Answer:
a) The large sample size 'n' = 1320.59
b) If the standard deviation and the margin of error are both doubled also the sample size is not changed.
Step-by-step explanation:
Explanation:-
a)
Given data the standard deviation of the population
σ = 70.5
Given the margin error = 5 units
We know that the estimate of the population mean is defined by
that is margin error = [tex]\frac{z_{\alpha } S.D }{\sqrt{n} }[/tex]
[tex]M.E = \frac{z_{\alpha } S.D }{\sqrt{n} }[/tex]
cross multiplication , we get
[tex]M.E (\sqrt{n} ) = z_{\alpha } S.D[/tex]
[tex]\sqrt{n} = \frac{z_{\alpha } S.D }{M.E }[/tex]
[tex]\sqrt{n} = \frac{2.578 X 70.5}{5} }[/tex]
√n = 36.34
squaring on both sides , we get
n = 1320.59
b) The margin error of the mean
[tex]\sqrt{n} = \frac{z_{\alpha } S.D }{M.E }[/tex]
the standard deviation and the margin of error are both doubled
√n = zₓ2σ/2M.E
√n = 36.34
squaring on both sides , we get
n = 1320.59
If the standard deviation and the margin of error are both doubled also the sample size is not changed.
Kim needs to buy 10 pounds of grapes to take to a party. Grapes cost $1.29 per pound. How much will she spend to
purchase 10 pounds of grapes?
Answer:
$12.90
Step-by-step explanation:
multiply a $1.29 by 10 pounds and you get your answer:)
Answer:
$12.90
Step-by-step explanation
10 x $1.29=$12.90
or
move the decimal 1 time to the right
Consider the following function. f ( x ) = 1 − x 2 / 3 Find f ( − 1 ) and f ( 1 ) . f ( − 1 ) = f ( 1 ) = Find all values c in ( − 1 , 1 ) such that f ' ( c ) = 0 . (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f ( − 1 ) = f ( 1 ) , there should exist a number c in ( − 1 , 1 ) such that f ' ( c ) = 0 . This does not contradict Rolle's Theorem, since f ' ( 0 ) = 0 , and 0 is in the interval ( − 1 , 1 ) . This does not contradict Rolle's Theorem, since f ' ( 0 ) does not exist, and so f is not differentiable on ( − 1 , 1 ) . This contradicts Rolle's Theorem, since f is differentiable, f ( − 1 ) = f ( 1 ) , and f ' ( c ) = 0 exists, but c is not in ( − 1 , 1 ) . Nothing can be concluded.
The function f(x) = 1 - x^2/3 has f(-1) = f(1) = 2/3. The derivative f'(x) = -2x/3 equals zero at x=0, which is in the interval (-1, 1). Therefore, this does not contradict Rolle's Theorem.
Explanation:The function given is f ( x ) = 1 - x ^ 2 /3. To find the values f(-1) and f(1), we simply substitute these values into the function. Therefore, f(-1) = 1 - (-1) ^ 2 /3 = 1 - 1/3 = 2/3 and f(1) = 1 - 1^2/3 = 2/3. As you can see, f(-1) = f(1).
Now, to find the value 'c' such that f'(c) = 0, first we need to determine the derivative of the function, f'(x) = -2x/3. Setting this equal to zero gives the equation 0 = -2x/3, which has the solution x = 0. Therefore, f'(c) = 0 at c = 0, which is within the interval (-1, 1).
Finally, regarding Rolle's Theorem which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f'(c) = 0, our results are consistent with Rolle's Theorem, since f is differentiable, f(-1) = f(1), and a 'c' value exists in the interval (-1, 1) such that f'(c) = 0.
Learn more about Rolle's Theorem here:https://brainly.com/question/34848837
#SPJ3
A circular swimming pool has a radius of 15 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?
Answer: HI
Step-by-step explanation:
Answer:
Wizard123Ambitious
C = 2*pi*radius
radius = 15+5 = 20
C = 2*pi*20 = 40*pi = 125.6
Step-by-step explanation:
According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans. We randomly select 50 sample college graduates from public universities and determine the proportion in the sample with student loans.
Answer:
[tex]\frac{31}{50}[/tex]
Step-by-step explanation:
percentage of graduates with loan = 62%
total sample = 50
Number of student in the sample with student loan
= (percentage of graduates with loan) x (total sample)
= 62% x 50
= 31
Proportion of student in the sample with student loan = [tex]\frac{31}{50}[/tex]
A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 198 like rock, 152 like country, and 113 like jazz. Moreover, 21 like rock and country, 22 like rock and jazz, 16 like country and jazz, and 5 like all three types of music. What is the probability that a radomly selected student likes jazz or country but not rock?
Answer:
The probability that a randomly selected student likes jazz or country but not rock is 0.422.
Step-by-step explanation:
The information provided is:
Total number of students selected, N = 500.
The number of students who like rock, n (R) = 198.
The number of students who like country, n (C) = 152.
The number of students who like jazz, n (J) = 113.
The number of students who like rock and country, n (R ∩ C) = 21.
The number of students who like rock and Jazz, n (R ∩ J) = 22.
The number of students who like country and jazz, n (C ∩ J) = 16.
The number of students who like all three, n (R ∩ C ∩ J) = 5.
Consider the Venn diagram below.
Compute the probability that a randomly selected student likes jazz or country but not rock as follows:
P (J ∪ C ∪ not R) = P (Only J) + P (Only C) + P (Only J ∩ C)
[tex]=\frac{80}{500}+\frac{120}{500}+\frac{11}{500}\\=\frac{211}{500}\\=0.422[/tex]
Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.
So, the required probability is,
P(Jazz or country but not rock) =0.422
To understand the calculations, check below.
Probability:It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that the number of students is 500.
Then the students like rock and country is [tex]21-5=16[/tex]
The students like rock and Jazz is [tex]22-5=17[/tex]
The students like country and Jazz is [tex]16-5=1[/tex]
Students like only rock is [tex]198-16-5-17=160[/tex]
Students like the only country are [tex]152-16-5-11=120[/tex]
Students like only Jazz are [tex]113-17-5-11=80[/tex]
So, the P(Jazz or country but not rock) is,
[tex]P(Jazz\ or\ country\ but\ not\ rock)=\frac{120+11+80}{500} \\P(Jazz\ or\ country\ but\ not\ rock)=0.422[/tex]
Learn more about the topic of Probability:
https://brainly.com/question/6649771
akua went shopping and she decided to buy 1.8LBS of apples and 3LBS of strawberries. the apples where on sale for $1.99 per pound and the strawberries cost 2.00 per pound. how much did she spend in total?
Answer:5
Step-by-step explanation:
Answer: $9.58
Step-by-step explanation: A pound of apples cost $1.99, so you multiply 1.99 and 1.8.(the pounds he got)
1.99x1.8= 3.58 (Cost of 1.8 pounds of apples)
A pound of strawberries cost 2.00, so you multiply 2.00 and 3 (the pounds he got)
2.00x3= $6.00
Add $3.58+$6.00= $9.58
There are 184 plants to put into pots each pot can hold 8 plants how many pots are needed
Answer:
think 23 pot
Step-by-step explanation:
Answer:
Step-by-step explanation:
23
I have a algebraic problem
7277+x=10245
Answer:
x = 2968
Step-by-step explanation:
7277 + x = 10245
-7277 -7277 (Subtract 7277 from both sides to leave x by itself)
_____________
x = 2968
Could you give brainliest
Answer:
x =2968
Step-by-step explanation:
7277+x=10245
Subtract 7277 from each side
7277-7277+x=10245-7277
x =2968
14. You are a manager at Dunkin Donuts. Last Friday, your store sold 350 chocolate munchkins, 220 glazed munchkins,
125 powdered munchkins, and 75 jelly munchkins. This week, you are in charge of deciding how much of each
munchkin to make. You are instructed that in all, you need to make 6000 munchkins for the week.
dL
Answer:
Step-by-step explanation:
An L shaped pool that one part is 8 meters by 6 meters the other part is 12 meters by 6 meters. The whole pool is 4 meters deep.
Answer: 480 meters. squared
Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method and they used it to select a sample each day for 50 days. Below are the estimated 50 samples. After the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
Answer: Group B
Step-by-step explanation:
The histogram constructed by group 2 is centered at 67.5, which is the true mean height of all students at the school, so this histogram displays low bias. The values of the statistics also do not vary greatly from the mean, as can be seen by the lower variability of the histogram. Group 2 produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
Answer:
The correct answer is (B).
Step-by-step explanation:
The histogram constructed by group 2 is centered at 67.5, which is the true mean height of all students at the school, so this histogram displays low bias. The values of the statistics also do not vary greatly from the mean, as can be seen by the lower variability of the histogram. Group 2 produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability.
A carpenter bought a piece of wood that was 4.9 centimeters long. Then he sawed 4.1 centimeters off the end. How long is the piece of wood now?
Final answer:
After subtracting the length sawed off (4.1 cm) from the original length of the piece of wood (4.9 cm), the remaining length of the piece of wood is 0.8 centimeters.
Explanation:
The student's question is about subtracting two lengths given in centimeters to determine the remaining length of a piece of wood. To find out how long the piece of wood is after cutting, we subtract the length sawed off from the original length. So if the original piece of wood was 4.9 centimeters long, and the carpenter sawed off 4.1 centimeters, we perform the subtraction 4.9 cm - 4.1 cm to find the remaining length. The calculation is as follows:
4.9 cm (original length)- 4.1 cm (length sawed off)Therefore, the piece of wood is now 0.8 centimeters long.
Learn more about Subtraction of Lengths here:
https://brainly.com/question/31768556
#SPJ11
From what root word is conversational made? A) conversate B) conversation C) vers D) converse
Answer:
B conversation
Answer:
c
Step-by-step explanation:
because i got it right
Two angles whose measures add up to 180 degrees are calledTwo angles whose measures add up to 180 degrees are called
Answer:
they are called supplementary angles
Two angles whose measures add up to 180 degrees are called supplementary angles.
What are angles?
Angles are geometric figures formed by two rays that share a common endpoint called the vertex. The rays are often referred to as the sides or arms of the angle. Angles are typically measured in degrees and are used to quantify the amount of rotation or deviation between the two rays. They are commonly represented by a symbol, such as ∠ABC, where A, B, and C are points on the rays, with the vertex at point B.
The size of an angle is determined by the amount of rotation between the two rays, starting from one ray and ending at the other. A full rotation is equivalent to 360 degrees, and angles are measured counterclockwise from the initial ray. Depending on their measurement, angles can be classified into different types, such as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), and straight (exactly 180 degrees).
When two angles are supplementary, it means that they combine to form a straight angle, which is a straight line measuring 180 degrees. Supplementary angles can be adjacent (sharing a common vertex and side) or non-adjacent, but their sum will always equal 180 degrees. This property is fundamental in geometry and has various applications in solving problems involving angles and shapes.
Read more about angles here: https://brainly.com/question/28293784
#SPJ6
Part of a usability study to assess voting machines measured the time on task (TOT) of voters casting ballots (efficiency). Specifically, the data are for the same ballot cast on two different voting machines at the same location (called a precinct). Your job is to perform a "t" test on these data and draw conclusions about which voting machine is better in terms of usability. A few background items:
• The voters (participants/users) are a homogeneous group.
• Voters were randomly assigned to the voting machines.
• Thus, the two groups of voters (one group using the DRE voting machine, and the other using the OptiScan voting machine) have equal variances.
• We have no advance information to indicate that one voting machine will be better than the other. If you need a refresher of the "t" test, read the "t-test description.pdf"
Question1 – What is the null hypothesis in this usability study?
Question 2 – How many degrees of freedom are in each group (the DRE and OptiScan groups)?
Question 3 – Which "t" test should be used – paired, unpaired/equal variance, unpaired/unequal variance?
Question 4 – Should a one-tail, or two-tailed test be used, and why?
Question 5 – What is the t value?
Question 6 – Is the t value significant at the 0.05 level, and why?
Question 7 – Is the t value significant at the 0.01 level, and why?
Question 8 – Considering the combination of the above analysis, and the number of ballots completed, which voting machine has better usability, and why?
Answer:
See attached file
Step-by-step explanation:
Suppose 100 stastisticians attended a conference of the American Statistical Society. At the dinner, among the menu options were a Caesar salad, roast beef, and apple pie. 35 had the Caesar salad, 28 had the roast beef, and 45 had the apple pie for dessert. Also, 15 had at least two of those three offerings, and 2 had all three. How many attendees had none of the three
Answer: 26 attendees had none of the three.
Step-by-step explanation:
The Venn diagram illustrating the situation is shown in the attached photo.
C represents the set of statisticians that had Caesar salad.
R represents the set of statisticians that had roast beef.
A represents the set of statisticians that had apple pie for dessert.
x represents the number that had Caesar salad and apple pie for dessert only.
y represents the number that had Caesar salad and roast beef.
z represents the number that had roast beef and apple pie for dessert only.
If 15 had at least two of those three offerings,it means that
x + y + z = 15
Therefore,
35 - (x + y + 2) + 28 - (y + z + 2) + 45 - (x + z + 2) + 2 + none = 100
35 - x - y - 2 + 28 - y - z - 2 + 45 - x - z - 2 + 2 + none = 100
35 + 28 + 45 - x - x - y - y - z - z - 2 - 2 - 2 + 2 + none = 100
108 - 2x - 2y - 2z - 4 + none = 100
108 - 4 - 2(x + y + z) + none = 100
Since x + y + z = 15, then
104 - 2(15) + none = 100
74 + none = 100
none = 100 - 74 = 26
North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person and wetsuits are x dollars each. Simplify the expression using the distributive property to find the total cost of one trip for a family of four if each person uses a wetsuit. 4(69 + x)
Answer:
4x + 276
Step-by-step explanation:
Multiply 4 by 69 and x.
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education.
Savings = β0+∂0 Edu + β1Inc+u
The variable ‘Edu’ takes a value of 1 if the person is educated and the variable ‘Inc’ measures the income of the individual.
Refer to the above model. If ∂0 > 0, _____.
a.
individual with lower income have higher savings
b.
individuals with lower income have higher savings
c.
educated people have higher savings than those who are not educated
d.
uneducated people have higher savings than those who are educated
Answer:
(C)Educated people have higher savings than those who are not educated
Step-by-step explanation:
The model which is used to determine the annual savings of an individual on the basis of his annual income and education is given below:
[tex]Savings = \beta_0+\delta_0 Edu + \beta_1Inc+u[/tex]
The variable "Edu" takes a value of 1 if the person is educated. The coefficient [tex]\delta_0[/tex] measures the impact of education on a certain individual’s annual savings. If [tex]\delta_0[/tex]>0, it has a positive impact. Therefore, educated people should have higher savings than those who are not educated.
One month Isabel rented 5 movies and 2 video games for a total of$26 . The next month she rented 3 movies and 8 video games for a total of $53. Find the rental cost for each movie and each video game.
Answer:
a movie, m is 3
a video game, v is 5.5
Brainliest would be really appreciated. (need it to unlock chat)
Feel free to ask further questions if you feel like it.
Till then, have a nice day
Step-by-step explanation:
I 5m+2v=26
II 3m+8v=53
I 5m+2v=26 devide by 2 on both sides
5/2m+v=13 subtract 5/2m om both sides
v=13-5/2m
Now put this whole thing in the other equation II, replacing the v there
3m+8(13-5/2m)=53 just calculate it
3m+104-20m=53
-17m+104=53 subtract 53 on both sides
-17m+51=0 add 17m on both sides
51=17m devide by 17
3=m
we found m, v is easy
now put m in an equation from the start, let's take equation I here
I 5m+2v=26
5*(3)+2v=26
15+2v=26 subtract 15 on both sides
2v = 11 devide by 2
v = 5.5
So we found m and v, prices for single items. we can proof this when we put m and v into a given equation and the if it equals a true value
m & v in II
II 3m+8v=53
3*(3)+8*(5.5)=53
9+44=53
53=53
Seems legit.
To find the rental cost for each movie and video game, set up a system of equations based on the given information and solve for the variables.
Explanation:To find the rental cost for each movie and video game, we can set up a system of equations based on the given information.
Let's assign variables to represent the rental cost for each movie and video game. Let's use 'm' for the cost of a movie and 'g' for the cost of a video game.
Based on the first month's information, we can write the equation: 5m + 2g = 26
Based on the second month's information, we can write the equation: 3m + 8g = 53
Now we can solve this system of equations to find the values of 'm' and 'g'.
By solving the system of equations, we find that the rental cost for each movie is $4 and the rental cost for each video game is $5.
Learn more about Rental cost for movies and video games here:https://brainly.com/question/22393405
#SPJ2
Wheat & Oats Inc. is planning a design for their new line of flavored oatmeal products. They have to choose one of these cylinder containers.
3 cylinders. Figure A has a height of 7 inches and diameter of 4 inches. Figure B has a height of 5.5 inches and radius of 3 inches. Figure C has a height of 10 inches and B = 12.57 inches squared.
It costs the company $0.02 per cubic inch of oatmeal to fill a container. The company does not want the new container to cost more than $2.00 to fill. Which of the proposed container sizes should the company use?
1. Container A
2. Container B
3. Container C
4. None. They all cost more than $2.00.
IF YALL HAVE THIS QUESTION ITS NUMER 1
Answer:
a) Container A
Step-by-step explanation:
i just did the assignment and that was the correct answer.
Answer:
container a
Step-by-step explanation:
Consider the function: y=2x+5
What will be the value of the function when x=10?
Answer:
y=25
Step-by-step explanation:
10*2=20
20+5=25
Final answer:
When x=10, the value of the function y=2x+5 is 25, found by substituting 10 for x and following the order of operations.
Explanation:
The value of the function y=2x+5 when x=10 can be found by substituting the value of x into the equation. To do this, multiply 2 by 10 and then add 5 to the result:
y = 2(10) + 5
y = 20 + 5
y = 25
Therefore, when x equals 10, the value of the function is 25.
Can someone please help
Answer:
just add every thing up to gether
Step-by-step explanation:
Answer:
P = 26 , A = 28
Step-by-step explanation:
P=a+b+c+d = 6+8+7+5=26
A = [tex]\frac{a+b}{2}h = \frac{6+8}{2} 4 = 28[/tex]
brainliest plz
Consider the matrix shown below:
What are the dimensions of A.
Group of answer choices
3 X 4
4 X 3
12
A and B
Answer:
3 time 4 is 12 a and b is the same
Answer:
Dimensions of matrix:
r × c
r: no. of rows
c: no. of columns
Can someone please help me ill give them brainliest awnser if its correct
it's also worth 20 pts
Answer:
153.9380400259 in2
Step-by-step explanation:
Answer:
49 pi or 153.86
Step-by-step explanation:
The area of a circle can be found using
a=pi*r^2
We know the radius is 7 so we can substitute that in
a=pi*7^2
a=pi*49
The answer in terms of pi is 49pi units^2
For an exact answer, substitute 3.14 in for pi
a=pi*49
a=3.14*49
a=153.86
The area is also 153.86 units^2
The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00? Question 33 options: 231 15 16 163
Answer:
a) 231
The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00
n = 231
Step-by-step explanation:
Explanation:-
Given data the population standard deviation is known σ =$15.50
Given the margin of error ±$2.00
we know that 95 percent confidence interval of margin of error is determined by
[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]
cross multiplication √n we get ,
[tex]\sqrt{n} = \frac{Z_{\alpha }S.D }{M.E }[/tex]
squaring on both sides, we get
[tex](\sqrt{n} )^2 = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]
[tex]n = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]
the tabulated z- value = 1.96 at 95% of level of significance.
[tex]n = (\frac{1.96(15.50) }{2 })^2[/tex]
n = 230.7≅231
Conclusion:-
The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00
n = 231
The required sample size to estimate the mean dollars spent on pharmaceutical products with 95% confidence and ±$2.00 margin of error is 231.
Explanation:To estimate the required sample size, we need to use the formula:
Sample size = (Z^2 * σ^2) / E^2
Where:
Z is the z-score for the desired confidence level (in this case, 95% confidence level corresponds to a z-score of 1.96)σ is the population standard deviation (given as $15.50)E is the desired margin of error (given as $2.00)
Plugging in the values into the formula gives us:
Sample size = (1.96^2 * 15.50^2) / 2^2 = 231.36
Rounding up to the nearest whole number, the required sample size is 231.
Learn more about Sample size calculation here:https://brainly.com/question/34288377
#SPJ3
Suppose that time spent on hold per call with customer service at a large telecom company is normally distributed with a mean µ = 8 minutes and standard deviation σ = 2.5 minutes. If you select a random sample of 25 calls (n=25), What is the probability that the sample mean is between 7.8 and 8.2 minutes?
Answer:
0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 8 minutes
Standard Deviation, σ = 2.5 minutes
Sample size, n = 25
We are given that the distribution of time spent is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Standard error due to sampling =
[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{2.5}{\sqrt{25}} = 0.5[/tex]
P(sample mean is between 7.8 and 8.2 minutes)
[tex]P(7.8 \leq x \leq 8.2)\\\\ = P(\displaystyle\frac{7.8 - 8}{0.5} \leq z \leq \displaystyle\frac{8.2-8}{0.5})\\\\ = P(-0.4 \leq z \leq 0.4})\\\\= P(z < 0.4) - P(z < -0.4)\\\\= 0.6554 -0.3446= 0.3108[/tex]
0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.
Description : Ella has a rechangle that has a side with a length of 1/4 foot and a side with a length of 3/4 foot She shaded a model to show that the area of her reciongle is 3/16 square foot Which models represents Ella's rectangle Explain how you know.
Answer:
What are the models?
Final answer:
Ella's rectangle has a length of 1/4 foot and a width of 3/4 foot. Multiplying these dimensions gives an area of 3/16 square foot, confirming that the model of her rectangle is correct.
Explanation:
The question presents a scenario where Ella has a rectangle with a length of 1/4 foot and a width of 3/4 foot. To find the area of a rectangle, you multiply the length by the width. Thus, the area of Ella's rectangle is calculated as follows:
Area = Length * Width
Area = (1/4) * (3/4)
Area = 3/16 square feet
The model that represents Ella's rectangle should be a scaled shape where the area corresponds to the given sides' lengths. Having a model with these dimensions and affirming that its area is 3/16 square foot simply verifies that the side lengths were used correctly to determine the rectangular area. This applies the concept that the area of a rectangle is a product of its length and width.
Suppose ADB pays an interest of 2%, Barclays pays an interest of
4% and GCB pays an interest of 5% per annum and an amount of ¢350 more was invested in
Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in
Barclays is 2 times the amount invested in GCB.
Correction
https://brainly.in/question/16846717
Answer:
Amounts invested in each bank:
GCB=$1,713,33
Barclays=$3,426.66
ADB=$1,363.33
Step-by-step explanation:
-Given that ADB pays 2% pa, GCB pays 4% and Barclays pays 5%
-From the information provided, the amount invested in each of the 3 banks can be expressed as:
-Let X be the Amount invested in GCB:
[tex]GCB=X\\\\Barclays=2X\\\\ADB=2X-X-350=X-350[/tex]
-Since the total interest earned on all 3 accounts after 1 year is $250, we can equate and solve for X as below:
[tex]I=Prt\\\\I_{GCB}=X\times 0.05\times1= 0.05X\\\\I_{Barclays}=2X\times 0.04\times 1=0.08X\\\\I_{ADB}=(X-350)\times 0.02\times 1=0.02X-7\\\\I=I_{GCB}+I_{ADB}+I_{Barclays}\\\\250=0.05X+0.08X+(0.02X-7)\\\\250=0.15X-7\\\\0.15X=257\\\\X=1713.33\\\\GCB=\$1713.33\\Barclays=2X=\$3426.66\\ADB=X-350=\$1363.33[/tex]
Hence, the amounts invested in each bank is GCB=$1,713,33 , Barclays=$3,426.66 and ADB=$1,363.33
Answer:
Amounts invested in each bank:
GCB=$1,713,33
Barclays=$3,426.66
ADB=$1,363.33
Step-by-step explanation:
A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor and brings a profit of $2.50. The football uses 3 ounces of foam and 30 minutes of labor and brings a profit of $2. The manufacturer has available 43.5 pounds of foam and 110 labor-hours a week. Use the simplex method to determine the optimal production schedule so as to maximize profits. Show that the geometric method gives the same solution.
To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method.
Explanation:To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method. Let's define our decision variables as follows:
x = number of large basketballs to producey = number of footballs to produceOur objective is to maximize the profit, so our objective function can be written as:
Z = 2.5x + 2y
We have the following constraints:
4x + 3y ≤ 43.5 (foam constraint)20x + 30y ≤ 110 (labor constraint)x, y ≥ 0 (non-negativity constraint)To solve this linear programming problem with the simplex method, we will use a software or calculator that supports linear programming.
A recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours. Which of the following is a 90% confidence interval for the mean time per week spent listening to the radio? (a) 11.5 +1.676 x 9.2 (b) 11.5 +1.282 x 9.2 (c) 11.5 +1.676 x 9.2/51(d) 11.5 +1.282 x 9.2/V51 (e) 11.4 +1.299 x 9.2/51
Answer:
90% confidence interval for the mean time per week spent listening to the radio is [tex]11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }[/tex] .
Step-by-step explanation:
We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.
Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average amount of time spent listening to music = 11.5
s = sample standard deviation = 9.2 hours
n = sample of students = 51
[tex]\mu[/tex] = population mean per week spent listening to the radio
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.676 < [tex]t_5_0[/tex] < 1.676) = 0.90 {As the critical value of t at 50 degree of
freedom are -1.676 & 1.676 with P = 5%}
P(-1.676 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.676) = 0.90
P( [tex]-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] , [tex]11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] ]
= [9.34 hours , 13.66 hours]
Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].