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3 years ago

The probability of getting a 6 is 4/5. The dice is rolled 500 times How many sixes would you expect to roll

Mathematics

1 answer:

slavikrds [6]3 years ago

4 0

Answer: 400

Step-by-step explanation:

From the question, we are informed that the probability of getting a 6 is 4/5 and that the dice is rolled 500 times.

The number of sixes that would be expected to roll will be 4/5 multiplied by the number the dice is rolled

= 4/5 × 500

= 400

There'll be 400 sixes.

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Do the rules described result in a fair situation?

AysviL [449]

yes it would be yes so yes

4 0

3 years ago

How do you do this question?

marishachu [46]

Answer:

100

Step-by-step explanation:

│an − L│< ε

│(1 − 1/n) − 1│< 1/100

│-1/n│< 1/100

1/n < 1/100

n > 100

3 0

3 years ago

Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B

Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

$|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}$

$|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}$

$2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4$

$10\cos{(m\angle{ABC})} = 4$

$\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}$

$m\angle{ABC} = cos^{-1}{(\frac{2}{5})}$

$m\angle{ABC} = 66.4218^{\circ}$

Rounded to two decimal places:

$m\angle{ABC} = 66.42^\circ$

3 0

2 years ago

1-22 teacher was no help

damaskus [11]

1) 1,2,3,4,5,6,7
2) -3,-2,-1,0,1,2,3,4,5,6,7
3)-3,-2,-1
4)1,2,3,4

3 0

3 years ago

You get GPS units from two manufacturers, A and B. You get 43% of your units from A and 57% of your units from B. In the past, 2

defon

Answer:

0.5015 = 50.15% probability that it came from manufacturer A.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: From manufacturer A.

Probability a unit is defective:

2% of 43%(from manufacturer A)

1.5% of 57%(from manufacturer B). So

$P(A) = 0.02*0.43 + 0.015*0.57 = 0.01715$

Probability a unit is defective and from manufacturer A:

2% of 43%. So

$P(A \cap B) = 0.02*0.43 = 0.0086$

What is the probability that it came from manufacturer A?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0086}{0.01715} = 0.5015$

0.5015 = 50.15% probability that it came from manufacturer A.

4 0

3 years ago