1. Determine all angles between 0 and 360 degrees that meet
sin3v = sin33
2. Find all angles v between −π and π that satisfy
4 cos (v)^2 − 4 cos (v) = -1

The point (-2, -10) does not lie on the line y = 3x - 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question:

y = 3x - 3

To check if the point (-2, -10) lies on the line y = 3x - 3, we need to substitute the values of x and y into the equation and see if it is true.

y = 3x - 3

Plug in x = -2 and y = -10

-10 = 3(-2) - 3

Simplify

-10 = -6 - 3

-10 = -9

But we know that -10 ≠ -9, hence, this is not a true statement.

Therefore, the point does not lie on the line.

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Answer:

0? and 14?

Step-by-step explanation:

thats what I see im so sorry if im wrong

The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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To find the roots of a third-degree polynomial, also known as a cubic polynomial, we can use a method called factoring or apply the cubic formula.

The first step is to check if there are any common factors that can be factored out. Next, we can use the rational root theorem to determine potential rational roots. By applying synthetic division or long division, we can divide the polynomial by the potential roots to see if they are indeed roots.

If a rational root is found, we can then use synthetic division to factor out the corresponding quadratic equation. Finally, we can solve the quadratic equation using methods like factoring, completing the square, or using the quadratic formula to find the remaining roots.

It's important to note that not all cubic polynomials can be easily factored or solved algebraically. In such cases, numerical methods or approximation techniques may be used to find the roots.

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To find the roots of a third degree polynomial, you can follow these steps: 1) Check for rational roots using the Rational Root Theorem. 2) Use synthetic division to divide the polynomial by a linear factor. 3) Factor the resulting quadratic equation. 4) Solve for the roots by setting each factor equal to zero.

To find the roots of a third degree polynomial, we can follow these steps:

Remember, the Fundamental Theorem of Algebra states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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a) The actual water phase mass flux, Gₓ is 0.148 kg m⁻²s⁻¹.

b) The mole fraction of acetone in the exit water stream is 0.000355.

c) The value of Hₓ, the height of the packing is 0.214 meters.

d) The height of the packing is 0.214 meters.

To solve this problem, we'll use the concept of mass transfer in a packed tower. Let's calculate the required values step by step:

(a) The actual water phase mass flux, Gₓ:

We know that Gᵧ is the gas phase mass flux, and the ratio of liquid to gas phase mass flux is given by Gₓ/Gᵧ = kᵧa / kₓa. Plugging in the given values, we have

Gₓ/0.82 = 0.048 / 0.266

Solving for Gₓ, we find Gₓ = 0.82 * (0.048 / 0.266) = 0.148 kg m⁻²s⁻¹.

(b) The mole fraction of acetone in the exit water stream:

Using the equilibrium relationship y* = 2.53x, we can relate the mole fractions of acetone in the gas phase (y) and liquid phase (x). Since we're removing 95% of acetone, the mole fraction of acetone in the exit gas stream is

0.018 * (1 - 0.95) = 0.0009

Using the equilibrium relationship, we find x = 0.0009 / 2.53 = 0.000355 for the exit water stream.

(c) Hₓ, the height of the packing:

Hₓ can be calculated using the formula Hₓ = (Gₓ / kₓa) * (y* - y). Substituting the known values, we have

Hₓ = (0.148 / 0.266) * (2.53 * 0.000355 - 0.0009) = 0.214 meters.

(d) The height of the packing:

The height of the packing is typically determined by factors such as desired separation efficiency, pressure drop, and other design considerations. In this case, we've only calculated Hₓ, which represents the height required for the given separation efficiency. Additional factors may need to be considered to determine the overall height of the packing in a practical design.

In summary, we've calculated the actual water phase mass flux, the mole fraction of acetone in the exit water stream, and the height of the packing required to achieve 95% removal of acetone. These values provide important insights for designing a packed tower for acetone removal using water as the solvent.

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Answer:

Step-by-step explanation:

Angle ABE = 90°

Angle CBE = 37° (opposite angle)

90 - 37 = 53°

Answer: B

Step-by-step explanation: Solve the equation.

\(3-3x < 20\)

\(-3x < 17\)

\(x > -17/3\)

We flip the sign to greater than because we used the division operator. Since -6 is less than -17/3, it falls out of the range of solutions and is therefore a non-possible solution.

Range is one of the important description of a data set. The range of the given data sets is given as:

Range = Maximum value of the data set - Minimum value of the data set.

For the given sets, we get their range as:

Maximum value = 48, minimum value = 11

Range of the data set = Maximum value - minimum value = 48-11 = 37

Maximum value = 49, minimum value = 40

Range of the data set = Maximum value - minimum value = 49 - 40 = 9

Maximum value = 96, minimum value = 31

Range of the data set = Maximum value - minimum value = 96-31=65

Maximum value = 175, minimum value = 112

Range of the data set = Maximum value - minimum value = 175-112 = 63

Thus, the range of the given data sets is given as:

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Answer:

B. 30 soda cans

Step-by-step explanation:

Range = max number - min number = 40 - 10 = 30

Therefore, the only solution is c1 = c2 = 0, which means that the set of functions {sin²(x), 1 - cos(2x)} is linearly independent on the interval (-∞, ∞).

To check if the given set of functions is linearly independent, we need to determine if there exist constants c1 and c2, not both zero, such that:

c1sin²(x) + c2(1 - cos(2x)) = 0 for all x in (-∞, ∞)

To do this, we can look for values of x that make one of the terms equal to zero, and then solve for the other constant.

If we let x = 0, then we have:

c10 + c2(1 - cos(0)) = c2 = 0

So we know that c2 = 0, which means that the equation reduces to:

c1*sin²(x) = 0 for all x in (-∞, ∞)

This can only be true if c1 = 0, because sin²(x) is never zero for all x.

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Answer:

D. E=5m+5c is the answer

Answer:

\(x = \frac{1}{4} \)

\(y = \frac{2}{4} \)

The approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

The probability that a seed germinates is 87%, which means the probability that a seed does not germinate is 13%.

To approximate the probability that fewer than 71 seeds germinate, we can use the normal approximation to the binomial distribution since the sample size is large (90 seeds) and the probability of success is not too close to 0 or 1 (0.87).

First, we calculate mean and standard deviation of this binomial distribution:

Mean = n * p = 90 * 0.87 = 78.3
Standard deviation =\(\sqrt{(n * p * (1 - p))}  = \sqrt{(90 * 0.87 * 0.13)}\) = 3.25

Now, we can standardize the random variable X (number of seeds that germinate) using the formula:

Z = (X - mean) / sd

For X = 70.5 (the midpoint of the interval "fewer than 71 seeds germinate"), we get:

Z = (70.5 - 78.3) / 3.25 = -2.40

Using a standard normal table or calculator, we find probability that Z value is less than -2.40, which equals to nearly 0.0082.

Therefore, the approximate probability that fewer than 71 seeds germinate is 0.0082, or 0.82%.

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The probability that at least two of the kittens will be chocolate brown is 0.3087.

We have,

Number of kittens = 5

Each kitten has a 30% chance of being chocolate brown.

So, p = 0.5 and q= 1-0.3 = 0.7

Now, P(X =2) = C( 5, 2) 0.3² (0.7)³

= 5! / 2!3! (0.09) (0.343)

= 10 x 0.03087

= 0.3087

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Answer:

It depends how many points you already have

Step-by-step explanation:

how much are the essays worth? i might be able to get your final score if you tell me

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Given equation is : $y'(t) = -\frac{y}{(-y/2)+4}$ To find the equilibrium solution, we need to set $y' = 0$ and solve for $y$:

Now, to sketch the direction field, we can use the formula $y' = f(t, y)$. We can create a table of values and plot the direction arrows based on the sign of $y'$: Next, we need to determine whether the equilibrium solution is stable or unstable. We can use the first derivative test to do this. We need to find the sign of $y'(t)$ for $y$ values that are slightly greater and slightly less than $0$.If $y$ is slightly greater than $0$, then $(-y/2)+4$ is slightly less than $4$, so $y'(t)$ is negative.

Therefore, the solution moves towards the equilibrium solution, which means that it is stable. If $y$ is slightly less than $0$, then $(-y/2)+4$ is slightly greater than $4$, so $y'(t)$ is positive. Therefore, the solution moves away from the equilibrium solution, which means that it is unstable. The equilibrium solution is $y = 0$. See the attached image for the direction field. The equilibrium solution is stable.

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Answer: pretty sure 25 feet

Step-by-step explanation:

The formula for a function that has vertical asymptotes is x=5 and x=8 and horizontal asymptote y=5 is f(x)=(5x²)/(x²-13x+40)

In order to find a function that fits the criteria given, you need to know how to find the asymptotes in the first place.

Vertical Asymptotes: we set the denominator equal to 0 and solve for x

Horizontal Asymptotes: we compare the degree of the numerator and denominator; if the degrees are equal, the HA equals the ratio of the leading coefficients, which is the case for this question

For the vertical asymptotes, if x = 8 and x = 5, then we can write the factors as (x - 8) and (x - 5).

For the horizontal asymptotes, if y = 5, the degree of the numerator and denominator are equal so the ratio of the leading coefficients must be 5/1.

f(x) = (5x²) / [(x-8)(x-5)]  which can be rewritten as f(x) = (5x²) / (x2-13x+40)

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Answer:

(9,  2)

Step-by-step explanation:

tell me in the comments if i'm right

Answer:

Hey! The image I not clear...Can you upload a more clear image?

Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Step 1: Problem

A pigeon was sitting 33 feet from the base of a telephone pole and flew 65 feet to reach the top of the pole. How tall is the telephone pole? ​

Step 2: Concept

Addition

Step 3: Method

The height of the telephone pole = 65 + 33

= 98 feet

Step 4: Final answer

The height of the telephone pole = 98 feet

Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

Based on the division of 6 and 2 over 5 by  negative 4 and 1 over 3, the result would be negative 1 and 31 over 65.

The operation required is to divide 6 and 2 over 5 by  negative 4 and 1 over 3.

As a math expression, this can be shown as:

= 6²/₅ ÷ -4¹/₃

First, make them improper fractions:

= 32/ 5 ÷ -13/3

This can be converted to multiplication as:

= 32/ 5 x -3/13

= 96 / 65

= -1³¹/₆₅

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Answer:

-1 31/65

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to find the horizontal and vertical distances between two points, and you want to know how to use those to find the distance between those points.

__

The x-coordinate of a point is its horizontal distance from the y-axis. The horizontal distance between two points will be the difference of their x-coordinates.

If the points are (3, -4) and (x, y), the x-coordinates are 3 and x. The difference between those coordinates can be written as x-3. (Usually, we subtract the first point from the second one.)

The horizontal distance from (3, -4) to (x, y) is (x -3).

__

In like fashion, the y-coordinate of a point is its vertical distance from the x-axis. The vertical distance between two points will be the difference of their y-coordinates.

For the points (3, -4) and (x, y), the y-coordinates are -4 and y. The difference between those coordinates is y -(-4) = y +4.

The vertical distance from (3, -4) to (x, y) is (y +4).

__

As the attachment shows, the horizontal and vertical distances between the two points can be considered to be the legs of a right triangle. The "total" distance between the points is the straight-line distance. It is the hypotenuse of that triangle.

The Pythagorean theorem gives the relation between the sides and hypotenuse of a right triangle. In this context, the Pythagorean theorem can be used to create an equation showing the relationship between the legs of the triangle and the distance from (x, y) to the center. (That distance is the radius.)

In particular, the equation created is ...

  (x -3)² +(y +4)² = 7²

_____

Additional comment

For right triangle legs 'a' and 'b', and hypotenuse 'c', the Pythagorean theorem tells you ...

  a² +b² = c²

The sum of the squares of the sides is equal to the square of the hypotenuse.

The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

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The method that may lead to revenue and cost of goods sold being translated/remeasured at different exchange rates is the temporal method of translation.

Under the temporal method of translation, different exchange rates are used to translate monetary assets and liabilities, including revenue and cost of goods sold. This occurs when a foreign subsidiary operates in a hyperinflationary economy or when the functional currency of the subsidiary differs from the reporting currency of the parent company.

Revenue and cost of goods sold are typically translated using different exchange rates due to the specific rules outlined by the temporal method. Revenue is generally translated using the exchange rate at the date of sale, which reflects the rate in effect when the economic activity occurs. On the other hand, cost of goods sold is translated using the exchange rate at the date of acquisition of the goods, which captures the rate when the inventory was purchased or produced.

These different exchange rates can lead to a discrepancy between revenue and cost of goods sold when the exchange rates fluctuate significantly between the sale and acquisition dates. This discrepancy affects the gross profit margin and can impact the financial performance and profitability analysis of a company. Therefore, it is important for multinational companies to carefully consider the choice of translation method and its potential effects on financial reporting.

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