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3 years ago

Please help me.. I don't understand what it is..

Mathematics

1 answer:

tatiyna3 years ago

8 0

9514 1404 393

Answer:

22.6

Step-by-step explanation:

The diagonal of the square is they hypotenuse of an isosceles right triangle with sides of 16 inches. The Pythagorean theorem tells you its length (d) is ...

d^2 = 16^2 +16^2 = (16^2)(2)

Taking the square root, we have ...

d = 16√2 ≈ 22.6 . . . . inches

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Solve each system by substitution<br><br> 2x - 3y = -1<br> X + 4y = -6

lord [1]

Answer:

(- 2, - 1 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = - 1 → (1)

x + 4y = - 6 → (2)

Rearrange (2) expressing x in terms of y by subtracting 4y from both sides

x = - 6 - 4y → (3)

Substitute x = - 6 - 4y into (1)

2(- 6 - 4y) - 3y = - 1 ← distribute and simplify left side

- 12 - 8y - 3y = - 1

- 12 - 11y = - 1 ( add 12 to both sides )

- 11y = 11 ( divide both sides by - 11 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = - 6 - 4(- 1) = - 6 + 4 = - 2

Solution is (- 2, - 1 )

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3 years ago

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3 years 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

There are three small rounds of cheddar cheese in Grace’s refrigerator.She want to bring a small wedge of cheese in her lunch fo

Snowcat [4.5K]

Answer: 1/4 round.

Step-by-step explanation:

Grace has 3 wheels of cheese and she wants to eat an equal amount each day for 12 days. So each wheel needs to last 12/3 = 4 days. So then she can eat 1 wheel/4 days = 1/4 wheel per day.

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4 years ago

Please help fast!!! Part A How many solutions does the pair of equations for lines A and B have?

amm1812

Answer:

Part A: 1

Explain: The solution for a pair of lines is where they intersect.

Part B: (3,4)

Explain: (3,4) is the place where the lines intersect.

7 0

2 years ago