The line CD passes through the points C (2, -1) and D (1.1). Which of the

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

nignag [31]

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,

The final answer is

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

3 0

1 year ago

Can someone help me and explain it to me

Alex_Xolod [135]

Answer:

1) 6

2)4

3)27

4)126

5)15

Step-by-step explanation:

1. We need to see how many 8-miles are in 24 miles, than multiple it with 2in.

(24/8)*2=3*2=6in

2. Fist we calcue how many 17-feets are in 68feets, and multiple that with 1in.

(68/17)*1=4

3. We first see how many 3ins are in 9ins, and than multiple that with 9feet

(9/3)*9=3*9=27

4. First see how many 2ins are in 36ins, and then multiple it with 7.

(36/2)*7=18*7=126feet

5. See how many 15fts are in 75ft And than multiple it with 3.

(75/15)*3=5*3=15

4 0

3 years ago

Read 2 more answers

You take a taxi to your sisters home. The driver charges you $8 for 3 kilometers and $2 for each additional kilometer. If you pa

vivado [14]

14-8=6. So far we have 3 km, then 6 divided by 2 which is 3 additional kilometers. 3+3 is 6 so the final answer is 6km

7 0

3 years ago

Read 2 more answers

Which fraction is larger than 1/2? 2/3 0r 2/4 or 2/5

nalin [4]

2/3 is the correct answer because it’s bigger then a half

6 0

3 years ago

Read 2 more answers

X-y=6 2x-3z=16 2y+z=4 Solve the systems of equations.

Neko [114]

Answer:

Given System of equation:

x-y =6 .....,[1]

2x-3z = 16 ......[2]

2y+z = 4 .......[3]

Rewrite the equation [1] as

y = x - 6 .......[4]

Substitute the value of [4] in [3], we get

$2(x-6)+z = 4$

Using distributive property on LHS ( i.e, $a \cdot (b+c) =a \cdot b+ b \cdot c$ )

then, we have

2x - 12 +z =4

Add 12 to both sides of an equation:

2x-12+z+12=4+12

Simplify:

2x +z = 16 .......[5]

On substituting equation [2] in [5] we get;

2x+z=2x -3z

or

z = -3z

Add 3z both sides of an equation:

z+3z = -3z+3z

4z = 0

Simplify:

z = 0

Substitute the value of z = 0 in [2] to solve for x;

$2x-3(0) = 16$

or

2x = 16

Divide by 2 both sides of an equation:

$\frac{2x}{2} =\frac{16}{2}$

Simplify:

x= 8

Substitute the value of x =8 in equation [4] to solve for y;

y = 8-6 = 2

or

y = 2

Therefore, the solution for the given system of equation is; x = 8 , y = 2 and z =0

5 0

3 years ago