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2 years ago

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Approximately 220 million tires are discarded in the U.S. each year. These tires present a disposal problem because they take up

space, harbor pests, and have been known to catch fire. One tire can generate about 250,000 BTUs (1 BTU = 3 x 10-4 kWh) when it is burned. The average American home consumes about 10,000 kWh of electricity per year. How many tires would be needed to meet the annual electricity demand of ten homes for one year if the production of electricity from tires is 50% efficient?

1 answer:

Marysya12 [62]2 years ago

3 0

Answer:

2667 tires

Step-by-step explanation:

<u>One tire can generate:</u>

250000 BTU's = 250000*3*10⁻⁴ kWh = 75 kWh electricity

<u>Considering efficiency of 50%, one tire can produce:</u>

75/2 = 37.5 kWh

<u>10 homes require electricity, amount of:</u>

10000*10 = 100000 kWh per year

<u>How many tires can cover this demand?</u>

100000/37.5 ≈ 2667 tires

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Consider the product (x + y + z)2. If the expression is multiplied out and like terms collected, the result is: x2 + y2 + z2 + 2

VLD [36.1K]

Answer:

Part a: The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b: The number of terms are 23751.

Step-by-step explanation:

part a

From the given equation the

$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx$

So the coefficient of any term $x^ny^nz^n$ is given as

$\dfrac{2!}{n!n!n!}$

Similarly for the generic equation of coefficient of the term $x_1^{r_1}x_2^{r_2}x_3^{r_3}......x_k^{r_k}$ in the equation of form $(x_1+x_2+x_3+x_4......x_k)^n$ is given as

$\dfrac{n!}{r_1!r_2!r_3!....r_k!}$

So now the coefficient of $v^9w^2x^5y^7z^2$ is given as

$=\dfrac{25!}{9!2!5!7!2!}\\=1.766 \times 10^{13}$

The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b:

The number of terms is given as $\left (\ {{m+n-1} \atop {n}} \right )$

where m is the number of variables which are 5 here

n is the power which is 25 so the number of variables is given as

$\left (\ {{5+25-1} \atop {25}} \right )\\\left (\ {{29} \atop {25}} \right )\\\dfrac{29!}{25!4!}=23751$

So the number of terms are 23751.

3 0

2 years ago

Bonzo went to a carnival. At the first

Shalnov [3]

Bonzo started with 2.1 dollars

Step-by-step explanation:

Assume that Bonzo has $x

1. Change $x to cents

2. Calculate the remaining money with him after each game

3. Equate the left money in the 3rd game by zero to find x

∵ $1 = 100 cents

∴ $x = 100 x cents

First game

∵ Bonzo has 100 x cents

∵ He paid 10¢ to get in

∴ The money left is (100 x - 10)

∵ He spent half the money he had left

- That mean the money left with him is the other have

∴ The money left with him = $\frac{1}{2}$ (100 x - 10) = (50 x - 5) cents

∵ He spent 10¢ to get out

∴ The money left after 1st game = (50 x - 5) - 10

∴ The money left after 1st game = (50 x - 15) cents

Second game

∵ Bonzo has (50 x - 15) cents

∵ He paid 10¢ to get in

∴ The money left is (50 x - 15) - 10 = (50 x - 25)

∵ He spent half the money he had left

∴ The money left with him = $\frac{1}{2}$ (50 x - 25) = (25 x - 12.5) cents

∵ He spent 10¢ to get out

∴ The money left after 2nd game = (25 x - 12.5) - 10

∴ The money left after 2nd game = (25 x - 22.5) cents

Third game

∵ Bonzo has (25 x - 22.5) cents

∵ He paid 10¢ to get in

∴ The money left is (25 x - 22.5) - 10 = (25 x - 32.5)

∵ He spent half the money he had left

∴ The money left with him = $\frac{1}{2}$ (25 x - 32.5) = (12.5 x - 16.25) cents

∵ He spent 10¢ to get out

∴ The money left after 3rd game = (12.5 x - 16.25) - 10

∴ The money left after 3rd game = (12.5 x - 26.25) cents

∵ He found he had no money left after the 3rd game

∴ Equate the left money with him by zero

∴ 12.5 x - 26.25 = 0

- Add 26.25 to both sides

∴ 12.5 x = 26.25

- Divide both sides by 12.5

∴ x = 2.1

<em>Bonzo started with 2.1 dollars </em>

Learn more:

You can learn more about money in brainly.com/question/1870710

#LearnwithBrainly

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2 years ago

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume

Paraphin [41]

Answer:

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t

Step-by-step explanation:

Notation

$\bar X_{1}$ represent the mean for male king penguins

$\bar X_{2}$ represent the mean for the female king penguins

$s_{1}$ represent the sample standard deviation for the sample male

$s_{2}$ represent the sample standard deviation for the sample female

$n_{1}$ sample size for the male penguins

$n_{2}$ sample size for the female penguins

t would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to check if the male king penguins weigh more than female king penguins, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} > \mu_{2}$

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t

7 0

2 years ago

Which of the following is a radical equation? x + StartRoot 5 EndRoot = 12 x squared = 16 3 + x StartRoot 7 EndRoot = 13 7 Start

d1i1m1o1n [39]

Answer:

x = 3

Step-by-step explanation:

$(8x-8)^{3/2}=64$

Multiply both sides by the exponent 2/3.

$8x - 8 = 64^{2/3}$

Solve for the exponent.

$8x-8=16$

Add 8 to both sides.

$8x = 16+8$

$8x=24$

Divide 8 into both sides.

$x=24/8$

$x=3$

6 0

2 years ago

If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?

Vinil7 [7]

Answer:

The expression used to represent g(x) as inverse of f(x) is $\frac{1}{5}(5x-25)+5$

Option B is correct.

Step-by-step explanation:

We are given:

$f(x)= 5x-25\\g(x)=\frac{1}{5}x+5$

We need to find the expression that could be used to verify g(x) is the inverse of f(x).

We know that $g(f(x))=x$ is inverse of function

So placing value of f(x) in g(x)

$g(f(x))=\frac{1}{5}(5x-25)+5$

So, the expression used to represent g(x) as inverse of f(x) is $\frac{1}{5}(5x-25)+5$

Option B is correct.

We can also solve to prove that $g(f(x))=x$

$g(f(x))=\frac{1}{5}(5x-25)+5\\g(f(x))=\frac{5}{5}(x-5)+5\\g(f(x))=x-5+5\\g(f(x))=x$

5 0

1 year ago

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