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1 year ago

14

Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger c

anister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.

1 answer:

azamat1 year ago

8 0

Answer:

The larger canister has 8 times the volume and 4 times the volume of the smaller one.

Step-by-step explanation:

The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.

The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.

The canisters are in the shape of a cylinder.

The volume of a cylinder is given as:

$V = \pi r^2h$

The surface area of a cylinder is given as:

A = 2πr(r + h)

SMALLER CANISTER

Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres

Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres

LARGER CANISTER

Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres

Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres

By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.

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Which of the following groups has terms that can be used interchangeably with the others?1. Percentage, Probability, and Proport

Dafna1 [17]

Answer: 1) Percentage, Probability, Proportion

Step-by-step explanation:

In statistics,

▪Proportion means a fraction of the total.

▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.

▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).

▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

In the four definitions, the odd one out is Critical Value.

So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.

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2 years ago

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A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

$t = 3.054$

4

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

5

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

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2 years ago

Four men are to divide K500 equally among them. When the money was given, 20% was taken away.

Agata [3.3K]

Answer: 20% of 500= 100

So 500-100 = 400

4x100= 400

Step-by-step explanation:

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2 years ago

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean ti

ser-zykov [4K]

Answer:

a) Null hypothesis: $\mathbf{H_0 : \mu \leq 15}$

Alternative hypothesis: $\mathbf{H_1 = \mu > 15}$

b) the test statistics is : 2.15

c) The p-value is 0.0158

d) NO, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

Step-by-step explanation:

The data in the Microsoft Excel are:

17;11;12;23;20;23;15;

16;23;22;18;23;25;14;

12;12;20;18;12;19;11;

11;20;21;11;18;14;13;

13;19; 16;10;22;18;23.

a) Formulate the null and alternative hypotheses for this application.

From the question, Fowle Marketing Research Inc. is taking base charge from a client on the given assumption that if the mean time of telephone survey is 15 minutes or less.

The null and alternative hypotheses are therefore as follows:

Null hypothesis: $\mathbf{H_0 : \mu \leq 15}$

The null hypothesis states that there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

Alternative hypothesis: $\mathbf{H_1 = \mu > 15}$

The alternative hypothesis states that there is evidence that the mean time of telephone survey exceeds 15 and premium rate is justified.

b) Compute the value of the test statistic.

Given that:

$\mu = 15$

$\sigma = 3.6$

n = 35

The sample mean $\bar x = \dfrac{ \sum x}{n}$ is;

$\bar x = \dfrac{ 17+11+12 ... 22+18+23}{35}$

$\bar x = 17$

Thus:

$z = \dfrac{ \bar x - \mu }{\dfrac{\sigma}{\sqrt{n}}}$

$z = \dfrac{ 17 - 15}{\dfrac{3.6}{\sqrt{15}}}$

$z = \dfrac{ 2}{0.9295}}$

$\mathbf{z =2.15}$

Thus; the test statistics is : 2.15

c) What is the p-value?

p-value = P(Z > 2.15)

p-value = 1 - P(Z ≤ 2.15)

From the standard normal table, the value of P(Z ≤ 2.15) is 0.9842

p-value = 1 - 0.9842

p-value = 0.0158

The p-value is 0.0158

d) At a = .01, what is your conclusion?

According to the rejection rule, if p-value is less than 0.01 then reject null hypothesis at ∝ = 0.01

Thus; p-value = 0.0158 > ∝ = 0.01

By the rejection rule, accept the null hypothesis.

Therefore, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.

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2 years ago

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side Line segment

prisoha [69]

Answer:

<h2>A 16mm</h2>

Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal.

Perimeter of an equilaterial triangle = 3s where;

s is one side of the triangle.

Given the perimeter of ABC = 96mm

Substituting into the formula above to get s;

96 = 3s

s = 96/3

s = 32mm

Hence the length of one side of the triangle is 32mm

If a perpendicular bisector is drawn from angle A to side Line segment B C at point M, then MC will be half of BC and ΔAMC will be a right angled triangle.

Since all the sides of the triangle are equal, hence BC = 32mm. Since MC is the half of BC, then MC = 1/2 of 32mm

MC = 1/2 * 32mm

MC = 16mm

<em>Hence the length of Line segment MC is 16mm</em>

<em></em>

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1 year ago

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