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Eva8 [605]
2 years ago
7

the volume of a sphere whose diameter is 18 centimeters is 246 324 648 972 π cubic centimeters. if its diameter were reduced by

half, its volume would be 1/2 1/4 1/6 1/8 of its original volume.
Mathematics
1 answer:
Hatshy [7]2 years ago
4 0
Radius of sphere = 18/2 = 9 cm

Volume of sphere = 4/3 πr^3 = 4/3 x π x (9)^3 = 972 π cubic cm

If the diameter is reduced by half, then
Volume = 4/3 x π x (9/2)^3 = 4/3 x π x (9)^3 x (1/2)^3 = 1/8(972)

Therefore, new volume is 1/8 of original volume.
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If a random variable X is exponentially distributed with parameter λ=2, then P(X≥1) is equal to
Rasek [7]

Answer:

D. 0.1353

B. 0.0473

Step-by-step explanation:

For an exponentially distributed random variable, the cumulative distribution function is:

P(x\leq a) = 1 - e^{-\lambda a}\\P(x\geq a) = e^{-\lambda a}

with parameter λ=2, then P(X≥1) is equal to:

P(x\geq 1) = e^{-2*1}=0.1353

D. 0.1353

with parameter λ=1.5, then P(2≤X≤4) is equal to

P(2\leq x \leq 4) = P(x \leq 4) - P(x\leq 2)\\P(2\leq x \leq 4) =1 - (e^{-1.5*4}) - (1-(e^{-1.5*2}))\\P(2\leq x \leq 4) = 0.0473

B. 0.0473

7 0
2 years ago
How much would Carol have to invest today at 6.2% compounded annually to have $4600 for a vacation to China in two years?
KiRa [710]
\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$4600\\
P=\textit{original amount deposited}\\
r=rate\to 6.2\%\to \frac{6.2}{100}\to &0.062\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, so once}
\end{array}\to &1\\

t=years\to &2
\end{cases}
\\\\\\
4600=P\left(1+\frac{0.062}{1}\right)^{1\cdot 2}

solve for P
5 0
2 years ago
Fredric worked 46 hours last week. his hourly rate is $8.50. What was his gross pay?
Nostrana [21]

Answer:

$391

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
PLS HALP ME!!!!!! You have $6.50 to make copies. Each copy costs $0.45. Write and solve an inequality that represents the number
serious [3.7K]

Step-by-step explanation:

Variable x = number of copies

6.50 <= 0.45x

Divide both sides by 0.45

6.50 ÷ 0.45 <= 0.45x ÷ 0.45

14.4444.... <= x

No more than 14 copies

6.50 <= 0.45x

6.50 <= 0.45(14.444)

7 0
2 years ago
Jenny makes food for her hummingbird feeders. The food is made up of 1 part sugar and 4 parts water. She uses 3434 cup of sugar
4vir4ik [10]
1:4
when sugar=34
times 34 both sides
34*4=136
1:4=34:136
should use 136 cups of water
that is alot of water
that's a big feeder (8.5 gallons. the water alone weighs about 74.8lb)

should use 136 cups (wow)
5 0
2 years ago
Read 2 more answers
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