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AveGali [126]
3 years ago
5

A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg. What is the densi

ty of ethyl alcohol in pound-mass per cubic foot? (Assume the density of ethyl alcohol is 9.01 ✕ 102 kg/m3.)
Mathematics
1 answer:
Rashid [163]3 years ago
3 0
<h2>Density of ethyl alcohol is 56.25 lbm/ft³ </h2>

Step-by-step explanation:

We have 1 lbm = 0.454 kg

1 kg = 2.203 lbm

1 m = 3.28 ft

Density of ethyl alcohol = 9.01 x 10² kg/m³

\texttt{Density = }\frac{9.01\times 10^2\times 2.203}{3.28^3}=56.25lbm/ft^3

So

Density of ethyl alcohol = 56.25 lbm/ft³

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2nd number:12-4=8

3rd number: given

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A crayon has a mass of 30 grams. How many crayons can be made with 30 kilograms of colored wax
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$10,000 at an annual rate of 7%, compounded semi-annually, for 2 years
forsale [732]

Answer:

\$13,107.96

Step-by-step explanation:

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Therefore, we can set up the following equation to find the new balance after 2 years:

\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}

8 0
2 years ago
Let X1, X2 and X3 be three independent random variables that are uniformly distributed between 50 and 100.
sergejj [24]

Answer:

a) the probability that the minimum of the three is between 75 and 90 is 0.00072

b) the probability that the second smallest of the three is between 75 and 90 is 0.396

Step-by-step explanation:

Given that;

fx(x) = { 1/5 ; 50 < x < 100

              0, otherwise}

Fx(x) = { x-50 / 50 ; 50 < x < 100

                          1 ;   x > 100

a)

n = 3

F(1) (x) = nf(x) ( 1-F(x)^n-1

= 3 × 1/50 ( 1 - ((x-50)/50)²

= 3/50 (( 100 - x)/50)²

=3/50³ ( 100 - x)²

Therefore P ( 75 < (x) < 90) =  ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx

= 3/50³ [ -2 (100 - x ]₇₅⁹⁰

= (3 ( -20 + 50)) / 50₃

= 9 / 12500 = 0.00072

b)

f(k) (x) = nf(x)  ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k

Now for n = 3, k = 2

f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))

= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)

= 6/50³ ( 150x - x² - 5000 )

therefore

P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx

= 99 / 250 = 0.396

3 0
3 years ago
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