The sum of the entries in C is dependent on the particular matrix A and vector B given in the problem.
If the only solution of the system of linear equations AX = B is the zero matrix, it implies that the system is inconsistent. In other words, there are no solutions that satisfy the equation AX = B other than the trivial solution (zero matrix).
In this case, when we form the augmented matrix [A|B] and row-reduce it to its reduced row echelon form (RREF), we will obtain a row of the form [0 0 0 ... 0 | c], where c is a non-zero entry.
The RREF of [A|B] is [I|C] if and only if the row of zeros in the RREF corresponds to the rightmost column of the augmented matrix.
Since the row of zeros in the RREF is [0 0 0 ... 0 | c], the sum of the entries in the column C is equal to c. However, we cannot determine the exact value of c without additional information about the specific matrix A and vector B.
Therefore, the sum of the entries in C is dependent on the particular matrix A and vector B given in the problem.
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Solve for u. Show all work, be sure to use the equation editor.
Help will mark brainliest
Answer:
u = 2√3 ≈ 3.46410162
Step-by-step explanation:
Because this is a right triangle, you can use the trigonometric formulas:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
Here, we have the measure of an angle, 60°. Side u is opposite to it and the hypotenuse, 4, is given. We can use these numbers to work with:
sine = opposite side/hypotenuse
sin(60) = u/4
sin(60)/1 = u/4
Cross multiply:
u = 4 (sin(60))
Input into calculator:
u = 2√3 ≈ 3.46410162
A 4 in. by 5 in. photo is enlarged so that its width (shorter dimension) is 5 in.
What is the length of the enlarged photo?
5.25 in.
7 in.
6.25 in.
6 in.
========================================================
Explanation:
The jump from 4 inches to 5 inches is 5/4 = 1.25
In other words, 4*1.25 = 5
So we need to multiply every dimension by the scale factor 1.25 to enlarge the image. The 5 inch dimension then goes to 5*1.25 = 6.25 inches
----------
Here's another way you can solve
(old width)/(old length) = (new width)/(new length)
4/5 = 5/x
4x = 5*5
4x = 25
x = 25/4
x = 6.25
find the slope (-2,-4) (-5,5)
Answer:
Your answer would be Slope m = -3
Step-by-step explanation:
Step 1: Graph the points on a coordinate plane( refer to image!)
Whenever your trying to find a slope of 2 order pairs, remember this
m = rise/run. ( Slope = rise over run.) = Δy/Δx
Now we solve:
M = rise/run = Δy/Δx
M = y2 - y1/x2-x1
M = 5 - (-4) / -5-(-2)
So we get M = 9/-3 and 9 divided by -3 is -3
So, the slope of (-2,-4) and (-5,5) is -3.
The scale factor of two similar polygons is given. Find the ratio of their perimeters and the ratios of their areas.
1) 3:1
2) 7/4
The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,
To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.
1) So, perimeter = 3:1
The ratio of areas between two similar polygons is equal to the square of the scale factor.
Since the scale factor is 3:1, the ratio of their areas is:
(Ratio of areas) = (Scale factor)² = 9/1 = 9:1
Similarly,
2) Perimeter = 7:4
Area = 49/16
Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.
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Write a polynomial function that meets the stated condition.
The zeros are -2/3 and , and the constant term of the polynomial is -10.
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The zeros are -2/3. Then the factor of the polynomial is given as,
x = - 2/3
3x = - 2
3x + 2 = 0
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be given as,
p(x) = 3x + 2 - 10
p(x) = 3x - 8
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
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leah has 28 more marbles than dan. 1 3 of the number of marbles leah has is equal to 4 5 of the number of marbles that dan has. find the number of marbles that leah has.
The number of marbles that Leah has is: 48 marbles
Information about the problem:
Leah = xDan = x - 281/3 x = 4/5 (x-28)To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.Solving the equation we have:
1/3 x = 4/5 (x-28)
Simplifying the equation we have:
5(1x) = 3*[4*(x-28)]
5x = 12(x-28)
5x = 12x-336
336 = 12x-5x
7x = 336
x = 336/7
x = 48
Leah = x
Leah = 48
Dan = x - 28
Dan = 48-28
Dan = 20
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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How to Convert Roman Numerals to Numbers?
Answer:
add the values of the symbols or symbol pairs
Step-by-step explanation:
You want to know how to convert Roman Numerals to decimal numbers.
Characters and valuesThe symbols used in Roman Numerals are {I, V, X, L, C, D, M}. Respectively, they have values {1, 5, 10, 50, 100, 500, 1000}. The values of these symbols are multiplied by 1000 by an overline.
ConversionA number can be converted to decimal by working right to left. In general, the value of a symbol is added to the total. When a symbol of lesser value than the previous one is encountered, its value is subtracted. (Usually, the value being subtracted is a power of 10.)
ExamplesI = 1II = 1 + 1 = 2IV = 5 - 1 = 4V = 5IX = 10 -1 = 9MCMLXIX = 10 -1 +10 +50 +1000 -100 +1000 = 1969Aliases exist. Without knowledge of the rules the Romans used for writing their numbers, we can invent numbers that can be written two or more ways:
1950 = MLM = MCML
As we noted above, the form MLM = 1950 would probably not be used, since the subtracted L is not a power of 10.
We expect that 1999 would likely be written MCMXCIX, rather than MIM. That way, the character being subtracted is not less than 10% of the character it is subtracted from.
__
Additional comment
Use of an overline is not the only way that the system is extended to higher values. Different notations are found in different contexts.
The basic idea of Roman Numerals is to express value by the character used, rather than its location in a number. It is not a "place value" system.
There is no zero. There are no negative numbers.
The reference to "symbol pairs" in the Answer section above is to recognize a pair of symbols in which the one on the left is subtracted.
What is b squared + 12 if b = 102?
I give brainliest if you right
Answer:
10416
Step-by-step explanation:
102 squared is 10404. 10404 + 12 = 10416
a radio tower is located 350 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 42 ∘ and that the angle of depression to the bottom of the tower is 20 ∘ . how tall is the tower? round to the nearest foot.
In linear equation, $ 442.54 tall is the tower.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Suppose A is the window, B is the top of the tower, C is the bottom of the tower, and D is the point on the tower at the same horizontal level as the window.
Find BD, DC then add these together to give this°.
For BD : AD is 350 ft, the angle CAD is 42.
So BD/350 = tan 42°.
BD = 0.9004 × 350
BD = 315.14
AD/350 = tan20°
AD = 0.364 × 350
AD = 127.4
AD + BD = 315.14 + 127.4 = $ 442.54
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What is 2^2 mean? In specific, what does the ^ mean?
Answer:
the "^" symbol is called the exponent symbol
exponent is fast multiplication
in other words x^y means multiplying 'x' y times
Step-by-step explanation:
Can someone please help me I’m stuck I don’t know what to do
Answer: its the 2nd one
Step-by-step explanation:
Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.
Answer:
x³+y³+z³=k , k from 1 to 100. To Find : x, y, and z. Solution: This Question can have lot of solutions as constraints are very less.
Step-by-step explanation:
Answer in the figure Hope it helps youAt an animal rescue, 80% of the animals are dogs and 20% of the animals are cats. If the average age of the dogs is 7 months and the average age of the cats is 12 months, what is the overall average age of the animals at the rescue?
A) 7 months
B) 8 months
C) 9 months
D) 10 months
Answer: b
Step-by-step explanation: 7% of 80 = 5.6
12% of 20=2.4
5.6+2.4=8.0
To calculate the overall average age of the animals at the rescue, we need to consider the proportions of dogs and cats and their respective average ages.
Let's calculate the overall average age:
Average age of dogs = 7 months
Average age of cats = 12 months
Proportion of dogs = 80% = 0.8
Proportion of cats = 20% = 0.2
Overall average age = (Proportion of dogs * Average age of dogs) + (Proportion of cats * Average age of cats)
= (0.8 * 7) + (0.2 * 12)
= 5.6 + 2.4
= 8
Therefore, the overall average age of the animals at the rescue is 8 months.
The correct answer is B) 8 months.
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Marcus has three random samples of the same size from a population of 700 people. In one sample, 53% of people have a library card. In another, 51% of people have a library card. In the third, 43% have a library card. Based on the three samples, how many people with a library card should he expect are in the population? Justify your answer.
Answer:
477
Step-by-step explanation:
hii please help i’ll give brainliest
Answer:
Oh THIS IS B TRUST I HAD DONE THIS BEFOR
I REALLY NEED BRAINLIST CAN U GIVE ME BRAINLIST PLZZZZZZZZZZZZz
Step-by-step explanation:
How many solutions does the system have? y=4x-8 4y=4x-8
Answer:
There is one solution (x=2, y=0)
Step-by-step explanation:
y=4x-8
4y=4x-8
Divide the second equation by 4
y = x - 2
Set the two equations equal
4x - 8 = x-2
Subtract x from each side
3x -8 = -2
Add 8 to each side
3x = 6
Divide by 3
x = 2
Now find y
y = x-2
y = 2-2=0
Answer:x=2,y=0
Step-by-step explanation:
4(4x-8)=4x-8
16x-4x=32-8
12x=24
X=2
Y=0
Please help me i need help with this please give me the answer
Part A:
$8.00+(r⋅$1.40)
Part B:
($26.00-($8.00)÷$1.40)=5
He can go on 5 rides.
Michael has $1,089.17 in his checking account. He is going to spend $525.20 on a new television and spend the rest on speakers that cost $49.00 each. Which of the following inequalities would determine the maximum number of speakers (y) Michael can buy without spending more money than is in his account?
A.$525.20 + $49.00(y) < $1,089.17
B. $1,089.17 + $525.20 > $49.00 + y
C. $525.20 < $49.00(y) + $1,089.17
D. $525.20 + $49.00 + y < $1,089.17
Answer:
The answer is A.
Michael wants to spend less money than his account hold, so the inequality must include " > 1,089.17. The inequality should also include 525.20 as the cost of the TV and 49y as the number and cost of the speakers.
Answer:
525.20 + 49 y ≤1089.17
Step-by-step explanation:
The cost of the tv plus the cost of the speakers times the number of speakers must be less than or equal to the amount in the account
525.20 + 49 y ≤1089.17
Name all the sets of numbers to which each real number belongs. Check all that apply. 4/7
Answer:
What are you talking about .
Step-by-step explanation:
If ƒ(x) = 2x2 – 3x, what is the value of ƒ(5)?
Answer:
35
Step-by-step explanation:
Finding a parametric description of the solution set of a linear system is the same as solving the system.Is this statement true or false?
A parametric description of the solution set of a linear system is the same as solving the system is the false statement.
If a linear system has at least one solution, only then can the solution set be stated using a parametric description. The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set. You'll discover what a solution set is in this tutorial and witness an example. By combining two equations with two variables into one equation with one variable, we can solve a system of equations. Since there are two variables in each equation in the system, replacing a variable with an expression can help minimize the number of variables in an equation.
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Keiko tosses one penny and Ephraim tosses two pennies. The probability Ephraim gets the same number of heads that Keiko gets is
(A)1/4
(B)3/8
(C)1/2
(D)2/3
(E)3/4
The probability that Ephraim gets the same number of heads that Keiko gets is (A)1/4.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Given that Keiko tosses one penny and Ephraim tosses two pennies.
We need to find the probability Ephraim gets the same number of heads that Keiko gets;
Probability = 1/4 chance for Ephraim
Probability = 1/2 chance for Keiko
Hence, the probability that Ephraim gets the same number of heads that Keiko gets is (A)1/4.
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5 ratio 4 = 35 ratio x
Answer:
5 ratio 4 is
35 ratio 28
they both multiply by 7.....
Answer:
\(\large \boxed{x=28}\)
Step-by-step explanation:
\(5:4=35:x\)
Ratios can be expressed as fractions.
\(5/4=35/x\)
Cross multiply.
\(5 \times x = 4 \times 35\)
\(5x=140\)
Divide both sides by 5.
\((5x)/5=140/5\)
\(x=28\)
Divide following polynomials 5x2 - 18x-27/x-5
Answer:
\(\frac{5x^{3}-18x^{2} -5x-27 }{x}\)
Step-by-step explanation:
16. James is making some trail mix. He needs 4 ounces of peanuts for every 7 ounces of M&M's.
How many cups of peanuts will he need if he has 84 ounces of M&M's?
Answer:
48
Step-by-step explanation:
84/7 = 12
12*4 = 48
A 10-pound bag of grass seed will cover an area of about 4000 square feet. The relationship between pounds (p) of grass seed and area (a) can be written as a = kp. What is the value of k? what does it represent
Answer:
it represent the 10 pound and 4000 multiply = ans
Solve by factoring. Check your answer.
\(x^2-4x=0\)
Please show all work. Thanks!!!
Answer:
x=0 or x=4
Step-by-step explanation:
Lets Solve!
First we need to factor the left side of the equation. Both terms include x.
\(x^2-4x =0\)
\(x(x-4) =0\)
If we multiplied x by (x-4) we would be back at \(x^2-4x =0\).
Set factors equal to 0.
x=0 or x−4=0
x=0 or x=4
Woohoo! Brainliest Appretiated! Hope I helped!
Answer:
\(x=0,4\)
Step-by-step explanation:
Factor out the common terms from x²-4x. You can factor out x:
\(x(x-4)=0\)
Multiplication can be seen as (_)(_). Rewrite:
\((x)(x-4)=0\)
Set both equal to 0:
\(x=0\\\\x-4=0\)
Simplify the second equation:
\(x-4=0\\\\x-4+4=0+4\\\\x=4\)
So, x=0 or x=4
:Done
Respond to the following in a minimum of 175 words: Models help us describe and summarize relationships between variables. Understanding how process variables relate to each other helps businesses predict and improve performance. For example, a marketing manager might be interested in modeling the relationship between advertisement expenditures and sales revenues. Consider the dataset below and respond to the questions that follow: Advertisement ($'000) Sales ($'000) 1068 4489 1026 5611 767 3290 885 4113 1156 4883 1146 5425 892 4414 938 5506 769 3346 677 3673 1184 6542 1009 5088 Construct a scatter plot with this data. Do you observe a relationship between both variables? Use Excel to fit a linear regression line to the data. What is the fitted regression model? (Hint: You can follow the steps outlined in Fitting a Regression on a Scatter Plot on page 497 of the textbook.) What is the slope? What does the slope tell us?Is the slope significant? What is the intercept? Is it meaningful? What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us? Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?
Yes, there is a relationship between advertisement expenditures and sales revenues. The fitted regression model is: Sales = 1591.28 + 3.59(Advertisement).
1. To construct a scatter plot, plot the advertisement expenditures on the x-axis and the sales revenues on the y-axis. Each data point represents one observation.
2. Use Excel to fit a linear regression line to the data by following the steps outlined in the textbook.
3. The fitted regression model is in the form of: Sales = Intercept + Slope(Advertisement). In this case, the model is Sales = 1591.28 + 3.59
4. The slope of 3.59 tells us that for every $1,000 increase in advertisement expenditures, there is an estimated increase of $3,590 in sales.
5. To determine if the slope is significant, perform a hypothesis test or check if the p-value associated with the slope coefficient is less than the chosen significance level.
6. The intercept of 1591.28 represents the estimated sales when advertisement expenditures are zero. In this case, it is not meaningful as it does not make sense for sales to occur without any advertisement expenditures.
7. The value of the regression coefficient, r, represents the correlation between advertisement expenditures and sales revenues. It ranges from -1 to +1.
8. The value of the coefficient of determination, r^2, tells us the proportion of the variability in sales that can be explained by the linear relationship with advertisement expenditures. It ranges from 0 to 1, where 1 indicates that all the variability is explained by the model.
9. To predict sales when the business spends $950,000 in advertisement, substitute this value into the fitted regression model and solve for sales. This will help determine if the model underestimates or overestimates sales.
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The function below has at least one rational zero.
Use this fact to find all zeros of the function.
g(x) = 5x4 +38x° +18x² – 22x–7
Answer:
\(x=-7,x=-1,x=-0.289898,x=0.689898\)
or \(x=-7,x=-1,x=\frac{1}{5}-\frac{\sqrt{6}}{5},x=\frac{1}{5}+\frac{\sqrt{6}}{5}\)
Step-by-step explanation:
Factor by grouping
\(g(x)=5x^4+38x^3+18x^2-22x-7\\\\g(x)=5x^4+33x^3-15x^2-7x+5x^3+33x^2-15x-7\\\\g(x)=x(5x^3+33x^2-15x-7)+1(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+35x^2-2x^2-14x-x-7)\\\\g(x)=(x+1)(5x^2(x+7)-2x(x+7)-1(x+7))\\\\g(x)=(x+1)(x+7)(5x^2-2x-1)\\\\0=(x+1)(x+7)(5x^2-2x-1)\\\)
We can easily see that the first two zeroes are \(x=-1\) and \(x=-7\), however, the third zero will need the help of the quadratic formula:
\(0=5x^2-2x-1\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(5)(-1)}}{2(5)}\\\\x=\frac{2\pm\sqrt{4+20}}{10}\\ \\x=\frac{2\pm\sqrt{24}}{10}\\ \\x=\frac{2\pm2\sqrt{6}}{10}\\ \\x=\frac{2}{10}\pm\frac{2\sqrt{6}}{10}\\ \\x=\frac{1}{5}\pm\frac{\sqrt{6}}{5}\\\\x_1\approx0.689898\\\\x_2\approx-0.289898\)
Therefore, the zeroes of the function are \(x=-7,x=-1,x=-0.289898,x=0.689898\)
Due to an unforeseen case of asthma, Big Wolf Demolition has to buy a wrecking ball. The ball, along with its equipment, will cost $10,000. The cash flows resulting from the investment are as follows: Year 1: $6,000; Year 2: $7,500; Year 3: $7,000; Year 4: $2,000. Calculate the IRR of the project
The project is expected to generate a return of 16.1% per year, which is higher than the company's cost of capital.
To calculate the IRR of the project, we need to find the discount rate at which the present value of the cash inflows equals the initial cost of the investment. We can use the following formula to find the IRR:
NPV = 0 = CF0 + CF1/(1+IRR)¹ + CF2/(1+IRR)² + CF3/(1+IRR)³ + CF4/(1+IRR)⁴
Where:
CF0 = initial investment = -$10,000
CF1, CF2, CF3, CF4 = cash flows in years 1, 2, 3, and 4, respectively
IRR = the discount rate we want to find
Using the given values, we can plug them into the formula and solve for IRR using a financial calculator or Excel. Alternatively, we can use a trial-and-error method to find the discount rate that makes NPV equal to zero.
Here is one way to solve for IRR using Excel:
In Excel, create a new spreadsheet.
In cells A1 to A5, enter the cash flows: -10000, 6000, 7500, 7000, and 2000.
In cell B1, enter the formula: =IRR(A1:A5)
Press Enter. The IRR of the project is displayed in cell B1 as a percentage.
Using this method, we find that the IRR of the project is approximately 16.1%.
Therefore, the Internal Rate of Return (IRR) of the project is calculated to be 16.1%, which indicates that the project is expected to generate a return that is greater than the cost of capital for the company. Hence, investing in this project is considered financially viable for Big Wolf Demolition.
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