Stat 3309 - Statistical Analysis for Business Applications I
Consider the following data representing the starting salary (in $1,000) at some company and years of prior working experience in the same ï¬eld. The sample of 10 employees was taken and the following data is reported.
Years of experience
Starting Salary (in $1,000)
0
45
2 50
5 55
7 62
8 63
10 70
12 68
15 75
18 81
20 92
Part 1: Use the formulas provided on the 3rd formula sheet to compute the following quantities. Open an Excel spreadsheet and write the table with data given above. Add columns for x2, y2, and xy, as well as the last row for Σ. For each of the following quantities, write the formula for it in a cell and evaluate it.
(a) Find the sample correlation coeï¬cient r.
(b) Find the slope b1 of the sample regression line.
(c) Find the y-intercept b0 of the sample regression line.
(d) What is the equation of the sample regression line?
(e) Find the predicted starting salary for a person who spent 15 years working in the same ï¬eld.
(f) Find the observed starting salary for a person who spent 15 years working in the same ï¬eld.
(g) What is the diï¬erence between the observed and the predicted starting salary for a person who spent 15 years working in the same ï¬eld?
(h) Find the total sum of squares SST.
(i) Find the sum of squares error SSE.
(j) Find the sum of squares regression SSR.
(k) Use the answers from (h)-(j) to conï¬rm that SST = SSR + SSE. (l) Find the coeï¬cient of determination R2.
(m) Use your answers for (a), (b) and (l), to conï¬rm that r = ±âR2.
(n) What proportion of variation is explained using the regression model?
(o) Find the standard error of the estimate se.
(p) Find the standard error of the regression slope sb.
(q) Does the number of years of prior working experience in the same ï¬eld aï¬ect the starting salary at this company ? Use the sample provided above and the signiï¬cance level of 0.05.
(hint: perform the hypothesis test for H0 : β1 = 0 vs. H1 : β1 6= 0.)
Part 2: Find and use Excel built-in-functions to check your answers for r, b1, and b0. Next to each cell from Part 1, calculate these three quantities using Excel built-in-functions and conï¬rm your answers from Part 1.
(hint: for example, for r the Excel built-in function is "CORREL")
Part 3: Bellow your answers from Parts 1 and 2, perform the regression analysis using Excel built-in-module which can be found under "DATA" â "Data Analysis" â "Regression" and double check your answers from Part 1. Draw the scatter plot of the data and, by visually observing the graph, determine if there is a linear relationship between the number of years of prior working experience in the same ï¬eld and the starting salary at this company.
Answers
Answer:
Solved below.
Step-by-step explanation:
The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.
(a)
The formula to compute the correlation coefficient is:
[tex]r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\[/tex]
The required values are computed in the Excel sheet below.
[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}[/tex]
Thus, the sample correlation coefficient r is 0.9855.
(b)
The slope of the regression line is:
[tex]b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132[/tex]
Thus, the slope of the regression line is 2.132.
(c)
The y-intercept of the line is:
[tex]b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418[/tex]
Thus, the y-intercept of the line is 45.418.
(d)
The equation of the sample regression line is:
[tex]y=45.418+2.132x[/tex]
(e)
Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:
[tex]y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4[/tex]
Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.
Answer:
Yes correct
Step-by-step explanation:
I think this is correct becase: 2 50
5 55
7 62
etc
these are all correct
Related Questions
Please answer this correctly
Answers
Answer:
2/7
Step-by-step explanation:
The numbers greater than 7 or less than 3 are 2 and 8.
2 numbers out of 7.
P(greater than 7 or less than 3) = 2/7
Answer:
2/7
Step-by-step explanation:
There are a total of 7 sample spaces also known as 2,3,4,5,6,7,8. Now we have to find a number greater than 7 and less than 3. 2 is less than 3, and 8 is greater than 7, so two numbers are selected. This would become 2/7 because out of all of the 7 outcomes, only two are selected.
true or false? the circumcenter of a triangle is the center of the only circle that can be inscribed about it
Answers
Answer:
TRUE
Step-by-step explanation:
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it
Answer:
False
Step-by-step explanation:
ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answers
Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
find the value of x...
Answers
Answer:
x = 7
Step-by-step explanation:
This problem can be solved using angular bisector theorem.
It states that if any angle of triangle is bisected by a line , then that line
divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.
__________________________________
Here one angle is is divided into parts theta
Thus,
using angular bisector theorem
14/21 = 6/3x-12
=> 14(3x-12) = 21*6
=> 3x-12 = 21*6/14 = 9
=> 3x = 12+9 = 21
=> x = 21/3 = 7
Thus, x = 7
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1) Choices: a. g(x) has to be: (1+x)/2 b. g(x) has to be: x/2 c. g(x) has to be: 2 – (1/x) d. Inverses
Answers
Answer:
(f o g) = x, then, g(x) is the inverse of f(x).
Step-by-step explanation:
You have the following functions:
[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]
In order to know if f and g are inverse functions you calculate (f o g) and (g o f):
[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]
[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]
(f o g) = x, then, g(x) is the inverse of f(x).
If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS
Answers
Answer:
Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.
Answer:
su+ut=rt
Step-by-step explanation:
The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Suppose that 43 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(_______,_________)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(______,_________)
If a single randomly selected individual is observed, find the probability that this person consumes is between 61.4 mL and 62.8 mL. ________
For the group of 43 pancake eaters, find the probability that the average amount of syrup is between 61.4 mL and 62.8 mL. _________
For part d), is the assumption that the distribution is normal necessary? No Yes
please only answer if you are able to answer all parts correctly
Answers
Answer:
(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
[tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Step-by-step explanation:
We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.
Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.
(a) Let X = amount of syrup that people put on their pancakes
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
n = sample of people = 43
So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)
P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)
P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)
= 1 - 0.50798 = 0.49202
P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)
= 1 - 0.54776 = 0.45224
Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)
P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)
P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)
= 1 - 0.53983 = 0.46017
P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)
= 1 - 0.79103 = 0.20897
Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
The Mathalot Company makes and sells textbooks. They have one linear function that represents the cost of producing textbooks and another linear function that models how much income they get from those textbooks. Describe the key features that would determine if these linear functions ever intercepted. (10 points)
Answers
You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal
Answers
Answer:
$904,510.28
Step-by-step explanation:
If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.
P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)
where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.
Filling in your values, we have ...
P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)
P = $904,510.28
You need to have $904,510.28 in your account when you begin withdrawals.
Answer:
You need to have $904,510.28 in your account when you begin
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answers
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
is a parallelogram sometimes always or never a trapezoid
Answers
yes
Step-by-step explanation:
parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.
quanto e 500x6-51-5x50
Answers
Answer:
2699
Step-by-step explanation:
you do all the multiplication first
500×6= 3000
5 ×50 = 250
so it becomes
3000-51-250 = 2699
Answer:
2699
Step-by-step explanation:
The nth term of a geometric sequence is given by an = 27(0.1)n - 1. Write the first five terms of this sequence.
Answers
Answer:
The first first five terms of this sequence are
27 ,2.7 ,0.27 ,0.027 , 0.0027Step-by-step explanation:
[tex]a(n) = 27(0.1)^{n - 1} [/tex]
where n is the number of term
For the first term
n = 1
[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]
= 27(1)
= 27Second term
n = 2
[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]
= 27(0.1)
= 2.7Third term
n = 3
[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]
= 0.27Fourth term
n = 4
[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]
= 0.027Fifth term
n = 5
[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]
= 0.0027Hope this helps you
When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house? centimeters How many years passed from the time Vlad moved in until the tree was 357 centimeters tall? years
Answers
Answer:
The tree was 175 centimeters tall when Vlad moved into the house.
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
Step-by-step explanation:
The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:
[tex]H(t) = H(0) + at[/tex]
In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.
He measured it once a year and found that it grew by 26 centimeters each year.
This means that [tex]a = 26[/tex]
So
[tex]H(t) = H(0) + 26t[/tex]
4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?
This means that when t = 4.5, H(t) = 292. We use this to find H(0).
[tex]H(t) = H(0) + 26t[/tex]
[tex]292 = H(0) + 26*4.5[/tex]
[tex]H(0) = 292 - 26*4.5[/tex]
[tex]H(0) = 175[/tex]
The tree was 175 centimeters tall when Vlad moved into the house.
How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?
This is t for which H(t) = 357. So
[tex]H(t) = H(0) + 26t[/tex]
[tex]H(t) = 175 + 26t[/tex]
[tex]357 = 175 + 26t[/tex]
[tex]26t = 182[/tex]
[tex]t = \frac{182}{26}[/tex]
[tex]t = 7[/tex]
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
An object is dropped from the top of a tower with a height of 1160 feet. Neglecting air resistance, the height of the object at time t seconds is given by the
polynomial - 16t square + 1160. Find the height of the object at t = 1 second.
The height of the object at 1 second is feet.
Answers
Answer:
Height at t = 1 sec is 1144 ft
Step-by-step explanation:
Given:
Initial height of object = 1160 feet
Height of object after t seconds is given by the polynomial:
[tex]- 16t ^2+ 1160[/tex]
Let [tex]h(t)=- 16t ^2+ 1160[/tex]
Let us analyze the given equation once.
[tex]t^2[/tex] will always be positive.
and coefficient of [tex]t^2[/tex] is [tex]-16[/tex] i.e. negative value.
It means something is subtracted from 1160 ft (i.e. the initial height).
So, height will keep on decreasing with increasing value of t.
Also, given that the object is dropped from the top of a tower.
To find:
Height of object at t = 1 sec.
OR
[tex]h (1)[/tex] = ?
Solution:
Let us put t = 1 in the given equation: [tex]h(t)=- 16t ^2+ 1160[/tex]
[tex]h(1)=- 16\times 1 ^2+ 1160\\\Rightarrow h(1) = -16 + 1160\\\Rightarrow h(1) = 1144\ ft[/tex]
So, height of object at t = 1 sec is 1144 ft.
Suppose H is an ntimesn matrix. If the equation Hxequalsc is inconsistent for some c in set of real numbers R Superscript n, what can you say about the equation Hxequals0? Why?
Answers
Answer:
The answer is explained below
Step-by-step explanation:
Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.
Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.
Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?
Answers
Answer:
3/10
Step-by-step explanation:
We have that the Armans last winter had 5/6 of a row of stacked logs and at the end of the winter he had 8/15 of the same row left, therefore:
Ambitious
First we have to do is that the denominator is the same.
in the case of 5/6 it would be 25/30
and for 8/15 it would be 16/30
Now if we can do the subtraction and it would be:
25/30 - 16/30 = 9/30 or what equals 3/10
3/10 was the amount of wood he burned in the winter
Answer:
D) 3/10 row
Step-by-step explanation:
Amanda is constructing equilateral triangle JKL inscribed in circle M. To construct the inscribed polygon, she is going to use a compass to partition the circle into congruent arcs. To what width should she set the compass when partitioning the circle? A. The width must be equal to the radius of circle M. B. The width must be equal the diameter of circle M. C. The width can be equal to either the radius or the diameter of circle M. D. The width can be any size greater than the radius but less than the diameter of circle M. E. The width must be less than the radius of circle M. help meee please!!!!!!!!!!!!!!!!!
Answers
Given:
An equilateral triangle JKL inscribed in circle M.
Solution:
To draw an equilateral triangle inscribed in circle follow the steps:
1: Draw a circle with any radius.
2. Take any point A, anywhere on the circumference of the circle.
3. Place the compass on point A, and swing a small arc crossing the circumference of the circle.
Remember the span of the compass should be the same as the radius of the circle.
4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.
5. Repeat this process until you return to point A.
6. Join the intersecting points on the circle to form the equilateral triangle.
So the correct option is A. The width must be equal to the radius of circle M.
Still timed. More math needing help with, i'll double points and mark brainliest! 1. (y - 6) (y + 3) 2. (4x - 5) (x - 7) 3.(3x - 2) ( 4x - 1)
Answers
Answer:
1. y² - 3x - 18
2. 4x² - 33x + 35
3. 12x² - 11x + 2
Step-by-step explanation:
All we do with these questions are expanding the factored binomials. Use FOIL:
1. y² + 3y - 6y - 18
y² - 3y - 18
2. 4x² - 28x - 5x + 35
4x² - 33x + 35
3. 12x² - 3x - 8x + 2
12x² - 11x + 2
Answer:
1) (y-6) (y+3)
=> [tex]y^2+3y-6y-18[/tex]
=> [tex]y^2-3y-18[/tex]
2) (4x-5) (x-7)
=> [tex]4x^2-28x-5x+35[/tex]
=> [tex]4x^2-33x+35[/tex]
3) (3x - 2) ( 4x - 1)
=> [tex]12x^2-3x-8x+3[/tex]
=> [tex]12x^2-11x+3[/tex]
What’s the probability of getting each card out of a deck?
Determine the probability of drawing the card(s) at random from a well-shuffled regular deck of 52 playing cards.
a. a seven __________
b. a six of clubs. ___________
c. a five or a queen ___________
d. a black card. ___________
e. a red card or a jack. ___________
f. a club or an ace. ___________
g. a diamond or a spade. ___________
Answers
Answer:
a. 1/13
b. 1/52
c. 2/13
d. 1/2
e. 15/26
f. 17/52
g. 1/2
Step-by-step explanation:
a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:
P(7) = 4/52 = 1/13
b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:
P(6 of clubs) = 1/52
c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen is:
P(5 or Q) = P(5) + P(Q)
= 4/52 + 4/52
= 1/13 + 1/13
P(5 or Q) = 2/13
d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:
P(B) = 26/52 = 1/2
e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:
P(R or J) = P(R) + P(J)
= 26/52 + 4/52
= 30/52
P(R or J) = 15/26
f. There are 13 cards in clubs suit and there are 4 aces, therefore:
P(C or A) = P(C) + P(A)
= 13/52 + 4/52
P(C or A) = 17/52
g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:
P(D or S) = P(D) + P(S)
= 13/52 + 13/52
= 26/52
P(D or S) = 1/2
Write an equation that is 10 less than 3 times a number y, multiplied by 2 and divided by 4. (10 less than 3 times a number y is to be done first)
Answers
Answer: (3y - 10)*2÷4
Step-by-step explanation:
Because 10 less than 3 times a number, y, is done first, it is in parenthesis. The 3 is there to represent the "three times" and the -10 is there to represent the "ten less". The *2 is there to represent the "multiplied by two" and the ÷4 is there to represent the "divided by 4"
Hope it helps, and tyvm <3
Answer:
[tex]\displaystyle \frac{2(3y - 10)}{4}[/tex]
Step-by-step explanation:
10 less than 3 times y.
The variable y is multiplied by 3, 10 is subtracted from 3 × y.
The result 3y - 10 is then multiplied by 2.
2(3y - 10) is then divided by 4.
Find the value of x.
Answers
Answer:
[tex]\huge\boxed{x=\sqrt{66}}[/tex]
Step-by-step explanation:
ΔADC and ΔABD are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]
Substitute
[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]
[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex] cross multiply
[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]
Plz. Can anyone explain and tell the answer of this question.I promise I will mark it as brainliest Question.
Answers
Answer:
x = 15
y = 90
Step-by-step explanation:
Step 1: Find x
We use Definition of Supplementary Angles
9x + 3x = 180
12x = 180
x = 15
Step 2: Find y
All angles in a triangle add up to 180°
3(15) + 3(15) + y = 180
45 + 45 + y = 180
90 + y = 180
y = 90°
The number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. A sample of 15 people is selected at random, and the number of hours worked per year per person is given below. Calculate the 98% confidence interval for the mean hours worked per year in this state. Round your answers to the nearest integer and use ascending order.Time205120612162216721692171218021832186219521962198220522102211
Answers
Answer:
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
Step-by-step explanation:
2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210 ,2211
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And we got:
[tex]\bar X=2169.67[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean
s=48.72 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]
Now we have everything in order to replace into formula (1):
[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]
[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]
And the confidence interval would be given by (2137, 2203)
State the coordinates of the vertex for each of the following
Answers
Answer:
[a] y=x^2+3, vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
[d] y= (1/2)x^2 - 5, vertex, V(0,-5)
Step-by-step explanation:
The vertex, V, of a quadratic can be found as follows:
1. find the x-coordinate, x0, by completing the square
2. find the y-coordinate, y0, by substituting the x-value of the vertex.
[a] y=x^2+3, vertex, V(0,3)
y=(x-0)^2 + 3
x0=0, y0=0^2+3=3
vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
y=2(x-0)^2+0
x0 = 0, y0=0^2 + 0 = 0
vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
y=-(x^2-0)^2 + 4
x0 = 0, y0 = 0^2 + 4 = 4
vertex, V(0,4)
y = (1/2)(x-0)^2 -5
x0 = 0, y0=(1/2)0^2 -5 = -5
vertex, V(0,-5)
Conclusion:
When the linear term (term in x) is absent, the vertex is at (0,k)
where k is the constant term.
Don’t know this one
Answers
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
In a random sample of 2,305 college students, 339 reported getting 8 or more hours of sleep per night. Create a 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answers
Answer:
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answers
Answer:
The integers are 7 and 14.
Step-by-step explanation:
y = 2x
1/y + 1/x = 3/14
1/(2x) + 1/x 3/14
1/(2x) + 2/(2x) = 3/14
3/(2x) = 3/14
1/2x = 1/14
2x = 14
x = 7
y = 2x = 2(7) = 14
Answer: The integers are 7 and 14.
The required two integers are 7 and 14
This is a question on word problems leading to the simultaneous equation:
Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1
Also, if the sum of the reciprocals of the two positive integers is 3/14, then:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2
Substitute equation 1 into 2
[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]
Find the LCM of 2y and y
[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]
Substitute y = 7 into equation 1:
Recall that x = 2y
[tex]x = 2(7)\\x = 14[/tex]
Hence the required two integers are 7 and 14.
Learn more here: https://brainly.com/question/17671977
Find the median of: 1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Answers
Answer:
4
Step-by-step explanation:
1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4
Arrange the numbers from smallest to largest
0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
There are 20 numbers
The middle number is between 10 and 11
0,1, 1,2,2, 3,3, 4, 4,4 ,4,4,4 , 4, 5, 6, 6, 7, 8, 9,
The median is 4
Solution,
Arranging the data in ascending order:
0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9
N(total number of items)= 20
Now,
Median:
[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]
Again,
Median:
[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wonders whether the relationship is statistically significant. Based on the partial regression output below and a 5% significance level, is the year statistically significant in determining the number of earthquakes above magnitude 7.0?Dependent Variable: Earthquakes above Magnitude 7.0 Coefficients Standard t Stat P-value Lower 95% Upper 95% ErrorIntercept 64.67 38.08 4.32 89.22 240.12Year -0.07 0.02 -3.82 -0.11 -0.04
Answers
Answer:
Step-by-step explanation:
Hello!
A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.
^Y= 164.67 - 0.07Xi
Y: earthquake above magnitude 7.0
X: year
The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0
The hypotheses are:
H₀: β = 0
H₁: β ≠ 0
α: 0.05
The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]
The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]
This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.
The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:
p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]
As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.
If you want to use the rejection region approach, the sample size is also needed to determine the critical values.
But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.
Using the CI, the decision rule is as follows:
If the CI includes the "zero", do not reject the null hypothesis.
If the CI doesn't include the "zero", reject the null hypothesis.
The calculated interval for the slope is: [-0.11; -0.04]
As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.
I hope this helps!
(full output in attachment)