Mathematics College

What’s the correct answer for this question?

Answers

Answer 1

Answer:

Step-by-step explanation:

In the attached file

Related Questions

The escape time (sec) for oil workers in a simulated exercise, gave the sample mean 370.69, sample standard deviation 24.36, and number of observations as n =26. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypothesis using a significance level of .05.

Answers

Answer:

Null hypothesis:[tex]\mu \leq 6[/tex]

Alternative hypothesis:[tex]\mu > 6[/tex]

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

Step-by-step explanation:

Information given

[tex]\bar X=370.69/60 =6.178[/tex] represent the sample mean

[tex]s=24.36/36=0.68[/tex] represent the standard deviation for the sample

[tex]n=26[/tex] sample size

[tex]\mu_o =6[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:

Null hypothesis:[tex]\mu \leq 6[/tex]

Alternative hypothesis:[tex]\mu > 6[/tex]

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

The degrees of freedom are:

[tex]df=n-1=26-1=25[/tex]

The p value would be given by:

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: y = x squared minus 6 x Table A a b c up or down y-intercept 1 -6 0 up (0,0) Table B a b c up or down y-intercept 1 0 0 up (0,-6) Table C a b c up or down y-intercept 1 6 0 up (0,0) Table D a b c up or down y-intercept 1 -6 0 down (0,0) a. Table A c. Table C b. Table B d. Table D Please select the best answer from the choices provided

Answers

Answer:

The table that illustrates this equation is table A:

1 -6 0 up (0,0)

Step-by-step explanation:

The values of the parameters a, b, and c have to agree with the values for the general quadratic equation in standard form:

[tex]y = a\,x^2+b\,x+c[/tex]

compared to:

[tex]y=x^2-6\,x[/tex]

So the coefficient "a" of the quadratic term in our case is: "1"

the coefficient "b" of the linear term is : "-6"

the coefficient "c" for the constant term s : "0" (zero)

since the coefficient "a" is a positive number, we know that the parabola's branches must be opening "UP".

The y intercept can be found by evaluating the expression for x = 0:

[tex]y=x^2-6x\\y=(0)^2-6\,(0)\\y=0[/tex]

Therefore the y-intercept is at (0, 0)

These results agree with those of Table "A"

Answer:

Table A.)

Step-by-step explanation:

a 1, b -6, c 0, up, (0, 0), Table A.

Lindsay needs to make some house repairs in four years that will cost $8,000. She has some money in an account earning 8% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs

Answers

Answer:

$5,882

Step-by-step explanation:

To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:

PV=FV/(1+i)^n

PV= present value

FV= future value= $8,000

i= interest rate= 8%

n= number of periods= 4

PV= 8,000/(1+0.08)^4

PV=8,000/1.08^4

PV=8,000/1.36

PV= 5,882

According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.

An office building loses a third of its heat between sundown and midnight and an additional half of the original amount of heat between midnight and 4 AM. If five-eighths of the remaining heat is lost between 4 AM and 5 AM, what proportion of the total heat loss occurs between 5 AM and sunrise?

Answers

Answer:

[tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]

Proportion of Heat Loss between midnight and 4 AM [tex]=\dfrac{1}{2}[/tex]

Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]

Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]

Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.

Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]

Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]

We therefore say that:

[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]

Please answer this correctly

Answers

Answer: 1-20=2 and 60-80=4

Step-by-step explanation:

the first is 2 number of building

and the third one is 4 number of buldings

Hope this helps :)

Please show me how to solve 40% of X is 23?

NOT what is 40% of 23. But what number is 40% of to equal 23.

Thank you!!

Answers

Answer: The answers are in the steps hopes it helps.

Step-by-step explanation:

40% * x = 23 convert 40% to a decimal

0.4 * x = 23 multiply 0.4 is by x

0.4x = 23 divide both sides by 0.4

x= 57.5

Check:

57.5 * 40% = ?

57.5 * 0.4 = 23

Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job collected by AARP (AARP Bulletin, April 2008) Shows that the mean number of weeks a worker aged 55 plus spent to find a job is 22 weeks. The sample standard deviation is 11.89 weeks and sample size is 40.a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.
b) At 95% confidence, what is the margin of error?
c) What is the 95% confidence interval estimate of the mean?
d) Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study?

Answers

Answer:

Step-by-step explanation:

Hello!

Be the variable of interest:

X: Number of weeks it takes a worker aged 55 plus to find a job

Sample average X[bar]= 22 weeks

Sample standard deviation S= 11.89 weeks

Sample size n= 40

The point estimate of the population mean is the sample mean

X[bar]= 22 weeks

It takes on average 22 weeks for a worker aged 55 plus to find a job.

To estimate the population mean using a confidence interval, assuming the variable has a normal distribution is

X[bar] ± [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]

[tex]t_{n-1; 1-\alpha /2}= t_{39; 0.975}= 2.023[/tex]

The structure of the interval is "point estimate" ± "margin of error"

d= [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]= 2.023*[tex](\frac{11.89}{\sqrt{40} })[/tex]= 3.803

The interval can be calculated as:

[22 ± 3.803]

[18.197; 25.803]

Using s 95% confidence level, you'd expect the population mean of the time it takes a worker 55 plus to find a job will be within the interval [18.197; 25.803] weeks.

Job Search Time (Weeks)

21 , 14, 51, 16, 17, 14, 16, 12, 48, 0, 27, 17, 32, 24, 12, 10, 52, 21, 26, 14, 13, 24, 19 , 28 , 26 , 26, 10, 21, 44, 36, 22, 39, 17, 17, 10, 19, 16, 22, 5, 22

To study the form of the distribution I've used the raw data to create a histogram of the distribution. See attachment.

As you can see in the histogram the distribution grows gradually and then it falls abruptly. The distribution is right skewed.

Can someone help me with this I’m sorry I really just don’t know

Answers

Answer:

Step-by-step explanation:

Because the two triangles are similar:

[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]

Hope this helps!

Consider the vector x: x <- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Options include sort(x), order(x), rank(x) and none of these

Answers

Completed Question

Outputs to be matched to the functions are:

1,2,3,4,51,5,3,2,41, 4, 3, 5, 2 2, 18, 27, 43, 96

Answer:

sort(x): 2, 18, 27, 43, 96 order(x): 1, 5, 3, 2, 4 rank(x) : 1, 4, 3, 5, 2none of these : 1, 2, 3, 4, 5

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

Sort

In R, the sort(x) function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

Rank

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

2 has a rank of 143 has a rank of 427 has a rank of 396 has a rank of 518 has a rank of 2

Therefore, the output of rank(x) is: 1, 4, 3, 5, 2

Order

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

2 was in the 1st position18 was in the 5th position27 was in the 3rd position43 was in the 2nd position96 was in the 4th position

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

The strength of paper used in the manufacturing of cardboard boxes (y) is related to percentage of hardwood concentration in the original pulp (x). Under controlled conditions, a pilot plant manufactures 16 samples, each from differential batch of pulp, and measures the tensile strength. Determine if there is significance relationship between x and y.
y = 101, 117, 117, 106, 132, 147, 147, 134, 111, 123, 125, 145, 134, 145, 144, 146.9
x = 1.0, 1.5, 1.5, 1.5, 2.0, 2.0, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3.0, 3.0, 3.2, 3.3

Answers

Answer:

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

P-value = 0.003.

Step-by-step explanation:

If we perform a regression analysis relating x and y, we get the best fitting line with equation:

[tex]y=15.82x+92.9[/tex]

and a correlation coefficient r:

[tex]r=0.693[/tex]

We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).

This can be written as:

[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]

where ρ is the population correlation coefficient for x and y.

The significance level is assumed to be 0.05.

The sample size is n=16.

The degrees of freedom are df=14.

[tex]df=n-2=16-2=14[/tex]

The test statistic can be calculated as:

[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]

For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:

[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]

The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

29.) in Mongolia the temperature can dip down to - 45°C
in January. The temperature in July may reach 40°C.
What is the temperature range in Mongolia?

Answers

Answer:

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]

Step-by-step explanation:

The temperature range is the difference between the maximum and the minimum temperature:

[tex]40^o-(-45^o)=40^o+45^o=95^o[/tex]

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents. How long will it take for this population to grow to

Answers

Answer:

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

[tex]\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}[/tex]

Seperate the differential equation and solve for the constant C.

[tex]\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}[/tex]

You have 100 rodents when:

[tex]100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months[/tex]

You have 1000 rodents when:

[tex]1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months[/tex]

What is the slope of the line that passes through the points (-3, -3) and
(-18, -23)? Write your answer in simplest form.

Answers

Answer:

work is shown and pictured

A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 452 cm3. The cost of the material for the base is 0.4 cents per square centimeter, and the cost of the material for the sides is 0.6 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost

Answers

Answer:

The box has sides of 11.07 cm and height of 3.69 cm.

The cost (minimum) is 147 cents per box.

Step-by-step explanation:

We have a box with open top, with a volume of 452 cm^3.

Let x: base side of the box, in cm, and y: height of the box, in cm.

Then, the volume can be expressed as:

[tex]V=x^2\cdot y=452\\\\y=452x^{-2}[/tex]

This box has 4 sides and 1 base. The material cost is 0.4 cents/cm^2 for the base and 0.6 cents/cm^2 for the sides.

Then, we can write the cost as:

[tex]C=0.4\cdot 1\cdot (x^2)+0.6\cdot 4\cdot (xy)\\\\\\xy=x\cdot(452x^{-2})=452x^{-1}\\\\\\C=0.4x^2+2.4(452x^{-1})\\\\\\C=0.4x^2+1084.8x^{-1}[/tex]

The value for x that gives a minimum cost can be found deriving the function C and equal to 0:

[tex]\dfrac{dC}{dx}=0.4(2x)+1084.8(-1\cdot x^{-2})=0\\\\\\0.8x-1084.8x^{-2}=0\\\\0.8x=1084.8x^{-2}\\\\0.8x^{1+2}=1084.8\\\\x^3=1084.8/0.8=1356\\\\x=\sqrt[3]{1356}\\\\x=11.07[/tex]

The height can be calculated with the equation:

[tex]y=452x^{-2}=452(11.07^{-2})=452\cdot 0.00816 =3.69[/tex]

The minimum cost can be calculated as:

[tex]C=0.4x^2+1084.8x^{-1}\\\\C(11.07)=0.4(11.07)^2+1084.8(11.07)^{-1}\\\\C(11.07)=0.4\cdot 122.51+1084.8\cdot0.09\\\\C(11.07)=49+98\\\\C(11.07)=147[/tex]

Simplify the quotient shown 3480 divided by 29

Answers

Answer:

120

Step-by-step explanation:

3480/29=120

120

Simplify ———

final result is 120

URGERNT!!!PLS AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESSS!! AND BLESS YOUR GRADES!

1. What could you prove about the following diagram, using the Hinge Theorem?
PIC BELOW
A) IJ>jk
B) HJ>HK
C) HK>HI
D) HI>HJ

2. Which theorem would explain why m∠CBD > m∠ADB? SECOND PICTURE
A) Hinge Theorem
B) Converse of Hinge Theorem
C) Pythagorean Theorem

Answers

Answer:

Dear Laura Ramirez

Answer to your query is provided below

1) option A is correct

2) option B is correct

Step-by-step explanation:

Explanation for the first question attached in image

Also note - The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.

Answer:

1) option A is correct2) option B is correct

Step-by-step explanation:

What else would need to be congruent to show that ABC=DEF by SAS?

Answers

Answer:

Step-by-step explanation:

Answer:

The answer here is A.

A) A is congruent to D.

Step-by-step explanation:

AP E

Fernando bought 8 pints of milk. How many fluid ounces of milk did Fernando buy? A. 16 fluid ounces B. 64 fluid ounces C. 128 fluid ounces D. 256 fluid ounces

Answers

Answer:

Step-by-step explanation:

There are 16 ounces in a pint. 8 * 16 = 128

A hiker starts at an elevation of 65 feet and descends 30 feet to the base camp . What is the elevation of the base camps ?

Answers

Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.

Answers

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:

[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).