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2 years ago

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Mathematics

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KiRa [710]2 years ago

3 0

Answer:

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. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the

FromTheMoon [43]

Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

<h2>Given</h2>

Two bottles of similar shape;
Larger bottle has volume of 100 ml;
The length of larger bottle is 10 cm;
The length of smaller bottle is 5 cm.

The volume of smaller bottle.

<h2>Solution</h2>

Find the scale factor, the ratio of corresponding dimensions:

$k = 5/10 = 1/2$

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

$V_{small}/V_{large} = k^3\\$

Substitute the known values and find the volume of small bottle:

$V_{small}/100= (1/2)^3\\$
$V_{small}/100= 1/8$
$V_{small}= 1/8*100=12.5$

The smaller bottle holds 12.5 ml of perfume.

4 0

1 year ago

Read 2 more answers

Data is collected to compare two different types of batteries. We measure the time to failure of 12 batteries of each type. Batt

-Dominant- [34]

Using the t-distribution, it is found that since the <u>test statistic is greater than the critical value for the right-tailed test</u>, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.

At the null hypothesis, it is <u>tested if it does not outlast by more than 2 hours</u>, that is, the subtraction is not more than 2:

$H_0: \mu_B - mu_A \leq 2$

At the alternative hypothesis, it is <u>tested if it outlasts by more than 2 hours</u>, that is:

$H_1: \mu_B - \mu_A > 2$

The sample means are: $\mu_A = 8.65, \mu_B = 11.23$

The standard deviations for the samples are $s_A = s_B = 0.67$

Hence, the standard errors are:

$s_{Ea} = S_{Eb} = \frac{0.67}{\sqrt{12}} = 0.1934$

The distribution of the difference has <u>mean and standard deviation</u> given by:

$\overline{x} = \mu_B - \mu_A = 11.23 - 8.65 = 2.58$

$s = \sqrt{s_{Ea}^2 + s_{Eb}^2} = \sqrt{0.1934^2 + 0.1934^2} = 0.2735$

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 2$ is the value tested at the hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{2.58 - 2}{0.2735}$

$t = 2.12$

The critical value for a <u>right-tailed test</u>, as we are testing if the subtraction is greater than a value, with a <u>0.05 significance level</u> and 12 + 12 - 2 = <u>22 df</u> is given by $t^{\ast} = 1.71$

Since the <u>test statistic is greater than the critical value for the right-tailed test</u>, it is found that there is enough evidence to conclude that Battery B outlasts Battery A by more than 2 hours.

A similar problem is given at brainly.com/question/13873630

7 0

2 years ago

Find the slope of the line passing through the two points.

GalinKa [24]

The fromula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$