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3 years ago

Which expression represents the distance between point (0, a) and point (a, 0) on a coordinate grid?

Mathematics

2 answers:

o-na [289]3 years ago

5 0

Answer:

$\sqrt{2} a$

Step-by-step explanation:

The distance between point (x1,y1) and (x2,y2) on a coordinate plane is given by expression $\sqrt{(x1-x2)^2+(y1-y2)^2}$

In the problem given coordinate points are

(0, a) and (a, 0).

Thus, distance between these points are given by

$distance = \sqrt{(x1-x2)^2+(y1-y2)^2}\\=>distance = \sqrt{(0-a)^2+(a-0)^2}\\=>distance = \sqrt{(a)^2+(a)^2}\\\\=>distance = \sqrt{2a^2}\\=>distance = \sqrt{2} a$

Thus , expression $\sqrt{2} a$ gives the distance between point (0, a) and point (a, 0) on a coordinate grid.

olasank [31]3 years ago

3 0

Answer:

A) √2a^2

Step-by-step explanation:

I just took the quiz on edge

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A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be c

Anna [14]

Answer:

The interval from the sample of size 400 will be approximately <u>One -half as wide</u> as the interval from the sample of size 100

Step-by-step explanation:

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the 95% confidence interval is dependent on the value of the margin of error at a constant sample mean or sample proportion

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

Here assume that $Z_{\frac{\alpha }{2} } \ and \ \sigma \$ is constant so

$E = \frac{k}{\sqrt{n} }$

=> $E \sqrt{n} = K$

=> $E_1 \sqrt{n}_1 = E_2 \sqrt{n}_2$

So let $n_1 = 400$ and $n_2 = 100$

=> $E_1 \sqrt{400} = E_2 \sqrt{100}$

=> $E_1 = \frac{\sqrt{100} }{\sqrt{400} } E_2$

=> $E_1 = \frac{1}{2 } E_2$

So From this we see that the confidence interval for a sample size of 400 will be half that with a sample size of 100

7 0

3 years ago

a sequence has a first term of 2 and a constant ratio of _3/2 what are the first five terms of the sequence

soldi70 [24.7K]

This is a geometric sequence with a=2, r= -3/2.
Therefore,
a₁ = 2
a₂ = 2*(-3/2) = -3
a₃ = 2*(-3/2)² = 9/2 = 4.5
a₄ = 2(-3/2)³ = -27/4 = -6.75
a₅ = 2(-3/2)⁴ = 81/8 = 10.125

Answer:
In fractions, the first five terms are
2, -3, 9/2, -27/4, 81/8
In decimals, the first five terms are
2.000, -3.000, 4.500, -6.750, 10.125

5 0

3 years ago

5(x+3)-7(6-3)+29=50-3(8-x)

Sveta_85 [38]

Answer:

$\quad x=\frac{3}{2}$

Step-by-step explanation:

$7\left(6-3\right)=21$ , $\mathrm{Expand\:}5\left(x+3\right)-21+29:\quad5x+23$ , $\mathrm{Expand\:}50-3\left(8-x\right):\quad 3x+26$ , Subtract 23 and 3x from both sides and simplify: $2x=3$ , Divide both sides by 2 and simplify: $x=\frac{3}{2}$