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fomenos
2 years ago
7

A multiple choice test has two parts. There are 4^12 ways to answer the 12 questions in Part A. There are 4^5 ways to answer the

5 questions on part B. How many ways are there to answer all 17 questions? If you guess each answer, what is the probability you will get them all right
Mathematics
1 answer:
LiRa [457]2 years ago
8 0

Using the Fundamental Counting Theorem and the probability concept, it is found that:

  • There are 4^{17} ways to answer all 17 questions.
  • 4^{-17} probability you will get them all right.

<h3>What is the Fundamental Counting Theorem?</h3>
  • It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

<h3>What is a probability?</h3>
  • A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

  • The questions in part A and in part B are independent.
  • For the 12 questions in part A, there are 4^{12} ways to answer, hence n_1 = 4^{12}.
  • For the 5 questions in part B, there are 4^{5} ways to answer, hence n_2 = 4^{5}.

Then:

N = n_1 \times n_2 = 4^{12} \times 4^5 = 4^{17}

There are 4^{17} ways to answer all 17 questions.

Only one outcome in which all the guesses are correct, hence:

p = \frac{1}{4^{17}} = 4^{-17} probability you will get them all right.

You can learn more about the Fundamental Counting Theorem at brainly.com/question/24314866

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olasank [31]
Honi maded the mistake in step 1
4 0
2 years ago
Read 2 more answers
What is the inverse of the function f(x) = 2x + 1? h(x) = 1/2x - 1/2
sweet-ann [11.9K]

Answer:

h(x) = x/2 - 1/2

Step-by-step explanation:

Here's the procedure for finding the inverse function algebraically:

1.  Replace the label 'f(x)' with the label 'y:'  y = 2x + 1

2. Interchange x and y:  x = 2y + 1

3.  Solve the resulting equation for y:  2y = x - 1, or y = (1/2)(x - 1) or y = x/2 - 1/2

This result corresponds to the 1st given possible answer choice.

The desired inverse function is h(x) = x/2 - 1/2

3 0
3 years ago
Dakota has \dfrac4{10} \text { kg} 10 4 ​ kgstart fraction, 4, divided by, 10, end fraction, start text, space, k, g, end text o
Savatey [412]

Answer:

There are <u>2.22 grams</u> of clay are in each pot.

Step-by-step explanation:

Given:

Dakota has 4/10 kg of clay. He divides the clay to make 888 equal-sized pots.

Now, to find the number of grams of clay are in each pot.

Dakota has clay = \frac{4}{10} \ kg.

So, by using conversion factor we convert it into grams:

\frac{4}{10} \times 1000\\\\=\frac{4000}{10} \\\\=400\ grams.

Quantity of clay he has = 400 grams.

Number of equal-sized pots to make = 888.

Now, to get the quantity of grams of clay are in each pot we divide number of equal-sized pots to make by quantity of clay he has:

\frac{888}{400}

=2.22\ grams.

Therefore, there are 2.22 grams of clay are in each pot.

3 0
3 years ago
-8/9 - (2 1/3)<br> show all your work
Sauron [17]

Answer:

1 8/9 - 1 2/3 = 2/

9

≅ 0.2222222

Step-by-step explanation:

How do you solve fractions step by step?

Conversion a mixed number 1 8/

9

to a improper fraction: 1 8/9 = 1 8/

9

= 1 · 9 + 8/

9

= 9 + 8/

9

= 17/

9

To find a new numerator:

a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/

9

= 9/

9

b) Add the answer from previous step 9 to the numerator 8. New numerator is 9 + 8 = 17

c) Write a previous answer (new numerator 17) over the denominator 9.

One and eight ninths is seventeen ninths

Conversion a mixed number 1 2/

3

to a improper fraction: 1 2/3 = 1 2/

3

= 1 · 3 + 2/

3

= 3 + 2/

3

= 5/

3

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/

3

= 3/

3

b) Add the answer from previous step 3 to the numerator 2. New numerator is 3 + 2 = 5

c) Write a previous answer (new numerator 5) over the denominator 3.

One and two thirds is five thirds

Subtract: 17/

9

- 5/

3

= 17/

9

- 5 · 3/

3 · 3

= 17/

9

- 15/

9

= 17 - 15/

9

= 2/

9

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(9, 3) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seventeen ninths minus five thirds = two ninths

8 0
2 years ago
1+4=5 2+5=12 3+6=21 8+11=?
satela [25.4K]
That whole eqation is 40
6 0
2 years ago
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