Write a linear equation for the graph in point-slope form. Show your work.

Answer:

(answer in explanation)

Step-by-step explanation:

so, whenever you divide factorials, as soon as you get it to be the same ! on the top and bottom of the fraction, they cancel out like any other fraction would.

So, lets say you're dividing 55! / 50!

55! can also be thought of as 55 x 54 x 53 x 52 x 51 x 50!

\(\frac{55*54*53*52*51*50!}{50!}\) = 55 * 54 * 53 * 52 * 51

Then you can simply solve the remaining equation

( 55 * 54 * 53 * 52 * 51 = 417,451,320)

hope this helps!!

Answer:

you can just divide them like normal fractions

Step-by-step explanation:

Do it as if it was the same number over the same number

The required probabilities are:(a) Pr(r ≤ 2) = 0.657.(b) Pr(r > 1) = 0.8718.(c) Pr(r < 2) = 0.783.(d) Pr(r ≥ 4) = 0.91854.

Given that r are a binomial random variable with parameters n and p. And the number of successes in a Bernoulli Trials experiment. We need to find the probability of given events.

(a) Pr(r\leq2), n = 3, p = 0.7

So, the binomial probability distribution function is

P (r = k) = (n C k) p^k q^(n-k)

where q = 1-p. Here, n = 3, p = 0.7, q = 0.3.

P (r \leq 2) = P (r = 0) + P (r = 1) + P (r = 2)P (r = k)

= (n C k) p^k q^(n-k)P (r = 0)

= (3 C 0) (0.7)^0 (0.3)^3

= 0.027P (r = 1)

= (3 C 1) (0.7)^1 (0.3)^2

= 0.189P (r = 2)

= (3 C 2) (0.7)^2 (0.3)^1

= 0.441 P (r \leq 2)

= 0.027 + 0.189 + 0.441

= 0.657.

(b) Pr(r>1), n = 4, p = 0.7

So, the binomial probability distribution function is

P (r = k) = (n C k) p^k q^(n-k)

where q = 1-p. Here, n = 4, p = 0.7, q = 0.3.

P (r > 1) = 1 - P (r ≤ 1)

= 1 - [P (r = 0) + P (r = 1)]P (r = 0) = (4 C 0) (0.7)^0 (0.3)^4

= 0.0081P (r = 1)

= (4 C 1) (0.7)^1 (0.3)^3

= 0.1201 P (r > 1)

= 1 - [0.0081 + 0.1201]

= 0.8718.

(c) Pr(r<2), n = 3, p = 0.3

So, the binomial probability distribution function is

P (r = k) = (n C k) p^k q^(n-k)

where q = 1-p. Here, n = 3, p = 0.3, q = 0.7.

P (r < 2) = P (r = 0) + P (r = 1)P (r = k)

= (n C k) p^k q^(n-k)P (r = 0)

= (3 C 0) (0.3)^0 (0.7)^3

= 0.342 P (r = 1)

= (3 C 1) (0.3)^1 (0.7)^2

= 0.441 P (r < 2)

= 0.342 + 0.441

= 0.783

(d) Pr(r\geq4), n = 5, p = 0.9

So, the binomial probability distribution function is

P (r = k) = (n C k) p^k q^(n-k)

where q = 1-p. Here, n = 5, p = 0.9, q = 0.1.

P (r \geq 4) = P (r = 4) + P (r = 5)P (r = k)

= (n C k) p^k q^(n-k)P (r = 4)

= (5 C 4) (0.9)^4 (0.1)^1

= 0.32805 P (r = 5)

= (5 C 5) (0.9)^5 (0.1)^0

= 0.59049 P (r \geq 4)

= 0.32805 + 0.59049

= 0.91854

Therefore, the required probabilities are:(a) Pr(r ≤ 2) = 0.657.(b) Pr(r > 1) = 0.8718.(c) Pr(r < 2) = 0.783.(d) Pr(r ≥ 4) = 0.91854.

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The new volume of the inflatable ball after the radius becomes half of the original one is 16π.

The original volume of the ball is given as 96π

The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.

The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³

With this the original volume of the ball is

(4/3)π X r³

and the new volume of the ball after it's halved is

V₂ = (4/3)π X (r/2)³

After simplification

V₂ = (4/3)π X (r³/8)

The new volume of the ball is:

V₂ = (1/6) X πr³

So the new volume is (1/6) of the original volume. We can calculate this as

V₂ = (1/6) X 96π

= 16π

Therefore, the new volume of the inflatable ball is 16π.

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The range of the projectile is approximately 6.9 meters when launched from an initial position of 0.4 meters relative to ground level.

To calculate the range of a projectile, we can use the following formula:

Range = (v₀² * sin(2θ)) / g

where:

v₀ is the initial velocity of the projectile

θ is the launch angle

g is the acceleration due to gravity

First, we need to convert the angle from degrees to radians:

θ_rad = 39 degrees * (π/180) ≈ 0.6807 radians

Now, we can substitute the values into the range formula:

Range = (16² * sin(2 * 0.6807)) / 9.8

Range ≈ 6.9 meters

Therefore, the range of the projectile is approximately 6.9 meters when launched from an initial position of 0.4 meters relative to ground level and lands at a position of -0.2 meters relative to ground level.

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Answer:

I got 38 and 11

Step-by-step explanation:

In triangles with the same altitude, area is proportional to the base length. Triangles CDE and BDE both have the same altitude (the perpendicular distance from D to BC), so their areas are in the proportion BE:EC = 1:5. Since ACDE = 5 in², ABDE = 1 in². The area of BDC is the total of those:

... ABDC = 6 in²

Likewise, triangles ABD and CBD both have an altitude that is the perpendicular distance from B to AC. Then, ...

... AABD : ACBD = AD : CD = 4:3

Thus AABD = 4/3 × ACBD = 4/3 × 6 in²

... AABD = 8 in²

Of course, AABC is the sum of AABD and ABDC, so is ...

... AABC = 6 in² + 8 in²

... AABC = 14 in²

i hope this helps

Total up the Consumption,Investment, Government Spending and Exports then minus the Total Imports. So the correct answer is C. $4,100

Answer:

\( - 120\)

that would be your answer thank you very much

Answer: It provides a total brain workout.” Research has shown that listening to music can reduce anxiety, blood pressure, and pain as well as improve sleep quality, mood, mental alertness, and memory.

Answer:

0+9+-3=6

Step-by-step explanation:

Is this what you were looking for? Instructions are very vague.

Answer:

I hope i typed it correctly xd

Answer:

Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.

Example...

x                       y

3                       5

4                       5

1                        2

Answer:

267.9 \(cm^{3}\)

Step-by-step explanation:

volume of a circle = 4/3 * π *\(r^{2}\)

=4/3 *3.14 *\(8^{2}\)

=12.56/3 *64

=803.84/3

=267.94

=267.9 \(cm^{3}\)

Answer:

c no

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Answer:

To write and solve an inequality that can be used to determine the number of 50-kilogram crates that can be loaded into the shipping container, we need to first find the total weight of the crates that can be loaded into the container. The maximum weight that can be loaded into the container is 27500 kilograms, and other shipments weighing 9500 kilograms have already been loaded, so the total weight of the crates that can be loaded is 27500 kilograms - 9500 kilograms = 18000 kilograms.

Next, we need to divide the total weight of the crates that can be loaded by the weight of each crate to find the number of crates that can be loaded. Since each crate weighs 50 kilograms, the number of crates that can be loaded is 18000 kilograms / 50 kilograms = 360 crates.

To express this as an inequality, we can use the following equation:

x <= 360

This inequality states that the number of crates that can be loaded into the shipping container (x) must be less than or equal to 360. Therefore, the number of 50-kilogram crates that can be loaded into the shipping container is x <= 360.

Step-by-step explanation:

The company will need 6π cubic inches of wax to make a single candle.

Given that the company makes wax candles in the shape of a cylinder, each candle has a diameter of 2 inches and a height of 6 inches.

Now, we need to find out how much wax will the company need to make candles.

The formula to find out the volume of a cylinder is given byπr²h,

where r is the radius of the circular base, h is the height of the cylinder and π is the mathematical constant (approx. 3.14159).

Here, Diameter of the cylindrical candle = 2 inchesTherefore, radius (r) of the candle = diameter / 2= 2 / 2= 1 inch

Height (h) of the candle = 6 inchesSubstitute the values of r and h in the formula for the volume of a cylinder and simplify to get,

Volume of the cylindrical candle = πr²h= π(1)²(6)= π(1)(1)(6)= 6π cubic inches

Therefore, the company will need 6π cubic inches of wax to make a single candle.

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The height of the mountain above sea level is 777.94 m.

The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.

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Step-by-step explanation:

Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently an event actually occurred in an experiment.

EXAMPLE-

Theoretical probability:

For instance, since a flipped coin has two sides and each side is equally likely to land up, the theoretical probability of landing heads (or tails) is exactly 1 out of 2.

Experimental probability:-

For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

mark me as brainliest if possible. :)

Answer:

option A and option B....

Answer:

50% if its one head and one tail. If it's two heads then it may be 25%

Step-by-step explanation:

Formula for the Circumference of a Circle = pi x diameter

---The diameter is the same thing as 2 x radius

Circumference = 8

pi = 3.14

Diameter = d

---First, plug in what we know

8 = 3.14 x d

---Divide by 3.14 to get d by itself

d = 8 / 3.14 = 2.54777

---Round to the nearest tenth

d = 2.5 cm

Hope this helps!

d=2.5

Hope it helps.

Do comment if you have any query.

Answer:

=4x

Step-by-step explanation:

The radical rule is √a^2 = a; assuming a≥0

√x^2 = x

= 4x

Hope this helps! Have a nice day!

Answer:

to simply

\( \sqrt{x \: } \)

is the answer

Therefore the correct option is, P(Z < -1.75) where Z is a standard normal random variable.

To calculate the probability P(X > 17.5) for a normally-distributed random variable X with mean 14 and standard deviation 2, we can use the standardization process.

First, let's calculate the z-score for the value 17.5:

z = (X - μ) / σ = (17.5 - 14) / 2 = 3.5 / 2 = 1.75

Now, let's evaluate the given options:

P(X < 10.5) where X is described as above:

To calculate this probability, we can calculate the z-score for the value 10.5 using the same formula as above:

z = (X - μ) / σ = (10.5 - 14) / 2 = -3.5 / 2 = -1.75

P(Z > 1.75) where Z is a standard normal random variable:

This probability represents the area under the standard normal distribution curve to the right of z = 1.75.

P(Z < -1.75) where Z is a standard normal random variable:

This probability represents the area under the standard normal distribution curve to the left of z = -1.75.

P(Y < 1.25) where Y is normally distributed with mean 10 and standard deviation 5:

This option involves a different random variable Y with a different mean and standard deviation. We cannot directly compare it to the other options without additional information or calculations.

From the given options, the probabilities that are equal to P(X > 17.5) are:

P(Z < -1.75) where Z is a standard normal random variable.

Therefore, the correct option is:

P(Z < -1.75) where Z is a standard normal random variable.

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Answer:

I'm not sure what you're asking. if their is supposed to be a picture try reposting, or if you forgot to type it leave a comment and I will try to help you the best I can.

Answer:

A

Step-by-step explanation:

24.8 x 7 = 173.6

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

The exponential distribution is a continuous probability distribution that describes the time between two consecutive events that occur randomly and independently of each other. This distribution is useful in the fields of reliability, physics, and finance, among others.

The exponential distribution has a single parameter known as the scale parameter, which is denoted by lambda (λ) and is typically expressed in terms of the mean time between failures.The mean, median, and standard deviation are three of the most common summary statistics used to describe a probability distribution.

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester can also be calculated using the exponential distribution.

Mean: The mean of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the mean is 1/λ = 1/0.143 = 6.993.

Median: The median of the exponential distribution is equal to ln(2)/λ.λ = 1/7 = 0.143

Therefore, the median is ln(2)/λ = ln(2)/0.143 = 4.837.

Standard deviation: The standard deviation of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the standard deviation is 1/λ = 1/0.143 = 6.993.

Probability: P(X > 16) = e^(-λx)λ = 1/7 = 0.143X = 16P(X > 16) = e^(-0.143 * 16) = 0.230

Therefore, the probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

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