In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered.East Westn1 = 40 n2 = 45= 72 (in $1,000) = 78 (in $1,000)s1 = 6 (in $1,000) s2 = 8 (in $1,000)a. Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use a = 0.05.b. At 95% confidence, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West.
Answers
We can estimate with 95% confidence that the difference between the average yearly incomes of marketing managers in the East and West is between $9,870 and $130.
a. To develop an interval estimate for the difference between the average yearly incomes of marketing managers in the East and West, we can use the two-sample t-test. Here are the steps:
Calculate the pooled standard deviation:
Sp = sqrt[((n1-1)s1^2 + (n2-1)s2^2)/(n1+n2-2)]
Sp = sqrt[((40-1)6^2 + (45-1)8^2)/(40+45-2)]
Sp = 7.054
Calculate the standard error:
SE = Spsqrt(1/n1 + 1/n2)
SE = 7.054sqrt(1/40 + 1/45)
SE = 2.299
Calculate the t-value:
t = (x1 - x2) / SE
t = (72 - 78) / 2.299
t = -2.61
Calculate the confidence interval:
CI = (x1 - x2) ± t(α/2, df)*SE
CI = (72 - 78) ± t(0.025, 83)*2.299
CI = (-9.87, -0.13)
Therefore, we can estimate with 95% confidence that the difference between the average yearly incomes of marketing managers in the East and West is between $9,870 and $130.
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Related Questions
Choose the number that makes the comparison true.
85.04 >
85.9
85.006
85.72
85.051
85.08
Answers
Answer:
85.006
hope this helps
have a good day :)
Step-by-step explanation:
Please help with this
Answers
Answer:
\(f(x) = 100(1.05)^t\)
A pizza place offers 2 different types of crust, 3 different types of cheese, and the option of 5 different toppings. How many different ways can
a pizza be made?
ways
Answers
if we're going with single topping, single cheese per pizza, the answer is 30.
consumer reports rated airlines and found that 71% of the flights involved in the study arrived on time (i.e., within 15 minutes of scheduled arrival time). assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 213 flights. (round your answers to two decimal places.) what is the expected number that will arrive on time? what is the standard deviation of this distribution?
Answers
The expected number that will arrive on time is; 151.23
The standard deviation of this distribution is; 6.62
How to find the mean and standard deviation?We are given;
Percentage of the flights involved in the study arrived on time; p = 71% = 0.71
Sample size; n = 213
Now, the formula for the mean which is the expected number that will arrive on time is;
μ = np
μ = 213 * 0.71
μ = 151.23
The formula for the standard deviation of the distribution is;
σ = √(np(1 - p))
σ = √(213*0.71(1 - 0.71))
σ = 6.62
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3
12
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s)..
The graph represents the piecewise function:
3
f(x) = {
if -3 ≤ x < -1
if -1 ≤ ≤ 1
Answers
The piecewise function for this problem is defined as follows:
f(x) = x + 3, -3 ≤ x < -1f(x) = 5, -1 ≤ x ≤ 1.What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
Between x = -3 and x = -1, the linear function has a slope of 1, with a x-intercept of -3, meaning that the parent function y = x was shifted left 3 units, hence it is given as follows:
f(x) = x + 3, -3 ≤ x < -1
Between x = -1 and x = 1, the function is constant at y = 5, hence it is given as follows:
f(x) = 5, -1 ≤ x ≤ 1.
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what is the number if k% of it is 2a?
Answers
The number, x, is equal to (2a) × (100/k).
Let's denote the number as "x." We are given that k% of x is equal to 2a.
To find the number, we need to translate the given information into an equation. The phrase "k% of x" can be expressed as (k/100) × x.
According to the given information, (k/100) × x is equal to 2a:
(k/100) × x = 2a.
To solve for x, we can isolate it on one side of the equation by dividing both sides by (k/100):
x = (2a) / (k/100).
To simplify further, we can multiply by the reciprocal of (k/100), which is (100/k):
x = (2a) × (100/k).
Therefore, the number, x, is equal to (2a) × (100/k).
In summary, if k% of a number is equal to 2a, the number itself can be calculated as (2a) × (100/k).
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find the $1314^{\text{th}}$ digit past the decimal point in the decimal expansion of $\dfrac{5}{14}$.
Answers
The $1314^\text{th}$ digit past the decimal point is 2.
To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.
The long division of $\frac{5}{14}$ is as follows:
```
0.35 <-- Quotient
-----
14 | 5.00
4.2 <-- Subtract: 5 - (14 * 0.3)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
100 <-- Bring down the 0
98 <-- Subtract: 100 - (14 * 7)
-----
20 <-- Bring down the 0
14 <-- Subtract: 20 - (14 * 1)
-----
60 <-- Bring down the 0
56 <-- Subtract: 60 - (14 * 4)
-----
40 <-- Bring down the 0
28 <-- Subtract: 40 - (14 * 2)
-----
120 <-- Bring down the 0
112 <-- Subtract: 120 - (14 * 8)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
...
```
We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.
Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.
So, the $1314^\text{th}$ digit past the decimal point is 2.
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What's the area of the quarter circle if the diameter is 3 inches?
Answers
Answer:
Area of the full circle(A)= pi*d^2/4
A=3.143*3^2/4
A=7.07in^2
Area of the Quarter of the circle(B)
B=1/4A
B=1.77in^2
Step-by-step explanation:
1. The probability of the students passing Chemistry and Physics are 70% and 50&, respectively. None of the students failed in both subjects. If 8 of them passed both subjects, how many students took the exam?
a. 30 b. 50 c. 40 d. 60
2. Five cards are picked from a deck of 52 cards. Find the probability that the cards picked are suited.
a. 0.0036 b. 0.0080 c. 0.0050 d. 0.0020
answer both with solution for thumbs up
Answers
1. The total number of students who took the exam is 40 is option c.
2. The probability that the five cards picked are suited is approximately is option d. 0.0020.
Probability is a branch of mathematics that deals with the likelihood of events occurring. In this response, we will provide detailed solutions to two probability problems. We will explain the steps involved in solving each problem using mathematical terms.
Solution to Problem 1:
Let's denote the number of students who took the exam as 'x.' We are given that the probability of passing Chemistry is 70% and Physics is 50%. None of the students failed in both subjects, and 8 students passed both subjects.
To solve this problem, we can use the principle of inclusion-exclusion. The principle states that to find the total number of students who passed at least one subject, we need to sum the number of students who passed Chemistry, the number of students who passed Physics, and then subtract the number of students who passed both subjects.
Let's calculate the number of students who passed at least one subject:
Number of students who passed Chemistry = 0.7x
Number of students who passed Physics = 0.5x
Number of students who passed both subjects = 8
Total number of students who passed at least one subject = (Number of students who passed Chemistry) + (Number of students who passed Physics) - (Number of students who passed both subjects)
Substituting in the values, we have:
Total number of students who passed at least one subject = 0.7x + 0.5x - 8
Since none of the students failed in both subjects, the number of students who passed at least one subject is equal to the total number of students. Therefore, we can set the equation equal to 'x' and solve for it:
0.7x + 0.5x - 8 = x
Simplifying the equation:
1.2x - 8 = x
0.2x = 8
x = 8 / 0.2
x = 40
Therefore, the total number of students who took the exam is 40.
Hence, the answer to Problem 1 is option c. 40.
Solution to Problem 2:
We are given that we are picking five cards from a standard deck of 52 cards. We need to find the probability that all five cards picked are suited, meaning they all belong to the same suit.
To solve this problem, we can use the concept of combinations. The number of ways to choose five cards from a particular suit is denoted as C(13, 5), as there are 13 cards in each suit (hearts, diamonds, clubs, spades) and we need to choose 5 cards. Similarly, the total number of ways to choose any five cards from the deck is C(52, 5).
The probability of picking five suited cards can be calculated as:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Number of favorable outcomes = Number of ways to choose 5 cards from a single suit = C(13, 5)
Total number of possible outcomes = Number of ways to choose any 5 cards from the deck = C(52, 5)
Using the formula for combinations, we have:
C(n, r) = n! / (r!(n-r)!)
Substituting in the values, we get:
Number of favorable outcomes = C(13, 5) = 13! / (5!(13-5)!)
Total number of possible outcomes = C(52, 5) = 52! / (5!(52-5)!)
Calculating the values:
Number of favorable outcomes = 1,287
Total number of possible outcomes = 2,598,960
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1,287 / 2,598,960
Simplifying the fraction:
Probability ≈ 0.000495
Therefore, the probability that the five cards picked are suited is approximately 0.000495.
Hence, the answer to Problem 2 is option d. 0.0020.
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factor 5a2 – 30a 40. question 17 options: a) 5(a – 2)(a 4) b) 5(a – 2)(a – 4) c) (5a – 5)(a – 8) d) (a – 20)(a – 2)
Answers
The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)
The following procedures can be used by us while factoring polynomials:
Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.
Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.
Eliminate any factors that are frequent.
In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).
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WILL MARK BRAINLIEST
Answers
Answer:
A
Step-by-step explanation:
Can y’all help plsss
Answers
Answer:
ok so a way to do this is that
124-180=56
75-180=105
105+56= 161
180-161= 19
180-19=161
so A.
Please mark Brainliest if helpful! :))
A quantity with an initial value of 890 grows continuously at a rate of 3-5% per decade. What is the value of the quantity after 99 years, to the nearest hundredth?
Answers
Let P represent the initial value
Let r represent annual growth rate
let n represent the number of periods
p = 890
r=3.5%
n = 10 ( since a decade is 10 years, 99 years after will be 10 decades)
the formula to calculate the value after 99 years is given by
\(\begin{gathered} A=p(1+\text{ }\frac{r}{100})^n \\ \\ A=\text{ 890(1 + }\frac{3.5}{100})^{10} \\ A=890(1.035)^{10} \\ A=890(1.410598) \\ A=1255.432897 \\ A\cong1255.43\text{ ( nearest hundredth)} \end{gathered}\)The value of the quantity after 99 years is 1255.43
fraction equivalent to 4/6 with 3 as denominator
Answers
Answer:
2/3
Step-by-step explanation:
6 divided by 3 is 2, so you have to divided 4 by 2, which is 2.
Answer:
⅔
Step-by-step explanation:
4 divide by 2 = 2
6 3
therefor 2/3 is equvelet too 4/6.
Hope this helped
(T/F) the estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line.
Answers
The given statement "the estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line." is True. The estimated simple linear regression equation is obtained by minimizing the sum of the squared deviations between each value of y and the line.
This is known as the method of least squares. The line that minimizes the sum of the squared deviations is called the regression line. It is the line that best fits the data, in the sense that it minimizes the difference between the observed values of y and the values predicted by the equation of the line.
The least squares method is a widely used technique in statistics and data analysis, and is used to fit linear models to data in many different fields, including finance, economics, and engineering.
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If the slope is -4/3 and the ordered pair is 3,-5 what is the equation?
Answers
Answer:
y=-4/3x-4
Step-by-step explanation:
y=mx+y intercept <--- formula i used
Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.
Answers
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.
For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.
To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.
The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
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What is the answer to this question?
Answers
Answer:
≈ 3.9 miles
Step-by-step explanation:
The third angle in the triangle is
180° - (53 + 78)° = 180° - 131° = 49°
Using the Sine rule in the triangle with distance from 2 being x, then
\(\frac{3}{sin49}\) = \(\frac{x}{sin78}\) ( cross- multiply )
x × sin49° = 3 × sin78° ( divide both sides by sin49° )
x = \(\frac{3sin78}{sin49}\) ≈ 3.9 ( to the nearest tenth )
Solve 0.48 ÷ 0.04 Help me please
Answers
Answer:
12
Step-by-step explanation:
\(0.48\div 0.04\)
If you multiply both terms by 100, the result will be the same, because 100/100=1. You can therefore rewrite this as 48/4, which is equal to 12. Hope this helps!
Answer:
12
Step-by-step explanation:
0.48x100=48
0.04x100=4
48/4=12
Please help! Can’t seem to find anyone who has an explanation for this.
Answers
The steps to explain and show how to evaluate a·b for a = 5 and b = 8 include the following:
Steps a·b___
Substitute 5 for a 5·b
Substitute 8 for b 5·8
Multiply 40
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
Expression = a·b
Expression = 5 × 8 (Substitute 5 for a and substitute 8 for b)
Expression = 40 (multiply).
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During Saturday’s game the football team gained 87 yards rushing and 213 yards passing how many more yards were gained passing than rushing.
Define a variable,write an equation, then solve.
Answers
the answer is 126 hope it helps
*starts crying from happiness*❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answers
Step-by-step explanation:
Nina’s total trip to and from work is 14 miles. If she works 243 days this year, how many miles will she drive to and from work?
Answers
Answer:
3,402
Step-by-step explanation:
Step 1:
243 × 14
Answer:
3,402
Hope This Helps :)
Answer:
3402
Step-by-step explanation:
At which values of x does the function F(x) have a vertical asymptote? Check all that apply.A.7B.-3C.9D.0E.3F.-9
Answers
Explanation
Given the function
\(f(x)=\frac{7}{2x(x+3)(x-9)}\)The vertical asymptotes occur for the x-values when we equate the denominator of the function to zero and solve for x
\(\begin{gathered} 2x(x+3)(x-9)=0 \\ therefore; \\ x=0;x=-3;x=9 \end{gathered}\)Answer: Option B,C,D
What are the properties of a parallelogram?
Answers
Wxndy~~
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
8
bushel per hour. The scenario is represented as
5
8
h + 1
1
2
= 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels of strawberries?
A. 2 and StartFraction 3 Over 16 EndFraction hours
B. 2 and StartFraction 3 Over 16 EndFraction hours
C. 5 and three-fifths hours
D. 10 and two-fifths hours
Answers
It was C, sorry about the other dude
Answer: The answer is C!
Step-by-step explanation: I got it right on Edge, Hope this helps :D
Which ratio is less then 7 to 15 is it 9 to 15 2 to 5 3 to 5 24 to 45
Answers
Answer:
2:5 is less than 7:15
Step-by-step explanation:
7:15 = 7/15 = .47 = .5
the other given ratios are,
9:15 = 3:5 = 3/5 = .6
2:5 = 2/5 = .4
3:5 =3/5 = .6
24:45 = 8:15 = 8/15 = .5
thus, the ratio which is less than 7:15 is 2:5
Solve for A: q^2=g(-h+A)
Answers
Answer:
I think it's a=gh+q2
------------
g
Step-by-step explanation:
flip
ag−gh=q2
Step 2: Add gh to both sides.
ag−gh+gh=q2+gh
ag=gh+q2
Step 3: Divide both sides by g.
agg=gh+q2g
a=gh+q2g
The solution of the equation q²=g(-h+A) for A is A=q²+gh)/g .
The given equation is q²=g(-h+A).
Apply distributive property on right hand side:
q²=-gh+gA
Add gh on both sides:
q²+gh=gA
Divide both sides by g:
(q²+gh)/g =A
Hence, the solution of the equation for A is A=q²+gh)/g .
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5. in the following figure, GE= r.
where ris the radius of the circle.
a) What is the nature of the triangle GEO? Justify your answer.
b) By calculating SEG in two different ways. using ares of the
Answers
Answer + Step-by-step explanation:
a) GE = r = GM
Then GEO is an isosceles triangle
b) since GEO is an isosceles triangle then :
m∠SEG = m∠GOM = measure of the arc GM (mGM) (result 1)
On the other hand :
m∠SEG = m∠SEG = (1/2)×(mAS - mGM) (it’s a formula) (result 2)
Now ,we equate (result 1) and (result 2) :
m∠SEG = mGM
m∠SEG = (1/2)×(mAS - mGM)
Then
mGM = (1/2)×(mAS - mGM)
c) mGM = (1/2)×(mAS - mGM)
⇔ 2mGM = mAS - mGM
⇔ 3mGM = mAS
⇔ 3m∠SEA = m∠SOA
Remember:
mGM = m∠GOM = m∠SEA
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.
1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10
Develop a 95% confidence interval estimating of the population mean rating for Miami.
Answers
CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)
We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:
1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.
To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so
Z' = 1.96)
s = sample standard deviation
n = sample size
Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92
Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41
Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.
Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67
Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72
Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately
(5.80, 7.72)
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