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WITCHER [35]
3 years ago
9

Cora takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 15 i

nches long and 8 inches wide, how long is the diagonal cut that Cora made? (This is pythagorean theorem btw)
​
Mathematics
1 answer:
Bogdan [553]3 years ago
7 0
Answer: 17 inches

Explanation: so we have a triangle with the two side lengths 8 and 15 and we’re trying to find the hypotenuse. so using the pythagorean theorem, we have 8^2 + 15^2 = c^2. when we solve we get 64 + 225 = c^2, which is 289 = c^2. next, we find the square root of both sides and c = 17 inches.

hope this helped!
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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
erma4kov [3.2K]

Answer:

\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

Step-by-step explanation:

Given

5 tuples implies that:

n = 5

(h,i,j,k,m) implies that:

r = 5

Required

How many 5-tuples of integers (h, i, j, k,m) are there such thatn\ge h\ge i\ge j\ge k\ge m\ge 1

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed:  This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

^{n}C_r => ^{n + 4}C_5

^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}

^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}

Expand the numerator

^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}

^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}

<u><em>Solved</em></u>

6 0
3 years ago
Answer please! (No explanation needed!) &lt;3
son4ous [18]

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------

Question A answer: 2.

To find the <u>median</u>, you simply need to order the set from lowest to highest and finding the <u><em>exact middle</em></u>. So it should look like this:

0, 1, <em><u>2</u></em>, 3, 4. So 2 is the median, therefore 2 is the answer to Question A.

------------------------------------------------------------------------------------------------

Question B answer: 2

To find the <u>mean</u>, you have to add all of the numbers together and then you have to <u>divide by the number of items in the set</u>. There are 5 numbers in the set so it should look like this:

0 + 1 + 2 + 3 + 4 = 10.  

Since there 5 numbers in the set, we need to divide by 5.

10 / 5 = 2.

Therefore, 2 is also the answer to Question B.

-------------------------------------------------------------------------------

<em>Edit:</em> <em>Whoops, sorry for the explanation...</em>

5 0
3 years ago
Read 2 more answers
Hey can somebody help y+5=2(x+1)
kifflom [539]
If you're looking for the equation, the answer is y=2x-3
3 0
3 years ago
Read 2 more answers
At what interest rate must you invest $4500 to have $7,000 after 6 years, if the interest is compounded quarterly?
labwork [276]

Answer:

The amount is $8358.7 and the interest is $3858.7.

Step-by-step explanation:

Explanation

STEP 1: To find amount we use formula:

A=P(1+rn)n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

P=$4500 , r=7% , n=2 and t=9 years

After plugging the given information we have

AAAA=4500(1+0.072)2⋅9=4500⋅1.03518=4500⋅1.857489=8358.7

STEP 2: To find interest we use formula A=P+I, since A=8358.7 and P = 4500 we have:

A8358.7II=P+I=4500+I=8358.7−4500=3858.7

4 0
3 years ago
The radius of a circle is 4.6 millimeters. Find the diameter.
kramer

Hi :)

Radius is half the diameter

4.6 mm (2) = 9.2 mm

The diameter of the circle is 9.2 mm.

4 0
3 years ago
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