A rectangular prism is 10.8 yards long and 10.1 yards wide. Its volume is 218.16 cubic yards. What is the height of the rectangular prism?

Answer:

175 cents

Step-by-step explanation:

1 quarter is equal to 25 cents.

Since there are 7 of them,

7 times 25 cents = 175 cents

Answer:

Jackson's kitten gained 21 ounces that moth, or 1.3125 pounds.

Step-by-step explanation:

56-35=21

Answer:

21 ounces

Step-by-step explanation:

2 pounds is equal to 32 ounces, plus the 3 ounces, so the kitten was originally 35 ounces. You subtract 56-35, and get 21 ounces.

Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.

Let's denote the total number of gold medals obtained by Russia as [tex]\( x \)[/tex]. Since we know Russia got 3 gold medals, we have [tex]\( x = 3 \)[/tex].

Now, let's denote the total number of gold medals obtained by the top 8 countries (including Russia) as T. We're told that the total number of gold medals obtained by all top 8 countries combined is 60. Since Russia got 3 gold medals, the gold medals obtained by the other top 7 countries is [tex]\( T - 3 \)[/tex].

So, the percentage of gold medals obtained by Russia can be calculated as:

Percentage of gold medals obtained by Russia = [tex]\frac{\text{Number of gold medals obtained by Russia}}{\text{Total number of gold medals obtained by the top 8 countries}} \times 100\%\][/tex]

Substituting the known values:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{T} \times 100\%\][/tex]

We know that the total number of gold medals obtained by the top 8 countries is 60, so [tex]\( T = 60 \).[/tex] Substituting this into the equation:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{60} \times 100\%\][/tex]

Solving this equation:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{1}{20} \times 100\% = 5\%\][/tex]

So, Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.

Answer:

[tex]I=7000C[/tex]

Step-by-step explanation:

Let C represent number of dairy cows.  

We have been given that each dairy cow produces 3500 gallons of milk per year. So amount of milk produced by C cows in 1 year would be [tex]3500C[/tex] gallons.

We are also told that the dairy sells milk for 2.00 per gallon. So yearly income I, in dollars for the dairy milk production would be 2.00 times the yearly milk production.

Since yearly milk production from C cows is [tex]3500C[/tex], so Income would be:

[tex]I=2.00(3500C)[/tex]

[tex]I=7000C[/tex]

Therefore, the formula [tex]I=7000C[/tex] represents yearly income (I) as a linear function of C.

Answer:378

Step-by-step explanation:32 times 4=178 +250=378

Alice Jones's gross pay for the week is the sum of her hourly earnings ($128 from working 32 hours at $4.00 per hour) and her tips ($250), totalling $378.

To calculate Alice Jones's gross pay, we need to consider both her hourly wage and her tips. Alice worked 32 hours this week and was paid $4.00 per hour. This means her earnings from her hourly wage are:

32 hours times $4.00/hour = $128

Alice also earned $250 in tips. To find her gross pay for the week, we add her hourly earnings to her tips:

$128 + $250 = $378

Therefore, Alice's gross pay for the week is $378.

Answer:

B) [tex]log_3 81=4[/tex]

Step-by-step explanation:

The definition of logarithm is the following:

The logarithm of a certain number x with respect to a certain base b is the exponent by which b should be raised in order to give x. Mathematically, given the equation

[tex]b^y = x[/tex] (1)

The logarithm of x to base b is defined as

[tex]y=log_b x[/tex] (2)

In this problem, we have the following equation:

[tex]3^4=81[/tex]

By comparing it with equation (1), we notice that:

b = 3

y = 4

x = 81

Therefore, by re-arranging the variables using equation (2), we can rewrite it as:

[tex]4=log_3 81[/tex]

Which corresponds to option B.

(a) Equilibrium point: x = 1

(b) Consumer surplus at equilibrium: 0

(c) Producer surplus at equilibrium: 0

We have,

To find the equilibrium point, we need to set the demand (D(x)) equal to the supply (S(x)):

D(x) = S(x)

Given:

D(x) = (x - 7)^2

S(x) = x^2 + 4x + 31

(a) Equilibrium point:

Setting D(x) equal to S(x):

(x - 7)^2 = x^2 + 4x + 31

Expanding and rearranging the equation:

x^2 - 14x + 49 = x^2 + 4x + 31

Simplifying and rearranging further:

-14x - 4x = 31 - 49

-18x = -18

x = 1

Therefore, the equilibrium point is x = 1.

(b) Consumer surplus at the equilibrium point:

Consumer surplus represents the difference between the price consumers are willing to pay and the price they actually pay.

At the equilibrium point, the price consumers are willing to pay (D(x)) is equal to the price they actually pay (S(x)).

Substituting x = 1 into the demand function D(x):

D(1) = (1 - 7)^2

D(1) = (-6)^2

D(1) = 36

Consumer surplus at the equilibrium point is the difference between what consumers are willing to pay and what they actually pay:

Consumer surplus = D(x) - S(x)

Consumer surplus = 36 - S(1)

Consumer surplus = 36 - (1^2 + 4(1) + 31)

Consumer surplus = 36 - (1 + 4 + 31)

Consumer surplus = 36 - 36

Consumer surplus = 0

Therefore, at the equilibrium point, the consumer surplus is 0.

(c) Producer surplus at the equilibrium point:

Producer surplus represents the difference between the price producers are willing to accept and the price they actually receive.

At the equilibrium point, the price producers are willing to accept (S(x)) is equal to the price they actually receive (D(x)).

Substituting x = 1 into the supply function S(x):

S(1) = 1^2 + 4(1) + 31

S(1) = 1 + 4 + 31

S(1) = 36

Producer surplus at the equilibrium point is the difference between what producers are willing to accept and what they actually receive:

Producer surplus = S(x) - D(x)

Producer surplus = 36 - D(1)

Producer surplus = 36 - (1 - 7)^2

Producer surplus = 36 - (-6)^2

Producer surplus = 36 - 36

Producer surplus = 0

Therefore, at the equilibrium point, the producer surplus is also 0.

Thus,

(a) Equilibrium point: x = 1

(b) Consumer surplus at equilibrium: 0

(c) Producer surplus at equilibrium: 0

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The equilibrium point in the market occurs when the demand and supply are equal, which can be found by solving the given function equations. Consumer surplus and producer surplus at the equilibrium point are computed as the area between the demand/supply curves and the equilibrium price.

The equilibrium point is when the demand and supply are equal, this happens i.e., D(x) = S(x). Therefore, we first equate (x-7)^2 = x^2 + 4x + 31. Solving this equation gives us the equilibrium quantity, x.
The consumer surplus is the area between the demand curve and the consumer's actual payment, i.e., the area under D(x) above the equilibrium price. This equals to the integral from 0 to x of D(x) minus the equilibrium price. The producer surplus is the area between the supply curve and the consumer's payment, i.e., the area under S(x) below the equilibrium price. This equals to the integral from 0 to x of the equilibrium price minus S(x).

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Answer:

d

Step-by-step explanation:

hope this helps

Answer:

1944 Inches Squared

Step-by-step explanation:

Surface area Formula for a Cube:

[tex]A = 6a^2[/tex]

The "edge", which is also the side, is 18 inches.

[tex]a = 18[/tex]

Solve the formula.

[tex]A= 6a^2 = 6(18)^2 = 6 * 18^2\\18^2 = 324\\324 * 6 = 1944\\A=1944[/tex]

The cube's surface area should be 1944 square inches.

Answer:

Step-by-step explanation:

1944 Inches Squared

Step-by-step explanation:

Surface area Formula for a Cube:

The "edge", which is also the side, is 18 inches.

Solve the formula.

The question is incomplete! Complete question along with answer and explanation is provided below.  

Question:  

Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.

The Probability is (2/12)(4/12) = 8/144

Answer:

P = (2/12)(4/11) = 2/33

Step-by-step explanation:

There are total 3 + 2 + 4 + 3 = 12 marbles

The probability of drawing a yellow marble is given by

P(yellow) = number of yellow marbles/total number of marbles

There are 2 yellow marbles and total 12 marbles

P(yellow) = 2/12

Then Francisco draws a red marble without replacing the first one so that means there are total 11 marbles left.

P(red) = number of red marbles/total number of marbles

There are 4 red marbles and total 11 marbles

P(red) = 4/11

Therefore, the overall probability is

P = (2/12)(4/11) = 2/33

Francisco made the error of calculating the probability with replacement whereas, in reality he did not replaced the marble after drawing the yellow marble, so he should have used total 11 marbles for the calculation of drawing red marble,

Answer:

(6) 1200 square feet

(7) 49 months

Step-by-step explanation:

Let the area of the living room be x square feet. Since the material cost is fixed as $2840 and cost ler square feet provided as $1.9 while and the total cost is given as $5120 then the the problem can be represented as

1.9x+$2840=$5120

Putting like terms together then

1.9x=$5120-$2840=$2280

Making x the subject of the above, by dividing both sides by 1.9 then

X=2280/1.9=1200 square feet.

Therefore, area is 1200 square feet.

(7)

Let the number of months when cost are similar be y.

For satelite option, since fixed cost of $298.9 is charged then monthly rate is $68.7 it means after y months, the expenditure for this plan will be 68.7y+$298.9

For cable option, since it only charges monthly fee of $74.80 then after y months, the expenditure amounts to 74.80y

Since after y months the expenses are same, then we equate both options to be equal. Therefore,

74.80y=68.70y+298.90

Putting like terms together then

74.80y-68.70y=298.90

6.1y=298.90

Dividing both sides by 6.1 to make y the subject then

Y=298.9/6.1=49 months

Answer:

0.18401015

Step-by-step explanation:

You should use an online calculator

Answer:

The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2

Step-by-step explanation:

If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.

Therefore, we prove with negative values.

Therefore, -2 is a root. We can find the other knowing that

p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)

The independent term is 11*2*(-r₂) = -22r₂ = -10

thus, r₂ = -10/-22 = 5/11.

Therefore, p(x) = 11*(x+2)*(x-5/11)

To write 11x2+17x−10 in factored form we find two numbers whose sum is 17 and product is -110. The correct pair is 2 and -55 which leads to the factored form (11x - 55)(x + 2).

The question involves factoring a quadratic expression, 11x2+17x−10. To re-write this expression in factored form, one needs to find two numbers, such that their sum equals to the coefficient of x, 17, and their product equals to the product of the coefficient of x² and the constant term (11*(-10)=-110). Diego started by listing all pairs of factors of the constant term, -10. The correct pair here, considering the product and the sum, are 2 and -55, because 2*(-55)=-110 and 2+(-55)=17. Therefore, our factored form will be: (11x - 55)(x + 2).

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Answer:

18

Step-by-step explanation:

Normally, when you multiply two numbers, their product equal to the product of their greatest common factor and their least common multiple

Let the number be y

The product of 12 and y is 12 y

Also, the product of their greatest common factor and their least common multiple is 6*36=216

Now

12y=216

Divide both sides by 12 to obtain y as

Y=216/12=18

Therefore, the other number is 18.

To prove

Factors of

12=2*2*3

18=2*3*3

Common factors for both are 2*3=6 equal to given GCD

The multiplies are 2*2*3*3=36

Answer:1/2m>50

Step-by-step explanation:Put a line under the sign.

The probability of drawing at least one face card when drawing two cards with replacement from a standard deck is approximately 0.407.

The student is asking for the probability of drawing at least one face card (Jack, Queen, or King) when drawing two cards with replacement from a standard deck of 52 cards. To find this, we can use the complement rule: subtract the probability of not drawing a face card in both draws from 1. There are 12 face cards in a deck of 52 cards, so the probability of drawing a non-face card (event N) on one draw is 40/52 (since there are 40 non-face cards).

Using the complement rule:

Now perform the calculations:

P(NN) = (40/52) * (40/52) = 0.5929 (approximately).

P(at least one F) = 1 - 0.5929 = 0.4071 (rounded to three decimal places).

Therefore, the probability of drawing at least one face card in two draws with replacement is approximately 0.407.

Answer:

49998 pennies left

Step-by-step explanation:

50000 - 2 = 49998

Answer:

50000-2=49998

Step-by-step explanation:

Answer:

(-12, 9)

Step-by-step explanation:

Answer:

8.2, 105.00

Step-by-step explanation:

Take the first measures and add the enlargements to get the dimensions of the third quilt. This probably is wrong I just had to answer a question

Answer:

P(A∪B) = 0.92

Step-by-step explanation:

Let's call A the event that the sandwich was made with raspberry Jelly and B the event that the sandwich was made with creamy peanut butter.

So, the probability P(A∪B) that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is calculated as:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where P(A) is the probability that a sandwich was made with raspberry jelly, P(B) is the probability that it was made with creamy peanut butter and P(A∩B) is the probability that it was made with raspberry jelly and creamy peanut butter.

So, replacing P(A) by 0.84, P(B) by 0.27 and P(A∩B) by 0.19, we get that P(A∪B) is equal to:

P(A∪B) = 0.84 + 0.27 - 0.19

P(A∪B) = 0.92

The probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%, computed using the formula for the probability of A or B happening in probability theory.

In probability, when we want to find the probability of event A or event B happening, we use the formula P(A U B) = P(A) + P(B) - P(A ∩ B). Here, event A is the event that a sandwich was made with raspberry jelly, and event B is the event that it was made with creamy peanut butter. Given P(A) = 0.84, P(B) = 0.27, and P(A ∩ B) = 0.19, we can substitute these values into the formula.

So, P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.84 + 0.27 - 0.19 = 0.92.

This means that the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%.

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Answer:

The correct answer is 25.

Step-by-step explanation:

A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year.

Number of publications by the magazine every year = 12.

Number of publications in 5 years = 12 × 5 = 60.

Out of these 12 magazines in a year, the photo of a main dish is on 5 magazines.

Therefore in 60 magazines, the photo of a main dish would be 5 × 5 = 25 magazines.

Thus in five years there would be 25 publications in which the front page will have a poster of a main dish.

Based on the number of times the photo appears per year, in 5 years it will appear 25 times.

Every year, the photo in question appears 5 out of 12 times.

If there were 5 years therefore, it would appear:

= Number of times per year x Number of years

= 5 x 5

= 25 times

In conclusion, the photo of a main dish will appear 25 times in 5 years.

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Answer: y = -0.5x + 6

Domain = 0≤x≤12

Range = 0≤y≤6

Answer:

solution is (-2, -4)

Step-by-step explanation:

I assume you want the solution?

so we want to find the intersection.

3x -  2y  = 2

5x = 5y + 10

simplify the last equation

x = y + 2  by dividing out the 5

substitute

3*(y + 2) - 2y = 2

3y + 6 - 2y = 2

y  + 6 = 2

y = -4

x  = -4 + 2 = -2

solution is (-2, -4)

Answer:

I think the answer is 38.

Answer:Since each type of drink (lemonade, water, and juice) is equally likely to be chosen, the probability of choosing a type of drink is 1 in 3 picks. Thus, in order to get all three types of drinks, one must pick 3

Step-by-step explanation:

Answer:[tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]

Step-by-step explanation:

Given

length of three sides are

[tex]3x, 7\ and\ 12[/tex]

according to Euclidean geometry

[tex]7+12>3x[/tex]

[tex]19>3x[/tex]

[tex]\frac{19}{3}>x[/tex]

also

[tex]3x+7>12[/tex]

[tex]3x>5[/tex]

[tex]x>\frac{5}{3}[/tex]

therefore value of [tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]

If x is an integer then x can be [tex]2,3,4,5,6[/tex]

Answer:

6,802

Step-by-step explanation:

Our first step is to change 76% into a decimal:

76% -> [tex]\frac{76}{100}[/tex] -> 0.76

Next, lets multiply and solve for x:

[tex]x=8,950(0.76)[/tex]

[tex]x = 6,802[/tex]

There were 6,802 public libraries that offered free access electronic books in 2012.

Answer:

6802 Libraries offered free electronic books.

Step-by-step explanation:

Answer:

49pi or about 153.94 square meters.

Step-by-step explanation:

Because the two semicircles together take up the 28m long edge of the rectangle, they each half that diameter and a quarter of that radius. This means that both semicircles have a radius of 28/4=7.  Since two semicircle with the same radius form a full circle, we can just calculate the area of a full circle of radius 7. [tex]\pi \cdot 7^2=49\pi\approx 153.94[/tex]. Hope this helps!

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: ( 8 , − 3 ) Equation Form: x = 8 , y = − 3

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