4. (10 points) Find the points on the surface x+y+z = 1 closest to the origin.

Answer:

315 inches long

135 is 75% of 180, so you can add 135 to 180.

135 + 180 = 315

Answer:

x=1/2, y=4

Step-by-step explanation:

2x+3y=13

or,y=(13-2x)/3 ........eq(i)

4x-y=-2

or,y=4x+2 ..............eq(ii)

From eq(i) and (ii),

(13-2x)/3=4x+2

or,13-2x=12x+6

or,13-6=12x+2x

or,7=14x

or,x= 7/14

x=1/2

y=4×(1/2)+2

y=4

Answer: y=−1/7x+13/7

Step-by-step explanation: m=x2-x1/y2-y1, then put it in slope formula

Answer:

6 days

Step-by-step explanation:

Let the time taken by Carpenter working alone = \(C\) days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2\(C\) days

Time taken working together = 2 days

Work done in one day working together = \(\frac{1}{2}\)

Work done in one day by Carpenter working alone = \(\frac{1}{C}\)

Work done in one day by apprentice working alone = \(\frac{1}{2C}\)

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =  \(\frac{1}{C}\)+\(\frac{1}{2C}\) = Work done in one day working together = \(\frac{1}{2}\)

\(\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days\)

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 \(\times\) 2= 6 days

We are required to calculate the number of days it would take the apprentice working alone

The number of days it takes the apprentice working alone is 6 days

let

Number of days taken for the carpenter to work alone = x

Number of days taken by the apprentice to work alone = 2x

Number of days taken to work together = 2 days

Work done per day Carpenter = 1/x

work done per day apprentice = 1/2x

work done per day together = 1/2

So,

work done per day together = Work done per day Carpenter + work done per day apprentice

1/2 = 1/x + 1/2x

1/2 = (2 + 1) / 2x

1/2 = 3/2x

cross product

1(2x) = 2(3)

2x = 6

x = 6/2

x = 3 days

Therefore,

Number of days taken by the apprentice to work alone = 2x

= 2(3)

= 6 days

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Step-by-step explanation:

ans...9days.......,........

The argument is not valid.

The argument form is: p ∧ ∼ q → r, p ∨ q, q → p, therefore r. We can use the truth table to determine whether this argument is valid or invalid. Here is the annotated truth table:


 
   p
   q
   ∼q
   p ∧ ∼q
   p ∨ q
   p ∧ ∼q → r
   q → p
   r
 
 
   T
   T
   F
   F
   T
   T
   T
   T
 
 
   T
   F
   T
   T
   T
   T
   T
   T
 
 
   F
   T
   F
   F
   T
   T
   F
   F
 
 
   F
   F
   T
   F
   F
   T
   T
   F
 

From the truth table, we can see that the conclusion r is not always true, even when all the premises are true. For example, in the third row of the table, all the premises are true, but the conclusion is false. This means that the argument is invalid. The truth table supports this conclusion because it shows that there are cases where the premises are true but the conclusion is false. Therefore, the argument is not valid.

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Answer:

x>-4

Step-by-step explanation:

flip sign when dealing with negative

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

5.20.10

Step-by-step explanation:

a. The value of the swap to firm XYZ is -$23,225.33.

b. This would help to protect the firm against an increase in interest rates.

a. Calculation of the value of the swap to firm XYZ

The value of the swap to firm XYZ can be calculated using the following formula:

Value of Swap = Value of Fixed Leg - Value of Floating Leg

Where Value of Fixed Leg = VFL = (Coupon Rate * Principal * (1 - (1 + r)-n / r))

Value of Floating Leg = VFL = (Interest Rate * Principal * (1 - (1 + r)-n / r))

Where, Coupon Rate = 4% p.a. Principal = $20 million

Interest Rate = LIBOR + Spread, Spread = 0, therefore,

Interest Rate = 4.5% p.a.

Time to Maturity, n = 15 months

Remaining Time to Next Payment = 6 - 2 = 4 months

Therefore, the current six-month LIBOR rate is required to calculate the value of the swap as follows:

Current six-month LIBOR rate = 4.5% * (4/6) + x% * (2/6)x = ((Value of Swap/Principal + (1 - (1 + r)-n / r)) * r) / (1 - (1 + r)-n / r) = 0.0251%

Value of Fixed Leg = VFL = (0.04 * 20,000,000 * (1 - (1 + 0.05/2)-30 / (0.05/2))) = $1,328,816.76

Value of Floating Leg = VFL = (0.0451 * 20,000,000 * (1 - (1 + 0.05/2)-10 / (0.05/2))) = $1,352,042.09

Value of Swap = $1,328,816.76 - $1,352,042.09 = -$23,225.33

Therefore, the value of the swap to firm XYZ is -$23,225.33.

b. Suggest a reason why XYZ entered into the swap in the first place

Firm XYZ might have entered into the swap in the first place to mitigate the risk of a rise in interest rates in the future. By entering into a fixed-for-floating interest rate swap, the firm has fixed its borrowing cost for the duration of the swap at 4%, regardless of the future interest rate changes.

Therefore, this would help to protect the firm against an increase in interest rates.

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Answer:

first problem) he messed up at 4(1 + 5n), only multiplying the 1 by 4, instead of both the 1 and 5n,

work-

-8n + 4(1 + 5n) = -6n - 14

-8n + 4 + 20n = -6n -14

12n + 4 = -6n - 14

18n +4 = -14

18n = -18

n= -1

second problem)  he messed up towards the end, where he put 3x = 3x, then x=0. in this case, x would equal x, so the answer is "infinitely many solutions"

all the other work is correct in that problem

third problem) on the right side of the equation, ( 4x+10+3x-6), when they were adding the like numbers, instead of subtracting 6 from 10, they added 6, giving them 16 instead of 4

correct work-

2x - 8 + 3x +2 = 4x +10 + 3x -6

5x - 6 = 7x + 4

-5x         -5x

-6 = 2x +4

-4           -4

-10 = 2x

-5 = x

hope i helped  :)

Answer:

Mark me as brain list plz for fun I need to get my expert rank

Step-by-step explanation:

There is no attachment to see any grams post then I will answer

A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

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It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

We are given a set of vectors S and we need to determine whether each given vector can be written as a linear combination of the vectors in S.

(a) For vector (2, -1, -2), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (2, -1, -2). By solving the system of equations, we find that k₁ = -1 and k₂ = 0, so the vector can be written as a linear combination of the vectors in S.

(b) For vector (8, -14, 27/4), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (8, -14, 27/4). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(c) For vector (1, -8, 12), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, -8, 12). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

(d) For vector (1, 1, -1), we need to check if there exist scalars k₁ and k₂ such that k₁(2, -1, 3) + k₂(5, 0, 4) = (1, 1, -1). By solving the system of equations, we find that there are no solutions, so the vector cannot be written as a linear combination of the vectors in S.

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Answer: 5cm

Step-by-step explanation:

You divide the area of green (93.75) by pink's length (7.5)

that gives you 12.5.

12.5 is the length of green.

12.5 - 7.5 = 5

You subtract the 7.5 because to get yellow's length because Yellow's length plus pink's length is equal to green's total length.

If the probability of failure is 0.001, then the probability that

(a) lot is accepted is 0.9277,

(b) lot is rejected on 20th test is 0.000981,

(c) lot is rejected in 10 or fewer trials is 0.01.

Let the random-variable "X" represent number of batteries to test to get the first-battery which fails; in other words, to get first success.

Since, the trials are independent, X has a geometric distribution

Part (a) :

Let X =  the number of trials,

So, the probability that the lot is accepted is :

⇒ P(X=75) = (0.999)⁷⁵×(0.001)⁰ = 0.9277,

Part (b) :

let Y = the numbers of trials before the first failure (geometric distribution and

So, the probability that lot is rejected on 20th-test is :

⇒ P(Y=20) = (0.001)⁰×(0.999)¹⁹ = 0.000981,

Part (c) :

The probability that it is rejected in 10 or fewer trials is :

⇒ 1- P(no Failures)

⇒ 1 – (0.001)⁰(0.999)¹⁰ = 0.01.

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Answer:

x=\(\frac{y}{m} -\frac{p}{m} +q\)

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation:

Answer: 1. multiplication

Step-by-step explanation:

Suppose that you want to change an object with length L with a scale factor a, then the lenght of the rescaled object will be:

L' = a*L

Then the correct option is 1) multiplication.

Notice that sometimes you may find that the scale factor is a number like 1/5 and when you find the new lenght you will end with something like:

L' = L/5 that seems like a division, but this is actually the multiplication between L and 1/5.

The largest amount of change i could have in my pocket without being able to give change for $2 exactly is $2.04.

The solution to this problem depends on what 'change' means. If it means lower denomination coins like quarters, dimes, nickels, and pennies then here is the solution for largest change.

We want to maximize our number of coins, but minimize the total value above $2.00.

Person should have 199 pennies- which is $1.99 and 1 nickel- which is $0.05. This is a total of $2.04.

So person has more than $2.00 in change, but cannot give exact change for $2.00.

This is also the largest amount of change. Any other combination will give you less number of coins.

Hence , the largest amount of change i could have in my pocket without being able to give change for $2 exactly is $2.04.

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An equation that can you use to find h, the height of the window in meters is: A. 1/2(2h - 2)h = 42.

The height of the window in meters is equal to 7 meters.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle = 1/2 × b × h

Where:

Since the window's base area is 2 meters shorter than twice the height, a mathematical expression which can be used to represent it is given by:

Base area, b = 2h - 2

Substituting the given parameters into the area of a triangle formula, we have the following;

Area of a triangle = 1/2 × b × h

42 = 1/2 × (2h - 2) × h

1/2(2h - 2)h = 42 [required equation].

Making the variable h the subject of formula, we have the following;

1/2(2h - 2)h = 42

Cross-multiplying, we have:

(2h - 2)h = 84

2h² - 2h = 84

2h² - 2h - 84 = 0

Dividing all through by 2, we have the following:

h² - h - 42 = 0

Next, we would solve the above quadratic function by using the factorization method;

h² - 7h + 6h - 42 = 0

h(h - 7) + 6(h - 7) = 0

(h + 6)(h - 7) = 0

h = -6 or 7 meters.

Therefore, the height of the window is 7 meters since it can't be negative.

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Given

The degree of a polynomial is the greatest exponent of x. In this case, the greatest exponent of x is 2.

Answer: false

Answer:

No

Step-by-step explanation:

A function cannot have two different points with the same x-coordinate. For instance in this one, (0,3) & (0,8) share the same value of x

The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

The equation is given as:

x^2 + 2x - 48 = 0

A quadratic equation is represented as:

ax^2 + bx + c = 0

By comparing both equations, we have

a = 1, b = 2 and c = -48

The solution of the quadratic equation is then calculated using

x = (-b ± √(b^2 - 4ac))/2a

Substitute values for a, b and c in the above equation

x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1

This gives

x = (-2 ± √196)/2

Evaluate the square root of 196

x = (-2 ± 14)/2

Divide through by 2

x = -1 ± 7

Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

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Answer:

the answer is C

Step-by-step explanation:

Answer:

Bottom Left is the right answer

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

We know that p(t) = 11:

11=2t+5

11-5=2t

6=2t

6/2 = t

3 = t

Answer:

D. 5√3

Step-by-step explanation:

tan 30° = x/15

or, 1/√3=x/15

or, x= 15/√3 = 5√3

Answer:

D

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exacy value

tan30° = \(\frac{1}{\sqrt{3} }\) = \(\frac{\sqrt{3} }{3}\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{15}\) = \(\frac{\sqrt{3} }{3}\) ( cross- multiply )

3x = 15\(\sqrt{3}\) ( divide both sides by 3 )

x = 5\(\sqrt{3}\) → D