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2 years ago

What is the volume of the following rectangular prism?

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

3 0

Answer:

73.5

Step-by-step explanation:

Step 1: 21/2 divided by 2 = 21/4

Step 2: 21/4 times 21/4 times 8/3 =

Answer: 73.5

The green shaded box is there to show that that is the base are to find the two sides that were multiplied to get that do the first step. Then do your basic volume formula: length times width times height.

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The half life of silicone-32 is 710 years. If 30 grams is present now, how much will be present in 300 years?

Irina18 [472]

Answer:

22.38 g of silicone-32 will be present in 300 years.

Step-by-step explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

$N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{1/2}}$

where,

$N(t)$ = quantity of the substance remaining

$N_0$ = initial quantity of the substance

$t$ = time elapsed

$t_{1/2}$ = half life of the substance

From the information given we know:

The initial quantity of silicone-32 is 30 g.
The time elapsed is 300 years.
The half life of silicone-32 is 710 years.

So, to find the quantity of silicone-32 remaining we apply the above equation

$N(t)=30\left(\frac{1}{2}\right)^{\frac{300}{710}}=30\left(\frac{1}{2}\right)^{\frac{30}{71}}\approx22.38 \:g$

22.38 g of silicone-32 will be present in 300 years.

7 0

2 years ago

Are 8x+ 16 and 4(2x+4) equivalent

8090 [49]

Yes they are equivalent

8 0

3 years ago

I need the answer for this problem please

Savatey [412]

Answer:

Step-by-step explanation:

Find all probabilities:

A. False

$Pr(\text{red shirt}|\text{large shirt})=\dfrac{\text{number red large shirts}}{\text{number large shirts}}=\dfrac{42}{77}=\dfrac{6}{11}\\ \\Pr(\text{large shirt})=\dfrac{\text{number large shirts}}{\text{number shirts}}=\dfrac{77}{165}=\dfrac{7}{15}$

B. True

$Pr(\text{blue shirt}|\text{large shirt})=\dfrac{\text{number blue large shirts}}{\text{number large shirts}}=\dfrac{35}{77}=\dfrac{5}{11}\\ \\Pr(\text{blue shirt})=\dfrac{\text{number blue shirts}}{\text{number shirts}}=\dfrac{75}{165}=\dfrac{5}{11}$

C. False

$Pr(\text{shirt is medium and blue})=\dfrac{\text{number medium and blue shirts}}{\text{number shirts}}=\dfrac{48}{165}=\dfrac{16}{55}\\ \\Pr(\text{medium shirt})=\dfrac{\text{number medium shirts}}{\text{number shirts}}=\dfrac{88}{165}=\dfrac{8}{15}$

D. False

$Pr(\text{large shirt}|\text{red shirt})=\dfrac{\text{number red large shirts}}{\text{number red shirts}}=\dfrac{42}{90}=\dfrac{7}{15}\\ \\Pr(\text{red shirt})=\dfrac{\text{number red shirts}}{\text{number shirts}}=\dfrac{90}{165}=\dfrac{6}{11}$