Write the equation of each circle. center at (-4, 3), radius 9

Answer:

On the trig unit circle,

tan 225 = tan (45 + 180) = tan 45 = 1

Answer:

A one tailed test

Step-by-step explanation:

Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.

Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.

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One-Tailed Test

Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.

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Answer:

A={21,24,27,30}

B={21,27}

C={24,30}

Step-by-step explanation:

a)A U B={21,24,27,30}

b)A n C ={24,30}

9514 1404 393

Answer:

  A ∪ B = {21, 23, 24, 25, 27, 29, 30, 31}

  A ∩ C = {24, 30}

Step-by-step explanation:

  A = {21, 24, 27, 30} . . . . . . . . . . . . . multiples of 3

  B = {21, 23, 25, 27, 29, 31} . . . . . . . odd numbers

  C = {20, 22, 24, 26, 28, 30, 32} . . . even numbers

The union is the list of numbers in either set.

  A ∪ B = {21, 23, 24, 25, 27, 29, 30, 31}

The intersection is the list of numbers in both sets.

  A ∩ C = {24, 30}

A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

Here,

From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,

98%C.I. = µ ± z * σ /   n = 98.90 ± 2.33 * 42.30 / sqrt of 16  = 98.90 ± 24.64 = 74.26 to 125.54

The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.

Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

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Answer:

- 5x

Step-by-step explanation:

note that + (-) = -

2.5x + (- 5x) - 2.5

= 2.5x - 5x - 2.5 ← collect like terms

= 2.5 - 2.5 - 5x

= 0 - 5x

= - 5x

1. The mean of a dataset represents the average value of the entire set of numbers. It is calculated by adding up all the values and dividing by the number of values in the dataset. Knowing the standard deviation of a dataset adds information about how much the values deviate from the mean.

A high standard deviation indicates that the values are more spread out from the mean, while a low standard deviation indicates that the values are closer to the mean. It can help to identify outliers and the overall variability of the dataset.

2. A p-value is a statistical measure that helps to determine whether the null hypothesis (there is no significant difference between two groups) is true or false.

It is the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. A p-value of less than 0.05 (typically) is considered statistically significant, which means that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis (there is a significant difference between the two groups).

3. Alpha is the level of significance that is set to determine whether a p-value is statistically significant or not. It is typically set at 0.05, which means that if the p-value is less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected.

If the p-value is greater than 0.05, then the result is not statistically significant and the null hypothesis cannot be rejected. In summary, alpha and p-value are related because alpha sets the threshold for determining whether a p-value is statistically significant or not.

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The measure of angle A in the isosceles triangle ABC is 62.5 degrees.

In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).

Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.

Therefore, we have:

∠A ≅ ∠C

Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:

∠A + ∠B + ∠C = 180

Substituting the given values:

∠A + 55 + ∠A = 180

Combining like terms:

2∠A + 55 = 180

Subtracting 55 from both sides:

2∠A = 180 - 55

2∠A = 125

Dividing by 2:

∠A = 125 / 2

∠A = 62.5

Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.

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Answer:

8x + 4

Step-by-step explanation:

Subtract the numbers: 2x + 5 + 6x - 1     2x + 4 + 6x

Then, you combine them like terms: 2x + 4 + 6x = 8x + 4

Answer:

B

Step-by-step explanation:

-2x<7-5

-2x<2 multiplied by -1 gives 2x>-2 and devided by 2 you have x>-1

To find the curvature of the curve defined by the vector function r(t) = < t^2, ln(t), t ln(t) > at a given point, we need to calculate the curvature using the formula:

κ = |dT/ds| / ||dT/ds||,

where dT/ds is the unit tangent vector and ||dT/ds|| is its magnitude.

Let's proceed with the calculations:

Step 1: Find the first derivative of r(t) to get the tangent vector T(t):

r'(t) = < 2t, 1/t, ln(t) + t/t > = < 2t, 1/t, ln(t) + 1 >.

Step 2: Calculate the magnitude of the tangent vector:

||r'(t)|| = sqrt((2t)^2 + (1/t)^2 + (ln(t) + 1)^2)

         = sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1).

Step 3: Differentiate r'(t) to find the second derivative:

r''(t) = < 2, -1/t^2, 1/t + 2/t > = < 2, -1/t^2, (t + 2)/t >.

Step 4: Calculate the magnitude of the second derivative:

||r''(t)|| = sqrt(2^2 + (-1/t^2)^2 + ((t + 2)/t)^2)

          = sqrt(4 + 1/t^4 + (t^2 + 4t + 4)/t^2)

          = sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2).

Step 5: Calculate the curvature:

κ = |dT/ds| / ||dT/ds||

  = (||r'(t)|| / ||r''(t)||^3)

  = ((sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1)) / (sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2))^3).

To find the curvature at a specific point, substitute the value of t into the expression for κ.

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The other set of polar coordinates for the point (-7, -7√3) is (14, 4π/3) or (14, 240°) in degrees.

To find the polar coordinates for a point given in rectangular coordinates, we use the formulas: r = √(x^2 + y^2) and θ = tan^-1(y/x).

Using these formulas, we can find the polar coordinates for the point (-7, -7√3):

r = √((-7)^2 + (-7√3)^2) = √(49 + 147) = √196 = 14

θ = tan^-1((-7√3)/-7) = tan^-1(√3) = π/3

Therefore, the polar coordinates for the point (-7, -7√3) are (14, π/3) or (14, 60°) in degrees.

It is important to note that there is another set of polar coordinates for this point, since the point (-7, -7√3) is in the third quadrant, and angles in the third and fourth quadrants are measured with respect to the negative x-axis. So, we add π to our angle to get:

θ = tan^-1((-7√3)/-7) + π = tan^-1(√3) + π = 4π/3

Therefore, the other set of polar coordinates for the point (-7, -7√3) is (14, 4π/3) or (14, 240°) in degrees.

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Answer:

\(5. \: \: 8 + 5(7) = 8 + 35 = 43\)

I hope I helped you^_^

Answer:

y = - 5x + 16

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 1 ) and (x₂, y₂ ) = (4, - 4 )

m = \(\frac{-4-1}{4-3}\) = \(\frac{-5}{1}\) = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 1 )

1 = - 5(3) + c = - 15 + c ( add 15 to both sides )

16 = c

y = - 5x + 16 ← equation of line

Step-by-step explanation:

3+21+7+3+21+7

Answer:

21

Step-by-step explanation:

You got it right.

Answer: 12

Step-by-step explanation: 4x3= 12 hope it helps! :)

A mathematical process called subtraction reflects the elimination of items from a collection. There are 14 pupils that enjoy pink polka dots.

A mathematical process called subtraction reflects the elimination of items from a collection.

Subtraction is symbolised by the negative sign.

Considering that there were 50 students in the sample as a whole, the number of pupils who enjoy pink polka dots is as follows:

50 students divided by (4+9+11+9+3) yields 14 students.

Thus, there are 14 students that enjoy pink polka dots.

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The complete question is:

A sample of 50 11th graders was asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were.

blue on grey 4

green 9

pink polka dots?

purple 11

red and orange stripes 9

yellow 3

The counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is the missing value in the table?

The Laplace transform of the given function is L{ \(e^(2-t^)\) u(t-2)} =  \(e^-^2^s\)  * e² * (1/(s + 1)).

The Laplace transform L{ \(e^(2-t^)\) u(t-2)} can be found using the following steps:

1. Identify the function: f(t) =  \(e^(2-t^)\) u(t-2)
2. Apply the time-shift property: L{ \(e^(2-t^)\) u(t-2)} = \(e^-^2^s\)  * L{e² *  \(e^-^t\) }
3. Calculate the Laplace transform: L{e² *  \(e^-^t\) } = e² * L{ \(e^-^t\) }
4. Apply the formula: L{ \(e^-^t\) } = 1/(s + 1)
5. Multiply:  \(e^-^2^s\)  * e² * (1/(s + 1))

In this process, we first identified the given function and then applied the time-shift property to simplify it.

Next, we calculated the Laplace transform of the simplified function using the formula for the Laplace transform of an exponential function. Finally, we combined the results to obtain the Laplace transform of the original function.

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Answer: Distributive Property

Step-by-step explanation:

The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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The equation

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

The line with that slope and that passes throught (1,6) is:

The following graph shows both equations:

The final number remaining in this sequence is the number 2.

We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.

After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.

Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.

After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.

We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.

Continuing this process, we will eventually reach a point where we have only one number left.

Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.

Therefore, the final number remaining in this sequence is the number 2.

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Answer:

6a^2-a-35

Step-by-step explanation:

(3a + 7) (2a – 5)

F: 6a^2

O: -15a

I: 14a

L: -35

combine like terms

6a^2-a-35

Answer:

The 6ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 13

Common Difference = (d) = 4

Now, For 6ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₆ = 13 + (6 - 1) × 4

a₆ = 13 + 5 × 4

a₆ = 13 + 20

a₆ = 33

Thus, The 6ᵗʰ term of this sequence is 33

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Answer:

It should be 60 degrees

Step-by-step explanation:

the yield received by the holder of the bill at the date of maturity is approximately 10.15%.

To calculate the yield received by the holder of the bill at the date of maturity, we need to use the formula for yield to maturity. The formula is:

Yield to Maturity = (Face Value - Purchase Price) / Purchase Price * (365 / Days to Maturity)

In this case:

Face Value = $150,000

Purchase Price = $138,222

Days to Maturity = 60 - 25 = 35

these values in the formula, we can calculate the yield to maturity:

Yield to Maturity = ($150,000 - $138,222) / $138,222 * (365 / 35)

Yield to Maturity ≈ 0.1015 or 10.15%

Therefore, the yield received by the holder of the bill at the date of maturity is approximately 10.15%.

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Answer:

Solution is (3, -3)

Step-by-step explanation:

To solve by graphing, you literally have to graph both lines to see where they intersect. That point of intersection is the solution to the given system.

Given the following linear equations:

y = - x   where the slope (m) = -1, and the y-intercept (b) = 0.

y = x - 6 where the slope (m) = 1, and the y-intercept (b) = -6.

Plot the intercepts (0, 0) for the first line, and (0, -6) for the second line, as a starting point, then use the given slopes (rise over run) of each line to plot the next points. Repeat the process until you have enough points to connect with and create a line.

Attached is a screenshot of the graphed systems of linear equations. It shows that the solution is (3, -3).

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Answer:

720 possible arrangements.

Step-by-step explanation:

The possible arrangement of the cars, given that the three cars of the same color are kept together is 4320.

The combination is a way of selecting items from a collection where the order of selection does not matter.

We have,

Number of cars = 8

Number of cars that are the same in color = 3

Cars that are the same in color can be arranged = 3!

There are 8 cars such that,

1 2 3 4 5 6 7 8

Three cars of the same color are taken out and we have,

1  2  3  4  5

We see that there are six spaces = 6!

where we can put the same color cars together so,

The possible arrangement of the cars, given that the three cars of the same color are kept together:

= 3! x 6!

= 3 x 2 x 1  x 6 x 5 x 4 x 3 x 2 x 1

= 4320

Thus,

The possible arrangement of the cars, given that the three cars of the same color are kept together is 4320.

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