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3 years ago

Evaluate the expression for a = 30, b = 30, c = 7, d = 24: a + b = c = d.

Mathematics

1 answer:

suter [353]3 years ago

4 0

Answer:

Not possible

Step-by-step explanation:

a + b = c = d Substitute

30 + 30 = 7 = 24 Add

60 = 7 = 24 This is not possible because these numbers aren't equal.

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Terry burnt a total of 654 calories working out. If Terry does the same workout routine a total of 7 times over the course of th

Flauer [41]

Answer: 4,578

Step-by-step explanation:

654 calories x 7

7 0

3 years ago

Watch help video If you place a 13-foot ladder against the top of a 12-foot building, how many feet will the bottom of the ladde

riadik2000 [5.3K]

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1 year ago

Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

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.

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) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

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

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105

Eduardwww [97]

Answer:

z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

y = kxz

We can find k from the given values.

40 = k(10)(9)

40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

y = (4/9)xz

9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

z = 9·105/(4·55)

z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)

4 0

3 years ago

Anyone know where I can get these answers? <br> (There’s also a back but I can’t send it)

Nutka1998 [239]

Answer:

See below

Step-by-step explanation:

<u>Covert equations in standard form into slope-intercept form of y = mx + b</u>

x - y = 3 ⇒ y = x - 3

5x + 3y = 6 ⇒ 3y = -5x + 6 ⇒ y = -5/3x + 2

x - 2y = 2 ⇒ 2y = x - 2 ⇒ y = 1/2x - 1

3x + 2y = -8 ⇒ 2y = -3x - 8 ⇒ y = -3/2x - 4

4 0

3 years ago