Find the domain and range of the function graphed below. Write your answers in interval notation.

Mathematics

1 answer:

AfilCa [17]2 years ago

8 0

Answer:

Domain: $(-\infty, \infty)$
Range: $(-\infty, -1]$

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

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There are approximately 3,000 bass in a lake. The population grows at a rate of 2% per year. Round answers to the nearest tenth.

Tamiku [17]

Answer:

years 1–4: 62.4 bass per year

years 5–8: 67.6 bass per year

Step-by-step explanation:

If the population in year n is ...

p(n) = 3000·1.02^n

then the average rate of change from year 1 to year 4 is ...

(p(4) -p(1))/(4 -1) = 3000(1.02^4 -1.02^1)/3 = 1020·(1.02^3 -1) ≈ 62.4

The average rate of change for years 1–4 is 62.4 bass per year.

For years 5–8, the rate of change is similarly computed:

(p(8) -p(5))/(8 -5) = 3000(1.02^8 -1.02^5)/3 = 1000·1.02^5·(1.02^3 -1) ≈ 67.6

The average rate of change for years 5–8 is 67.6 bass per year.

5 0

3 years ago

Read 2 more answers

Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean’s weekly income

Sauron [17]

Answer:

d. 0.303

Step-by-step explanation:

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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.

Distribution of the difference between Sean's and Evan's income:

Sean has mean 225, Evan 240. So

$\mu = 225 - 240 = -15$