Find the equation of the line that passes through both points (6,-5) (0,3)

Condition of the event on tails on the first flip, the new sample space is

p + [(I1 - P) / (2 - P)] * (1 - p) = 1 / (2 - p)

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Utilize complete probability to solve the issue. E is the first head on an odd toss in the event. the sample area was divided into two cases. The first throw is either heads H₁ or tails T₁. Note that the subscript denotes the first toss.

[E] = [H₁] ∪ {E∩T₁} ⇒ (The first throw is indicated by the subscript.)

P (odd number of tosses until first H) = P(H₁) + P(E|T₁) P(T₁)

P (ET₁) = (1 - p) p + + (1 - p)³ p + (1 - p)⁵ p+ ...

= p (1 - p) [1 + (1 - p)² + (1 - p)⁴ +...]

= p(1 - p) [1 / 1 - (1 - p)²]

= (1 - P) / (2 - P)

P (odd number of tosses until 1st H) = p + [(I1 - P) / (2 - P)] * (1 - p) = 1 / (2 - p)

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COMPLETE QUESTION:

Solve the problem using total probability. Event E is the 'first head on an odd toss'. Cut the sample space into two cases: the first toss is heads H₁ or the first toss is tails T₁. N.B.: The subscript indicates the first toss.

{E} = {H₁} ∪ {E∩T₁}

Hints: Apply conditional probability

P(A∩B)=P(A)P(B∣A)

and model the sample space. H Cut the sample space into two mutually exclusive events. TH TTH TTTH TTTTH TTTTTH TTTTTTH and so forth ad infinitum. The first outcome in the sample space, H, is one of the desired outcomes. All the rest of the outcomes share the same feature of tails on the first toss. Notice in this subset that the desired outcomes are alternate outcomes. When you condition the event E on tails on the first flip T₁

​what is the new sample space? What is the complement of the event E? Finally, how is P(E∣T₁) and 1 − P(E) related? Write your solution with the relevant steps.

If an "E" statement is true, the truth value of its corresponding "A" statement is logically undetermined.

An "E" statement is a universal negative statement, which means that it asserts that no members of a certain class have a specific property. For example, "No dogs are fish" is an "E" statement. On the other hand, an "A" statement is a universal affirmative statement, asserting that all members of a class have a specific property. For example, "All dogs are mammals" is an "A" statement.
When an "E" statement is true, it only provides information about the nonexistence of a certain relationship between two classes. It doesn't provide enough information to determine the truth value of its corresponding "A" statement. The truth value of the "A" statement could be true, false, or undetermined, depending on the specific classes and properties involved.
In summary, if an "E" statement is true, the truth value of its corresponding "A" statement is logically undetermined, as there is not enough information available to determine whether the "A" statement is true or false.

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There is a 0.25 and a 0.5 chance that the flight will arrive no more than 5 and 10 minutes late, respectively. 130 minutes is the estimated flight time.

Probability density function: It can take on any value and is used to define the random unknown probability falling inside a specific range of values.

For its flights from Cincinnati to Tampa, Delta Airlines reports a flight duration of 2 hours and 5 minutes.

Let's say we think the range of real flight timings is 2 hours to 2 hours and 20 minutes.

a)Between 120 and 140 minutes, the probability density function for a continuous uniform random variable is given as

\(f(x)=\left \{ {{\frac{1}{140-120},120 \leq x\leq 140}\\ \atop {0.o.e}} \right.\)

b)The likelihood that the flight will arrive no later than five minutes late is

integration from 130 to 125 of 1/20dx=5/20=1/4=0.25

c)There is a 10% chance that the flight will arrive no more than 10 minutes late.

integration from 135 to 125 of 1/20dx=10/20=0.5

d)The anticipated duration of the flight, in minutes, is

integration from 140 to 120 of x/20dx=(5200*5)/(2*20)=130

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Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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Answer:

5

Step-by-step explanation:

I=30

T=5

P=500

r=3

PLS BRAINLIEST

The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

The equation of a circle is given by the formula,

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

where (a,b) is the coordinate of the center of the circle, and r is the radius of the circle.

According to the given equation, if we compare this equation with the general equation of the circle.

\((x-4)^{2} + (y-12)^{2} = 9\)

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

\((x-4)^{2} + (y -9)^{2} = 3^{2}\)

On  observing this equation we will get that the value of (a,b) is (4,12).

Thus, The equation indicates that the center of the window is 12 feet from the ground

window span = diameter of circle

window span = 2r

= 2 × 3 (radius = 3)

= 6

Hence, The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

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Answer:

Option 1

Step-by-step explanation:

The given equation equals 3072, so find the other equation that equals 3072.

Option 1 = 3072 - correct

Option 2 = 432 - wrong

Option 3 = 2883 - wrong

Option 4 = 432 - wrong

I hope this helps!

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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Answer:

y = 3x + 7

Step-by-step explanation:

As we move from (2, 13) to (5, 22), x (the "run") increases by 3 and y (the "rise") increases by 9.  Thus, the slope, m, must be m = rise / run = 9/3, or 3.

Then we have y = 3x + b and must find b.  Subbing 2 for x and 13 for y, we get

13 = 3(2) + b, so that b must be 7.

The desired equation is y = 3x + 7.

Answer:

B Q¹(1,2).............

The power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

To find the power series expansion of the product f(x)g(x), we need to multiply the power series expansions of f(x) and g(x) and collect like terms.

First, let's find the power series expansion of f(x):

\(f(x) = e^56 - 2(5x)^"\)

Using the formula for the power series expansion of e^x:

\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...\)

We can write the power series expansion of f(x) as:

\(f(x) = e^56 - 2(5x)^"\)

\(= (1 + 56 + (56^2)/2! + (56^3)/3! + ...) - 2(5x)^(1)\)

= \(1 - 5x + (56 - 25x^2) +\)...

Now let's find the power series expansion of g(x):

g(x) = sin 8x

= (8x) - (8x)^3/3! + (8x)^5/5! - ...

Finally, we can multiply the power series expansions of f(x) and g(x) to get the power series expansion of f(x)g(x):

\(f(x)g(x) = (1 - 5x + (56 - 25x^2) + ...) * ((8x) - (8x)^3/3! + (8x)^5/5! - ...)\)

\(= (8x) - (40x^2) + (568x^2)/2! + ((56-8*8)/2!)x^4 + ...\)

Collecting like terms up to order 3, we get:

\(f(x)g(x) = (8x) - (40x^2) + (224x^3)/3! + ...\)

Therefore, the power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

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The link utilization for the server links is 1 .

Given,

Servers are sending at maximum rate possible .

Now,

1. The maximum achievable end-end throughput is the capacity of the link with the minimum capacity i.e. Rc which is 300Mbps

2. The bottleneck link is the link with the smallest capacity between RS, RC, and R/4 i.e smallest between 400, 300 and 200 Mbps which is 200Mbps

3.The server's utilization = R(bottleneck)/ RS = 200/400 = 0.5

4.The client's utilization = R(bottleneck) / RC = 200/300 = 0.667

5.The shared link's utilization = R(bottleneck)/ (R / 4) = 200 / (800/4) = 1

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The empirical probability of drawing the cards will be 6 / 55.

The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.

Given that a card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 1 king is drawn.

The number of kings in a well-shuffled deck consists of 52 cards which is 4.

The number of ways of drawing consists of 4 kings in 13 repetitions which is ¹³C₄.

In 13 repetitions, 2 kings are drawn by ¹³C₂ ways,

The empirical probability will be calculated as,

P(E) = ¹³C₂ / ¹³C₄

P(E) = [ (13!) / (13-2)! ] ÷ [ (13!) / ( 13-4)!(4!) ]

P(E) = ( 4 x 3 ) / ( 11 x 10)

P(E) = 6 / 55

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

cos A = 3/5

Step-by-step explanation:

sin A = 4/5

sin^2 A + cos^2 A = 1

(4/5)^2 + cos^2 A = 1

16/25 + cos^2 A = 1

cos^2 A = 9/25

cos A = 3/5

Answer:7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

420÷60 is the same as 42÷6.

42 goes into 6, 7 times:

6, 12, 18, 24, 30, 36, 42.

Therefore, 420÷6 is 7.

Please use a calculator next time.

Answer:

85x(500-0.10x)

Step-by-step explanation:

Answer:

Choice A

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

let the other number be x

according to the question equation is

-12x = 96

x = 96/-12

x = -8

The value of the expression when n equals -8 is 61

Algebraic expressions are expressions made up of variables, constants and factors.

They also consist of mathematical operations sch as addition, subtraction, multiplication, division, etc

From the information given, we have;

h(n) = n²-3

For h(-8), we substitute the value do n as -8

h(-8) = (-8)^2 - 3

Find the square

h(-8) = 64 - 3

h(-8) = 61

Thus, the value of the expression when n equals -8 is 61

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Answer:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: f(x)=(3)x

Horizontal Shift: Right 8 Units

Vertical Shift: None

Reflection about the x-axis: Reflected

Vertical Stretch: Stretched

Step-by-step explanation:

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Answer: A. 4/3 x

Step-by-step explanation:

x miles in 90 minutes to ? miles in 120 minutes

90 miles to 120 miles is 1.3333 which is equal to 4/3.

Multiply it to x and you have A. 4/3x

Answer:

We know that the number of scoops of powder varies directly with the number of cups of milk. This means that there is a constant ratio between the two quantities.

Let's call this constant ratio k. Then, we can set up a proportion:

scoops of powder / cups of milk = k

We also know that 3 scoops of powder are needed for 5 cups of milk. We can use this information to find k:

3 / 5 = k

Simplifying this gives us:

k = 0.6

Now that we know k, we can use the proportion we set up earlier to find the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m:

p / m = k

Multiplying both sides by m gives us:

p = km

Substituting the value of k we found earlier gives us:

p = 0.6m

Therefore, the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m, is:

p = 0.6m

The slant height of the triangular pyramid is 8.7 feet.

Given a triangular pyramid.

The surface area of the triangular pyramid = 174 square feet

A triangular pyramid consists of 4 triangular faces.

Given that all the triangular faces are equilateral triangle with a length of side as 10 feet.

We have to find the slant height of the pyramid.

The formula to find the surface area of the triangular pyramid is,

Surface area = base area + 1/2 (perimeter × slant height)

Base area = 1/2 × 10 × √(10² - 5²) = 5√75 feet²

Perimeter = 3 × 10 = 30 feet

Substituting,

174 = 5√75 + 1/2 (30h)

174 = 5√75 + 15h

h = (174 - 5√75) / 15

h = 8.7 feet

Hence the slant height is 8.7 feet.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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As per the given coordinates, dimensions of the rectangle are √13 x √13.

One way to do this is to find the distance between two parallel sides of the parallelogram. In this case, we can look at sides AB and CD, which are parallel to each other.

The distance between points A and B is the

=> √((3-1)² + (2-(-1))²) = √13

which simplifies to the square root of 13. Similarly, the distance between points C and D is the

=> √((1-(-1))² + (3-0)²) = √13.

Therefore, the length of the rectangle is the distance between sides AB and CD, which is the square root of 13.

Therefore, the width of the rectangle is 2 units. So the dimensions of the rectangle are 2 units by the square root of 13 units.

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Answer:

4 units by 4 units

Step-by-step explanation:

i got it correct on edg :)

Answer:

Area of the triangle = 12 square feet

Step-by-step explanation:

Area of a triangle is calculated by the formula,

Area = \(\frac{1}{2}(\text{Base})(\text{Height})\)

From the picture attached,

Height of the given triangle = Vertical distance of the top vertex = 4 feet

Base of the triangle = 6 feet

Area of this triangle = \(\frac{1}{2}(6)(4)\)

                                 = 12 square feet

Therefore, area of the given triangle will be 12 square feet.