Convert 78 1/50 as a decimal

The height of a plant, y, in centimeters, is measured x weeks after planting a seed. The height can be modeled by the regression

Gnoma [55]

Answer:

D. The limiting value for the height of the plant is 6.88 cm.

Step-by-step explanation:

5 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution 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.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

So

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

I NEED HELP special right triangle 45-45-90

poizon [28]

Answer:

x=6

y=9

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The measure of angle

igor_vitrenko [27]

Answer:
120 degrees

Explanation:
Opposite angles (angles that are on opposite sides of an intersection) are equal to each other. Because angle 2 and 120 degrees are opposite angles, angle 2 is equal to 120 degrees.

I hope this helped if it did, a brainliest would be much appreciated:)

8 0

3 years ago

3 csc^2(2x) + 2 cosec 2x = 1-cot^2(2x)

asambeis [7]

I am assuming you want to solve for x:-

Now cosec^2 2x = 1 - cot^2 2x so the equation becomes

3 cosec^2(2x) + 2 cosec 2x = cosec^2 2x

2 cosec^2 2x + 2 cosec 2x = 0

2 cosec 2x ( cosec 2x + 1) = 0

so 2 cosec 2x = 0 or cosec 2x = -1

cosec 2x = 0 or cosec 2x = -1

cosec 2x = 0 is indeterminate so we ignore the first one

cosec 2x = -1 can be written as 1 / sin 2x = -1

so sin 2x = -1

giving 2x = 270 degrees

Therefore x = 135 degrees answer

3 0

3 years ago