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3 years ago

Brian rides his bike for 7.5 miles. The diameter of his bicycle tires is 20 inches. Estimate the

Mathematics

1 answer:

alekssr [168]3 years ago

7 0

Answer:

7500 revolutions

Step-by-step explanation:

1 rotation of his bicycle tires is equivalent to 1 circumference in linear distance.

circumference = π*diameter = π*20 = 62.8 in

If 1 foot is equivalent to 12 inches, then 62.8 in are equivalent to:

1 ft / x ft = 12 in / 62.8 in

x = 62.8/12 = 5.2 ft

If 5280 ft are equivalent to 1 mile, then 5.2 ft are equivalent to:

5280 ft / 5.2 ft = 1 mile / x mile

x = 5.2/5280 = 0.001 mile

So, when 1 revolution is made, 0.001 mile had been travelled. To compute the number of revolutions after 7.5 miles are travelled, the following proportion must be satisfied:

1 revolution / x revolutions = 0.001 mile / 7.5 miles

x = 7.5/0.001 = 7500 revolutions

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84. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value

Yakvenalex [24]

Answer:

a) 1/27

b) 16

c) 1/8

Step-by-step explanation:

a) $x^{-3/2}$

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

$x^{-3/2}=\frac{1}{x^{3/2} }$

And now, solving for x = 9 we have:

$\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} } =\frac{1}{27}$

b) $y^{4/3}$

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

$y^{4/3}=8^{4/3}=16$

c) $z^{-3/4}$

Using the same property we used in a) we have:

$z^{-3/4}=\frac{1}{z^{3/4} }$

And now, solving for z = 16 we have:

$\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}$

4 0

3 years ago

Surveys conducted in American high schools concluded that 90% of the students in a sample of 400 students had more than one acti

kenny6666 [7]

The sample proportion has an approximately normal distribution, with the mean being the population mean and the standard deviation (i.e. the standard error of the sampling proportion) equal to

SE = sqrt(p*q/n) where p is the population proportion q is 1-p, and n is the sample size.

<span>(Typically, for a confkdence interval, the sample proportion and its complement are substituted for p and q.) </span>

The margin of error will be Zc*SE, where Zc is the critical value of Z for the level of confidence required. The confidence interval, then, will be the sample proportion, plus or minus the margin of error.

For a 90% confidence interval, Zc is 1.645.

<span>So the margin of error is 1.645 * sqrt(.9*.1/400), roughly .025. So your confidence interval would be around [.875, .925]

The best and most correct answer among the choices provided by your question is the second choice or letter C which is 3%.
I hope my answer has come to your help. Thank you for posting your question here in Brainly.</span>

4 0

3 years ago

Read 2 more answers

Given the matrices: 1 2 A= 1 -1 2 1 1 B= 3 4 Calculate AB: C11 C12 [2.1] х 1 2 3 4 C21 C22 C11 = C12 = -2 C22 - C215 DONE

eduard

Answer:

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

Step-by-step explanation:

Given the matrices

$A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}$

$B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}$

Calculating AB:

$\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}$

Multiply the rows of the first matrix by the columns of the second matrix

$=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}$

$=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}$

Hence,

$\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}$

Therefore,

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

5 0

3 years ago

Read 2 more answers

A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain numbe

VikaD [51]

The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

<h3>Simultaneous equation</h3>

let

Number of decorative pillows for twin bed = x
Number of decorative pillows for queen bed = y

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

Substitute x = 15 - y into (2)

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

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2 years ago

I was just wondering this is one of my questions in my math books and i needed help (Its really long i did all the work i just w

slava [35]

Answer:

no not that wuch

Step-by-step explanation:

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3 years ago