Administrators want to understand how currently enrolled students are placing into their current math class. They randomly choose five math courses and ask the instructors to post a survey on their Canvas site for students to complete within the first week of class. The administrators will calculate the proportion of students that placed into their math class by their high school GPA..
a) What is the population of interest?
b) What is the population parameter of interest?
c) What is the sampling frame?
d) Describe the sample.
e) What type of sampling method was used for this study?
f) Who was possibly left out of this study?!

Answer:

Step-by-step explanation:

We are given the matrix

[tex] A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right] [/tex]

a) To find the characteristic polynomial we calculate [tex]\text{det}(A-\lambda I)=0[/tex] where I is the identity matrix of appropiate size. in this case the characteristic polynomial is

[tex]\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0[/tex]

Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is

[tex](4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0[/tex]

which is the characteristic polynomial of A.

b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are [tex]\lambda=4,3,-1[/tex]

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression [tex]A-\lambda I[/tex] and solve the system [tex](A-\lambda I)x =0[/tex] by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider [tex]\lambda = 4[/tex]. We get the matrix

[tex]\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right] [/tex]

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

[tex](x,y,z) = (5z,5z,z) = z(5,5,1)[/tex]

So, the base for this eigenspace is the vector (5,5,1).

If [tex]\lambda = 3[/tex] then the base is (0,4,3) and if [tex]\lambda = -1[/tex] then the base is (0,0,1)

Answer:

C. Independent, 49/1296

Step-by-step explanation:

A jar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.

Total balls = 12+7+10+7

Total balls= 36

Two balls are chosen at random with replacement.

The probability that the both balls are green = probability of the first ball to he green * probability of the second ball to be green

The probability that the both balls are green= 7/36 * 7/36

The probability that the both balls are green= 49/1296

The probability that the both balls are green= 49/1296

Answer:

I am from India telangana

Answer:

Answer:

Step-by-step explanation:

Hello!

The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.

Sample 1: Advanced tennis players

X₁: Force (N) on the hand just after impact on a one- handed backhand drive for an advanced tennis player.

n₁= 6

X[bar]₁= 40.29 N

S₁= 11.29

Sample 2: Intermediate players

X₂: Force (N) on the hand just after impact on a one- handed backhand drive for an intermediate tennis player.

n₂= 8

X[bar]₂= 21.40

S₂= 8.30

Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.

If the force is greater for the advanced players than for the intermediate players, then you'd expect the population mean for the advanced players to be greater than the population mean for the intermediate players:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

α: 0.05

[tex]t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{5*127.51+7*68.92}{6+8-2} }= 9.66[/tex]

[tex]t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62[/tex]

Using the p-value approach, the decision rule is

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.

This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.

I hope this helps!

Answer:

B)

Step-by-step explanation:

Slope = -3

Y-intercept = 3

So

Equation is

y = mx+b

Where m is slope and b is y-intercept

y = -3x+3

Answer: A

Step-by-step explanation: A is the correct answer because once you do the math (6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.

If you found this answer helpful, give it a five star rating and a thanks!

(Even a brainliest if you want ;D)

Answer:a

Step-by-step explanation:

Answer:

  -23

Step-by-step explanation:

We note that as x increases by 36 from -72 to 36, y decreases by 24 from 25 to 1.

Increasing x from -36 by another 36 to zero will correspond to a decrease in y by another 24 from 1 to -23.

The y-intercept is -23.

_____

You could go to the trouble to use these observations to compute the slope as -24/36 = -2/3. Then you could pick one of the points and write the equation in point-slope form as ...

  y = -2/3(x +36) +1 . . . point-slope form with m=-2/3, (h, k) = (-36, 1)

  y = -2/3x -24 +1 . . . . . eliminate parentheses

  y = -2/3x -23 . . . . . . . y-intercept is -23

Answer:

A 90° counterclockwise rotation about the origin and then a translation 16 units right and 16 units up

Solution -Rotating the triangle 90° counterclockwise will take the triangle to 3rd quadrant and then further moving it 16 steps right will take it to 4th quadrant and followed by 16 steps upward will take it to the desired position which is in 1st quadrant.

Answer:

5 cm

Step-by-step explanation:

Use lenght times wight times height

So, you need to do 4 times 4 times ________ is 80

Answer:16/16c-4/8d

Step-by-step explanation:

Answer:

Probability of a sum of 9 = 0.111111

OR

Probability of a sum of 9 = 1/9

Step-by-step explanation:

Carrie rolls 2 fair dice and adds the results from each.

The total sample space = 36

Gotten from 6²= 36

The probability of getting a total of 9

Now let's look at the possible sum to give us a 9 (3 and 6, 4 and 5) twice.

So we gave number of occurrence of 9 to be four.

Probability of a sum of 9 = 4/36

Probability of a sum of 9 =1/9

Probability of a sum of 9 = 0.111111

The probability of getting a total of 9 is 0.111111 and this can be determined by using the concept of probability.

Given :

Carrie rolls 2 fair dice and adds the results from each.

The sample space is equal to [tex]6^2[/tex] that is 36. The numbers require on both the dices to get the sum equal to 9 are 4 and 5 or 6 and 3.

So, there is a total of 4 numbers in 36 sample size in order to get the sum of 9.

Now, the probability of getting a total of 9 is given by:

[tex]\rm P=\dfrac{4}{36}[/tex]

Further, simplify the above expression.

[tex]\rm P = \dfrac{1}{9}[/tex]

P = 0.111111

So, the probability of getting a total of 9 is 0.111111.

For more information, refer to the link given below:

https://brainly.com/question/23017717

Answer:

[tex]scalene \: triangle[/tex]

Step-by-step explanation:

The above given triangle represents the unequal lengths of three sides properties of scalene triangle

Hope this helps you out!!!

Answer:

Create equivalent expressions in the equation that all have equal bases, then solve for  

x

.

Exact Form:

5/3

Decimal Form:

x

=

1.6

Mixed Number Form:

x

=

1  2/3

Answer:-3

Step-by-step explanation:

Answer:

8 ( 6 m 5^ + n 2^ )

Answer:

8( 6m^5 + n^2)

Step-by-step explanation:

48m^5+8n^2

Factor out 8

8* 6m^5 + 8 * n^2

8( 6m^5 + n^2)

Answer:

Step-by-step explanation:

Answer:

[tex]t \approx 36.1\,min[/tex]

Step-by-step explanation:

The time constant for the isotope decay is:

[tex]\tau = \frac{8\min}{\ln 2}[/tex]

[tex]\tau \approx 11.542\,min[/tex]

Now, the decay of the isotope is modelled after the following expression:

[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]

The time is now cleared with some algebraic handling:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]

Finally, the time need for the element X to decay to 43 grams is:

[tex]t = - (11.542\,min)\cdot \ln\left(\frac{43\,g}{980\,g} \right)[/tex]

[tex]t \approx 36.1\,min[/tex]

Answer:

2.34-1.7*0.2=2

Step-by-step explanation:

Well to solve this, we need to use PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Multiplication comes first before subtraction. You can do long multiplication for this and multiply 1.7 and 0.2 together. Once done that, the product of those 2 numbers are 0.34.

Now 2.34-0.34=2.00

Our answer is 2.

Answer:

2

Step-by-step explanation

1.7 x 0.2 = 0.34

2.34-0.34=2

Answer:

The Net Present Value =  $451180.733

Step-by-step explanation:

Given that:

the initial cost of the project is $1670000

the initial increase in working capital is $198000

The total investment will be ; initial cost of the project + initial increase in working capital

The total investment = $1670000 + $198000

The total investment = $1868000

So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;

Now; lets determine the rate of the annual depreciation

The annual depreciation = [tex]\dfrac{Initial \ cost \ of \ project }{life \ of \ project}[/tex]

The annual depreciation = [tex]\dfrac{1670000}{4}[/tex]

The annual depreciation = $417500

Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:

annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )

Given that the tax rate = 21% = 0.21

annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)

annual operating cash flow = 812000 × 0.79 + 87675

annual operating cash flow = 641480 +  87675

annual operating cash flow = $729155

So; let's calculate the after tax salvage value for the project

We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)

Thus; the book value is zero

The after tax salvage value for the project can now be determined by the relation:

after tax salvage value = sale value - tax (sale value - book value)

after tax salvage value =  435000  - 0.21 (435,000 -0)

after tax salvage value = 435000 - 91350

after tax salvage value = $343650

Similarly; given that the recovering rate of the project is $198000;

The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital

cash flow in year 4 = $(729155 + 343650 + 198000)

cash flow in year 4 = $ 1270805

This implies that the cash flow from year one to three is : 729155

the cash flow in year four is : 1270805

Given that the Required return rate = 16.4% = 0.164

We can therefore determine the Present cash inflows by using the relation:

[tex]Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}[/tex]

[tex]Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}[/tex]

[tex]Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}[/tex]

Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)

Present Value = $2319180.733

Finally, The net present value = Present Value - Total Investment

Net Present Value = $(2319180.733 - 1868000)

Net Present Value =  $451180.733

Therefore; The Net Present Value =  $451180.733

Answer:

2 / 77

Step-by-step explanation:

Each number appears 3 times in the urn.

After picking any number, the number picked will appear only two more times in the urn, and the total slips of paper will be 77.

So for any first number we pick, the probability of the second number picked being the same number as the first pick is the number of times the same number appears in the urn (2) over the total number of slips in the urn (77):

Probability = 2 / 77

Step-by-step explanation:

There is no question asked here, bit of course it is possible to predict the life expectancies of a lot of things. This takes patience, resistance, and persistence, because working on something that takes time without persistence would result in a painful waste of time.

To predict the life expectancy of an effect is to predict how long it is going to take before it goes extinct, or seize from existence.

Answer:5

Step-by-step explanation:

Car B, the SUV, obviously holds more fuel after 0 driven miles, 60 gallons, while car A holds 10 gallons after 0 miles.

let's speak about miles with the abbreviation x.

sk at x=0 Car B got more fuel.

Car A gets 60 Miles per gallon, it's consuming 1/60 gallon per mile. The amount of fuel decreases by 1/60 per mile

After each mile, or each x-step, Car A has

This can be expressed mathematically:

A(x) = -1/60*x + 10

The -1/60x is, again, the consumption per mile, the +10 is the full tank at the start.

A(0)= -1/60*0 + 10

=10

For Car B the consumption is 1/2 gallons per mile and the tank holds 60 gallons of fuel, wich ammount is decreases with traveled distance.

B(x) = -1/2*x + 60

See that we could draw these two functions as lines in a coordinate system. (I did it with desmos btw). This step is just to help understand.

After some distance/ amount x of miles, Car A will hold more fuel than car B, because it drives more efficiently.

In the picture we can see that this is after about 100 miles and we could guess the amount of fuel, but I won't. Let's calculate it and then answer the question precisely.

We get the intersection of the two lines by setting them equal, a(x)=b(x)

-1/60x + 10 = -1/2x + 60

Exactly one point lies, equally, on both lines

So let's solve for x

Further on the right, each step is explained. we have to do the same operation on both sides of the equation, just to not break it.

-1/60x + 10 = -1/2x + 60 | -10

-1/60x = -1/2x + 50 | + 1/2x

-1/60x + 1/2x = 50 | *60

-1x + 30x = 3000

29x = 3000 | /29

x = 103.448275862

so after about 103.45 miles, Car B holds less fuel than Car A (and Car A more than Car B), until both are empty. Car B could therefore drive more miles

We can also ask how much fuel is left in both tanks at the intersection point by plugging the x-value we got into one of the equations (doesn't matter which one, since the point is the same)

a(103.4482) = -1/60 * 103.4482 + 10 = 8.28

If you want it to be precise, stay with fractions

a(3000/29) = -1/60 * 3000/29 + 10

= -50/29 +10

= 9 -21/29

= 8 + 8/29

Finding out how far each car could travel would be achieved by setting their fuel-equation equal to 0, because that's the value of it when they run of of fuel. For example 0 = -1/60x+10, then you (just) solve for x.

I did overshoot the given problem to offer offer you understanding that's spans more of the topic you are dealing with

(would really appreciate the brainliest)

Answer: B. 4 hours

Step-by-step explanation:

Answer:

The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.

Ha: p < 0.32

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Let p represent the proportion of the students surveyed that rarely or never use academic advising services.

The null hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is equal to 32% or 0.32.

H0: p = 0.32

The alternative hypothesis is that the proportion of the students surveyed that rarely or never use academic advising services is less than 32% or 0.32. That is the students use of academic advising has increased.

Ha: p < 0.32

Answer:

c) 118°

Step-by-step explanation:

PN is the diameter of the given circle.

[tex] \purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\[/tex]

Now, by inscribed angle theorem:

[tex] m\widehat {MN} = 2\times m\angle MPN\\

\therefore m\widehat {MN} = 2\times 31°\\

\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\[/tex]

Now,

[tex] \because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\

\therefore m(\widehat{MP}) + 62° =180°\\

\therefore m(\widehat{MP}) =180°-62°\\

\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\[/tex]

Answer:

A. True

B. True

C. False

D. True

Step-by-step explanation:

A) To find the probability of the letters spelling CAT go to the letter C, then A, and finally T. there is only one sequence that does this, so the numerator will be 1. There are 6 outcomes overall, so the denominator will be 6. The probability of the letters spelling CAT would be 1/6. The answer is true.

B) To find the probability of T being the first letter go to the letter T. All sequences after the letter T will all be included in the answer. TAC and TCA are both possible solutions, this means there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of T being the first letter is 2/6, which is equal to 1/3. The answer is true.

C) To find the probability of A being the first letter go to the letter A. All sequences after the letter A will all be included in the answer. ACT and ATC are both possible solutions, this mean there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of A being the first letter is 2/6. The answer is false.

D) To find how many total outcomes are possible go to the tree diagram and look to the far right. Go down each of the rows to find all of the outcomes, there is T,C,T,A,C, and A. That means there are six possible outcomes. The answer is true.

Answer:

b) equals 20 hours.

Step-by-step explanation:

The sampling distribution of means refers to the distribution of all the possible sample means, with a certain sample size (in this case, n=100) extracted from the population.

The sampling distribution of the means is equal to the population mean. That does not mean that every sample will result in a mean equal to the population, but that the population of sample means will have an average of 20 hours.

Answer:

A = $ 181,824 rounded

Step-by-step explanation:

A = $ 181,823.93

A = P + I where

P (principal) = $ 69,000.00

I (interest) = $ 112,823.93