10 to the tenth power

PLEASE HELP 20 POINTS solve the system of equations y=-5x-7 and -4x-3y=-1 by substitution.

Ainat [17]

Answer:

Solution: x = -2; y = 3 or (-2, 3)

Step-by-step explanation:

Equation 1: y = -5x - 7

Equation 2: -4x - 3y = -1

Substitute the value of y in Equation 1 into the Equation 2:

-4x - 3(-5x - 7) = -1

-4x +15x + 21 = -1

Combine like terms:

11x + 21 = - 1

Subtract 21 from both sides:

11x + 21 - 21 = - 1 - 21

11x = -22

Divide both sides by 11 to solve for x:

11x/11 = -22/11

x = -2

Now that we have the value for x, substitute x = 2 into Equation 2 to solve for y:

-4x - 3y = -1

-4(-2) - 3y = -1

8 - 3y = -1

Subtract 8 from both sides:

8 - 8 - 3y = -1 - 8

-3y = -9

Divide both sides by -3 to solve for y:

-3y/-3 = -9/-3

y = 3

Therefore, the solution to the given systems of linear equations is:

x = -2; y = 3 or (-2, 3)

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7 0

3 years ago

Let x denote the lifetime of a mcchine component with an exponential distribution. The mean time for the component failure is 25

aliina [53]

Answer:

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The mean time for the component failure is 2500 hours.

This means that $m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004$

What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?

The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).

$P(X > x) = e^{-0.0004*5000} = 0.1353$

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

4 0

3 years ago

3. Sam and Tim each have savings accounts. Every month they each put in some of their

Setler [38]

Answer:

$y = 30x +50$ --- Sam

$y = 20x +80$ --- Tim

Step-by-step explanation:

Given

Sam Tim

х --- f(x) --------------- g(x)

1 --- 80 --------------- 100

2 --- 110 --------------- 120

3 --- 140 --------------- 140

4 --- 170 -------------- 160

Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,80)$

$(x_2,y_2) = (4,170)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{170 - 80}{4 - 1}$

$m = \frac{90}{3}$

$m = 30$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 80 = 30(x - 1)$

$y - 80 = 30x - 30$

Make y the subject

$y = 30x - 30 + 80$

$y = 30x +50$

Calculating the equation of Tim

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,100)$

$(x_2,y_2) = (4,160)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{160 - 100}{4 - 1}$

$m = \frac{60}{3}$

$m = 20$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 100 = 20(x - 1)$

$y - 100 = 20x - 20$

Make y the subject

$y = 20x - 20+100$

$y = 20x +80$

7 0

3 years ago

Is the inequality true or false?

Goryan [66]

Answer:

true -6 is greater than -7

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Select the correct answer.

skad [1K]

Answer:

D

Step-by-step explanation:

7 is it because it is positive

6 0

3 years ago

10 to the tenth power​

10 to the tenth power