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2 years ago

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If the national economy shrank at an annual rate of 6% per year for four consecutive years, then the economy shrank by 24% ov

er the four-year period

1 answer:

vodka [1.7K]2 years ago

7 0

What is the question?

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Mrs. Smith's class is working on a variety of science experiments. Each

SVETLANKA909090 [29]

Answer:

66

Step-by-step explanation:

If there are <em>n</em> students, then the number of pairs is $\frac{n(n-1)}{2}$ .

With 12 students, $\frac{12(12-1)}{2} = \frac{132}{2}=66$ pairs can be formed.

The reason the formula works is this: Each of the 12 students can be paired with 11 other students (no student is paired with him/her self). But counting 12 x 11 = 132 counts each pair <u>twice</u>. Example: student A can be paired with student B,..., student B can be paired with student A. The pair was counted two times.

See the attached image that shows pairings of 5 students. There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.

8 0

2 years ago

1. John’s age is three times that of his sister. When you add John’s age to his sister's age, you get 36. How old are John and h

iren [92.7K]

Answer:

sister = 6 years

John=18 years

Step-by-step explanation:

A(S) + 12 = 3 * A(S), subtracting A(S) from both sides one gets 12 = 2 * A(S). Now dividing both sides by 2 we get A(S) = 12/2 = 6 . Therefore, the age of the sister is 6 years when her brother John is three times as old, that is 18 years.

6 0

2 years ago

Read 2 more answers

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

2 years ago

Which equation describes how the parent function y=x^3, is vertically streched by a factor of 4

Murljashka [212]

Answer:

$y=4x^{3}$

Step-by-step explanation:

It is known that,

<em>'Vertical stretch, stretches the function up and down towards the y-axis'.</em>

The general form of vertical stretch is given by 'kf(x)', where k>1 is the factor by which function is stretched.

As, we have the function $y=x^{3}$ which is stretched by a factor of 4.

Thus, the new function will be $y=4x^{3}$ .

Hence, the equation for the vertical stretch is $y=4x^{3}$ .

8 0

3 years ago

Please help will give you Brainliest *image

Drupady [299]

Answer:

5 folders and 5 pens = yes

6 pens and 6 erasers = yes

1 pen and 4 notebooks = no

3 folders and 7 erasers = no

4 folders and 2 notebooks = yes

Step-by-step explanation:

Max total = $10

(5 folders x 1.29) + (5 pens x 0.70)

6.45 + 3.50 = 9.95

(6 pens x 0.70) + (6 erasers x 0.89)

4.20 + 5.34 = 9.54

(1 pen × 0.70) + (4 notebooks × 2.35)

0.70 + 9.40 = 10.10

(3 folders × 1.29) + (7 erasers × 0.89)

3.98 + 6.23 = 10.21

(4 folders × 1.29) + (2 notebooks × 2.35)

5.16 + 4.70 = 9.86

7 0

2 years ago