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4 years ago

Which of the following statements have the same result? Explain each step in solving each one.

Mathematics

1 answer:

LiRa [457]4 years ago

7 0

f(x) = 3x +2

f(2) = 3(2) + 2 = 8

Now

f(x) = (2x -7) / 3

let f(x) = y and f(y) = x;

y = (2x -7) / 3

x = (3y + 7) / 2

f(y) = (3y + 7) / 2

this f(y) is the inverse of f(x); hence

f^-1 (x) = (3x + 7) / 2

Now f^-1(3) = (9+7) / 2 = 8

For the third and last part,

2y + 14 = 4y – 2

2y = 16

y = 8

<span>Hence all the three parts gives the same results.</span>

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If < D is a right angle and < E is a right angle, and you said that < D is congruent to < E, the reason would be ___

SVEN [57.7K]

Answer:

(B)All right angles are congruent

Step-by-step explanation:

Given that:

$\angle D$ is a right angle, and\\\angle E$ is a right angle\\\\\angle D=90^\circ\\\angle E=90^\circ\\$Therefore: \angle D \cong \angle E$

The reason for this congruency is that both are right angles and in fact, all right angles are congruent.

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3 years ago

You’ve bought a half-dozen (six) eggs from the store but you forgot to check them first! The probability that no eggs are broken

GREYUIT [131]

Answer:

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

b) 56.77% probability that an even number of eggs is broken.

Expectation: 0.8496

Variance: 0.7293

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either it is broken, or it is not. The probability of an egg being broken is independent from other eggs. So 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.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

There are 6 eggs

So $n = 6$

The probability that no eggs are broken is 0.4.

This means that $P(X = 0) = 0.4$ . So

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

$P(X = 0) = C_{6,0}.p^{0}.(1-p)^{6}$

$(1 - p)^{6} = 0.4$

Taking the sixth root from both sides of the equality

$(1 - p) = 0.8584$

p = 0.1416

Each egg has a 0.1416 probability of being broken

(a) Write out the pmf of X.

Probability of each value, from 0 to 6

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

(b) Compute the probability that an even number of eggs is broken.

0, 2, 4 or 6

$P = P(X = 0) + P(X = 2) + P(X = 4) + P(X = 6) = 0.4 + 0.1633 + 0.0044 + 0.00001 = 0.5677$

56.77% probability that an even number of eggs is broken.

(c) Compute the expectation and variance of X.

Expectation:

$E(X) = np = 6*0.1416 = 0.8496$

Variance:

$V(X) = np(1-p) = 6*0.1416*0.8584 = 0.7293$

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4 years ago

Evaluate the following expression using the values given by three X to the power of two minus Y to the power of three minus Y to

earnstyle [38]

203 and that is the answer

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3 years ago

As a puppy, Cricket weighed 3.75 pounds. At her 1-year check-up with the vet, Cricket

k0ka [10]

Answer:

8.75

Step-by-step explanation:

12.5 - 3.75 = 8.75

Hope this helps! :)

8 0

3 years ago

Read 2 more answers

Find the value of x. Then find the measure of Arc AN. Show work on a piece of paper.

Arada [10]

Answer:

a. x = 36

b. ∠(AN) = 144°

Step-by-step explanation:

All the angle in the circle should add up to 360°.

x + x + 4x + 4x = 360

2x + 8x = 360

10x = 360

x = 36

∠(AN) = 4x

∠(AN) = 4(36)

∠(AN) = 144°

7 0

4 years ago