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2 years ago

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Mathematics

1 answer:

trapecia [35]2 years ago

8 0

Answer:

The volume of water that will fill the spa tub is 5.9 cubic meters.

Step-by-step explanation:

Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)

i. volume of first cylinder = $\pi$ $r^{2}$ h

where r is the radius and h is the height of the cylinder.

r = $\frac{0.75}{2}$ = $\frac{3}{8}$

= 0.375 m

h = 0.80 m

volume of the first cylinder = $\frac{22}{7}$ x $(\frac{3}{8} )^{2}$ x 0.8

= 0.3536 cubic meters

ii. volume of the cylinder underneath = $\pi$ $r^{2}$ h

r = $\frac{1.25}{2}$ = $\frac{5}{8}$

= 0.625

h = 0.70 m

volume of the cylinder underneath = $\frac{22}{7}$ x $(\frac{5}{8}) ^{2}$ x 0.7

= 0.8594 cubic meters

iii. volume of the semi sphere = $\frac{2}{3}$ $\pi$ $r^{3}$

where r is the radius = 1.5 m

volume of the semi sphere = $\frac{2}{3}$ x $\frac{22}{7}$ x $(1.5)^{3}$

= 7.0714 cubic meters

Thus,

volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)

= 5.8584

The volume of water that will fill the spa tub is 5.9 cubic meters.

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What is the purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aero

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The purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aeronautics (pilot), engineers, landscapers, and architects is discussed below

<h3>What is angle of elevation and depression?</h3>

If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object. If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.

If the pilot looks straight out, that line of sight is horizontal (focused on the distant horizon). The pilot might see the airport's runway, distant buildings, or even mountains in her field of view.

If the pilot looks down at the ground, the one will see the ground crew. The angle of depression is the angle that is formed between the horizontal and the downward looking angle. It is always a downward view, an angle below the horizon.

For the ground crewmember, looking down would not be much help in communicating with the pilot in her cockpit seat. The crewmember will look up, above the horizontal line, to see the pilot. The ground crewmember's angle of vision if an angle of elevation, the angle above the horizon.

Angle of elevation or depression in a survey can be defined as the angle subtended between the line of sight passing through the scope and the horizontal axis of the instrument.

Engineers, landscapers, architects all use trigonometry in their everyday life to help them efficiently and safely create or design something new.

Learn more about angle of elevation and depression here:

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2 years ago

A red die, a blue die, and a yellow die (all six sided) are rolled. we are interested in the probability that the number appeari

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5/54 or approximately 0.092592593
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
r = 4, y = 2, b = 1, so n = 3 + 1 = 4
r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
r = 5, y = 2, b = 1, so n = 9 + 1 = 10

And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
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2 years ago

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is

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Answer:

a) On this case we are interested on the population proportion of students that have a GPA of 3.00 or below.

b) $z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{200}}}=-1.77$

$p_v =P(z$

c) Null hypothesis: $p\geq 0.2$

Alternative hypothesis: $p$

d) The significance level provided is $\alpha=0.05$ . If we compare the p value obtained and the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the population proportion of students that have a GPA of 3.00 or below is significantly lower than 0.2.

Step-by-step explanation:

Data given and notation n

n=200 represent the random sample taken

X=30 represent the students with a GPA of 3.00 or below.

$\hat p=\frac{30}{200}=0.15$ estimated proportion of students with a GPA of 3.00 or below.

$p_o=0.2$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

a. In testing the university's belief, how does on define the population parameter of interest?

On this case we are interested on the population proportion of students that have a GPA of 3.00 or below.

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion of graduates with GPA of 3.00 or below is less than 0.2.:

Null hypothesis: $p\geq 0.2$

Alternative hypothesis: $p$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

b. The value of the test statistics and its associated p-value are?

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{200}}}=-1.77$

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

Since is a one left tailed test the p value would be:

$p_v =P(z$

c. In testing the university's belief, the appropriate hypothesis are?

Null hypothesis: $p\geq 0.2$

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