A. Find the parametric form for the plane containing the points
(1, -2, 1), (0, 5, 3) and (2, 4, 7)
B. Find the normal form ax + by + cz = d for the plane
containing the points (1,-2,1), (0, 5, 3) and (2, 4, 7)

The given conditions are:\(y1=3x+3,y2=2x+6\),and y1 > y2To find the solution set, we need to solve the inequality given:\(y1 > y23x + 3 > 2x + 63x - 2x > 6 - 33x > 3x > 3/3x > 1\)

Therefore, the solution set for the given inequality is \({ x | x > 1 }\).This means that x belongs to the interval (1, ∞).To express this in interval notation, we use the square bracket [ ] for inclusive endpoints and the round bracket ( ) for exclusive endpoints. As there is an inclusive endpoint, we use square bracket [ ] for 3.

The interval notation will be [3, ∞).Thus, the correct option is C. [3,[infinity]).

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The given problem involves Simple Single Server queuing model.In the given problem, a vending machine at City Airport dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed).

The operating characteristics of this system can be determined by using the following formulas:Average Number of Customers in the System, L = λWwhere, λ= Average arrival rateW= Average waiting timeAverage Waiting Time in the System, W = L/ λProbability of Zero Customers in the System, P0 = 1 - λ/μwhere, μ= Service rateThe given problem can be solved as follows:Given that, λ = 60 per hourSo, the average arrival rate is λ = 60/hour. We know that the exponential distribution (which is a Poisson process) governs the time between arrivals. Therefore, the mean time between arrivals is 1/λ = 1/60 hours. Therefore, the rate of customer arrivals can be calculated as:μ = 1/20 secondsTherefore, the rate of service is μ = 3/hour.

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Answer: just multiply 9 and y together: 9 x y

we know angles A and B are supplementary, thus their sum is 180°.

\(\stackrel{\measuredangle A}{(2x+26)}~~ + ~~\stackrel{\measuredangle B}{(x+25)}~~ = ~~180\implies 3x+51=180\implies 3x=129\\\\\\x=\cfrac{129}{3}\implies x=43~\hspace{10em}\stackrel{\measuredangle B = 43 + 25}{68}\)

The measure of angle m∠B = 112°

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.

Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 2x+26 ) + ( x+25 ) = 180

Now we can combine like terms and apply the operations to find the value of x:

⇒ ( 2x+26 ) + ( x+25 ) = 180

⇒ 3x + 51 = 180

⇒ 3x  = 180 - 51

⇒ 3x  = 129

⇒ x = 129/3

⇒ x = 43

Then Angle B will have a measure of x+25 = 43 + 25 = 68°

m∠ B = 112°

The measure of Angle A will be :2x+26  = 2(43) + 26 = 112°

m∠A = 68°

Thus, the measure of angle m∠B = 112°

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Answer:

\(-\frac{6}{x^{2} } -6x-2\)

Step-by-step explanation:

\(x^{-2}\)  is equivalent  \(\frac{1}{x^{2} }\)

Then, that is multiplied by the coefficient of -6

Thus \(-6x^{-2}\) becomes \(-\frac{6}{x^{2} }\)

Answer:

It's G

Step-by-step explanation:

It has an acute angle while two of the other answers are vertical angles & the other answer choice is obtuse

The angle 12 has the greatest measure than the angle 5,7 and angle 8 option (F) ∠12 is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

From the figure

The angle 5 and angle 7 are vertically opposite angles.

The angle 8 is an acute angle which is less than 90 degree.

The angle 12 is an obtuse angle which is greater than 90 degree.

Thus, the angle 12 has the greatest measure than the angle 5,7 and angle 8 option (F) ∠12 is correct.

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Answer: 105m^2

Step-by-step explanation:

multiply the two

If this figure was a parallelogram, then the opposite angles would be congruent. This would make angles B and D the same measure

angle B = angle D

x^2+20 = 7x+50

x^2+20-7x-50 = 0 .... get everything to one side

x^2-7x-30 = 0

(x-10)(x+3) = 0 ... see note below

x-10 = 0 or x+3 = 0

x = 10 or x = -3

Note: In this step is where the factoring occurs. To factor, we need to find two numbers that multiply to -30 which is the last term, and also add to -7 which is the middle coefficient. This is a trial and error process. You should find that -10 and 3 both multiply to -30 and add to -7. I suggest making a table as shown below (attached image) to list out all the possible choices.

Perhaps a much more efficient route is to use the quadratic formula.

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

We found two possible solutions for x. If x = 10, then 7x+50 is 7(10)+50 = 120 which is an obtuse angle. If x = -3, then 7x+50 = 7(-3)+50 = 29 which is acute.

Assuming the diagram is drawn to scale, this means angle D is obtuse and we'll go with x = 10 and 7x+50 = 120

Angles A and D add to 180 degrees. This is true for any pair of adjacent angles in a parallelogram.

A+D = 180

A+120 = 180

A = 180-120

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

This answer is based on the assumption that the diagram is drawn to scale and that this quadrilateral is a parallelogram.

Answer:

\(\angle A=60\textdegree\)

Step-by-step explanation:

So we have the following parallelogram and we wish to solve for ∠A.

To do so, we will need to solve for x first. Look carefully at the parallelogram...

Notice that ∠A and ∠D are consecutive angles. In other words:

\(\angle A+\angle D=180\)

Since we have an equation for ∠D, substitute:

\(\angle A+7x+50=180\)

Notice that ∠A and ∠B are also consecutive angles. So:

\(\angle A+\angle B=180\)

We know the equation for ∠B. Substitute:

\(\angle A+x^2+20=180\)

Since both equations equal 180, we can set them equal to each other:

\(\angle A+7x+50=x^2+20+\angle A\)

Let's subtract ∠A from both sides. This gives us:

\(7x+50=x^2+20\)

Now, we can solve for x. This is a quadratic, so let's move all the terms to one side. To start off, let's subtract 50 from both sides:

\(7x=x^2-30\)

Now, let's subtract 7x from both sides:

\(0=x^2-7x-30\)

Solve for x. We can factor.

Here's the trick to factoring. If we have the following:

\(0=ax^2+bx+c\)

The we will need to find two numbers, p and q, such that:

\(p+q=b\text{ and } pq=ac\)

In our equation, a is 1, b is -7, and c is -30.

So, we want two numbers that sum to -7 and multiply to (1)(-30)=-30.

We can use -10 and 3. -10+3 is -7 and -10(3) is -30. So, let's substitute our b term for -10x and 3x. In other words, we have:

\(0=x^2-7x-30\)

Substitute -7x for 3x-10x. This gives us:

\(0=x^2+3x-10x-30\)

This is equivalent to our old equation.

Now, we can factor. Factor out a x from the first two terms:

\(0=x(x+3)-10x-30\)

And factor out a -10 from the two last terms:

\(0=x(x+3)-10(x+3)\)

Since the expressions within the parentheses are the same, we can use grouping to acquire:

\(0=(x-10)(x+3)\)

Note that this is essentially the distribute property. If we distribute, we will get the same as above.

Zero Product Property:

\(x-10=0\text{ or }x+3=0\)

Solve for x:

\(x=10\text{ or } x=-3\)

So, we have two cases for x. Each case will yield a different answer for ∠A.

Case I: x=10

Use our original equation of:

\(\angle A+7x+50=180\)

Substitue 10 for x:

\(\angle A+7(10)+50=180\)

Multiply:

\(\angle A+70+50=180\)

Add:

\(\angle A+120=180\)

Subtract 120 from both sides:

\(\angle A=60\textdegree\)

So, in our first case, ∠A is 60°

Case II: x=-3

Again, same equation:

\(\angle A+7x+50=180\)

This time, substitute -3 for x. This yields:

\(\angle A+7(-3)+50=180\)

Multiply:

\(\angle A-21+50=180\)

Add:

\(\angle A+29=180\)

Subtract 29 from both sides:

\(\angle A=151\textdegree\)

So, in our second case, ∠A is 151°

However, 151° doesn't seem likely with how the figure is drawn.

Therefore, our final answer is 60°.

And we're done!

Edit: Fixed Incorrect Answer

Answer:

a. True

Step-by-step explanation:

a. True

A cost that changes in total as output changes is indeed a variable cost. Variable costs are expenses that vary in direct proportion to the level of production or business activity. As output increases, variable costs increase, and as output decreases, variable costs decrease. Examples of variable costs include direct labor, raw materials, and sales commissions.

Answer:

ayyyyytttsss.........

The correct square root of the given expression is 4√2. Hence,  option B is correct.

The given  number is:

√32

To find the square root of the given number,

Factoring the number 32,

32 = 2x2x2x2x2

32 = 2⁵

This can also be written as,

32 =  2⁴(2)

Now taking square root on both sides we get,

√32 = 4√2

Hence,

The correct square root of the given expression is 4√2 which is option B.

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The complete question is:

Which of the following is equivalent to the square root of 32.

A: fift root of 64

B: 4√2

C: 2√5

D: 3√2

Answer: D, \(8(\sqrt[10]{2^{7} } )\)

Step-by-step explanation:

We need to first multiply \(\sqrt{32}\)  by \(\sqrt[5]{64}\). To do this, we can convert both of them into exponents, making them \(32^{\frac{1}{2} }\) and \(64^{\frac{1}{5} }\). To multiply the exponents, we need to give both of them the same denominator, so they become \(32^{\frac{5}{10} }\) and \(64^{\frac{2}{10} }\). Now we can convert them back into roots and multiply them together to get \(\sqrt[10]{32^{5} 64^{2} }\). Now focusing on the inside of the roots, to multiply them together, we need to give them the same base. \(2^{5}\) is 32 and \(2^{6}\) is 64, and substituting them back into the roots, we get \((2^{5})^{5}\) and \((2^{6}) ^{2}\), which we can simplify by multiplying the exponents together, giving us \(2^{25}\) and \(2^{12}\). Now we can multiply them together by adding the exponents, leaving the same base, to get \(2^{37}\). Putting this back into the root, we have \(\sqrt[10]{2^{37} }\). From here, we simplify. From 37, 30 goes into 10 perfectly, with 30/10 being 3. To get rid of it, we do \(2^{3}\), which is 8, so in the end, the answer is D, \(8(\sqrt[10]{2^{7} } )\).

The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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The smallest possible value of doughnuts in each box is 2. The smallest possible value of doughnuts in each box is 2.

In order for Donna to rearrange the remaining doughnuts into bags so that each bag contains the same number of doughnuts and none are left over, the number of doughnuts in each box must be divisible by the number of bags. Since there are no doughnuts left over, this means that the number of doughnuts in each box must be a multiple of the number of bags.

To find the smallest possible value, we need to find the smallest common multiple of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 (since there are 9 possible numbers of bags). The smallest common multiple of these numbers is 2, so the smallest possible value of doughnuts in each box is 2.Therefore, the smallest possible value of doughnuts in each box is 2.

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40=4(3d-5)

40=12d-20

60=12d

5=d

d=5

Answer:

16x - 17

Step-by-step explanation:

Answer:

16x-17

Step-by-step explanation:

Answer:

\(\frac{2,000}{365}\)=\(\frac{x}{500}\)

The probability that the student will get exactly four correct answers is approximately 0.1706

To solve this problem, we can use the binomial distribution, which gives the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each question has three possible answers, only one of which is correct. So the probability of getting a correct answer by guessing is 1/3.

Let X be the number of correct answers out of 8. Then X follows a binomial distribution with n=8 and p=1/3.

To get exactly four correct answers, we need to get four successes and four failures in any order. The number of ways to choose four questions to answer correctly is 8 choose 4 (written as 8C4), which is equal to 70. The probability of getting four successes and four failures is therefore

P(X=4) = (8C4) × (1/3)^4 × (2/3)^4

= 70 × 1/81 × 16/81

= 1120/6561

≈ 0.1706

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Answer:

1) 2 × 2 × 5 × 7 + 9 -7×1 = 142

2) 9 × 7 × 2 + 5 × 2 + 7 - 1 = 142

3) 2 × 9² - 7 - 7 - 5 - 1 = 142

4) 2 × 7² + 9 + 7 × 5 × 1 = 142

Step-by-step explanation:

1) 2 × 2 × 5 × 7 + 9 -7×1 = 142

Multiply 2 by 2 by 5 by 7 add to 9 then subtract 7 multiplied by 1

2) 9 × 7 × 2 + 5 × 2 + 7 - 1 = 142

Multiply 9 by 7 by 2 by 7 add to 5 multiplied by 2 then add to 7 and subtract 1

3) 2 × 9² - 7 - 7 - 5 - 1 = 2 × 9² - (7 + 7 + 5 + 1) = 142

Multiply 2 by 9 raised to the power of 2 then subtract  the sum of 7, 7, 5 and 1

4) 2 × 7² + 9 + 7 × 5 × 1 = 142

Multiply 2 by 7 raised to the power of 2 then add 9 and add 7 multiplied by 5 multiplied by 1.

Answer:

x = 79

Step-by-step explanation:

Part A:

It's stated that line p and line q are parallel, if it is so then the angle represented with w and the angle with measure 79 are alternate and their measure is equal to each other:

Part B:

Jacob likely thought angle represented with W and the angle with the measure 101 are alternate so he made a mistake and found wrong result.

Answer:

1,632

Step-by-step explanation:

the 15% of 1,920 is 288 subtract it to 1,920 so you'll get 1,362 is the number of athletes finished the race this year

Answer:

What is the question?

Step-by-step explanation:

The definition, property, postulate, or theorem that justifies each statement are given as follows:

5. C. Whole Greater Than Its Part Property.

6. B. Exterior Angle Inequality Theorem.

7. E. If Unequal Sides, then Unequal Angles.

Segment AD is given by the combination of segments AM and MD, hence it's length is given by:

AD = AM + MD.

Segment length's are never negative nor zero, hence:

Thus statement C is correct.

C. Whole Greater Than Its Part Property.

The exterior angle inequality theorem states that the measure of any of the exterior angles of a triangle is greater than either of the opposite angles, hence:

Thus statement B is correct.

B. Exterior Angle Inequality Theorem.

We are given that the length of segment AM is less than the length of segment AG.

Applying the law of sines, we have that:

\(\frac{AM}{\sin{G}} = \frac{AG}{\sin{M}}\)

Hence:

\(AG = AM\frac{\sin{M}}{\sin{G}}\)

Since AG < AM, sin(M) < sin(G) and m<AGM < m<AMG. This is used to explain statement E, as follows:

E. If Unequal Sides, then Unequal Angles.

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we can say that years of experience explain 95.4% of the variation in the number of units sold per day by the digital music retailer. years of experience explain approximately 95.4% of the variation in the number of units sold by the digital music retailer.

In the given problem, we need to find out how much variation in the number of units sold does years of experience explain. The given problem can be solved with the help of regression analysis.Regression Analysis:Regression analysis is the method used to understand how one variable is affected by another variable. It shows the relationship between two variables with the help of a line of best fit. The line of best fit can be represented with the help of the following equation:y = a + bxwhere,y = dependent variablea = interceptb = slope of the line of best fitx = independent variableLet's represent the given data with the help of the table below:Given DataTable:We know that, y = a + bxWe also know the following terms:    * y-intercept (a) = 21.01    * Slope of the line of best fit (b) = 3.2Hence, we can write the following equation:y = 21.01 + 3.2xWe can interpret the above equation as follows:For each additional year of experience in the market, the digital music retailer sells an additional 3.2 units per day.The coefficient of determination (R²) is a statistical measure that shows how much of the variance in the dependent variable is explained by the independent variable(s). In the given regression analysis table, the value of R² is 0.954.

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Answer:

16:8 2:1

Step-by-step explanation:

it's both 8 and 4 times 2 on each side, and then divided on each side

Answer: m∠EFG = 70

Step-by-step explanation:

m∠EFG = 2x35

m∠EFG = 70

In conclusion the answer is 70

Answer:

7

Step-by-step explanation:

-x+2+5x=10(x-4)

4x+2=10x-40

2+40=10x-4x

42=6x

42/6=6x/6

7=x

Answer:

x = 7

Step-by-step explanation:

-x + 2 + 5x = 10 (x - 4)

=> 4x + 2 = 10x - 40

=> 4x - 10x = -40 - 2

=> -6x = -42

=> 6x = 42

=> x = 42/6

=> x = 7

The periodic payment required to amortize a loan of $18,000 is

$22,775.74.

Given, the periodic payment R required to amortize a loan of P dollar over t year with interest charged at a rate of r% year compounded m times a year. P=18,000, r=4, t=3, m=2

As, Amount = P(1 + r/100)^t

Now, using the formula, we get

Amount = 18000(1 + 4/100)^(3×2)

Amount = 18000(1.04)^6

Amount = 18000×1.265

Amount = 22,775.74

Hence, the periodic payment required to amortize a loan of $18,000 is

$22,775.74.

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