2. A random variable is normally distributed with a mean of u = 50 and a standard deviation of a = 5.


a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45,


50, 55, 60, and 65.


b. What is the probability that the random variable will assume a value between 45 and 55? Empirical Rule.


c. What is the probability that the random variable will assume a value between 40 and 60? Empirical Rule.


d. What is the probability that the random variable will assume a value between 35 and 65? Empirical Rule.


e. What is the probability that the random variable will assume a value 60 or more?


f. What is the probability that the random variable will assume a value between 40 and 55?


g. What is the probability that the random variable will assume a value between 35 and 40?

Answer:

24

Step-by-step explanation:

To find how old Mrs. Roberts was when her son was born, we first need to know both of their ages. I'm going to give Mrs. Roberts the variable m and her son the variable s.

Let's turn the two sentences about their ages into equations:

m=Mrs. Roberts and 3s= three times as old as her son

m=3s

m+s is the sum of their ages

m+s=48

Now substitute the first equation into the second one:

m+s=48

(3s)+s=48

4s=48

s=12

The son is 12 years old. Now substitute s into one of the equations to solve for the mother's age:

m=3s

m=3(12)

m=36

Mrs. Roberts is 36. Since they are asking how old she was when her son was born, we will subtract her son's age from her age, since she would be 12 years younger:

36−12=24

Mrs. Roberts was 24 when her son was born.

credit to CountryGirl on Socratic Q&A

Answer: Answer is A. y = 4x - 3

Graph the line using the slope and y-intercept, or two points.

Slope:  2/ 5

y-intercept:  ( 0 , − 1 )

x           y

0          − 1

5/ 2       0

Step-by-step explanation:

How do you graph y=4x-3?

In graphing an equation, a very valuable graphing technique is the ability to recognize the kind of graph that a certain type of equation produces.

Any equation that is of the form y = mx + b is in the "slope-intercept" form for the equation of a straight line, where x and y are variables, where “m” is a real number representing the slope of a line, and where “b” is a real number representing the y-intercept of a line , i.e., the y-coordinate of the point of intersection between a straight-line graph and the y-axis.

Since the given equation y = 4x ‒ 3 is in the slope-intercept form, where m = 4 and b = ‒3, then it’s a linear equation and its graph is a straight line. Also, looking at the given equation, we know that the independent variable x can take on any real number as a replacement.

Now that we know that the graph of the given equation is a straight line and that there are no restrictions on the variable x, we need to determine and then draw the straight-line graph on a Cartesian (rectangular) coordinate system with the y-axis as the vertical axis and the x-axis as the horizontal axis. We know that two points determine a straight line; So, all we need to do is find the point where the straight-line graph of the given equation y = 4x ‒ 3 intersects the x-axis, i.e., the point of the x-intercept, and find the point where the straight-line graph of y = 4x ‒3 intersects the y-axis, i.e., the point of the y-intercept. Also, it would be a good idea to plot a third point as a check.

(1.) Determining the point of the x-intercept:

For any point on the x-axis, the y-coordinate is zero; therefore, in our given equation, let y = 0 and solve for x as follows:

y = 4x ‒3

0 = 4x ‒3

0 + 3 = 4x ‒3 + 3

(1/4)(4x) = (1/4)(3)

x = 3/4

Therefore, the x-intercept is x = 3/4, and the graph of the given equation y = 4x ‒3 intersects the x-axis at the point (3/4, 0).

(2.) Determining the point of the y-intercept:

To get the y-intercept, we can simply select it from the given equation y = 4x ‒3 which is already in slope-intercept form (y = mx + b), i.e., y = 4x ‒3 or y = 4x + (‒3); therefore, the y-intercept of the straight-line graph of the given equation is y = b = ‒3, which is the y-coordinate of the point of intersection between the straight-line graph of the given equation and the y-axis. Also, for any point on the y-axis, the x-coordinate is zero; therefore, the straight-line graph of the given equation intersects the y-axis at the point (0, ‒3).

(3.) Check Point

In generating a third point as a check point, choose a convenient value for x so that the corresponding value for the dependent variable y is nice and even. Let x = 2, then:

y = 4x ‒3

= 4(2)‒ 3

= 8 ‒ 3

y = 5

Consequently, the third point (check point) on the straight-line graph of the given equation is (2, 5).

(4.) Plot the points

Now, create the straight-line graph of the given equation by plotting the three points: (3/4, 0), (0, ‒3), and (2, 5) on a Cartesian (rectangular) coordinate system, and then use a straight edge to draw the straight line through all three plotted points. Draw the line past the two outer points and then draw an arrowhead at each “end” of the line to show that the line goes on indefinitely in both directions. NOTE: If the third point (2, 5)(the check point) is not on the drawn line, then go back and look for an error. The error was either made in finding the x- and y-intercepts, or the error was made in generating the coordinates of the check point, or both. When the error is found, make the appropriate correction(s), and then redraw the graph (straight line) of the given equation.

These are four steps that you can use to graph the given equation y = 4x ‒3 or any equation that is in the slope-intercept form for the equation of a straight line: y = mx + b.

Answer:

Side PN=26

y=16

Step-by-step explanation:

I put a photo of my work. It’s easier to do that then to try and put it all in words

Answer:

$6

Step-by-step explanation:

$75 - $40 = $30

With $30, the maximum number of scarves you can get is 2.

$30 - $24 = $6

Hope that helps!

Step-by-step explanation:

$6

the max number of scarves she can get is 2

hope this helps

Answer:

367meters

Step-by-step explanation:

220.2 = 0.6 * h

220.2/0.6 = 0.6 * h / 0.6

367 = h

367 meters

Answer:

7.76 × 10^8

Step-by-step explanation:

Answer:

i think i would be 1.94x10^8

Step-by-step explanation:

Answer:

answer 1. 12. 2nd is 2. and 3rd is 14pq

hope it helps

Perpendicular lines has negative reciprocal slopes.

"Negative reciprocal" is just a fancy way of

saying flip the fraction and change the sign.

So flipping the fraction gives us -3/2 and change the sign to get +3/2.

Answer:

1., 3., and 4.

Step-by-step explanation:

It's C.  

Or how other people say it,

3 or –2.5 < –2

Answer:

x = 18

Step-by-step explanation:

diagonals bisect each other so 12x = 216

x = 216/12

x = 18

Answer:

May be c but I am not sure dear.

Answer:

vertical maybe if try it and see

9514 1404 393

Answer:

  (b)  30

Step-by-step explanation:

The standard form of a quadratic is ...

  y = ax^2 +bx +c

For such a function, the axis of symmetry is ...

  x = -b/(2a)

Your quadratic function has a=-5, b=+300, so the axis of symmetry is ...

  x = -300/(2(-5) = 30

The peak of the curve is on the axis of symmetry. So, profit is maximized when 30 items are produced.

_____

Of course, a graphing calculator can display the maximum of the function easily.

First we can find the line RT which is the square root of 40^2-32^2 which is equal to 24.

RT=24

Right Triangle Altitude Theorem Part: The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

The geometric mean of 32 and TS is 24, so set up equation.

2nd root or square root of 32*TS=24

32*TS=576

TS=18

QS=18+32=50

I hope this answer helped if you have any questions feel free  to ask me in the comments.

Answer:

whegvrjrbel)hbrbeueuejneje

Answer:

Area = 64pi, Circumfrence=2pi(8)

Step-by-step explanation:

Answer:

Depends. Down below.

Step-by-step explanation:

It depends.

Area of the circle = [tex]\pi[/tex] x [tex]8^{2}[/tex] ≈ 201.06 ft

Circumference of the circle = 2 x [tex]\pi[/tex] x 8 ≈ 50.27 ft

Answer:

Step-by-step explanation:

(-2 + 3)/(2 + 1) = 1/3 is the slope

Step-by-step explanation:

2/5 x 1/3 = 2/15 inches squared

Answer:

y=7x+6

Step-by-step explanation:

hope i helped

Answer: x² + 2xy + y² = 9

x² + 2xy + y² = (x + y)²

with x = 2 + 3i and y = [tex]\frac{3+i}{i}[/tex], we have:

[tex](x + y)^{2}=(2+3i+\frac{3+i}{i})^{2}\\\\=(\frac{2i+3i^{2}+3+i }{i})^{2}\\\\=(\frac{3i-3+3}{i})^{2} \\\\=(\frac{3i}{i})^{2}\\\\=3^{2}=9[/tex]

Step-by-step explanation:

Answer:

1.  (q² + 8) - (4q² + 1)

Simplify each term.

q²+8−4q²−1

Simplify by adding terms.

−3q²+7

2. (3x + 7x² - 6) - (5x² + x + 9)​

Simplify each term.

3x+7x²−6−5x²−x−9

Simplify by adding terms.

Tap for more steps...

2x²+2x−15

Step-by-step explanation:

Answer:

You can't solve since there is no variables

The inequality from the question is true

Answer:

The complete square of the given quadratic equation

( x - 10)² = 67

The solution of the quadratic equation

  x = 18.2     and x = 1.8

Step-by-step explanation:

Step(i):-

Given that the quadratic equation

         x² - 20 x +33 =0

         x² - 2(10) x +(10)²-(10)²+ 33 =0

By using (a-b)² = a² -2ab + b²

       ( x - 10)² -100 +33 =0

         ( x - 10)² - 67 =0

        ( x - 10)² = 67

Step(ii):-

The complete square   (x - 10)² = 67

                                     x -10  = ±√67

                                    x -10 = ± 8.1853

                      x -10 = 8.2   and x -10 = -8.2

                      x = 10+8.2   and x = 10 -8.2

                      x = 18.2     and x = 1.8

Answer:

x + 9.50 = 35

Step-by-step explanation:

The missing variable in this case is the number of dollars they spent on tickets. In total, combined the tickets and popcorn is equal to 35$,

We already know the amount they spent on popcorn.

X, the amount they spent on tickets + 9.50=35

Answer:

x and p equal 92 and y equals 88

Answer:

I think it is 5 if I did it right

S