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saul85 [17]
3 years ago
11

Betty needs 4 1/3 balls of yarn for every 7 scarves she knits how many will she need for 14

Mathematics
1 answer:
Harman [31]3 years ago
8 0
Well, the answer comes out to 24.5, but round it up to 25.
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Find the radius of a sphere with a surface area of 1024π square inches
agasfer [191]

Answer:

<h2>R = 16 in</h2>

Step-by-step explanation:

The formula of a Surface Area of a sphere:

S.A.=4\pi R^2

R - radius

We have

S.A.=1024\pi\ in^2

Substitute:

4\pi R^2=1024\pi               <em>divide both sides by π</em>

4R^2=1024             <em>divide both sides by 4</em>

R^2=256\to R=\sqrt{256}\\\\R=16\ in

4 0
3 years ago
Planes Q and R are parallel. Explain how you know lines a and b are skew.
IrinaVladis [17]
By definition, skew lines are a pair of lines that are not parallel but do not intersect each other either. Hence, the conclusion would be, the lines are non-coplanar. An example would two random lines drawn in the x and y axes in a cartesian plane, respectively.
7 0
3 years ago
Read 2 more answers
The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i
kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

Now,

1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of 1+9\times2=19.

So, the sum of the first 1234 terms in the sequence is 2419.

8 0
2 years ago
A circle has an area of 2511 square centimeters. What is the length of its<br> radius?
romanna [79]

Answer:

r=28.27 cm aprox

Step-by-step explanation:

Well you know that the area of a circle is A= \pir^{2} so

2511=\pir^{2} so

r^{2}=2511/\pi

r=28.27 cm aprox

8 0
3 years ago
Read 2 more answers
A cyclist is riding from the city to the country. She rides 20 miles each hour. At the beginning of the 1 st hour, she is 10 mil
strojnjashka [21]

Answer:

450miles

Step-by-step explanation:

Because she is riding at 20 miles per houre means that she ride 450 miles in 5 houre.

7 0
2 years ago
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