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Vsevolod [243]
3 years ago
10

A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350

butterflies in the first generation, how many will there be by the 19th generation?
Answer the question with all work shown. Thanks
Mathematics
1 answer:
kap26 [50]3 years ago
7 0

Answer:

378.5 or just 378

Step-by-step explanation:

This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by.  When x = 0, y = 350 so that's the y-intercept of our equation.)

The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.

Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.

If we want y when x = 19, plug 19 in for x and solve for y:

y = 1.5(19) + 350

y = 378.5

Since we can't have .5 of a butterfly we will round down to 378

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For h(x) = -7x + 10, x =1

For r(x) = 4/5x+ 7 , x = -15

Step-by-step explanation:

in order to find the value of x on which the functions will have given values, we will put the functions equal to the given values

So,

<u>h(x) = -7x + 10; h(x) = 3</u>

h(x) = -7x+10\\3 = -7x+10\\3-10 = -7x+10-10\\-7 = -7x

Dividing both sides by -7

\frac{-7x}{-7} = \frac{-7}{-7}\\x = 1

<u>r(x) =  4/5x+7; r(x) = -5</u>

r(x) = \frac{4}{5}x +7\\-5 = \frac{4}{5}x +7\\-5-7 = \frac{4}{5}x\\-12 = \frac{4}{5}x\\x = -12 * \frac{5}{4}\\x = -15

<u></u>

Keywords: Functions

Learn more about functions at:

  • brainly.com/question/1406585
  • brainly.com/question/1414350

#LearnwithBrainly

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A reflection of the pink triangle is shown. Which transformation makes this reflection?
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Step-by-step explanation:


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I think A is the answer

Step-by-step explanation:

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Iris wants to buy two necklaces, one for her sister and one for herself. The necklace for her sister costs $42.00, and the neckl
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Answer:

$75.60

Step-by-step explanation:

First, find the total cost without tax:

42 + 28

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Then, to find the price with sales tax, multiply this by 1.08:

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= 75.6

So, the total cost of her purchases was $75.60

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3 years ago
Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distribut
defon

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125:

This means that n = 125, s = \frac{7320}{\sqrt{125}} = 654.72

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{39000 - 39725}{654.72}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample mean would be at least $39000

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