x = 12x²

The area of the door is the product of its height and width.

... door area = (7 t)×(3 ft) = 21 ft²

Then the net wall area, exclusive of the door is ...

... net wall area = gross wall area - door area

... net wall area = 12x² -21 . . . . square feet

Answer:

Following are the solution to the given points:

Step-by-step explanation:

[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]

For point a:

[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]

For point b:

[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]

For point c:

[tex]Probability\ = 0.794614436 \\\\[/tex]

[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]

For point d:

[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]

For point e:

[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]

For point f:

[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

Answer:

It would be B. 16 centimeters^2

Step-by-step explanation:

Answer:

a) 0.3571 = 35.71% probability that the stock price will be more than $25.

b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed between $16 and $30 per share.

This means that [tex]a = 16, b = 30[/tex]

a) More than $25?

[tex]P(X > x) = \frac{30 - 25}{30 - 16} = 0.3571[/tex]

0.3571 = 35.71% probability that the stock price will be more than $25.

b) Less than or equal to $18?

[tex]P(X < 18) = \frac{18 - 16}{30 - 16} = 0.1429[/tex]

0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Here, we want to find the interest rate and principal

The interest rate, r = 6% and the principal, P = Rs 65,000

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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Answer:

Yes, it is rational number.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) =  6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

Answer:

8 ounces of tomato paste for each cup of water.

Step-by-step explanation:

Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.

Hope this helps!

Work Shown:

48 oz of tomato paste = 6 cups of water

48/6 oz of tomato paste = 6/6 cups of water

8 oz of tomato paste = 1 cup of water

In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.

Answer:

12

Step-by-step explanation:

Find the LCM (Least Common Multiple) of the three numbers.

We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.

6 x 2 = 12

4 x 3 = 12

3 x 4 = 12

Hope this helps!

Answer:

an arithmetic sequence

Step-by-step explanation:

an arithmetic series is wrong also heres an example i found of an arithmetic sequence

The terms in the given sequence represents an arithmetic sequence.

Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence of numbers is,

-8, -4, 0, 4, 8, 12, ......

We have to find which sequence does it represent.

This is not a series since they are not represented as the sum.

If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.

If it is arithmetic sequence, then the difference of consecutive numbers will be same.

Here, ratio is not same.

Difference are same.

-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........

Common difference is 4.

Hence it is an arithmetic sequence.

Learn more about arithmetic Sequence here :

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Answer:

The Hong Kong dollar equivalent of K70 is HK $ 94.71.

Step-by-step explanation:

Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:

1,353 x 70 = X

94.71 = X

Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.

Answer:

5 over 9

Step-by-step explanation:

multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5

Answer:

12

Step-by-step explanation:

113.04=3.14 x 3^2 x h/3

Answer:

Step-by-step explanation:

This is a geometric means problem where 60, the side common to both the triangles, is the geometric mean. Set it up like this:

[tex]\frac{36}{60}=\frac{60}{x}[/tex] and cross multiply to get

36x = 3600 so

x = 100

Answer:

$7153.84

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

P = 5000

r = 12% = 0.12

n = 12

t = 3

Step 2: Find Interest

Given:

The functions are:

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

To find:

The rational expression for [tex]p(x)-q(x)[/tex].

Solution:

We have,

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

Now,

[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]

[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]

[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]

Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].

Answer: 14 seed packs

Step-by-step explanation:

You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.

Answer:

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Step-by-step explanation:

The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 candidates, which means that [tex]N = 6[/tex]

2 are the aunt and father, which means that [tex]k = 2[/tex]

3 are chosen, which means that [tex]n = 3[/tex]

What is the probability that either your aunt or your father will become a city commissioner?

Probability of at least one of them being chosen, which is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8[/tex]

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Answer:

D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]

9514 1404 393

Answer:

  ΔGHF ~ ΔMLF by AA theorem

Step-by-step explanation:

Answer: The answer is 0.182

Hope this help :)

Answer:

Hello,

Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3

Step-by-step explanation:

[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]

the third of the sum of the cube of x and double of the square of x ( cm³)

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

Volume is the amount of space occupied by a three dimensional shape or object.

Area of the square base = x * x = x² cm²

Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)

Volume of pyramid = (x³ + 2x²) / 3

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

Find out more on volume at: https://brainly.com/question/12410983

Answer:

C

Step-by-step explanation:

[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]

Answer:

The number of positive real zeros is 2 or 0

Step-by-step explanation:

Given

[tex]f(x)=x^5+3x^2-4x+2[/tex]

Required

Number of positive real zeros

Using Descartes rule of signs;

We write out the signs in front of each term;

Sign = + + - +

Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive

From positive to negative, we have: 1 (i.e. + - )

From negative to positive, we have: 1 (i.e. - +)

Add up the count

[tex]count = 1+1[/tex]

[tex]count = 2[/tex]

Hence, the number of positive real zeros is 2 or 0

Answer:

-60 60 30 -30 one of it is answer

Answer:

38.6 cm

Step-by-step explanation:

add all of the sides up to get your perimeter

Answer:

x=3

Step-by-step explanation:

The ratios need to be the same

AB             CB

---------- = ----------

AD             ED

3           x

-----  = ---------

3+9       12

3           x

-----  = ---------

12          12

X must equal 3

Answer: For flour it is 360g

3 eggs

900ml of milk

Step-by-step explanation:

Answer:

First, find the amount of ingredient for one pancake:

Multiply that amount by 12 to find the amount needed for 12 pancakes:

Answer:

256

Step-by-step explanation:

How to find subsets = 2 raise the power n.

N=number of elements in a set.

=2raise the power 8 which is 256.