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rosijanka [135]
3 years ago
7

Kali has a 20 foot ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 5 feet away from t

he base of the tree. How high into the tree will the ladder reach? Round your answer to the nearest tenth of a foot.
Mathematics
1 answer:
Musya8 [376]3 years ago
3 0
A^2 + b^2 = c^2
5^2 + b^2 = 20^2
25 + b^2 = 400
b^2 = 375
b = 19.4 feet
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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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Using all four of the digits 5,6,7,9 and any of the 4 operations, +,-, division, and x can you make 36
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Step-by-step explanation:

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6. (4.2.12) Of the items manufactured by a certain process, 20% are defective. Of the defective items, 60% can be repaired. a. F
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Answer:

(a) Probability that a randomly chosen item is defective and cannot be repaired is 8%.

(b) Probability that exactly 2 of 20 randomly chosen items are defective and cannot be repaired is 0.2711.

Step-by-step explanation:

We are given that of the items manufactured by a certain process, 20% are defective. Of the defective items, 60% can be repaired.

Let Probability that item are defective = P(D) = 0.20

Also, R = event of item being repaired

Probability of items being repaired from the given defective items = P(R/D) = 0.60

<em>So, Probability of items not being repaired from the given defective items = P(R'/D) = 1 - P(R/D) = 1 - 0.60 = 0.40 </em>

(a) Probability that a randomly chosen item is defective and cannot be repaired = Probability of items being defective \times Probability of items not being repaired from the given defective items

              = 0.20 \times 0.40 = 0.08 or 8%

So, probability that a randomly chosen item is defective and cannot be repaired is 8%.

(b) Now we have to find the probability that exactly 2 of 20 randomly chosen items are defective and cannot be repaired.

The above situation can be represented through Binomial distribution;

P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....

where, n = number of trials (samples) taken = 20 items

            r = number of success = exactly 2

           p = probability of success which in our question is % of randomly

                  chosen item to be defective and cannot be repaired, i.e; 8%

<em>LET X = Number of items that are defective and cannot be repaired</em>

So, it means X ~ Binom(n=20, p=0.08)

Now, Probability that exactly 2 of 20 randomly chosen items are defective and cannot be repaired is given by = P(X = 2)

   P(X = 2) = \binom{20}{2} \times 0.08^{2} \times  (1-0.08)^{20-2}

                 = 190 \times 0.08^{2}  \times 0.92^{18}

                 = 0.2711

<em>Therefore, probability that exactly 2 of 20 randomly chosen items are defective and cannot be repaired is </em><em>0.2711.</em>

             

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