The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500. Is there sufficient evidence at the ?= 0.05 level to conclude that the mean cost has increased. Solve the question by traditional approach.

Answers

Answer 1

Answer:

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Step-by-step explanation:

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.

At the null hypothesis, we test if the mean cost is still the same, that is:

[tex]H_0: \mu = 13252[/tex]

At the alternative hypothesis, we test if the mean cost has increased, that is:

[tex]H_1: \mu > 13252[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

13252 is tested at the null hypothesis:

This means that [tex]\mu = 13252[/tex]

The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.

This means that [tex]n = 20, X = 15560, s = 3500[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}[/tex]

[tex]t = 2.95[/tex]

P-value of the test and decision:

The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.


Related Questions

Can someone help me with me? Thanks!

Answers

Answer:

(0.38, 4.79)

Step-by-step explanation:

Please help me with solving these. I’d really appreciate your help. Thank you very much.

Answers

Answer:

Problem 17)

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

Step-by-step explanation:

Problem 17)

We have the curve represented by the equation:

[tex]\displaystyle 4x^2+2xy+y^2=7[/tex]

And we want to find the equation of the tangent line to the point (1, 1).

First, let's find the derivative dy/dx. Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[4x^2+2xy+y^2\right]=\frac{d}{dx}[7][/tex]

Simplify. Recall that the derivative of a constant is zero.

[tex]\displaystyle \frac{d}{dx}[4x^2]+\frac{d}{dx}[2xy]+\frac{d}{dx}[y^2]=0[/tex]

Differentiate. We can differentiate the first term normally. The second term will require the product rule. Hence:

[tex]\displaystyle 8x+\left(2y+2x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0[/tex]

Rewrite:

[tex]\displaystyle \frac{dy}{dx}\left(2x+2y\right)=-8x-2y[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{-8x-2y}{2x+2y}=-\frac{4x+y}{x+y}[/tex]

So, the slope of the tangent line at the point (1, 1) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=-\frac{4(1)+(1)}{(1)+(1)}=-\frac{5}{2}[/tex]

And since we know that it passes through the point (1, 1), by the point-slope form:

[tex]\displaystyle y-1=-\frac{5}{2}(x-1)[/tex]

If desired, we can simplify this into slope-intercept form. Therefore, our equation is:

[tex]\displaystyle y=-\frac{5}{2}x+\frac{7}{2}[/tex]

Problem 18)

We have the equation:

[tex]\displaystyle y=\tan^{-1}\left(x^3\right)[/tex]

And we want to find the equation of the tangent line to the graph at the point (1, π/4).

Take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\tan^{-1}(x^3)][/tex]

We can use the chain rule:

[tex]\displaystyle \frac{d}{dx}[u(v(x))]=u'(v(x))\cdot v(x)[/tex]

Let u(x) = tan⁻¹(x) and let v(x) = . Thus:

(Recall that d/dx [arctan(x)] = 1 / (1 + x²).)

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2[/tex]

Substitute and simplify. Hence:

[tex]\displaystyle \frac{d}{dx}\left[\tan^{-1}(x^3)\right]=\frac{1}{1+v^2(x)}\cdot 3x^2=\frac{3x^2}{1+x^6}[/tex]

Then the slope of the tangent line at the point (1, π/4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{x=1}=\frac{3(1)^2}{1+(1)^6}=\frac{3}{2}[/tex]

Then by the point-slope form:

[tex]\displaystyle y-\frac{\pi}{4}=\frac{3}{2}(x-1)[/tex]

Or in slope-intercept form:

[tex]\displaystyle y=\frac{3}{2}x-\frac{3}{2}+\frac{\pi}{4}[/tex]

The total number of labor hours for a construction project by week x is given by: Week 1 4 7 10 13 16 19 Total hours 25 158 1254 5633 9280 10,010 10,100 Look at its scatter plot, an appropriate model for this data is:

Answers

Answer:

Logistic model

Step-by-step explanation:

A scatter plot is a mathematical representation or diagram which is used to shoe the relation between two given variables. It uses the Cartesian coordinates which is used to display the values for a typically two variables for the given set of data.

In the context, a scatter plot is made between two variables. The two variables are the total number of hours and the number of weeks.

From the graph shown, we can say that model is a logistic model as the shape of the graph is S shaped.

Therefore, the appropriate model for the data given is logistic model.

1 1/3 bushels of seed are needed to plant 1 acre of wheat. How many bushels of seed would be required to plant 30 acres?

Answers

An acre requires 1.33 bushels of seed.

Thirty acres thusly require 30 times 1.33 bushels of seed.

So we have, [tex]1.33\cdot30=\boxed{39.9}[/tex] bushels of seed.

Hope this helps.

calculate the value of X in the diagram​

Answers

Answer:

that is the answer

Step-by-step explanation:

use triangle RSQ

from pythogrus theorem

a² + b² = c²

4² + 5² = RQ²

16 + 25 = RQ²

41 = R

Jordan rides a bike from Clovis to Millerton Lake. On the flatland Jordan travels at 36 mph for 1 hour, and in the mountains rides for 3 hours traveling at 20 miles per hour. Which of the following choices is the average speed for the trip?

Answers

Answer:

24 mph

Step-by-step explanation:

1 hour of 36 mph

3 hours of 20 mph

(36 + 20 + 20 + 20)/4

96/4

24

Answer:

24 mph

Step-by-step explanation:

36 miles = 1 hour

60 miles = 3 hours

36+60= 96

1+3+4

96/4= 24

solve this fast please… and thank you so much :)

Answers

Answer:

hi

Step-by-step explanation:

The answer is the second one !

HELP! AAHHHHH SOMEBODY HELP!

If each square of the grid below is $0.5\text{ cm}$ by $0.5\text{ cm}$, how many square centimeters are in the area of the blue figure?

Answers

Answer:

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls.
Three balls are selected, one after the other, without replacement.
Find the probability that all three balls are purple
Express your answer as a decimal, rounded to the nearest hundredth.

Answers

Answer:

The probability is P = 0.08

Step-by-step explanation:

We have:

2 pink balls

7 purple balls

6 white balls

So the total number of balls is just:

2 + 7 + 6 = 15

We want to find the probability of randomly picking 3 purple balls (without replacement).

For the first pick:

Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)

p₁ = 7/15

Second:

Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:

p₂ = 6/14

third:

Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:

p₃ = 5/13

The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:

P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13)  = 0.08

Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.

Answers

Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other

The resultant of the two forces is given by

[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]

Insert the values

[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]

Resultant makes an angle of

[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]

So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force

Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]

Answer:

Step-by-step explanation:

3. L = 5 cm
W = 30 cm
H= 14
V=____ ​

Answers

Answer:

Step-by-step explanation: as the formula to find volume is L*W*H

so v=lwh

=   5*30*14

= 2100cm^3

Examine the following expression.

p squared minus 3 + 3 p minus 8 + p + p cubed

Which statements about the expression are true? Check all that apply.
The constants, –3 and –8, are like terms.
The terms 3 p and p are like terms.
The terms in the expression are p squared, negative 3, 3 p, negative 8, p, p cubed.
The terms p squared, 3 p, p, and p cubed have variables, so they are like terms.
The expression contains six terms.
The terms p squared and p cubed are like terms.
Like terms have the same variables raised to the same powers.
The expression contains seven terms.

Answers

Answer:

the terms in the expression are p squared, negative 3,3p, negative 8,p,p cubed

Step-by-step explanation:

hope that helps

What is the mean of this data? 7,5,5,3,2,2

Answers

Answer:

4

Step-by-step explanation:

The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.

The values in this data set;

[tex]7,5,5,3,2,2[/tex]

The number of values in this data set,

[tex]6[/tex]

Find the mean;

[tex]\frac{sum\ of\ vlaues}{number\ of\ values}[/tex]

[tex]=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4[/tex]

help me please ineed your help

Answers

I can’t see the problem

Suppose the composition of the 107th Senate is 45 Republicans, 50 Democrats, and 5 Independents. A new committee is being formed to study ways to benefit the arts in education. If 3 senators are selected at random to head the committee, find the probability of the following:
Part 1. The group of 3 consists of all Republicans.
Part 2. The group of 3 consists of all Democrats.
Part 3. The group of 3 consists of 1 from each party, including the Independent.

Answers

Answer:

1 : 0.088

2 : 0.12

3 : 0.07

Step-by-step explanation:

45 Rebullicans

50 Democrats

5 independents

Total = 100

Selection =  3

Part 1:

(45 C 3) / (100 C 3) = 0.088

Part 2:

(50 C 3) / (100 C 3) = 0.12

Part 3:

(45 C 1) x (50 C 1) x (5 C 1) / (100  C 3) = 0.07

HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.

Answers

36 jersey with green

A basketball team is to play two games in a tournament. The probability of winning the first game is .10.1 the first game is won, the probability of winning the second game is 15. If the first game is lost, the probability of winning the second game is 25. What is the probability the first game was won if the second game is lost? Express the answer with FOUR decimal points.

Answers

Answer:

[tex]P(\frac{A}{B'})[/tex]=0.111

Step-by-step explanation:

Given:

The probability of winning the first game is 10.1

The first game is won

The probability of winning the second game is 15

If the first is lost, the probability of winning the second game is 25

Solution:

[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]

Answer:

[tex]P(W_1/W_2')=0.1110[/tex]

Step-by-step explanation:

Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]

Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:

[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]

[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]

[tex]P(W_2)=0.24[/tex]

Hence the probability of losing the second game:

[tex]P(W_2')=1-P(W_2)[/tex]

[tex]P(W_2')=0.76[/tex]

Probability of winning the first game when the second game is won:

[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]

[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]

[tex]P(W_1/W_2)=0.0625[/tex]

Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:

[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]

[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]

[tex]P(W_1/W_2')=0.1110[/tex]

I don’t think I got the right answer?

Answers

Answer:

it's third option the one who says 10 units up

its the third answer 10units

4 mangoes and Pears cost $24 while to Mangos in three pears cost $16. Write a pair of simulataneous equations in x and y to represent the information given. State clearly what x and y represent​

Answers

Answer:

x- cost of mango, y- cost of pear, 4x+4y=24 and 2x+3y=16

Step-by-step explanation:

For this, you first must assign variables. In this case, let's say x is the cost of a mango and y is the cost of a pear.

Therefore the total cost for the first part can be given by 4x+4y=24.(or 4 × the cost of a mango + 4 × the cost of a pear = $24).

Following this method, the second equation can be given by 2x+3y=16.

** building upon this knowledge (extension)**

To solve simultaneous equations, we need like terms. To make like terms, we can multiply the entire second equation by 2. This gives 2 equations of 4x+4y=24 and 4x+6y=32.

We solve this by subtracting one equation from another, giving (4x-4x)+(6y-4y)=(32-24), or 2y=8.

We can divide by 2 to get y=4, meaning a pear costs $4.

By substituting y with 4, we can work out x. 4x+4×4=24, also known as 4x+16=24.

We can subtract 16 to get 4x=8, and divide by 4, giving x=2, or a mango costs $2.

**This content involves writing simultaneous equations, which you may wish to revise. I'm always happy to help!

To teach computer programming to employees, many firms use on the job training. A human resources administrator wishes to review the performance of trainees on the final test of the training. The mean of the test scores is 72 with a standard deviation of 5. The distribution of test scores is approximately normal. Find the z-score for a trainee, given a score of 82.

Answers

Answer:

The z-score for the trainee is of 2.

Step-by-step explanation:

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.

The mean of the test scores is 72 with a standard deviation of 5.

This means that [tex]\mu = 72, \sigma = 5[/tex]

Find the z-score for a trainee, given a score of 82.

This is Z when X = 82. So

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

[tex]Z = \frac{82 - 72}{5}[/tex]

[tex]Z = 2[/tex]

The z-score for the trainee is of 2.

simple equation:
6m=12​

Answers

Step-by-step explanation:

Divide both sides of the equation by the same term

6m/6 =12/6

Cancel terms that are in both the numerator and denominatorDivide the numbers

m=2

Answer:

m=2

Step-by-step explanation:

Divide 6 on both sides

6m / 6 = 12/6

m= 12/6 = 2

So, m=2

Verification:

LHS = 6m   m=2

6 * 2 = 12

RHS = 12

Both the LHS and RHS are same, so our answer is correct

An experimental drug is administered to 130 randomly selected individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial experiment

Answers

Answer:

Yes, as for each trial there are only two possible outcomes, the trials are independent, and the number of trials is fixed.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they respond favorably, or they do not. The probability of a student responding favorably is independent of any other student, and the number of trials is fixed. Thus, this probability experiment represents a binomial experiment.

Situation:
You invest $4,000 in an account that
pays an interest rate of 5.5%,
compounded continuously.
Calculate the balance of your account after 15
years. Round your answer to the nearest
hundredth.

Answers

Answer:

[tex]{ \bf{A=(P + \frac{r}{100} ) {}^{n} }} \\ { \tt{ = (4000 + \frac{5.5}{100} ) {}^{15} }} \\ \\ { \tt{ = \: 1.074 \times {10}^{54} \: dollars}}[/tex]


x °
68°
26 °
Find the measure of x (Hint: The sum of the measures
of the angles in a triangle is 180°

Answers:

6 °
86 °
90 °
180 °

Answers

Answer:

86°

Step-by-step explanation:

180° is the sum of all angles in a triangle

The two angles given are 68° and 26°

The equation is : 180° - 68° - 26° = x°

180° - 68° - 26° = 86°

x° = 86°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

15.18. Find the area of the region bounded by
TC
the curve y = cosx, x=0, x= pi/
2 and x-axis.

Answers

Answer:

please mark me brainlist

Step-by-step explanation:

If the bearing of A from B is 125.Find the bearing of B from A

Answers

Answer:

305°

Step-by-step explanation:

The bearing in the reverse direction is 180° plus the bearing in the forward direction, that is

bearing of B from A = 180° + 125° = 305°

Use the graph to find the y-intercept and axis of symmetry

Answers

Answer:

axis of symmetry=-2

y intercept=(0,-1)

Divide: (2n3+4n−9)÷(n+2).

Answers

Answer:

2n+2

_____

9 2n

Find the direction in which the function is increasing most rapidly at the point Po.

f(x, y,z)= xy -lnz , Po (1,1,1)

Answers

The largest rate of change occurs in the same direction as the gradient of f at the point.

f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y, x, -1/z)

==>   ∇f (1, 1, 1) = (1, 1, -1)

In other words, f changes at the highest rate in the direction of the vector (1, 1, -1).

What is the value of x?

Answers

Answer:

22

Step-by-step explanation:

3x-14= 4(x-9)

3×-14= 4x-36

4x-36-3x+14=0

×-22÷0

x=22

Other Questions
Which of the following correctly describes the actions taken in the process represented by section K and L? Evaluate S8 for the series 1+3+6+9+12......... what is photosynthesis Ahmad Conan deposited 60 quarters, 53 dimes, 44 nickels, and 50 pennies into his checking account. The total of the checks he deposited equaled $17 less than twice his total deposit. If Ahmad received 2 twenty-dollar bills in cash, what was his total deposit? p = 6, q = 7 and r = 4 Work out a2 pr compare the following rational number[tex] \frac{4}{5} and \frac{7}{5} [/tex] Randel Manufacturing has five activity cost pools and two products (a budget tape vacuum and a deluxe tape vacuum). Information is presented below: Cost Drivers by Product Activity Cost Pool Ordering and Receiving Machine Setup Machinine Assembly Inspection Cost Driver Estimated Overhead Budget Deluxe $130,000 Orders Setups Machine hours Parts 400 400 150,000 100,000 600 297,000 500 1,000,000 600,000 1,200,000 800,000 300,000 550 450 Compute the overhead cost per unit for each product. Production is 700,000 units of Budget and 200,000 units of Deluxe. (Round overhead cost per unit to 2 decimal places, eg. 12.25 and cost assigned to O decimal places, eg. 2,500) Overhead cost per unit Budget S per unit Deluxe $ per unit s borrows $12,000 for a shortterm purpose. The loan will be repaid after 120 days, with Simpson paying a total of $12,400. What is the approximate cost of credit using the APR, or annual percentage rate, calcula A conservative customer is invested in a large-cap, value-managed equity fund. The stock market drops 10% due to a poor economic forecast for the country. Your customer is upset that his conservative mutual fund lost almost as much as the stock market. What risks does your customer need to understand? Find the length of the arc.A. 539/12 kmB. 9/3 kmC. 9/2 kmD. 18 km I need to solve this, showing work would be appreciated! Nigel makes the claim that x=6 is the solution to the equation 4(5x12)7x=5x. His work to support his claim follows. Given: 4(5x12)7x=5x Step 1: 20x487x=5x Step 2: 20x7x48=5x Step 3: 13x48=5x Step 4: 13x13x48=5x13x Step 5: 048=8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,Step 6 is justified by the Associative Property. Which is the best way to accumulate wealth: a) Save your money by putting it into a savings account at the bank. b) Invest as much money as you can, at the end of each year, (A lump sum) into some sort of long term investment vehicle. c) Contribute to a monthly annuity as early as possible for the long term. d) Invest monthly into an investment vehicle that pays the minimum return. Choose a, b, c, or d and state four reasons why. Find the gradient, picture below Which of the following is a reduction half-reaction? Arrange the following in order of increasing melting point: NaCl, H2O, CH4, C6H4(OH)2.a. NaCl < H2O < CH4 < C6H4(OH)2b. CH4 < H2O < NaCl < C6H4(OH)2c. CH4 < H2O < C6H4(OH)2 < NaCld. CH4 < C6H4(OH)2 < H2O < NaCle. CH4 < NaCl < C6H4(OH)2 < H2O PLEASE HELP!!!The following data are the distance from the workplace ( in miles) for the 5 employees of a small business.10,17,12,14,12Assuming that these distance constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places. Rebecca buys a new couch for $1,200. She plans on making a monthly payment of $75 on the balance, starting the monthafter she buys the couch. Which recursive function models the amount of money Rebecca still has to pay for the couch? Aaron is going to see a movie and is taking his 2 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $3.50 each. How much total money would Aaron have to pay for his family if he were to buy 2 snacks for everybody to share? How much would Aaron have to pay if he bought x snacks for everybody to share? Denny Corporation is considering replacing a technologically obsolete machine with a new state-of-the-art numerically controlled machine. The new machine would cost $130,000 and would have a ten-year useful life. Unfortunately, the new machine would have no salvage value. The new machine would cost $16,000 per year to operate and maintain, but would save $46,000 per year in labor and other costs. The old machine can be sold now for scrap for $13,000. The simple rate of return on the new machine is closest to (Ignore income taxes.):