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3 years ago

What is 3(x-1)<12 or x+7>10

Mathematics

1 answer:

Otrada [13]3 years ago

6 0

Simplifying

3[x + -1] = 12

Reorder the terms:

3[-1 + x] = 12

[-1 * 3 + x * 3] = 12

[-3 + 3x] = 12

Solving

-3 + 3x = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + 3x = 12 + 3

Combine like terms: -3 + 3 = 0

0 + 3x = 12 + 3

3x = 12 + 3

Combine like terms: 12 + 3 = 15

3x = 15

Divide each side by '3'.

x = 5

Simplifying

x = 5

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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

Members of a soccer team raised $1428 to go to a tournament. They rented a bus for $955.50 and budgeted $31.50 per player for me

natali 33 [55]

Answer:

16 players can be brought to the tournament. The equation is written within my step-by-step explanation.

Step-by-step explanation:

Variable p = number of players

Set up an equation:

974.50 + 60.75p = 1946.50

Isolate variable p:

60.75p = 972

Divide:

p = 16

Check your work:

974.50 + 60.75(16) = 1946.50

974.50 + 972 = 1946.50

1946.50 = 1946.50

7 0

3 years ago

The pair of points (-4, y) and (5, 7) lie on a line with slope . What is the value of y? You must show all of your work to recei

Svetach [21]

The slope of a line is given by the ratio of the rise to the run of the line.

The value of, y is 4

Reasons:

The given points on the line are; (-4, y), and (5, 7)

The slope of the line, = $\dfrac{1}{3}$

Required:

To find the value of y

Solution:

The formula for the slope is given as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where;

(x₁, y₁) = (-4, y)

(x₂, y₂) = (5, 7)

Which gives;

$Slope, \, m =\dfrac{7-y}{5-(-4)} = \dfrac{7-y}{5+4} =\dfrac{1}{3}$

3·(7 - y) = 1·(5 + 4) = 9

21 - 3·y = 9

3·y = 21 - 9 = 12

$y = \dfrac{12}{3} = 4$

The value of, y = 4

Learn more here:

brainly.com/question/1617757

8 0

3 years ago

How would you solve this:

kykrilka [37]

3xy over 8 is the answer go to mathway
and you can find your answer and it shows you how to do it

7 0

3 years ago

(sec²0 + tan²0)(cosec²0+cot²0) = 1sec²5 sin 0

iren2701 [21]

Answer:

865

Step-by-step explanation:

if minus than answer

4 0

2 years ago