which equation can be used to determine the length of DE

It is determined while using the binomial distribution that there is still a 1.145=114.5% chance that she produces no more than 11 of them.

There are just two possible results for each throw. Either she succeeds or she fails. The binomial probability distribution is employed to answer this issue since the probability of completing a shot is regardless of all other throws.

Binomial probability distribution-

\(P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}\)

\(C_{n,x} = n!/x! (n-x)!\)

where,

the no. of success= x

the no. of trials = n

the probability of a success on one trial = p

The probability of throwing not more than 11 will be:

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

Where,

\(P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}\)

\(P(X=0) = C_{18,0} .(0.689)^{0}(0.311)^{18}\)≈0

\(P(X=1) = C_{18,1} .(0.689)^{1}(0.311)^{17}\)≈0

\(P(X=2) = C_{18,2} .(0.689)^{2}(0.311)^{16}\)≈0

\(P(X=3) = C_{18,3} .(0.689)^{3}(0.311)^{15}\)≈0

\(P(X=4) = C_{18,4} .(0.689)^{4}(0.311)^{14}\)≈0

\(P(X=5) = C_{18,5} .(0.689)^{5}(0.311)^{13}\)= 0.0003

\(P(X=6) = C_{18,4} .(0.689)^{6}(0.311)^{12}\)=0.0016

\(P(X=7) = C_{18,7} .(0.689)^{7}(0.311)^{11}\)=0.0062

\(P(X=8) = C_{18,8} .(0.689)^{8}(0.311)^{10}\)=0.0188

\(P(X=9) = C_{18,9} .(0.689)^{9}(0.311)^{9}\)=0.0463

\(P(X=10) = C_{18,10} .(0.689)^{10}(0.311)^{8}\)=0.9232

\(P(X=11) = C_{18,11} .(0.689)^{11}(0.311)^{7}\)=0.1488

So,

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

=0+0+0+0+0+0.0003+0.0016+0.0062+0.0188+0.0463+0.9232+0.1488 =1.145

Therefore, she makes 1.145=114.5% probability, no more than 11 of them.

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The probability that Kendra will win a card game is 2/3. If Kendra plays 7 games the probability that Kendra wins exactly 4 games is 0.137.

The probability of winning one game is 2/3, and the probability of losing one game is 1/3. If you want to know the likelihood of a particular number of wins, you'll need to use the binomial distribution formula.

Binomial probability refers to the probability of obtaining a certain number of successes in a set number of trials (or independent experiments).

P(x = k) = nCk x pk x (1 - p)n - k

where, nCk is the number of combinations of n things taken k at a time,

n is the number of trials,

p is the probability of success, and

k is the number of successes.

Here, n = 7, p = 2/3, and k = 4.

Using the formula, we get:

P(x = 4) = 7C4 x (2/3)4 x (1/3)3= 35 x 16/81 x 1/27= 0.137.

Hence, the probability that Kendra wins exactly 4 games is 0.137.

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Answer:

\(\boxed {\boxed {\sf 102.1 \ meters}}\)

Step-by-step explanation:

Let's assume the tree forms a right angle with the ground.

The distance from the tree to the man is 18 meters. The angle of elevation, which is 80 degrees, is the angle from where the man is to the top of the tree. We want to find the height of the tree, which we can call x.

Let's draw a diagram. (not to scale)

We can use sine (opposite/hypotenuse), cosine (adjacent/hypotenuse) or tangent (opposite/adjacent). We base the sides off of the elevation angle.

x is opposite the elevation angle and 18 is adjacent to the angle. So, we must use tangent.

\(tan(\theta)=opposite/adjacent\)

The angle (θ) is 80. The opposite is x. The adjacent is 18.

\(tan(80)=x/18\)

Now, solve for x by isolating it.

x is being divided by 18. The inverse of division is multiplication. Multiply both sides of the equation by 18.

\(18*tan(80)=x/18*18\)

\(18*tan(80)=x\)

\(18*5.67128182=x\)

\(102.0830728=x\)

Round to the nearest tenth. The 8 in the hundredth place tells us to round up.

\(102.1\approx x\)

The height of the tree is about 102.1 meters.

**diagram is not to scale

Answer:

Equation on the left table: y = 3/5x

Equation on the right table: y = 3/5x - 2

Answers:

length of rope = 2 meters

perimeter of meadow = 12.56 square meters

=========================================================

Explanation:

Assuming there are no structures (buildings, fences, etc) to get in the way of the goat, this means the goat's area that it can roam is a circle with radius r

The area of the circle is pi*r^2 which is equal to 12.56 square meters

pi*r^2 = 12.56

3.14*r^2 = 12.56

r^2 = 4

r = sqrt(4)

r = 2

The radius of the circle is 2 meters. This is the length of the rope. If the goat goes out as far as it can go, and tries to move left/right, then it will trace out a circle of radius 2. This is assuming the rope is kept fully taut the entire time.

The perimeter of the circle is the same as the circumference

circumference = 2*pi*r

circumference = 2*pi*2

circumference = 4*pi

circumference = 4*3.14

circumference = 12.56

The circumference and area are the same because r^2 = 4 and 2*r = 4 when r = 2. For any other positive r value, the area and circumference will be different values.

So in short, if a friend says that the area of a circle is the same as its perimeter, then you can immediately conclude the radius is 2.

Side note: throughout all of this solution, I used the approximation pi = 3.14 though pi has more decimal digits

Answer:

2m

12.56 m

Step-by-step explanation:

A= 12.56 m²

r=? P=?

---------

A= πr²

The question in English is as follows:

How far does a bicycle wheel with a diameter of 40cm go in one turn?

The diameter of the wheel = d = 40 cm

So, the radius of the wheel = r = 0.5 d = 0.5 * 40 = 20 cm

we need to find the circumference of the wheel

So, it will be:

So, the bicycle will travel a distance of 125.6 in one turn

So, the answer will be 125.6 cm

Answer:

$7886.16

Step-by-step explanation:

If the balance increases by 4%, it will be 104% of the original amount.  104% as a decimal is 1.04.  Therefore, to calculate the balance with annual compound interest applied, multiply the balance of the account by 1.04 each year.

As Hei makes additional deposits of $1,400 for each year after the 1st year, add $1,400 to the account balance from year 2 onwards before adding the interest.

Let A = account balance

After 1 year

A = 1400 × 1.04 = $1456

After 2 years

A = (1456 + 1400) × 1.04 = $2970.24

After 3 years

A = (2970.24 + 1400) × 1.04 = $4545.05

After 4 years

A = (4545.05 + 1400) × 1.04 = $6182.85

After 5 years

A = (6182.85 + 1400) × 1.04 = $7886.16

Therefore, after 5 years her account balance will be $7886.16

Total number of cases possible when 3 Dice roll= 6^3=216

Now we have to find the number of cases when values shown on two of the dice sum to the value shown on the remaining, probability is 0.28

Now we need to count the instances where the values on two dice add up to the value on the other die, which is one. If a die shows 6, the remaining two dice must either show (5,1) or (4,2), or (3,3)

Total number of scenarios that could occur in this situation: 3!+3!+3!/2!=15

2. If a die shows 5, the other two dice must either display (4,1) or (3,2)

The total cases that could occur in this scenario are 3!+3! =12.

3. If a die shows 4, the other two dice must either display (3,1) or (2,2)

Total number of scenarios that could occur in this situation: 3!+3!/2!=9

4. If a die shows 3, the other two dice must also show 3. (2,1)

The total number of cases possible in this scenario= is 3!/2! =3

Total cases possible= 15+12+9+6+3=45

Probability= 45/216=5/24= 0.208

probability is 0.208

correct option is (D).

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The question was incomplete. Check below the complete question.

Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die?

(A) 1/6

(B) 13/72

(C) 7/36

(D) 5/24

(E) 2/9

Answer:

0.9646

Step-by-step explanation:

:)

Answer:

495

Step-by-step explanation:

Answer:

Well, as it turns out, when two figures are similar or congruent, they have certain properties, and these properties can be used to prove relationships between the figures. When two figures are similar figures, they have the following properties: Corresponding angles have equal measure.

Step-by-step explanation:

Answer:

y-4=4/5*(x+6)

Step-by-step explanation:

First you need to find the vaules for y-y₁=m(x-x₁) point slope form

y1 =4

x1=-6

m=4/5( because thats the slope)

Second plug in:

y-4 = 4/5(x+6)

done easy peesy :)

The duration the rocket will be in the air, which is the parameter Lily wants to know, is the time of flight of the rocket, indicates;

The parameter Lily is looking for is; The time of flight of the rocket

The time of flight is the duration an object such as a projectile spends in the air. The formula for finding the time of flight can be presented as the following equation;

t = 2 × V₀ × sin(α)/g

The height from which Lily's rocket is launched = 1.5 ft

Therefore, the parameter Lily is looking for is; How long the rocket will stay in the air.

The parameter that Lily is looking for is therefore, the time the rocket projectile will remain in the air which is the time of flight of the rocket.

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The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

$55

Step-by-step explanation:

5 tickets = $25

1 ticket = $5 (divide by 5 on both sides)

multiply by 11

11 tickets = 5 ×11

11 tickets = $55

Answer:

4 hours

Step-by-step explanation:

3.6 / .8

Answer:

(0, 1)

Step-by-step explanation:

Basically, substitute the x and y coordinates into the inequality and check whether the solution tallies with the inequality given.

y < 6x + 2 is the equation provided.

For (-1, 0) , when x = -1 , y = 0 , 0 < 6(-1) + 2     -> 0 < -4 (False)

For (1, 8) , when x = 1, y = 8, 8 < 6(1) + 2      ->  8 < 8 (False)

For (0, 1) , when x = 0, y = 1, 1 < 6(0) + 2      ->  1 < 2 (True)

For (2, 15) , when x = 2, y = 15, 15 < 6(2) + 2      ->  15 < 14 (False)

Hence, the only coordinate that satisfies the inequality is (0, 1)

Answer:

5 thirteenth ti the nearest tenth Is .6

Answer:

0.4

Step-by-step explanation:

First make it a decimal:

5/13 (divide)

0.38 (round)

So you get 0.4

The equation that represents the deer population after "n" years is p = 10(2^n). No given option is correct.

This equation takes the initial population of 10 and multiplies it by 2 raised to the power of "n," which represents the number of years. As the population doubles every year, we need to use exponential growth to calculate the population at any given year.

Option A (p = 10(2)') and option B (p = 2(10)') are incorrect because they do not properly account for the exponential growth of the population. Option C (+ = 10 2D + = 2(10)) is also incorrect as it is not a valid equation and does not make sense in the context of the problem. Therefore, the correct equation is p = 10(2^n). No given option is correct.

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The argument that the sun will rise tomorrow morning and set tomorrow evening is based on inductive reasoning, using past observations of consistent sunrise and sunset patterns to predict future occurrences.

1. The observation: Throughout your entire life, you have consistently noticed that the sun rises every morning and sets every evening. This is an observation based on personal experience.

2. Inductive reasoning: Based on this observation, you make an inference or prediction about the future. You reason that since the sun has always risen in the morning and set in the evening in the past, it is likely to continue doing so in the future.

3. Pattern and consistency: The assumption is that natural phenomena, such as the rising and setting of the sun, follow a pattern or regularity. This assumption is based on the principle of uniformity of nature, which suggests that the future will resemble the past in terms of natural occurrences.

4. The limitations of inductive reasoning: While inductive reasoning provides a useful way to make predictions based on past observations, it is not foolproof. There is always a small possibility that something unexpected could happen, such as a rare astronomical event or an external factor that alters the pattern. However, based on the available evidence and the consistency of the observed pattern, the prediction that the sun will rise tomorrow morning and set tomorrow evening is highly probable.

In summary, the argument relies on inductive reasoning, using the past consistent observation of the sun's rising and setting to predict that it will continue to do so in the future. While this reasoning is not infallible, it is a reasonable and practical way to make predictions based on observed patterns in nature.

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Answer:

y = 2x - 16

Step-by-step explanation:

Slope-intercept form: y = mx + b

Given:

Slope(m): 2

Point: (5, -6)

To write the equation in slope-intercept form we need to find the slope(m) and the y-intercept(b).

Since we were given the value of the slope, the only thing we have to do is find the y-intercept. To do this, input the values of the slope and the given point into the equation and solve for b:

y = mx + b

-6 = 2(5) + b

-6 = 10 + b

-16 = b

The y-intercept is -16.

Now that we know the slope and the y-intercept, we can write the equation:

y = 2x - 16

Answer:

The answer will be -5

You are welcome:)

Step-by-step explanation:

The best way for the data to be measured is called ordinal.

Option b.

Ordinal data is a type of categorical data in which the categories have a natural order or ranking. In this case, the students are ranking the instructor on a scale of 0 to 5, with 0 being the lowest and 5 being the highest. This type of data is best measured using ordinal measures, as it allows for the ranking of the data in a meaningful way.

Filtered data refers to data that has been filtered or sorted in some way. Nominal data is a type of categorical data in which the categories do not have a natural order or ranking. Numerical data is a type of data that is measured on a numerical scale, such as height or weight.

Therefore, the correct answer is b. ordinal.

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Answer:

513100

Step-by-step explanation:

(5.13 * 100)(1 * 100)=513100

The puck travelled a distance of 53.8 meters when the puck is 120 centimeters before the opponent's goal and puck travelled a distance of 56.2 meters when the puck is 120 centimeters after the opponent's goal.

Given that the distance to the opponent's goal from the player's current position is 55 meters. And after the shot, the puck is 120 centimeters from his opponent's goal.

We need to find out how many meters the puck travelled.

Also given there are 100 centimeters in 1 meter.

So, 55 meters = 55 × 100 centimeters

⇒ 55 metets = 5500 centimeters

Now, we are given that the puck is 120 centimeters from the opponent’s goal. It is not clear whether the puck landed before or after the goal post. So, considering both cases.

Case 1: the puck is 120 centimeters beyond the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters + 120 centimeters = 5620 centimeters

Divide 5620 by 100 to convert centimeters to meters.

The puck travelled a distance of 5620 cm or 56.2 meters.

Case 2: the puck is 120 centimeters before the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters - 120 centimeters = 5380 centimeters

Divide 5380 by 100 to convert centimeters to meters.

The puck travelled a distance of 5,380 cm or 53.8 meters.

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The correct choice is C. x1​+x2​+x4​.

To determine the correct choice, we need to analyze the given matrix A and find the vector x that satisfies the equation Ax = 0.

Calculating the product of matrix A and the vector x = [x1​, x2​, x3​, x4​]:

A * x = ⎣⎡​104​−51−16​17−548​−134−36​⎦⎤​ * ⎡⎢⎣x1​x2​x3​x4​⎤⎥⎦​

This results in the following system of equations:

104x1 - 51x2 - 16x3 + 17x4 = 0

17x1 - 548x2 - 134x3 - 36x4 = 0

To find the solutions to this system, we can use Gaussian elimination or matrix inversion. However, since we are only interested in the form of the solution, we can observe that the variables x1, x2, x3, and x4 appear in the first equation but not in the second equation. Therefore, we can conclude that the correct choice is C. x1​+x2​+x4​.

The correct choice is C. x1​+x2​+x4​.

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While the WHO finalized ICD-10 in 1990, the specific timing of the transition from ICD-9 to ICD-10 varied across different countries and healthcare systems.

In order to communicate diseases, symptoms, aberrant findings, and other components of a patient's diagnosis in a way that is widely recognised by people in the medical and insurance industries, healthcare professionals use the International Classification of Diseases (ICD) codes. ICD-10 is the name of the most recent edition, which is the tenth.

The World Health Organization (WHO) indeed finalized the ICD-10 (International Classification of Diseases, 10th Edition) in 1990. However, the transition from the previous version, ICD-9, to ICD-10 varied across different countries and healthcare systems.

In the US, for example, the transition to ICD-10 took place on October 1, 2015. This means that healthcare providers, insurers, and other entities in the US started using the ICD-10 codes for diagnoses and procedures from that date onwards. Therefore, in the context of the US, the transition to ICD-10 occurred more than 20 years after its finalization by the WHO.

However, it's important to note that other countries may have implemented ICD-10 at different times. The timing of adoption and implementation varied globally, and some countries may have transitioned to ICD-10 earlier or later than others.

In summary, while the WHO finalized ICD-10 in 1990, the specific timing of the transition from ICD-9 to ICD-10 varied across different countries and healthcare systems.

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Answer:

x2+10x+24

Step-by-step explanation:

The expanded expression in standard form is: \(x^2 - 10x + 24\)

To expand the expression (x - 4)(x - 6), you can use the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Let's do that step by step:

(x - 4)(x - 6)

Step 1: Multiply x from the first parentheses by both terms in the second parentheses:

\(x * x = x^2\\x * -6 = -6x\)

Step 2: Multiply -4 from the first parentheses by both terms in the second parentheses:

-4 * x = -4x

-4 * -6 = 24

Now, put everything together: (x - 4)(x - 6) = \(x^2 - 6x - 4x + 24\)

Combine like terms: \(x^2 - 10x + 24\)

So, the expanded expression in standard form is:

\(x^2 - 10x + 24\)

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