Answer:
36 ft
Step-by-step explanation:
9x4=36. if the bulletin board is 9ft on each side, (9x4) the amount of border she needs would be 36ft.
A landscaper has enough concrete paving stones to create a patio with an area of at most 250 square feet. The landscaper wants the length of the patio to be six feet longer than three times the width.
Select the statement that accurately describes the situation and justifies a possible width of the patio.
A.
A possible width is 10 feet because w = 10 satisfies 3w2 + 6 ≥ 250.
B.
A possible width is 11 feet because w = 11 satisfies 3w2 + 6w ≥ 250.
C.
A possible width is 8 feet because w = 8 satisfies 3w2 + 6w ≤ 250.
D.
A possible width is 9 feet because w = 9 satisfies 3w2 + 6 ≤ 250.
Answer:
C
Step-by-step explanation:
+) L = 3W + 6
+) L×W = (3W + 6)×W = 3W² + 6W ≤ 250
On the Y axis we have the profit from the trucking company and on the X axis we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
The volume of a pyramid whose base is a right triangle is 108 units^3
. If the two legs of the right triangle measure 8 units and 9 units, find the height of the pyramid.
According to the question the volume formula to find the height of the pyramid is 9 units.
What is formula?Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.
The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h
108 = (1/3) × 36 × h
108 = 12 × h
h = 9 units
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Look at the image provided below
The density of nitrogen in the space will be 3.13 kg/m³
What is density?Density is the ratio of mass to volume of a substance. It is measured in kg/m³.
The volume of the shade part = volume of the cone- volume of the hemisphere
volume of the hemisphere = 2/3 πr³
= 2/3 × 3.14 × 40³
= 401920/3
= 133973.33m³
volume of the cone = 1/3 πr²h
= 1/3 × 3.14 × 40²× 500
= 2512000/3
= 837333.33 m³
volume of the shaded part = 837333.33-133973.33 = 703360m³
The density of the space = 2200000/703360
= 3.13kg/m³.
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Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?
In statistics, critical value is value that is used to determine whether to reject null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
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The annual profits for a company are given in the following table, where x represents the number of years since 2005, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2016, rounded to the nearest thousand dollars.
The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars.
What is data in mathematics?Data in math is information that is organized and analyzed to help draw conclusions and make predictions. It can be numerical, or it can be non-numerical, such as words or images. Data can be collected through experiments, surveys, or other methods. Data analysis helps mathematicians to uncover patterns, relationships, and trends that could not be seen through traditional methods. Data can be used to solve problems, make decisions, or create models to help explain the behavior of a system.
x y
0 1150
1 1550
2 1850
3 2150
4 2500
Linear regression equation:
y = 442.86x + 1150
Projected profit for 2016 (in thousands of dollars):
7,427.
The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars. Using this equation, the projected profit for 2016 (in thousands of dollars) can be calculated to be 7,427. This shows that the company's profits are expected to increase steadily over time.
It is important to note that the linear regression equation is just a model of the data and may not accurately predict the actual profits in 2016. Other factors such as economic conditions, competition, and market trends can all affect a company's profits and should be taken into consideration when making any predictions.
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Consider 8 = − 2/3x. 1 Which is the BEST first step to take when solving the given equation?
the equation for a projectile's height versus time is h(t)=-16t^2+v0t+h0 a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. what is the maximum height, in feet, the ball will attain?
round to the nearest whole foot
Therefore, the maximum height the ball will attain is 221.875 feet.
We are given the equation for the height of a projectile as a function of time:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:
[tex]h(t) = -16t^2 + 120t + 2[/tex]
To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:
[tex]t = -b/2a[/tex]
where a = -16 and b = 120. Substituting these values, we get:
[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]
To find the corresponding maximum height, we can plug this value of t back into the equation:
[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]
Therefore, the maximum height the ball will attain is 221.875 feet.
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A crew painted a house. Each of the 4 crew members started with the same number of gallons of paint, and each used 12 gallons. When they were finished, there were 24 gallons left over. How many gallons did each crew
member have at the start?
Answer:
18gall
Step-by-step explanation:
BELLRINGER:
In the function below, b is a constant. If f (2) = 0, what is the value of f(-1)?
f(x)=3/2 x + b
Answer:
-9/2
Step-by-step explanation:
f(x) = 3/2x + b
f(2) = 0
Find out what the variable b is.
3/2(2) + b = 0
3 + b = 0
Subtract 3 from both sides.
b = -3
f(-1) = 3/2(-1) - 3
f(-1) = -4.5
-4.5 = -9/2
A flag in the shape of a right triangle has one side length equal to 4.0 feet, and the length of the hypotenuse is 6.5 feet. Approximately what are the three interior
angles of this triangle?
A.10°,22°,90°
B.30°,60°,90°
C.38°,52°,90°
D.40°,65°,90°
The three interior angles of the triangle are answer (C): 38°, 52°, 90
What do you understand by the term Hypotenuse in Trigonometry ?Hypotenuse: This is the largest side of the triangle. It is also opposite the right angle of the triangle. Base: The side on which a right triangle stands is called its base. We can use trigonometric ratios to find the angles of this right triangle.
Let's call the angle between the hypotenuse and the side of the 4 legs "A" and the angle between the hypotenuse and the other leg "B". Then we have:
sin(A) = opposite/hypotenuse = 4/6.5 = 0.615
cos(A) = adjacent/hypotenic =√ (1 - sin²(A)) = 0.789
tan(A) = opposite/adjacent = 4/√(6.5² - 4²) = 0.646
We also have:
sin(B) = opposite/hypotenuse = 6.5/6.5 = 1
cos(B) = adjacent/hypotenuse = 4/6.5 = 0.615
tan(B) = opposite/adjacent = √(6.5² - 4²)/4 = 1.361
Since angle A is opposite the 4-foot side, it is the smallest angle of the triangle. Therefore, the answer must be either A or C.
To distinguish between the two, we can use the fact that the sum of the angles of a triangle is always 180 degrees. So if you add A, B and the right angle (90 degrees) you should get 180 degrees.
A + B + 90 = 180
A + B = 90
Using the values we calculated for the tangent of A and B, we can solve for their sum:
tan(A) + tan(B) = 0.646 + 1.361 = 2.007
We can then use the inverse tangent function to find the angle whose tangent is 2.007:
[tex]tan^-1(2.007)[/tex] = 63.4 degrees
Since A B = 90, we can subtract 63.4 from 90 to find the value of angle A:
A = 90 - 63.4 = 26.6 degrees
Therefore, the answer is C: 38°, 52°, 90
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Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used.
2
one half
4
one fourth
Answer: there all divided by 2
so it's 2
given that log x = 3, log y=7
PLEASE HELP SOLVE 20 PTsS
A card is dealt from a complete deck of fifty-two playing cards (no jokers). Use probability rules (when appropriate) to find the probability that the card is as stated. (Count an ace as high. Enter your answers as fractions.)
What is
both under a 3 and above an 8
The probability of the card is as stated at 7/52, which simplifies it to 1/8.
What is probability?Probability is the study of the possibility that an event or phenomenon will occur. It can be expressed numerically as a number between 0 and 1, where 1 implies a certain outcome of an event and 0 denotes an inconceivable chance of occurrence.
There are four cards that are under a 3 (the 2, the Ace, the King, and the Queen) and four cards that are above an 8 (the 9, the 10, the Jack, and the Queen). However, the Queen is both above an 8 and under a 3, so we need to subtract one from the total count.
Therefore, the number of cards that are either under a 3 or above an 8 is 4 + 4 - 1 = 7.
Therefore, the probability that the card is as stated is 7/52, which simplifies it to 1/8.
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Use the formula z = x-μ/σ
and the given information to find the missing piece of information
1. Given x = 75, μ = 80, o = 5, find z.
The missing piece of information z-score is -1.
Explain information
Information refers to data or knowledge that has been transmitted or received. It can be expressed in different forms, including numerical data, text, images, or sound. The information serves as a basis for understanding, analysis, and decision-making. It can be processed and analyzed using mathematical methods and tools such as statistics, probability, and data analysis. The effective management and utilization of information are essential for progress and innovation in many fields, including science, technology, and business.
According to the given information
Using the formula z = (x - μ) / σ, we can plug in the given values and calculate:
z = (75 - 80) / 5
z = -1
Therefore, the z-score is -1.
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Consider the two-node circuit shown below:
The node voltages V₁ and V₂ (in volts) satisfy the following system of equations:
15V₁ = 7V₂ + 60
3V₂ + 10 = 3V₁
a) Write the system of equations in the matrix form AV-B, where V = [V1, V2]
b) Find V₁ and V₂ using the matrix algebra method. Perform all matrix computations and show all steps.
a) The system of equations can be written in the matrix form AV-B as: | -3 3 | | V2 | | -10 |
b) V1 = 369/22 volts and V2 = -51/22 volts.
What is matrix?A matrix is a rectangular array of numbers or symbols, arranged in rows and columns. Matrices are often used in mathematics, science, engineering, and other fields to represent and manipulate data, perform operations, and solve equations. The size of a matrix is determined by the number of rows and columns it contains, and is usually written in the form "m x n", where "m" is the number of rows and "n" is the number of columns. Matrices can be added, subtracted, multiplied, transposed, and inverted, and can be used to represent a wide range of mathematical objects, including systems of linear equations, transformations, and graphs.
a) The system of equations can be written in the matrix form AV-B as:
| 15 -7 | | V1 | | 60 |
| | x | | = | |
| -3 3 | | V2 | | -10 |
b) To solve for V1 and V2 using matrix algebra, we can use the inverse of matrix A as follows:
AV = B
V = A⁻¹B
First, let's find the inverse of matrix A:
A = | 15 -7 |
| -3 3 |
To find the inverse of A, we need to calculate the determinant of A:
det(A) = (15)(3) - (-7)(-3) = 66
Then, we can find the inverse of A as follows:
A⁻¹ = (1/det(A)) x | 3 7 |
| 3 15 |
Now, we can solve for V by multiplying A⁻¹ and B:
| V1 | | 3 7 | | 60 | | 369/22 |
| | = | | x | | = | |
| V2 | | 3 15 | |-10 | | -51/22 |
Therefore, V1 = 369/22 volts and V2 = -51/22 volts.
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question is in the picture
The calculated value of the volume of the solid is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
Finding the volume of the solidTo find the volume of the solid when the region R is rotated about the horizontal line y = -1, we can use the method of cylindrical shells.
The height of each cylindrical shell will be the difference between the function y = 2x and the horizontal line y = -1, which is (2x + 1).
The radius of each cylindrical shell will be the distance from the axis of rotation (y = -1) to the function y = x².
This distance is given by (x² + 1).
The thickness of each cylindrical shell will be dx.
Thus, the volume of the solid can be expressed as:
V = ∫[0,2] (x² + 1) - (2x + 1) dx
Hence, the expression is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
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Please help me with this problem
The area of the poster in square meters is 0.014 m².
How to calculate the areaIt should be noted that to convert the area from square centimeters to square meters, we need to divide by 10,000 (since 1 square meter is equal to 10,000 square centimeters).
The area of the poster is:
14 cm × 10 cm = 140 cm²
To convert this to square meters, we divide by 10,000:
140 cm² ÷ 10,000 = 0.014 m²
Therefore, the area of the poster in square meters is 0.014 m².
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Heather has a rectangular poster that is 14 centimeters long and 10 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
The thickness of a one-dollar bill is 1.1 × 10-4 meters. Each measurement below is the thickness of a stack of one-dollar bills. Drag each measurement to the correct dollar amount.
Thickness of 10 dollar bill is 1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill is 1.375×10⁻¹meters
Thickness of 137 dollar bill is1.507 ×10⁻²meters
Define thicknessThickness is the measure of the distance between opposite surfaces of an object. In other words, it is the distance between two parallel planes that bound an object or material. Thickness is often used to describe the dimension of a flat or sheet-like object, such as paper, fabric, or metal, as well as the distance between the front and back surfaces of a three-dimensional object, such as a book or a wall. Thickness can be measured in units such as millimeters, inches, or micrometers.
The thickness of a one-dollar bill is 1.1 × 10⁻⁴ meters
Thickness of 10 dollar bill=10×1.1 × 10⁻⁴
=1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill=1.25 × 10³ ×1.1 × 10⁻⁴
=1.375×10⁻¹meters
Thickness of 137 dollar bill=137 ×1.1 × 10⁻⁴
=1.507 ×10⁻²meters
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Evaluate the expression without using a calculator. sin−1(cos(2)) sin^−1 (cos( − /2))
The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
Describe Algebraic Expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.
Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.
To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).
cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.
Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.
Substituting this value into the expression, we get:
sin⁻¹(0) = 0
Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
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you are opening an ice cream shop. The new equipment and ice cream for the shop will cost $6,000. The supplier requires a down payment of 25% of the total cost at the time of purchase. What is the balance you owe after making the down payment?
Answer:
$4500
Step-by-step explanation:
Find out 25% of $6000. 25/100 × 6000 = 1500
6000 - 1500 = 4500
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
find the surface area of a cylinder with a. height of 7 m and a base radius of 3 m.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the base, h is the height, and π is approximately 3.14.
Plugging in the values given, we get:
SA = 2π(3²) + 2π(3)(7)
SA = 2π(9) + 2π(21)
SA = 18π + 42π
Adding these two terms, we get:
SA = 60π
So the surface area of the cylinder is 60π square meters. If you want a numerical approximation, you can use a calculator and round to an appropriate number of decimal places.
Drag each coordinate pair to the correct location on the figure. Not all coordinate pairs will be used.
The ratios of the line segments are given below.
Determine the coordinates of point B and point D.
(1,2) (-4,6) (5,0)
(-2,-6)
AB: BC = 2:1
AC: CD H 3:2
(-1,0)
(-6,10)
(-1,-4)
B
(-3,4)
The coordinate pairs to the correct location are:
B: (-4, 6)
D: (-1, 0)
What is coordinate pair?A coordinate pair, also known as an ordered pair, is a pair of numbers used to locate a point on a two-dimensional plane. The two numbers in the pair represent the horizontal and vertical distances from the origin (0, 0) on the plane, and are written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.
AC: Δx = -3 - (-6) = 3
Δy = 10 - 4 = 6
AB:BC = 2:1
B: x = -6 + (2/3 × 3) = -4
y = 10 - (2/3 × 6) = 6
so, B: (-4, 6)
AC:CD = 3:2
AC: Δx = 3, Δy = 6
So, CD: Δx = 3 × 2/3 = 2
Δy = 6 × 2/3 = 4
D: x = -3 + 2 = - 1
y = 4 - 4 = 0
Thus, D: (-1, 0).
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k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
For this discussion post, we are going to create a linear regression model from a set of data. Suppose we get a job working for a company that provides their employees with company stock every year they work with the company. The amount of stock earned may be based on a few other variables, but all we are looking at right now is time served with the company. Here is the data we collected:
The linear regression model from a set of data is y =5.2956+4.0946*X.
What is linear regression model?A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.
The regression line is determined using the formula:
y = bo + b1 X
Now, using the table we have:
sum of (x) = ∑x = 103
sum of (y) = ∑y = 480
Calculating the squares we have:
sum of (x^2)= ∑x² = 1073
sum of (y^2)= ∑y² = 22868
Multiplying the variables we have:
sum of (x*y)= ∑x*y = 4939
mean(x)= ∑x/n = 9.3636
mean(y)= ∑y/n = 43.6364
Now, the intercept is given as:
intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²
Substituting the values we have:
intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2
intercept (bo) = (515040-508717) / (11803-10609)
intercept (bo) = 5.2956
The slope is given as:
slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²
Substituting the values we have:
slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2
slope (b1) = (54329-49440)/(11803-10609)
slope (b1) = 4.0946
regression equation is, y = bo + b1 X
Substituting the values we have:
y =5.2956+4.0946*X
Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.
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The complete question is:
Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
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Rewrite in simplest terms: 4(0.7n-6n-0.3)-0.4n
Answer:
21.6n-1.2
Step-by-step explanation:
=2.8n-24n-1.2-0.4n
=21.6n-1.2
Consider the two-node circuit shown below:
The node voltages V₁ and V₂ (in volts) satisfy the following system of equations:
15V₁ = 7V₂ + 60
3V₂ + 10 = 3V₁
a) Write the system of equations in the matrix form AV-B, where V = [V1, V2]
b) Find V₁ and V₂ using the matrix algebra method. Perform all matrix computations and show all steps.
Using matrix form, the solution to the system of linear equations are 55/12 and 5/4
What is the solution to the system of linear equationsa) To write the system of equations in matrix form, we can use the coefficient matrix A and the vector of constants B:
| 15 -7 | | V₁ | | 60 |
| -3 3 | * | V₂ | = | -10 |
b) To find V₁ and V₂, we can use matrix algebra to solve the equation AV = B for V:
AV = B
V = A^-1 B
First, we need to find the inverse of the coefficient matrix A:
| 15 -7 | | 3 7 |
| -3 3 | → | -5 15 | * (1/60)
So, A^-1 = (1/60) * | 3 7 | |-5 15 |
Solving for both equations
v₁ = 55/12, v₂ = 5/4
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If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order