The answer is: 3.91 inches .
___________________________________________

Note: Volume of cylinder: V = (base area) * (height);

in which: V = volume = 384 in.³ ;
h = height = 8 in. ;
Base area = area of the base (that is; "circle") = π r² ;
in which; "r" = radius;
___________________________________________
Solve for "r" :
___________________________________________
V = π r² * (8 in.) ;

384 in.³ = (8 in.) * (π r²) ;
___________________________________________
Divide EACH SIDE of the equation by "8" ;
___________________________________________
(384 in.³) / 8 = [ (8 in.) * (π r²) in.] / 8 ;
___________________________________________
to get:
___________________________________________
48 in.³ = (π r²) in.² * in. ;
___________________________________________
↔ (π r²) in.² * in. = 48 in.³ ;
___________________________________________
Rewrite this equation; using "3.14" as an approximation for: π ;
__________________________________________________
(3.14 * r²) in.² * in. = 48 in.³
_______________________________________
Divide EACH SIDE of the equation by:

"[(3.14)*(in.²)*(in.)]" ; to isolate "r² " on one side of the equation;
(since we want to solve for "r") ;
_____________________________________________________
→ [(3.14 * r²) in.² * in.] / [(3.14)*(in.²)*(in.)] = 48 in.³ / [(3.14)*(in.²)*(in.)] ;
__________________________________________________
→ to get: r² = 48/3.14 ;
________________________
→ r² = 15.2866242038216561 ;
_______________________________________
To solve for "r" (the radius; take the "positive square root" of EACH side of the equation:
__________________________________________________
→ +√(r²) = +√(15.2866242038216561)
__________________________________________________
→ r = 3.9098112747064475286 ; round to 3.91 inches .
___________________________________________________

4 0

3 years ago

Read 2 more answers

What is the circumference if a circle is 3cm

alekssr [168]

Answer:

0.48 cm

Step-by-step explanation:

6 0

4 years ago

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.

nalin [4]

Answer:

Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.

Step-by-step explanation:

The answer choices are:

Gus: 2.11 repeats because there are two 1s.
Gus: 2.11 is a repeating decimal because it stops.
Hannah: 2.11 is a rational number because it's a decimal.
Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.

The correct one is:

Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.

8 0

3 years ago

Scores on a test have a mean of 78.2 and 8 percent of the scores are above 89. The scores have a distribution that is approximat

anyanavicka [17]

Answer:

The standard deviation is 7.7

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 78.2$