Answer: Taylor, by 3.9 pp ($184.81)
Step-by-step explanation:
Marcus: Invested 80 x 74.19 = 5935.20
Taylor: Invested 65 x 85.21 = 5538.65
After 2 y
Marcus: Sold for 6404.57
Taylor: Sold for 6192.83
Net profit
Marcus: 6404.57 - 5935.20 = 469.37
Taylor: 6192.83 - 5538.65 = 654.18
ROI
Marcus: 469.37/5935.20 * 100 = 7.91%
Taylor: 654.18/5538.65 * 100 = 11.81%
Taylor had a higher ROI by 3.9 percentage points (11.81 - 7.91)
Write this expression in standard form by collecting like terms:
9 (a - b) + 5 (2a - 2b)
A. 14a - 14b
B. 8a - 7b
C. 19a - 19b
D. -19a + 14b
please help asap, thank you!
9 (a - b) + 5 (2a - 2b)
mutiply the first bracket by 9
(9)(a)= 9a
(9)(-b)= -9b
mutiply the second bracket by 5
(5)(2a)=10a
(5)(-2b)= -10b
9a-9b+10a-10b
9a+10a-9b-10b ( combine like terms)
Answer : C. 19a - 19b
To simplify the expression 9(a - b) + 5(2a - 2b), we first distribute each term in the parentheses by the factor outside the parentheses and then gather like terms, getting 19a - 19b.
Explanation:To solve this problem, we need to distribute each term in the parentheses by their respective factor outside the parentheses and then collect like terms.
Step 1: Distribute the terms
9(a - b) becomes 9a - 9b
5(2a - 2b) becomes 10a - 10b
Step 2: Collect like terms
9a + 10a = 19a
-9b - 10b = -19b
So, the expression 9(a - b) + 5(2a - 2b) simplifies to 19a - 19b, which is answer choice C.
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Tony loves to put stickers on his papers. Tony has 15 shark stickers. Tony has 21 whale sticker. Tony has 47 dolphi Stickers. Tony has 40 papers. Tony puts a dolphine sticker on every paper. Tony puts a shark sticker on every fourth paper. Tony puts a whale sticker on every fifth paper. When tony finishes putting all the stickers on the papers, how many papers will all three kinds of stickers on them.
Answer:
2 papers
Step-by-step explanation:
shark stickers : 15
whale stickers : 21
dolphin stickers : 47
papers:40
papers with dolphin stickers: 47
papers with shark stickers: 4, 8 , 12, 16, 20,24,28,32,36, 40 (every fourth paper, multiples of 4 till 40)
40/4 = 10 papers with shark stickers
papers with whale stickers: 5, 10,15, 15, 20, 25,30,35,40 (multiples of 5 till 40)
Papers with the three kinds of stickers : 2 (paper 20 and 40 )
Answer:
2 papers
Step-by-step explanation:
Solve the inequality.
[tex]12( \frac{1}{2} \times - \frac{1}{3} ) > 8 - 2 \times [/tex]
A.
[tex] \times > - \frac{1}{2} [/tex]
B.
[tex] \times > \frac{3}{2} [/tex]
C.
[tex] \times > \frac{1}{2} [/tex]
D.
[tex] \times > 3[/tex]
What is the solution to this system of equations?
4x−3y=26
3x+2y=11
5,2
8,2
-2,5
5,-2
Answer:
(x, y) = (5, -2)
Step-by-step explanation:
A graphing calculator provides a quick and easy way to find the solution.
_____
There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:
The intercepts of the first equation are ...
x-intercept = 26/4 = 6 1/2y-intercept = -26/3 = -8 2/3So the graph of it will form a triangle with the axes in the 4th quadrant.
The intercepts of the second equation are ...
x-intercept = 11/3 = 3 2/3y-intercept = 11/2 = 5 1/2So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.
The only 4th-quadrant answer choice is (5, -2).
Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form.
2x + y − 3z= −20
x + 2y + z= −3
x − y + 5z= 19
What is the solution to the system of equations?
Take the augmented matrix,
[tex]\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right][/tex]
Swap the row 1 and row 2:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right][/tex]
Add -2(row 1) to row 2, and -1(row 1) to row 3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right][/tex]
Add -1(row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right][/tex]
Multiply through row 3 by 1/9:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right][/tex]
Add 5(row 3) to row 2:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right][/tex]
Multiply through row 2 by -1/3:
[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]
Add -2(row 2) and -1(row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]
So we have [tex]\boxed{x=-3,y=-2,z=4}[/tex].
Answer:
1 0 0 -3
0 1 0 -2
0 0 1 4
AND
(-3, -2, 4)
Step-by-step explanation:
I don't have a step-by-step explanation because I still don't understand this sh*t myself. The reason I know it's the right answer is because I just got a 30% on my quiz and it shows you the right answers after. Good luck in this class! You're gonna need it.
The price of one share of Starbucks declined five dollars per day for four days in a row. How much did the price of one share change in total after the four days?
Answer:
Each share lost $20 in value over 4 days time
Step-by-step explanation:
$5 loss for 4 days
5 x 4 = 20
$20 loss in 4 days.
Simplify (-2)(-3)^2 -2(2 - 5)
To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.
Explanation:To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:
First, we calculate (-3)^2, which is equal to 9.Next, we substitute the values in the expression: (-2)(9) - 2(2 - 5).Then, we simplify the expression inside the parentheses: (-2)(9) - 2(-3).Multiplying -2 by 9 gives us -18, and multiplying 2 by -3 gives us -6.Finally, we subtract -6 from -18 to get the final result, which is -12.Therefore, the simplified expression is -12.
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IF the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.
a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?
Answer:
a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel
b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel
c. The wheel was moving at 0.70 [tex]\frac{rad}{min}[/tex]
Step-by-step explanation:
Navy pier wheel circumference = Cn
First ferris wheel circumference = Cf
Cn = 0.56*Cf
a.
Circumference Perimeter = 2*π*Radius
Navy pier wheel radius = Rn
First ferris wheel radius = Rf
Cn = 0.56*Cf
2*π*Rn = 0,56*2*π*Rf (equation 1)
dividing both sides by 2π
Rn = 0,56*Rf
b.
From equation 1
2*π*Rn = 0,56*2*π*Rf
dividing both sides by 2π
Rn = 0.56*Rf
dividing both sides by 0.56
Rf = [tex]\frac{1}{0.56}[/tex]*Rn
Rf = 1.79*Rn
c.
9 minutes / revolution
1 revolution = 2π radians
The wheel makes 2π radians in 9 minutes
Wheel velocity = [tex]\frac{2\pi }{9} \frac{rad}{min}[/tex]
Wheel velocity = 0.70 [tex]\frac{rad}{min}[/tex]
PLEASE!!! HELP NEEDED!!!
Given the following equation, x^4 - x^3 - 3x - 2. Use synthetic division to test the following 3 points and show which one is a root. Must show synthetic division for all 3 of the following test points. Test these 3 possible root points also called possible zeros using synthetic division: (x,y) = (-1, 0) (-3, 0) (2, 0).
PLEASE SHOW YOUR WORK!!!
Answer:
(x, y) = (-1, 3), (-3, 115), (2, 0)
Step-by-step explanation:
The first two test points are not roots. The last one is a root.
Zoey is reading a 100-page novel. If she averages reading 1 page in 1 minute, which is a reasonable estimate of the amount of time it will take her to read the novel? A) between 1 1/2 and 2 hours B) between 1 and 1/2 hours Eliminate C) between 2 and 3 hours D) between 0 and 1 hour
Answer:
The answer to your question is: letter A
Step-by-step explanation:
data
Book = 100 pages
Zoey reads 1 page per minute
Now we solve it using rule of three
1 page ------------------ 1 min
100 pages ---------------- x
x = 100x1/1 = 100 min will take Zoey to read the book
60 min ------------------ 1 hour
100 min --------------------- x
x = 100/60 = 10/6
and convert it to a mix fraction = 1 2/3 = 1 hour 40 minutes
Then, the answer is letter A
Answer:
A
Step-by-step explanation:
well since she reads 1 page per minute and there are 100 pages then that means it takes 100 minutes.
100 minutes= 1 2/3 hours which is in between 1 1/2 and 2 so the answer would be A
Take as input two opposite corners of a rectangle: (x1,y1) and (x2,y2). Finally, the user is prompted for the coordinates of a third point (x,y). Find whether the point (x,y) lies inside the rectangle.
Answer:
The answer is a point [tex](x,y) / x1\leq x\leq x2 , y1\leq y\leq y2[/tex]
Step-by-step explanation:
That happens because the points you have are in opposite corners, which means that they are the limits of the rectangle. so any point inside the rectangle is between that segment
What is X if X + R = S?
Answer:
The correct answer is the second option.
Step-by-step explanation:
If X + R = S, then X = S - R. You need to subtract each pair:
-2 - 0 = -2
-8 - 3 = -11
0 - (-4) = 4
2 - 5 = -3
Answer:
B
Step-by-step explanation:
Edge2020
Michael starting a savings account with $300. After 4 weeks he had $350 and after 9 weeks he had $400. What is the rate of change in his savings account per week
Answer:
$12.5 per week
Step-by-step explanation:
(300)+12.5 +12.5+12.5+12.5=350
The rate of change in Michael's savings account per week is $12.50.
Explanation:To find the rate of change in Michael's savings account per week, we need to determine how much the account balance increased per week. We can subtract the initial balance from the final balance and divide that by the number of weeks:
Rate of change per week = (Final balance - Initial balance) / Number of weeks
Using the given information, the rate of change per week is:
(350 - 300) / 4 = 50 / 4 = 12.5
Therefore, the rate of change in Michael's savings account per week is $12.50.
A package of 4 mechanical pencils comes with 2 free erasers. If you get a total of 12 free erasers, how many packages of pencils did you buy? If you get 18 free erasers,how many packages of pencils did you buy?
Answer:
6 packs, 9 packs
Step-by-step explanation:
The ratio of mechanical pencil to free eraser is 2:4, or 1:2.
So that means, for every free eraser you get, you bought the double amount of pencils.
12 free erasers x 2 = 24 pencils
18 free erasers x 2 = 36 pencils
And a pack of pencils contains 4.
24/4 = 6 packs
36/4 = 9 packs
Answer:
6 packs and 9 packs
Step-by-step explanation:
For the lines defined by the following equations indicate with a "V" if they are vertical, an "H" if they are horizontal, and an "S" (for slanted) if they are neither vertical nor horizontal. S 3x+4y+5=0
Answer:
The answer is the function 3x+4y+5=0 is Slanted
Step-by-step explanation:
To be able to to know if this function is horizontal, vertical or slanted we should look at the gradient.
If the gradient is zero, then the line is horizontal.
If the gradient is infinite, then the line is vertical.
if not, then the line is slanted
We can look the gradient by the general form equation of a line:
y = mx + c
where y = dependent variable, x = independent variable, m = gradient, c = intercept.
With our equation, we can change things around to get the general form equation:
3x + 4y + 5 = 0
4y = 3x - 5
[tex]y = \frac{3}{4}x - \frac{5}{4}[/tex]
Where the gradient is 3/4
Therefore, as the gradient is a number other than zero or infinite, we know that this function is slanted.
Alice and Bob play the following game: they start with an empty 2008x2008 matrix (p.s. take a wild guess which year this was) and take turns writing numbers in each of the 20082 positions. Once the matrix is filled, Alice wins if the determinant is nonzero and Bob wins if the determinant is zero. If Alice goes first, does either player have a winning strategy?
Answer:
Bob wins
Step-by-step explanation:
Think first in a simpler case. In a 2x2 matrix the determinant is zero if two columns or rows are proportional. So Alice writes the first number, then Bob write the same number in the same column but in the other row. Bob repeat the procedure after Alice's second number, and win.
If the matrix is nxn where n is even (like 2008) Bob will win following the previous procedure. Alice writes a number anywhere, Bob writes the same number in the same column in the above (or below) row. Every time Alice write a number in the same row as her first one, Bob copy that number in the above (or below) row. Any other rows are not important, i.e, the determinant will be zero with any values in them.
Let M ∈ N >1 . Let M be a non-perfect square. Or in other words M /∈ {4, 9, 16, · · · } (a) Prove that there exists a prime p, whose exponent in the prime factorization of M is odd. [Hint: Prove by a method of contradiction]
Answer:
Step-by-step explanation:
By the fundamental theorem of arithmetic given [tex]n\in \mathbb{N}_{\ge2}[/tex] there exists primes [tex]p_{i}[/tex] and integers [tex]\alpha_i[/tex] such that [tex]n[/tex] can be written as [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}[/tex], now suppose that [tex]n[/tex] is a non-perfect square, we are going to prove that there exists [tex]\alpha_i[/tex] such that is odd. By contradiction, suppose that [tex]\alpha_i[/tex] is even for all [tex]i[/tex], then writing [tex]\alpha_i=2\beta_i[/tex] for all [tex]i[/tex], we can write [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}= p_1^{2\beta_1}p_2^{2\beta_2}p_3^{2\beta_3}\cdots p_t^{2\beta_t}=(p_1^{\beta_1}p_2^{\beta_2}p_3^{\beta_3}\cdots p_t^{\beta_t})^2[/tex], thus we conclude that [tex]n[/tex] is perfect square, a contradiction, and then we conclude that there exists [tex]\alpha_i[/tex] such that is odd.
The area of the southern ocean is about 7.85 x 10^6 square miles. The difference between the areas of the indian ocean and the southern ocean is about 1.865 x 10^7 square miles. Explain how to find the area of the indian ocean. Then find the area.
Answer:
The answer to your question is: 2.65 x 10⁷ square miles
Step-by-step explanation:
Data
Southern ocean area = 7.85 x 10⁶ square miles
Difference between areas Indian ocean = 1.865 x 10⁷ square miles
and the southern ocean
Process
a) To find the area of the Indian ocean we need to sum of the values of the area of the Southern ocean and the area of the difference between the Indian ocean and the southern ocean.
b)
Area of the Indian Ocean = 1.865 x 10⁷ + 7.85 x 10⁶
= 2.65 x 10⁷ square miles
Answer:
The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Step-by-step explanation:
Given : The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles. The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
To find : Explain how to find the area of the Indian ocean. Then find the area.
Solution :
The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles.
i.e. [tex]A_s=7.85\times 10^6[/tex]
The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.
i.e. [tex]A_i-A_s=1.865\times 10^7[/tex]
Substitute the value of [tex]A_s[/tex]
[tex]A_i-7.85\times 10^6=1.865\times 10^7[/tex]
[tex]A_i=1.865\times 10^7+7.85\times 10^6[/tex]
[tex]A_i=1.865\times 10^7+0.785\times 10^7[/tex]
[tex]A_i=(1.865+0.785)\times 10^7[/tex]
[tex]A_i=2.65\times 10^7[/tex]
Therefore, The area of the Indian ocean is [tex]2.65\times 10^7[/tex]
Which of the following is a factor of 5x3 − 135?
135
x + 3
x2 + 3x + 9
x - 5
Answer:
The answer to your question is:
Step-by-step explanation: The third one is a factor
Factor
5x³ − 135
Find the prime factors of 135
135 3
45 3
15 3 Then 135 = 3³ x 5
5 5
1
5x³ - 5(3)³
Factor 5
5[ x³ - (3)³]
5 [ (x - 3)(x² + 3x + 9)]
Answer:
5 [ (x - 3)(x² + 3x + 9)]
Step-by-step explanation:
The first hill on a roller coaster is 155 feet tall. The first drop on a second roller coaster is about 11/20 as tall as the first coaster. Find the height of the hill on the second roller coaster
Answer:
85.25
Step-by-step explanation:
155 x (11/20) =85.25 feet
What is the multiplicative rate of change for the exponential function f(x) = f start bracket x end bracket equals two start bracket five-halves end bracket superscript negative x
Answer:
a) 0.4
Step-by-step explanation:
Got it right on quiz
The multiplicative rate of change for the exponential function is 5/2, indicating that the function increases by a factor of 5/2 for each unit increase in x.
The multiplicative rate of change for an exponential function
[tex]\( f(x) = a \times b^x \)[/tex]
is given by the base of the exponential term, b .
In the function
[tex]\( f(x) = 2 \left(\frac{5}{2}\right)^{-x} \),[/tex]
the base of the exponential term is 5/2.
So, the multiplicative rate of change is 5/2
Point \blue{A}Astart color blue, A, end color blue is at \blue{(-4, 8)}(−4,8)start color blue, left parenthesis, minus, 4, comma, 8, right parenthesis, end color blue and point \purple{M}Mstart color purple, M, end color purple is at \purple{(1, 7.5)}(1,7.5)start color purple, left parenthesis, 1, comma, 7, point, 5, right parenthesis, end color purple. Point \purple{M}Mstart color purple, M, end color purple is the midpoint of point \blue{A}Astart color blue, A, end color blue and point \green{B}Bstart color green, B, end color green. What are the coordinates of point \green{B}Bstart color green, B, end color green?
Answer:
The coordinates of point B are (6,7).
Step-by-step explanation:
Given points are
Blue = A(-4,8)
Purple = M(1,7.5)
Green = B
It is given that point M is the midpoint of point A and B.
Let coordinates of points are (a,b).
Midpoint of two points is
[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]M=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]
Coordinates of midpoint are (1,7.5).
[tex](1,7.5)=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]
On comparing both sides we get
[tex]1=\dfrac{-4+a}{2}\Rightarrow 2=-4+a\Rightarrow a=6[/tex]
[tex]7.5=\dfrac{8+b}{2}\Rightarrow 15=8+b\Rightarrow b=7[/tex]
Therefore, the coordinates of point B are (6,7).
In terms of paying less in interest, which is more economical for a $150,000 mortgage: a 30-year fixed-rate at 8% or a 20-year fixed-rate at 7.5%? How much is saved in interest?
Answer:
20-year fixed-rate at 7.5%$106,219.32Step-by-step explanation:
The shorter the term, the lower the amount of interest.
The lower the interest rate, the lower the amount of interest.
The loan that has both a shorter term and a lower interest rate will cost less in interest.
___
The total of payments for the 30-year loan is 396,232.87.
The total of payments for the 20-year loan is 290,013.55.
The amount saved by taking the shorter loan is the difference of these amounts: $106,219.32.
_____
You can use an amortization formula, spreadsheet, or a financial calculator to compute the payments for each loan. The total repayment amount is the product of the monthly payment and the number of them, 360 for the 30-year loan; 240 for the 20-year loan.
and a list of numbers the pattern increases by 0.001 as you move to the right if the third number list is 0.0 64 what is the first number in the list answer
Answer:
0.062
Step-by-step explanation:
The numbers will decrease by 0.001 as you move the the left, so the list of numbers can be found as ...
3rd number: 0.064
2nd number: 0.064 -0.001 = 0.063
1st number: 0.063 -0.001 = 0.062
what is the probability of drawing a black card or a card with a letter?
Standard deck of 52
A:
4/12
1/2
21/26
17/26
Answer:
17/26.
Step-by-step explanation:
Prob(Drawing a black card) = 26/52 = 1/2.
Prob(Drawing a card with a letter)
= Prob( Ace, King, Queen or Jack of either Hearts or Diamonds)
= 8/52.
So the required probability = 26/52 + 8/52
= 34/52
= 17/26.
Colton and gage were building a castle together. Colton was 3 times as fast at building the castle than gage. If it takes 80 blocks to build the castle, how many blocks did colton build on the castle?
Answer:
60
Step-by-step explanation:
For each 3 blocks Colton placed, Gage place 1, so Colton placed 3/4 of the total number blocks.
3/4 × 80 = 60
Colton placed 60 blocks on the castle.
Answer:
60
Step-by-step explanation:
I WILL GIVE BRAINLYIST!
Which graph shows a system of equations with exactly one solution?
Answer:
The last graph, where the functions intersect at only one point.
Step-by-step explanation:
A system of equations with only one solution is the one that in some point the solutions of each ecuation is exactly the same. In the graphs 1 and 3, where the equations does not intersect each other, the system of equations have no solution. In the second graph, the equations intersect 2 times, so the system of equations have 2 solutions.
Answer:
The last graph:/ D
Step-by-step explanation:
i got it right on the test
We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2 ; for each toss of coin B, we obtain Heads with probability 1/3 . All tosses of the same coin are independent. We toss coin A until Heads is obtained for the first time. We then toss coin B until Heads is obtained for the first time with coin B. The expected value of the total number of tosses is:
Answer:
The expected value is 5.
Step-by-step explanation:
Let X represent the number of tosses until the event described in the question happens. Let Y represent the number of tosses with coin A until Heads is obtained.Let Z represent the number of tosses with coin B until Heads is obtained.As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that
[tex]E(X)=E(Y)+E(Z).[/tex]
We will compute E(Y) and E(Z).Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,
[tex]E(X)=\sum^\infty_{n=1}nP(Y=n)[/tex],
[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)[/tex],
Then:
for each [tex]n\in \mathbb{N}[/tex], the probability of Y=n is given by [tex](0.5)^{n-1}(0.5)=(0.5)^{n}[/tex] (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore[tex]E(Y)=\sum^\infty_{n=1}nP(Y=n)=\sum^\infty_{n=1}n(\frac{1}{2} )^n=\\\\\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{1}{2} )^n=\sum^\infty_{m=1}(\frac{1}{2} )^{m-1}=\sum^\infty_{m=0}(\frac{1}{2} )^{m}=2.[/tex]
For each [tex]n\in \mathbb{N}[/tex], the probability of Z=n is given by [tex](\frac {2}{3})^{n-1}(\frac {1}{3})[/tex] (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)=\frac{1}{3}\sum^\infty_{n=1}n(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}[/tex]
Observe that, by the geometric series formula:
[tex]\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\sum^\infty_{n=1}(\frac{2}{3} )^{n-1}-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=3-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=\\\\3-\sum^{m-2}_{n=0}(\frac{2}{3} )^{n}=3-\frac{1-(\frac{2}{3})^{m-1} }{1-\frac{2}{3}}=3(\frac{2}{3})^{m-1}[/tex]
Therefore
[tex]E(Z)=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}3(\frac{2}{3})^{m-1} =\\\\ \sum^\infty_{m=1}(\frac{2}{3})^{m-1} = \sum^\infty_{m=0}(\frac{2}{3})^{m} =3.[/tex]
Finally, E(X)=E(Y)+E(Z)=2+3=5.
Using the binomial distribution, it is found that the expected value of the total number of tosses is of 5.
For each coin, there are only two possible outcomes, either it is heads, or it is tails. The outcome of a coin is independent of any other coin, hence the binomial distribution is used to solve this question.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
For coin A, we obtain Heads with probability 1/2, hence:
[tex]E_{sA}(X) = \frac{1}{\frac{1}{2}} = 2[/tex]
For coin B, we obtain Heads with probability 1/3, hence:
[tex]E_{sB}(X) = \frac{1}{\frac{1}{3}} = 3[/tex]
2 + 3 = 5, hence, the expected value of the total number of tosses is of 5.
More can be learned about the binomial distribution at https://brainly.com/question/14424710
Brian is a salesman at a furniture store. He is paid a weekly salary of $300 plus a 10% commission on any sale he closes. Last week, Brian was paid $900. How much merchandise did Brian sell last week?
A.) $6000
B.) $4500
C.) $2000
D.) $5000
E.) $2500.
Answer:
here merchandise sell is $6000
correct option is A
Step-by-step explanation:
given data
salary = $300 + 10 % commission
paid = $900
to find out
merchandise sell
solution
we consider here sell is x
so paid will be
paid = salary + 10% of x
so here put value
900 = 300 + 10% × x
900 - 300 = 10% × x
x = 600 / 10%
x = 6000
so here merchandise sell is $6000
correct option is A
If a company charges x dollars per item, it finds that it can sell 1500 - 3x of them. Each item costs $8 to produce.
(a) Express the revenue, R(x), as the function of price.
(b) Express the cost, C(x), as a function of price.
(c) Express the profit, P(x), which is revenue minus cost, as a function of price.
The profit is $496.30
a. The revenue function will be calculated thus:
R(x) = (1500 - 3x) × x
R(x) = 1500x - 3x²
b. The cost function will be:
C(x) = 8 × x = 8x
c. The profit function will be:
P(x) = Revenue - Cost
= 1500x - 3x² - (8x)
= 1500x - 3x² - 8x
Divide through by x
= (1500x - 3x² - 8x) / x
= 1500 - 3x - 8
1500 - 3x - 8 = 0
Collect like terms
3x = 1500 - 8.
3x = 1492
x = 1492/3
x = 496.3
The profit is $496.30
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