Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20} Let sets A and B be subsets of S, where: Set A = {3, 4, 10, 11, 12, 16, 18} Set B = {4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 18, 19, 20} Find the following: The number of elements in the set (A U B): n(A U B) = The number of elements in the set (A B) n(A B) is You may want to draw a Venn Diagram to help answer this question.

Answer:

\(1+6i\)

Step-by-step explanation:

The expression \(1-6i\) represents a complex number. Particularly, complex solutions can't happen in odd number, for example, the minimum complex solutions an expression can have is 2.

Additionally, complex solutions are related by conjugates, which means the second solution to this polynomial is \(1+6i\), because is the conjugate of the given complex root.

The points on function g(x) are: (-3,-2), (-2,-1), (-1,0), (0,1) and (1,2)

The points in the table below are on the linear function f.

x 0 1 2 3 4

f(x) -4 -2 0 2 4

Function g is a transformation of function f using a horizontal shift 3 units left and a vertical compression by a factor of 1/2 . Plot the corresponding points on function g.

The table of values of function f(x) are given as:

x 0 1 2 3 4

f(x) -4 -2 0 2 4

The function f(x) is transformed to g(x) as follows:

Horizontal shift 3 units left

The rule of this shift is:

(x,y) ⇒ (x - 3, y)

So, we have:

x     -3  -2 -1  0  1

f'(x) -4  -2  0  2  4

Vertical compression by 1/2

The rule of this compression is:

(x,y) ⇒ (x, y/2)

So, we have:

x     -3  -2 -1  0  1

g(x) -2  -1  0  1  2

Hence, the points on function g(x) are:

(-3,-2), (-2,-1), (-1,0), (0,1) and (1,2)

See attachment for the graph of g(x)

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If a=4, b= 7, and B= 75°, the area of triangle ABC is approximately 13.476 square units.

To find the area of triangle ABC given the values of a, b, and B, we can use the formula:

Area = (1/2) * a * b * sin(B)

where a and b are the lengths of two sides of the triangle and B is the angle between them, measured in degrees.

Substituting the given values, we get:

Area = (1/2) * 4 * 7 * sin(75°)

Using a calculator to evaluate the sine of 75°, we get:

Area = (1/2) * 4 * 7 * 0.96593

Area ≈ 13.476 square units

The formula for the area of a triangle involves using the length of two sides and the angle between them.

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The values of α and β that make αA + βB + C parallel to the y-axis are α = 2 and β = -1.

To determine the values of α and β, we need to find the coefficients that make the sum αA + βB + C parallel to the y-axis.

First, let's calculate αA + βB + C:

αA = 2(5ax + 3ay - 2az) = 10ax + 6ay - 4az

βB = -1(-ax + 4ay + 6az) = ax - 4ay - 6az

Adding αA, βB, and C together:

αA + βB + C = (10ax + 6ay - 4az) + (ax - 4ay - 6az) + (8ax + 2ay)

= 19ax + 4ay - 10az

To make the expression parallel to the y-axis, the coefficients of ax and az should be zero. Therefore, we equate the coefficients to zero and solve for α and β:

19a = 0 (coefficient of ax)

4a = 0 (coefficient of az)

From these equations, we find that a = 0.

Substituting a = 0 back into the expression αA + βB + C, we get:

αA + βB + C = 19(0)ax + 4ay - 10(0)az = 4ay

Since the expression is now 4ay, it is parallel to the y-axis.

Therefore, the values of α and β that satisfy the condition are α = 2 and β = -1, given that a = 0.

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Answer:

Step-by-step explanation:

Volume of the pool = 30 gallons

It took 5 min to fill 1/4 of the pool

Filling rate:

Filling rate is 1.5 gal/min

Time needed to fill the pool:

Answer:

You are right

Step-by-step explanation:

80% of a number is always going to be less than 100% of a number. Assuming the numbers positive, which it said

Answer: its >

Step-by-step explanation: beacuse80% x .01 =0.008 and 0.008= 0.8%

The Integral Test can be used to determine if an infinite series is convergent or divergent based on whether or not an associated improper integral is convergent or divergent. The given infinite series is ∑n=1​ 1/(3n+1)2​.

The Integral Test states that an infinite series

∑n=1​ a_n is convergent if the associated improper integral converges. The associated improper integral is ∫1∞f(x)dx where

f(x)=1/(3x+1)^2.∫1∞1/(3x+1)2 dxThis integral can be solved using a u-substitution.

If u = 3x + 1, then du/

dx = 3 and

dx = du/3. Using this substitution yields:∫1∞1/(3x+1)2

dx=∫4∞1/u^2 * (1/3)

du= (1/3) * [-1/u]

4∞= (1/3) *

[0 + 1/4]= 1/12Since this integral is finite, we can conclude that the infinite series

∑n=1​ 1/(3n+1)2​ is convergent. To determine how many terms of the series are needed to approximate the sum to within an accuracy of 0.001, we can use the formula:|R_n| ≤ M_(n+1)/nwhere R_n is the remainder of the series after the first n terms, M_(n+1) is the smallest term after the first n terms, and n is the number of terms we want to use.For this series, we can find M_(n+1) by looking at the nth term:1/(3n+1)^2 < 1/(3n)^2

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first of all you have to draw a rhombus

area (d+d)/2

(4+6)/2

5

The requreid Miriam's test does not provide significant evidence that the true population mean is less than 18.

Since the sample size is small (n = 7) and the population standard deviation is unknown, we should use a t-test for this hypothesis test.

The test statistic is calculated as follows:

t = (x - μ) / (s / √n)

Given that Miriam's test statistic is t = -1.9, we can estimate the p-value associated with this test statistic. This denotes the probability of observing a test statistic as extreme as -1.9 or more extreme, assuming the null hypothesis is true.

Using a t-distribution table with 6 degrees of freedom (n-1), we find that the p-value for a one-tailed test at the 5% significance level is approximately 0.051.

Since the p-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is less than 18 at a 5% level of significance.

Thus, Miriam's test does not provide significant evidence that the true population mean is less than 18.

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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In question 5, the graph of equation 4x - 22 + 4y^2 + 122 = 0 is sketched, and the coordinates of any vertices are labeled. In question 6, the graph of equation x^2 + y^2 - 22 - 62 + 9 = 0 is sketched, and the coordinates of any vertices are labeled.

5. To sketch the graph of the equation 4x - 22 + 4y^2 + 122 = 0, we can rewrite it as 4x + 4y^2 = 0. This equation represents a quadratic curve. By completing the square, we can rewrite it as 4(x - 0) + 4(y^2 + 3) = 0, which simplifies to x + y^2 + 3 = 0. The graph is a parabola that opens horizontally. The vertex is located at the point (0, -3), and the axis of symmetry is the y-axis. The graph extends infinitely in both directions along the x-axis.

The equation x^2 + y^2 - 22 - 62 + 9 = 0 represents a circle. By rearranging the equation, we have x^2 + y^2 = 22 + 62 - 9, which simplifies to x^2 + y^2 = 49. The graph is a circle with its center at the origin (0, 0) and a radius of √49 = 7. The circle is symmetric with respect to the x and y axes. The graph includes all points on the circumference of the circle and extends to infinity in all directions.

In both cases, the coordinates of the vertices are not labeled since the equations represent curves rather than polygons or lines. The graphs illustrate the shape and characteristics of the equations, allowing us to visualize their behavior on a Cartesian plane.

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Answer:

Only 1 flavour ??

Only 1 flavour ??anyway ....

Only 1 flavour ??anyway ....number of different ice cream desserts

desserts= 3 x 1 x 4

= 12

Answer :

3 (1 + 5) = 1 + 19

3(6) = 20

18 = 20

x = 20-18

x = 2 is the answer

Hope it helped

Answer:

m=1

Step-by-step explanation:

2m+7=9

subtract 7 on both sides

2m=2

divide 2 on both sides

m=1

hope it helped

Answer: m=1

Step-by-step explanation:

The constant is 7 and the coefficient is 2m. You would subtract 7 to both sides and then divide by 2 and you should get 1

(a) For Rolling a dice the outcomes and probabilities are,

Outcomes = {1, 2, 3, 4, 5, 6}

Probability to get 1 on the face = p(1) = 1/6

Probability to get 2 on the face = p(1) = 1/6

Probability to get 3 on the face = p(1) = 1/6

Probability to get 4 on the face = p(1) = 1/6

Probability to get 5 on the face = p(1) = 1/6

Probability to get 6 on the face = p(1) = 1/6

(b) For Flipping a coin the outcomes and probabilities are,

Outcomes = {Head, Tail}

Probability of getting Head = 1/2

Probability of getting Tail = 1/2

(a) Here the event is Rolling a dice.

So the possible outcomes under the event rolling a dice are each of the face values on the dice.

So outcomes are = {1, 2, 3, 4, 5, 6}

Now, the probabilities are,

Probability to get 1 on the face = p(1) = 1/6

Probability to get 2 on the face = p(1) = 1/6

Probability to get 3 on the face = p(1) = 1/6

Probability to get 4 on the face = p(1) = 1/6

Probability to get 5 on the face = p(1) = 1/6

Probability to get 6 on the face = p(1) = 1/6

(b) Here the event is Flipping a coin.

So the possible outcomes under this event can be getting a Head or getting a Tail.

Outcomes = {Head, Tail}

Probability of getting Head = 1/2

Probability of getting Tail = 1/2

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Answer:

\( - 5.5 \times 0.021 = - 0.1155\)

Answer:

-0.1155

Step-by-step explanation:

You just need to calculate it and that's it.

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

We have drawn the number line and included the given points, see attached number line.  

What is the fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely the numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

On the number line above, the decimal values and fractions are labeled as follows:

0.63 is labeled between 0 and 1.

34/100 is labeled at the same point as 0.34, between 0 and 1.

0.02 is labeled between 0 and 1.

7/10 is labeled at the same point as 0.7, between 0 and 1.

Therefore, we have drawn the number line and included the given points, see attached number line.  

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Hence, there is 330 ml of lemonade in the special edition bottles.

The special edition bottles have 10% extra free, which means the total amount of lemonade in the special edition bottle is 100% (normal amount) + 10% (extra amount).

To calculate the amount of lemonade in the special edition bottles, we first need to determine the 10% of the normal amount (300 ml).

10% of 300 ml = (10/100) * 300 ml

= 30 ml

Therefore, the special edition bottles contain an extra 30 ml of lemonade.

To find the total amount of lemonade in the special edition bottles, we add the normal amount (300 ml) to the extra amount (30 ml):

Total amount of lemonade in special edition bottles = 300 ml + 30 ml

= 330 ml

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Answer:

I have no idea.

Step-by-step explanation

Answer: A - (-5, 43)

Step-by-step explanation:

Answer:

no they are not equal just look at the picture carefully and you will realise it's not equal

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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The time when the velocity of the particle is zero is t = 2 seconds.  The average velocity when t = 3 seconds is 4 m/s, and the average speed is 0 m/s.

To determine the time when the velocity of the particle is zero, we need to find the value of t for which the derivative of the position function with respect to time is equal to zero.

Given that the position function is \(s = 2t^2 - 8t + 6\), we can find the velocity function by taking the derivative of s with respect to t:

\(v = ds/dt = d/dt(2t^2 - 8t + 6)\)

Taking the derivative, we get:

v = 4t - 8

Now we set the velocity equal to zero and solve for t:

0 = 4t - 8

4t = 8

t = 2

Therefore, the time when the velocity of the particle is zero is t = 2 seconds.

To find the average velocity when t = 3 seconds, we can evaluate the derivative at that time:

v = 4t - 8

v(3) = 4(3) - 8

v(3) = 12 - 8

v(3) = 4 m/s

So, the average velocity when t = 3 seconds is 4 m/s.

To find the average speed when t = 3 seconds, we need to calculate the total distance traveled by the particle between t = 0 and t = 3 seconds. The average speed is the total distance divided by the time interval.

The total distance can be calculated by finding the difference in position between t = 3 seconds and t = 0 seconds:

\(s(3) - s(0) = (2(3)^2 - 8(3) + 6) - (2(0)^2 - 8(0) + 6)\)

           = (18 - 24 + 6) - (0 - 0 + 6)

           = 0

The total distance traveled is 0 meters.

Since the time interval is 3 seconds, the average speed is:

Average speed = Total distance / Time interval

            = 0 / 3

            = 0 m/s

Therefore, the average speed when t = 3 seconds is 0 m/s.

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Answer:

C

Step-by-step explanation:

The vectors u and v are orthogonal when k equals 5 or -2.

Two vectors u and v are orthogonal if their dot product is equal to zero. The dot product of two vectors u and v is given by the formula:

u · v = u₁ × v₁ + u₂ × v₂ + u₃ × v₃

where u₁, u₂, u₃ are the components of vector u, and v₁, v₂, v₃ are the components of vector v.

Let's calculate the dot product of u and v:

u · v = (k × -5) + (k × (k + 2)) + (-2 × 5)

= -5k + k² + 2k - 10

= k² - 3k - 10

For the vectors to be orthogonal, the dot product must be zero:

k² - 3k - 10 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula:

(k - 5)(k + 2) = 0

From this equation, we can see that the values of k that satisfy the equation are:

k = 5 or k = -2

Therefore, the vectors u and v are orthogonal when k equals 5 or -2.

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H: p = 0.25 is the null hypothesis, whereas H: p > 0.25 is the alternative hypothesis.

According to the null hypothesis, any difference between the chosen qualities that you see in a set of data is assumed to be the consequence of chance.

The claim is made that the card was identified far more frequently than chance would suggest, based on the information presented.

The percentage of cards chosen will be 1 ÷ 4 = 0.25.

As a result, H: p = 0.25 is the null hypothesis, whereas H: p > 0.25 is the alternative hypothesis.

The two alternatives being equal is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.

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