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docker41 [41]
3 years ago
5

Shaun is 4 years older than her sister Charmaine. If the sum of their ages is 16, how old is Charmaine?

Mathematics
1 answer:
skad [1K]3 years ago
4 0

Step-by-step explanation:

let \: the \: age \: of \: charmaine \: be \: x

according \: to \: question

4 + x = 16

x = 16 - 4

12

so \: the \: age \: of \: shaun \: is \:

x + 4

12 + 4

16

hope it helps if it helps don't forget to like and mark me

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Given the function f(x) = 2(x + 8), find x if f(x) = 12.
mina [271]

Answer:

C.) -2

Step-by-step explanation:

solve by putting 12 in for f(x)

12 = 2(x + 8)

Divide by 2

6 = x + 8

Subtract 8

-2 = x

4 0
3 years ago
he time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the a
Eva8 [605]

Answer:

The answer is below

Step-by-step explanation:

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places.

(a) What is the probability that more than three aircraft arrive within an hour?

(b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals?

(c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.1.

Solution:

a) A poisson distribution is given by the formula:

P(X=x)=\frac{e^{-\lambda }\lambda^x}{x!}

λ = 1 hour

Therefore:

P(X > 3) = 1 - P(X < 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(x = 3)]

P(X=0)=\frac{e^{-1}*1^0}{0!}=0.3679

P(X=1)=\frac{e^{-1}*1^1}{1!}=0.3679

P(X=2)=\frac{e^{-1}*1^2}{2!}=0.1839

P(X=3)=\frac{e^{-1}*1^3}{3!}=0.0613

P(X > 3) = 1 - [0.3679+0.3679 + 0.1839 + 0.0613] = 0.019

b) Assuming 30 1 hour intervals, hence:

P(X \leq 3)^{30}=[1-P(X\geq 30)]^{30}=(1-0.019)^{30}=0.5624

c) mean = 1 hour

mean = 1 / λ

1 = 1 / λ

λ = 1

The cumulative distribution function of a continuous variable is:

F(x)=1-e^{-\lambda x}

0.1=1-F(x)\\\\0.1=1-(1-e^{- x})\\\\0.1=e^{- x}\\\\-x=ln(0.1)\\\\-x = -2.3\\\\x=2.3\ hours

4 0
3 years ago
Which of the following expressions is equivalent to 5 + 2(10 – 3)?
Mekhanik [1.2K]

Answer:

4

Step-by-step explanation:

1. 7(10-3)

7×7

49

2. 70-3

67

3. 5+20-3

25-3

22

4.5+2(7)

5+14

24

5+2(10-3)

5+2×7

5+14

24

5 0
3 years ago
Fill in the missing values from the similar figures in the table
Tems11 [23]

Step-by-step explanation:

9 × 1/2 = 4.5

8 × 1/2 = 4

hope it's helpful

3 0
1 year ago
-2(-4y+1)-(2y-3)-3y+2 simplify the expression
Softa [21]

1

Simplify brackets

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2

Collect like terms

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3

Simplify

−2(−4y+1)−5y+5-2(-4y+1)-5y+5−2(−4y+1)−5y+5


4

Expand

8y−2−5y+58y-2-5y+58y−2−5y+5


5

Collect like terms

(8y−5y)+(−2+5)(8y-5y)+(-2+5)(8y−5y)+(−2+5)


6

Simplify

3y+33y+33y+3


3 0
3 years ago
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