The answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.A table is drawn according to the given information.
(Refer to the table below)
So,
let d be the event that the person is a Democrat.let r be the event that the person is republican.let 2013 be the event that the person retires 2013.let 2015 be the event that the person retires 2015.let 2017 be the event that the person retires in 2017.From the table:
p(d) = 42 / 78 because there are 42 democrats out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(r) = 36 / 78 because there are 36 republicans out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(2013) = 29 because there are 29 senators who retired in 2013 out of a total of 78 senators who retired in all 3 yearsp(2015) = 35 because there are 35 senators who retired in 2015 out of a total of 78 senators who retired in all 3 years.p(2017) = 14 because there are 14 senators who retired in 2017 out of a total of 78 senators who retired in all 3 years.Then,
Our universe is 78 senators who retired in all 3 years (2013, 2015, 2017).
42 are democrats and 36 are republicans.29 retired in 2013 and 35 retired in 2015 and 14 retired in 2017.(A) From the table, we can see that there are 20 democrats who retired in 2015.
p(d and 2015) = 20/78.(B) This one is asking for p(r or 2013)
The formula to use here is p(r or 2013) = p(r) + p(2013) - p(r and 2013).
From the table, we can see that:
p(r) = 36/78p(2013) = 29/78p(r and 2013) = 8So, p(r or 2013) is equal to p(r) + p(2013) - p(r and 2013) which is equal to 36/78 + 29/78 - 8/78 = 57/78.
(C) This is one is asking for p(r given 2017).
The formula to use here is p(r given 2017) = p(r and 2017) / p(2017).
From the table, you can see that:
p(2017) = 14/78p(r and 2017) = 13/78So, p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) = 13/14.
(D) if they were independent, then p(r and 2017) would be equal to p(r) * p(2017).
Therefore p(r given 2017) would be equal to p(r and 2017) / p(2017) which would be equal to p(r) * p(2017) / p(2017) which would be equal to p(r).From the table, you can see that p(r) = 36/78.From the table, you can see that p(r and 2017) = 13/78) and p(2017) = 14/78.Therefore p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) which is equal to 13/14 which is not equal to p(r) = 36/78Therefore the two events are not independent.Therefore, the answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.Know more about the random selection here:
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The complete question is given below:
Congressional Terms Below is given the summary from
112th Congress of Senators whose
terms end in 2013, 20.
2017.
2015
20
15
CAPPARE
PRESENTADAL
SCHED
2013
Democrat
21
Republican 8
Choose one of these Senators at random and find
a. P(Democrat and term expires in 2015)
b. P(Republican or term expires in 2013)
c. P(Republican given term expires in 2017)
d. Are the events “Republican” and “term expires in 2015” independent? Explain.
Wheat Corporation pays for shares to acquire % common stock of Grain Investments, Inc. on January 5, 2018. Wheat Corporation sells shares for on January 6, 2018. Which of the following is the correct journal entry for the transaction on January 6, 2018? (Round any intermediate calculations to two decimal places, and your final answer to the nearest dollar.)
Marketable securities are 63,360 credits (refer to the table below for journal entries).
What are journal entries?A journal entry is an act of keeping or making records of any economic or non-economic transaction.An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry can be made up of multiple recordings, each of which is either a debit or a credit. Otherwise, the journal entry is considered unbalanced if the total of the debits does not equal the total of the credits.So,
The following can be deduced from the information provided in the question:
The purchase price per share will be as follows:
= $528,000/100,000= $5.28The share price will be as follows:
= $54,000/12,000 = $4.50The following is the loss on the sale of marketable securities:
= 12,000 x (4.50 - 5.28)= 12,000 × 0.78= $9,360Then, the journal entries are: (Refer to the table below)
Therefore, marketable securities are 63,360 credits (refer to the table below).
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The correct question is given below:
Wheat Corporation pays $ 528 comma 000 for 100,000 shares to acquire 45% common stock of Grain Investments, Inc. on January 5, 2018. Wheat Corporation sells 12 comma 000 shares for $ 54 comma 000 on January 6, 2018. What is the correct journal entry for the transaction on January 6, 2018? (Round any intermediate calculations to two decimal places, and your final answer to the nearest dollar.)
Six friends each use $2-off coupons to but themselves a movie ticket. They spend a total of $42. What is the price of one movie ticket without coupon?
Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.
Total money spent by 6 friends on purchasing of the movie tickets = $ 42
So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.
So, cost of 1 ticket = 4 42 / 6 = $ 7
Coupon is of $2-off.
This means that with the coupon, $2 is subtracted from the ticket price.
So, price of ticket will be = $ 7 + $ 2 = $ 9.
Therefore, the price of the ticket without the coupons will be $ 9.
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Tony's Used Car Dealership is selling a car for $12,000. This price represents a 20%
reduction from the original price of the car. What was the original price of the car?
The original price of the car is $15,000
Let us assume the original price of car be x. So, forming the equation to find the value of x and hence the original price of the car.
Equation -
x - 20% × x = 12000
x - 20/100×x = 12000
Cancelling zero as common in both numerator and denominator, on the left hand side of the equation
x - x/5 = 12000
Taking LCM on Left Hand Side of the equation
(5x - x)/5 = 12000
Rewriting the equation
4x = 12000 × 5
Performing multiplication on Right Hand Side of the equation
4x = 60,000
x = 60,000 ÷ 4
Performing division
x = 15,000
Therefore, the original price of the car is $15,000.
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Answer these 3, please. ( Statistics )
1) This narrative is an example of a sample survey.
2) This narrative is an example of an experiment.
3) This narrative is an example of an observational study.
What is the type of Statistical study?
There are some common methods of data collection in statistical studies which are sample survey, observational study, experiments e.t.c
A sample survey is a survey that is done by taking a sample of people or items that represent a larger population.
An observational study is a type of study whereby a researcher utilizes observed information to gain more information about a group of individuals.
An experiment is where a researcher purposely applies different treatments to different groups and then does a comparison of the groups to determine if there is any difference in a specific variable of interest.
1) This narrative is an example of a sample survey because he studied a sample of 50 people who exercise regularly to determine if their blood pressures are low or average.
2) This narrative is an example of an experiment because we see that he studies 20 people who exercise and another 20 who don't exercise and uses the result to generate a conclusion about both groups.
3) This narrative is an example of an observational study because he is using the information he gets from the question he asks every fifth patient to learn about a group of individuals.
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Select the lesser of The two given numbers -152, 12
Answer:
-152
Step-by-step explanation:
-152 < 12
-152 is negative, which means it is less than 1.
12 is positive, which means it is greater than 1.
Therefore, -152 is the lesser of the two given numbers.
Have a great rest of your day! :)
Hi!
-152 is less than 12, because:
It's negative, and 12 is positive!It's to the left of 12 on the number line![tex]\mathbb{NUMBER \ LINE}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
[tex]-152[/tex] [tex]12[/tex]
Cheers!
Have a nice day!
I hope this helps!
If a family has 5 children, in how many ways can the parents have 2 boys and 3 girls as children?
Considering the definition of combination, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following expression is applied:
[tex]mCn=\frac{m!}{n!(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
Ways the parents have 2 boys and 3 girlsIf a family has 5 children, you can know that:
Among the 5 children, 3 are boys = 5C3 = [tex]\frac{5!}{3!(5-3)!}[/tex]= [tex]\frac{5!}{3!2!}[/tex]Among the 5 children, 2 are girls = 5C2 = [tex]\frac{5!}{2!(5-2)!}[/tex]= [tex]\frac{5!}{2!3!}[/tex]So, you can observe that 5C3 is equal to 5C2. Then:
5C3 = 5C2 = [tex]\frac{5!}{3!2!}[/tex]= 10
Finally, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
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6216÷21 please show me the work
Therefore, on dividing 6216 by 21 we get 126
Given 6216 / 21
21 ) 6216 ( 296
42
(-)................... (By subtracting these two numbers we get )
201
189
(-)..................
126
126
.(-)..........................
0
Therefore 6216 / 21 = 126
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0.50x +0.15(30) = 23.5
Answer: x=38
Step-by-step explanation:
SOLVE FOR X
STEPS FOR SOLVING LINEAR EQUATION
0.50x+0.15(30)=23.5
Multiply 0.15 and 30 to get 4.5.
0.5x+4.5=23.5
Subtract 4.5 from both sides.
0.5x=23.5−4.5
Subtract 4.5 from 23.5 to get 19.
0.5x=19
Divide both sides by 0.5.
[tex]x=\frac{19}{0.5}[/tex]
Expand [tex]\frac{19}{0.5}[/tex] by multiplying both numerator and the denominator by 10.
[tex]x=\frac{190}{5}[/tex]
Divide 190 by 5 to get 38.
x=38
7h
t: h²k²
-7k
k² - h²
Answer:
i'm pretty sure it's the second option
Step-by-step explanation:
Write the expression. Then, check all that apply.
twice the difference of a number and six
The algebraic expression for the given statement is: 2(n - 6).
How to Write an Algebraic Expression?To translate the statement, "twice the difference of a number and six", follow the steps below:
The two operations we would use are multiplication and subtraction.
The constants are 2 and 6.
Twice is translated as 2 ×, (-) is "difference".
Let the number be "n" .
The difference of a number, n, and 6, would be: n - 6.
Therefore, we would have the following algebraic expression: 2(n - 6).
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Please answer the screenshot
The set of ordered pairs that represents a function is the third option.
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
Which set of ordered pairs represents a function?
For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.
Now, a relation is only a function if input are only mapped to only one output.
For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.
For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8
The only set where each input appears only once is the third one:
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
This relation represents a function, so this is the correct option.
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whats 20,973 rounded to the nearest thousand
Answer:
21000
Step-by-step explanation:
21000
An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying.
Lisa studies 6 hr for a particular test and gets a score of 76. At this rate, how many hours would she have had to
study to get a
score of 91?
Answer:
7.18421051
Step-by-step explanation:
76 ÷ 6 = 12.6666667
91 ÷ 12.6666667 = 7.18421051
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(e) For what value(s) of x is f(x) = 0?
Step-by-step explanation:
For the value of x = 0 then the f(x) will became f(o) = 0
How many inches are in 75 mm
Answer: 2.95 I think
Step-by-step explanation:
How to solve x+5/-6= -4
x+5/-6= -4
multiply each side by -6
x-5/6= -4
*-6 *-6
x+5=24
subtract 5 from each side
x=19
THE TRIANGLE SHOWN HERE IS REFLECTED IN X-AXIS AND THEN IN Y-AXIS. WRITE THE FINAL COORDINATES OF TRIANGLE:
Answer:
Option 4
Step-by-step explanation:
This is the same as a rotation of 180° about the origin, which means we can negate the x and y coordinates of the preimage to get the coordinates of the image.
Find the volume generated by rotating the given region about the specified line. I tried it 4 different times and have 1 try left! Please help only if you're sure of how to do it
Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.
How to use integrals to find the volume of a curve?Rotating a function f(x) around a function g(x), the volume is given by the following integral:
[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]
In which a and b are the intersection points of the curve.
For this problem, from the graph, we have that:
[tex]f(x) = 2\sqrt[4]{x}[/tex].g(x) = 2x.a = 0.b = 1.Hence:
[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]
[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]
[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]
[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]
[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]
[tex]V = \frac{4\pi}{5}[/tex]
V = 0.8π cubic units.
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PLEASE HELP ME TY!!!!!!
Answer:
3.82×10^7
Step-by-step explanation:
3.82e+7= 3.82×10^7
The angles of a triangle add up to 180 degrees.
The second angle is 20 degrees larger than the smallest angle.
The third angle is 3 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).
Answer:
32 degrees
Step-by-step explanation:
You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.
SetupThe sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...
x +(x +20) +3x = 180
SolutionCollecting terms gives ...
5x +20 = 180
5x = 160 . . . . . . subtract 20
x = 32 . . . . . . divide by 5
The smallest angle is 32 degrees.
which statements about doubling in investment are true check all that apply an investment of $5000 will double in six years at an annual compound interest rate of 12% An investment of $1000 will double at an annual compound interest rate of 18% in six years an investment of $350 will double in nine years At a compound interest rate of 8% an investment of $2000 will double at a simple interest rate of 5% in 20 years and investment of $700 will double in 12 years at a simple interest rate of 6%
The following statement are true:
An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.An investment of $350 will double in 9 years at a compound interest rate of 8%. An investment of $2000 will double at a simple interest rate of 5% in 20 years.What is rule 72?It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.
Using the formula
time for doubling money= 72/R
First, An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.So, 72/12 = 6 years
Thus, It will take 6 years to double the investment. This statement is true.
Second, An investment of $1000 will double at an annual compound interest rate of 18% in 6 years.So, 72/18 = 4 years
Thus, It will take 4 years to double the investment. This statement is not true.
Third, An investment of $350 will double in 9 years at a compound interest rate of 8%.so, 72/8= 9 years.
Thus, It will take 9 years to double the investment. This statement is true.
Fourth, An investment of $2000 will double at a simple interest rate of 5% in 20 years.So, interest = PRT/100
I = (2000 × 0.05 × 20)
I = $2000
Thus, This statement is true.
Fifth, An investment of $700 will double in 12 years at a simple interest rate of 6%Interest = ( 700 × 0.06 × 12 ) = $504
Amount after 12 years
=700 + 504
= $1204.
Thus, This statement is not true.
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Which of the following is an existential quantifier?
Oa) Few
Ob) None
Oc) Every
O d) All
Answer:
A
Step-by-step explanation:
It might be the best one!
There are 15 floors of an office building each floor is 10 2/5 feet tall 24 9/10 feet of the building are completed 1 1/4 feet of the building can be finished each day how many days are needed to complete the building
The days it would take to complete the building is 104 22/25 days.
How many days would it take to complete the building?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
The first step is to determine the total height of the office bulding = height of each floor x total number of floors
15 x 10 2/5
15 x 52/5 = 780 /5 = 156
The next step is to determine the floors left to complete the office building :
156 - 24 9/10 = 131 1/10 feet
The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :
1311/10 ÷ 1 1/4
1311 / 110 ÷ 5/4
1311 / 10 x 4/5 = 104 days 44/50
104 22/25 days
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Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
You must show your working.
Using the together rate, it will take more 3.45 days to complete the work.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
The together rate is given by the sum of each separate rate.
For this problem, the rates are given as follows,
Ann,1/10 = 0.1
Ben,1/12 = 0.0833
Together,1/x
Hence the amount completed in 2 days is:
2 x (0.1 + 0.0833) = 0.3666
The amount it would take them to complete 100% of the project working together is found by the together rate as follows,
x = 60/11
x = 5.45 days.
The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is,
0.6334 x 5.45 = 3.45 days.
It will take more 3.45 days to complete the work.
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what is an equation of the line that passes through the points (0,8) and (5,2)
A line passes through the point (-2, 6) and has a slope of -8.
Write an equation in slope-intercept form for this line.
The given equation of the straight line is y +8x+10=0
We are required to find the equation of a straight line passing through the point (-2, 6) and has a slope of -8.
An equation of a straight line can be easily found if the slope and any of the points is given
The general form of equation is given by
y-y1 = m (x-x1)
where x1,y1 is the coordinate of the known point
m is the slope of the line
It is given that the coordinate of the known point is (-2,6)
the slope is given to be -8
Thus using these values to form the equation,
y-6 = -8 (x--2)
y-6 = -8 (x+2)
y-6 = -8x-16
y+8x-6+16=0
y+8x+`10=0
Hence, The straight line equation is y +8x+10=0
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Ronnie is playing a card game where the goal is to get the lowest possible score. In
the first round, Ronnie scored -6 points. In the second round, he scored -12 points.
What is Ronnie's total score
Jackie buys 6 packs of 100 post-its, 4 packs of 10 post-its, and 4 fancy post-its by themselves.
Then, her friend gives her 3 more fancy post-its. How many post-its does she have now?
Step-by-step explanation:
Number of post-it's = 6*100=600+4*10+4+3=647post-its
1000 divided by 3 answer
Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]
Step-by-step explanation:
Draw LMN with vertices L(2,-2), M(7,-3), and N(5,2). Find the coordinates of the vertices after a 90 degree rotation about the origin and about each of the points L, M, and N.
The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
If the point is in first quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
We know that the rotation of a point (x,y) about the origin by 90° is (-y,x).
Given vertices of ΔLMN are L(2,-2), M(7,-3), and N(5,2).
Let consider the rotations of L, M, and N are L', M', and N' respectively.
The rotation of a point L(2,-2) about the origin by 90° is L'(-2,-2).
The rotation of a point M(7,-3) about the origin by 90° is M'(-7,-3).
The rotation of a point N(5,2) about the origin by 90° is N'(5,2).
Hence, the points L'(-2, -2), M'(-7, -3), and N'(5, 2) are the rotation of vertices.
Therefore, L, M, and N of ΔLMN about the origin by 90°.
Hence, The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
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