Answers
Answer: m = -1 , b = -8
Step-by-step explanation:
y=mx+c
m = gradient of the line / slope of the line
c = y intercept
-x=-1x so the gradient is -1
-8 = y intercept
Related Questions
-5 - y = -3x find the slope and y-intercept
Answers
Answer:
slope = 3 , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 5 - y = - 3x ( add 5 to both sides )
- y = - 3x + 5 ( multiply through by - 1 )
y = 3x - 5 ← in slope- intercept form
with slope m = 3 and y- intercept c = - 5
3, 1.6, 2.8, 2.5, 1.7, 2.8
What is the mean absolute deviation of these numbers?
Answers
The mean absolute deviation of the given numbers is 0.5.
What is a mean?The mean is the sum of all values divided by the total number of values.
The mean of the given number is obtained by dividing the sum of the values by its total number of value.
i.e. (1.6+1.7+2.5+2.8+2.8+3)/6 = 2.4
Then taking the difference of each number from the mean.
i.e. (1.6-2.4), (1.7-2.4),(2.5-2.4),(2.8-2.4),(2.8-2.4),(3-2.4)
i.e. -0.8,-0.7,0.1,0.4,0.4,0.6
Take the sum of the absolute value of the above numbers
i.e. |-0.8+-0.7+0.1+0.4+0.4+0.6| = 3
Divide 3 by 6 to obtain mean absolute deviation.
i.e 3/6 = 1/2 =0.5
Hence, 0.5 is the mean absolute deviation of the given numbers.
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How many leave were longer then 7 centimeters
Answers
Answer:
You could pick as many as you like. Ideally you would use all the leaves on the tree, but that would be rather a large number to measure, and your parents might not be very happy if you stripped the tree bare!So let's try 100 leaves.How to get a random sample?Here is one way you could get a random sample:Try taking all the leaves on one branch of the tree. After you've discarded any that are broken, then see how many there are. If there are less than 100, then get the leaves from another branch until you have more than 100. Then write a different number (starting with 1) on each leaf with a marking pen.Write the same numbers on small pieces of paper.Fold the pieces of paper.Put them into a hat and mix them up.Draw 100 pieces of paper (without looking) from the hat. The first 100 pieces of paper you draw would give you the numbers of the leaves to use in the experiment.The next thing you need to decide is how to measure the leaves, andhow accurate your measurements should be:How to measure?Keeping your leaves flat, use a ruler to measure the length of each leaf from the pointy part at one end of the leaf to the point where the leaf joins the stalk at the other end. Maybe your leaves bend a bit, but don't follow the main rib of the leaf as this would make measurement too difficult.Just measure in a straight line as shown in the following diagram:leafHow accurate?You should measure the length of each leaf to the nearest millimeter.Now you're ready to begin.Measure the length of each leaf to the nearest millimeter and record you results in a table, as follows:
Step-by-step explanation:
A student claims that the graph shows the player earned more points from Level 2 to Level 3 than from Level 4 to Level 5. Is the student correct?
O No, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5
O No, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.
O Yes, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5.
OYes, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.
Answers
The surface area of a rectangular prism is A=2lw+2lh+2wh, where l, w, and h are the length, width, and height of the prism, respectively. Determine the width of a rectangular prism with a surface area of 930 square units if its length is 12 units and its height is 9 units. (1 point)
1. 108 units
2. 12,11/12units
3. 8,11/12
4.17 units
Complete the input-output table below for f(x)=2(x−1)2−4.(2 points)
Answers
The width of a rectangular prism with a surface area of 930 square units is 21.4 units.
What is the surface area of the rectangle?
The area of the rectangle can be calculated by multiplying l×w, The units associated with the surface area will always be units squared. The area is the result of multiplying two dimensions, length, and width, which can be represented as a power of 2.
The surface area of the rectangular prism is given by:
SA = 2lw + 2lh + 2wh
Where,
l: length
w: width
h: height
Therefore, by substituting values we have:
the surface area of 930 square units if its length is 12 units and its height is 9 units.
SA = 2lw + 2lh + 2wh
930 = 2(12)w + 2(12)(9) + 2w(9)
930 = 24w + 33 + 18w
930 - 33 = 24w + 18w
897 = 42w
w = 897/42
w = 21.4
Hence, the width of a rectangular prism with a surface area of 930 square units is 21.4 units.
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If a fair coin is tossed 4 times, what is the probability, to the nearest thousandth, of getting exactly 4 heads?
Answers
Answer: The probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%.
Step-by-step explanation:
We can use the formula for combinations, which is:
n! / (r! * (n - r)!)
In this case, n is the total number of tosses (4) and r is the number of successes we want to count (4 heads). Plugging these values into the formula, we get:
4! / (4! * (4 - 4)!) = 4! / (4! * 0!) = 4! / (4! * 1) = 1 / 1 = 1
The probability of getting exactly 4 heads in 4 tosses of a fair coin is therefore 1, or 100%. However, this is assuming that the coin is not fair and always lands on heads. If the coin is fair, the probability of getting 4 heads in 4 tosses is actually much lower.
To find the probability of getting 4 heads in 4 tosses of a fair coin, we need to use the formula for binomial probability, which is:
(n! / (r! * (n - r)!) * p^r * (1 - p)^(n - r)
In this case, p is the probability of getting a head in a single toss of the coin (0.5), r is the number of successes we want to count (4 heads), and n is the total number of tosses (4). Plugging these values into the formula, we get:
(4! / (4! * (4 - 4)!) * 0.5^4 * (1 - 0.5)^(4 - 4) = 1 * 0.5^4 * (1 - 0.5)^0 = 0.5^4 * 1 = 0.0625
Thus, the probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%, to the nearest thousandth.
according to a jhu study published in the american journal of public health, widows live longer than widowers. consider the following survival data collected on 100 widows and 100 widowers following the death of spouse: years lived widow widower less than 5 25 39 5 to 10 42 40 more than 10 33 21 can we conclude at 0.05 level of significance that the proportions of widows and widowers are equal with respect to the different time periods that a spouse survives after the death of his or her mate?
Answers
To determine whether the proportions of widows and widowers living different lengths of time after the death of their spouse are equal, you can conduct a chi-squared test of independence. This test compares the observed frequencies (the number of widows and widowers living different lengths of time) to the expected frequencies, which are the frequencies that you would expect to see if the two variables (widowhood and length of time survived) were independent.
To perform the chi-squared test, you will need to calculate the chi-squared statistic and the corresponding p-value. If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers.
To calculate the chi-squared statistic and p-value, you will need to follow these steps:
Calculate the expected frequencies for each group (widows and widowers) in each time period (less than 5 years, 5-10 years, more than 10 years). To do this, you will need to multiply the total number of widows (100) by the proportion of widows in each time period, and the total number of widowers (100) by the proportion of widowers in each time period.
Subtract the expected frequencies from the observed frequencies and square the result for each time period.
Divide each squared difference by the expected frequency and sum the results. This is the chi-squared statistic.
To calculate the p-value, you will need to consult a chi-squared table or use a statistical software program to determine the p-value corresponding to the chi-squared statistic and the degrees of freedom (which is equal to the number of time periods minus 1).
If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers
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4x² -16x+16=0
how to find the roots by factoring
Answers
4x^2 - 16x + 16 = 0
factor out the CGF which is 4
rewrite
x^2 - 4x + 4
factor
(x - 2)(x-2)
x = 2
The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off
$25,000 in student loan debt. What is the college graduate's new net worth?
O$16,081
O $21,167
O$13,833
O $33,097
Answers
The college graduate's new net worth is given as follows:
$13,833.
How to calculate the net worth?The net worth of a company or of a person is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts of the person.
The assets if the student are given as follows:
Signing bonus: $10,000.Furniture: $14,278.Savings Account Balance: $4,337.Car Value: $14,950.Computer and Software: $11,774.The liabilities of the student are given as follows:
Car Loan: $3,250.Credit Card Balances: $5,129.Student Loans: $58,097 - $25,000 = $33,097.Thus the student's net worth is calculated as follows:
(10000 + 14278 + 4337 + 14950 + 11774) - (3250 + 5129 + 33097) = $13,863.
Which is closest to the third option among those given.
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Answer:
the correct answer is 12057
Step-by-step explanation:
in order to calculate net worth, add up the assets, and then subtract the debt. be sure to pay attention to details
heres an UNRELATED TO THE QUESTION example:
i have...
$500 in my savings
$20 in my wallet
but im $200 deep in credit card debt..
(add 500 + 20, then subtract 200)
net worth: 320
a frequent cause of measurement error in polls is due to a. the increased use of cell phones. b. push polling. c. poorly worded questions. d. too large sample sizes.
Answers
Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.
Limited respondent selections, a lack of knowledge, difficulty assessing intensity, and lack of interest in political matters are just a few of the factors that might make a poll unreliable.
Survey mistake, fewer respondent alternatives, a lack of knowledge, problems assessing intensity, and a lack of interest in political matters are some potential polling weaknesses.
The drawback of polling is that if there are too many devices to check, it may take longer to service an I/O device than it does to poll all of the devices.
Instrumental, environmental, procedural, and human errors are frequent causes. Depending on how they affect the outcomes, each of these errors can either be random or systematic.
Therefore,
Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.
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THIS IS URGENT!
In orde to keep a specific bacteria alive,the temperature in a science lab cannot exceed -20 degrees farenheit. The electricity went out when the temperature was -72 degrees farenheit,but it increasing at a rate of 6.5 degrees per hour. How many hours do scientists have until the bacteria is not safe?
Answers
H ≤8
So 8 hours
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Apples cost $1.47 per pound. Danielle buys an apple that weighs 0.62 pound. To the nearest cent, how much does Danielle's apple cost?
Answers
Answer:
x = 0.91
Step-by-step explanation:
x = 1.47 x 0.62
x = 0.9114
round x = 0.9114 to the required place
x = 0.91
Factor each completely.
5) 250a³ +54
Answers
The required factorized form of the given expression is 2(125a³ + 27).
What is the greatest common factor?The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.
Here,
In the given expression,
Taking 2 common,
= 250a³ + 54
= 2(125a³ + 27)
Thus, the required factorized form of the given expression is 2(125a³ + 27).
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Which of the following equations has a solution different from the rest? (1 point)
¾ x+5=− ¼
½ x−3= ½
−1/7 x−34=¼
−0.35x−0.52=1.93
Answers
Answer: (-1/7)x - 34 = 1/4
Step-by-step explanation: The solution for all other equations is 7 and for the 3rd equation, the solution is 239.75 or 959/4
1) 3/4 X +5=-1/4
x=-7
2) 1/2X - 3 = 1/2
x=7
3) x = -137×7 /4
4) x= -7
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Select all the possible solutions of 20y < -5 + 18y.
A) y> -2.5
B)y> -
5
2
□C) y < - //
5/2
□E) y >
□F)y <-
-
☐D)-2.5> y
5
38
5
38
Answers
The possible solutions of the inequality expression given as 20y < -5 + 18y are (c) y < -5/2, y < -2.5 and (d) -2.5 > y
How to determine the possible solutions of the inequality?From the question, we have the following parameters that can be used in our computation:
20y < -5 + 18y.
To start with, we need to collect the like terms of both sides
Using the above as a guide, we have the following:
20y -18y < -5
Next, we need to evaluate the like terms of both sides
Using the above as a guide, we have the following:
2y < -5
Lastly, we divide both sides by 2
y < -5/2
Express as decimal
y < -2.5
Switch the positions
-2.5 > y
Hence, the solutions are y < -5/2, y < -2.5 and -2.5 > y
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What is the axis of symmetry? What are the coordinates of the vertex?
y=-x² +8x+12
Answers
Answer:
axis of symmetry : x = 4
coordinates of the vertex : (4, 28)
Step-by-step explanation:
Before we start solving, let's define what the coefficients of this quadratic equation is.
[tex]y = ax^2 + bx + c[/tex]
[tex]y = -x^2 + 8x + 12[/tex]
a = -1
b = 8
c = 12
⭐What is the axis of symmetry?
the vertical line that cuts through the vertex and makes the parabola into 2 symmetrical halvesequation: x=To find the axis of symmetry, we need to find the x-coordinate of the vertex.
Equation for the x-coordinate of the vertex:
[tex]x = \frac{-b}{2a}[/tex]
Substitute the values of a, b, and c into this equation and compute.
[tex]x = \frac{-(8)}{2(-1)}[/tex]
[tex]x = \frac{-8}{-2}[/tex]
[tex]x = 4[/tex]
∴ The axis of symmetry is x = 4
⭐What is the vertex of a parabola?
the absolute highest or lowest point of the parabolaTo find the x-coordinate of the vertex, you can use the formula: [tex]x = \frac{-b}{2a}[/tex].
To find the y-coordinate of the vertex, substitute the x-coordinate of the vertex and compute.
x-coordinate: 4
y-coordinate:
[tex]y = -x^2 + 8x + 12[/tex]
[tex]y = -(4)^2 + 8(4) + 12[/tex]
[tex]y = -(16) + 32 + 12[/tex]
[tex]y = -16 + 44[/tex]
[tex]y = 28[/tex]
y-coordinate: 28
∴ The coordinates of the vertex is (4,28)
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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.
Answers
The answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given byy = mx + c
where -
[m] : slope of line
[c] : y - intercept
Given is the graph of a straight line as shown.
[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -
(0, 4) and (4, 1)
Let the line be -
y = mx + c
m = (1 - 4)/(4 - 0) = -3/4
m = -3/4
So, the equation will be -
y = (-3/4)x + 4
[B] -
For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.
Therefore, the answer to each part is -
for infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.To solve more questions on functions, expressions and polynomials, visit the link below -
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Rewrite:4/6 : 1/3
as a unit rate.
Answers
Answer:
I think it's 2:1
Step-by-step explanation:
if I'm wrong in sorry
Answer:
Step-by-step explanation:To rewrite 4/6 : 1/3 as a unit rate, we need to first find a common denominator for the fractions. The least common multiple of 6 and 3 is 6, so we can use this as the common denominator.
We can then rewrite the fractions as follows:
4/6 : 1/3 = (4/6) * (3/3) : (1/3) * (2/2)
Simplifying, we get:
2/3 : 2/3
This is a unit rate, with a value of 2/3.
55 is 40% of what number?
Answers
Answer:
55 is 40% of 137.5.
Step-by-step explanation:
To find the number that 55 is 40% of, you can divide 55 by 40% to get 137.5. This means that 55 is 40% of 137.5.
What is transpose of matrix
Answers
Step-by-step explanation:
it is the process of changing rows to columb
Graph the equation. y=-x^2-6x-3
Answers
Answer:
Step-by-step explanation:
It is easier to graph using a free online graphing utility, such as DESMOS. See the attached graph. If the goal is to make a graph with pencil and graph paper, then select a few values of x and put them into the equation to find y.
A talble of a few random values is attached.
The graph includes both the generated DEMOS line (a downwards parabola) and the calculated points from the attached table. Add the points to a blank graph and draw a line as best you can that connects all the points. It is clear that a few more points with negative values of x would help with the line drawing.
John can ride his bicycle at a rate of 14 miles per hour. Convert this rate to
feet per second.
O 20.53 feet per second
O 25.03 feet per second
O205.33 feet per second
O250.33 feet per second
Answers
correct answer is a) 20.53 feet per second
John can ride his bicycle at a rate of 20.53 feet per second.
How do I calculate feet per second?
Multiplying your foot-per-minute speed by 60. This is how many seconds there are in a minute. Your speed in feet per second is the outcome. For instance, 88 feet per second is equal to 5,280 feet per minute divided by the 60 seconds in a minute.
How long is a second in feet?
One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.
Is feet per second velocity?
A unit of velocity and speed (scalar) is the foot per second (plural feet per second) (vector quantity, which includes direction). It represents the traveled or displaced distance in feet (ft) divided by the time (in seconds) (s).
[tex]\frac{14 miles}{1 h}[/tex] × [tex]\frac{5280 ft}{1 mile}[/tex]= [tex]\frac{73920 ft}{1 hr}[/tex]
[tex]\frac{73920 ft}{1 hr}[/tex] × [tex]\frac{1 hr}{60 min}[/tex]= [tex]\frac{1232 ft}{1 min}[/tex] ×[tex]\frac{1 min}{60s}[/tex]= [tex]\frac{20.53ft}{1s}[/tex]
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In the diagram below, the point O is referred to as the _____.
Answers
Answer:
d. Orthocenter
Step-by-step explanation:
⭐What is an orthocenter?
the point of concurrency of the altitudes of a triangle⭐What is an altitude?
a perpendicular segment from the vertex to the opposite side of the vertexcreates a right angle (90°)We can see that point O is the point of concurrency of the altitudes of this given triangle because there are 90° formed by the perpendicular lines.
Thus, O is referred to as the orthocenter.
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If x< 0 and y > 0, where is the point (x,y) located ???
Answers
The points (x, y) lie in the 2nd quadrant when x<0 and y>0.
What are quadrants?Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.
The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.
The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.
These areas include coordinates or positive and negative values of the x- and y-axes.
So, refer to the graph attached below.
Now, we know that:
Quadrant 1: x>0, y>0
Quadrant 2: x<0, y>0
Quadrant 3 x<0, y<0
Quadrant 4: x>0, y<0
We are given: x<0 and y>0
We can say that when x<0 and y>0 the point (x, y) lies on the 2nd quadrant.
Therefore, the points (x, y) lie in the 2nd quadrant when x<0 and y>0.
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In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Answers
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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The bears in Alaska are limited to a certain area to live due to the resources available for
food and shelter. After years, the number of bears living in the area is modeled by the function below. Using the function, find the number of bears after 17 years.
Answers
The number of bears living in the area after 17 years is; 22555
How to solve exponential functions?We are given the function;
f(t) = 103/(1 + 26e^(-0.31t))
Where f(t) is a function that models the number of bears living in the area after t period of years.
Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;
f(17) = 103/(1 + 26e^(-0.31*17))
f(17) = 103/0.00456653759
f(17) ≈ 22555 bears
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PLEASE HELP
A moth crawled 2 meters down a wall, 3 meters along the same wall, and 4 meters along an adjoining wall. Given that the walls join at a 90° angle, which most accurately expresses the distance in meters the moth will travel when flying in a straight line back to its original position?
Answers
The length of the diagonal path that leads to the original position of the moth that travels 2 meters down and, 3 meters along a wall, then 4 meters along a perpendicular wall, representing the dimensions of a rectangular prism is √(29) meters
What is the diagonal of a rectangular prism?The diagonal of a rectangular prism is a segment that stretches from one corner of the prism to the opposite corner of the prism, passing through the center of the prism.
The distance down the wall the moth crawled = 2 meters
The distance along the same wall the moth crawled = 3 meters
The distance the moth crawled along the adjoining wall = 4 meters
Angle at which the walls join = 90°
The distance distance traveled by the moth when flying in a straight line back to its original position is a diagonal of a rectangular prism of height, h = 2 meters, width, w = 3 meters, and length, l = 4 meters
The length of the diagonal of a rectangle that has height, h, width, w, and length, l, is found using the following formula;
d = √(h² + w² + l²)
The length of the diagonal along which the moth flies is therefore;
d = √(2² + 3² + 4²) = √(29)
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Given the equation 18 equals y over -5, solve for y. NEED ANSWER ASAPPP!!
90
−90
23
−13
Answers
Answer: -90
Step-by-step explanation: To solve this equation for y, we need to isolate the variable y on one side of the equation. To do this, we can multiply both sides of the equation by -5 to get rid of the fraction on the right side:
18 = y / -5
18 * -5 = y / -5 * -5
-90 = y
Therefore, the value of y that satisfies the equation is -90.
the accuracy of a sample is a measure of how closely it reports the true values of the population it represents. true false
Answers
A sample's accuracy is determined by how well it captures the genuine characteristics of the population it represents true
Accuracy is a measure of how closely a sample reflects the true values of the population it is representing. A sample that is accurate is one that accurately reflects the characteristics of the population it is representing. For example, if a sample is taken from a population of 1000 people, the sample should represent the diversity of the population, such as age, gender, race, and other characteristics. If the sample accurately reflects these characteristics, then it can be said to be accurate. The accuracy of a sample can be determined by comparing it to the population it is representing, either through surveys, interviews, or other data collection methods. If the sample closely matches the true values of the population, then it can be said to be accurate. If there are discrepancies between the sample and the population, then the sample is not accurate.
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yu want to determine the percentage of fortune 500 ceos who think indiana university (iu) deserves its current business week rating. you mail a questionnaire to all 500 ceos and 160 respond. exactly half of the respondents believe iu does deserve its ranking. calculate a 95% confidence interval for the fraction of fortune 500 ceos who believe iu deserves its ranking. round your answers to three decimal places, if necessary.
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A 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking is ( 0.279, 0.361)
According to the question,
Total number of sample taken for questionnaire = 500
Number of people responded = 160
Sample Proportion : p = 160/500
=> p = 0.32
Proportion of people who has not responded : q = 1 - p
=> q = 0.68
We have to create a 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking.
Formula of C.I = p ± z√pq/n
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 95% = 0.32 ± 1.96√0.32×0.68/500
=> 0.32 ± 1.96 √0.0004352
=> 0.32 ± 1.96 × 0.0208
=> 0.32 ± 0.0408
C.I = ( 0.32 - 0.0408, 0.32 + 0.0408)
=> C.I = ( 0.279, 0.361)
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