Trigonometry<br> Special Right Triangles <br> Find the exact value of tan 0* + cos 90*

The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.a. Comp

Kobotan [32]

Answer:

1). Z score = 1.464733

Mean = 38.87917

Standard deviation = 3.609405

2). Quartiles:

Q1 = 37.025

Q2 = 38.450

Q3 = 40.800

3). IQR = 3.775

4).

CI (lower fence) = 37.4351

CI (upper fence) = 40.32323

5). There is outlier in the data set. Please see attached box plot for evidence.

Step-by-step explanation:

1). By Z score, we mean:

Z = $\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ ,

where:

x-bar ==> mean(g) = 38.87917

$\mu$ = 37.80

standard deviation = 3.609405

sample size (n) = 24.

2). By quantile, we mean:

Q = L + (i*(n/4) - Cf)*c

Where L is the lower class limit of the quartile class

Cf is the cumulative frequency before the quartile class

c is the class size.

3) . IQR = Q3 - Q1

4). CI = $\mu \pm *Z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ ,

Where $Z_{\alpha/2}$ ==> 1.96

In order to replicate and obtain the result, please use the R code below:

g = c(31.5, 36.0, 37.8, 38.5, 40.1, 42.2,34.2, 36.2, 38.1, 38.7, 40.6, 42.5,34.7, 37.3, 38.2, 39.5,

41.4, 43.4,35.6, 37.6, 38.4, 39.6, 41.7, 49.3)

boxplot(g)

Z = (mean(g) - 37.8)/(sd(g)/sqrt(length(g)))

mean(g)

quantile(g)

IQR(g)

CIl = mean(g) - 1.96*(sd(g)/sqrt(length(g)))

CIU = mean(g) + 1.96*(sd(g)/sqrt(length(g)))

4 0

3 years ago

When a river flows, the strength or force of the river depends on how far the river falls vertically compared to how far it flo

strojnjashka [21]

The figure is missing. There are several problems with same wording but different numbers

Here, we can use:

Horizontal distance: 258 feet

Vertical fall: 56.0 feet

Answer:

Slope = 56.0 ft / 258 ft ≈ 0.217

Explanation:

The <em>slope</em> measures how the rate of change of the vertical distance (vertical fall) with respect to the horizontal distance.

There are several forms to express this with words, which represent the same formula. Here are some of them:

Slope = rise / run
Slope = vertical change / horizontal change
Slope = change in y / change in x
Slope = Δy / Δx
Slope = (y₂ - y₁) / (x₂ - x₁)

As said, all those forms mean the same; they are equivalent.

Here, we have vertical fall = 56.0 feet, and horizontal distance = 258 feet, and by specifications of the problem (in the hint) the slope must be positive. Thus, you get:

Slope = vertical fall / horizontal distance = 56.0 feet / 258 feet ≈ 0.217

8 0

3 years ago

2. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 55% of the 25,00

svlad2 [7]

Using the binomial distribution, it is found that:

a) There is a 0.0501 = 5.01% probability that you need to contact four people.

b) You expect to contact 1.82 students until you find one who lives within five miles of you.

c) The standard deviation is of 1.22 students.

d) There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.

e) It is expected that 2.75 students live within five miles of you.

For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

55% of the students live within five miles of you, thus $p = 0.55$ .

Item a:

This probability is P(X = 0) when n = 3(none of the first three living within five miles of you) multiplied by 0.55(the fourth does live within five miles), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125$

$p = 0.091125(0.55) = 0.0501$

0.0501 = 5.01% probability that you need to contact four people.

Item b:

The expected number of trials in the binomial distribution until q successes is given by:

$E = \frac{q}{p}$

In this problem, $p = 0.55$ , and 1 trial, thus $q = 1$ , hence:

$E = \frac{1}{0.55} = 1.82$

You expect to contact 1.82 students until you find one who lives within five miles of you.

Item c:

The standard deviation of the number of trials until q successes are found is given by:

$S = \frac{\sqrt{q(1 - p)}}{p}$

Hence, since $q = 1, p = 0.55$ :

$S = \frac{\sqrt{0.45}}{0.55} = 1.22$

The standard deviation is of 1.22 students.

Item d:

This probability is $P(X = 3)$ when $n = 5$ , hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369$

There is a 0.3369 = 33.69% probability that 3 of them live within five miles of you.

Item e:

The expected value of the binomial distribution is:

$E(X) = np$

Hence, since $n = 5, p = 0.55$ :

$E(X) = 5(0.55) = 2,75$

It is expected that 2.75 students live within five miles of you.

A similar problem is given at brainly.com/question/25343741

7 0

3 years ago

Help please I’ll mark you

kumpel [21]

Answer:

32

Step-by-step explanation:

If you already have an angle of 148 on the arc TU, then 180-148=32

5 0

2 years ago

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the ____

lbvjy [14]

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the Poisson probability distribution.

How do you find the probability of success for each trial?

Each trial has a head (success) and a tail (failure) outcome (failure). Each trial's chances of success are p = 1/2 and its chances of failure are q = 1 1/2 = 1/2.
The variable X, which counts the number of successes across 12 trials, is the one that interests us. This is an illustration of a 12-trial Bernoulli experiment.

What is the probability formula?

Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) E is the event, P is the probability, and S is the sample area.

Learn more about probability

brainly.com/question/11234923

#SPJ4

4 0

1 year ago

Trigonometry Special Right Triangles Find the exact value of tan 0* + cos 90* - sin 0*.