In Exercises 17-24, for each matrix A. find (a) a permutation matrix P such that PA has an LU decomposition and (b) an LU decomposition of PA. -1 2 -2 2 3 5 17. 18. TO 2 26 3 19. 2. 2 -3 - 2 :: 8 to s

If a = -3 when g = 9, the two values for a, which will make g equal 25 will be ± 9/5.

If G is inversely proportional to the square of A, then we can write the relationship as:
G = k/A^2 Where k is a constant.

We can use the given values of A and G to find the value of k:
9 = k/(-3)^2
9 = k/9
k = 81

Now we can use the value of k and the desired value of G to find the values of A:

25 = 81/A^2
A^2 = 81/25
A = ± √(81/25)
A = ± 9/5

So the two values of A that will make G equal 25 are 9/5 and -9/5.

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Answer: About 942.48 pounds

Step-by-step explanation:

The volume of a cylinder is πr²h

Plug in values:

(diameter is 2, so the radius is 1)

Volume = π(1)²6

Volume = 6π

Volume ≈ 18.8496 (to 4 decimal places)

Multiply that by 50:

18.8496 x 50 = 942.48

The smallest cylinder will weigh about 942.48 pounds.

Note the answer may change depending on how many decimal places you were told to go out. The standard is 4 places.

Hope this helps!

The resulting polynomial in descending order is 11x7 + 5x6

To combine like terms and write the resulting polynomial in descending order, we need to first identify the like terms and then add or subtract their coefficients. Like terms are terms that have the same variable and the same exponent.

In this case, the like terms are 2x^(7) and 9x^(7).

We can combine these like terms by adding their coefficients:

2x^(7) + 9x^(7) = 11x^(7)

Now we have:

11x^(7) + 5x^(6)

Since the exponents are different, we cannot combine these terms.

Therefore, the resulting polynomial in descending order is 11x7 + 5x6

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

To use the elimination method to solve the system of equations 7.4x-y=-255 and 12.1x-y=-233, we need to eliminate one of the variables. We can do this by multiplying one of the equations by a constant to make the coefficients of one of the variables the same, and then subtracting the equations.

1. Multiply the first equation by -1 to make the coefficients of y the same:

-7.4x + y = 255

2. Subtract the second equation from the first equation:

-7.4x + y = 255

-12.1x + y = -233

---------------------

4.7x = 488

3. Solve for x:

x = 488/4.7

x ≈ 103.83

4. Substitute the value of x back into one of the original equations to find y:

7.4(103.83) - y = -255

765.342 - y = -255

y = 765.342 + 255

y ≈ 1020.342

5. Round the solution to the nearest whole number:

x ≈ 104

y ≈ 1020

So the solution to the system of equations is (104, 1020).

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1. The equation for the cost of adult tickets is:

$8.97 x number of adult tickets

The equation for the cost of child tickets is:

$6.79 x number of child tickets

The equation for the cost of renting out the theater is:

$190

2. Yes, you can get at least 5 adult tickets and 4 kids tickets.

3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.

4.  It would be a better deal to rent out the theater if you had more than 24 people.

You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.

The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.

Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.

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The answer of the number of offers you received are as follow,

1. Mean is equal to 1.96.

2. Standard deviation is equal to 1.17 (rounded to two decimal places) .

1.Mean (or expected value) is represented by E(X)

Formula of the expected value is,

E(X) = ∑xP(x)

Substitute the value from the table we get,

⇒E(X) = (0)(0.19) + (1)(0.12) + (2)(0.38) + (3)(0.16) + (4)(0.15)

⇒E(X)  = 0 + 0.12 + 0.76 + 0.48 + 0.6

⇒E(X)  = 1.96

2. Standard deviation of the number of offers received ,

⇒ Standard deviation 'σ' = √[ Σ(x - E(X))² P(x) ]

Substitute the values from the table we get,

⇒ Standard deviation 'σ'

= √[ (0 - 1.96)² (0.19) + (1 - 1.96)² (0.12) + (2 - 1.96)² (0.38) + (3 - 1.96)²(0.16) + (4 - 1.96)²(0.15) ]

= √[ 1.3728 ]

≈ 1.171665

≈1.17(rounded to two decimal places)

Therefore, the mean and the standard deviation of the number of offers received is approximately 1.96 and 1.17 (rounded to two decimal places) respectively.

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The above question is incomplete, the complete question is:

Suppose you applied for positions at four different companies and let X be the number of offers you received

X      :            0               1               2               3                4

P(x)  :             0.19         0.12           0.38         0.16            0.15

1.  Find the mean

2.  standard deviation

of the number of offers you received. Round your answer to two decimal places

Answer: 3rd one

Step-by-step explanation:

formula : 2πrh+2πr^2

Answer:

144

Step-by-step explanation:

6*6=36

36*4=144

The simplified answer is (5x)/(x^(2)-49)-(6)/(x+7) = -(x - 42)/((x + 7)(x - 7)).

To subtract and simplify the given expression, we need to find a common denominator and combine the numerators. The common denominator in this case will be (x^2 - 49), which can be factored into (x + 7)(x - 7).

So, the expression becomes:

(5x)/((x + 7)(x - 7)) - (6)/(x + 7)

To get a common denominator, we need to multiply the second term by (x - 7)/(x - 7):

(5x)/((x + 7)(x - 7)) - (6(x - 7))/((x + 7)(x - 7))

Now we can combine the numerators:

(5x - 6(x - 7))/((x + 7)(x - 7))

Simplifying the numerator gives us:

(-x + 42)/((x + 7)(x - 7))

And finally, we can simplify the expression by factoring out a -1 from the numerator:

-1(x - 42)/((x + 7)(x - 7))

So the final answer is:

-(x - 42)/((x + 7)(x - 7))

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Answer:

kindly update the question

To find the total amount of milk used, we simply add the amount of milk used for the pancake recipe and the amount used for drinking. So we add 9 cups and 394 cups together, giving us a total of 403 cups of milk.

We can calculate the total amount of milk that Luke used for the pancake recipe and the additional amount he used for drinking.

For the pancake recipe, Luke used 9 cups of milk.

For drinking, Luke used an additional 394 cups of milk.

Total amount of milk used = Milk used for pancake recipe + Milk used for drinking

= 9 cups + 394 cups

= 403 cups of milk.

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The complete question is:

Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on the recipe?

The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.

A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.

Vοlume is calculated using the fοrmula LWH

Here each cube has side 1/3 yd

Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)

It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3

Thus, οptiοn B is cοrrect.

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Complete question:

Answer: i thank it is s=6 (w+6)

Step-by-step explanation:

Answer:

the answer is 88 square inches

Step-by-step explanation:

[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]

The correct answer is $9.50 of credit is left on the card. To find out how much credit is left on the card after Deshaun uses it for 30 minutes of calls, we need to plug in the value of x into the equation C=15.50-0.20x.

Deshaun has a card with $15.50 of credit on it. He is using it to make calls and the cost of each minute of calling is $0.20. To calculate how much credit Deshaun has left on his card after 30 minutes of calls, we need to use the equation C=15.50-0.20x, where x is the number of minutes of calls.

Since x represents the number of minutes of calls, we will plug in 30 for x:

C = 15.50 - 0.20(30)

C = 15.50 - 6

C = 9.50

Therefore, there is $9.50 of credit left on the card after Deshaun uses it for 30 minutes of calls.

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Answer:

101.80

Step-by-step explanation:

Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.

Answer:385

Formulate and substitute:F=350+350rt

Calculate the product or quotient:350x1+0.1

Calculate the sum or difference:350x1.1

Calculate the product or quotient:385

Without evaluating the expression, the sum of given expression is 80 is this why its even number.

Using letters or alphabets to represent numbers without giving their exact values is the idea behind algebraic expressions. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables.

In an algebraic expression, both constants and variables can be used. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.

An algebraic expression in mathematics is one that contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are built upon terms.

Calculate the power: 81

Calculate the sum or difference: 81 - 1

Answer is 80

Thus, here we know that 80 is an even number.

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We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.

Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.

Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.

Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.

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Answer: Dragonfly wings for the boys cost $1 while fairy wings for the girls cost $2. Phoebe's mom spent $18 on the gifts. How many dragonfly wings and fairy wings

Step-by-step explanation:

Answer:

The answer to the first question is A) P(c) = 2c, because the wings will be sold for double the cost of supplies.

The answer to the second question is B) N(p) = p - 0.3, because the price will be marked down by 30%.

The answer to the third question is A) 0.9c, which represents the markup of the discounted price over the supply cost.

The domain of all the functions is A) [0, infinity), because prices and costs must be positive numbers. Therefore, options B, C, and D are incorrect.

Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.

Using Cramer's Rule, we can solve the system of linear equations 13x - 6у = 17 and 26x -12y = 8 by following these steps:

Step 1: Find the determinant of the coefficient matrix, which is:

| 13 -6 |
| 26 -12 |

= (13)(-12) - (-6)(26)

= -156 - (-156)

= 0

Step 2: Since the determinant of the coefficient matrix is 0, we cannot use Cramer's Rule to solve this system of equations.

Step 3: We can check if the system has no solution or infinitely many solutions by comparing the ratios of the coefficients of x and y in the two equations.

The ratio of the coefficients of x in the two equations is 13/26 = 1/2, and the ratio of the coefficients of y in the two equations is -6/-12 = 1/2. Since these ratios are equal, the system has infinitely many solutions.

Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.

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The Johnston index of each voter is 3.317 and the Deegan-Packel index of each voter is  0.154

The Johnston index and the Deegan-Packel index are two measures of voting power that take into account the number of votes each voter has and the number of votes required for passage.

a) The Johnston index is calculated by taking the square root of the product of the number of votes a voter has and the number of votes they need for passage. In this case, the Johnston index for each voter is:
MA: √(4*(12-4)) = √32 = 5.657
ME: √(3*(12-3)) = √27 = 5.196
NH: √(2*(12-2)) = √20 = 4.472
CT: √(4*(12-4)) = √32 = 5.657
RI: √(3*(12-3)) = √27 = 5.196
VT: √(1*(12-1)) = √11 = 3.317

b) The Deegan-Packel index is calculated by taking the number of winning coalitions that a voter is a part of and dividing it by the total number of winning coalitions. In this case, the Deegan-Packel index for each voter is:
MA: 20/26 = 0.769
ME: 14/26 = 0.538
NH: 8/26 = 0.308
CT: 20/26 = 0.769
RI: 14/26 = 0.538
VT: 4/26 = 0.154

Overall, the Johnston index and the Deegan-Packel index provide different perspectives on the voting power of each voter. The Johnston index takes into account the number of votes each voter has and the number of votes required for passage, while the Deegan-Packel index takes into account the number of winning coalitions each voter is a part of.

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You need to deposit $13 into a account to have amount $5000 in 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, Amount =$5000, rate of interest =5.89% and time period = 2 year = 104 weeks.

Now, 5000=P(1+5.89/100)¹⁰⁴

5000=P(1+0.0589)¹⁰⁴

5000=P(1.0589)¹⁰⁴

5000=384.5P

P=5000/384.5

P=$13

Therefore, you need to deposit $13 into a account to have amount $5000 in 2 years.

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The required length of side CD is 22 units.

Since the perimeter of the rectangle is 80 units, we can use the formula for the perimeter of a rectangle, which is:

perimeter = 2(length + width)

In this case, we know that the perimeter is 80 units, so we can write:

80 = 2(length + width)

We also know that CD is a side of the rectangle, so it must be either the length or the width. Let's assume that CD is the length, so we can write:

CD = 4z + 2

Substituting this expression for the length into the formula for the perimeter, we get:

80 = 2(4z + 2 + width)

Simplifying the right-hand side, we get:

80 = 8z + 4 + 2width

Subtracting 4 from both sides, we get:

76 = 8z + 2width

Dividing both sides by 2, we get:

38 = 4z + width

Now we can use the fact that CD is a side of the rectangle to substitute for width. Since the opposite side of the rectangle must also have length 4z + 2, we can write:

width = 3z + 3

Substituting this into the previous equation, we get:

38 = 4z + 3z + 3

Simplifying the right-hand side, we get:

38 = 7z + 3

Subtracting 3 from both sides, we get:

35 = 7z

Dividing both sides by 7, we get:

5 = z

Now we can substitute this value of z into the expression for CD:

CD = 4z + 2 = 4(5) + 2 = 22

Therefore, the length of side CD is 22 units.

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The midpoint is   [(Yx + Fx)/2, (Yy + Fy)/2]

The distance between 2 points in the map is √[(FVx - CSx)^2 + (FVy - CSy)^2]

To determine the distance between two points on a map, we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]

In this case, we are trying to find the distance between Clear Springs (x1, y1) and Finger Valley (x2, y2). Plug in the coordinates for each point into the formula and solve for d.
d = √[(x2 - x1)^2 + (y2 - y1)^2]

= √[(Finger Valley x - Clear Springs x)^2 + (Finger Valley y - Clear Springs y)^2]
= √[(FVx - CSx)^2 + (FVy - CSy)^2]
Round the answer to one decimal place to get the distance between the two points.

To find the coordinates of the meeting point between you and your friends, we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

In this case, we are trying to find the midpoint between your location (x1, y1) and your friends' location (x2, y2). Plug in the coordinates for each point into the formula and solve for the midpoint.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
= [(Your x + Friends' x)/2, (Your y + Friends' y)/2]
= [(Yx + Fx)/2, (Yy + Fy)/2]
Round the coordinates to one decimal place to get the midpoint, which is the meeting point between you and your friends.'

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The monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent is $599.55.

To find the monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent, we need to use the following formula:

Monthly Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))

First, we need to convert the interest rate from a percentage to a decimal by dividing it by 100:

Interest Rate = 6 / 100 = 0.06

Next, we need to calculate the number of payments over the life of the loan. Since there are 12 months in a year, and the loan is for 30 years, the number of payments is:

Number of Payments = 12 * 30 = 360

Now we can plug these values into the formula:

Monthly Payment = ($100,000 * 0.06) / (1 - (1 + 0.06)^(-360)) = $599.55

Therefore, A $100,000 mortgage with a 30 year term and a 6% interest rate has a $599.55 monthly payment.

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The number of residents in a city is a discrete variable with ratio level of measurement. Therefore, the correct option is option 3. When a pair of dice are rolled, the pair of mutually exclusive events are getting an odd number on the first die; getting a 4 on the second die. Therefore, the correct option is option 2.

The number of residents in a city is a discrete variable because it can only take on whole number values. The level of measurement for this variable is ratio level because there is a true zero point (a city with zero residents) and the differences between values are meaningful. Therefore, the correct answer is discrete, ratio level which is the third option.

Mutually exclusive events are events that cannot occur at the same time. In the case of rolling a pair of dice, the pair of mutually exclusive events is "Getting an odd number on the first die; getting a 4 on the second die." This is because if the first die is an odd number, the second die cannot be a 4 at the same time.

The other options are not mutually exclusive because they can occur at the same time. For example, it is possible to get an even number on the first die and a double 5 at the same time. Therefore, the correct answer is "Getting an odd number on the first die; getting a 4 on the second die" which is the second option.

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Answer:

.

Step-by-step explanation: