2 cos 0 = =, tan 8 < 0 Find the exact value of sin 6. 3 O A. - √5 √√5 OB. 2 √√5 oc. 3 D. 3/2 --

a)  The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)

b) The probability of waiting less than 2 minutes to check out is 0.427

c) The probability of waiting between 4 and 6 minutes is 0.242

d) The probability of waiting more than 5 minutes to check out is 0.082

a. The equation for the exponential distribution of waiting times is given by:

\(f(x) = \lambda e^{-\lambda x}\)

where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.

b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:

P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)

Solving this integral yields:

P(X < 2) = 1 - \(e^{(-2\lambda)}\)

Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:

E(X) = 1/λ

2.5 = 1/λ

λ = 0.4

Therefore, the probability of waiting less than 2 minutes to check out is:

P(X < 2) = 1 - \(e^{-2*0.4}\)

P(X < 2) ≈ 0.427

c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:

P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)

P(2 < X < 4) ≈ 0.242

d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:

P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(X > 5) = \(e^{(-5\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(X > 5) = \(e^{(-5*0.4)}\)

P(X > 5) ≈ 0.082

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Answer:

12/2

Step-by-step explanation:

The solution for the system of equtaions is (57/11, 42/11)

Here we have the system of equations:

x/3 = 6 - y/3

3x/4 - 3 = 2y

We can isolate x on the first equation to get:

x = 18 - 3*y/3

x = 18 - y

Replacing that on the other equation we will get

3*(18 - y)/4 - 3 = 2y

We can solve this for y.

3*(18 - y)/4 = 2y + 3

54 - 3y = 4*(2y + 3) = 8y + 12

54 - 12 = 8y + 3y

42 = 11y

42/11 =y

And the value of x will be:

x = 9 - 42/11

x  = 99/11 - 42/11 = 57/11

That is the solution of the system.

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Answer:

761090000

Step-by-step explanation:

10⁸ = 100000000

7.6109 * 100000000 = 761090000

Answer:

761090000

Step-by-step explanation:

=7.6109×10^8

=761090000

ANS

Answer:

\( y = x^2 -5x +6\)

And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:

\( y = (x-r) (x-s)\)

The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2

\( y=(x -2)) (x-3)\)

Step-by-step explanation:

For this problem we have the following polynomial given:

\( y = x^2 -5x +6\)

And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:

\( y = (x-r) (x-s)\)

The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2

\( y=(x -2)) (x-3)\)

The standard deviation of the sample mean is also known as the standard error of the mean. It can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is $2 and the sample size is 100. So, the standard deviation of the sample mean is $2/sqrt(100) = $2/10 = $0.2. Is there anything else you would like to know?

I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

B

Step-by-step explanation:

Answer:

133 is the answer! hoep it helps you out

Answer:

85°

Step-by-step explanation:

Hope this helps!

Answer:

8

Step-by-step explanation:

x²-6x+1 +8=x²-6x+9=(x-3)²

Answer:

c

Step-by-step explanation:

rectangle: 6×7=42

triangle: (4×6)÷2= 12

the whole area: 42+12=54

To calculate the standard deviation, you must first calculate the mean of the data set. This is done by adding up all the values in the data set and dividing by the number of values. Once you have the mean, you must subtract it from each value in the data set and square the result.

Then, you must add up all of the squared values, divide by the total number of values, and take the square root of that number. The result is the standard deviation.

Standard deviation is important because it can be used to compare the data to its mean and can help determine the amount of risk associated with a particular data set. Standard deviation is a measure of how spread out a data set is from its mean or average. It is used to measure the amount of variability or dispersion for a given data set.

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Answer:

\( \frac{1}{2} (4 + 8) \times 3 = 6 \times 3 = 18\)

Answer: 0.6

Step-by-step explanation:

The slope is the change in y over the change in x.  y is 4-1 = 3.  x is 3 - (-2) = 5

Slope is 3/5 or 0.6

[The y intercept is 2.2, so the equation of a line going through these two points is y = 0.6x + 2.2]

Answer:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The formula to find the slope is

m = (y2 - y1)/ (x2 - x1)

Where (x1, y1) and (x2, y2) are the two points

The two points given are (-3, 4) and (2, -1)

Substituting it in the formula

m = (-1 - 4)/ (2 - (-3))

By further calculation

m = -5/ (2 + 3)

So we get

m = -5/5

m = -1

Therefore, the slope of the line is -1.

The Kantian triangle consists of three fundamental concepts: freedom, morality, and equality.

The Kantian triangle is a conceptual framework developed based on the philosophy of Immanuel Kant, a prominent figure in Western philosophy. The triangle represents the interconnectedness of three essential ideas: freedom, morality, and equality.

Freedom, the first component of the Kantian triangle, refers to the inherent capacity of individuals to act autonomously and make choices without external coercion. According to Kant, human beings possess rationality and a moral duty to exercise their freedom responsibly.

Morality, the second component, represents the ethical principles and obligations that guide human behavior. Kant believed that moral actions should be grounded in reason and universalizable, meaning that individuals should act in a way that they would want everyone else to act in similar situations. For Kant, morality is not based on consequences but on the inherent value and dignity of rational beings.

Equality, the final component of the Kantian triangle, emphasizes the equal moral worth and inherent dignity of all individuals. Kant argued that every person possesses rationality and should be treated as an end in themselves, rather than a means to an end. This concept of equality underpins Kant's ethical theory and his notion of human rights.

In summary, the Kantian triangle consists of freedom, morality, and equality, which are interconnected and central to Kant's philosophical framework. These concepts highlight the importance of individual freedom, moral responsibility, and the equal worth of all human beings.

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Answer:

When we say that an allele is "fixed," it means that a particular allele has reached a frequency of 100% in a population.

Step-by-step explanation:

Alleles are different forms of a gene that occupy the same position on homologous chromosomes. In a population, different alleles can exist for a specific gene. However, through various evolutionary processes such as natural selection, genetic drift, or gene flow, one allele may become predominant and eventually fixate within the population.

The fixation of an allele can occur through different mechanisms. For example, if a beneficial allele provides a selective advantage to individuals carrying it, it is more likely to increase in frequency and eventually become fixed in the population. On the other hand, genetic drift, which is the random change in allele frequencies due to chance events, can also lead to the fixation of an allele, especially in small populations.

Once an allele is fixed in a population, it means that all future generations will inherit that allele, and no alternative alleles will be present at that particular gene locus.

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5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

Answer:

0.6

Step-by-step explanation:

I used 30 60 90 triangle.

In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

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Answer:

hope this helps

Step-by-step explanation:

The expression for V(t), the value of Rick's snowmobile, in dollars, after t years can be given by:

V(t) = $10,500 * (1 - 0.14)^t

Simplifying this expression, we get:

V(t) = $10,500 * 0.86^t

So, the required expression for V(t) is:V(t) = 10,500 * 0.86^t

4/7 i.e. 4 : 7 is the ratio of the boys to the total number of students.

Given, A class has 16 boys and 12 girls.

So, the total number of students in the class be 16 + 12 = 28 students

We have to find the ratio of boys to the total number of students be,

number of boys/total students

= 16/28

= 8/14

= 4/7

Hence, 4/7 is the ratio of the boys to the total number of students.

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To make parallelogram WXYZ a square, the following conditions must be met:

1. All four sides of the parallelogram must have equal length.

2. The angles between adjacent sides must be 90 degrees.

Since a square is a special type of parallelogram with all sides equal and all angles equal to 90 degrees, we can determine the value of m that would make WXYZ a square by ensuring that these conditions are met. To find the value of m, we need more information about the dimensions or properties of the parallelogram WXYZ. Please provide additional details or measurements related to the parallelogram. The diagonals of a square are equal in length and bisect each other at 90-degree angles. The perimeter of a square is the sum of all four sides, and the area of a square is calculated by squaring the length of one side.In order for parallelogram WXYZ to be a square, it must have congruent sides and right angles at each vertex.

Since opposite sides of a parallelogram are congruent, we can equate the lengths of adjacent sides to find the value of m that would make it a square.

Let's assume that WX and XY are adjacent sides of the parallelogram.

If WX = XY, then the parallelogram would have congruent sides.

Let's say WX = m and XY = m.

To form a square, the angles at each vertex must be right angles. This means that WX and XY must be perpendicular to each other.

In a square, opposite sides are parallel, so the slopes of WX and XY must be negative reciprocals of each other.

The slope of WX can be represented as (change in y) / (change in x). Since it is perpendicular to XY, its slope will be the negative reciprocal of the slope of XY.

Let's assume the slope of XY is denoted as a. Then the slope of WX would be -1/a.

We can now equate the slopes of WX and XY:

-1/a = (change in y) / (change in x)

Simplifying this equation, we get:

a = -1

Therefore, the slope of XY is -1.

Now, we can equate the lengths of WX and XY:

m = m

Since WX = XY and both sides have length m, we can say that m = m.

So, any value of m would make parallelogram WXYZ a square as long as the sides WX and XY are congruent and perpendicular to each other, with a slope of -1.

hence, the value of m = -1.

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Answer:

$117.87

Step-by-step explanation:

4 trees x $21.99 = $87.96

34% x $87.96 = $29.91 tip

Total = $87.96 + $29.91 = $117.87

Answer:

The answer is B

Step-by-step explanation:

Because 2 in B answer is in hundreth while in 37.632 the value of number 2 is thousandth

We will determine the area of the green section as follows:

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:

Now, we transform it to radians:

*Second: We replace on the equation:

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

Answer:

A ≈ 43.4 cm²

Step-by-step explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

  given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² × \(\frac{138}{360}\) ( simplify fraction by dividing numerator/denominator by 6 )

   = π × 6² × \(\frac{23}{60}\)

   = 36π × \(\frac{23}{60}\)

   = \(\frac{36\\pi (23) }{60}\)

   ≈ 43.4 cm² ( to the nearest tenth )

Mean (m): 2.978

Variance (s²): 2.389

Standard deviation (s): 1.544

Mean (m):

The mean can be calculated as follows:

Mean = Σ(x * p(x))

where Σ is the summation operator, x is the value of the random variable, and p(x) is the probability of x.

In this case, the mean is calculated as follows:

Mean = (0 * 0.022) + (1 * 0.113) + (2 * 0.144) + (3 * 0.273) + (4 * 0.201) + (5 * 0.193) + (6 * 0.054) = 2.978

Variance (s²):

The variance can be calculated as follows:

Variance = Σ(x² * p(x)) - m²

where Σ is the summation operator, x² is the square of the value of the random variable, p(x) is the probability of x, and m is the mean.

In this case, the variance is calculated as follows:

Variance = (0² * 0.022) + (1² * 0.113) + (2² * 0.144) + (3² * 0.273) + (4² * 0.201) + (5² * 0.193) + (6² * 0.054) - 2.978² = 2.389

Standard deviation (s):

The standard deviation can be calculated as follows:

Standard deviation = √Variance

In this case, the standard deviation is calculated as follows:

Standard deviation = √2.389 = 1.544

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Answer:

y=x+1

Step-by-step explanation:

First find the slope by subtracting the y values from both points and dividing it by the subtraction of the x values from both points:

-4--2/ -3--1= -2/-2= 1

so the slope is 1

Now find the y-intercept by plugging in the x and y from one of the points into the equation y=x+b

-3=-4+b

1=b

now plug the slope and y intercept in:

y=x+1

hope this helps :D

Answer:

for the x^2 =1 the first solution is 1x1 the other solution is -1x-1

4x^2=1 the "x" equals to 1/2

Step-by-step explanation:

Because the answer is "1" it is positive. Negative and negative equals to positive. Positive and positive equals to positive.