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2 years ago

Now Cathy is three times as old as Katie. In six years Cathy will be only twice as old as Katie. How old is each girl now?

1 answer:

6 0

Katie is 6; Cathy is 18!

X- Katie’s age now and 3x -Cathys age now
In 6 years, Katie is 12 and Cathy is 24.

2 x (X+6) = 3x + 6
2x + 12 = 3x + 6
6 = x

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The number of flaws in a fiber optic cable follows a Poisson distribution. It is known that the mean number of flaws in 50m of c

boyakko [2]

Answer:

(a) The probability of exactly three flaws in 150 m of cable is 0.21246

(b) The probability of at least two flaws in 100m of cable is 0.69155

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is 0.13063

Step-by-step explanation:

A random variable X has a Poisson distribution and it is referred to as Poisson random variable if and only if its probability distribution is given by

$p(x;\lambda)=\frac{\lambda e^{-\lambda}}{x!}$ for x = 0, 1, 2, ...

where $\lambda$ , the mean number of successes.

(a) To find the probability of exactly three flaws in 150 m of cable, we first need to find the mean number of flaws in 150 m, we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 150 m of cable is $1.2 \cdot 3 =3.6$

The probability of exactly three flaws in 150 m of cable is

$P(X=3)=p(3;3.6)=\frac{3.6^3e^{-3.6}}{3!} \approx 0.21246$

(b) The probability of at least two flaws in 100m of cable is,

we know that the mean number of flaws in 50 m of cable is 1.2, so the mean number of flaws in 100 m of cable is $1.2 \cdot 2 =2.4$

$P(X\geq 2)=1-P(X$

$P(X\geq 2)=1-p(0;2.4)-p(1;2.4)\\\\P(X\geq 2)=1-\frac{2.4^0e^{-2.4}}{0!}-\frac{2.4^1e^{-2.4}}{1!}\\\\P(X\geq 2)\approx 0.69155$

(c) The probability of exactly one flaw in the first 50 m of cable, and exactly one flaw in the second 50 m of cable is

$P(X=1)=p(1;1.2)=\frac{1.2^1e^{-1.2}}{1!}\\P(X=1)\approx 0.36143$

The occurrence of flaws in the first and second 50 m of cable are independent events. Therefore the probability of exactly one flaw in the first 50 m and exactly one flaw in the second 50 m is

$(0.36143)(0.36143) = 0.13063$

4 0

2 years ago

Which expression is equivalent to the expression below? StartFraction m + 3 Over m squared minus 16 EndFraction divided by Start

Kamila [148]

Option B: $\frac{1}{(m-4)(m-3)}$ is the correct answer.

Explanation:

The given expression is $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$

Simplifying the expression, we have,

$\frac{m+3}{m^{2}-16}\times\frac{m+4}{m^2-9}$

Factor the equations, $m^{2}-16\right$ and $m^{2}-9$ ,we get,

$m^{2}-16\right=m^{2}-4^{2}=(m+4)(m-4)$

$m^{2}-9=m^{2}-3^2=(m+3)(m-3)$

Substituting these factored expressions in the above expression, we have,

$\frac{m+3}{(m+4)(m-4)}\times\frac{m+4}{(m+3)(m-3)}$

Cancelling the common terms $m+3$ and $m+4$ , we get,

$\frac{1}{(m-4)(m-3)}$

Thus, the expression equivalent to $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$ is $\frac{1}{(m-4)(m-3)}$

Hence, Option B is the correct answer.

3 0

2 years ago

Read 2 more answers

A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping. Find the surface area

Lelu [443]

We would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2

3 0

1 year ago

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Charlie wants to order lunch for his friends. He'll order 5 sandwiches and a $3 kid's meal for his little brother. Charlie has $

Dominik [7]

Inequality:
5x - 3 ≤ 28

Answer:
5x - 3 ≤ 28
5x ≤ 31
x ≤ 31/5 or 6.2 ($6.20)

8 0

1 year ago

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The equation y=−0.0088x2+0.79x+15 models the speed x (in miles per hour) and average gas mileage y (in miles per gallon) for a v

rewona [7]

Answer: 30.72 miles per gallon

To find best approximate for the average gas mileage at a speed of 60 miles per hour you need to replace the variable x with 60. The calculation would be:

 y=−0.0088x2+0.79x+15
y= -31.68 +47.4 + 15
y= 30.72

5 0

2 years ago

Read 2 more answers