What is the value of x in the figure?

Enter your answer in the box.

Answer:

attached below

Step-by-step explanation:

Given :  FX (x) = 3/4x  (2-x)    0 ≤ x ≤ 2

a) Calculate the cumulative distribution function FX

Cdf =

attached below is the detailed solution

b) Let Y = √ X. determine CDF

attached below  

c) calculate PDF

To find the slope of line AB, we can use the slope formula:

slope of AB = (y2-y1)/(x2-x1) = (3-8)/(2-(-10)) = -5/12

Since we want to find the equation of a line parallel to AB and passing through point X(-5,10), we know that the slope of this new line will also be -5/12.

Now we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1), where m is the slope of the line and (x1,y1) is a point on the line.

So, plugging in the values we know:

y - 10 = (-5/12)(x - (-5))

Simplifying:

y - 10 = (-5/12)x - (25/12)

y = (-5/12)x + (145/12)

This is the slope-intercept form of the equation of the line parallel to AB and passing through point X.

Answer:

nhyh

Step-by-step explanation:

h

mhhhygvvvx VC ghv h h h b

Answer:

a is -9

b is 4

Step-by-step explanation:

we know that a and b are whole numbers.

we know that they are factors of 36.

1 * 36

2 * 18

3 * 12

4 * 9

6 * 6

i just did this as guess and check.

what numbers have a difference of 5?

the factors 4 and 9.

so, if a is the negative one, a has to be -9 to get -5 because

-9 + 4 = -5

and

(-9)(4) = 36

The abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent is not provided in the given information.

The given information states that ∠c and ∠f are right angles (rt. ∠'s), and ∠b is not explicitly mentioned. In order to determine the abbreviation of the postulate or theorem that supports the conclusion of triangle congruence, we would need additional information regarding the sides or angles of the triangles.

Triangle congruence can be established using various postulates and theorems, such as the Side-Angle-Side (SAS) postulate, Angle-Side-Angle (ASA) theorem, Side-Side-Side (SSS) postulate, and others. These criteria establish specific conditions that need to be met in order to prove that two triangles are congruent.

Without knowing the specific side or angle relationships between the triangles in the given information, it is not possible to determine the appropriate postulate or theorem that supports the conclusion of triangle congruence.

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First Dave picks his swimming day, then his running day, and then his biking day. Since each activity is different, the order in which he selects the days matters. Therefore the number of selections is P(7, 3).

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 1/2.

Here,

He does 3 activities in 7 days,

P(7,3) is the ways to select the schedule.

Dave chooses his swimming, running, and biking days in that order. The sequence in which he chooses the days is important because each activity is distinct. Consequently, P is the number of choices (7, 3).

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95% of 140 is:

(95:100)*140 =

(95*140):100 =

13300:100 = 133

Answer:

-1/2, 5/3

Step-by-Step Explanation:

6z^2 - 7z - 5 = 0

=> 6z^2 - 10z + 3z - 5 = 0

=> 2z(3z - 5) + 1(3z - 5) = 0

=> (2z + 1)(3z - 5) = 0

=> z = -1/2, 5/3

Hope it helps.

If you have any query, feel free to ask.

Answer:

constant -10

Explanation:

To get the constant we multiply the constants of each term

which is our answer!

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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Answer: 432

Step-by-step explanation:

Four squared = 16 since 4 times 4 = 16

3 to the power of 3 = 27 since 3 times 3 times 3 = 27

Finally, multiply them together, 16 times 27 = 432

Answer: 432

Step-by-step explanation:

(4^2)×(3^3)

4×4=16

16×3^3=16×(3×3×3)

16×27=432

We need to find the probability that no students arrive during the professor's one-hour nap using the Poisson distribution. In this case, the average arrival rate (λ) is 3 students per hour (60 minutes / 20 minutes per student).

The probability mass function (PMF) for the Poisson distribution is given by:

P(X=k) = (e^(-λ) * λ^k) / k!

For k=0 (no student arrivals):

P(X=0) = (e^(-3) * 3^0) / 0!
P(X=0) = (e^(-3) * 1) / 1
P(X=0) ≈ 0.05

So the probability that the professor's nap will not be disrupted by any student arrivals is 0.05, which corresponds to option B.

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Answer:

Step-by-step explanation:

An exponential function has a standard form of

\(y=a(b)^x\) where a is the initial value and b is the growth/decay rate in decimal form.

If the walk had an attendance of 500 the first year, that means that for us,

a = 500

If the attendance is expected to increase by 5% each year, then not only does b retain its initial attendance, it is added to by 5%: 100% + 5% = 105% or, in decimal form, 1.05

Our function, then, is

\(y=500(1.05)^x\) and we need to solve for the number of people, y, that will attend in year x = 10:

\(y=500(1.05)^{10}\)

First raise 1.05 to the 10th power to get

y = 500(1.628894627) and then multiply those 2 numbers together to get

y = 814.4 or 814 people in the 10th year

In the 10th year, there were 776 people in attendance.

An exponential growth function is given by:

y = abˣ

where y,x are variables, a is the initial value of y and b is the multiplier.

Given that the first year had an attendance of 500, hence a = 500. Also, there is an increase of 5% each year, hence b = 5% + 100% = 1.05

Therefore the exponential function is given by:

\(y = 500(1.05)^{x-1}\\\\In\ the\ 10th\ year:\\y = 500(1.05)^{10-1}=776\)

Hence in the 10th year, there were 776 people in attendance.

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The equation which has exactly one solution is 4 (x + 3) = 7x – 6, and the solution is x = 6.

To solve the equations, we can use Multiplicative Distribution Law.

The first equation, 4 (x + 3) = 7x – 6, has exactly one solution that is x = 6.

4 (x + 3) = 7x – 6

4x + 12 = 7x – 6

4x – 7x = – 6 – 12

– 3x = – 18

x = 6

The second equation, 4 (x + 3) + 8 = 4x + 20, has all real numbers.

4 (x + 3) + 8 = 4x + 20

4x + 12 + 8 = 4x + 20

4x – 4x = 20 – 12 – 8

0 = 20 – 12 – 8

0 = 0

The third equation, 4 (x + 3) + 3x = 7x + 12, has all real numbers.

4 (x + 3) + 3x = 7x + 12

4x + 12 + 3x = 7x + 12

4x + 3x – 7x = 12 – 12

7x – 7x = 0

0 = 0

The last equation, 4 (x + 3) + 6 = 4x + 9, has no solution. It is a wrong equation.

4 (x + 3) + 6 = 4x + 9

4x + 12 + 6 = 4x + 9

4x – 4x = 9 – 12 – 6

0 = - 9

Hence, by using the Multiplicative Distribution Law, the equation which has exactly one solution is 4 (x + 3) = 7x – 6.

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Answer: (A)

Step-by-step explanation: 4(x + 3) = 7x - 6

trust

The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

The number of tornadoes that occur in the United States each year is 1158

Let's call the number of tornadoes in the United States each year "x".

The number of tornadoes in Florida each year is 5.7% of this total

So we can write:

66 = x * 5.7%

Divide both sides by 5.7%

x = 66/5.7%

Evaluate

x = approximately 1158

So, approximately 1162 tornadoes occur in the United States each year.

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Answer:

Exact form:

1/24

Decimal form:

0.0416

Answer:

What your question?

Step-by-step explanation:

Answer:

I think the question is yes

Answer:

Linear

Step-by-step explanation:

The x value side goes up by 7 while y values are going down by 5. Its a constant proportionality of 7 and 5.

Answer:

1. 2/3

2. 15/2 (7.5)

Step-by-step explanation:

1. Scale down from larger to smaller:

6/9 = 4/6 = 2/3

ΔDEF ⇒  ΔABC  \(=\frac{2}{3}\)

2. \(EF=\frac{5}{\frac{2}{3} } =\frac{(5)(3)}{2} =15/2\)  or 7.5

I hope this help you

the wavelength of the electron is approximately 122 nm To find the wavelength of an electron, we can use the de Broglie wavelength formula:

wavelength (λ) = h / (m * v)

where:
- h is Planck's constant (6.63 x 10^-34 Js)
- m is the mass of the electron (9.11 x 10^-28 g, which needs to be converted to kg)
- v is the speed of the electron (5.97 mm/s, which needs to be converted to m/s)

Step 1: Convert the mass of the electron to kg:
9.11 x 10^-28 g * (1 kg / 1000 g) = 9.11 x 10^-31 kg

Step 2: Convert the speed of the electron to m/s:
5.97 mm/s * (1 m / 1000 mm) = 5.97 x 10^-3 m/s

Step 3: Plug the values into the de Broglie wavelength formula:
λ = (6.63 x 10^-34 Js) / (9.11 x 10^-31 kg * 5.97 x 10^-3 m/s)

Step 4: Calculate the wavelength:
λ = (6.63 x 10^-34 Js) / (5.44 x 10^-33 kg m/s) ≈ 1.22 x 10^-10 m

Step 5: Convert the wavelength to nm:
1.22 x 10^-10 m * (1 x 10^9 nm / 1 m) ≈ 122 nm

So, the wavelength is approximately 122 nm.

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Answer:

18

Step-by-step explanation:

4 divided by 24 is 6

6x3=18

The rate at which profit change when x items produced and sold for the given revenue function and cost function is equal to  P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3 and for x = 0 P'(x) is undefined.

Total revenue function r(x) = 900√x² - 0.1x

Total cost function c(x) = 1400( x² + 2)1/3 + 800

Profit of the function = Revenue function - Cost function

⇒ P(x) = r(x) - c(x)

Rate at which profit is changing for 'x' items produced and sold

⇒P'(x) = r'(x) - c'(x)

Differentiate r(x) and c(x) we get,

r(x) = 900√x² - 0.1x

⇒ r'(x) = 900 ( (1/2)(2x - 0.1 )/ √(x² - 0.1x)

⇒ r'(x) = 450(2x - 0.1 )/ √(x² - 0.1x)

c'(x) = 1400/3 (2x) / ( x² + 2)2/3

Substitute the value we get,

P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3

For x = 0

P'(x) is undefined.

Therefore, rate at which total profit is changing for the given revenue function and cost function is equal to P'(x) = 450(2x - 0.1 )/ √(x² - 0.1x) - 2800/3 (x) / ( x² + 2)2/3 and for x = 0 P'(x) is undefined.

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The above question is incomplete , the complete question is :

total-revenue function r(x)=900√x² - 0.1x  and a total-cost function c(x)=1400( x² + 2)1/3 + 800 , both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold.

Answer:

9-16y

Step-by-step explanation:

9-x^2y when x=4

plus in 4: 9- (4)^2y

=9-16y

Answer:

steps below

Step-by-step explanation:

f(x) = x + 5

g(x) = x - 4

f(g(x)) = f(x-4) = (x-4) + 5

Answer:

11 years old

Step-by-step explanation:

Create an equation. Let x = the age of Carlos.

2x + x = 33

3x = 33

x = 11

Answer:

ye Carlos us 11 years old

a. The probability that 1 or more nonconforming units are found is 0.2311.

b. The probability that exactly 3 units are nonconforming is 0.000058.

a. To solve the problem, you can use the complement rule. The complement rule states that the probability of an event occurring is 1 minus the probability of the event not occurring. So, in this case, the probability that no nonconforming units are found in a sample of 25 units is:

P(no nonconforming) = (0.99)²⁵ = 0.787.

Therefore, the probability that 1 or more nonconforming units are found is:

P(1 or more nonconforming) = 1 - P(no nonconforming) = 1 - 0.787 = 0.213.

Rounded to four decimal places, this is 0.2311.

b. To solve the problem, you can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k).

Here, n = 25 is the sample size, k = 3 is the number of nonconforming units, and p = 0.01 is the probability of a unit being nonconforming.

Using the formula, we get:

P(X=3) = (25 choose 3) * (0.01)³ * (0.99)²² = 2300 * 0.000001 * 0.5459 = 0.000058.

Rounded to six decimal places, this is 0.000058.

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Answer:

$1.62

Step-by-step explanation: