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snow_tiger [21]
2 years ago
13

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors

. A random sample of 300 students taken from this year's student body showed the following number of students in each class.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
A) What is the expected number of freshmen?
B) What is the expected number of seniors?
C) What is the calculated value for the test statistic?
D) What is the p-value?
E) At 95% confidence, should the null hypothesis be rejected?
Mathematics
1 answer:
goblinko [34]2 years ago
8 0

Answer:

1.66

Step-by-step explanation:

We need to conduct a chi square test

The statistic used to check this is given by the below

∑(n, 1) = [(O(i) - E(i)] / E(i)

From the question, we're told the observed value is

Freshmen

Sophomore

Junior

Senior.

After that, we then calculate the expected value.

Freshman

0.3 * 300 = $90

Sophomore

0.24 * 300 = $72

Statistics then finally gives us this

X² = (93 - 90²)/90 + (68 - 72)²/72 + (85 - 78)/78 + (64 -60)²/60

X² = 3² / 90 + 4² / 73 + 13² / 78 + 4² / 60

X² = 0.1 + 0.212 + 2.167 + 0.266 x+

X² = 2.745

X = √2.745

X = 1.66

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What is a obtuse angle? ​
Brrunno [24]

Answer:

An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.

Step-by-step explanation:

6 0
2 years ago
A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
dexar [7]

Answer:

The total revenue is TR=580x-10x^2.

The marginal revenue is MR=580-20x.

The fixed cost is $900.

The marginal cost function is MC=50x+300.

Step-by-step explanation:

The Total Revenue (TR) received from the sale of x goods at price p is given by

                                                         TR=p\cdot x

The Marginal Revenue (MR) is the derivative of total revenue with respect to demand and is given by

                                                       MR=\frac{d(TR)}{dx}

From the information given we know that the price they can sell cakes is given by the function p=580-10x, where x is the number of cakes sold per day.

So, the total revenue is

TR=(580-10x)\cdot x\\TR=580x-10x^2

And the marginal revenue is

MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x

The Fixed Cost (FC) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost (MC) function is the derivative of the cost function and is given by

                                                   MC=\frac{d(TC)}{dx}

We know that the total cost function of the company is given by C=(30+5x)^2, which it is equal to

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300

4 0
3 years ago
A system of two equations is shown.
Delvig [45]

Answer:

x=-2;y=-7

Step-by-step explanation:

y=5x+3

y=3x-1

3x-1=5x+3

-2x=4

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8 0
2 years ago
Solve the SYSTEM: <br> 2x - 3y = 12<br> 3x - 2y = 13
dangina [55]

Answer:

x =69 y= 420

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6 0
2 years ago
Factor completely 56a2b3 − 35ab.
VMariaS [17]

I would start off by taking away 1a. That would make the problem be 56ab3-35b.I only took away 1 because each have at least 1a and is okay to do.


Next I would deal with the variable b. I would cross of 1 b. That's because both sides have at least 1b.  Now, it's shortened to be 56ab2-35.


Since you cannot take away anymore variables, you have to deal with 56 and 35. I start small with dividing each by 2. I am trying to see what the greatest number could be while making the numbers still be whole. That turns 56 into 28 when it's cut in half. The 35 now turns into 17.5.


I would assume your teacher would want the numbers to be whole. seeing as though when 35 is cut in half and makes a decimal number, I would leave them. What I mean by that is to leave the numbers as 56 and 35.


So, that means the answer is 56ab2-35.


I hope this helps!! (And makes sense)

5 0
3 years ago
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