1. Given the points P (1, - 4). Q (3,-2), R (-3,5), find the coordinates of the mid-points A and B of PO and PR respectively and distance AB.

2. Calculate the value of cand the mean of the distribution with probability density function f(x) = cx? where x = 2,3,4 and 5.

- 3. Calculate P(A) given that P (AUB)= 0.98 where, P(B) = 0.72, if A and B are mutually exclusive events.

4. Given the center of a circles as (1,2) and radius 13 find its equation.

5. Find the eccentricity and the foci of the ellipse x2 - y2 16 9 1.​

Using the double angle identity, rewrite the equation as

cos(2x) - cos(x) = (2 cos²(x) - 1) - cos(x)

==>   2 cos²(x) - cos(x) - 1 = 0

Factorize the left side:

(2 cos(x) + 1) (cos(x) - 1) = 0

Then

2 cos(x) + 1 = 0   or   cos(x) - 1 = 0

cos(x) = -1/2   or   cos(x) = -1

In the interval [0, 2π], we get

x = 2π/3   or   x = 4π/3   or   x = π

Answer:

Step-by-step explanation:

Answer:

OK so he gets 3000 a year

so 3000t is what we need. thats 3000 times the number of years.

His starting salary is 41250, so we would add that on.  

K = 3000t + 41250.

Step-by-step explanation:

The translational speed of a cylinder is 15.02 m/s.

For this question, we will use the Law of Conservation of Energy.

At the top the energy of the cylinder is E1, and at the bottom of incline - it is E2. Using the law, we can write

                                                          E1 = E2 .

where,

E1 = mgh (the potential energy of the cylinder)

E2 = E(tr) + E(rot) (the total kinetic energy of the cylinder)

E(tr) = \(\frac{1}{2}mv^{2}\) (the translational energy)

E(rot) = \(\frac{1}{2}Iw^{2}\) (the rotational energy)

\(I = \frac{1}{2}mR^{2}\)(moment of inertia of the cylinder)

\(w = \frac{v}{R}\) (angular velocity of the cylinder)

Now, substituting the values, we have:

mgh = \(\frac{1}{2}mv^{2} + \frac{1}{4}mR^{2} (\frac{v^{2} }{R^{2} } ) = \frac{3}{4}mv^{2}\)

From this equation, translational velocity, v:

v = \(\frac{\sqrt{4gh} }{3}\) = \(2\frac{\sqrt{gh} }{3}\)

Plugging in the values of g and h,

g = 9.8 \(m/s^{2}\), h = 7.20m

v = 15.02 m/s

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Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:

\(\displaystyle y = 3sin\:1\frac{3}{5}\pi{x} + 5\)

Step-by-step explanation:

\(\displaystyle \boxed{y = 3cos\:(1\frac{3}{5}\pi{x} - \frac{\pi}{2}) + 5} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 5 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{5}{16}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{3}{5}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{4}} \hookrightarrow \frac{2}{1\frac{3}{5}\pi}\pi \\ Amplitude \hookrightarrow 3\)

OR

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{4}} \hookrightarrow \frac{2}{1\frac{3}{5}\pi}\pi \\ Amplitude \hookrightarrow 3\)

From the above information, you should now have an ideya of how to interpret trigonometric equations like this.

I am delighted to assist you at any time.

Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Answer:

17

Step-by-step explanation:

4a - 4 = 2a + 30

2a = 34

a = 17

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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The first question:

"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"

Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.

To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:

P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.

Therefore, the probability of landing on both region three and region six is 1/64.

The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.

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

The second question:

"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"

To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.

The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.

The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.

To find the probability of either event occurring, we add the probabilities together:

P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.

Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.

The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.

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

The third question:

"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"

To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.

The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.

The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.

To find the probability of either event occurring, we add the probabilities together:

P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.

Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.

The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.

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

The fourth question:

"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"

The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.

The probability of rolling an even number on the die is 3

/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.

To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:

P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.

Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.

The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

-46

Step-by-step explanation:

4(-8x + 5) = -32x - 26

-32x + 20 = -32x - 26

-32x + 32x = -26 - 20

x = -46

Answer:

-32x+20=-32x-26

20=-26

so unequal or undefined

hope this helps

have a good day :)

Step-by-step explanation:

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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ANSWER:

9zy

STEP-BY-STEP EXPLANATION:

With the help of the statement we can establish the final expression, like this:

The result is 9zy

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

12 weeks because 12weeks*$10 is $120 total.

Step-by-step explanation:

you didn't post a pic of the graph so this is my best guess.

Answer:

4

Step-by-step explanation:

(x - h)² + (x - k)² = r²

r is the radius of the circle. We are given r as 16. So,

r² = 16

√r² = √16

r = 4

And we have our final answer!

Answer:

4

Step-by-step explanation:

(x - h)² + (x - k)² = r²

r is the radius of the circle. We are given r as 16. So,

r² = 16

√r² = √16

r = 4

This is the final answer!

Answer:

17x + 37

Step-by-step explanation:

looked it up

As per the given function rule , y = -6x + 1 , the values will be 31, 7, 1, -5 -5 , 1, 1, -6X+1, -17.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

As per the given function rule in the question i.e y = -6x + 1

X                         Y

-5                         31

-1                          7

0                           1

1                           -5

1                           -5

0                            1

0                            1

X                   -6X +1

3                         -17

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9514 1404 393

Answer:

  g(x)

Step-by-step explanation:

f(x) is cubic, so can have at most 3 x-intercepts.

g(x) has 4 x-intercepts listed.

h(x) has 2 x-intercepts listed.

__

g(x) has the most x-intercepts.

a Markov chain is the probability defined by the below transition matrix. [ 1/3 2/3 1/5 4/5] has the steady state C. (10/13 3/13]

The steady state of a Markov chain is the probability distribution of possible states of the system. In this case, the steady state from the transition matrix ( Matrix can also be used to represent relationships between different variables.It is commonly used in mathematics, science and engineering to represent a variety of data. ) can be found by solving the system of equations:

P(X0) = P(X0) * 1/3 + P(X1) * 2/3

P(X1) = P(X0) * 1/5 + P(X1) * 4/5

Solving this system of equations yields the steady state of (10/13, 3/13).

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Answer:

Step-by-step explanation:

First, let's turn them both into improper fractions.

3 3/8 = 27/8

Now we can multiply

It is 5*27 / 13 * 8

This equals: 135 / 104

Simplified even further is:

1 31/104

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Notice that Alex measured the height of the hourglass. To find its volume he also has to measure the radius of the circumference of the base.

We know that the height and radius of the volume are directly proportional, which means if one increases then the other one also increases. Therefore, the answer is yes, if the volume of sand is increasing at a constant rate, the height is increasing at a constant rate because those magnitudes are directly proportional.

Answer:

Step-by-step explanation:

hello :

the coordinates of the point on the unit circle at the given angle.-225°:

x= cos(-225°)= -√2/2

y = sin (-225°)= √2/2

The coordinates of the point on the unit circle at an angle -225°° are \((\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )\).

" The coordinates of the point is defined as the pair of such points which represents the exact location of the point."

" Unit circle means a circle with radius equals to 1unit."

Formula used

Equation of the circle with center (0, 0) and radius r

\(x^{2} +y^{2} =r^{2}\)

Coordinates of the point on the circle (rcosθ , rsinθ)

cos(-θ) = cosθ

sin (-θ) = -sinθ

cos (\(\frac{3\pi }{2}\) -θ) = -cosθ

sin (\(\frac{3\pi }{2}\) -θ) = -sinθ

According to the question,

Given θ = -225°

Unit circle 'r' = 1

Therefore Coordinates are,

'x' coordinates represented by  rcosθ

'y' coordinates represented by  rsinθ

Substitute the value of r and θ in the coordinates of the point we get,

x = rcosθ

 = 1 × cos (-225°)

 = cos (225°)

 = cos ( 270° - 45°)

 \(=cos(\frac{3\pi }{2} -\frac{\pi }{4} )\)                      

\(= - sin(\frac{\pi }{4}) \\= - \frac{1}{\sqrt{2} } \\=-\frac{\sqrt{2} }{2}\)

y = rsinθ

 = 1 × sin (-225°)

 = -sin (225°)

 = -sin ( 270° - 45°)

 \(=-sin(\frac{3\pi }{2} -\frac{\pi }{4} )\)                      

\(= -( - cos(\frac{\pi }{4})) \\= \frac{1}{\sqrt{2} } \\=\frac{\sqrt{2} }{2}\)

Hence, coordinates of the point on the unit circle at an angle -225°° are \((\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )\).

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Answer:

3.75 hours.

Step-by-step explanation:

Just add both of the decimals in the question to get the sum, which is 3.75.

Answer:

3.75 she worked 3 and 3 quarters of an hour

Step-by-step explanation:

Answer:

A = 530.929158457

Answer:

Area = 706.8583471

Explanation:

The used law to measure the surface area of the sphere is

\(area \: = 4\pi \: {r}^{2} \)

Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:

\(4\pi \: {7.5}^{2} = 706.8583471\)

Answer:

400 feet long

50 feet wide

Step-by-step explanation:

Length = l

Width = w

2l + 2w = 900

l = 8w

Plug the l from the bottom equation into the top equation

2 x 8w+ 2w = 900

16w = 900

Divide both sides by 16

16w/16 = 900/16

w = 50

The width is 50 feet

Now plug the new w into one of the original equations; we'll use the bottom one

l = 8(50)

l = 400

Step-by-step explanation:

line A can be written as y1= 3/4.x -5/4

line B is a linear function : y2= ax +b

4a+b=7 and -a +b =3 so a=4/5 and b=19/5

so y2=4/5x +19/5

so they are not parallel

Line A goes through (0,-5/4) and (1,-1/2)

Gradient of line A = G1= (-1/2 - (-5/4))/(1-0) =3/4=0.75

Gradient of line B= G2= (7/3)/(4-(-1))=4/5=0.8

The Line A and Line B are not parallel to each other.

The equation of line A is,

                           \(3x-4y=5\)

Now write in slope intercept form,

                       \(3x-4y=5\\\\4y=3x-5\\\\y=\frac{3}{4} x-\frac{5}{4}\)

Slope of line A is \(\frac{3}{4}\).

Equation of line B is,

                    \(y-7=\frac{3-7}{-1-4}(x-4) \\\\y-7=\frac{4}{5} x-\frac{16}{5}\\ \\y=\frac{4}{5} x+\frac{19}{5}\)

Slope of line B is \(\frac{4}{5}\)

Since, the slope of both line A and B are different. therefore, Line A and Line B are not parallel to each other.

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