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3 years ago

How would you solve the equation y-5=m(x-2)

1 answer:

7 0

One equation with 3 variables cannot be solved in the sense that you can find "the" 3 values for x, y and m. You can observe that this equation represents a family of straight lines with varying slope (depending on m).

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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

Isabella is making cookies. The recipe requires 3/4 of a cup of flour and 1/2 of a cup of sugar.

podryga [215]

Measure of the flour is greater than the measure of the sugar

3 0

3 years ago

Read 2 more answers

If sec= 5/3 and the terminal point determined by is in quadrant 4, then

OLga [1]

$\bf sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{5}{3}\implies \cfrac{1}{cos(\theta)}=\cfrac{5}{3}\implies \cfrac{3}{5}=cos(\theta)
\\\\\\
\textit{now, }\theta\textit{ is in the 4th quadrant}$

so... notice the picture below, the angle in the fourth quadrant
now... notice, the cosine is just the distance the angle makes with the x-axis
so... using the pythagorean theorem, get the opposite side, from that triangle, keeping in mind that, "y" is negative in the 4th quadrant

once you get "y", get any other trigonometry value you need :)

7 0

3 years ago

Read 2 more answers

X + 2y = 10

Crazy boy [7]

Answer:

(-12,11)

Step-by-step explanation:

x + 2y = 10

3x + 4y = 8

(-2)x + (-2)2y = (-2)10

3x + 4y = 8

-2x - 4y = -20

3x + 4y = 8

Add to eliminate:

x = -12

Substitute x to solve y:

x + 2y = 10

(-12) + 2y = 10

-12 + 2y = 10

2y = 10 + 12

2y = 22

y = 22 ÷ 2

y = 11

Check:

x + 2y = 10

(-12) + 2(11) = 10

-12 + 22 = 10

10 = 10

8 0

3 years ago

Read 2 more answers

What is the answer to -2x+3=x-6 ?

saveliy_v [14]

Answer:

x=3

Step-by-step explanation:

-2x+3=x-6

-3x+3=-6

-3x=-9

-x=-3

x=3

5 0

3 years ago