please solve
If P(A) = 0.2, P(B) = 0.3, and P(AUB) = 0.47, then P(An B) = (a) Are events A and B independent? (enter YES or NO) (b) Are A and B mutually exclusive? (enter YES or NO)

Answer:hope this helps

0.75x + 3 = 0.25x + 5.25

Constants are $3 and $5.25 respectively

Topping costs $0.75 and $0.25 respectively

To have same cost the toppings number would be different as cost is different.

Suppose the number of toppings is x in one shop and y in the other, then the spending if same, we get this equation:

0.75x + 3 = 0.25y + 5.25

Constants are $3 and $5.25 respectively

Answer:

Answer is y = 25/4

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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Answer:

Square matrix is a matrix where the number of rows is the same as the number of columns for example

a 2×2 matrix is an example of a square matrix

Here let's use python to find our median.(Console attached)

Spare way:-

Let's use statistics

\(\\ \sf\longmapsto Median=\dfrac{n}{2}+\dfrac{n+1}{2}\)

\(\\ \sf\longmapsto Median=\dfrac{10}{2}+\dfrac{10+1}{2}\)

\(\\ \sf\longmapsto Median=5th+6th/2\)

Order from largest to smallest

\(\\ \sf\longmapsto Median=\dfrac{150+149}{2}\)

\(\\ \sf\longmapsto 149.5\)

Answer: While I don’t have the picture to actually know the answer I will explain how to get it.

Step-by-step explanation:

1. If the shapes are on a grid count the amount of grid squares that are located between each end point of the shape. If it’s not on a grid use a ruler to measure the side lengths. You will need to find out the side amounts for both shapes L and S.

2. From there if the L shape is SMALLER than the S shape, then take the S shape’s sides and divide it by the L shape’s sides, and whatever number you get from each of your division problems will be your scale factor. BUT If the L shape is BIGGER than the S shape then easiest way to find out your scale factor is to take the last scale factor you got and convert it into a fraction. For example, if you got 3 then it would be 1/3. Hope this helped!

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

The critical numbers of the function on the interval 0 ≤ θ < 2π are:

θ = 0, θ = π, θ = π/3, θ = 2π/3, θ = 4π/3, and θ = 5π/3.

we now have the smaller values of θ are θ = 0 and θ = π/3, while the larger values are θ = 2

The critical numbers of a function are described as the values of the independent variable for which the function is not differentiable.

In our own case, the function f(θ) = 2cos(θ) +(sin(θ))^2, the critical numbers are the values of θ for which the derivative is not defined.

We can write the derivative of the function as:

f'(θ) = -2sin(θ) + 2sin(θ)cos(θ) = sin(θ)(2cos(θ) - 1)

The derivative is not defined when sin(θ) = 0 or cos(θ) = 1/2.

The values of θ for which sin(θ) = 0 are θ = 0, θ = π, θ = 2π, etc.

The values of θ for which cos(θ) = 1/2 are θ = π/3, θ = 2π/3, θ = 4π/3, θ = 5π/3, etc.

Hence, the critical numbers of the function on the interval 0 ≤ θ < 2π are:

θ = 0, θ = π, θ = π/3, θ = 2π/3, θ = 4π/3, and θ = 5π/3.

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complete question:

Find the critical numbers of the function on the interval 0≤ θ < 2π.

f(θ) = 2cos(θ) +(sin(θ))2

θ =? (smallervalue)

θ =? (larger value)

The distance that Erika is from the building is given as follows:

417 feet.

Then, considering his angle of elevation is x, Brad's distance is calculated as follows:

tan(x) = 1454/d.

Finally, we must subtract d by 417 feet to obtain the distance between Brad and Erika.

The three trigonometric ratios are defined as follows:

For the angle of 74º, we have that:

Hence Erika's distance is obtained as follows:

tan(74º) = 1454/d

d = 1454/tangent of 74 degrees

d = 417 feet.

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Answer:

120 seats

Step-by-step explanation:

Total seats in the hall = 300

Percentage of filled seats = 60 %

Number of seats filled = (60 / 100) 300

                                     = 60 * 3

                                     = 180

Therefore, number of empty seats = 300 - 180

                                                          = 120

Hope it helps :)

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Answer:

The equation for this is:

n(g) + 49 - 3

Step-by-step explanation:

The term "Product" means "multiplication." And "number" can be reduced to the term "n," like "g" is. The word "and" means "addition." And, "3 less" means - 3:

n(g) + 49 - 3

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Answer:

49g -3

Step-by-step explanation:

3 less than the product of a number g and 49

Writing an algebraic expression

less than means it comes after

the product of a number g and 49

49g

3 less than

49g -3

The Results:

a) The measure of ∠BDC = 67°

b) The measure of arc DAC = 46°

a) The measure of ∠BDC

Since DC ⊥ AB, ∠DCB is a right angle, which means it measures 90°. Also, given that m∠DCB = 23, we can use the fact that the angles in a triangle sum to 180° to find ∠DBC.

∠DBC + ∠DCB + ∠B = 180 (angles in a triangle sum to 180)

∠DBC + 90 + 23 = 180 (substituting values)

∠DBC = 180 - 90 - 23 = 67°.

Thus, the measure of ∠BDC = 67°

b) The measure of arc DAC:

Since AB = AC, it implies that ∠ABC = ∠ACB (angles opposite to equal sides of an isosceles triangle are equal). Therefore, ∠ACB is also 23°.

Now, since ∠ACB is an inscribed angle that intercepts the arc DAC, the measure of the arc DAC is twice the measure of ∠ACB.

Arc DAC = 2 × ∠ACB = 2 × 23 = 46°.

Therefore, the measure of arc DAC is 46°.

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Answer:

acute

Step-by-step explanation:

the angles are all less than 90°

they are not equal so not equialteral

has to be acute

To solve the system of equations using elimination, we'll eliminate one variable by manipulating the equations.

Let's follow the steps: Given equations: 3x + 2y = -3. 9x + 4y = 3. To eliminate the y variable, we can multiply equation (1) by 2 and equation (2) by -1, which will allow us to add the two equations together: 2(3x + 2y) = 2(-3). -1(9x + 4y) = -1(3). Simplifying the equations: 6x + 4y = -6. -9x - 4y = -3. Now, let's add the two equations together: (6x + 4y) + (-9x - 4y) = -6 + (-3). Simplifying the equation: -3x = -9. Dividing both sides by -3: x = 3. Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation (1): 3(3) + 2y = -3. 9 + 2y = -3. Subtracting 9 from both sides: 2y = -12.  Dividing both sides by 2: y = -6. Therefore, the solution to the system of equations is x = 3 and y = -6.

The solutions of system of equations can be represented as the ordered pair (x, y) = (3, -6).

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There are 79 passengers in the ninth carriage.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Let's assume that the ninth carriage is the middle carriage in a group of three consecutive carriages.

Then, the total number of passengers in those three consecutive carriages would be 99 x 3 = 297.

We know that the train has a total of 381 passengers, so the remaining passengers must be in the other eight carriages.

The total number of passengers in those eight carriages is 381 - 297 = 84.

Since there are eight carriages without the three consecutive carriages, we know that there are 24 carriages in total (11 + 8 + 5).

So, on average, each of those eight carriages contains 84 / 8 = 10.5, passengers.

Since the ninth carriage is one of those eight carriages, it must contain 10 or 11 passengers.

However, we know that the ninth carriage is part of a group of three consecutive carriages containing 99 passengers.

Therefore, the middle carriage (the ninth carriage) must contain 99 - (10 + 10) = 79 passengers.

Therefore, there are 79 passengers in the ninth carriage.

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equation for a tractrix, hence it proves that the trace of the tractrix is given as (t, t tan t).

The trace of the tractrix is given as:

Trace = (x, y) = (t, t tan t)

To show that the trace is that of a tractrix, we will use the equation for a tractrix, which is given as:

x = t – t tanh t

where t is the angle that the y-axis makes with the vector.

Substituting the value of x in the trace equation, we get:

t – t tanh t = t

Simplifying the equation, we get:

t tanh t = 0

This is the equation for a tractrix, hence it proves that the trace of the tractrix is given as (t, t tan t).

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A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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The classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent. The Option B is correct.

We have a consistent independent equation when a system of linear equations has exactly one solution. When this occurs, the graphs of the system's lines cross at exactly one point.

For our question, we can start by rearranging the first equation to isolate y:

\(4x + y = 4\\y = -4x + 4\)

We can see that the second equation is already in the form y = mx + b, where m is the slope and b is the y-intercept. So we can identify that the slope of the second equation is -4 and the y-intercept is 4.

Now we can compare the slopes and y-intercepts of the two equations to determine the classification of the system of equations:

In this case, we can see that the slopes of the two equations are different (-4 and 0) and the y-intercepts are the same (4). Therefore, the system is consistent and there is a unique solution. So the classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent

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Answer:

Step-by-step explanation:

You want to know which of several equations have x=3 as a solution. The equations are ...

The value x=3 will be a solution if it satisfies the equation. Substituting that value into the given equations, we find ...

The value x = 3 is a solution to ...

Answer:

\(y = -3x\)

Step-by-step explanation:

Given

The attached graph

Required

Determine the graph equation

To do this, we pick any 3 corresponding points of x and y

\((x_1,y_1) = (0,0)\)

\((x_2,y_2) = (2,-6)\)

\((x_3,y_3) = (-4,12)\)

The equation can then be solved using linear interpolation as follows:

\(\frac{y-y_3}{x-x_3} = \frac{y_2 - y_1}{x_2-x_1}\)

This gives:

\(\frac{y-12}{x-(-4)} = \frac{-6 -0}{2-0}\)

\(\frac{y-12}{x+4} = \frac{-6 -0}{2-0}\)

\(\frac{y-12}{x+4} = \frac{-6}{2}\)

\(\frac{y-12}{x+4} = -3\)

Multiply both sides by x + 4

\((x + 4) * \frac{y-12}{x+4} = -3 * (x + 4)\)

\(y - 12 = -3 *(x + 4)\)

Open bracket

\(y - 12 = -3x -12\)

Add 12 to both sides

\(y - 12+12 = -3x -12+12\)

\(y = -3x\)

Answer:

Step-by-step explanation:

3 roots

namely -7/9,-1/4.-4/3

An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.

The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.

In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].

R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.

The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.

Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.

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Answer:

A

Step-by-step explanation:

Answer: 47/6

Step-by-step explanation:

-2 1/3 - (-10 1/6)

= -7/3 + 10 1/6

= -7/3 + 61/6

= 47/6

Step-by-step explanation:

\( - \frac{6 + 1}{3} - ( \frac{10 \times 6 + 1}{6} ) \\ - \frac{7}{3} - ( \frac{10 \times 6 + 1}{ 6} \\ - \frac{7}{3} - ( - \frac{61}{6} ) \\ - \frac{7}{ 3} + \frac{61}{6} \\ - \frac{14}{6} + \frac{61}{ 6} = 7.8333333\)

the answer is recurring

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\(y - 8 = 10 - x\)

Add sides 8

\(y - 8 + 8 = 10 - x + 8\)

\(y = 18 - x\)

Add sides x

\(y + x = 18 - x + x\)

\(y + x = 18\)

\(x + y = 18\)

Done...

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At point(s) 0 on the - axis is the electric field zero = 5.833

What is Axis?

An object rotates or spins around an unseen line known as an axis. The North and South Poles of an object are the places where an axis crosses its surface.

So we can take a midpoint of the charges..

as x₁ = 4.5

x₂ = 6.5

Now

from the figure,there is one positive sign on the right side of the charge, so, lets take one positive sign as q then charge on the right side of the particle is q.

the charge on the left side of the charge will be 4q because there are 4 plus sign on the charge.

Consider the neutral point where electric field would be zero.

So electric filed due to q

E₂ = kq/(x₂-x²)

also electric filed due to 4q

E₁ = k4q/(x-x₁)²

So at the neutral point both electric filed will be equal.

E₁ =E₂

\(\frac{k(4q)}{(x-x_{1^{2} } } \\= kq/(x_{2}-x^{2} )\\\\\)

= 4/(x-4.5)²

=1/(6.5-x)²

x = 5.8333

x= 6

At point(s) 0 on the - axis is the electric field zero = 5.833

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A) The solution to m² + (1/m²) is gotten as; 14

B) The solution to m³ + ¹/₃ is gotten as; 52.312

We are given the algebraic equation;

(m² + 1)/m = 4

Multiply through by m to get;

m² + 1 = 4m

m² - 4m + 1 = 0

From online quadratic equation calculator, we have;

m = 3.732 or 0.268

A) Thus;

m² + (1/m²) = 3.732² + (1/3.732²)

⇒ 14

B) m³ + ¹/₃ gives;

3.732³ + (1/3) = 52.312

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Different lampshades that could be used together are A) 5.

How to determine the value of any factorial value?
The factorial function (symbol:!) instructs us to multiply all whole numbers starting at the number we have chosen down to one.

Examples:

4! = 4 × 3 × 2 × 1 = 24

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

according to the question,  five lamp bases and four lampshades that could be used together. so the calculation will be 5C4

using factorial,

Hence, 5 different arrangements of base and shade can be offered together. (using factorial)

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Answer:

h = 10 bc 4.7 x 10 = 47

f = 36 bc 6 x 36 = 216

g = 3.5 bc 3.5 + 1.6 = 5.1

unlock number equation = f - g x h or 36 - 3.5 x 10

unlock number: 1

Answer:

Unlock number: 1

Step-by-step explanation:

6f = 216

6f/6 = 216/6

f = 36

1.6 + g = 5.1

5.1 - 1.6 = 3.5

g = 3.5

4.7h = 47

4.7h/4.7 = 47/4.7

h = 10

f - g x h

36 - 3.5 x 10

36 - 35

1