What is the equation of the line that has a slope of -5 and passes through the point (0,2)

10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

$p = \frac{4}{6} = 0.6667$

10 normal six sided dice are thrown.

This means that $n = 10$

Find the probability of obtaining at least 8 failures.

This is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

So

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

$P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951$

$P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867$

$P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174$

Then

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992$

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0

2 years ago

Each of the numbers 1 through 7 is written on a small piece of paper and placed in a box. What is the probability of picking a p

gregori [183]

Answer:

Either C or B I’m not quite sure which one. I’m sorry

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

If I have a 74 in geometry, and I have an assignment worth 100 points then I get a zero, what would my grade be?

Paraphin [41]

................

Step-by-step explanation:

it would at LEAST be like around 20-30 because a 0 can drop something FAST

3 0

2 years ago

if there is a 10% chance of sun tomorrow and 20% chance of wind and no sun what is the probability that it is windy given that i

harkovskaia [24]

Answer:

=22%

Step-by-step explanation:

Since we have given two conditions simultaneously that is windy and not sunny. So we will use the concept of conditional probability.

The probability of sunny day= P(sunny)=10%

P(sunny)=10%=0.1

The probability of windy and not sunny=P(windy|not sun)=20%

P(windy|not sun)=20% = 0.2

Now divide the both probabilities:

P(windy|not sun)/P(sunny)

=0.2/[1-0.1]

{Hence there are 10% chances of sun tomorrow than there are (1 - 0.1) chances of no sun}

If we subtract 1 from 0.1 than it becomes:

=0.2/0.9

=2/9

=0.2222222222

=22%

Hence the probability that it is windy = 22% ....

6 0

2 years ago

The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the ma

andreev551 [17]

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

$\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end$

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

$\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end$

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

Learn about relative error from here brainly.com/question/13106593

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3 0

1 year ago