By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. In mathematics, larger than symbol (>), less than symbol (<), less than or equal to a symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), and not equal to a symbol (≠).So, is the artist in profit if he sells 15 necklaces:
The cost to rent a booth is $170.The cost of making a necklace is $3.50.The selling price is $12.Inequality is 12n ≥ 170 +3.50n: (let n = 15)
12n ≤ 170 +3.50n12(15) ≤ 170 +3.50(15)180 ≤ 170 + 52.5180 < 222.5Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.
A single piecewise-defined function f(x) has been
graphed for you on the display to the left.
At how many values c on the interval x€[−6, 4) is it
true that the limx→cf(x) = 1?
Answer: 1
Step-by-step explanation:
[tex]\lim_{x \to -6} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
[tex]\lim_{x \to -1} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.
REINFORCEMENT #1 IN MATHEMATICS 10Please draw and fill the table :)
A set of data is given. It is required to find the first, second, and third quartile.
The given data is:
[tex]2,8,9,10,14,15,16,16,17,17,20[/tex]Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.
The lower half is:
[tex]2,8,9,10,14[/tex]Find the median of the lower half to get the first quartile, Q₁:
Hence, Q₁=9.
Recall that the second quartile Q₂ is the same as the median of the data.
The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Notice that the middle number is 15.
Hence, second quartile Q₂=15.
The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.
The upper half of the data is:
[tex]16,16,17,17,20[/tex]Calculate the median to find the third quartile, Q₃:
It follows that Q₃=17
The complete table is shown below:
ax^2 + bx + c (a in not equal to 0) is a ____?____Select one:a. Quadraticb. Vertexc. Domaind. None of the above
We have the following expression
[tex]ax^2+bx+c[/tex]This can't be a vertex, since, in geometry, a vertex is a point where two or more elements meet.
A domain is not either, since, in mathematics, the domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
The Standard Form of a Quadratic Equation looks something like this:
[tex]ax^2+bx+c=0[/tex]Where a, b, and c are known values and a cannot be 0.
In conclusion, the answer is that is a Quadratic
a city has two water towers. one tower holds 8.4 x 103 gallons of water and the other tower holds 9.5 x 104 gallons of water. what is the combined water capacity of the two towers in scientific notation?
Total capacity the tower holds 1.034 x 10^5 gallons of water
One tower holds 8.4 x 10^3 gallons of water
Other tower holds 9.5 x 10^4 gallons of water
The combined water capacity of the two towers in scientific notation is,
Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3
= 9.5 x 10^4 + 0.84 x 10^4
= 10.34 x 10^4
= 1.034 x 10^5
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PLEASE HELP 50 POINTS
Use matrices A, B, and C to find the following:
A+B
C-B
A+B+C
By solving matrices we get,
[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]
A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.
Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.
Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.
When solving by using the matrices solving method we get
[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]
[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]
[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]
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3. Use the following map to calculate distance between the cities. Calculate the distance between Brookline and Charleston.
cooling towers are used to remove or expel heat from a process. a cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. what is the width of the cooling tower at the base of the structure? round your answer to the nearest whole number. 100 meters 50 meters 48 meters 40 meters
The width of the cooling tower at the base of the structure is (D) 40 meters.
Where are cooling towers located?Typically, cooling towers are found on rooftops or other outdoor locations. Lower cooling system efficiency occurs as a result of operation and maintenance specialists commonly ignoring them because they are typically out of sight.Now, calculate the cooling tower's width:
Equation: x2/400 given (y-90)
²/1600=1Calculating the width:
Width of the cooling tower: 2400Width of cooling tower = 22040-meter cooling tower widthTherefore, the width of the cooling tower at the base of the structure is (D) 40 meters.
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Ms. lange drove about 150kms east from la sarre, to senneterre, quebec. she drove another 75kms north to lebel-sur-quevillon, what is the approximate air distance from la sarre to lebel-sur-quevillon
The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.
To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.
When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)
Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.
c² = a² + b²
where a = 150 km and b = 75 km
distance² = 150² + 75²
distance² = 22500 + 5625
distance² = 28125
distance = 167.71 km
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5. suppose waiting time until the next failure of oil pump system is exponentially dis tributed, with mean of 37 hours. the pump is continuously in operation. what is the probability that the system does not fail for 2 days?
The Probability that the system does not fail for 2 days is 0. 053
Given ,
Mean (u) = 37 hours .
Step 1 : Calculate the rate parameter, λ.
λ = 1/ mean
λ = 1/ 37 = 0.02703
Step 2 : Find the probability that the system does not
fall for two days, P ( x[tex]\leq[/tex]2 )
P ( x[tex]\leq[/tex]2 ) .= 1 - e power (lamda(x))
= 1 - e - 2(lamda)
= 1 - e power -2(0. 02703 )
By solving,
P ( x[tex]\leq[/tex]2 ) = 0.05263
P ( x[tex]\leq[/tex]2 ) = 0. 053 [ upto three decimals]
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the distribution of the number of text messages young adults send per day is approximately normal, with a mean of 128 messages and a standard deviation of 30 messages. based on the distribution, what is the percentage of young adults send fewer than 218 text messages?
The percentage of young adults who send fewer than 218 text messages is 99.87%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 218
μ = mean = 128
σ = standard deviation = 30
z-score = (218 - 128) / 30
z-score = 90 / 30
z-score = 3
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 3
probability = 0.9987
To get the percentage, multiply the probability by 100.
percentage = probability x 100
percentage = 0.9987 x 100
percentage = 99.87%
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True or False: The set of whole numbers is closed under multiplication.
Explanation:
Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.
Examples:
2*3 = 65*7 = 3511*12 = 132In other words,
(whole number)*(whole number) = whole number
This is why we consider the set closed under multiplication.
Solve using elimination.–10x − 10y = –1010x + 8y = –8
The question asks us to solve the following system of equations by elimination:
[tex]\begin{gathered} -10x-10y=-10 \\ 10x+8y=-8 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -10x-10y=-10\text{ (Equation 1)} \\ 10x+8y=-8\text{ (Equation 2)} \\ \\ \text{Add Equation 1 and 2 together.} \\ \\ -10x-10y+(10x+8y)=-10+(-8) \\ -10x-10y+10x+8y=-10-8 \\ -10x+10x+8y-10y=-18 \\ -2y=-18 \\ \text{Divide both sides by -2} \\ -\frac{2y}{-2}=-\frac{18}{-2} \\ \\ \therefore y=9 \\ \\ \text{Substitute the value of y into equation 1.} \\ -10x-10y=-10 \\ -10x-10(9)=-10 \\ -10x-90=-10 \\ Add\text{ 90 to both sides} \\ -10x=-10+90 \\ -10x=80 \\ \text{Divide both sides by -10} \\ -\frac{10x}{-10}=\frac{80}{-10} \\ \\ \therefore x=-8 \end{gathered}[/tex]
Answer
The solution to the system of equation is:
x = -8
y = 9
Solve for b
-73 = b/7- 81
Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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If the equation be -73 = b/7- 81 then the value of b is 56.
What is meant by Linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Solve for b
-73 = b/7- 81
b= 56
-511=b-567
b-567=-511
Hence,
b=-511+567
b=56
Solution 2
Add 81 to both sides.
-73+81= b/7
simplify -73+81 to 8
8=b/7
8*7=b
simplify 8*7 to 56
56=b
switch sides b= 56
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What is the value of q − 7 if q = −17? 24 10 −10 −24
PLEASE HELP!!!
When q = -17, the value of the equation, q - 7 would be: d. -24.
How to Evaluate an Equation?If we are given an equation to evaluate for a given value of a variable, we are to substitute the value of the variable into the equation and solve or simplify.
For example, if an equation is given as 3x + 4, and we are told that the x = 3, to determine the value of the equation, 3x + 4, substitute x = 3 into the equation as:
3(3) + 4
= 9 + 4
= 13
Here, we can now conclude that the value of the equation is 13.
Given the equation, q - 7, to find the value of the equation when q = -17, substitute the value of q into q - 7.
Therefore:
q - 7 = -17 - 7
= -24.
The value of the equation is: d. -24.
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The value of q - 7, when q = - 17 is - 24.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, q = - 17.
∴ q - 7.
To solve our expression we'll substitute the numerical value of q in the given expression.
= (-17) - 7.
= - 17 - 7.
= - 24.
We can also take negative sign common in the second step and distribute them later.
- 17 - 7.
= - (17 + 7).
= - (24).
= -24.
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Sandra purchased $1,200 worth of electronic equipment on her new credit card, with an annual interest rate of 14.99%. If she has no other charges on the card and does not pay off the balance at the end of the month, how much money will she owe the credit card company after 1 month? Estimate the interest using the monthly periodic rate.
Given data:
The given amount of equipment purchased by the Sandra is A=$1,200.
Please help! I’ve tried this a couple times now and still don’t understand it! Math is not my thing.
The function f(z) is graphed below. (Picture below)
a) What is f(0)?
b) What is f(3)?
c) What is f(1)?
Answer:
Step-by-step explanation:
Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16
two lines are perpendicular when their slope is inverted and have the opposite sign
the general form of the equation line is-3,1
[tex]y=mx+b[/tex]where m is the slope
rewrite
[tex]\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=\frac{3x-16}{8} \\ y=\frac{3}{8}x-2 \end{gathered}[/tex]so, the slope 3/8
the slope of the other line is
[tex]\frac{3}{8}\longrightarrow-\frac{8}{3}[/tex]to write the new equation of the line we use the slope and replace the point (-3,1)
[tex]\begin{gathered} (1)=(-\frac{8}{3})(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}[/tex]now, replace b and the slope to create the line
[tex]y=-\frac{8}{3}x-7[/tex]andrea wants to cut a board into three pieces the board is 3 2/3 feet long how long will each piece be
Answer:
7/6 feet
Step-by-step explanation:
The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.
3 + 1/2 = ?
3/1 + 1/2 = ?
6/2 + 1/2 = ?
(6 + 1)/2 = ?
= 7/2
3 + 1/2 = 7/2
In other words, the board is 7/2 feet long.
Now we have to divide by 3 since Andrea is cutting the board in three pieces.
So:
(7/2)/3 or (7/2) ÷ 3 or [tex]\frac{\frac{7}{2}}{3}[/tex] or (7/2) × (1/3)
= 7/(2×3)
= 7/6
So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.
Use matrices to write the equation of the function in the form y = Ax? + Br + C that contains the points (0, 1), (-2, 15), (3,10).
The most appropriate choice for matrices will be given by-
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
What are matrices?
If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.
Here,
The equation is [tex]y =Ax^2 + Bx + C[/tex]
The function contains the points (0, 1), (-2, 15), (3,10).
On putting these coordinates in the equation,
C = 1
[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)
[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)
Here matrix method will be used
Let
[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]
PQ = R
[tex]Q = P^{-1}R[/tex]
Adjoint P =
[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]
Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]
= [tex]2\times 1 - 3 \times (-1)\\5[/tex]
[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]
A = 2, B = -3
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
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Complete Question
Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).
If p and q are integers and pq +p is an odd number, which of the following numbers must be even?
1-p
2-q
3- pq-3
4- p^2
Answer:Answer: number 2 is correct
Use the graph or table to find the equation that represents the relationship.
Answer:
1) y = 3x + 5
2) y = -12x + 2
3) y = 5/4 - 5
4) y = -6x + 3
Step-by-step explanation:
3What is the inverse of the function h(x) = - 2 + 12?h-'(x) =(2
We have the next function
[tex]h(x)=\frac{3}{4}x+12[/tex]First we need to make h(x)=y
[tex]y=\frac{3}{4}x+12[/tex]Then we make x=y and y=x
[tex]x=\frac{3}{4}y+12[/tex]Then we isolate the y
[tex]x-12=\frac{3}{4}y[/tex][tex]4(x-12)=3y[/tex][tex]y=\frac{4(x-12)}{3}[/tex][tex]y=\frac{4x-48}{3}[/tex]Therefore the inverse function is
[tex]h^{-1}(x)=\frac{4x-48}{3}[/tex]are 60/55 and 7/42 porportinal
What is the solution to the inequality? 3(x+5)>12
Answer:
x>-2
Step-by-step explanation:
3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.
given angle 1 is congruent toangle 3 and angle 12 is congruent to angle 8 prove l is parallel to m
Given that;
[tex]\angle1\cong\angle3,\angle12\cong\angle8[/tex]Line a and b are two straight lines cut by two transversal lines l and m.
The tranversal line l shows that;
[tex]\begin{gathered} \angle8\cong\angle6 \\ \end{gathered}[/tex]But also;
[tex]\angle8\cong\angle12[/tex]Thus,
[tex]\angle6\cong\angle12[/tex]Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Thus, line l is parallel to m
Question 5
The equation 2x² - 8x = 10 is rewritten in the form of 2(x-p)²+ q = 0. What is the value of q?
-18
2
-2
18
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation -2x²-8x = 10 consists of the two equations is rewritten in the form of 2(x-p)²+ q = 0. , which are separated by the 'equal' sign.
What are two illustrations of equations?Answer :q = -2
-2x²-8x = 10 (divide both sides by -2)
x² + 4x = -5 (Apply completing the square method)
x² + 4x + (4/2)²= -5 + (4/2)²
x² + 4x + 2²= -5 + 2² (reduce left hand side using a²+2ab+b² = (a+b)² )
(x+2)² = -5 +4
(x+2)² = -1
(x+2)² + 1 = 0 (multiply both sides by -2)
(-2)(x+2)² + 1 (-2) = 0
-2[x - (-2)]² + (-2) = 0 ---> compare this with -2(x-p)² + q = 0
We can see that p = 2 and q = -2
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Lydia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $2.50 per mile. The total fare was $36.60, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.
Answer:
4.10 + 2.50x = 36.60
x = 13 miles
Step-by-step explanation:
I hope this helped
have a good day ^^
The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Area of circle A is 113.04 in²
Area of circle B is 200.96 in²
Area of circle C is 452.16 in²
Area of circle B is 254.34 in²
The number of times that the area of Circle D greater than Circle A is 2.25
What are the areas of the circles?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 3.14R = radiusArea of circle A = 3.14 x 6² = 113.04 in²
Area of circle B = 3.14 x (6 + 2)² = 200.96 in²
Area of circle C = 3.14 x (8 + 4)² = 452.16 in²
Area of circle B = 3.14 x (12 - 3)² = 254.34 in²
Number of time that is the area of Circle D greater than Circle A = 254.34 in² / 113.04 in² = 2.25
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What is the perimeter of this rectangle?
The perimeter of the rectangle is 6.89
Perimeter of the rectangle:
The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.
The formula for the perimeter of the rectangle is
P = 2(l + w)
The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.
Given,
Here we have the graph with the following points:
(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)
Now we need to find the perimeter of the rectangle.
To calculate the perimeter, first we have to find the length and width of the rectangle.
To calculate the length, we have to use the values of x axis,
That is,
=> -3/2 + 7/2
=> (-3+7)/2
=> 4/2
=> 2
Therefore, the length of the rectangle is 2.
Now, we have to find the width of the rectangle using the y axis coordinates,
=> -1 7/9 + 3 2/9
Convert the mixed fraction into normal form, then we get,
=> -16/9 + 29/9
=> (-16 + 29)/9
=> 13/9
Therefore, the width of the rectangle is 13/9
Now, we have to use this to calculate the perimeter of the triangle,
P = 2 (2 + 13/9)
P = 2 ((18+13)/9)
P = 2 (31/9)
P = 62/9
P = 6.89
Therefore, the perimeter of the rectangle is 6.89.
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. Represent Real World Problems Lorena and Benita are saving
money. They began on the same day. Lorena started with $40. Each
week she adds $8. The graph describes Benita's savings plan. Which
girl will have more money in 6 weeks? How much more will she
have? Explain your reasoning.
We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.
We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.
amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88
Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.
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