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2 years ago

Help please and thank you

Mathematics

1 answer:

vladimir2022 [97]2 years ago

6 0

Answer:

Step-by-step explanation:

how i figured this out was not by using the table, but you can use the table

i just asked myself what two numbers multiplied together has a product of -12, one number must me negative

the two numbers must also add up to -4, meaning the bigger number had to be negative

the only answer that worked was 2 and -6

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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c

GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

$f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0$

The value of E (X) is 10.

The parameter λ is:

$\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10$

(a)

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679$

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

$P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353$

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

$P(X$

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of <em>x</em> as follows:

$P(X$

Take natural log on both sides.

$ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30$

Thus, the value of x is 30.

7 0

3 years ago

For all parts of this question, use the function y + 2 = 3(x + 4)

vekshin1

i would start by simplifying the equation to get y by itself, you don't need to do this, but it makes it a little easier

y + 2 = 3 ( x + 4) distribute the 3 through the parenthesis

y + 2 = 3x + 12. subtract 2 from both sides

y = 3x +10

now to fill in the chart simply plug in the value of x to see what value of y it produces

y = 3(-2) +10

y = -6+10

y = 4

(-2,4)

y = 3(0) + 10

y = 0 + 10

y = 10

(0,10)

y = 3(2)+10

y = 6 + 10

y = 16

(2,16)

y = 3(4) + 10

y = 12 + 10

y = 22

(4,22)

8 0

2 years ago