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goblinko [34]
4 years ago
13

@potatoeewedge

Mathematics
1 answer:
lyudmila [28]4 years ago
4 0
The given problem is a right triangle, we can use Pythagorean theorem and SOH CAH TOA in solving the unknown.
For item#1, 
sin B = AC/AB
sin 32° = AC/12
AC=6.36 cm

For item#2, 
cos B = BC/AB
cos 41° = BC/5
BC = 3.77 cm

For item#3,
tanA=BC/AC
tan 56 = 24/AC
AC = 16.19 cm
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A. How many ways can you distribute $4$ different balls among $4$ different boxes? B. How many ways can you distribute $4$ ident
zysi [14]

Answer:

The answer is explained below

Step-by-step explanation:

A. How many ways can you distribute 4 different balls among 4 different boxes

The number of ways in which 4 different balls can be distributed among 4 different boxes is 4^4=256\ ways

B. How many ways can you distribute 4 identical balls among 4 identical boxes?

The number of ways in which 4 identical balls can be distributed among 4 identical boxes = P(4,1) + P(4,2) +P(4,3) + P(4,4) = 1 + 2 + 1 + 1 = 5 ways

Where P(k,n) is the number of partitions that k can be divided into n parts

P(4,1) = 4 = 1

P(4,2) = 1 + 3, 2+2 = 2

P(4,3) = 1 + 1 + 2 = 1

P(4,4) = 1 + 1 + 1 + 1 = 1

C. How many ways can you distribute 4 identical balls among 4 different boxes

The number of ways in which 4 identical balls can be distributed among 4 different boxes = C(4\ ball+4\ box-1,4\ box-1)=C(7,3)=\frac{7!}{(7-3)!3!}=35\ ways

7 0
3 years ago
You randomly choose one of the tiles shown. Select the favorable outcome(s) of choosing a 6.<br>​
Alona [7]

Answer:

If there are 6 tiles, the probability is 1/6

Step-by-step explanation:

6 0
4 years ago
A test has 20 true/false questions. What is the probability that a student passes the test if they guess the answers? Passing me
Minchanka [31]

Using the binomial distribution, it is found that:

The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.

For each question, there are only two possible outcomes, either the guess is correct, or it is not. The guess on a question is independent of any other question, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • There are 20 questions, hence n = 20.
  • Each question has 2 options, one of which is correct, hence p = \frac{1}{2} = 0.5

The probability is:

P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)

In which:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 15) = C_{20,15}.(0.5)^{15}.(0.5)^{5} = 0.0148

P(X = 16) = C_{20,16}.(0.5)^{16}.(0.5)^{4} = 0.0046

P(X = 17) = C_{20,17}.(0.5)^{17}.(0.5)^{3} = 0.0011

P(X = 18) = C_{20,18}.(0.5)^{18}.(0.5)^{2} = 0.0002

P(X = 16) = C_{20,19}.(0.5)^{19}.(0.5)^{1} = 0

P(X = 17) = C_{20,20}.(0.5)^{20}.(0.5)^{0} = 0

Then:

P(X \geq 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0 + 0 = 0.0207

The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.

You can learn more about the binomial distribution at brainly.com/question/24863377

6 0
3 years ago
A cell phone provider charges $30 each month to have a cell on their plan, but their talk and text are not free. It costs $0.05
Annette [7]

Answer:

30+0.10x+0.05t

talk more than text

Step-by-step explanation:

8 0
3 years ago
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Alexxx [7]

Answer:

There is a 91.6% increase from 12 to 23 ft


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