Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second city. Let x represent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation

Answer:

a) The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).

b) 0.81

c) 0.039.

d) 0.101

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.

This means that [tex]n = 100, \pi = \frac{81}{100} = 0.81[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 - 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.709[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 + 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.911[/tex]

The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).

b) Give the value of the point estimate described in this scenario.

Sample proportion of [tex]\pi = 0.81[/tex]

c) Give the value of the standard error for the point estimate.

This is:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.039[/tex]

The standard error is of 0.039.

d) Give the value of the margin of error if you were to calculate a 99% confidence interval.

This is:

[tex]M = zs = 2.575*0.039 = 0.101[/tex]

9514 1404 393

Answer:

  x = (10√3)/3 ≈ 5.7735 m

Step-by-step explanation:

The 30°-60°-90° right triangle is one of the "special" right triangles, so you know its side ratios are ...

  BC : AB : AC = 1 : √3 : 2

Then ...

  x = BC = AB/√3 = (10 m)/√3 = (10√3)/3 m ≈ 5.7735 m

Answer:

- 8

Step-by-step explanation:

56 ÷ (- 7)

56 ÷ - 7

- 8

Answer:

-8

Step-by-step explanation:

A positive number divided by a negative one results in a negative quotient.

Thus, 56 ÷ (–7) = -8

Answer:

70

Step-by-step explanation:

X is equal to 70 degrees because angle x and the angle that is 70 degrees are alternate interior angles.

These are alternate interior angles. If two angles are alternate interior angles they are congruent. That means x is also 70 degrees.

Answer:  50 degrees

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

Explanation:

There's a lot of filler and visual distraction going on here. We only need to focus on the points H, C and E. Also, we need to focus on the circle as well. The other stuff is stuff we can ignore.

We're told that angle HCE is 50 degrees. This is a central angle that subtends, or cuts off, arc HE. By definition of arc measures, arc HE is also 50 degrees.

There's not much else to this problem to be honest.

The required value of function g is (-4x - 5)/(x+2) and graph is shown below.

The parent function of a function is the simplest form of the function, which satisfies all the conditions of the given function.

Given that,

Parent function f(x) = 3/x,

And function g(x) = f(x + 2) - 4.

To find the graph of function g(x), first determine the value of function g(x),

Substitute x = x+2 in function f(x), to determine g(x),

g(x)  = 3/(x+2) -4

       = 3-4(x+2)/x+2

       = 3 - 4x - 8/(x + 2)

       = (-4x - 5)/(x+2)

The required function g(x) is (-4x - 5)/(x+2) .

The graph of function g(x) is shown below.

To learn more about Parent function on:

https://brainly.com/question/17939507

#SPJ2

Answer:

Yes there is alternative way in solving and arithmetic sequence .An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

Answer:

36

Step-by-step explanation:

Simple:

(4)(3)+2((5)(3)−2)−2

=12+2((5)(3)−2)−2

=12+2(15−2)−2

=12+(2)(13)−2

=12+26−2

=38−2

=36

Answer:

x=30°

Step-by-step explanation:

50 + x =80 degree (sum of two interior opposite angles is equal to the exterior angles formed)

x=80-50

x=30 degree

Answer:a

Step-by-step explanation:

Answer:

they would have bike 544 miles together with each other.

Step-by-step explanation:

since Elsa went more than Linda Linda had to stop while Elsa kept going.

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 15.4 inches, and standard deviation of 3.5 inches.

This means that [tex]\mu = 15.4, \sigma = 3.5[/tex]

16 items are chosen at random

This means that [tex]n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875[/tex]

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16.8 - 15.4}{0.875}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Answer:

182

2.0239

3.97

(178, 186)

Step-by-step explanation:

Given :

Sample mean, n = 250

Sample mean, xbar = 182

Sample standard deviation, s = 32

Point estimate for the mean ;

According to the central limit theorem ; for n > 30, the sample mean equal to the population mean.

Hence, point estimate of mean cholesterol level for men is 182

B.) The standard error = s/√n

s= 32 ; n = 250

Standard error = 32/√250 = 2.0239

C.) Margin of error :

TCritical * standard error

TCritical at 95% ; df =250 -1 = 249 = 1.96

1.969 * 2.0239 = 3.966 = 3.97

D.) The confidence interval :

Point estimate ± margin of error

182 ± 3.97

182 - 3.97 = 178.03

182 + 3.97 = 185.97

(178, 186)

Answer:

28.5

Step-by-step explanation:

X*2/3=19, X=19/(2/3)=57/2=28.5

Answer:

The number is 28.5

Step-by-step explanation:

Let the number be x

Two - third of the number is 19 means

                                                            [tex]\frac{2}{3} \ of \ x = 19[/tex]

Solve for x

[tex]\frac{2}{3} \times x = 19\\\\2 \times x = 19 \times 3\\\\x = \frac{19 \times 3}{2} = 28.5[/tex]

Answer:

2 3/5

Step-by-step explanation:

13/5​

5 goes into 13 2 time

2*5 =10

13-10 =3

There is 3 left over.  This goes over the denominator

2 3/5

2 3/5

Step-by-step explanation:

13/5

5*2=10

reminder=3

divisor = 5

Answer:

see graph

Step-by-step explanation:

Step-by-step explanation:

here is your answer

here is your answer

Answer:

The answer is B

Step-by-step explanation:

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Answer:

4x^2-9x+7+\frac{x-2}{x^2+x+1}

Step-by-step explanation:

Here is a hopefully helpful answer! :)

Answer: [tex]\dfrac{x^2+1}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x)=\sqrt{2x-1}[/tex]

We can write it as

[tex]\Rightarrow y=\sqrt{2x-1}[/tex]

Express x in terms of y

[tex]\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}[/tex]

Replace y be x to get the inverse

[tex]\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}[/tex]

To prove, it is inverse of f(x). [tex]f(f^{-1}(x))=x[/tex]

[tex]\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x[/tex]

So, they are inverse of each other.

Answer: 34767.2

Step-by-step explanation:

given p = $16,000, n = 14 years, y = 5.7%

amount in bank after 14 years = p ( 1 + </100)

= 16,000 (1 + 5.7/ 100) 14

= 34767.2

Answer:

Step-by-step explanation:

Required formula:

Substitute values and solve:

9514 1404 393

Answer:

  B.  F(-9/2, 0), x = 9/2

Step-by-step explanation:

One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.

The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.

The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:

  focus: (-9/2, 0), directrix: x = 9/2

__

The equation of a parabola with its vertex at the origin can be written as ...

  x = 1/(4p)y^2

In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).

Answer:

-15

Step-by-step explanation:

So it's a-1-2x.

rewrite as -4-1-(2*5)

-4-1-10

-4+-1-10

-5+-10

-15

Answer:

- 15

Step-by-step explanation:

a - 1 - 2 x

- 4 - 1 - 2 ( 5 )

- 5 - 10

- 1 5

Answer:

282.12 ft

Step-by-step explanation:

Please find attached a graphical illustration of the question

We are given the value of the opposite side and we are to determine the value of the adjacent side. Thus, tan would be used

Tan 65 = opposite / adjacent

2.1445 = 605 / x

x = 605 / 2.1445

x = 282.12 ft

Answer:

60 different meal packages are possible.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

4 types of drinks

5 types of sandwiches.

3 types of chips.

They are independent events, so, by the fundamental counting principle:

4*5*3 = 60

60 different meal packages are possible.

Answer:

3 white to 5 yellow

the third choice

Step-by-step explanation:

white     9 parts

yellow   15 parts

9 white to 15 yellow

Divide by 3

3 white to 5 yellow