What is the best price?

I will give lots of points please help

aalyn [17]

Answer:

a) 81π in³

b) 27 in³

c) divide the volume of the slice of cake by the volume of the whole cake

d) 10.6%

e) see explanation

Step-by-step explanation:

The cake can be modeled as a <u>cylinder </u>with:

diameter = 9 in
height = 4 in

$\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in$

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

$\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}$

$\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}$

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

$\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}$

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

$\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}$

Probability is approximately 10.6% (see above for calculation)

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

3 0

1 year ago

Terrance's garden is 3/ 5 yard by 1 2/ 5 yards. Each square is 1/ 5 yard long. He needs to know the area so he can buy the right

Vanyuwa [196]

Answer:

brain

Step-by-step explanation:

5 0

2 years ago

Simplify please help

olchik [2.2K]

Answer:

all work is shown/pictured

3 0

3 years ago

The figure below is a scale drawing of Quinto's bedroom. The scale used to create the drawing is 1/2 inch = 4 feet. What is the

Nezavi [6.7K]

We know that

the scale is <span>is 1/2 inch = 4 feet

using a graph tool
</span><span>the approximate measurements in the drawing are
</span>5 cm x 4 cm
convert to in
5/2.54--------> 1.97 in
4/2.54------> 1.57 in

convert drawing to actual
if 0.5 in---------> 4 ft
1.97in-------> X
X=1.97*4/0.5------> X=15.76 ft

if 0.5 in---------> 4 ft
1.57 in-------> X
X=1.57*4/0.5------> X=12.56 ft

<span>the approximate area of Quinto's bedroom is 12.56*15.76=197.95 ft</span>²

the answer is
the option C)192 ft²

6 0

3 years ago

A sample of 140 Vopstra customers have had their annual phone charge recorded for the previous calendar year. The data were used

taurus [48]

Answer:

Correct option: (a)

Step-by-step explanation:

A confidence interval is an interval estimate of the parameter value.

A (1 - <em>α</em>)% confidence interval implies that the confidence interval has a (1 - <em>α</em>)% probability of consisting the true parameter value.

OR

If 100 such confidence intervals are made then (1 - <em>α</em>) of these intervals would consist the true parameter value.

The 92% confidence interval for the mean annual phone charge of all Vopstra customers is:

$\$470\pm \$65=(\$405, \$535)$

This confidence interval implies that true mean annual phone charge of all Vopstra customers is contained in the interval ($405, $535) with 0.92 probability.

Thus, the correct option is (a).

6 0

3 years ago