All categories

2 years ago

UNIT 5: CEREAL BOX PROJECT / PORTFOLIO HELP

Mathematics

1 answer:

Mrrafil [7]2 years ago

3 0

Using the formula for volume and surface area of solids, we have the following:

1. 180 in.³; 258 in.²; $12.9

2. 144 in.³; 184 in.²; $9.2

3. 75 in.³; 228 in.²; $11.4

<h3>What is Volume and Surface Area?</h3>

Volume of a rectangular prism = l × w × h

Surface area of a rectangular prism = 2(wl+hl+hw)

Volume of a square pyramid = 1/3 × a² × h

Surface area of a square pyramid = a² + 2al

Volume of a cylinder = πr²h

Surface area of a cylinder = 2πr( h + r)

1. Volume of the rectangular prism cereal box = 7.5 × 2 × 12 = 180 in.³

Surface area of the rectangular prism cereal box = 2(wl+hl+hw) = 2(2 × 7.5 + 12 × 7.5 + 12 × 2) = 258 in.²

Cost of material for the the rectangular prism cereal box = 258 × 0.05 = $12.9.

2. Volume of the square pyramid cereal box = 1/3 × a² × h = 1/3 × 6² × 12 = 144 in.³

Surface area of the square pyramid cereal box = a² + 2al = 6² + 2(6)(12.3) ≈ 184 in.²

Cost of material for the the square pyramid cereal box = 184 × 0.05 = $9.2.

3. Volume of the cylinder cereal box = πr²h = π(2.5²)(12) = 75 in.³

Surface area of the cylinder cereal box = 2π(2.5)(12 + 2.5) ≈ 228 in.²

Cost of material for the the cylinder cereal box = 228 × 0.05 = $11.4.

Learn more about the surface area and volume of solids on:

brainly.com/question/16599646

You might be interested in

In Exercise, describe how the graph of g is related to the graph of f.<br> g(x)=-1+f(x)

Jet001 [13]

Answer:

The graph of g is the graph of f shifted down 1 unit.

Step-by-step explanation:

Suppose you have a function y = f(x), you can do these following operations on the function:

Shift up a units: y = f(x) + a

Shift down a units: y = f(x) - a

Shift left a units: y = f(x + a)

Shift right a units: y = f(x - a)

In this problem, we have that:

g(x) = -1 + f(x) = f(x) - 1

So the graph of g is the graph of f shifted down 1 unit.

7 0

3 years ago

Which of these numbers is irrational? A) −0.125 B) −50 C) π D) 7 10

Marrrta [24]

Your answer would be C

7 0

3 years ago

Read 2 more answers

A small company plans to invest in a new advertising campaign. There is a 20% chance that the company will lose $5,000, a 50% ch

Viktor [21]

A small company plans to invest in a new advertising campaign.

There is a 20% chance that the company will lose $5,000 ,

50% chance of a break even, and a 30% chance of a $10,000 profit

So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000

= -1000 + 0 + 3000

= 2000

The expected value from the advertisement campaign is $2000.

So the Company must go ahead with the campaign.

Answer : Option A

Hope it helps.

Thank you ..!!

3 0

3 years ago

A researcher finds that of 1000 people who said that they attend a religious service at least once a week, A stopped to help a p

Ne4ueva [31]

Answer:

There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).

Step-by-step explanation:

The question is incomplete:

<em>"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."</em>

This is a hypothesis test for the difference between proportions.

The claim is that the proportions are not equal.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=1000 has a proportion of p1=0.031.

$p_1=X_1/n_1=31/1000=0.031$

The sample 2, of size n2=1200 has a proportion of p2=0.018.

$p_2=X_2/n_2=22/1200=0.018$

The difference between proportions is (p1-p2)=0.013.

$p_d=p_1-p_2=0.031-0.018=0.013$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{31+22}{1000+1200}=\dfrac{53}{2200}=0.024$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.024*0.976}{1000}+\dfrac{0.024*0.976}{1200}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0}=0.007$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.013-0}{0.007}=\dfrac{0.013}{0.007}=1.98$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z>1.98)=0.048$

As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions are not equal.

6 0

3 years ago

3 to the third power +6(2+ 3/6)

Oliga [24]

Answer:
42

Explanation:
Using Order of Operations, we have to evaluate the exponent first:
27 + 6(2 + 3/6)

Simplifying the fraction, we have:
27 + 6(2 + 0.5)

Add the values inside the parenthesis:
27 + 6(2.5)

Multiply:
27 + 15

Add:
42

4 0

2 years ago