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3 years ago

PLEASE HELP Simplify the expression 5^3+3(5-3) A.137 B.131 C.27 D.21

Mathematics

1 answer:

mojhsa [17]3 years ago

5 0

Answer:

the correct answer is 131

Step-by-step explanation:

5^3 +3(2)

= 125 +6

=131

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A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path. which number line cor

Fynjy0 [20]

Given :

A bike path is 3 miles long. there are distance markers every path one fourth mile to the end of the path.

To Find :

Which number line correctly models this situation and the total number of distance markers.

Solution :

It is given that their are markers every 1/4 part of mile.

So, their are 4 markers per mile.

Numbers of markers in 3 miles long path is :

$n = 3\times 4\\\\n = 12$

Therefore, the total number of distance markers in 3 mile path is 12.

Hence, this is the required solution.

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An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d

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Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}$

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}$

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}$

For the first ice cream with one scoop

$\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}$

For the second ice cream with two scoops

$\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}$

For the third ice cream with three scoops

$\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}$

Hence,

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The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream

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