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stich3 [128]
3 years ago
7

Distance between (-5,2) and (-5,-4)

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
7 0

Answer:

The distance between these two points is 6

Step-by-step explanation:

distance formula

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5 2/5+a=71/2 what is the answer to this problem
Gre4nikov [31]
Answer:
30 1/10

Step by step explanation:
71/2-5 2/5= 30 1/10
30 1/10 divided by a (also know as 1) = 30 1/10
3 0
3 years ago
Please help fast!!!!!!!!!!!!!!
denis-greek [22]

Answer:

The third option, -1/2(30) = -15

Step-by-step explanation:

If it decreases by 1/2, we know it has to be -1/2, and the days we are given are 30. We need to multiply -1/2 by 30 in order to find the water level after 30 days, which would be -15 (inches?) I hope this helped.

5 0
3 years ago
In Pennsylvania the average IQ score is 101.5. The variable is normally distributed, and the population standard deviation is 15
blsea [12.9K]

Answer:

We conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, \bar{x} = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

H_{0}: \mu = 101.5\\H_A: \mu > 101.5

We use one-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{106.4 - 101.5}{\frac{15}{\sqrt{30}} } = 1.789

Now, z_{critical} \text{ at 0.05 level of significance } = 1.96

Since,  

z_{stat} > z_{critical}

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

5 0
3 years ago
What value of r is a solution to this equation? 387 divide by r = 9
Vlad1618 [11]

Answer:

A. 43

Step-by-step explanation:

8 0
3 years ago
Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find
inna [77]

Best guess for the function is

\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}

By the ratio test, the series converges for

\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1

When x=1, f(x) is a convergent p-series.

When x=-1, f(x) is a convergent alternating series.

So, the interval of convergence for f(x) is the <em>closed</em> interval \boxed{-1 \le x \le 1}.

The derivative of f is the series

\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n

which also converges for |x| by the ratio test:

\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1

When x=1, f'(x) becomes the divergent harmonic series.

When x=-1, f'(x) is a convergent alternating series.

The interval of convergence for f'(x) is then the <em>closed-open</em> interval \boxed{-1 \le x < 1}.

Differentiating f once more gives the series

\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)

The first series is geometric and converges for |x|, endpoints not included.

The second series is f'(x), which we know converges for -1\le x.

Putting these intervals together, we see that f''(x) converges only on the <em>open</em> interval \boxed{-1 < x < 1}.

6 0
2 years ago
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