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3 years ago

What does proportion mean in algebra when dealing with graphs

1 answer:

andrey2020 [161]3 years ago

3 0

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if y=Mc

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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.

3 0

3 years ago

The ratio of a basketball player's completed free throws to attempted free throws is 4 to 7. if she completed 12 free throws, fi

Artemon [7]

Ratio of the free throws completed to attempted free throws is given to be 4:7. This ratio should be equal to the ratio of the next case. Let x be the number of free throws attempted. The proportion takes a form of,
(4 completed / 7 attempted) = (12 completed / x attempted)
Solving for x gives x = 21. Thus, the answer is letter c. which is the second among the choices.

6 0

3 years ago

Read 2 more answers

All of the following fractions are proper fractions, except

eduard

Answer:

1/2

Step-by-step explanation:

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3 years ago

Answer this question! i am having some trouble in khan..

anzhelika [568]

The correct answer is 33 days

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2 years ago

Stephen purchased a guitar, which was originally priced at $80 but discounted at 25%. He also had to pay 5% sales tax. What amou

nikdorinn [45]

Discounted by 25% means he paid 75% of the original price:

80 x 0.75 = $60

Now multiply the sale price by 1 + tax rate:

60 x 1.05 = 63

He paid $63 total.

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2 years ago