Answer: y^2 - z^2 + 2xy - 2xz
Step-by-step explanation:
(x+y)^2 - (x+z)^2
(x^2 + 2xy + y^2) - (x^2 + 2xz + z^2)
x^2 + 2xy + y^2 - x^2 - 2xz - z^2
x^2 - x^2 + 2xy - 2xz + y^2 - z^2
y^2 - z^2 + 2xy - 2xz
Solve for x. Help me and I will do anything for you.
x = 8
Step-by-step -e-x-p-l-a-n-a-t-i-o-n- below
The angles shown are vertical angles
Vertical angles are congruent (equal to each other)
This means that 8x + 36 = 5x + 60
Using this equation we can solve for x
8x + 36 = 5x + 60
==> subtract 36 from both sides
8x = 5x + 24
==> subtract 5x from both sides
3x = 24
==> divide both sides by 3
x = 8
Answer:
[tex]\huge\boxed{\sf x = 8}[/tex]
Step-by-step explanation:
From the diagram,8x + 36 = 5x + 60 (Vertically opposite angles are equal)
Subtract 5x to both sides
8x - 5x + 36 = 60
3x + 36 = 60
Subtract 36 to both sides
3x = 60 - 36
3x = 24
Divide 3 to both sides
x = 24/3
x = 8[tex]\rule[225]{225}{2}[/tex]
Write the equation of the line that passes through the points (1,-3) and (3,3)
The equation of line is y = 3x - 6
Define Equation of line.
A line in geometry is a collection of points that can be stretched infinitely in two different ways. To put it another way, a line is created by continually extending the two end points in any direction. As a result, we can assert that a line lacks end points. However, because it just has length and no width, it is a one-dimensional geometric form. Based on the information provided, we can create multiple forms of equations for lines algebraically, such as point slope form, slope-intercept form, and two point form. Two Point Form Formula,y - y₁ = m (x - x₁)
We have the given points,
(1, -3) and (3, 3)
Let, (x₁ , y₁) = (1, -3) and,
(x₂, y₂) = (3, 3)
Formula for equation of line is,
y - y₁ = m (x - x₁)
Where m is slope and for that we have formula for slope is
m = (y₂ - y₁) / (x₂ - x₁)
plug in the values,
m = (3 - (-3) ) / (3 - 1)
m = 6 / 2
m = 3
Now, we get the slope. Now, just put the values in equation of line formula
y - y₁ = m (x - x₁)
y - (-3) = 3 (x - 1)
y + 3 = 3x - 3
y = 3x - 6
Hence, the equation of line is y = 3x - 6
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I’ll give brainlist!!!
What is the slope?
The slope of the line is 1/3
First we have to choose two points from the graph
The first point = (1, -5)
The second point = (7, -3)
The slope of the line is the change is y coordinate with respect to the change in x coordinate of the function
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinate of the first point
[tex](x_2,y_2)[/tex] is the coordinate of the second point
Substitute the values in the equation
The slope of the line = (-3 - (-5) / (7 - 1)
= (-3+5) / 6
= 2 / 6
= 1/3
Hence, the slope of the line is 1/3
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All stereos are 20
%
off of the original price. If stereos normally cost $160, what is the sale price?
Answer:
128 dollars
Step-by-step explanation:
hope it helped! :)
Find the simple interest of Rs. 20,000 for 5 years at 10% per annum? Also, at what time will Rs. 50,000 earn the same amount of interest at 5% of simple interest per annum?
Answer:
below
Step-by-step explanation:
Simple interest = 20 000 * .1 * 5 (.1 is 10% in decimal)
at 1/2 the 10% interest it will take twice as long = 10 years
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The completed table of coordinates for the exponential function can be presented as follows;
x; -2, -1, 0, 1, 2
y ; 16/9, 4/3, 1, 3/4, 9/16
Please find attached the graph of the function created with MS Excel
The correct graph is therefore, option D
What is an exponential function?
An exponential function is one that has the argumant as an exponent
The values in the table can be found as follows;
[tex]f(x) = \left(\frac{3}{4} \right)^x[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{-2} = \dfrac{16}{9}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{-1} = \dfrac{4}{3}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{0} = 1[/tex] The y-intercept
[tex]f(x) = \left(\frac{3}{4} \right)^{1} = \dfrac{3}{4}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{2} = \dfrac{9}{16}[/tex]
The completed table is therefore;
x; -2, -1, 0, 1, 2
y ; 16/9, 4/3, 1, 3/4, 9/16
The graph of the function , [tex]f(x) = \left(\frac{3}{4} \right)^x[/tex], therefore, has a y-intercept of 1, and a maximum value of 16/9 at x = -2
The best cprect option for the graph is therefore option D
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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1. Determine the solution for the system of equations shown in this graph. Enter your answer as a coordinate pair without any spaces, infinite solutions, or no solutions.
The solution for the system of equations shown in this graph is (-2, 1)
In this question, we need to determine the solution for the system of equations shown in this graph.
From given graph of system of equations we can observe that the system of equations represent lines intersected at point.
This means that the system of equations has a solution.
The point of intersection of given line is (-2, 1)
Therefore, the solution for the system of equations shown in this graph is (-2, 1)
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Sally adds 3.13 moles of argon to a 5.29 liter balloon that already contained 2.51 moles of argon. What
is the volume of the balloon after the addition of the extra gas?
The volume of the balloon after the addition of the extra gas is 11.87 liters
The initial volume of the balloon = 5.29 liters
Initial quantity of argon in the balloon = 2.51 mole
Here we have to use the unitary method
The volume of the 1 mole of argon = The initial weight of the balloon / Initial quantity of argon in the balloon
Substitute the values in the equation
The volume of the 1 mole of argon = 5.29 / 2.51
= 2.11 liters
Additional argon added = 2.51 mole
Total quantity of argon = 2.51 + 3.13
= 5.64 mole
The volume of the 5.64 mole of argon = 5.64 × 2.11
= 11.87 liters
Hence, the volume of the balloon after the addition of the extra gas is 11.87 liters
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Probability: Discrete, Binomial, Normal
IB Math Applications SL
1. Jae Hee plays a game involving a
biased six-sided die. The score for
the game, X, is the number which
lands face up after the die is rolled.
The table shows the probability
distribution for X.
a. Find the exact value of p.
Score x
P(X=x)
Name: Somatar
Date:
-3
1
18
-1
P
Period:
0
3
18
1 point: Correct p-value
b. Jae Hee plays the game once. Calculate the expected score.
1
1
18
1 point: Correct substitution into formula
2 points: Correct substitution and answer
c. Jae Hee plays the game twice and adds the two scores together.
Find the probability Jae Hee has a total score of -3.
2
18
The precise value of p is 4/18. Jae Hee's expected score in the game is 1.833. Jae Hee has a 1/162 chance of receiving a total score of -3. The likelihood that something will happen is defined as probability.
How to calculate Probability ?Probability is calculated by dividing the number of possible outcomes by the total number of outcomes. Probability and odds are distinct concepts. Odds are the probability that something happens divided by the probability that it does not happen. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or a statement being true.Therefore,
Value of p is,
∈p = 1
1/18 + p + 3/18 + 1/18 + 2/18 + 7/18 = 1
14/18 + p = 1
p = 4 / 18
So the exact value of p is 4/18
Expected score of the game :
∈(x) = ∈xi pi
= -3 (1/18) - 1 (4/18) + 0 (3/18) + 1 (1/18) + 2 (2/18) + 5 (7/18)
= 33/18
= 1.833
Expected score of the game Jae Hee plays is 1.833
Calculate Probability of Jae Hee getting total score of -3
p (total score -3 )
= p(x= -3) and p(x=0) + p(x=0) and p (x=3)
= 1/18 × 1/18 + 1/18 × 1/18
=1/162
Probability of Jae Hee getting total score of -3 is 1/162
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Answer:
Step-by-step explanation:
51.765 rounded 2 decimal places
Answer:
The answer would be 52 if you rounded by the nearest whole number.
Step-by-step explanation:
Find your place
Look next door (to the minor digit)
Four or less just ignore
Five or more let it sore.
Given the explicit formula u(n) = 4n - 1, where u(1) = 1, find the recursive formula for u(n).
A. u(1) = 1 and u(n + 1) = 4u(n), for n = 1, 2, 3, . . .
B. u(1) = 1 and u(n + 1) = u(n) + 4, for n = 1, 2, 3, . . .
C. u(1) = 1 and u(n + 1) = u(n) + 8, for n = 1, 2, 3, . . .
D. u(1) = 1 and u(n + 1) = 8u(n), for n = 1, 2, 3, . . .
The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 .... , the correct option is (b) .
In the question ,
it is given that ,
the explicit formula is u(n) = 4n - 1 .
and u(n) = 1 ,
we need to find the recursive formula ,
We substitute n + 1 in place of n , in the equation u(n) = 4n - 1
after substitution , we get
u(n+1) = 4(n + 1) - 1
u(n+1) = 4n + 4 - 1
u(n+1) = 4n + 3
Subtracting u(n) = 4n - 1 from u(n+1) = 4n + 3 ,
we get
u(n+1) - u(n) = 4n + 3 - (4n - 1)
u(n+1) - u(n) = 4n + 3 - 4n + 1
u(n+1) - u(n) = 3 + 1
u(n+1) - u(n) = 4
u(n+1) = u(n) + 4
Therefore , The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 ....
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What is the degree of the polynomial below?
x +32x² + 4x² - 4x
A.
7
B.
6
C.
5
D.
4
Answer:
2
Step-by-step explanation:
Degree is the largest exponent = 2 (as written)
In the diagram, the lines L and M appear to be parallel. How do you know for sure?
Proved that the line L and M are parallel lines
Here we have to prove that L and M are parallel
One angle at the point at F is given that 139 degrees
We know sum of angles on a straight line is 180 degrees
Then the other angle will be
139 + a = 180
a = 180 - 139
a = 41 degrees
Now consider the triangle and find the value of x
The sum of interior angles of a triangle is 180 degrees
then
(3x+8) + (3x) + (9x+7) = 180
3x+8 +3x +9x + 7 = 180
15x + 15 = 180
15x = 180 - 15
15x = 165
x = 165/15
x = 11
Then the value of angle 3x + 8 = 3 × 11 + 8
= 33 + 8
= 41 degrees
Before that we have solved the angle at f = 41 degrees, therefore both are equal angles which is called corresponding angles
Therefore, the line L and M are parallel
Hence, proved that the line L and M are parallel lines
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l
Ashley's bill for dinner at a restaurant was $100. She left a 15% tip. What was the amount
of the tip?
Answer:
Step-by-step explanation:
ashleys bill was 100 so by knowing any percentage times 100 is itself ashleys tip was $15
Answer:
the amount on the tip is 15.00$
but when you add the amount of the total cost and the tip it would be $115 dollar they spend
Step-by-step explanation:
Which system of linear inequalities is graphed?
A.
x<-3
y ≤-x+1
B.
x<-3
y ≤-x-1
C.
x<-2
y ≤-x-1
D.
x ≤-3
y ≤-x-3
Answer:
A x<-3
y ≤-x+1
Step-by-step explanation:
x<-3
y ≤-x+1
Sari made pancake batter. She has 1 cup of batter left. How much batter did she use?
If this problem cannot be solved with the information provided, write additional information
and then solve the problem.
Answer:
3 cups
Step-by-step explanation:
let's assume that sari made pancake batter in a jar.
1 jar is equivalent to 4 cups
so if 1 cup of batter is left, it can be concluded that Sari uses 3 cups of batter in making pancakes.
the breaking strength x of a certain rivet used in a machine engine has a mean 5000 psi and standard deviation 400 psi. a random sample of 36 rivets is taken. consider the distribution of , the sample mean breaking strength. what is the probability that the sample mean falls between 4800 psi and 5200 psi?
The probability that the sample mean falls between 4800 psi and 5200 psi is 0. 0.9973.
Probability refers to the numerical descriptions of how likely an event is to occur. For the given information, the mean µ = 5000 psi and standard deviation σ = 400 psi.
For a random sample, n = 36, in order to determine the probability that the sample mean falls between 4800 psi and 5200 psi, the z test statistics for the range must be calculated.
z = (x - µ)/ (σ/√n) = (4800 - 5000)/ (400/√36) = -3
z = (x - µ)/ (σ/√n) = (5200 - 5000)/ (400/√36) = 3
Hence, the probability that the sample mean falls between 4800 psi and 5200 psi would be p ( -3< z < 3).
From the table,
p ( -2.4 < z < 2.4) = 0.9973
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1.31 (a) possible coverage error: only employees in a specific division of the company were sampled. (b) possible nonresponse error: no attempt is made to contact nonrespondents to urge them to complete the evaluation of job satisfaction. (c) possible sampling error: the sample statistics obtained from the sample will not be equal to the parameters of interest in the population. (d) possible measurement error: ambiguous wording in questions asked on the questionnaire.
B. No attempt is made to contact noncorrespondents.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.Hence,B. No attempt is made to contact noncorrespondents.
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Write a rate that represents the situation.
Need help on 5 & 6
Answer:
5. (6 hours)/(1 day)
6. (8 quarts)/(1 container)
Step-by-step explanation:
5. The number line shows both hours and days. It does not indicate why the relationship exists. Perhaps the hours are the ones worked in a day. What’s important is whether the relationship between the two is the same for all data pairs. E.g., 12/2 = 6; 36/6 = 6; 60/6 - 5, and so forth. They are all the same ratio, or rate: (6 hours)/(1 day)
6. The number line shows both quarts and containers. The relationship between the two is the same for all data pairs. E.g., 8/5, 16/10 or 8/5; 24/15 or 8/5; 32/20 or 8/5, and 40/25 or 8/5. They are all the same ratio, or rate: (8 quarts)/(1 container).
8–7. The block brake conit of a pin-connected lever and
friction block at B. The coefficient of tatic friction between
the wheel and the lever i m = 0. 3, and a torque of 5 N # m
i applied to the wheel. Determine if the brake can hold the
wheel tationary when the force applied to the lever i
(a) P = 30 N, (b) P = 70 N
If the brake can hold the wheel stationary when the force applied to the lever i
(a) P = 30 N -> No
(b) P = 70 N -> Yes
To hold lever,
x + Σ[tex]M_{O} = 0[/tex] [tex]F_{B}(0.15) - 5 = 0[/tex] [tex]F_{B} = 33.333 N[/tex]
Require
[tex]N_{B} = \frac{33.333}{0.3}[/tex]
= 111.1 N
Lever,
x + Σ[tex]M_{A} = 0[/tex] [tex]P_{Reqd.}[/tex](0.6) - 111.1(0.2) - 33.333(0.5) = 0
[tex]P_{Reqd.}[/tex] = 39.8 N
(a) P = 30 N < 39.8 N No
(b) P = 70 N > 39.8 N Yes
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When can you use proportional reasoning to solve a problem?
A. When two quantities add to 1
B. When one quantity is a constant multiple of the other
C. When the two quantities multiplied equal a constant
D. When one quantity is 1 more than the other
We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.
Hence, Option (C) is correct.
What is a proportion?
A proportion is a type of ratio in which the denominator also contains the numerator. For example, the proportion of male deaths would be deaths to males divided by deaths to males plus deaths to females (i.e. the total population).
Let 'x' be the numerator and 'y' be denominator,
then one ratio is 'x/y' and its reciprocal by using the proportion would be 'y/x'
and then their multiplication will be
[tex]=\frac{x}{y}*\frac{y}{x} \\\\\=1[/tex]
Multiplication gave us '1', which is a constant.
Hence option (C) is the correct answer.
We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.
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a farmer raises chickens and sheep on his farm. the ratio of the total number of legs of the chickens to the total number of legs of the sheep is 4:7. find the minimum number of chickens and sheep he has.
Answer:
8 chickens, and 28 sheep.
Step-by-step explanation:
The chickens have the ratio of 4. Chickens have 2 legs, so 4 x 2 = 8 chickens.
The sheep have the ratio of 7. Sheep have 4 legs, so 7 x 4 = 28 sheep.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The function c(x) = 14x + 13 represents the cost (in dollars) of renting a surfboard, where x is the number of hours you rent
the surfboard.
a. Graph the function and identify its domain and range.
The domain of this function c(x) = 14x + 13 using interval notation is (0, ∞).
The range of this function c(x) = 14x + 13 using interval notation is (13, ∞).
How to identify the domain and range any graph?In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
Additionally, the vertical extent of any graph represents all its range values and they are always read and written from smaller to larger numerical values, and from the bottom of a graph to the top.
By critically observing the graph of this function shown in the image attached below, we can reasonably infer and logically deduce the following:
Domain = (0, ∞).
Range = (13, ∞).
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a baseball player averages 2 hits per game. The player already has 18 hits this season. another player has 22 hits so far this season and averages 1 hit per game. After how many games will both players have the same number of hits?
Answer: 20
Step-by-step explanation:
i got 100
help please (see picture)
Also if it’s not clear cus of the smudge, it says “6” and “U”
The perimeter of the triangle is 64 when the triangle is ZTW.
Given that,
In the picture we have a triangle ZWT.
The U and V are mid points of WT and Y and X are midpoints of ZW.
We have to find the perimeter of the triangle.
We get the sides
ZT=22
We have,
TU/ZY= UV/YX= VW/XW (Thales theorem)
6/8= a/12= 3/b
3/4=a/12= 3/b
Take,
3/4=a/12
a=3/4×12
a=3×3
a=9
Take,
3/4=3/b
b=3×4/3
b=4
The side TW=6+9+3=18
The side ZW=8+12+4=24
The perimeter of the triangle is sum of the sides.
The perimeter of the triangle=ZT+ZW+TW
The perimeter of the triangle= 22+24+18
The perimeter of the triangle= 64
Therefore, The perimeter of the triangle is 64 when the triangle is ZTW.
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salma has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. each small cup holds 12 ounces of lemonade and each large cup hold 16 ounces of lemonade. salma sold 60 cups of lemonade totaling 920 ounces. determine the number of small cups sold and the number of large cups sold
If Salma sold 60 cups of lemonade with total 920 ounces, then the number of small cups is 10 and the number of large cups is 50.
The problem can be translated into a system of linear equations.
Let:
p = the number of small cups sold
q = the number of large cups sold
"Salma sold 60 cups" can be translated into equation:
p + q = 60 (equation 1)
"totaling 920 ounces" can be translated into equation:
12p + 16q = 920 (equation 2)
Multiply equation 1 by 12 then substracted from equation 2:
12p + 16q = 920
12p + 12q = 720 _
4q = 200
q = 50
Substitute q = 50 into equation 1:
p + 50 = 60
p = 10
Hence, the number of small cups = 10, the number of large cups = 50.
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PLEASE HELP!!!! I BEG YOU!!!
What is the solution to the system of equations graphed below? Give the answer as a coordinate point (x, y)
Answer:
(1,3)
Step-by-step explanation:
The solution to a system of equations graph is the point of intersection of the two lines.
In this case the point where both lines meet is at x = 1 and y = 3
hence the answer being (1,3)
In a class of 29 students, 9 play an instrument and 14 play a sport. There are 8 students who do not play an instrument or a sport. What is the probability that a student does not play an instrument given that they play a sport?.
The probability of a student playing a sport but not playing an instrument is around 0.4286.
The likelihood of a student not playing an instrument, provided they play a sport, is:
[tex]Probability=\dfrac{Number\ of\ students\ who\ play\ a\ sport\ but\ do\ not\ play\ an\ instrument}{Number of \students\ who\ play\ a\ sport}[/tex]
It is known that 14 students participate in a sport, while 8 students do not engage in either a musical instrument or a sport. Thus, the number of students who play a sport but do not play an instrument is:
Number of students who play a sport but do not play an instrument = 14- 6
= 6
Now, let's calculate the probability:
Probability = 6/14
= 0.4286
Rounded to four decimal places, the likelihood of a student playing a sport but not playing an instrument is approximately 0.4286.
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I would like to know the answer..
Answer:
Ann’s work is correct
Step-by-step explanation:
