Answers
Answer:
angle 3 is 127 and angle 4 is 31
Step-by-step explanation:
If you see the base of the triangle looks like an angle measurer of 180 degrees. so if 2 is 53 then subtract 180-53 to get 127. Once you have 3 just subtract 180 - 22 and 127 to get 31
:D
Related Questions
A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.
Answers
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
Exponential growth:The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.
We can use the formula:
C = C₀ × (1 + r)ⁿHere we have
A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.
Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.
We can use the following formula to calculate C₁₀:
C₁₀ = C₀ × (1 + r)ⁿ
Where r is the annual growth rate, n is the number of years
The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀
That is:
Amount of increase = C₁₀ - C₀
Substituting the values given in the problem, we get:
C₁₀ = C₀ (1 + 0.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀ = C₀ × 2.84
Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:
Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀
Therefore,
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
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Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. Jeremy's drone is closer to him than to Leslie, and Leslie's drone is closer to her than to Jeremy. Jeremy's drone is 30 meters above the ground, and he is located 50 meters to
the left from the point directly below the drone. The angle of elevation from Leslie's location on the ground to her dronp is 55°, and the distance between her location on the ground and her drone is 70 meters.
1. Calculate whose drone is higher. Show all work.
2. The angle elevation from the lower drone to the higher drone is 25 degrees. Use this information to calculate the distance between Jeremy and Leslie. Show all work.
3. Jeremy now flies his drone vertically so that it is the same height as Leslie’s drone. Draw a new diagram that includes Jeremy, Leslie, and the drones after Jeremy flies his drone to the same height as Leslie’s.
4. Explain why the angle of elevation from Jeremy’s location on the ground to his drone is different from the angle of elevation between Leslie’s location on the ground and her drone, given that both drones are at the same elevation above the ground.
5. Calculate the angle of elevation from Jeremy’s location on the ground to his drone to validate your reasoning. Show all work.
Answers
The solutions are explained below.
Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.
Height of Jeremy's drone = 30 m
Height of Leslie's drone = x m
h / 70 = sin 53°
h = 70 × sin 53°
h = 57.34
Therefore, Leslie's drone is higher than Jeremy's drone.
Difference of height = 57.34 - 30 = 27.34 m
27.34 / x = tan25°
x = 58.63 m
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1 1/9 x 2 2/5 as a mixed number in simplest form
Answers
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
1 1/9 x 2 2/5 = ?
1 1/9 = 10/9
2 2/5 = 12/5
[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]
So, the answer is 2 [tex]\frac{2}{3}[/tex]
Can someone help me with this?
Answers
Answer: 63,932
Step-by-step explanation:
September: 11,724
October: 14,380 + 11,724 = 26,104
November: 14,380 + 11,724 = 26,104
Combine all 3 months to get your answer= 63,932
Need some help
50 points!!
Answers
Answer:
145°
Step-by-step explanation:
The exterior angle 3 is equal to the sum of angle 1 and 2.
Using substitution we can say that:
5x + 4x + 10 = 10x -5
9x + 10 = 10x -5
10x-9x=10+5
x= 15
We have just found that the value of x is equal to 15.
By substituting this back to the angle 3 expression, 10x-5, we get
10(15) - 5
150 - 5
145°
The line joining (-3p, 0) to (-1, 5) is parallel to the line joining (p, 1) to (2p, 3). Find p.
Answers
Answer:
write ✍️
Step-by-step explanation:
justification for the following line translation . line 1 3p-
The number of students who ride the school bus is 110%of the number of students who walk.How many students ride the school bus
Answers
If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Step-by-step explanation:
Let f(x, y) = x² + xy + y². What is the direction of minimum rate of change at point (5,2)? (Enter a vector, using [,] brackets, such that the first coordinate (x-coordinate) is 1, 0, or -1.) Components of vector of minimum change direction are
Answers
Answer:
Step-by-step explanation:
To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.
First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:
∂f/∂x = 2x + y
∂f/∂y = x + 2y
Now, evaluate the gradient vector at the point (5, 2):
∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)
The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:
Orthogonal vector = (-1, 12)
So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].
PERCENTAGES QUESTIONSS
Answers
So, the answer in its simplest form is 1/200.a) Here's the completed frequency tree: Drink tea.
So, the number of people who drink at least 3 cups of tea each day is:[tex]10 * 0.2 = 2[/tex]Therefore, the fraction of the 400 people who drink at least 3 cups of tea each day is: 2 / 400This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:1 / 200So, the answer in its simplest form is 1/200.
What is fraction?A fraction is a numerical quantity representing a part of a whole or a ratio between two quantities. It is expressed as one number (the numerator) divided by another number (the denominator), separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, in the fraction 3/4, the numerator is 3, which represents three parts out of a total of four equal parts. Fractions can be used to represent many different types of quantities, such as parts of a whole, ratios, percentages, and probabilities.
b) Out of the 400 people, 10 said yes to drinking tea, and 20% of those (or 0.20*10 = 2) said they drink at least 3 cups each day. Therefore, the fraction of people who drink at least 3 cups of tea each day is 2/400, which simplifies to 1/200.
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Need help with question #4
Answers
Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign.
When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).
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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%
Answers
The probability of drawing a prime is 40%.
Calculating probability:To calculate the probability of drawing a prime number, use the formula
P(E) = Number of favorable outcomes / Total number of outcomes
Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.
Here we have
Ten cards numbered 1 to 10 are placed in a box.
The total number of outcomes will get in a random experiment = 10
Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}
Number of favorable outcomes that are getting prime number = 4
Hence, the probability of getting a prime number
= 4/10 = 2/5 = 0.4 = 40% [ Multiplied by 100 ]
Therefore,
The probability of drawing a prime is 40%.
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue). a. 9 c. One-fourth b. Four-thirds d. three-fourths Please select the best answer from the choices provided A B C D
Answers
Answer:
The probability of not getting a blue marble is the probability of getting either a red or a green marble. P(not blue) = P(red or green) P(red or green) = P(red) + P(green) P(red or green) = 8/12 + 1/12 P(red or green) = 9/12 P(not blue) = 3/4 Therefore, the answer is D. three-fourths.
Can someone please help ASAP!
Answers
The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
What is a Parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.
Check the attached file for the image of this problem.
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Dean qualifies for a 5-year loan from his credit union with a 5.25% APR. Assuming he uses the $4,300 as a down payment. You have already calculated his loan amount and his monthly payment. Considering all the monthly payments and the down payment, what will be the total amount that he pays for the car if he gets the loan and pays it off as scheduled? Round to two decimal places.
Answers
The total amount that he will pay for the car will be $17,093.40, assuming a loan amount of $15,000, a down payment of $4,300, a 5-year loan term, and a 5.25% APR.
Assuming that Dean has used the $4,300 as a down payment, his loan amount would be the total cost of the car minus the down payment, which is not given in the question.
However, assuming that the loan amount is $15,000 (which would be the case if the total cost of the car was $19,300), the monthly payment would be $284.89.
To calculate the total amount that Dean pays for the car over the course of the loan, we can multiply the monthly payment by the number of payments (60 payments over 5 years) and add the down payment:
Total amount = (Monthly payment x Number of payments) + Down payment
Total amount = ($284.89 x 60) + $4,300
Total amount = $17,093.40
Therefore, if Dean gets the loan and pays it off as scheduled, the total amount that he will pay for the car will be $17,093.40.
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what is the best estimate of 2/3+3/4
Answers
2/3 = 8/12 (multiply the numerator and denominator by 4)
3/4 = 9/12 (multiply the numerator and denominator by 3)
Now, we can add the fractions:
8/12 + 9/12 = (8 + 9)/12 = 17/12
However, this is an improper fraction, which means we need to convert it to a mixed number:
17/12 = 1 5/12
Therefore, the best estimate of 2/3 + 3/4 is approximately 1 5/12.
Let's add the fractions first and then we can estimate the sum.
[tex]= \dfrac{2}{3} +\dfrac{3}{4}[/tex]
change to common denominators
[tex]= \dfrac{8}{12} +\dfrac{9}{12}[/tex]
add numerators only
[tex]\dfrac{17}{12}[/tex] or [tex]1\dfrac{5}{12}[/tex] or [tex]1.42[/tex]
ANSWER: 13 is the best estimate of the answer. Normally we round up to 1.4 with a number like 1.42, but since that is not a choice, we can estimate 1 as the answer.
A bird flying at 15 m
above sea level dives vertically 2 m
into the sea to catch a fish and returns to its initial height.
What was the total vertical distance it travelled?
Answers
The bird covered 34 metres of vertical space overall. Warm-blooded, feathery animals with the ability to fly are known as birds.
The bird soared 15 m above the water, dove 2 m vertically, and descended to a depth of the water that was 15 + 2 = 17 m below its starting height. The bird must fly 17 m vertically upwards in order to cover the same distance in the other direction in order to return to its starting height.
Consequently, the bird travelled a total vertical distance of 34 metres (17 metres when diving and 17 metres while returning to its starting height).
Hence, the bird covered 34 metres of vertical space overall.
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Find the value of x, y, and z in the rhombus below.
(-x-8)
107⁰
(3y-1)
(-42-7)
Answers
Step-by-step explanation:
It is not clear from the given information which angles and sides are being referred to as "107⁰", "-x-8", "-42-7", and "3y-1". However, we can use some properties of rhombuses to solve for x, y, and z.
Opposite angles in a rhombus are equal. Therefore, if one angle is 107⁰, then the opposite angle is also 107⁰.
The diagonals of a rhombus are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.
The diagonals of a rhombus bisect each other's angles. This means that the angles formed by each diagonal with the sides of the rhombus are equal.
Using these properties, we can set up some equations to solve for x, y, and z:
Let's assume that "-x-8" and "-42-7" are the lengths of the diagonals of the rhombus, and that "3y-1" is the length of one of the sides.
Since the diagonals bisect each other's angles, we know that the angles formed by each diagonal with the side of the rhombus are equal. Let's call each of these angles "z":
-z + 107⁰ + z = 180⁰ (sum of angles in a triangle)
107⁰ = 180⁰ - 2z
2z = 73⁰
z = 36.5⁰
Now let's use the fact that the diagonals are perpendicular bisectors of each other:
(-x-8)/2 = (-42-7)/2
-x-8 = -49
-x = -41
x = 41
Finally, let's use the fact that the sides of a rhombus are equal:
-x-8 = 3y-1
41-8 = 3y-1
33 = 3y
y = 11
Therefore, the values of x, y, and z in the rhombus are:
x = 41
y = 11
z = 36.5⁰
Help with math problems
Answers
The answer choice which is not a true statement include the following: C. the solution set of |3k + 3| ≤ -9 is {k|-4 ≥ k ≥ 2}.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In order to determine the solution set to the given inequality, we would write out the absolute value function (inequality) as shown below.
|3k + 3| ≤ -9
Since |3k + 3| would always be positive and negative nine (-9) is negative, |3k + 3| will always be greater than negative nine (-9), and as such, the inequality cannot be true and has no solution set.
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PART A: A can of cat food measures 1" tall and a diameter of 3.5". What is the volume of cat food in the can? To solve Give your answer in cubic inches. Round to the nearest hundredth.
PART B: Cat food is sold by ounces (weight).
If the can holds 5.8 ounces, write a ratio to show cubic inches (your answer from slide 3) to ounces.
Answers
A)The volume of cat food in the can is 9.62 cubic inches .
B) A ratio to show cubic inches to ounces is 4.83.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.
The volume of a cylinder can be calculated using the formula
=> [tex]V = \pi r^2h,[/tex]
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).
To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,
Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.
So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).
Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.
Now ,To find the ratio of cubic inches to ounces,
Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:
=> 5.8 ounces / 1.2 ounces per cubic inch
= 4.83 cubic inches (rounded to the nearest hundredth).
Therefore, a ratio to show cubic inches to ounces is 4.83.
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sophomores have 26% please help me with math!
Answers
Answer: 234 are sophomores
Step-by-step explanation:
You would take 26% of 900 to get 234
It's simple, don't overthink it :)
Have a nice day.
Step-by-step explanation:
Sophomores are 26 % of 900 students
26 % * 900 = the number of sophomores
26% * 900 = .26 * 900 = 234 sophomores
how many 1/3s are in three
Answers
(1/x-y)-(2/2x+y)+(1/x+y)-(2/2x-y)
Answers
Answer:
6xy^2/(x-y)(x+y)(2x+y)(2x-y)
Step-by-step explanation:
1 - 2 + 1 - 2
x-y 2x+y x+y 2x-y
= take LCM
Then simplify.
Answer:
-2x+2/x
Step-by-step explanation:
A school newspaper took a survey of 100 students the results of the survey showed that 43 students are fans of Buffalo Bills 27 students are fans of New York Jets and 48 students do not like either team how many of the students surveyed are fans of both the Buffalo Bills and the New York Jets?
Answers
Answer: 18 students
Step-by-step explanation: 43+27+48=118 118-100=18
Let x be the number of students who are fans of both teams. Then, we can fill in the Venn diagram as follows:
43 - x students are only fans of Buffalo Bills.
27 - x students are only fans of New York Jets.
x students are fans of both teams.
48 students do not like either team.
The total number of students surveyed is 100, so we can write an equation based on the sum of these numbers:
(43 - x) + (27 - x) + x + 48 = 100
Simplifying this equation, we get:
118 - x = 100
x = 18
Therefore, 18 of the students surveyed are fans of both the Buffalo Bills and the New York Jets.
find exact value in radians
arccos(- square root 3/2)
Answers
= (6π - πi)/6
Step-by-step explanation:
We know that the range of arccosine is [0, π]. Since -√3/2 is less than -1, there is no real number x such that cos(x) = -√3/2. Therefore, the equation arccos(-√3/2) has no solution in the real numbers.
However, if we extend the range of the arccosine function to include complex numbers, we can find a solution using the formula:
arccos(z) = π - i ln(z + i√(1-z²))
where ln denotes the natural logarithm.
Substituting z = -√3/2, we get:
arccos(-√3/2) = π - i ln(-√3/2 + i√(1-(-√3/2)²))
Simplifying the expression under the natural logarithm, we get:
arccos(-√3/2) = π - i ln(-√3/2 + i/2)
To evaluate the natural logarithm, we can write -√3/2 + i/2 in polar form:
-√3/2 + i/2 = e^(i(π/6))
Therefore, we have:
arccos(-√3/2) = π - i ln(e^(i(π/6)))
Using the property ln(e^z) = z of the natural logarithm, we can simplify further:
arccos(-√3/2) = π - i (π/6)
Simplifying the expression, we get:
arccos(-√3/2) = (6π - πi)/6
Therefore, the exact value of arccos(-√3/2) in radians is (6π - πi)/6.
I hope this help
Let f(x)=2x-1, h(x) = -x-5.
Find (f o h)(-3).
(foh)(-3)=
Answers
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))
What is function?An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).
Given:
f(x) = -2x - 1
h(x) = -x - 5
First, we evaluate h(-3):
h(-3) = -(-3) - 5
h(-3) = 3 - 5
h(-3) = -2
Now, we plug the result of h(-3) into the function f(x):
f(h(-3)) = f(-2)
f(h(-3)) = -2(-2) - 1
f(h(-3)) = 4 - 1
f(h(-3)) = 3
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)
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At one college, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.
Answers
The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.
We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.
The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:
[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]
As a result, the GPA that represents the 70th percentile is roughly 3.246.
We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:
0.5244 = (x - 2.9) / 0.6
x = 3.246
Once more, doing so yields the same outcome as using a calculator.
In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.
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The perimeter of a rectangle is 34 feet. The length, l, of the garden is 14.38. the length, l, of the garden is 5 more than 2 times the width. Find the measurement of the width of the garden
Answers
The width of the garden is 4 feet.
What is Rectangle ?
A rectangle is a quadrilateral with four right angles, opposite sides that are parallel, and equal in length. It is a type of parallelogram where the adjacent sides are equal in length, but the opposite sides are not necessarily equal.
Let's start by using the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
We know that the perimeter is 34 feet, so we can plug in that value and simplify:
34 = 2(l + w)
17 = l + w
We also know that the length is 5 more than 2 times the width, so we can write an equation for that:
l = 2w + 5
We can substitute this expression for l into the first equation:
17 = (2w + 5) + w
Simplifying, we get:
17 = 3w + 5
12 = 3w
w = 4
Therefore, the width of the garden is 4 feet.
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QUESTION 3
If y varies inversely as x, find the inverse variation equation for the situation.
y = 1/8 when x = 40
Answers
[tex]yx=5[/tex]
Explanation:
If [tex]y[/tex] varies inversely as [tex]x[/tex] then
[tex]y\times x=k[/tex] for some constant [tex]k[/tex]
Since [tex]y = \frac{1}{8}[/tex] when [tex]x=40[/tex]
[tex]\huge \text(\dfrac{1}{8}\huge \text)\times(40)=k[/tex]
[tex]\longrightarrow k=5[/tex]
HELP ASP 20 POINTS PLSp
Answers
Answer:
Step-by-step explanation:
$499.99 - 15% will give your answers
Answer:
424.99
Step-by-step explanation:
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $135 of the population mean, and the population standard deviation is known to be $538.
54
62
43
86
Answers
Answer:
the correct answer is option B.
Step-by-step explanation:
We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:
Margin of error = z*σ/√n
where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.
We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.
Substituting the values into the margin of error formula and solving for n, we have:
$135 = 1.96*($538)/√n
Squaring both sides and solving for n, we get:
n = [1.96*($538)/$135]^2 ≈ 62
Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.
So the correct answer is option B.