find the equations of the tangents to the curve x = 6t2 6, y = 4t3 2 that pass through the point (12, 6).

The best next step to finish solving the equation is Subtract 27 from both sides of the equation

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. That will be regarded as a phrase.

Given that the equation is

3 - 15x + 24 + 16x = 4x - 24 - 4x

Combining like terms to simplify the equation we get

27 + x = -24

To finish solving, subtract 27 from both sides of the equation, we get

x = -24 - 27

x = -51

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Answer:

( k-4)(k+2)

Step-by-step explanation:

k² - 2k - 8

What 2 numbers multiply to -8 and add tp -2

-4*2 = -8

-4+2 = -2

( k-4)(k+2)

Refer to the attachment for steb-by-step explanation.

Answer:

See Below

Step-by-step explanation:

A reciprocal is a fraction that is flipped over and multiplied. For a drawing, you could put something like:

2/3 times 3/2 = 1.

The answer to the given question is <0.01.

What is confidence level?

The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.

What is p-value?

P-value is the probability of getting the results you did, given that the null hypothesis is true.

When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).

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True. The element (3) is indeed an element of the set A = {2, 3, 5, 7, 11}.

To determine if (3) is an element of A, we need to check if the number 3 is present in the set A. Upon inspecting the elements of A, we can see that 3 is one of the elements in the set. Therefore, the statement "True" is correct.

In set notation, we represent a set by listing its elements within curly brackets {}. The set A is defined as A = {2, 3, 5, 7, 11}, which means that A contains the elements 2, 3, 5, 7, and 11. Since 3 is one of the elements listed in the set A, we can conclude that (3) is indeed an element of A.

It's important to note that in set theory, elements can be repeated only once in a set. Therefore, even though the number 3 appears twice in the given set A (once as an element and once in the parentheses), it is still considered a single element in the set. Thus, we can confidently state that the element (3) is present in the set A, and the correct answer is "True".

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Answer:

Step-by-step explanation:

Answer:

the answer is 9

because 8 8/9 is first

1 plus 8 8/9 is 9

Answer:

-3125

Step-by-step explanation:

Solution:

-5^6

-5 * -5 * -5 * -5 * -5

-15,625

Best of Luck!

Answer:

50 times

Step-by-step explanation:

Total number of faces = total possible outcomes = 8

Number of 2 or 3 on spinner = required outcome = 2

Probability of obtaining a 2 or 3 = required outcome / Total possible outcomes

P(2 or 3) = 2 / 8 = 1/ 4

From 200 ; prediction for the number of 2 or 3

1/4 * 200

= 50 times

Journal entries for Southeastern College as a public university:

1. Donation received for capital addition:

Restricted Cash - Capital Additions Dr. $502,000

Donation Revenue Cr. $502,000

2. Contribution to the permanent endowment:

Cash Dr. $210,000

Permanently Restricted Net Assets Cr. $210,000

3. Interest and dividends received on endowment investments:

Restricted Cash - Scholarships Dr. $50,000

Investment Income Cr. $50,000

4. Increase in fair value of investments:

Investment Gain  Dr. $7,100

Unrestricted Net Assets  Cr. $7,100

To record the transactions for Southeastern College as a public university, the following journal entries are made:

1. Recording the donation received for capital addition:

Restricted Cash - Capital Additions  Dr. $502,000

Donation Revenue Cr. $502,000

The restricted cash is increased by $502,000, representing the additional donation received for capital additions. The corresponding revenue account is credited.

2. Recording the contribution to the permanent endowment:

Cash Dr. $210,000

Permanently Restricted Net Assets Cr. $210,000

The cash received from the alum is debited, and the permanently restricted net assets (part of the endowment) are credited.

3. Recording interest and dividends received on endowment investments:

Restricted Cash - Scholarships Dr. $50,000

Investment Income Cr. $50,000

The interest and dividends received on the endowment investments are debited to restricted cash for scholarships, and the investment income account is credited.

4. Recording the increase in fair value of investments:

Investment Gain  Dr. $7,100

Unrestricted Net Assets  Cr. $7,100

The increase in the fair value of the investments is recorded as an investment gain. The unrestricted net assets account is credited, as gains or losses from changes in fair value are not distributed and remain in the endowment.

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Answer:

To obtain the third side of an isosceles triangle with two sides known, use the Pythagorean theorem if it is a right triangle or provide additional information if it is no

Step-by-step explanation:

You can follow these steps:

Identify the two sides that are known. In an isosceles triangle, these will be the two equal sides, often referred to as the legs of the triangle.

Determine the length of the base. The base is the third side of the triangle, and it is the side that is not equal to the other two sides.

If the isosceles triangle is also a right triangle, you can use the Pythagorean theorem to find the length of the base. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, you can use the formula:

base^2 = (leg1)^2 + (leg2)^2

Take the square root of both sides to solve for the base:

base = √((leg1)^2 + (leg2)^2)

If the isosceles triangle is not a right triangle, you need additional information to determine the length of the base. This could be the measure of an angle or another side length.

Remember that the lengths of the two equal sides (legs) in an isosceles triangle are always equal, while the length of the base is different.

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(a) Marginal pdfs of X, Y, and Z found by integrating joint pdf.

(b) Computed probabilities for specified ranges.

(c) Determined independence of X, Y, and Z.

(d) Calculated expectation E(X^2YZ + 3XY^4Z^2).

(e) Found cdfs of X, Y, and Z.

(f) Obtained conditional distribution and evaluated E(X + Y | z).

(g) Determined conditional distribution and computed E(X | y, z).

(a) To find the marginal probability density functions (pdf) of X, Y, and Z, we integrate the joint pdf f(x, y, z) over the respective variables:

Marginal pdf of X:

f_X(x) = ∫∫ f(x, y, z) dy dz

      = ∫∫ 2(x + y + z)/3 dy dz

      = ∫ [2xy + 2yz + 2xz]/3 dy dz

      = [xy^2 + yz^2 + xz^2]/3 evaluated from y = 0 to y = 1 and z = 0 to z = 1

      = (x + xz^2)/3

Similarly, we can find the marginal pdfs of Y and Z:

Marginal pdf of Y:

f_Y(y) = ∫∫ f(x, y, z) dx dz

      = ∫ [2(x + y + z)/3] dx dz

      = [xy + y^2 + yz]/3

Marginal pdf of Z:

f_Z(z) = ∫∫ f(x, y, z) dx dy

      = ∫ [2(x + y + z)/3] dx dy

      = [xz + yz + z^2]/3

(b) To compute the probabilities P(0 < X < 1/2, 0 < Y < 1/2, 0 < Z < 1/2) and P(0 < X < 1/2) = P(0 < Y < 1/2) = P(0 < Z < 1/2), we integrate the joint pdf over the respective ranges:

P(0 < X < 1/2, 0 < Y < 1/2, 0 < Z < 1/2) = ∫∫∫ f(x, y, z) dx dy dz

                                       = ∫∫∫ 2(x + y + z)/3 dx dy dz

                                       = ∫ [x^2/3 + xy/3 + xz/3] evaluated from x = 0 to x = 1/2, y = 0 to y = 1/2, z = 0 to z = 1/2

                                       = 1/8

P(0 < X < 1/2) = P(0 < Y < 1/2) = P(0 < Z < 1/2) = 1/8 (since the ranges of integration are the same for all three variables)

(c) To determine if X, Y, and Z are independent, we need to check if the joint pdf can be factored into the product of the marginal pdfs:

f(x, y, z) = f_X(x) * f_Y(y) * f_Z(z)

If this condition holds, then X, Y, and Z are independent. We can check this by comparing the joint pdf with the product of the marginal pdfs.

(d) To calculate E(X^2YZ + 3XY^4Z^2), we multiply the function X^2YZ + 3XY^4Z^2 by the joint pdf f(x, y, z) and integrate over the respective ranges:

E(X^2YZ + 3XY^4Z^2) = ∫∫∫ (X^2YZ + 3XY^4Z^2) * f(x, y, z) dx dy dz

(e) To determine the cumulative distribution functions (cdf) of X, Y, and Z, we integrate the marginal pdf

s over their respective ranges:

CDF of X:

F_X(x) = ∫ f_X(t) dt evaluated from t = 0 to t = x

Similarly, we can find the cdfs of Y and Z:

CDF of Y:

F_Y(y) = ∫ f_Y(t) dt evaluated from t = 0 to t = y

CDF of Z:

F_Z(z) = ∫ f_Z(t) dt evaluated from t = 0 to t = z

(f) To find the conditional distribution of X and Y, given Z = z, we need to calculate the conditional pdf f(x, y | Z = z). This can be done using the joint pdf and applying the conditional probability formula.

Once we have the conditional pdf, we can evaluate E(X + Y | z) by integrating (x + y) * f(x, y | Z = z) over the respective ranges.

(g) To determine the conditional distribution of X, given Y = y and Z = z, we calculate the conditional pdf f(x | Y = y, Z = z). This can be done using the joint pdf and applying the conditional probability formula.

Once we have the conditional pdf, we can compute E(X | y, z) by integrating x * f(x | Y = y, Z = z) over the respective range.

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Answer:

18

Step-by-step explanation:

The key of this leaf stem-leaf plot is:

4 | 5 = 45

Therefore, the data points that represents children with weight that is less than 50 pounds would be as follows:

First row => 12, 13, 15, 15 15, 16, 16, 19

Second row => 23, 25

Third row => 33, 35, 37, 38, 39

Fourth row => 44, 45, 45

Therefore, the number of children that weigh less than 50 pounds = 18

Answer:

12

Step-by-step explanation: has to do with ratios and proportionalities. 3/8 is going to equal b/32. B = to number of basil leaves. 32/8= 4. 4x3=12.

Answer:

Twelve.

Step-by-step explanation:

This scenario can be interpreted by the ratio 3:8, with 3 being the amount of basil leaves and 8 being the amount of tomatoes. If there were 32 tomatoes in the sauce, then there would have been 12 basil leaves.

3:8

6:16

9:24

12:32

All of these ratios can simplify back down to 3:8.

X = 5 boxes

figure out the X for each person

Lizzy sold: 5 * 5 = 25 boxes

Suzy sold: 5 * 1 = 5 boxes

John sold: 5 * 3 = 15 boxes

Mark sold: 5 * 8 = 40 boxes

Lamar sold: 5 * 4 = 20 boxes

→ How many boxes did Lamar sell?

Answer: 20 boxes

→ How many more boxes did John sell than Suzy?

Answer: 10 boxes

workout: 15 boxes - 5 boxes = 10 boxes more

→  How many more boxes would Lizzy have to sell to equal how many Mark sold?

Answer: 15 boxes

workout: 40 boxes - 25 boxes = 15 boxes more

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Here we go ~

Each Cross (X) represents 5 boxes

Now, let's move on to questions :

-) 4 Cross = 4 × 5 = 20 boxes

-) (4× Cross) - (1 × cross)

-) (3 × 5) - (5)

-) 25 - 5 = 10more boxes than Suzy

-) (8 × Cross) - (5 × Cross)

-) (8 × 5) - (5 × 5)

-) 40 - 25

-) 15 more boxes to be sold to get equal to the number of boxes mark sold.

To be able to test the claim it implies that  the mean blood glucose level of senior citizens is higher than 100 mg/dL at the 0.05 level of significance, so, one can carry out a one-sample t-test.

The steps to conduct the test are:

So, Rejecting the null hypothesis implies that there is ample evidence to back the argument that senior citizens' average blood glucose level is higher than 100 mg/dL. If we do not reject the null hypothesis, we cannot definitively say that the average blood glucose level is higher than 100 mg/dL.

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Answer:

12

Step-by-step explanation:

If the perimeter is 58,

take 17(2) for booth sides.

Which you will get 34.

58-34=24

Now you know that the remainder is the two vertical sides.

24/2=12

BC=12

Answer:

[3,0]

[0,9]

Step-by-step explanation:

9x+3y=27

9x+3(0)=27

9x=27

x=3

9(0)+3y=27

3y=27

y=9

Answer:

y ≤ 1/2x + 5

Step-by-step explanation:

-3x + 6y ≤ 30

add 3x on both sides:

6y ≤ 3x + 30

divide 6 on both sides:

y ≤ 3/6x + 30/6

This is simplified to:

y ≤ 1/2x + 5

Answer:

32n

Step-by-step explanation:

Product means to multiple

So “product of a number” is something times a variable, in this case I used “n” to represent “number” but you don’t have to use “n” if you don’t want to, you could other letters to represent the “number”. The “number” is unknown so that way it is a variable.

The “and 32” is what the “number” is multiple to, so the answer would be: 32n

The Polynomial of least degree with roots 7 and -9 is x^2 + 2x - 63.

To polynomial with roots at 7 and -9, we can use the fact that if a number r is a root of a polynomial, then the corresponding factor is (x - r).

Let's begin by setting up the factors for the given roots:

Factor 1: (x - 7)

Factor 2: (x - (-9)) = (x + 9)

To find the polynomial of least degree, we multiply these factors together:

Polynomial = (x - 7)(x + 9)

To simplify further, we can use the distributive property:

Polynomial = x(x + 9) - 7(x + 9)

Expanding the terms:

Polynomial = x^2 + 9x - 7x - 63

Combining like terms:

Polynomial = x^2 + 2x - 63

Therefore, the polynomial of least degree with roots 7 and -9 is x^2 + 2x - 63. This polynomial is in standard form with a leading coefficient of 1, which is the desired format.

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Answer:

4 hours

Step-by-step explanation:

3.6 / .8

According to the angle bisector theorem, AB/AD = BC/CD.

It means that 13/4 = (3.5x + 8) / 7x.

13 * 7x = (3.5x + 8) * 4

91x = 14x + 32

77x = 32

x = 32/77.

Answer:

add 21 five times

Step-by-step explanation:

The domain and range of the inverse relation are {2, 3, 5, 7, 8} for both.

The given relation consists of the points 2, 3, 5, 7, and 8. To find the domain and range of the inverse relation, we need to swap the x-values with the y-values. The resulting set of values will represent the domain and range of the inverse relation.

In the given relation, the x-values are 2, 3, 5, 7, and 8, and the corresponding y-values are not provided. To find the inverse relation, we swap the x-values with the y-values.
After swapping the values, we obtain the following set of points: (2, 2), (3, 3), (5, 5), (7, 7), and (8, 8). These points represent the inverse relation.
The domain of the inverse relation is the set of x-values from the swapped points, which is {2, 3, 5, 7, 8}. This means that these are the values for which there exist corresponding y-values in the original relation.
Similarly, the range of the inverse relation is the set of y-values from the swapped points, which is also {2, 3, 5, 7, 8}. These are the values that correspond to the x-values in the original relation.
Therefore, the domain and range of the inverse relation are {2, 3, 5, 7, 8} for both.

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69.1° is the value of C by Law of Cosines .

What is the cosine law?

The formula for the Law of Cosines is c2=a2+b22ab cosC. With the exception of the third component, which equals 0 if C is a right angle because the cosine of 90° is 0 and we have the Pythagorean Theorem, this is similar to the Pythagorean Theorem.

The Law of Cosines is given as

c² = a² + b² - 2ab-cosC

substitute the values in a, b, c

Plugging in given values, we get

  16² = 8² + 17² - 2 . 8 . 17 . cosC

   256 = 64 + 289 - 272. CosC

    256 = 353 - 272 . cosC

     256 - 353 = 272 . CosC

         -97 =   272 . CosC

            cosC = -97/-272

          C = across(97/272)

            C  = 69.1°

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Answer:

C= 83.04

Step-by-step explanation:

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. It is a point at which there is no net change, or a point of equilibrium.

A stable solution is a solution to a problem that does not change when the parameters of the problem are slightly varied. The parameters of a problem can refer to the data, assumptions, constraints, or other factors that are used to define the problem. When the parameters are changed, a stable solution will remain intact, indicating that it is the best solution to the problem.

For example, if a mathematics problem has a solution of 3, this solution is considered to be stable, as changing any of the parameters of the problem will not alter the solution of 3.

Stable solutions are important as they provide a point of equilibrium, or a point at which there is no net change. This can help to ensure that the solution is the most effective one to the problem.

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