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Alchen [17]
3 years ago
7

14. Consider the following questions: give the distribution name, carefully define the random variables you use and find the fin

al answer. a) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receive a hard test
Mathematics
1 answer:
malfutka [58]3 years ago
6 0

Answer: the probability that no sections receive a hard test is 0.1022

Step-by-step explanation:

Given that;

total number of exams = 20

hard exams = 8

reasonable = 7

easy exam = 5

so total exams that are bot hard = 7 + 5 = 12

we will make use of the probability mass function of hyper geometric distribution;

so the probability that no section of the received a hard test can be determined as follows;

P( x=0; N=20, n=4, k=8 ) = [ ⁸C₀ × ²⁰⁻⁸C₄₋₀ ] / ²⁰C₄

= [1 × ¹²C₄ ] / ²⁰C₄

= [1 × (12!/(4!×(12-4)!) ] / (20!/(4!×(20-4)!)

= [1 × 495 ] / 4845

= 495 / 4845

= 0.1022

Therefore the probability that no sections receive a hard test is 0.1022

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Which sequence of similar transformations could map △ABC onto △A'B'C'?
nadya68 [22]

Answer:  A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.


Step-by-step explanation:

Similar transformations:  If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.

In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.

7 0
3 years ago
Read 2 more answers
Write an integer that represents the situation. Do not type any units, labels, or spaces on your answer will be scored as incorr
NISA [10]

Answer:

The integer that represents the situation is 5.

Step-by-step explanation:

When you gain 5 yards, that is considered a positive increase in value.

You can either put 5 or +5 because they indicate the same positive value.

3 0
3 years ago
The area of a square is 25/36 in.2 what is the length of it's side?
Lesechka [4]
Our hint here is the identity of the shape. It is mentioned that the shape is a square. By definition, a square is a two-dimensional with four sides having equal measures. The formula for its area is:

A = s², where s is the length of its side
Substituting the value of A,
25/36 in² = s²
s = √(25/36)
s = 5/6 inches or 0.833 inches
4 0
3 years ago
The numbers 1, 2, 3, 4, 5, 6, 7, and 8 are arranged to form four two-digit numbers. What is the largest amount of primes that co
artcher [175]
<h3>Answer:  3 primes</h3>

==========================================================

Reason:

The only even prime number is 2. The other primes are odd.

The list of the first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

A prime is any number that has factors of 1 and itself, and nothing else.

For instance, 13 is prime because 1 and 13 are the only factors.

-----------

As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).

So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.

So we reduce the list of choices to 1, 3, 7, 9 for the units digit.

Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.

-----------

Let's try to build some primes.

Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.

On the other hand, 31 is prime since only 1 and 31 are factors.

The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.

Cross 1 and 4 off the list.

The next odd number is 3 which is our units digit. The value 23 is prime.

So far we have 41 and 23 as our two primes.

Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.

The number 67 is prime for similar reasoning mentioned earlier.

------------

We have these primes: 41, 23, 67

The next number either 58 or 85 isn't prime

This is one way to show an example of why we're only able to get 3 primes out of this.

4 0
2 years ago
You and your friend are making mashed potatoes. You get sent to the store with $10 and are asked to buy the potatoes. Your frien
Mariulka [41]

Answer:

0.40x ≤ 10

x = 22

Step-by-step explanation:

divide .40 on each side and you get 22.2 repeating

so, itd be 22, 23 would be over budget

5 0
3 years ago
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