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ICE Princess25 [194]

3 years ago

7

Help with math homework find the missing values in the generic rectangles and factoring diamonds write an equation to represent

the solution as both product and a sum

1 answer:

DENIUS [597]3 years ago

3 0

7. x² + 11x - 26

8. x² + 14x - 120

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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

A caterer charges $120 to cater a party for 15 people and $200 for 25 people.

Jlenok [28]

The equation in slope-intercept form for this function is y = 8 x

The slope represents the unit cost

A party for 40 people would cost $320

Step-by-step explanation:

The linear equation in the form of slope-intercept is:

y = mx + b, where m is the slope of the line and b is the y-intercept

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line
To find b substitute x and y of the equation by the coordinates of any point on the line

A caterer charges $120 to cater a party for 15 people and $200 for

25 people.

Assume that the cost, y, is a linear function of the number of people x

We need to write an equation in slope-intercept form for this function

We need to explain that the slope represent what

We need to find how much a party for 40 people would cost

∵ The slope-intercept form of the equation is y = mx + c

∵ y is the cost and x is the number of people

∴ x = 15 and y = 120 is a point on the line

∴ x = 25 and y = 200 is another point on the line

- Now we can use them to find the slope of the line

∵ $m=\frac{200-120}{25-15}=\frac{80}{10}$

∴ m = 8

∴ y = 8 x + b

- To find b substitute x by 15 and y by 120 in the equation

∴ 120 = 8(15) + b

∴ 120 = 120 + b

- Subtract 120 from both sides

∴ b = 0

∴ y = 8 x

The equation in slope-intercept form for this function is y = 8 x

∵ The slope = change of y ÷ change of x

∴ The slope = cost ÷ number of people

∴ The slope represents the cost per person

The slope represents the unit cost

∵ There are 40 people

∴ x = 40

∵ The equation of the cost is y = 8 x

∴ y = 8 × 40

∴ y = 320

∴ The cost is $320

A party for 40 people would cost $320

Learn more:

You can learn more about the linear function in brainly.com/question/4152194

#LearnwithBrainly

4 0

3 years ago

Which equation has 4 as a possible value of y? ^2=8 y^3=8 y^2=16 y^3=16

zepelin [54]

The Y^2 because 4 to the power of 2 would give you 4x4 which gives you 16

4 0

3 years ago

Elise is a project manager

gregori [183]

Answer:

£11.85

Step-by-step explanation:

In the question, we are told that:

In 2016 she earned a monthly salary of £2,100

In 2017 she had a 3% raise

This means 3% of £2,100

3/100×£2,100 = £63

This means her salary for 2017 =

£63 + £2,100 =£2,163

Step 2

We are told in the question that she worked 42 hours per week for 45 weeks in 2017

Since her monthly pay for 2017 = £2,163

She worked 42 hours per week

There are 7 days in one week

The number of hours she worked per day = 42 hours ÷ 7 = 6 hours per day

4.345 weeks= 1 month

The number of hours she worked per month = 42 hours × 4.345 weeks

= 182.49 hours.

We can say that for 182.49 hours she was paid = £2,163

Her average pay per hour is calculated as:

If 182.49 hours = £2,163

1 hour = represented by Y

Cross multiply

182.49Y = £2,163

Y = £2,163 ÷ 182.49

Y = £11.852704258

Approximately = £11.85

Therefore, Elise Average pay per hour for the year = £11.85

8 0

3 years ago

Read 2 more answers

Plezz help me q is in the screenshot <br> im bad at math

Dima020 [189]

Answer:
C. 2

Explanation:

Mode is the value that appears most frequently in a data set. In this case the number 2 appears 3 times which is why c is correct. I hope this helps!

4 0

3 years ago