Answer:
I assume you mean pi (π) squared, which is π^2. Calculating with π^2 is similar to calculating with any other number, except that you use π^2 instead of a regular number. Here are a few examples:
Example 1: Find the circumference of a circle with radius 5π.
The formula for the circumference of a circle is C = 2πr, where r is the radius. Substituting 5π for r, we get:
C = 2π(5π) = 10π^2
Therefore, the circumference of the circle is 10π^2.
Example 2: Find the area of a circle with diameter 3π.
The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter is 3 times the radius, we have:
r = (1/2)(3π) = (3/2)π
Substituting this into the formula, we get:
A = π((3/2)π)^2 = (9/4)π^3
Therefore, the area of the circle is (9/4)π^3.
In general, whenever you see π^2 in a formula, you can just substitute it for the regular number. Keep in mind that π is an irrational number (it goes on forever without repeating), so you may need to use an approximation like 3.14 or 22/7 depending on the level of accuracy required in your calculations.
Step-by-step explanation:
explanation included above with examples.
How to calculate Standard Error of the Y intercept and standard error of the slope, given the table below, without the SE coefficient given.
Answer:
Step-by-step explanation:
the stabdard error is given with the se coefficient snf the y slope
i need the answers please
Answer:
(7) AB is a tangent , (8) AB is not a tangent
Step-by-step explanation:
the angle between a tangent and the radius is 90°
if AB is a tangent then Δ ABC is right with hypotenuse AC
using Pythagoras' identity
the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
if AC² = AB² + BC² , then AB is a tangent to the circle
(7)
AC² = 34² = 1156
AB² + BC² = 30² + 16² = 900 + 256 = 1156
since AC² = AB² + BC² , then AB is a tangent to the circle
(8)
AC² = 28² = 784
AB² + BC² = 21² + 20² = 441 + 400 = 841
since AC² ≠ AB² + BC² , then AB is not a tangent to the circle
The measure of each interior angle of a
regular polygon is 135°. How many sides does the polygon have?
A. 5
B. 6
C. 7
D. 8
E. Cannot be determined from the
information given.
Answer:
8 sides
Step-by-step explanation:
Let n be the number of sides
Then sum of internal angles [tex]=(n-2)180[/tex]
——-(1)
It is given that one internal angle [tex]=135[/tex]
So sum of n equal internal angles [tex]=135n[/tex] ————(2)
From(1) and(2)
[tex](n-2)180=135n[/tex]
[tex]180n-360=135n[/tex]
[tex]180n-135n=360[/tex]
[tex]45n=360[/tex]
[tex]n=360\div45=8[/tex]
[tex]\bold{So \ the \ number \ of \ sides=8}[/tex]
PLEASE HELP LATE HOMEWORK
The number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
What is meant by intersection?
In mathematics, the intersection of two sets A and B is a new set that contains all the elements that are common to both sets. In symbols, the intersection of A and B is denoted by A ∩ B, and it is defined as:
A ∩ B = {x : x ∈ A and x ∈ B}
Let A represent the set of students who have a cell phone, and B represent the set of students who have a tablet. The intersection of A and B, denoted by A ∩ B, represents the set of students who have both a cell phone and a tablet. Therefore, we want to find the cardinality (or size) of the set A ∩ B.
From the frequency table, we know that the total number of seventh graders surveyed is 100. We also know that there are 32 students who have a cell phone (i.e., |A| = 32) and 70 students who have a tablet (i.e., |B| = 70). We are given that 19 students who have a cell phone do not have a tablet, which means that there are 32 - 19 = 13 students who have both a cell phone and a tablet (i.e., |A ∩ B| = 13).
Therefore, the number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.
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X A A. B. C. D. B any of the perpendicular bisectors of the sides of the hexagon either diagonal of the square any of the perpendicular bisectors of the sides of the square there are no lines across which this figure can reflect onto itself....*******?Got answer off here and showing wrong ones in pic....thanks!
In a regular hexagon, where FGHIJK shares a common center with square ABCD on a coordinate plane. ||. It is Across any of the perpendicular bisectors of the sides of the square that the combined figure can reflect onto itself.
What is the explanation for the above response?
In Regular Hexagon FGHIJK, we have 6 lines of reflection across which the hexagon reflects onto itself. Those lines are:
3 perpendicular bisectors of sides i.e. perpendicular bisector of IJ , IH and GH
3 lines passing through vertices i.e. HK, IF and GJ.
While in Square, we have 4 line of reflection across which the square reflects onto itself. Those lines are:
2 perpendicular bisectors of sides AB and BC i.e. HK and perpendicular bisector of CD
2 diagonals of square i.e. AC and BD
Note as well that from figure we know that perpendicular bisector of CD and perpendicular bisector of IJ is the same line.
So, for combined figure we have to take common lines from both figures i.e. perpendicular of sides CD or IJ and line HK.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See the attached image and the questions below.
In a regular hexagon, FGHIJK shares a common center with square ABCD on a coordinate plane. || . Across which lines can the combined figure reflect onto itself?
A. any of the perpendicular bisectors of the sides of the hexagon
B. either diagonal of the square
C. any of the perpendicular bisectors of the sides of the square
D. there are no lines across which this figure can reflect onto itself
The Box Has A Volume Of 845. Find X
Answer: x=6.5
Step-by-step explanation: 13 x 10=130
845/130= 6.5
The picture is below
The surface area of the rectangular prism graphed is given as follows:
10.12 ft³.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
Converting the mixed numbers to decimal, the dimensions of the rectangular prism are given as follows:
1.3 ft, 1.4 ft and 1.2 ft.
Hence the surface area of the prism is given as follows:
S = 2 x (1.3 x 1.4 + 1.3 x 1.2 + 1.4 x 1.2)
S = 10.12 ft³.
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Please help, this was due yesterday!!!!!
Answer:
x =65°( being alternate angel)
A gold and diamond bracelet sells for $1200. Find the sales tax and the total price if the sales tax rate is 3.5%.
Answer:42
Step-by-step explanation:
In a survey by the Pew Research Center, adult members of the Church of Jesus Christ of Latter-day Saints in the U.S. were asked how important religion is in their life. 558 adults said religion is “very important” in their lives, 79 adults said religion is “somewhat important” in their lives, 20 adults said religion is “not too important” in their lives, and 7 adults said religion is “not at all important” in their lives. Which of the following columns (A, B, C, D, or E) correctly shows the responses to this question as a probability model? (A) (B) (C) (D) (E) Very important 63.5% 84% 84% 12% 77% Somewhat important 22.5% 12% 14% 84% 21% Not too important 2% 3% 5% 1% 5% Not at all important 1% 1% 3% 3% 3%
The correct column is (A), which correctly represents the responses as probability.
Define probabilityProbability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The sum of all the responses is 558 + 79 + 20 + 7 = 664.
To represent the responses as a probability model, we need to divide each response by the total number of respondents, 664.
The correct column is (A), which correctly represents the responses as probabilities:
(A)Very important 558/664 = 0.841
Somewhat important 79/664 = 0.119
Not too important 20/664 = 0.030
Not at all important 7/664 = 0.011
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The vertex of the graph of the equation
y = -x² + 6x + 1 is
A. O neither a maximum nor a minimum
B. O both a maximum and a minimum
C. O a minimum
D. O a maximum
The vertex is ( 6 , 1 ). The vertex of the graph of the equation maximum.
What is parabola in math?
Each point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here since it is a crucial component of the conic section subject.
the equation y = -x² + 6x + 1
Use the formula: -b/2a
= -6/-1
= 6
The x-coordinate of the vertex is 6
Plug the x value back into the original equation to find the y-coordinate of the vertex
y = -x² + 6x + 1
= -(6)² + 6 * 6 + 1
= -36 + 36 + 1
= 1
The vertex is = ( 6 , 1 )
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13. A bag contains 40 balls, each of which is black or gold. Anele reaches into the bag and randomly removes two balls. Each ball in the bag is equally likely to If the be removed. probability that two gold balls are removed is how 12 many of the 40 balls are gold?
The number of gold balls in the given bag is determined as 25 gold balls.
How many of the 40 balls are gold?Let's use the formula for calculating probability:
Probability of an event = Number of favorable outcomes / Total number of outcomes
The total number of possible ways to choose 2 balls from a bag of 40 is:
40C2 = (40 x 39) / (2 x 1) = 780
Now we need to find the number of ways to choose 2 gold balls from the bag.
Let's say there are "g" gold balls in the bag. Then the number of ways to choose 2 gold balls is:
gC2 = (g x (g-1)) / (2 x 1)
We want to find the probability that 2 gold balls are removed, so we use the formula above to get:
Probability of choosing 2 gold balls = Number of ways to choose 2 gold balls / Total number of ways to choose 2 balls
Therefore, we have:
Probability of choosing 2 gold balls = gC2 / 40C2
We are given that this probability is 12/95, so we can set up an equation:
(g x (g-1)) / (2 x 1) / (40 x 39) / (2 x 1) = 12/95
Simplifying, we get:
g x (g-1) = (12/95) x (40 x 39)
g x (g-1) = 624
Expanding and rearranging, we get a quadratic equation:
g² - g - 624 = 0
Solving this quadratic equation, we get:
g = 25 or g = -24
We discard the negative solution, as the number of gold balls must be a positive integer. Therefore, there are 25 gold balls in the bag.
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Katya owns two cockatoos, an older white cockatoo and a younger Galah cockatoo. At present, the sum of the cockatoos' ages is 44 years. In n years, where n > 0, the white cockatoo's age will be four times the Galah cockatoo's age. If n is an integer, determine the possible present ages of each cockatoo.
The possible present ages of each cockatoo, given the sum of the cockatoos would be Galah cockatoo is currently 10 years old and the white cockatoo would be 34 years old
How to find the ages of the cockatoos?Let's use variables to represent the present ages of the two cockatoos. Let W be the present age of the white cockatoo and G be the present age of the Galah cockatoo. We're given that the sum of their ages is 44 years:
W + G = 44 (1)
In n years, the white cockatoo will be W + n years old, and the Galah cockatoo will be G + n years old:
W + n = 4(G + n) (2)
Since n > 0, 5G - 44 must be positive. We can try different values of G to find possible integer values for n.
For G = 8:
44 - 5(8) = 4
4 = -3n
n is not an integer.
For G = 10:
44 - 5(10) = -6
-6 = -3n
n = 2
So one possibility is that the Galah cockatoo is currently 10 years old. In this case, the white cockatoo would be 34 years old (since W + G = 44).
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Find the measures of angles a and b and of arc c Please
The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.
Therefore, angle BCD is equal to angle ACD, which is 90 degrees.
Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.
Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.
Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.
Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.
Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.
Hence, the measure of arc CD is 120 degrees.
Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,
Which is also 180 - 60 = 120 degrees.
Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:
angle BCD = angle BFC + angle FCB
= 120 + 120
= 240 degrees
Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.
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describe the key features que f the graph of the quadratic function f(x)=x^2-8-20
The graph is a parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
Define quadratic functionA quadratic function is a type of polynomial function of degree 2. It can be defined as a function in which the highest power of the independent variable x is 2.
The quadratic function f(x) = x² - 8x - 20 has a graph that is a parabola with a vertical axis of symmetry.
Vertex: The vertex of the parabola can be found using the formula x = -b/2a, where a and b are the coefficients of x² and x respectively.
In this case, a = 1 and b = -8, so the x-coordinate of the vertex is x = -(-8)/(2×1) = 4.
To find the y-coordinate of the vertex, substitute x = 4 into the equation: f(4) = 4² - 8(4) - 20 = -4. Therefore, the vertex is located at (4,-4).
Axis of symmetry: The axis of symmetry of the parabola is a vertical line passing through the vertex.
In this case, the axis of symmetry is the line x = 4.
Intercepts: To find the x-intercepts set y = 0 and solve for x: x² - 8x - 20 =0.
this quadratic equation can be factored as (x - 10)(x + 2) = 0
so the x-intercepts are x = 10 and x = -2.
To find the y-intercept, set x = 0 and evaluate f(0) = 0² - 8(0) - 20 = -20. Therefore, the y-intercept is (0,-20).
Image is attached below.
The graph is a upward-facing parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).
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helo please show work
Answer:
Step-by-step explanation:
Solution:
We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).
The GCF of 305 and 60 is 5.
Divide both terms by 5.
305 ÷ 5 = 61
60 ÷ 5 = 12
Therefore:
305 : 60 = 61 : 12
Helena sketches a circular backyard skating pond that fits into a square section of her yard. In her sketch, what is the area of the shaded region?
Answer:
The area of the shaded region equals 21.43 sq. units.
Step-by-step explanation:
Why do we use area?When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.
Given, A circle is circumscribed in the square,
Area of shaded region = area of square - area of circle
Area of square = Side²
= 10 × 10 = 100 sq. units,
Area of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 unitsArea of circle = Πr²
Radius = Diameter / 2
radius = 10 / 2 = 5 units
Area of circle = 22/7 × 5 × 5
= 78.57 sq. units
Area of shaded region = 100 - 78.57,
Area of shaded region = 21.43 sq. units
What are the coordinates of the point on the directed line segment from ( − 7 , 3 ) (−7,3) to ( 3 , − 9 ) (3,−9) that partitions the segment into a ratio of 3 to 1?
The coordinates of the point on the directed line segment are (-6, 0)
Define the term coordinates of the point?Coordinates of a point refer to a set of numbers that represent the location of the point in a particular coordinate system.
To find the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1, we can use the following formula:
P = [tex]( (3/4)*x_1 + (1/4)*x_2 , (3/4)*y_1 + (1/4)*y_2 )[/tex]
where P is the point that partitions the line segment, (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the segment, and the coefficients 3/4 and 1/4 correspond to the ratio in which the segment is divided.
Plugging in the values, we get:
P = ( (3/4)*(-7) + (1/4)*3 , (3/4)3 + (1/4)(-9) )
= (-21/4 - 3/4 , 9/4 - 9/4)
= (-6, 0)
Therefore, the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1 are (-6, 0).
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Ten cards numbered 1 thru 10 are placed in a box. If a card is de random from the box, what is the probability of drawing a prime a 10% b 25% c 40% d 50%
Answer:
a) There are four prime numbers between 1 and 10: 2, 3, 5, and 7. So the probability of drawing a prime number is 4/10 or 2/5, which is 20% and not 10%. Therefore, option (a) is not correct.
b) As we saw in part (a), the probability of drawing a prime number is 2/5 or 40% (since 2/5 is equivalent to 0.4). Therefore, option (b) is correct.
c) The probability of drawing a prime number is 2/5 or 40%, which is not 25%. Therefore, option (c) is not correct.
d) As we saw in part (a) and (b), the probability of drawing a prime number is 2/5 or 40%, which is not 50%. Therefore, option (d) is not correct.
So, the correct answer is (b) 25%.
Hope This Helps!
The polynomials (-3y²-y-8) + (-y² + 2y - 4) when added is:
Answers options
O -4y² + y - 12.
O -4y²-y-12.
O 4y² + y - 12.
O-4y2-3y - 12.
O 4y2-3y - 12.
Answer:
-4y2 +y - 12
Step-by-step explanation:
-3y2 - y2= -4y2
-y+2y= y
-8 - 4= -12
-4y2 + y - 12
Triangle WXY with W(0, 1), X(-4, 4), Y(0, 2)
in y-axis
(x, y) ⇒ (x − 1, y — 4)
a) Reflection
b) Translation
(a)The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
(b)The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
What is reflection ?a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.
The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
The reflected triangle would be W'X'Y'.
b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.
The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
The translated triangle would be W'X'Y'.
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Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
__ __
Answer:
[tex]13 < \sqrt{181} < 14[/tex].
Step-by-step explanation:
We have been given an inequality ___[tex]< \sqrt{181} <[/tex]___. We are asked to fill in the blank with two consecutive integers to complete the given inequality.
We know that square root of 181 is not an integer. We can see that 181 is greater than square root 169 and and square root of 196.
[tex]\sqrt{169} < \sqrt{181} < \sqrt{196}[/tex]
We know that [tex]\sqrt{169}=13[/tex] and [tex]\sqrt{196}=14[/tex].
Therefore, our required inequality would be [tex]13 < \sqrt{181} < 14[/tex]
Which expression is equivalent to 5(2 + 1)?
Step-by-step explanation:
5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:
5(2 + 1) = 5(2) + 5(1)
Simplifying the expression further, we get:
5(2) + 5(1) = 10 + 5 = 15
Therefore, 5(2 + 1) is equivalent to 15.
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten.
The volume of the solid with a hole in the shape of a rectangular prism passing through the center of a cylinder with a radius of 10 yards is approximately 1410 cubic yards, rounded to the nearest ten.
The cylinder with the hole can be viewed as the difference of two solids: the cylinder and the rectangular prism. The volume of the cylinder is given by the formula V_cyl = π[tex]r^2h[/tex], where r is the radius and h is the height.
The height of the cylinder is equal to the height of the rectangular prism that passes through its center. The height of the rectangular prism is given as 12 yards, which is also the diameter of the cylinder. Therefore, the height of the cylinder is h = 12/2 = 6 yards.
The volume of the cylinder is therefore V_cyl = π[tex](10)^2(6)[/tex] = 600π cubic yards.
The rectangular prism has a length of 20 yards, a width of 10 yards, and a height of 12 yards. Therefore, its volume is V_prism = 20 × 10 × 12 = 2400 cubic yards.
The volume of the solid with the hole is then:
V = V_cyl - V_prism = 600π - 2400 = 600(π - 4) ≈ 1412.2 cubic yards.
Therefore, the volume of the solid is approximately 1410 cubic yards.
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Determine f(3) for f(x)
A. 9
B. 19
C. 22
D. 27
cost of jacket: $249.96 markup: 80% discount: 50% tax: 2%
Answer:249.98
Step-by-step explanation: i had a question like this before.
Drag each expression to show whether it is equivalent to 36x+9 or 9(4x-1)
1. 36x+8- 3rd column;
2. (9·4x)+(9·1)=36x+9 - 1st column;
3. (3·12x)-(3·3)=36x+9 - 2nd column;
4. 9(4x+1)=36x+9 - 1st column;
5. 36x-9- 2nd column;
6. 4(9x+2)=36x+8 - 3rd column
Define equationIn mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign (=). Equations can contain one or more variables, which are quantities that can take on different values.
Start with expressions in blue boxes:
1st column) 36x+9;
2nd column) 9(4x-1)=36x-9;
3rd column) (4·9x)+(4·2)=36x+8.
You have 6 expressions. Consider all them:
1. 36x+8- 3rd column;
2. (9·4x)+(9·1)=36x+9 - 1st column;
3. (3·12x)-(3·3)=36x+9 - 2nd column;
4. 9(4x+1)=36x+9 - 1st column;
5. 36x-9- 2nd column;
6. 4(9x+2)=36x+8 - 3rd column
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The complete question is;
Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).
Two stores have a laptop computer for sale.
Part A: Store A is selling the laptop for
and has a discount coupon for
off. Calculate the amount of the discount at Store A.
Part B: Store B is selling the laptop for
and has a discount coupon for
off. Calculate the amount of the discount at Store B.
Part C: Which store should you purchase the laptop from? Use details to support your answer.
Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.
What is discount?
Discount means the amount which is deducted by sellers from the amount to be payable by buyers.
Part A:
Store A is selling the laptop for $900 and has a discount coupon for 15% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:
Discount amount = $900 x 15% = $135
Therefore, the amount of the discount at Store A is $135.
Part B:
Store B is selling the laptop for $950 and has a discount coupon for 10% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:
Discount amount = $950 x 10% = $95
Therefore, the amount of the discount at Store B is $95.
Part C:
At Store A, the final price would be:
Final price at Store A = $900 - $135 = $765
At Store B, the final price would be:
Final price at Store B = $950 - $95 = $855
Therefore, Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.
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A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width is 10 inches. Find the length of the prism and explain how you found it. ASAP
Answer:
14
Step-by-step explanation:
Volume = height x width x length
6 x 10 = 60
480 divided by 60 = 14
Weekly wages at a certain factory are
normally distributed with a mean of $400 and
a standard deviation of $50. Find the
probability that a worker selected at random
makes between $450 and $550.
250
350 400 450 500 550
P = [? ]%
Hint: use the 68- 95 - 99.7 rule.
300
There is a 15.74% chance that a randomly chosen employee will earn between $450 and $550.
Define probabilityThe study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To find : the probability that a worker selected at random makes between $450 and $550
z = (x - μ) / б
where б is the standard deviation, μ is the mean, and x is the value we wish to normalize.
For $450, we have:
z₁ = (450 - 400) / 50 = 1
For $550, we have:
z₂ = (550 - 400) / 50 = 3
We can then use a standard normal distribution table or calculator to find the area under the standard normal curve between z₁and z₂:
P(z₁< z < z₂) = P(1 < z < 3) = 0.1574
This means that the probability that a worker selected at random makes between $450 and $550 is 15.74%.
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