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timurjin [86]
3 years ago
8

A history exam features five questions. Three of the questions are multiple-choice with four options each. The other two questio

ns are true or false. If Caroline selects one answer for every question, how many different ways can she answer the exam?
Mathematics
1 answer:
nadezda [96]3 years ago
8 0

There are total 500 ways in which Caroline can answer the exam.

Step-by-step explanation:

Here, the total number of questions in the test  = 5

The total number of multiple choice questions = 3

The total number of True/False question = 2

Let the numbers of the given question be 1,2 ,3,4, and 5.

Now, the total number of options available to answer question 1 = 5 options

Similarly,  number of options available to answer question 2 = 5 options

The number of options available to answer question 3 = 5 options

The number of options available to answer question 4 = 2 options ( T or F)

The number of options available to answer question 5 = 2 options ( T or F)

So, here the total available options to answer all 5 questions

= The total option available for  question ( 1 x 2 x 3 x 4 x 5)

= ( 5 ways  x 5 ways x 5 ways x 2 ways x 2 ways)

= 500 ways

Hence, there are total 500 ways in which Caroline can answer the exam.

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PLEASE HELP ME IM STUCK ON THIS QUESTION.
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Answer:

You got it right. Triangle DAC

Step-by-step explanation:

Line segment DA is a perpendicular bisector(it cuts line segment CE perfectly in half making line segment AE an CA congruent. Since the triangle share line segment DA that makes them congruent by the SAS postulate

6 0
3 years ago
What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth
iVinArrow [24]
Approximate solutions are

X subset 2 is approximately equal to -2.72

X subset 1 is approximately equal to -0.28
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3 years ago
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The point halfway between two end points of a line segment is a
Liula [17]
The point halfway between two end points is called a midpoint
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11. A roofer calculates his bid price using the formula P = 1.85s + 4.2f, where s is the area of the roof in square feet and f i
storchak [24]

Replace f with 190, replace P with 4148 and solve for  s:

4148 = 1.85s + 4.2(190)

Simplify:

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Divide both sides by 1.85:

s = 1,810.81

Rounded to nearest square foot = 1811 square feet.

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3 years ago
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Find the mean and variance of the following data<br><br> 52,34,64,49,55,26,38,63
BlackZzzverrR [31]

Answer:

Mean = 47,625

Variance, ignoring the commas = 157

Explanation:

The mean is quite simple: is the mid value of an amount (m') of numbers.

Examples:

Mean of 2, 4:  2 + 4/2 = 3

Mean of 5, 6 and 8: 1+6+8/3 = 15/3 = 5

Generalizing: M' = An + Bn-1 + Cn-2 +... + Y1/ n

So, for the enunciated, we have:

M = 52 + 34 + 64 + 49 + 55 + 26 + 38 + 63/8

M = 47,625

Variance is quite harder.

The mathematics definition is also quite harder:

∑n, i=1 (Xi - X')²/n

Traduction: the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, divided by the number of observed terms is the square of the standard deviation, that is, the variance.

Don't worry, you don't need to understand that. I'll do the question, then you will see in practice what that means.

First, we need the mean of the observerd terms. We already have done that.

M = 47,625.

Next, we will do the the difference o<em>f the square </em>of the dispersion measures by the arithmetic mean of them. Which are:

A.52 - 47,625 = (4,375)²

B.34 - 47,625 = (-13,625)² - <em>Because of a value like that, you know see why</em>

C.64 - 47,625 = (16,375)²

D.49 - 47,625 = (1,375)²

E.55 - 47,625 = (7,375)²

F.26 - 47,625 = (-21,625)² - <em>we need to square everything: because a negati</em>

G.38 - 47,625 = (-9,625)² - <em>ve result doest not help in the statisc.</em>

K.63 - 47,625 = (15,375)²

I am using a calculator, but really with that, I'll aproximately the values. If you need a accurate measure, just square them all the way.

A = 16     D  = 1     G = 100

B = 169    E = 49    K = 225

C = 256   F = 441

The last part is the sum of the difference of the square of the dispersion measures by the arithmetic mean of them, dividing them by the number of observations.

16 + 169 + 256 + 1 + 49 + 441 + 100 + 225/ 8 = 157,125

8 is the number of observations.

___________________________

But why we do the variance? The variance serves to us for know how much the mean is precise.

So, the lower is the variance, the better is the mean.

Take a look on this example:

Imagine three persons, A, B and C.

They are in pub, talking about how much they receive. A gets, per month, 1000US$, b 2000 and C 3000US$.

So, their mean are 3000US$.

Now imagine that Bill Gates joins the group. And Bill, last month, got 100 milion US$.

Now the mean will be almost 25 milions of dollars.  So, she is VERY far from the reality of the major part of the group. And is in there that cames the variance. Looking to the variance, we will see that there is a big discrepancy for each observed term.

5 0
3 years ago
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