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3 years ago

At Emily's summer camp, there are

Mathematics

2 answers:

nataly862011 [7]3 years ago

7 0

Answer:

15 counselors

Step-by-step explanation:

The ratio of counselors to girls is 6:40. Set this as a proportion:

$\frac{6}{40}$ = $\frac{x}{100}$

Cross multiply to solve: 6×100=40x

600=40x

x=15

To satisfy the ratio, there needs to be 15 counselors for 100 girls.

Stells [14]3 years ago

6 0

Answer:

Step-by-step explanation:

3 counselors for every 20 girls

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3 years ago

What is the length of the radius? startfraction 6 over 85 endfraction startfraction 85 over 12 endfraction startfraction 121 ove

melomori [17]

The length of the radius will be 22 units.

<h3>What is the radius?</h3>

The radius of a circle is defined as the distance of the center of the circle to its outer layer. It is a locus of a point present at some distance from the center point.

Now from the question, we have an expression:

$r=(\dfrac{6}{85} )\times(\dfrac{85}{12} )\times (\dfrac{121}{36} )\times (\dfrac{157}{12} )$

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Hence the length of the radius will be 22 units.

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2 years ago

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Step-by-step explanation:

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3 years ago

Write and solve the equation. Show all work.

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Step-by-step explanation:

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3 years ago

For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of

Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is $(-1)^{k+1}(\frac{1}{2^{k}})$ .

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as $(-1)^{k+1}(\frac{1}{2^{k}})$ .

where k is from 1 to 10.

By the given expression sequence will be $\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......$

In this sequence first term "a" = $\frac{1}{2}$

and common ratio in each successive term to the previous term is 'r' = $\frac{\frac{(-1)}{4}}{\frac{1}{2} }$

r = $-\frac{1}{2}$

Since the sequence is infinite and the formula to calculate the sum is represented by

$S=\frac{a}{1-r}$ [Here r is less than 1]

$S=\frac{\frac{1}{2} }{1+\frac{1}{2}}$

$S=\frac{\frac{1}{2}}{\frac{3}{2} }$

S = $\frac{1}{3}$

Now we are sure that the sum of infinite terms is $\frac{1}{3}$ .

Therefore, sum of 10 terms will not exceed $\frac{1}{3}$

Now sum of first two terms = $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

Now we are sure that sum of first 10 terms lie between $\frac{1}{4}$ and $\frac{1}{3}$

Since $\frac{1}{2}>\frac{1}{3}$

Therefore, Sum of first 10 terms will lie between $\frac{1}{4}$ and $\frac{1}{2}$ .

Option D will be the answer.

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3 years ago