In the given word "WISCONSIN" there are exactly 9 letters, but some are repeated, so we can rearrage the letters in the word in 9!/8 ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical approach that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Permutations are commonly mistaken with combinations, a different mathematical concept. The sequence in which the components are selected does not, however, affect combinations. In other words, whereas ab and be are equivalent in combinations, they are deemed to be distinct arrangements in permutations.
What is the formula for calculating the permutation?The formula for calculating the permutation is:
p(n,k) = n! /(n-k)!
where , n - Total number of elements in a set
k - Number of selected elements
In the above question , the number of ways to rearrange 9 letters would be 9! but, since there are 2Ss , 2Ns and 2Is so the number of ways to rearrange 9-letter strings will be:
9!/(2!*2!*2!) = 9!/8
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Given the two rectangles below. Find the area of the shaded region.
3
☐
7
5
2
The area of the shaded region in the rectangle is given as follows:
42 units squared.
How to calculate the area of a rectangle?The area of a rectangle of base b and height h is given by the multiplication of these dimensions, as follows:
Area = base x height.
For the shaded region in this problem, given by the image shown at the end of the answer, the area can be obtained as the subtraction of the area of the entire rectangle by the area of the non-shaded region.
The entire rectangle has base 11 and height 12, hence it's area is given as follows:
Ar = 11 x 12 = 132 units².
The non-shaded region has base of 9 units and height of 10 units, hence it's area is given as follows:
An = 9 x 10 = 90 units².
Then the area of the shaded region on the rectangle is calculated as follows:
As = Ar - An = 132 - 90 = 42 units².
Missing InformationThe rectangle is given by the image shown at the end of the answer.
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8n +9=7n+15 please solve this for me??
Answer:
n=2/5
Step-by-step explanation:
look it up
Answer:
n = 6
Step-by-step explanation:
8 x 6 = 48
48 + 9 = 57
=
7 x 6 = 42
42 + 15 = 57
So n = 6
Find the measure of each angle indicated.
A. 84 degree
B. 96 degree
Please help!!!
Answer:
84 Degrees
Step-by-step explanation:
This is because they are alternate interior angles
Which means they are both the same angle and are both inside the parallel line
The equation for line c can be written as y=-3/7x+4. Perpendicular to line c is line d, which passes through the point (2,4). What is the equation of line d?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation of the perpendicular line is y = (7/3)x - 2/3. And the slope of the line is 7/3.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
y = -(3/7)x + 4
The equation of the line that is perpendicular to y = -(3/7)x + 4 will be given as,
y = (7/3)x + d
The equation passes through (2, 4) will be given as,
4 = (7/3) × 2 + d
c = - 2/3
Then the equation of the perpendicular line is given as,
y = (7/3)x - 2/3
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Please help me respond this
Option 2 is correct that is 1.79
What is third quartile ?When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
The quartiles formula is as follows:
Upper Quartile (Q3) = 3/4(N+1)
Lower Quartile (Q1) = (N+1) * 1/3
Middle Quartile (Q2) = (N+1) * 2/3
Interquartile Range = Q3 -Q1,
1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.
Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.
The data set has 8 values.
hence, n = 8; third quartile: 3/4 (n+1)th term
Q3 =3/4 of a term (9) term
Q3 =27/4 th term
Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)
equals 1.76
Thus Q3 is 1.76 that is option 2
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the number of miles mario can drive varies directly with the amount of gas that he has. he can drive 18 miles on ½ a gallon of gas. how many miles can mario drive with 9 gallons of gas?
Given a quadratic with vertex of (-4,1) and point (-3,3) write the equation of the function in general form
The general form of an equation having vertex and point is y=a(x-h)²k. Then, the general form equation with the vertex of (-4,1) and point (-3,3) is y=3x²+24x+48.
The vertex form is an alternative way to state a parabola's equation. The equation y=a(x-h)²k is the formula for this, where k denotes the vertical translation, h is the horizontal translation, and a is a vertical stretch factor.
Here, given the vertex (h,k) is (-4,1) and the point (x,y) is (-3,3)
Start by substituting the values of h and k in the vertex equation, we get,
y=a(x+4)²(1)
Given that the point where the vertex meets is (-3,3). If we substitute this point into the equation above, we obtain,
3=a(-3+4)
a=3
To obtain the general form, now substitute the values of a and (h,k) in the vertex equation. We get,
y=3(x+4)²
y=3(x²+8x+16)
y=3x²+24x+48
Therefore, the required answer is y=3x²+24x+48.
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Question 20
A rectangular courtyard has a cement walkway around its perimeter. The area of the courtyard can be represented by the expression 24(5x - 1).
The area of the cement walkway can be represented by the expression 32(5x-1 + 8)- 24(5x-1). Write an equivalent expression that
represents the area of the cement walkway.square yards
Answer:
To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 on the right side of the equation to get 32(5x-1 + 8) = 32(5x-1) + 32(8). Then, we can subtract the area of the courtyard, 24(5x-1), from this expression to get 32(5x-1) + 32(8) - 24(5x-1) = 8(5x-1) + 32(8). This is an equivalent expression that represents the area of the cement walkway in square yards.
6
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation with the correct solution.
2 = 15
H=
7/3
x =
x=8
8
x= -15
H=
4(3x + 5) - 3
1
7/3
= 9x
7
5(z + 7)-3(2-4)= 7x + 2
(529) = 2 ( + 6)
x = -9
x = 9
100
a. The solution to the equation 1/3(5x - 9) = 2(1/3x + 6) is x = 15.
b. The solution to the 4(3x + 5) - 3 = 9x - 7 is x = -8.
c. The solution to the equation 5(x + 7) - 3(x - 4) = 7x + 2 is 9
How to calculate the equation?a. Give the equation 1/3(5x - 9) = 2(1/3x + 6)
We want to find the value of x
5/3x - 3 = 2/3x + 13
x - 3 = 12
Collect the like terms
x = 12 + 3
x = 15
b. 4(3x + 5) - 3 = 9x - 7
12x + 20 - 3 = 9x - 7
Collect the like terms
3x + 17 = -7
3x = -24
Divide
x = -24 / 3
x = -8
c. 5(x + 7) - 3(x - 4) = 7x + 2
5x + 35 - 3x + 12 = 7x + 2
2x + 47 = 7x + 2
Collect the like terms
5x = 45.
Divide.
x = 45 / 5
x = 9
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Joeph drove 27 mile in 1 1/3 hour. If he drove at a contant rate, how far did he travel in one hour?
The number of miles Joseph traveled in one hour is calculated to be 20.25 miles
Since Joseph drove 27 miles in 1 1/3 hours, we first convert 1 1/3 into simpler form as follows;
1 1/3 hours = 4/3 hours
Now we can determine how far he traveled in one hour if he drove at a constant rate by cross multiplication as follows;
4/3 hours = 27 miles
1 hour = x
Here x represents the number of miles traveled in one hour;
1 × 27 = 4/3x
27 = 4/3x
x = 27/(4/3)
x = 27 × 3/4
x = 20.25 miles
Hence Joseph travels 20.25 miles in one hour.
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I NEED HELP PLS!!!!
Reese is installing an in-ground rectangular pool in her backyard. Her pool will be 30 feet long, 14 feet wide, and have an average depth of 8 feet. She is installing two pipes to bring water to fill the pool; these pipes will also be used to drain the pool at the end of each season. One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
Use this information and what you know about solving rational equations to answer the questions below.
1. When Reese opens the pipes to fill the pool, she finds that only the slower pipe is working. Write a rational equation that you can use to find out how long it will take to fill the pool under these circumstances. Explain how you came up with your equation.
2. Solve the equation that you wrote in question 1. You can round your final answer(s) to the nearest hundredth. Show all your work.
3. Interpret your answer(s) to question 2 in context of the problem. What do the number(s) represent?
The slower pipe if working alone can fill the tank in 10.5 hours.
What is the volume of a cuboid?A cuboid is a three-dimensional solid that has 6 faces (rectangular), 8 vertices, and 12 edges. A cuboid has three dimensions such as length, width, and height. A perfect cuboid is said to be a cuboid that has integer edges and the formula for its volume is: V = length ×breadth× width
Given here dimensions of the swimming pool as 30 feet long, 14 feet wide, and an average depth of 8 feet, therefore the volume of the swimming pool V = 30×14×8
= 3360 feet³
Again the two pipes working together can fill the pool in 3.5 hours and let their speeds 2x and x then, their relative speed = 3x
thus we have 3.5 = 3360/3x
⇒ x = 320 feet³/hr
Therefore the individual speeds are equal to 320 feet³/hr and 640 feet³/hr
Accordingly, the time taken by the slower pipe to fill the entire tank alone is = 3360/320
= 10.5 hours
Hence, the time taken by the slower pipe is 10.5 hours
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in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0. group of answer choices true false
in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.
In exponential smoothing, a weight is assigned to each data point in the series.
If a small weight is assigned, close to 0, it means that the more recent data points will have a lesser influence on the overall result.
This will therefore show the overall long-term tendency of the series.
in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.
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please help i dont know the answer
Answer:
Step-by-step explanation:
do your work ok you go it and who still do ixl
In ΔPQR, r = 38 cm, ∠P=49° and ∠Q=127°. Find the length of p, to the nearest centimeter.
The length of p is 411 cm.
What is a Triangle?Every three-sided polygon having three edges and three vertices is referred to as a triangle in geometry. The most important attribute of a triangle is that its internal angles sum to 180 degrees. The triangle's angle sum attribute is what is known as.
As per the given data:
We are given a triangle, and we know 2 angles of the triangle and one side.
In ΔPQR:
r = 38 cm
∠P = 49°
∠Q = 127°
From the angle sum property for a triangle:
∠P + ∠Q + ∠R = 180°
49° + 127° + ∠R = 180°
∠R = 180° - 176°
∠R = 4°
By using the sine rule in a triangle:
sin(∠P)/p = sin(∠R)/r
p = [sin(∠P)/sin(∠R)] × r
p = [sin(49°)/sin(4°)] × 38
p = 411 cm
The length of p is 411 cm.
Hence, the length of p is 411 cm.
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A teacher makes an annual salary of $65,800.
If the income tax withholding is 14%, how
much income tax is paid?
The income tax can be paid by the teacher =$ 9212.
What is income tax:An income tax is a sort of tax that is levied on the earned and unearned income of an individual or corporation.
For instance, the United States levies a federal income tax on its residents, regardless of where they reside—in the country or overseas. The majority of the money the US government receives comes from this income tax.
Here we have
The annual salary of a teacher is $ 65,800
The rate of income tax = 14%
The income tax can be paid = 14% of 65800
=> [tex]\frac{14}{100} \times 65800[/tex]
= [tex]14 \times 658[/tex]
= 9212
Therefore,
The income tax can be paid by the teacher =$ 9212
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Someone needs help with my homework, help me! Can you fill in the blinks of Angle chase?
Answer:
in order of going down:
1) 77
2) 103
3) 77
4) 37
5) 53
Step-by-step explanation:
Answer:
77°
103°
77°
37°
Step-by-step explanation:
The outer quadrilateral in black is a rectangle because of the angles it has at the vertices.
Look at the upper green line. It intersects the vertical sides of the outer rectangle.
The upper green line intersects the left vertical segment of the outer rectangle at a 103° angle. That makes the top yellow box 77°.
The top yellow box is an angle of a quadrilateral.
360 - 77 - 66 - 114 = 103
The second yellow box is 103°.
The third yellow box is 77°.
The bottom yellow box is 180 - 66 - 77 = 37°
How much does it cost to buy 1500g of cornflakes?
Answer:
£2.94
Step-by-step explanation:
1500g = 750g x 2 = 2 boxes
£1.96 = price for 1 box
÷ by 2 = 98p
add that to £1.96 = £2.94
PLEASE HELP FAST WILL BE BRAINLIEST
Answer:
See below
Step-by-step explanation:
5z/(z-2) = - 1/z
1) z [tex]\neq[/tex] 2 the expression (z-2) in 5z/(z-2) would be 0, leaving 5/0. Division by 0 is undefined.
2) Similiarly, the expression - (1/z) requires that z [tex]\neq[/tex] 0, since division by 0 is not allowed (undefined).
Solve for X.
A. 8 degree
B. 5 degree
C. 7 degree
D. 6 degree
Please help quickly!!!
Answer:
c
Step-by-step explanation:
when we use the word automobile to refer to a category of transport vehicles, we are using this word as a(n)
When we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept. The correct answers is concept
A concept is an abstract idea that takes form in your mind. This is known as the structures of thoughts and beliefs. They are important because it gives a clear explanation of a particular subject.
An automobile, byname auto, also called motorcar or car, a usually four-wheeled vehicle designed primarily for passenger transportation and commonly propelled by an internal-combustion engine using a volatile fuel, this term is generally used for an vehicle when refering to its category.
When we think of the word automobile, the first thing that comes to your mind is a category of transport. The mind connects the thoughts around the structures build. That’s a concept
Thus, when we use the word automobile to refer to a category of transport vehicles, we are using this word as a concept.
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a statistics student made the following grades on the first 7 tests: 76, 80, 91, 94, 78, 85. 90. what is her median score for the whole semester?(chapter 3) a. 85 b. 90 c. 91 d. 94
The median score for the whole semester is 85. Thus, option a is correct.
It is given to us that -
The grades on first 7 tests of a statistics student are -
76, 80, 91, 94, 78, 85. 90
We have to find out the median score for the whole semester.
To find out the median, we have to first arrange the grades in ascending order from lowest to highest. Thus, arranging them in ascending order, we have -
76, 78, 80, 85, 90, 91, 94
Now, from this arrangement from lowest to highest, the median can be found out as the middle number in the given order which is equal to 85.
Therefore, the median score for the whole semester is 85. Thus, option a is correct.
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Which formula is correct formatting for a nested function? =and(b2>3000,c2>2000,"bonus","no bonus") =if(and(b2>3000,c2>2000),"bonus","no bonus") =ifand(b2>3000,c2>2000,"bonus","no bonus") =if(=and(b2>3000,c2>2000),"bonus","no bonus")
Correct formatting for a nested function is
=IF(AND(B2>3000,02>2000),"Bonus","No Bonus")
A nested If statement is used when 1 or more conditions are to be tested. The result of the nested function depends based on the true value of the function.
i.e. If the nested statement is true, certain operations are to be done otherwise, do something else. In other words, the IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if True or False.
The syntax of a nested function goes thus
IF( condition1, value_if_true1, IF( condition2, value_if_true2, value_if_false2 ))
This would be equivalent to the following in Excel
= IF(condition1,"value_if_true",value_if_false)
Base on the above explanation, only option B is right.\
And what it does is that
it checks if cell B2 is greater than 3000 AND cell 02 is greater than 2000.
If both statement are true, "Bonus" will be the output result
If one ore both statement are false, "No Bonus" will be the output result
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Answer: B
Step-by-step explanation:
i just did it
Write an equation for the line parallel to the given line that contain C. C(2,4);
An equation for the line parallel to the given line that contains C(2,4) is y = (3/4)x + (1/2).
We may use the slope-intercept version of the expression of a line, which is provided by "y = mx + b," where m seems to be the slope of the line & b is the y-intercept, to express the linear function that is perpendicular to a given line as well as contains a particular point.
We may easily utilize the same value of m again for the equation of a parallel line if the slope-intercept form of a line's equation is provided. For instance, if the provided line's equation is "y = 2x + 1," a parallel line's equation would be "y = 2x + c," where c is a constant.
By restructuring the equation in slope-intercept form if the equation of a line is provided in another form, such as "ax + by + c = 0," it is possible to determine the slope of the line. If the expression of the single sequence is "3x - 4y + 5 = 0," for instance, we may rewrite it in slope-intercept form by focusing just on y on one side of the equation:
3x - 4y + 5 = 0
-4y = -3x - 5
y = (3/4)x + (5/4)
The slope of the line is 3/4.
4 = (3/4)(2) + b
4 = (3/2) + b
b = 4 - (3/2)
b = (4 - 3/2)
b = (4 - 3)/2
b = (1/2)
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Please help mee I will give brainlyest
Answer:
Step-by-step explanation:
answer is A. n is parallel to both l and m
Subtract 5x²+2x-11 from 3x²+8x-7. Express the result as a trinomial
Answer:
[tex] \sf \: -2x² + 6x + 4 [/tex]
Step-by-step explanation:
Given problem,
→ (3x² + 8x - 7) - (5x² + 2x - 11)
Let's solve the problem,
→ (3x² + 8x - 7) - (5x² + 2x - 11)
→ 3x² + 8x - 7 - 5x² - 2x + 11
→ (3x² - 5x²) + (8x - 2x) + (-7 + 11)
→ (3 - 5)x² + (8 - 2)x + 4
→ -2x² + 6x + 4
Hence, answer is -2x² + 6x + 4.
Statistics problem: Independent, find this P(A and B) =
Event A has probability 0.4. Event B has probability 0.5 If A and B are independent, then the probability that both events occur is
A) 0.0
B) 0.9
C) 0.7
D) 0.2
E) 0.1
The probability P(A and B) has a value of (d) 0.2
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Event A has probability 0.4. Event B has probability 0.5These mean that
P(A) = 0.4
P(B) = 0.5
From the question, we have
The events are independent events
This means that
P(A and B) = P(A) * P(B)
So, we have
P(A and B) = 0.4 * 0.5
Evaluate
P(A and B) = 0.2
Hence, value is 0.2
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The base of a triangle is √20 cm and its height is√8 cm. Find its area. Write your answer in simplified radical form.
Answer: the area of the triangle is (1/2) * √20 cm
Step-by-step explanation:
The area of a triangle is equal to one half of the product of the base and the height. In this case, the base of the triangle is √20 cm and the height is √8 cm, so we can find the area by doing this:
Area = (1/2) * (√20 cm) * (√8 cm)
To simplify this expression, we can first multiply the numerator and denominator by the square root of the denominator:
Area = (1/2) * (√20 cm * √8 cm) / (√8 cm)
This gives us:
Area = (1/2) * (√160 cm^2) / (√8 cm)
Now we can cancel out the square root of 8 in the numerator and denominator:
Area = (1/2) * √160 cm^2 / √8 cm
Area = (1/2) * √20 cm
Thus, the area of the triangle is (1/2) * √20 cm, which is the simplified radical form of the answer.
Answer: [tex]2\sqrt{10} \ \ \text{square cm}[/tex]
==================================================
Work Shown:
[tex]\text{area} = 0.5*\text{base}*\text{height}\\\\\text{area} = 0.5*\sqrt{20}*\sqrt{8}\\\\\text{area} = 0.5*\sqrt{20*8}\\\\\text{area} = 0.5*\sqrt{160}\\\\\text{area} = 0.5*\sqrt{16*10}\\\\\text{area} = 0.5*\sqrt{16}*\sqrt{10}\\\\\text{area} = 0.5*4*\sqrt{10}\\\\\text{area} = 2\sqrt{10}\\\\[/tex]
The area units are in square centimeters.
----------------------------
Explanation:
As the steps above indicate, I used this rule
[tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex]
This is to combine the roots in the 3rd step, but also to pull them apart in the 6th step. The idea is to pull out the largest perfect square factor to simplify the square root.
Hi please help , you don't need to show work.
The value of function (f+g)(x) is x²-3x+7, (f-g)(x) is 3x²-3x+7, (fg)(x) is -2x⁴+3x³-7x² and (f/g)(x) is -2x²+3x-7/x²
What is a function?A relation is a function if it has only One y-value for each x-value.
The given two functions are
f(x)=3x-2 and g(x)=4+x
at x=-1
f(-1)=-5, g(-1)=3
at x=2,
f(2)=4, g(2)=6
at x=5,
f(5)=13, g(5)=9
Now the functions are f(x)=2x²-3x+7 and g(x)=-x².
We need to find (f+g)(x)
f(x)+g(x)
2x²-3x+7-x².
x²-3x+7
(f-g)(x)
f(x)-g(x)
2x²-3x+7+x²
3x²-3x+7
(fg)(x)
(2x²-3x+7)(-x²)
-2x⁴+3x³-7x²
f/g(x)=-2x²+3x-7/x²
Hence, the functions (f+g)(x)=x²-3x+7, (f-g)(x)=3x²-3x+7, (fg)(x)=-2x⁴+3x³-7x² and (f/g)(x)=-2x²+3x-7/x²
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Claire buy a pair of earring for $4, a necklace for $10, and a ring for $7. She ha a 30% off coupon for her whole tranaction. What i her total if the ale tax i 6. 35%?
If the sales tax is 6. 35% then Claire's total is $15.63
In this questiion we have been given Claire buys a pair of earrings for $4, a necklace for $10, and a ring for $7.
So, her total purchase is:
4 + 10 + 7 = 21 dollars
She has a 30% off coupon for her whole transaction.
We find the 30 percent of 21
(30/100) * 21 = 6.3 dollars
So, she will get discount of 6.3 dollars.
So, the amount would be,
21 - 6.3 = $14.7
The sales tax is 6. 35%
Now we find 6.35 percent of 14.7
6.35% of 14.7
= 0.0635 × 14.7
= 0.933
So, the total purchase amount would be,
$14.7 + $0.933 = $15.63
Therefore, the total is $15.63
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A vertical number line is given. A vertical number line starting at negative 9 with tick marks every one-half unit up to 2. The value negative 5.5 is labeled. The change in the value of a stock was plotted on a number line in the image. If 0 represents the original cost, which of the following is true about the plotted value? The stock is −5.5 less than the original value, and the absolute value is 5.5. The stock is 5.5 less than the original value, and the absolute value is 5.5. The stock is −5.5 greater than the original value, and the absolute value is 5.5. The stock is 5.5 greater than the original value, and the absolute value is 5.5.
The correct statement about the plotted value on the number line is given as follows:
The stock is 5.5 less than the original value, and the absolute value is 5.5.
How to interpret the number line and the value plotted?The value plotted on the number line is given as follows:
-5.5.
The fact that the value is negative means that the stock is now less than the original amount, and the amount that it is less is the absolute value of the number plotted.
The absolute value of a number is represented by the number without the signal, hence the absolute value of -5.5 is given as follows:
|-5.5| = 5.5.
(just removed the negative symbol).
Hence the second statement is correct about the interpretation of the number line in this problem.
More can be learned about number lines at https://brainly.com/question/24644930
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