Answer:
coefficient
Step-by-step explanation:
the 4 is the coefficient
Julianna bought 45 feet of fencing to go around the edge of the garden. If each unit in the coordinate plane represents 1 foot, does Julianna have enough fencing for the garden? Be sure to explain your answer.
The solution is:
No, this statement is not true, we know that these dimensions are not possible given the amount of fencing.
We have,
Perimeter measures the distance around a shape.
Perimeter Formula
The perimeter is 2w + 2l = P, where w is the width and l is the length. This formula is used because together, it adds together the distance of every side.
If wanted, it can be rewritten as w + w + l + l = P. This form of the formula shows all 4 sides being added together.
Inequality
We can set up an inequality to represent the situation. We know that the perimeter must be less than or equal to 150 because that is the amount of fence John has. So, we can plug the information that we know into the formula.
2(50) + 2(40) ≤ 150
Then, solve.
180 ≤ 150
Since this statement is not true, we know that these dimensions are not possible given the amount of fencing.
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complete question:
John is building a fence around his garden and has 150 feet of
fencing. The length of his garden is 40 feet and the width of
his garden is 50 feet. Does John have enough fencing to go
around the perimeter of his garden? Explain why or why not.
What is the result when the number 36 is decreased by 25%
Answer:
27
Step-by-step explanation:
1. 100% - 25% = 75%
2). 3/4 x 36 = 27
Answer:
27
Step-by-step explanation:
There are 2 ways we can solve this:
The first way is with percents:
100%-25%=75%
75/100=0.75 or 3/4
3/4·36
27
The second way is to use common knowledge:
We know that 25% is 1/4 of anything. So, 1/4 of 36 is 9.
36-9=27
Hope this helps! :)
3
Period
Date
5. If a teacher were to distribute sheets of
paper so that each student got two
sheets, there would be 8 sheets
remaining. However, if three sheets
were given to each student, the teacher
would be 11 sheets short. Which
equation could be used to find how
many students are in the class?
If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11.
A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
Let number of students in class be denotes as "x",
If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,
If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,
So, the equation which is used to find number of students in class is 2x+8=3x-11,
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?
(a) 2(x - 8) = 3(x + 11)
(b) 2(x + 8) = 3(x - 11)
(c) 2x-8 = 3x + 11
(d) 2x+8 = 3x - 11
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of flour and 34 cup of water. Mitch wants to make more pizzas without changing the ratio of flour to water. The number of cups of flour must always be
how many times the number of cups of water
The number of cups of flour must always be 6 times the number of cups of water, under the condition Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water.
In order to make 4 more pizzas without changing the ratio of flour to water, Mitch have to use 12 cups of flour and 2 cups of water.
To evaluate this we need to perform multiplication
Mitch used 3 cups of flour and 1 cup of water for 2 pizzas. So for each pizza, he used 1.5 cups of flour and 0.5 cups of water.
To make 4 more pizzas, he needs to use 6 cups of flour and 2 cups of water (since he needs twice as many pizzas).
Then, for each pizza, he needs to use 1.5 cups of flour and 0.5 cups of water (since he wants to keep the ratio the same).
So for 4 more pizzas, he needs to use 6 x 2 = 12 cups of flour and 2 x 2 = 4 cups of water.
Since he wants to keep the ratio the same, he needs to use 12 cups of flour and 2 cups of water.
Therefore, the number of cups of flour must always be 6 times.
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The complete question is
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water. Mitch wants to make 4 more pizzas without changing the ratio of flour to water. Enter a number to make the sentence about the ingredients true.
The number of cups of flour must always be___ times the number of cups of water.
Geometry- finding the volume. Please help I’m confused?!
Answer:
V = 5/3πr³1130.4 in³Step-by-step explanation:
You want a formula for the volume of the given figure, which is a hemisphere of radius r atop a cylinder of the same radius and height r.
Volume formulasThe volume of a sphere is given by ...
V = (4/3)πr³
The volume of a cylinder is given by ...
V = πr²h
CompositionThe given figure is composed of half a sphere, and a cylinder. The total volume will be the sum of the volumes of these parts.
total volume = 1/2(sphere volume) + (cylinder volume)
A Total volumeUsing a height of r for the cylinder, we can substitute the above formulas to get ...
total volume = 1/2(4/3πr³) +(πr²·r)
total volume = 2/3πr³ + πr³ = (2/3 +1)πr³
total volume = (5/3)πr³
B How much glassWhen the height is 12 inches, the radius is 6 inches, so the volume of the object is ...
total volume ≈ (5/3)(3.14)(6 in)³ = 1130.4 in³
About 1130.4 cubic inches of glass will be needed for a paperweight that is 12 inches tall.
HELP I have this due tommorow click link and use surface area I need verification
Answer:
Question 3: would equal 30.5 and Question 4: would equal 19
What is the perimeter and area of parallelogram WXYZ if 1 unit equals 1 centimeter? Round to the nearest centimeter.
a.) perimeter= 20cm; area 22cm²
b.) perimeter= 22cm; area= 20cm²
c.) perimeter= 26cm; area= 39cm²
d.) perimeter= 39cm; area= 26cm²
The perimeter and area of parallelogram WXYZ is b.) perimeter= 22cm; area= 20cm²
How to determine the valueThe formula for calculating the perimeter of a parallelogram is expressed as;
P = 2(a + b)
Such that the parameters are;
P is the perimetera and b are the parallel sidesThen, we have;
Perimeter = 2(4 + 7)
Add the values
Perimeter = 22 cm
The area of a parallelogram is expressed as;
Area = bh
Where the parameters of the formula are;
h is the height b is the base lengthArea = 5(4)
Area = 20cm²
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Could someone answer and explain this to me plss
Step-by-step explanation:
in geometry, a minor arc is an arc that measures less than 180°, and a major arc is one that measures greater than 180°. Arc measure is the angle measure of the center angle corresponding to the arc. An arc is a part of the circumference of a circle.
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.x = t^4 + 3y = t^3 + tt = 1y(x) =
The equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.
To find the equation of the tangent to the curve at the point corresponding to t=1:
We first need to find the corresponding values of x and y. Substituting t=1 into the given equations, we get:
[tex]x = 1^4 + 3 = 4[/tex]
[tex]y = 1^3 + 1(1) = 2[/tex]
So the point on the curve corresponding to t=1 is (4,2).
To find the equation of the tangent at this point,
we need to find the slope of the curve at this point. We can do this by taking the derivative of y(x) with respect to x:
[tex]dy/dx = (dy/dt)/(dx/dt) = (3t^2+t)/(4t^3)[/tex]
Substituting t=1, we get:
dy/dx = (3+1)/(4) = 1
So the slope of the curve at the point (4,2) is 1.
Now we can use the point-slope form of the equation of a line to find the equation of the tangent:
y - 2 = 1(x - 4)
Simplifying, we get:
y = x - 2
So the equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.
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What’s the unit rate of 144 pages in 3 minutes ?
there were 11 students running a race. How many diffenert arrangments of first,second,and third place are possible?
Answer:
165
Step-by-step explanation:
there are 165 different arrangements of 1,2,3 place possible of the 11 students
Draw the isosceles triangle shown, divide each leg into eight congruent segments. connect the highest point of one leg with the lowest point of the other leg. then connect the second highest point of one leg to the second lowest point of the other leg. continue this process. write a quadratic function whose graph models the shape that appears
The equation of the graph or function y=-1/9x²
From the given instruction we obtain a parabola with an x-coordinate equal to the midpoint of I of the endpoints of the base or −6+6/2 =0
And y-coordinate equal to the midpoint of the y-coordinates of the vertex and an endpoint of the base or 4+(−4)/2=0
So the vertex is (0,0)
From the function y=x² above graph is the reflection about x-axis
so we have y=−ax²
So, to find "a" we will put (6,-4) in equation 1 we get
-4=-a(6)²
a=1/9
Hence, the equation of the graph is y=-1/9x²
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Find the radius of the sphere which passes through points A, B, C, and D in space if BAC = BAD =CAD = 90 and AB = AC = AD = 6.
To find the radius of the sphere passing through points A, B, C, and D in space, we can use the fact that the sphere will be the circumsphere of triangle ABC and triangle ABD.
Since BAC = BAD = CAD = 90, we know that triangle ABC and triangle ABD are both right triangles.
Using the Pythagorean theorem, we can find the length of BC and BD:
BC^2 = AB^2 + AC^2 = 6^2 + 6^2 = 72
BD^2 = AB^2 + AD^2 = 6^2 + 6^2 = 72
Since BC = BD, we know that triangle BCD is an isosceles triangle. Therefore, the altitude from vertex C to side BD will bisect BD, and the altitude from vertex B to side CD will bisect CD. Let E be the point where the altitudes intersect.
Now we can use the Pythagorean theorem again to find the length of CE:
CE^2 = BC^2 - BE^2 = 72 - (BD/2)^2 = 72 - 36 = 36
CE = 6
Since the sphere passes through point C, its center must be equidistant from points A, B, and D. Let O be the center of the sphere. Then we have:
OA = OB = OD
OA^2 = OC^2 + AC^2 = OC^2 + 36
OB^2 = OC^2 + BC^2 = OC^2 + 72
OD^2 = OC^2 + AD^2 = OC^2 + 36
Since OA = OB = OD, we can equate the expressions for OA^2, OB^2, and OD^2:
OC^2 + 36 = OC^2 + 72 = OC^2 + 36
72 = 2(OC^2 + 36)
OC^2 = 18
Therefore, the radius of the sphere is:
r = OC = sqrt(18) = 3sqrt(2)
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the u.s. bureau of labor statistics reports that 11.3% of u.s. workers belonged to unions in 2013. suppose a sample of 400 u.s. workers is collected in 2018 to determine whether union efforts to organize have increased union membership. if the sample results show that 58 of the workers belonged to unions, what is the p-value for your hypothesis test?
Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.
We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.
The null hypothesis is that the population proportion is equal to 11.3%:
H0: p = 0.113
The alternative hypothesis is that the population proportion is greater than 11.3%:
Ha: p > 0.113
The sample proportion is P = 58/400
= 0.145
The standard error of the sample proportion is:
SE = √(p*(1-p)/n)
= √(0.113*(1-0.113)/400)
= 0.0197
The test statistic is:
z = (P - p) / SE
= (0.145 - 0.113) / 0.0197
= 1.6244
The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:
p-value = P(Z > 1.6244)
= 0.0515 (using a standard normal distribution table)
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(Chapter 12) For any vectors u and v in V3, |u à v| = |v à u|
So the magnitude of the cross product between two vectors is the same regardless of the order of the vectors.
This statement is true. The magnitude of the cross product between two vectors u and v is defined as:
|u à v| = |u||v|sinθ
where θ is the angle between the two vectors. The cross product is anti-commutative, meaning that if we switch the order of the vectors, the sign of the result changes:
v à u = - (u à v)
Therefore, taking the magnitudes of both sides, we have:
|v à u| = |- (u à v)|
|v à u| = |u à v|
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Which of the following inequalities are correct?
A -6<-4
B 4<6
C 0>-4
Answer:
Step-by-step explanation:
Both options A and B are correct, while option C is incorrect.
Option A, -6 < -4, is true because -6 is less than -4 on the number line.
Option B, 4 < 6, is also true because 4 is less than 6 on the number line.
Option C, 0 > -4, is incorrect because 0 is not greater than -4. In fact, -4 is less than 0, so the correct inequality would be -4 < 0.
Therefore, the correct options are A and
Help me on all questions it’s due soon
(1) The value of x is in the inscribed chords is 110⁰.
(2) The length of PT is 7.48 cm.
(3) The length of EC is 1.93.
What is the value of x?The value of x is calculated by applying intersecting chord theorem as shown below;
x = ¹/₂ ( 360 - ( 40⁰ + 100⁰ )
x = ¹/₂ (360 - 140 )
x = ¹/₂ (220)
x = 110⁰
2. The length of PT is calculated as follows;
The radius of the circle = length NT, is calculated as follows;
A = πr²
r² = A/π
r = √ (A/π)
r = √ (25π/π)
r = 5 cm = NT = NM
PT is calculated by applying Pythagoras theorem as follows;
NP = NM + MP
NP = 5cm + 4 cm
NP = 9 cm
PT = √ (9² - 5²)
PT = 7.48 cm
3. The length of EC is calculated by applying chord theorem as follows;
AE. ED = BE . EC
ED = AD - AE
ED = 12 - 3 = 9
Now, solve for EC;
AE. ED = BE . EC
3 x 9 = 14(EC)
27 = 14(EC)
EC = 27/14
EC = 1.93
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Mr Andrew harvested 3 056 dasheens. He packed them into bags of 8 dasheens each. How many bags of dasheen did he pack?
Answer:
382 bags of dasheen
Step-by-step explanation:
Divide the total number of dasheens harvested by the number of dasheens per bag:Therefore, My. Andrew packed a total of 382 bags of dasheen
suppose you have 6 red cards, 8 green cards, and 13 blue cards. the cards are well shuffled and you randomly draw one card. a. how many elements are there in the sample space
The sample space has 27 elements.
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is drawing one card from a well-shuffled deck of 27 cards.
To determine the number of elements in the sample space, we can count the total number of cards in the deck.
The number of red cards is 6, the number of green cards is 8, and the number of blue cards is 13. Therefore, the total number of cards in the deck is:
6 + 8 + 13 = 27
Hence, there are 27 possible outcomes when drawing one card from the deck. These outcomes consist of the 6 red cards, the 8 green cards, and the 13 blue cards in the deck.
So the sample space has 27 elements.
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[NEED HELP!]
Frederick reduced triangle A
proportionally.
He made each side 23
times as long.
The unknown side length in triangle B has a measure of 7.5 units.
It is given that Alejandro reduced triangle A proportionally.
It means triangle A and B are similar and their corresponding sides are proportional.
Scale factor = 6/12
=1/2
Each side of triangle A is changed by a factor of 1/2.
Let the unknown side of triangle B be x.
x/15=1/2
2x=15
x=7.5
Therefore, the unknown side length in triangle B has a measure of 7.5 units.
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how long will it take joe to turn the sheet metal into 5 pieces?
Answer:
Unclear, but assuming it takes 2 minutes to cut one piece, your answer would be 10 minutes to cut 5 pieces.
Step-by-step explanation:
We have 5 pieces, each takes 2 minutes, so:
5×2=10
If it takes more or less than 2 minutes per piece, replace the "2" with another value. (EXAMPLE: 5 minutes per piece would be 5×5=25)
Other:
If this is wrong, I apologize, as there was not enough information given to your question.
the difference between john's and paul's heights is twice the difference between john's and thom's heights. if john is the tallest, what is the average (arithmetic mean) height of the three? (1) paul is 163 centimeters tall. (2) thom is 173 centimeters tall.
We're given that the difference between John's and Paul's heights is twice the difference between John's and Thom's heights.
Let's use variables to represent their heights: J for John, P for Paul, and T for Thom. The equation can be written as:
J - P = 2(J - T)
Now, we're given two pieces of information:
1) Paul is 163 centimeters tall (P = 163).
2) Thom is 173 centimeters tall (T = 173).
We'll use this information to solve for John's height and then find the average height of the three.
Step 1: Plug in the given values into the equation.
J - 163 = 2(J - 173)
Step 2: Distribute the 2 on the right side.
J - 163 = 2J - 346
Step 3: Rearrange the equation to isolate J.
J - 2J = 346 - 163
Step 4: Combine like terms.
-1J = 183
Step 5: Divide by -1 to find John's height.
J = -1(-183)
J = 183 cm
Now that we have John's height, we can find the average height of the three.
Average height = (John's height + Paul's height + Thom's height) / 3
Average height = (183 + 163 + 173) / 3
Average height = 519 / 3
Average height = 173 cm
So, the average height of John, Paul, and Thom is 173 centimeters.
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Assume that there are 21 homes in the Quail Creek area and four of them have a security system. Three homes are selected at random:
a. What is the probability all three of the selected homes have a security system? (Round the final answer to 4 decimal places.)
b. What is the probability none of the three selected homes has a security system? (Round the final answer to 4 decimal places.)
c. What is the probability at least one of the selected homes has a security system? (Round the final answer to 4 decimal places.)
d. Did you assume the events to be dependent or independent?
The probability that all three selected homes have a security system is 0.0014.
The probability that none of the three selected homes have a security system is 0.3583.
The probability that at least one of the selected homes has a security system is 0.6417.
a. The probability that the first selected home has a security system is 4/21. Since there are now only 3 homes left with security systems out of 20 total homes, the probability that the second selected home also has a security system is 3/20. Similarly, the probability that the third selected home has a security system is 2/19. Therefore, the probability that all three selected homes have a security system is:
[tex](4/21) * (3/20) * (2/19) = 0.0014[/tex]
So, the probability that all three selected homes have a security system is 0.0014.
b. The probability that the first selected home does not have a security system is 17/21. Since there are now only 16 homes left without security systems out of 20 total homes, the probability that the second selected home also does not have a security system is 16/20. Similarly, the probability that the third selected home does not have a security system is 15/19. Therefore, the probability that none of the three selected homes have a security system is:
(17/21) * (16/20) * (15/19) = 0.3583
So, the probability that none of the three selected homes have a security system is 0.3583.
c. The probability that none of the three selected homes have a security system is 0.3583 (as found in part b). Therefore, the probability that at least one of the selected homes has a security system is:
1 - 0.3583 = 0.6417
So, the probability that at least one of the selected homes has a security system is 0.6417.
d. We assumed the events to be dependent because the probability of each event is affected by the outcomes of the previous events. For example, the probability of selecting a home with a security system on the second draw is influenced by whether a home with a security system was selected on the first draw.
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If tan(A+B)=8 and tan B = 1/57 find tan A
Step by Step Please
The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses H 0: Mu = 3.54 pounds; pounds. What is a Type II error in this situation?
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is less than 3.54 pounds when the true mean weight is less than 3.54 pounds.
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is not less than 3.54 pounds.
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is less than 3.54 pounds when the true mean weight is actually not less than 3.54 pounds.
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.
answer d
The Type II error in this situation is the fourth option: (d) based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.
A Type II error occurs when the null hypothesis (in this case, that the mean weight of the banana bunches is 3.54 pounds) is not rejected, even though it is false. In other words, the owner fails to reject the shipment of bananas, even though it does not meet the required weight standard. In this scenario, the owner may face a loss in business or reputation due to the low quality of bananas, and may also incur losses by selling the underweight bananas at a lower price or even disposing of them.
The probability of making a Type II error can be minimized by increasing the sample size or decreasing the significance level (alpha level) of the test. However, a Type II error can never be completely eliminated.
Therefore, the correct option is d.
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Grace is in charge for selecting the batting order for her club baseball team. If there are 12 players on the team and the batting order is a total
of ten batters, in how many different ways can she select the order?
Number of Different Ways:
There are 19,958,400 different ways Grace can select the batting order for her club baseball team.
How to determine how many different ways can she select the orderUsing permutation formula: P(n,r) = n! / (n - r)!
where n is the total number of players on the team (12) and r is the number of batters in the batting order (10).
So, we have:
P(12,10) = 12! / (12 - 10)!
P(12,10) = 12! / 2!
P(12,10) = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3
P(12,10) = 19,958,400
Therefore, there are 19,958,400 different ways Grace can select the batting order for her club baseball team.
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PLEASE HELP I NEED HELP!!!!!!!!!!!!!!!!!!
Answer:
y = -3√(x -1) +2
Step-by-step explanation:
You want the equation of the translated, reflected, and scaled square root function in the given graph.
TranslationWe can find the amount of translation by looking at the position of the point that corresponds to (0, 0) on the graph of the parent function. That end point where the slope is vertical is located at (1, 2) on the given graph.
When a function y = f(x) is translated by (h, k), it becomes ...
y = f(x -h) +k
For (h, k) = (1, 2) the translated function is ...
y = f(x -1) +2 = √(x -1) +2
Scale factorWhen the function is scaled, its value is multiplied by the scale factor. If that factor is 'a', our scaled and translated function is ...
y = a√(x -1) +2
To find the scale factor, we can use the second point on the curve: (2, -1). Using these values for x and y gives ...
-1 = a√(2 -1) +2
-3 = a . . . . . . . . . . subtract 2, simplify
The transformed function is ...
y = -3√(x -1) +2
__
Additional comment
The function is scaled before it is translated, so the scale factor does not apply to the translation.
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The ages of children taking a hip-hop dance class are 10, 9, 9, 7, 12, 14, 14, 9, and 16 years old
Which of the following Describe the distribution of the data
The ages range from 1 of 7.
Select Choice
years to 2 of 7.
Select Choice
years.
The middle half of the data range from 3 of 7.
Select Choice
years to 4 of 7.
Select Choice
years.
The median is 5 of 7.
Select Choice
years; half of the children taking the class are older than 10 years old and half of them are younger than 10 years old.
Because the left whisker and left box combined are shorter than the right whisker and right box, there is 6 of 7.
Select Choice
variation among the lower half of the data. Having less variation means there is a 7 of 7.
Select Choice
consistency among the ages of children younger than 10 years old.atistical questions? Select all that apply. (Example 1)
Answer:
Step-by-step explanation:
easy its 7
Which relation is displayed in the table?
A: {(-2, -3), (1, -1), (2, -2), (3, 3)}
B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}
C: {(-2, -3), (-1, 1), (-2, 2), (3, 3)}
D: {(-2, -3), (-1, 1), (-2, -2), (3, 3)}
The relation that is displayed in the table can be found to be B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}
How to find the relation ?The relation displayed on the table would simply refer to the points seen on the table. When writing the coordinates of a point, you should give the x value first and then give the y value.
The relations on the table are therefore { ( - 3 , - 2 ) , ( - 1 , 1 ) , ( 2 , - 2 ) , ( 3 , 3 ) }. This represents the entire point portfolio seen on the table and therefore encompasses all the relation.
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Tyrone is an investment broker who tells his clients that some investments are a moderate risk and others are an aggressive risk. He wants to know the difference between the annual return on the investments in each category. He sampled 17 investments from each category. There was a mean annual return of 6.2% on the investments in the moderate sample, with a standard deviation of 9.3%. The aggressive investments had a sample mean of 7.3% and a standard deviation of 12.4%. Assume that the conditions for inference have been met, and that Tyrone will use the conservative degrees of freedom corresponding to a sample size of 17. Leta - Am be the difference in mean annual return (in percents) of the groups of investments. Which of the following is a 90% confidence interval for p - um? Choose 1 answer: a. (-5.49, 7.69) b. (-5.464, 7.664)c. (-5.084, 7.284) d. (-3.926, 6.126) e. (-2.659,4.859)
the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).
The point estimate for the difference in mean annual return is:
a - m = 7.3 - 6.2 = 1.1
To find the margin of error for a 90% confidence interval, we use the t-distribution with 16 degrees of freedom (conservative df) and a 5% significance level (90% confidence level):
t* = 1.745
The margin of error is then:
ME = t* * sqrt[(s1^2/n1) + (s2^2/n2)]
= 1.745 * sqrt[(0.093^2/17) + (0.124^2/17)]
= 0.916
The 90% confidence interval is:
(a - m) ± ME
1.1 ± 0.916
Thus, the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).
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