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3 years ago

Which expression shows the correct way to find the distance between (23,43) and (17,14) ?

Mathematics

2 answers:

oksano4ka [1.4K]3 years ago

6 0

I am pretty sure you subtract but in case it would be
(23,43) - (17,14).
(6,19) should be the answer

Oxana [17]3 years ago

4 0

Answer:

$d=\sqrt{(14-43)^{2}+(17-23)^{2}}$

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

In this problem we have

$A(23,43)\\B(17,14)$

substitute the values

$d=\sqrt{(14-43)^{2}+(17-23)^{2}}$

$d=\sqrt{841+36}$

$d=\sqrt{877}\ units$

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The director of a state agency believes that the average starting salary for clerical employees in the state is less than $35 c

MrRissso [65]

Answer:

There is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 35,000 dollars per year

Sample mean, $\bar{x}$ = 34,700 dollars per year

Sample size, n = 100

Alpha, α = 0.10

Population standard deviation, σ = 3,500 dollars per year

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}$

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

$z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571$

Now, $z_{critical} \text{ at 0.10 level of significance } = -1.28$

Since,

$z_{stat} > z_{critical}$

We fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.

3 0

3 years ago

Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e

Bingel [31]

Assuming the series is

$\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}$

The series will converge if

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|$

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

So the series will certainly converge if $-1$ , but we also need to check the endpoints of the interval.

If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

$\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0$

and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

6 0

4 years ago

SIMPLE SEVENTH GRADE MATH PROBLEM. GOVING BRAINLIEST

adelina 88 [10]

Answer:

D is the answer

Step-by-step explanation:

Well 35 dollar one time fee

plus 15 per hour

If used 1 hour 15+35=50

5 0

3 years ago

Read 2 more answers

Reporting Category: Geometry Standard: 10 G.3 Recognize and solve problems involving angles formed by transversals of coplanar l

Alexxx [7]

The measure in degrees would be 15<span />

4 0

3 years ago

1 L of a 78% acid solution was mixed with 6 L of a 64% acid solution. Find the concentration of the new mixture.

JulijaS [17]

The first solution contributes 0.78*1 = 0.78 L of acid.

The second contributes 0.64*6 = 3.84 L of acid.

There will be 7 L total of the new solution, and 3.84 + 0.78 = 4.62 total L of acid in it. So the new solution has a concentration of 4.62/7 = 0.66, or about 66%.

8 0

4 years ago