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4 years ago

What is the following quotient? √96/√8

Mathematics

2 answers:

Kipish [7]4 years ago

7 0

Hope this helps. Might have a few extra steps.

inysia [295]4 years ago

4 0

Answer:

$2\sqrt{3}$

Step-by-step explanation:

We are asked to find the quotient of expression: $\frac{\sqrt{96}}{\sqrt{8}}$

Upon using the quotient rules for radicals we will get,

$\frac{\sqrt{96}}{\sqrt{8}} =\sqrt{\frac{96}{8}$

Now let us cancel out GCF of 96 and 8.

$\sqrt{\frac{96}{8}}=\sqrt{12}$

Now let us factor out perfect square from $\sqrt{12}$

$\sqrt{12}=\sqrt{4}\times\sqrt{3}$

$\sqrt{4}\times\sqrt{3}=2\sqrt{3}$

Therefore, our radical expression simplifies to $2\sqrt{3}$ .

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

App 19.study

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Answer:

$1 \to 22 \to 0.176$

$2 \to 13 \to 0.104$

$3 \to 18 \to 0.144$

$4 \to 29 \to 0.232$

$5 \to 37 \to 0.296$

$6 \to 6 \to 0.048$

Step-by-step explanation:

Given

$n = 125$

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

$Pr = \frac{Frequency}{n}$

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

$Pr(2) = \frac{13}{125} = 0.104$

$Pr(4) = \frac{29}{125} = 0.232$

$Pr(6) = \frac{6}{125} = 0.048$

When the frequency is to be calculated, we use:

$Pr = \frac{Frequency}{n}$

$Frequency = n * Pr$

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

$Frequency(3) = 125 * 0.144 = 18$

$Frequency(5) = 125 * 0.296 = 37$

For roll of 1 where the frequency and the probability are not known, we use:

$Total \ Frequency = 125$

So:

Frequency(1) added to others must equal 125

This gives:

$Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125$

$Frequency(1) + 103 = 125$

Collect like terms

$Frequency(1) =- 103 + 125$

$Frequency(1) =22$

The probability is then calculated as:

$Pr(1) = \frac{22}{125}$

$Pr(1) = 0.176$

So, the complete table is:

$1 \to 22 \to 0.176$

$2 \to 13 \to 0.104$

$3 \to 18 \to 0.144$

$4 \to 29 \to 0.232$

$5 \to 37 \to 0.296$

$6 \to 6 \to 0.048$

5 0

3 years ago

Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the n

-Dominant- [34]

Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

$A=P(1+r)^t$

Plugging values in formula, we get

$329.49=300(1+r)^2$

$\mathrm{Divide\:both\:sides\:by\:}300$

$\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}$

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Taking square root on both sides, we get

$1+r=\sqrt{1.0983}$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1+r-1=\sqrt{1.0983}-1$

$r=\sqrt{1.0983}-1$

$r=1.048-1$

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

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3 years ago

Ron finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his s

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Answer:

15,120 for the first question. 1,680 if one of the books is a must

Step-by-step explanation:

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Multiplying all of that out gets you 15,120.

The second problem is even easier. Since one of the books is already chosen for him, he starts off only having 8 options. Since he is only choosing four books this time, we are only multiplying four numbers.

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Multiplying all of that out tells you there are 1,680 ways he can make his selection in the second scenario.

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3 years ago