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Wewaii [24]
2 years ago
6

Will ran the diagonal distance across a square field measuring 40 yards on each side. James ran the diagonal distance across a r

ectangular field with a length of 25 yards and a width of 35 yards. Will ran a longer distance. How much longer did he run?
Mathematics
1 answer:
Zepler [3.9K]2 years ago
4 0
<h2>∴Will ran 13.55 yards more than James.</h2>

Step-by-step explanation:

Given Will ran the diagonal distance across a square field measuring 40 yards each sides .

∴The distance covered by Will was =\sqrt{40^{2}+40^2 } yards

                                                         = 40\sqrt{2} yards=56.56 yards

Again James ran diagonal distance across a rectangle field with a length of 25 yards and a width of 35 yards.

So,distance covered by James was =\sqrt{25^2+35^2} yards

                                                             =5\sqrt{74} yards = 43.01 yards

∴Will ran longer distance.

∴Will ran 13.55 yards more than James.

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Aiden borrows a book from a public library. He read a few pages on day one. On day two, he reads twice the number of pages than
Fofino [41]

Let the number of pages read on day 1 be = x

Then on day 2 he read twice the pages from day one, it is = 2x

On 3rd day he read 6 pages less than 1st day, it is = x-6

Total pages are = 458

The equation becomes: x+2x+x-6=458

4x-6=458

4x=464

x=116

So on the third day, Aiden read x-6=116-6=110 pages.

5 0
2 years ago
713.49 written in a standard form
Vikki [24]

Answer: one hundred  seven thirteen and forty-nine hundreds

Step-by-step explanation: Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.

7 0
2 years ago
It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the
JulijaS [17]

Answer:

1)  n=48  

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p represent the real population proportion of interest

\hat p represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.10 and \alpha/2 =0.05. And the critical value would be given by:  

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64  

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}} (a)  

And on this case we have that ME =\pm 0.1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2} (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:  

n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63  

And rounded up we have that n=48  

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7  

And rounded up we have that n=298  

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:  

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96  

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}} (a)  

And on this case we have that ME =\pm 0.04 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2} (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:  

n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22  

And rounded up we have that n=426  

3 0
2 years ago
A Shampoo Problem: A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 of the bottle. How much shampoo is left? a. I
kotykmax [81]

Answer:

a) There is no a word problem for both expressions (m = 0.25\cdot 25.4 and m = 25.4-0.25), b) A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.75 of the bottle. How much shampoo is left? A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 fluid ounces of the bottle. How much shampoo is left?

Step-by-step explanation:

a) The shampoo problem is a word problem for:

(Final content) = (Initial content) - (Used content)

Then,

m = 25.4 - 0.25\cdot 25.4

Or:

m = 0.75\cdot 25.4

Hence, there is no a word problem for both expressions (m = 0.25\cdot 25.4 and m = 25.4-0.25).

b) The word problem for m = 0.25\cdot 25.4 is:

A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.75 of the bottle. How much shampoo is left?

The word problem for m = 25.4-0.25 is:

A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 fluid ounces of the bottle. How much shampoo is left?

7 0
2 years ago
The total number of degrees, D, in an n-sided polygon is given by the formula D=180(n-2). When Janelle solves for n, she gets n=
Rus_ich [418]
<span>D = 180 * (n -2)
D = 180n -360
180n = D +360
n = (D / 180) + 2

So, the answer is "A"
And we can test this with a square, sum of angles = 360
n = (D / 180) +2
n = (360 / 180) +2
number of sides = 4
correct

Source:
http://www.1728.org/polygon.htm



</span>
3 0
2 years ago
Read 2 more answers
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