A large pool has a faucet to allow water to enter the pool and a drain to allow water to leave the pool.

Suppose that lithium calculator battery with a charge of 3 volts, actually has a voltage with uniform distribution between 2.93

Dmitrij [34]

Answer:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

$M = \frac{a + b}{2}$

The standard deviation of the uniform distribution is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

Uniform distribution between 2.93 and 3.1 volts

This means that $a = 2.93, b = 3.1$ . So

Mean:

$M = \frac{2.93 + 3.1}{2} = 3.015$

Standard deviation:

$S = \sqrt{\frac{(3.1 - 2.93)^{2}}{12}} = 0.049$

What is the probability that a battery has a voltage less than 2.98?

$P(X \leq 2.98) = \frac{2.98 - 2.93}{3.1 - 2.93} = 0.2941$

So the correct answer is:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

6 0

3 years ago

Michael’s weight can be represented by the expression 72x^5. Al’s weight can be represented by the expression 9x^7.

podryga [215]

Answer:

a) $\frac{72x^5}{9x^7}$

b) $=\frac{8}{x^2}$

c), Yes; $8x^2$

Step-by-step explanation:

Michael's Weight: $72x^5$

Al's weight: $9x^7$

a) Ratio of Michael's weight to Al's weight: $\frac{72x^5}{9x^7}$

b) This ratio simplifies to: $\frac{8\times 9x^5}{9x^5\timesx^2}$

$=\frac{8}{x^2}$

c) Yes, If the exponent in each expression were negative, then we have:

Ratio of Michael's weight to Al's weight: $\frac{72x^{-5}}{9x^{-7}}$

This ratio simplifies to: $8x^{-5--7}=8x^2$

The two ratios are not the same.

3 0

3 years ago

Confused someone help

jekas [21]

Answer:

y = -5x - 21

Step-by-step explanation:

Given in the question,

equation of a parallel line

y = -5x + 6

point through which it passes

(-4,-1)

Step1

Find the gradient of the equation given, as it is parallel so it will have same gradient

equation of straight line

y = mx + c

where m is gradient

c is y intercept

y = -5x + 6

m =-5

Step2

Find y-intercept

-1 = -5(-4) + c

-1 = 20 + c

c = -20 - 1

c = -21

Step3

form the equation

y = -5x - 21

8 0

3 years ago

Read 2 more answers

Gary just started a new job as a nurse. he is given a starting salary of $58,550 per year. he is also told that his salary will

IRINA_888 [86]

Firts we need to find the rate of change, or in other words, the slope of the line.

Question 1:

a)

For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)

The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)

b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:

$\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}$

In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:

$m=\frac{58,550-71,950}{0-10}=\frac{-13400}{-10}=1340$

c) "The rate of change in Gary's salary is $1340 per year."

Question 2:

a) The slope intercept form of a line is:

$y-y_1=m(x_{}-x_1)$

Where:

y is the output of the function.

x is the input of the function. (we provide the function with a value for x and the function give us a value of y)

m is the slope of the line. We calculate it in question 1.

x1 is the x coordinate of a point we choose.

y1 is the y-coordinate of the same point of x1.

In this case, we know:

m = 1340;

And we can take the point (0, $58,550), thus:

x1 = 0

y1 = 58,550

b) Now we need to use all this values and use the slope-intercept form:

$y-58,550=1340(x-0)$

And solve to get:

$y=1340x+58,550$

Question 3:

a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:

$\begin{gathered} \begin{cases}y=1340x+58,550 \\ x=13\end{cases} \\ y=1340\cdot13+58,550 \\ y=75,970 \end{gathered}$

B) The salary of Gary in 13 years will be $75,970.

6 0

1 year ago

Huh what dont get it?!...

Fed [463]

Answer:

I believe the correct answer is C.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers