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3 years ago

Which expression is equivalent to

Mathematics

1 answer:

Mrac [35]3 years ago

7 0

$\sqrt{ \cfrac{225}{625}m^4n^6 }= \cfrac{15}{25}m^2|n|^3= \cfrac{3}{5}m^2|n|^3$

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Is <img src="https://tex.z-dn.net/?f=2%5E%7B-3%7D" id="TexFormula1" title="2^{-3}" alt="2^{-3}" align="absmiddle" class="latex-f

TEA [102]

Answer:

Rational

Step-by-step explanation:

$2^{-3}$ simplifies to $\frac{1}{8}$ .

Therefore, it is rational.

$2^{-3}\\\\\text {Apply negative exponent rule: } a^{-n} = \frac{1}{a^n} \\2^{-3}= \frac{1}{2^3}\\ \rightarrow 2^3 = 2*2*2=8\\\boxed{2^{-3}=\frac{1}{8}}$

<em>Brainliest Appreciated. </em>

5 0

2 years ago

A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a diam

Inga [223]

Answer:

$a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}$

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

Let A denotes the event that the card is a diamond and B denotes the card is red.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}$

Let A denotes the event that the card is red and B denotes the card is diamond.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}$

Let A denotes the event that the card is nine and B denotes the card is red.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}$

Let A denotes the event that the card is a king and B denotes the card is a face card.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}$

7 0

2 years ago

Victoria kicked a soccer ball laying on the ground. It was in the air for 6 seconds before it hit the ground. While the soccer b

aniked [119]

Answer:3, 25

Step-by-step explanation:

The seconds should be the x-axis and the height is y axis. Also thinking about how a kicked ball makes an arch, the max is 25, and the mid point between 0 and 6 is 3.

7 0

2 years ago

Earl is spending money at a average rate of $675 per week after 11 weeks his savings is down to $13,500. Write an explicit equat

Gala2k [10]

Answer:

20925

Step-by-step explanation:

multiply 675 by 11 to get 7425. Add 7425 to 13500 to get 20925. To check minus 20925 by 7425. I got 13500. So this answer is reasonable.

6 0

2 years ago

At a university, Todd deposits $100 into his cafeteria account. He spends $5 on dinner every day. Seth deposits $140 into his ac

wolverine [178]

Answer:

The answer is 8 days.

Step-by-step explanation:

By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table

Day - Todd - Seth

1 - 95 - 130

2 - 90 - 120

3 - 85 - 110

4 - 80 - 100

5 - 75 - 90

6 - 70 - 80

7 - 65 - 70

8 - 60 - 60

7 0

2 years ago