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3 years ago

What is the value of n in the equation 1/2(n-1) - 3 = 3 - (2n + 3)?

Mathematics

1 answer:

natulia [17]3 years ago

4 0

Hey there! :)

1/2(n - 1) - 3 = 3 - (2n + 3)

Simplify.

1/2n - 1/2 - 3 = 3 - 2n - 3

Add like terms.

1/2n - 3 1/2 = -2n

Add 3 1/2 to both sides.

1/2n = -2n + 3 1/2

Then, add 2n to both sides.

1/2n + 2n = 3 1/2

Simplify!

2 1/2n = 3 1/2

Make everything into improper fractions!

5/2n = 7/2

Multiply everything by 2 to get rid of the denominators.

5/2n × 2 = 7/2 × 2

Simplify!

5n = 7

Divide both sides by 5.

n = 7/5

Hope this helped! :)

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When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was o

Roman55 [17]

Answer:

Option C.

Step-by-step explanation:

Given information:

Sample size = 150

Number of Opinions = 3 (Yes, No, No Opinion)

Yes = 40

No = 60

No opinion = 50

We need to find the expected frequency for each group.

Expected frequency for each group is the quotient of sample size and number of opinions.

$\text{Expected frequency for each group}=\dfrac{\text{Sample size}}{\text{Number of Opinions}}$

$\text{Expected frequency for each group}=\dfrac{150}{3}$

$\text{Expected frequency for each group}=50$

Therefore, the correct option is C.

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3 years ago

(5 points)

Schach [20]

Answer:

The original Slope is y=-1/3x-2

The perpendicular slope would be y=3x+b

Step-by-step explanation:

Original Slope:

You already have the y-interecpet, (0,-2), and you know two points (0,-2) and (-6,0), so you can find the slope with (y1-y2)/(x1-x2) so in this case, it would be (0-(-2))/(-6-0)= -1/3 and you can find y=1/3x-2.

Perpendicular Slope:

The slope of any perpendicular line would be the reciprocal of the original. So the reciprocal of -1/3 is 3. The b can be any real number because no matter the y-intercept the slope would still be perpendicular

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3 years ago

A researcher is planning to compare the effects of two different types of lights on the growth of bean plants. She expects that

kicyunya [14]

Answer:

The sample size is $n = 36$

Step-by-step explanation:

From the question we are told that

The sample standard deviation is $s = 1.5$

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The standard error is $SE = \frac{ \= x_1 - \= x_2}{4}$

=> $SE = \frac{1}{4}$

Let assume that the confidence level is 95% hence the level of significance is

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

=> $\alpha = 0.05$

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

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

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * SE$

$E = 1.96 * \frac{1}{4}$

$E = 0.49$

Generally the sample size is mathematically represented as

$n =[ \frac{Z_{\frac{\alpha }{2} * s^2}}{E}]^2$

=> $n = [\frac{1.96 * 1.5}{0.49} ]^2$

=> $n = 36$

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