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3 years ago

What is the value of (f – g)(144)?

1 answer:

5 0

(f - g) (144) Multiply 144 by both variables in the other set of parentheses.

[(144) (f) - (144) ( g)] Simplify

144 f - 144g

You might be interested in

Find two consecutive integers whose sum is the square of 7

Maksim231197 [3]

Answer:

Step-by-step explanation:

Two consecutive integers be x and (x+1)

x + x +1 = 7²

2x + 1 = 49

2x = 49 - 1

2x = 48

x = 48/2

x = 24

The consecutive integers are: 24,25

3 0

3 years ago

How do you solve the system 3x-y z=5, x 3y 3z=-6, and x 4y-2x=12?

dlinn [17]

3x - y + z = 5 . . . (1)
x + 3y + 3z = -6 . . . (2)
x + 4y - 2z = 12 . . . (3)

From (2), x = -6 - 3y - 3z . . . (4)
Substituting for x in (1) and (3) gives
3(-6 - 3y - 3z) - y + z = 5 => -18 - 9y - 9z - y + z = 5 => -10y - 8z = 23 . . (5)
-6 - 3y - 3z + 4y - 2z = 12 => y - 5z = 18 . . . (6)

(6) x 10 => 10y - 50z = 180 . . . (7)
(5) + (7) => -58z = 203
z = 203/-58 = -3.5

From (6), y - 5(-3.5) = 18 => y = 18 - 17.5 = 0.5
From (4), x = -6 - 3(0.5) - 3(-3.5) = -6 - 1.5 + 10.5 = 3

x = 3, y = 0.5, z = -3.5

8 0

3 years ago

How many solutions does the equation have?<br> -4x - 9 = 12 - 4x

pickupchik [31]

Answer:

No Solution

Step-by-step explanation:

-4x - 9 = 12 - 4x

You add 4x on both sides

-9 ≠ 12

No Solution

4 0

2 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

Determine the common ratio and find the next three terms of the geometric sequence t8, t5, t2

attashe74 [19]

The common ratio of the given geometric sequence is the number that is multiplied to the first term in order to get the second term. Consequently, this is also the number multiplied to the second term to get the third term. This cycle goes on and on until a certain term is acquired. In this item, the common ratio r is,

r = t⁵/t⁸ = t²/t⁵

The answer, r = t⁻³.

The next three terms are,

n₄ = (t²)(t⁻³) = t⁻¹
n₅ = (t⁻¹)(t⁻³) = t⁻⁴
n₆ = (t⁻⁴)(t⁻³) = t⁻⁷

The answers for the next three terms are as reflected above as n₄, n₅, and n₆, respectively.

3 0

3 years ago

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