When building a regression model provided the given information from the four remaining independent variables the variable to be entered next (second) would be variable with the highest coefficient of partial determination. (Option A)
A regression model refers to a function that illustrates the relationship between one or more independent variables and a response, target, dependent variable. The primary uses of regression analysis are forecasting, time series modeling and identifying the cause-and-effect relationship between variables. When building a regression model with five potential independent variables to explain the variation in the dependent variable, at step 1, variable x3 enters the regression model. Of the four remaining independent variables, the variable entered next into the model would be the variable with the highest coefficient of partial determination. A coefficient of partial determination refers to the measurement of marginal (extra) contribution of X variable or percentage of variation in the response variable that can be explained by the explanatory variables and can be used to measure how strongly two variables are related to one another.
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A factory process requires 3 steps to finish a product. The steps each have a mean completion time of u = 10 seconds and a standard deviation of o = 5 seconds. The time it takes to complete each step is independent from the other steps. Let I be the total completion time of the 3 steps on a randomly chosen product.
Answer:
square root 75
Step-by-step explanation:
every fifth adult entering an airport is checked for extra security screening. what sampling technique is used?
It belongs to isometric sampling or systematic sampling in every fifth adult entering an airport is checked for extra security screening.
What is systematic sampling?
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.
Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening.
After that person, they choose every 50th person who passes through for extra screening as well
By the topic
The sampling interval is 50, which is periodic.
It belongs to isometric sampling or systematic sampling.
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Explain how you know that the sum of 2,3,and -2 is positive without computing
Technically, it would be impossible to truly know without "computing" at all, but once you add 2 and 3, you would be able to know that the sum of all three numbers of positive without accounting for the -2, because 6 is a greater absolute value than -1.
Some examples:
12 + - 4
7 + - 3
18 + -10
All will be positive because those positive numbers (12, 7, 18) are greater than the others (4, 3, 10).
In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)
To view the sketched cubic function and label the zeros using the factors check the attached image and the rewrite the function in general form is
2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] -26x + 30.
What do you mean by factors and give example?A number or algebraic expression that divides another number or expression evenly that is with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.
Given that :
f(x) = (x + 3)(-x + 5)(2 - 2x)
To find : zeroes of f(x) , sub f(x) = 0
(x + 3)(-x + 5)(2 - 2x) = 0
x + 3 = 0
x = -3
- x + 5 = 0
x = 5
2 - 2x = 0
x = 1
The zeroes are -3 , 1 , 5
Rewrite the function in general form
f(x) = (x + 3)(-x + 5)(2 - 2x)
= (- [tex]x^{2}[/tex] + 2x + 15 )(2 - 2x)
f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30
Therefore, f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30 is a general form.
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Mr. Jones has driven 180 miles to Dallas. He has 60% of the trip left to go. How many more miles does Mr. Jones have to drive to get to his destination? Round your answer to the nearest whole mile.
Mr Jones have to drive 270 miles to get to his home
How to find the number of miles Mr Jones have to driveThe question is a percentage problem, percentage deals with a fraction hundred and used to solve the problem
From the equation 180 miles represents 40% of the journey
let the total journey be x, hence we say
0.4x = 180
x = 180 / 0.4
x = 450 miles
Then the 60% left is calculated
60% of 450
= 0.6 * 450
= 270 miles
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Find the value of u² - v² when u = 5 and v = 3
Answer: 16
Step-by-step explanation:
u=5
v=3
u² - v²
5² - 3²
——————————
5² = 5 • 5 = 25
3² = 3 • 3 = 9
——————————
25 - 9 = 16
I went to dinner and the dessert was 17% of the $85 meal. How much did we spend on dessert?
Answer:
$14.45
Step-by-step explanation:
To make the equation easier you would have to make the percent decimal and to do that move it twice to the left. So it would be 0.17 x 85 which is 14.45 and add that dollar sign there. :)
a manufacturer must test that his bolts are 4.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14cm. he knows that the population standard deviation is 0.83cm. assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
p < 0.05, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.
Given,
The test statistics formula for finding the z-score is,
z = (X - μ)/(σ/√n)
Where,
X = sample mean
μ = population mean
σ = population standard deviation
n = sample size
This z-score is used to determine the p-value. The null hypothesis is not rejected if p > α, and it is rejected if p < α.
Here,
The population mean μ = 4.00
The sample size n = 196
The sample mean X = 4.14
The standard deviation σ = 0.83
The significance level α = 0.05
So, the hypothesis is:
The null hypothesis: H0: μ = 4
The alternative hypothesis: Ha: μ ≠ 4
Thus, the test statistic value is,
z = (X - μ)/(σ/√n)
= (4.14 - 4)/(0.83/√196)
= 2.36
So, for z = 2.36, the p-value is 0.009137
Therefore,
The provided significance level of 0.05 is not met by the p-value of (0.009137). Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.
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what is $0.4\overline 8 0.\overline{37}$? express your answer as a common fraction in lowest terms.
The answer of the given expression as a common fraction in lowest terms is 437/495 .
In the question ,
it is given that ,
the expression is 0.4overline 8 + overline 0.37 ,
that can be written as [tex]0.4\overline{8}[/tex] + [tex]0.\overline{37}[/tex]
On further simplifying the above expression further ,
we get ,
= (48 - 4)/90 + 37/99
= 44/90 + 37/99
taking the LCM of 90 and 99 as 990 and solving further ,
we get ,
= 484/990 + 390/990
= ( 484 + 390 )/990
= 874/990
in lowest form it is = 437/495 .
Therefore , the answer to the expression is 437/495 .
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Select all the equivalent solution sets to the compound inequality 27>−1/2(4x+6)≥100?
A. −15
B. −10.5
C. −10.5
D. −15
E. −10.5
F. −15
G. −15
find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 40. b) 48. c) 56. d) 64.
With any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, considering that n is 40:
n = 40 as a positive integer
Probability of not choosing any of the six ideal numbers in a lottery:
C(34 , 6)/C(40 , 6)
The likelihood of choosing none of the six correct integers in a lottery:
1344904/3838380
Probability of not winning a lottery with any of the six correct integers:
0.35
Therefore, with any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.
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Correct question:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)
a) 0.40
b) 0.48
c) 0.56
d) 0.64
e) 0.35
a gardener uses a total of 61.5 gallons of gasoline in one month. Of the total amount of gasoline, 3/5 was used in his lawn mowers. How many gallons of gasoline did the gardener use in his lawn mowers in the one month
Answer:
36.9 gallons were used in one month.
Step-by-step explanation:
In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other:
3 ÷ 5 = 0.6
Then, we can set up this equation to figure out how much gallons of gasoline was used:
0.6 x 61.5 = 36.9
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 2 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer: 36.9 gallons were used in one month.
Step-by-step explanation:
In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other: 3 ÷ 5 = 0.6
Then, we can set up this equation to figure out how much gallons of gasoline was used: 0.6 x 61.5 = 36.9
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40 divided by 5 times (24-23)
in how many ways may a student mark a 20 questions test, if 7 questions mark correctly and 13 incorrectly?
The 20 questions test answers may a student mark 8192 ways.
What is the combinations?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Since there are 20 questions, and each question can be answered in if 7 questions mark correctly and 13 incorrectly then:
7 questions can be answered correctly.
13 questions can be answered incorrectly.
The 2 questions can be answered in
2 × 2 ways.
The 3 questions can be answered in 2×2×2 ways and so on.
So we have:
1 × 1 × 1 × 1 × 1 × 1 × 1 × 2¹³
= 8192
Hence, the 20 questions test answers may a student mark 8192 ways.
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A square and rectangle the same perimeter. Each side of the square measures 4x+4 units. The rectangle measures x and 2x+13 units on opposite sides. Find the value of x and the perimeter of the figure?
Answer:
x = 1, p = 32
Step-by-step explanation:
4(4x+4) = 2(x+2x+13)
16x+16 = 6x+26
10x+16=26
10x=10
x=1
4(4(1)+4) = 4(4+4) = 4(8) = 32
Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.
DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(3xy - 1)(4xy + 2)
Answer:
12x^2.y^2 + 2xy - 2
Step-by-step explanation:
I put the dot so you don't get confused thinking it is 2y. Tell me if I misinterpreted the question
A track and field team was calculating their long jump scores. The long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m. Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m. What score would Alaina have to get to tie the Winning teams score? Show your work.
The score that Alaina would have to get to tie the winning team's score is of:
4.4 meters.
What is the needed score?The combined score of the winning team is given as follows:
25.6 m.
The scores of Alaina's teammates are given as follows:
5.46 m, 4.84 m, 4.92 m, 5.98 m.
Considering Alaina's score, the scores of her team are given as follows:
5.46 m, 4.84 m, 4.92 m, 5.98 m, x m.
In which x is the unknown Alaina's score.
Then their combined scores are given as follows:
5.46 + 4.84 + 4.92 + 5.98 + x = 21.2 + x.
The scores will be tied when they are equal, that is:
21.2 + x = 25.6.
Then the score that Alaina needs is obtained as the subtraction of 25.6 and 21.2, as follows:
x = 25.6 - 21.2
x = 4.4 meters.
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Surface Area =
A. 52 in2
B. 78 in2
C. 45 in2
Answer:
78 in² (Choice B)
Step-by-step explanation:
Since they have exploded the 3-D cuboid into 2-D, it is easier to compute
Looking at the 2-D version you can see 4 rectangles each 3" x 5"
At the bottom on each side are 2 squares each 3" x 3"
Area of a rectangle = l x w
In this case, area of each rectangle = 3 x 5 = 15
Since there are 4 rectangles, total area of these four = 4 x 15 = 60 in²
Each square is area 3" x 3" = 9"
Since there are 2 such squares, total area of these two = 9 x 2 = 18in²
Total area of the 2-D blowup which is the same as the Surface Area of the prism = 60 in² + 18in² = 78 in²
Let x and y be some integers. Consider the following statement: If xis odd and y is odd, then xy is odd. Proof. Assume that x is odd and y is odd. Then there exists some k integers such that x=2k+1 and m=2k+1. Then xy=(2k+1)(2k+1)=4k2+4k+1=2(2k2+2k)+1. Since 2k2+2k is an integer because k is an integer then xy is odd. The proof is correct but the statement is incorrect The statement is correct, but the proof is incorrect. The statement and proof are incorrect. The statement and the proof are correct.
hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.
Odd number integers = 2k + 1, where k is integer
Even number integer = 2k
Odd integer + even integer
= 2k + 1 + 2k
= 4k + 1
= 2(2k) + 1
Let 2k = t, where t is integer
= 2t + 1
= Odd integer by definition
If number is 2t + 1 where t belongs to integer, then it is odd integer.
Hence proved.
The question is incomplete. The complete question is :
Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd
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Determine the factors of x2 + 4x - 12.
Answer:
(x+6)(x-)
Step-by-step explanation:
a consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. what is the probability that a car chosen at random will need a) norepairs? b) nomorethanonerepair? c) some repairs?
The probability that a car chosen to random will need:
A) no repairs: 72%
B) No more than one repairs: 89%
C) some repairs: 11%
The total amount of cars that will need some type of repair is 28%; 17% will need to be repaired once + 7% will need to be repaired twice + 4% will need to be repaired more than two times.
The amount of cars that wouldn´t need any type of repairs is the total amount of cars minus the percentage that need some type of repair:
100% - 28% = 72%.
The amount of cars that will need no repairs or only one repair is the total amount of cars minus the percentage that need more than one of repair:
100% - (7% + 4%) = 89%.
The amount of cars that need some repairs is the sum of those cars that need two repairs plus those that need three or more repairs:
7% + 4% = 11%
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In a class of 25 students, 5 have a cat and 9 have a dog. There are 3 students who have a cat and a dog. What is the probability that a student has a cat given that they do not have a dog?.
The probability that:
A student has a cat and they do not have a dog = 1/8 or 0.125.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for an event's taking place.
Given that,
The number of students in the class = 25
[tex]5[/tex] students have a cat.
[tex]9[/tex] students have a dog.
[tex]3[/tex] students have both a cat and a dog.
The objective is to find the probability that given that they don't have a dog, a student has a cat.
To find the probability that one of the pupils has a cat because there isn't a dog in the class:
First, determine the total number of pupils without a dog..
Since there are 25 students in total and 9 have a dog,
Now, 25 - 9 = 16
So the number of students who do not have a dog = 16
Now, determine the number of students who have both a cat and a dog.
According to the question:
There are 3 students who have both,
Subtract this from the percentage of students who own cats.
Therefore,
5 - 3 = 2
So, there are 2 students who have a cat but not a dog.
[tex]Probability = \frac{\text{(Number of students with only a cat)}}{\text{ (Number of students who do not have a dog)}}[/tex]
Probability = 2 / 16
Probability = 1 / 8
Hence,
The required probability that a student has a cat given that they do not have a dog = 1/8 or 0.125.
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given vector u equals open angled bracket negative 11 comma negative 5 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu?
The value of the vector VU is <44, 40>
Vector:
in math vector consist an object that has both a magnitude and a direction.
Given:-
Here we have the vector v and u with the value of v = <11, 5> and the value of u = <4, 8>.
Now, we have to find the value of VU.
In order to find the value of VU, we have to perform the multiplication operation on the given vector,
In order to perform the multiplication on it, we have to arrange them in the following order,
=> VU = <11, 5> x <4,8>
Now, we have to combine the values like the following,
=> <(11 x 4) , (5 x 8)>
Now, do the multiplication then we get,
=> <44, 40>
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explain why the analysis of differences is important in the confirmation of accounts receivable, even if the misstatements in the sample are not material.
The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.
Here,
Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.
The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.
Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.
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Express five eighths as a decimal.
A. 0.375
B. 0.40
C. 0.625
D. 0.875
Answer:
C. 0.625
Step-by-step explanation:
5 divided by 8 is .625
A.
.625
8 5.000
- 48
20
- 16
40
- 40
0
B.
or you can multiply by 8 the answers to see if you get 5
A. 0.375 * 8 = 3
B. 0.40 * 8 = 3.2
C. 0.625 * 8 = 5
D. 0.875 * 8 = 8
C.
if you dont have to you could estimate using the first number after the decimal to see if you get 5
A. 0.375
first number after the decimal is 3
3 * 8 = 24 ≈ 2.4 ≈ 3
B. 0.40
first number after the decimal is 4
4 * 8 = 32 ≈ 3.2 ≈ 3
C. 0.625
first number after the decimal is 6
6 * 8 = 48 ≈ 4.8 ≈ 5
D. 0.875 * 8 = 8
Mr. Wright is investing $1 million. He has options with Bank of Munich, Coralbank, and Lone Star Credit Union.
Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
Lone Star Credit Union is offering an interest rate of 1.75% on all funds invested with them.
Mr. Wright plans to leave whatever funds he invests in the account for 15 years.
ROUND ALL ANSWERS TO THE NEAREST TEN THOUSAND AND DO NOT USE COMMAS IN YOUR RESPONSE.
How much money should Mr. Wright expect to have after 15 years if he invests all of his funds with Coralbank?
How much money would he have if he invests everything with Bank of Munich for the full 15 years?
If he plans carefully and invests his funds to gain the maximum amount of interest across all three institutions, how much money will he have in each bank
after 15 years?
Bank of Munich:
Coralbank
Lone Star Credit Union:
In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97
What is Interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
Given:
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
So, After 15 years
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 500,000.00[tex](1 + 0.03/1)^{(1)(15)[/tex]
A = 500,000.00[tex](1 + 0.03)^{(15)[/tex]
A = $778,983.71
and, for Another $500,000
A = P[tex](1 + r/n)^{nt[/tex]
A = 500,000.00 [tex](1 + 0.00/1)^{(1)(15)[/tex]
A = 500,000.00 [tex](1 + 0.01/1)^{(1)(15)[/tex]
A = $580,484.48
Total he Invests= $ 1,359,468.19
and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Then solve the equation for A
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 250,000.00[tex](1 + 0.02/1)^{(1)(15)[/tex]
A = 250,000.00 [tex](1 + 0.02)^{(15)[/tex]
A = $336,467.08
and, for Another $750,000 .
A = P[tex](1 + r/n)^{nt[/tex]
A = 750,000.00[tex](1 + 0.0125/1)^{(1)(15)[/tex]
A = 750,000.00 [tex](1 + 0.0125)^{(15)[/tex]
A = $903,621.89
Total he Invests= $ 1,240,088.97
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What i the point-lope from the line with lope -1/4 that pae through the point (-2,9)
The equation of the line in point slope form is y = -1/4x + 17/2.
Define the term point slope form?A line's equation written using a single point mostly on line and the line's slope is referred to as the point-slope form. The slope is really the rise over distance, or the proportion of the change there in y values over change in the x values, and the point form is denoted as (x,y).The slope of the equation of the line is given as;
slope m = -1/4
Passing point = (-2,9)
Equation of the line;
y - y1 = m(x - x1)
y - 9 = -1/4(x + 2)
y = -1/4x -1/2 + 9
y = -1/4x + 17/2
Thus, the equation of the line in point slope form is y = -1/4x + 17/2.
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Let n be the number of trials and p be the probability of success in the binomial distribution. Under which conditions do the Binomial and Poisson distributions give approximate results? n → [infinity], p → 0 n → [infinity], p → 1 n → 0, p → 0 n → 0, p → 1
Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.
The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.
The number of trails is indefinitely large i.e., n → ∞
The probability of success, “p” is very small i.e., p → 0
np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.
However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.
Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.
Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
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in a study to compare the perceived effects of two pain relievers, 200 randomly selected adults were given the first pain reliever, and 93% indicated appreciable pain relief. of the 450 individuals given the other pain reliever, 96% indicated experiencing appreciable relief. a) give an estimate for the difference in the proportions of all adults who would indicate perceived pain relief after taking the two pain relievers. provide a 95%-confidence interval for the estimate.
7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
Given that,
In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain. 96% of the 450 people who received the other painkiller reported feeling noticeably relieved.
We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller. give the estimate's 95% confidence interval.
We know that,
p=(186+432)/(200+450)
p=0.95
We get
L.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
L.B= 0.07
Therefore, 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
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jo adds up all the positive integers from 1 to 100. kate does a similar thing with the first 100 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values. what is the positive difference between jo's sum and kate's sum?
Jo's sum is easy = (100)(101)/2 = 50 * 101 = 5050
Given,
In the question:
Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers.
She first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values.
To find the what is the positive difference between jo's sum and Kate's sum?
Now, According to the question:
Kate would first start with 5 [ since 1 - 4 ] are rounded to 0
Starting with 5 thru 14 she will have ten 10s
15 - 24 she will have ten 20s
25 - 34 she will have ten 30s
.
.
.
.
.
85 - 94 she will have ten 90s
95 - 100 she will have six 100s
So.....her sum is
10 [10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90] + 6 [100]
10 [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100]
10 (10) [ sum of the first nine positive integers ] + 6 [ 100]
100 [ (9)(10) / 2 ] + 6[100]
100 [ 45] + 6[100]
100 [ 45 + 6 ]
100 [ 51 ]
5100
Hence, The positive difference is 5100 - 5050 = 50
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