The given problem involves a normally distributed random variable with a mean (μ) of 50 and a standard deviation (σ) of 5.
We are required to calculate probabilities associated with specific ranges of values using the Empirical Rule.
a. The normal curve represents the probability density function (PDF) of the random variable. It is symmetric and bell-shaped. Labeling the horizontal axis with the given values of 35, 40, 45, 50, 55, 60, and 65 helps visualize the distribution.
b. According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean. In this case, one standard deviation is 5. Therefore, the probability of the random variable assuming a value between 45 and 55 is approximately 68%.
c. Similarly, within two standard deviations of the mean, approximately 95% of the data is expected to fall. So, the probability of the random variable assuming a value between 40 and 60 is approximately 95%.
d. Within three standard deviations of the mean, approximately 99.7% of the data lies. Thus, the probability of the random variable assuming a value between 35 and 65 is approximately 99.7%.
e. To find the probability that the random variable will assume a value of 60 or more, we need to calculate the area under the normal curve to the right of 60. This probability is approximately 0.15 or 15%.
f. To determine the probability of the random variable assuming a value between 40 and 55, we calculate the area under the curve between these two values. Applying the Empirical Rule, this probability is approximately 81.5%.
g. The probability of the random variable assuming a value between 35 and 40 can be found by calculating the area under the curve between these two values. Since it lies within one standard deviation of the mean, according to the Empirical Rule, the probability is approximately 34%.
The calculations above are approximate and based on the Empirical Rule, which assumes a normal distribution.
To learn more about Empirical Rule visit:
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solve for x or find x
Answer:
x = 18
Step-by-step explanation:
diagonals bisect each other so 12x = 216
x = 216/12
x = 18
Find the slope of a line that passes through the points (-1, -3) and (2, -2).
Answer:
Step-by-step explanation:
(-2 + 3)/(2 + 1) = 1/3 is the slope
If Danielle can spend no more than $75 on clothes, and wants a pair of shoes for $40 and will spend the rest of the money on $12 scarves, what is her rate of change ?
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
find the value of the expression :
[tex]{x}^{2} + 2xy + {y}^{2} [/tex]
[tex]y = \frac{3 + i }{i} \\ x = 2 + 3i[/tex]
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:
find the common factors of the given terms 1. 12x, 36. 2. 2y, 22x. 3. 14pq, 28p^2 q^2
Answer:
answer 1. 12. 2nd is 2. and 3rd is 14pq
hope it helps
please help me on this will give you brainliest
Answer:
7.76 × 10^8
Step-by-step explanation:
Answer:
i think i would be 1.94x10^8
Step-by-step explanation:
Greg’s family went to the movie theater and bought tickets and popcorn. They spent $35 altogether with $9.50 spent on popcorn. Write an equation that can be used to find out how much money x they spent on tickets.
Answer:
x + 9.50 = 35
Step-by-step explanation:
The missing variable in this case is the number of dollars they spent on tickets. In total, combined the tickets and popcorn is equal to 35$,
We already know the amount they spent on popcorn.
X, the amount they spent on tickets + 9.50=35
use greatest common factor and distributive property to write equivalent expressions 5x+20y
Answer:
I think it is 5 if I did it right
S
can anyone help me create 3 Algebra Word Problems
Find the missing part .
So hard. Dont reports I actually cant take the pictures off, I needed help with a question but they dont come off. Also what's the square root of 282.93?
Answer:
whegvrjrbel)hbrbeueuejneje
help this makes no sense to me and its due in 1 day
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.
If using the method of completing the square to solve the quadratic equation x^2-20x+33=0x
2
−20x+33=0, which number would have to be added to "complete the square"?
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
Solve the inequality.
20 + 8.1 > 28
Answer:
You can't solve since there is no variables
The inequality from the question is true
A number line going from negative 3 to positive 3 in increments of 1.
Which statements are true? Check all that apply.
Negative 2.5 = negative 2 and one-half
–1.5 > –0.5
–0.5 < 0
–2.5 < –2
1 and one-half greater-than 1.5
Answer:
1., 3., and 4.
Step-by-step explanation:
It's C.
Or how other people say it,
3 or –2.5 < –2
I don't remember how to do this question,
also I'm really sorry I keep posting alot of math stuff today, I just have a lot of math that needs to get done today, I'd rather not spend my whole weekend doing school work LOL
Answer:
x and p equal 92 and y equals 88
compare the rates to find which is greater.
50 envelopes for $2.49 or
90 envelopes for $5.50
Can some one help please
Answer:
y=7x+6
Step-by-step explanation:
hope i helped
Radius is 8 ft. whats the answer
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
give all relationships between angle 1 and angle 2 select all that apply
Answer:
vertical maybe if try it and see
Write a rule for the linear function shown in the graph.
y = 4x – 3
y = –x + 4
y = 2x + 5
y = 1/4x +1
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.
A rectangle is 2/5 inches long and 1/3 inches wide. What is the area of the rectangle?
Step-by-step explanation:
2/5 x 1/3 = 2/15 inches squared
El perímetro de un rectángulo es 36cm Uno de los lados es 6cm más que el otro lado ¿ Cual es el área del rectángulo?
Subtract the following polynomials
1. (q² + 8) - (4q² + 1)
2. (3x + 7x² - 6) - (5x² + x + 9)
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:
Determine the length of PN and the value of y
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
PLS, HELP is it A. B. C. D.
Answer:
May be c but I am not sure dear.
Line G has a slope of -2/3. Line age is perpendicular to G. What is the slope of line h?
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.
Jackson hikes 220.2 meters up a mountain. If he is 60% of the way up, how tall is the mountain? 132.12 meters
Answer:
367meters
Step-by-step explanation:
220.2 = 0.6 * h
220.2/0.6 = 0.6 * h / 0.6
367 = h
367 meters
PLEASE EXPLAIN HOW U DID IT, giving brainliest
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.
122 cats
Mrs. Roberts is 3 times as old as her son. The sum of their ages is 48 years.
How old was Mrs. Roberts when her son was born?
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