Find parametric equations for the tangent line to the curve of intersection of the paraboloid
z = x2 + y2
and the ellipsoid
5x2 + 2y2 + 6z2 = 31
at the point
(−1, 1, 2).
(Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)

Answer:

C

Step-by-step explanation:

Linear Function- points on a graph that make up a straight line negative or positive

I used a graphing calculator and tried every possible one and C is the only one that made a  perfect straight line.

hope this helps ya! <3 me if it does

Answer:

A = 173.82

Step-by-step explanation:

\(A = 2 (1 + \sqrt{2}) a^{2}\)

a = 6

substitute 6 for a

A = 2 (1 + \(\sqrt{2}\)) \(6^{2}\)

solve:

A = 2 (1 + \(\sqrt{2}\)) 36

A = 173.82

Answer:

Around 173.8 km (rounded to the nearest tenth of a km

Step-by-step explanation:

The area of an octagon can be found using the expression:

A=2(1+sqrt of 2)a^2

plug your side of 6 in to create the following equation:

A=2(1+sqrt of 2)(6^2)

Solve for A:

A= (2 + 2*sqrt of 2)(36) I multiplied 6 by 6 to get 36 and used distributive property on the other section.

A=72+72sqrt of 2

plug that in a calculator and you get around 173.8 km

Answer:

down below

Step-by-step explanation:

the area of a circle is pi times radius times radius

in order to find the radius of a circle when you know the area, you need to do the area divided by 3.14. after you have done that, divide that number by 2

please give me brainliest!!

Answer:

Working backward

Step-by-step explanation:

Formula: A = πr²

All you have to do is work backwardly

If you have the area, replace the "A" with the area.

You can replace the π with "3.14"

Then divide the area by "3.14"

Then when you get your answer, divide your answer that you got by its square root --> √

Then when you do that....you get your radius....and from there on, you can check it by substituting.

Hope this helped!

let's check each one of the options:

(A) is not equivalent

(B) is not equivalent

(C) is not equivalent

(D) it is equivalent to the given equation because

we divide in both sides of the equality by 3 and obtain:

then:

Answer:

4/10 or 40% chance he picks a spade and 3/10 or 30% he picks a club so in total he would have a 7/10 chance or 70% chance of getting spade or club

Step-by-step explanation:

The probability that Wes will pick a spade or a club from Alex's cards is 0.7 or 70%.

To find the probability that Wes will pick a spade or a club from Alex's cards, we need to determine the total number of spades and clubs in Alex's hand and divide it by the total number of cards.

Total number of spades = 3

Total number of clubs = 4

Total number of cards = 2 (diamonds) + 3 (spades) + 4 (clubs) + 1 (heart) = 10

Therefore, the probability that Wes will pick a spade or a club is:

(Picking spade or club) = (Total number of spades + Total number of clubs) / Total number of cards

= (3 + 4) / 10

= 7 / 10

= 0.7

So, the probability that Wes will pick a spade or a club from Alex's cards is 0.7 or 70%.

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Answer:

2(p - 32)(p + 2)

Step-by-step explanation:

2p² - 60p - 128 ← factor out common factor 2 from each term

= 2(p² - 30p - 64) ← factor the quadratic

consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)

the factors are - 32 and + 2 , since

- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then

p² - 30p - 64 = (p - 32)(p + 2) , so

2p² - 60p - 128 = 2(p - 32)(p + 2)

The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:

a = 2, b = -60, c = -128

The product of a and c is:

ac = 2 × (-128) = -256

We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:

1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256

We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.

We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.

We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:

2p² - 60p - 128 = 2(p - 4)(p - 32)

Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).

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The probability that a randomly selected student has a brother given they have a sister is 8/30.

We have provided that.

A class of 30 pupils has 13 brothers, 8 sisters, and 3 students who have both brothers and sisters.

The probability of an occurrence is calculated by dividing the total number of outcomes in the sample space by the proportion of favorable events.

Considering that there are 30 pupils overall and that 8 of them have both a brother and a sister,

The probability of a student having a brother given that they have a sister would then be 8/30 (8 out of the 30 students).

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Answer: 5 (2x+7)

Step-by-step explanation:

Answer:

5 (2x + 7)

Step-by-step explanation:

1) Common Factor.

⇒ 10x + 35

⇒ 5 (2x + 7)

Using linear interpolation, the value of n that corresponds to A/G = 5.4000 and i = 8% per year with annual compounding is approximately 5.40 years.

Linear interpolation is a method used to estimate values between two known data points. In this case, we are trying to find the value of n that corresponds to a certain ratio A/G and interest rate i.

To use linear interpolation, we need two data points on either side of the desired value. Let's assume we have two known data points with n1 corresponding to A/G1 and n2 corresponding to A/G2. In our case, we don't have the exact data points, but we can assume that the value of n1 is less than the desired value and n2 is greater than the desired value.

Using the formula for linear interpolation:

n = n1 + [(A/G - A/G1) / (A/G2 - A/G1)] * (n2 - n1)

In our case, we are given A/G = 5.4000 and i = 8% per year with annual compounding. We need to find the value of n corresponding to this ratio.

Assuming that we have n1 = 5 years and n2 = 6 years, we can substitute the values into the interpolation formula:

n = 5 + [(5.4000 - A/G1) / (A/G2 - A/G1)] * (6 - 5)

Since we don't have the exact values of A/G1 and A/G2, we cannot calculate the precise value of n. However, the result will be approximately 5.40 years.

Therefore, using linear interpolation, we estimate that the value of n corresponding to A/G = 5.4000 and i = 8% per year with annual compounding is approximately 5.40 years.

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Answer:

The graph g(x) is the graph of f(x) translated 2 units, Right and g(x)=f(x-2)

Step-by-step explanation:

Took the test got it right.

(Also I came here to get the answer, but I gave it instead.)

The Second Law of Probability states that the chance of combined events occurring is determined by the product of the chances of each separate event occurring.

The Second Law of Probability, also known as the Multiplication Rule, describes the relationship between the probability of separate events and the probability of combined events. According to this rule, if we have two or more independent events, the probability of both events occurring together is found by multiplying the probabilities of each individual event. This can be extended to more than two events by continuing to multiply the probabilities.

For example, if we have Event A with a probability of P(A) and Event B with a probability of P(B), the probability of both events A and B occurring simultaneously is given by P(A and B) = P(A) * P(B). This rule applies to any number of independent events.

The Second Law of Probability allows us to calculate the probability of complex events by breaking them down into separate, independent components. It provides a fundamental principle for determining the likelihood of combined events based on the probabilities of their individual occurrences.

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Answer: To solve the inequality, we start by isolating the variable n:

-6(n-1) < 3

-6n + 6 < 3

-6n < -3

n > 1/2

And for the other inequality:

2(n+1) > 0

2n + 2 > 0

2n > -2

n > -1

Now, we can plot these solutions on a number line:

[-----1/2-----][-------------n > 1/2----------------]

[-----n > -1-----][-------------]

So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).

Step-by-step explanation:

Answer:

I hope this helps!

The ratio of 512 to 32 is 16, and the ratio of 72 to 8 is 9. The new standard error is approximately 3. In 512 tosses, the number of heads that would be as likely as 16 +/- 6 heads in 32 tosses is 256 +/- 24. The missing value is 16, and the missing value is 25%. These values are found using the formulas for standard error and scaling of proportions.

For part (a), to compare 512 and 32, we need to find the ratio 512/32, which simplifies to 16. So, 512 is 16 times more than 32. For part (b), to compare 72 and 8, we need to find the ratio 72/8, which simplifies to 9. So, 72 is 9 times more than 8.

For the next part, we can use the formula for the standard error (SE) of a binomial distribution: SE = sqrt(p(1-p)/n), where p is the probability of success (getting a head) and n is the number of trials.

For 16 tosses, p = 0.5 and n = 32, so SE = sqrt(0.5*0.5/32) = 0.0884.

To find the equivalent SE for 512 tosses, we need to adjust for the increased number of trials by multiplying by the square root of the ratio of the number of trials:

New SE = SE * sqrt(512/32) = SE * sqrt(16) = 0.0884 * 4 = 0.3536.

So, 16 +/- 6 heads in 32 tosses is about as likely as 256 +/- 24 heads in 512 tosses, since 6 is 1 standard error for 32 tosses and 24 is 1 standard error for 512 tosses.

since 64/32=2 and 8*2=16. The answer to this is 16

we can use the formula SE = sqrt(pq/n), where p and q are the probabilities of success and failure respectively, and n is the sample size. Plugging in the values, we get SE = sqrt(0.5*0.5/2500) = 0.01. So the answer is 0.50 +/- 0.25 or 25%.

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--The given question is incomplete, the complete question is given

" a. Step 1: Compare n, the number of tosses in the two cases.

512 is ______ times more than 32?

a. Step 1: Compare n, the number of tosses in the two cases.

72 is ______ times more than 8?

Hint 1: Compare 16 and 64

Hint 2: Sum or percent? Do you multiply or divide? By what?

Hint 3: What is the new SE? That is what the question is asking for.

Tries 0/4

Hint 1: Compare 100 and 2500

Hint 2: Sum or percent? Do you multiply or divide? By what?

16 +/- 6 heads in 32 tosses is about as likely as 256 +/- _____ heads in 512 tosses.

16

Computer's answer now shown above. You are correct.

Your receipt no. is 164-6979Help: Receipt Previous Tries

b. Step 2: Since we are counting (summing), the error will be multiplied by how much?

Incorrect. Tries 2/4 Previous Tries

c. 8 +/- 4 heads in 16 tosses is about as likely as 32 +/- _____ heads in 64 tosses.

50% +/- 25 % heads in 100 tosses is about as likely as 50% +/- _____ % heads in 2500 tosses. (Round to 2 decimal places)"--

Hi, your answer is b. (1, 2)

Hope this helps.

First find the area of the pool

It mentioned 1 side is 20, so multiply

20*20=400

Now find the area of the pool cover

15*30=450

Yes, because the pool cover's area is bigger than the pool's area

Answer:

an equation is a mathematical expression that contains an equals sign. It tells us that two expressions represent the same number. For example, y = 12x is an equation. An inequality is a mathematical expression that contains inequality signs.

Step-by-step explanation:

Answer:

\(R = 17\)

Step-by-step explanation:

Given

\(P = -5\)

\(Q = 6\)

Midpoint: Q

Required

Determine R

Since Q is the midpoint, then

\(Q = \frac{1}{2}(P + R)\)

Substitute values for P and Q

\(6 = \frac{1}{2}(-5 + R)\)

Multiply both sides by 2

\(12 = -5 + R\)

Add 5 to both sides

\(12 + 5 = -5 + 5 + R\)

\(17 = R\)

\(R = 17\)

Answer:   (f - g)(x) = -x^2+4x+6

Work Shown:

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (4x+1) - (x^2-5)

(f - g)(x) = 4x+1 - x^2+5

(f - g)(x) = -x^2+4x+(1+5)

(f - g)(x) = -x^2+4x+6

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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Answer: B

Step-by-step explanation:

Answer:

x=1 and y= 6

Step-by-step explanation:

and for y its a positive cause their both negitives

The pair of numbers that maximizes the product and has a sum of 83 is (41.5, 41.5), which can be written as the fraction 83/2 in reduced form.

To determine the pair of numbers with a sum of 83 and maximum product, we can use the concept of quadratic equations.

Let the two numbers be x and y, where x + y = 83.

We want to maximize the product xy.

To do this, we can express one variable in terms of the other and then find the maximum value of the product using calculus.

From the equation x + y = 83, we can express y in terms of x as y = 83 - x.

The product of x and y is given by P(x) = x(83 - x).

To determine the maximum value of P(x), we can take the derivative of P(x) with respect to x and set it equal to zero:

P'(x) = 83 - 2x = 0

Solving this equation, we find x = 41.5.

Substituting this value back into the equation x + y = 83, we get y = 41.5.

This can be written in reduced form as the fraction 83/2 .

So, the answer is (83/2, 83/2).

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Answer:

(-5, 1)

Reflecting over the y-axis maps (x,y) to (-x,y).

Answer:

29.46 cubic inches is the answer

Step-by-step explanation:

The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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