The mass of 75000 molecules of oxygen is _

Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 125 in^3 and the volume of the l

Fittoniya [83]

Answer:

$\boxed{ \frac{ 5}{ 9}}\\$

Step-by-step explanation:

Data:

V₁ = 125 in³

V₂ = 729 in³

Calculations:

A scale factor (C) is the ratio of corresponding side lengths (l) of the two prisms.

$C=\frac{ l_{1}}{ l_{2}}\\$

The volume ratio is the cube of the scale factor.

$\frac{V_{1}}{ V_{2}} = C^{3}\\$

$\frac{125}{ 729} = C^{3}\\$

$C = \sqrt [3]{\frac{ 125}{729 }} = \frac{5 }{9 }\\$

$\boxed{ \textbf{The scale factor is } \frac{ 5}{ 9}.}\\$

7 0

3 years ago

Jesse has a bottle of lemonade one third has been drunk he shares it between himself and his three friends what fraction of the

Tasya [4]

Answer:

1/9

Step-by-step explanation:

1/3 times 1/3 = 1/9

4 0

3 years ago

Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he

algol13

ANSWER
0.756

EXPLANATION

Let x represent number of correct answers.

We can find

$P(x = 0 \text{ or } x = 1)$

which leads us to

$P(x\ge 2) = 1 - P(x = 0\text{ or }x = 1)$

which uses the compliment of $P(x = 0\text{ or }x = 1)$ to find the probability of getting at least 2 questions correct.

Note that since $P(x=0)$ and $P(x=1)$ are mutually exclusive, we have

$P(x = 0\text{ or }x = 1) = P(x=0) + P(x=1)$

Then $P(x=0) = 3^{10}/4^{10} = (3/4)^{10}$ as we have $3^{10}$ to answer the questions incorrectly divided by the total $4^{10}$ to answer the questions.

Exactly 1 answer correct: $P(x=1) = {}_{10}C_1 \cdot(3/4)^9(1/4)^1$

Therefore

$\begin{aligned}
P(x \ge 2) &= 1 - P(x = 0\text{ or }x =1) \\
&=1 - \big[P(x=0) + P(x=1)\big] \\
&=1 - \left[ (3/4)^{10} + {}_{10}C_1 \cdot (3/4)^9(1/4)^1 \right] \\
&\approx 0.756
\end{aligned}$