What type of angle is this? A. Straight angle B. Supplementary C. Complementary

Consider a machine that fills 275 gallon tanks of water. The owner discovers that the machine does not always dispense exactly 2

fenix001 [56]

Answer:

(a) The random variable X is a continuous random variable.

(b) The probability density function is shown below.

(c) The probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water is 0.285.

Step-by-step explanation:

Let the random variable X be denoted as the amount of water filled by the machine in a 275 gallon tank.

(a)

The random variable X is a continuous random variable.

A continuous random variables assumes infinite values. That is, they assume values in a fixed interval. For example, the distance covered by a car.

A discrete random variable assumes fixed definite values. They assume whole number values. For example, number of customers visiting a bank in an hour.

The amount of water in the tank can be any value between 0 to 275 gallon.

Hence, the random variable X is a continuous random variable.

(b)

The probability density function of the continuous random variable X is given as follows:

$0.25;\ 272$

$f_{X}(x) =0.20;\ 273$

$0.55;\ 274$

(c)

Compute the value of P (272.5 < X < 273.8) as follows:

$P(272.5$

Thus, the probability that a 275 gallon tank gets less than 272.5 gallons or more than 273.8 gallons of water is 0.285.

4 0

3 years ago

Determine the equation of the line that passes through the points of intersection of the graphs of the quadratic functions f(x)

timofeeve [1]

Answer: $x-2y-2=0$

Step-by-step explanation:

Given :

$f(x) = x^2 - 4 \\ g(x) = - 3x^2 + 2x + 8$

Point of intersection :

$f(x)=g(x)\\x^2-4=-3x^2+2x+8\\4x^2-2x-12=0\\2x^2-x-6=0\\2x^2-4x+3x-6=0\\2x(x-2)+3(x-2)=0\\(x-2)(2x+3)=0\\x=2\,,\,\frac{-3}{2}$

$x=2\,;f(2)=2^2-4=0\\x=\frac{-3}{2}\,; f\left ( \frac{3}{2} \right )=\left ( \frac{3}{2} \right )^2-4=\frac{-7}{4}=-1.75$

So, we have points $\left ( 2,0 \right )\,,\,\left ( -1.5,-1.75\ \right )$

Equation of line passing through two points $\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left ( x-x_1 \right )$

Let $\left ( x_1,y_1 \right )=\left ( 2,0 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -1.5,-1.75\ \right )$

So, equation is as follows :

$y-0=\frac{-1.75-0}{-1.5-2}\left ( x-2 \right )\\y=\frac{-1.75}{-3.5}\left ( x-2 \right )\\y=\frac{1}{2}(x-2)\\2y=x-2\\x-2y-2=0$

4 0

4 years ago

Convert 40g into degrees

Lera25 [3.4K]

Answer:

40g= 36 in degrees (decimal), and 36 degrees 0' 0" in degrees (Minutes&Seconds)

Step-by-step explanation:

8 0

3 years ago

A cone has a diameter of 10 inches. If its height is twice its radius, about what is the volume of the cone in cubic inches? Use

GuDViN [60]

Answer:

C) 261.67 inch³

Step-by-step explanation:

radius = 10/2 = 5

height = 10

Volume = ⅓×pi×r²×h

= ⅓×3.14×5²×10

= 261.6666666667

6 0

3 years ago

17. Identify the amplitude, period, and vertical shift for the

Stella [2.4K]

Answer:

$f(x)=2cos(x+\frac{\pi}{2})+3$

Step-by-step explanation:

Because the function is symmetric about the y-axis, using the cosine function is most appropriate.

Refer to the equation for a cosine function:

$f(x)=acos(bx+c)+d$

Amplitude: $|a|$

Period: $\frac{2\pi}{|b|}$

Phase shift: $-\frac{c}{b}$

Midline: $y=d$

The amplitude would be the average of the maximum and minimum y-values of the function, which would be $|a|=|\frac{5-1}{2}| =|\frac{4}{2}| =|2|=2$ .

The value of $b$ in $\frac{2\pi}{|b|}$ represents the length of the period, so since the length of the period is $2\pi$ , this means that $b=\frac{2\pi}{|2\pi|} =1$ .

The phase shift, $-\frac{c}{b}$ , describes the horizontal shift of a function. Because the phase shift is $-\frac{\pi}{2}$ , then we can set up the equation $-\frac{\pi}{2}=-\frac{c}{1}$ where we determine $c=\frac{\pi}{2}$ .

The midline (or vertical shift), $d$ , is the horizontal line that passes through between the maximum and minimum points, which the function oscillates. In this case, the midline would be located at the line $y=3$ , therefore, $d=3$ .

Putting all our information together, your final equation is:

$f(x)=2cos(x+\frac{\pi}{2})+3$

3 0

3 years ago

What type of angle is this? A. Straight angleB. Supplementary C. Complementary ​

What type of angle is this? A. Straight angleB. Supplementary C. Complementary