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3 years ago

If 8^y=16^y+2, what is the value of y? A) -8 B) -4 C) -2 D) -1

1 answer:

Pie3 years ago

6 0

$8=2^3;\ 16=2^4$

$Use:\ (a^n)^m=a^{nm}$

$8^y=16^{y+2}\\\\(2^3)^y=(2^4)^{y+2}\\\\2^{3y}=2^{4(y+2)}\iff3y=4(y+2)\\\\3y=4y+8\ \ \ |-4y\\\\-y=8\to y=-8$

Answer: A) -8.

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Two posts that hold up a sign are parallel. M < 1 = 75° use the given measurements to find the value of x. I think it’s 19 bu

polet [3.4K]

The two posts are parallel lines. The ground is a transversal.

The angles measuring 4x and 75 are same side interior angles, so they are supplementary. Their measures add up to 180.

4x + 75 = 180

4x = 105

x = 26.25

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3 years ago

Read 2 more answers

A jar contains 8 4/9 pounds of jam. If Sam eats 3 2/5 pounds of the jam, how many pounds of jam remains in the jar?

zepelin [54]

$\bf 8\frac{4}{9}\implies \cfrac{8\cdot 9+4}{9}\implies \cfrac{76}{9}
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3\frac{2}{5}\implies \cfrac{3\cdot 5+2}{5}\implies \cfrac{17}{5}\\\\
-------------------------------\\\\
\cfrac{76}{9}-\cfrac{17}{5}\impliedby \textit{let's use an LCD of 45}\implies \cfrac{5\cdot 76-9\cdot 17}{45}
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\cfrac{380-153}{45}\implies \cfrac{227}{45}\implies \boxed{5\frac{2}{45}}
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5\frac{2}{45}\implies \cfrac{5\cdot 45+2}{45}\implies \cfrac{227}{45}$

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3 years ago

Maria studied the traffic trends in India. She found that the number of cars on the roads increases by 10% each year. If there w

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You would do

(1.1)(80,000,000)=88,000,000

That is the total cars for year two. To find the increase you would do

(1.1)(88,000,000)=96,800,000

Then you would subtract year 2 from year three

96,800,000-88,000,00=8,800,000

That gives you ur answer.

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3 years ago

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Number 6,8, and 10.

Aliun [14]

I think number 10 is 4/9

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3 years ago

Suppose that a random sample of 10 adults has a mean score of 62 on a standardized personality test, with a standard deviation o

aniked [119]

Answer:

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*\frac{4}{\sqrt{10}} = 2.08$

The lower end of the interval is the sample mean subtracted by M. So it is 62 - 2.08 = 59.92

The upper end of the interval is the sample mean added to M. So it is 62 + 2.08 = 64.08.

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

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2 years ago