A right triangle has side lengths 7, 24 and 25as shown below.
Use these lengths to find tan L, sin L, and cos L.

The joint distribution of X(t) and Y(t) is P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)

The joint distribution of customers remaining and having left can be expressed using the Poisson process as follows:

Let N(t) be the number of customers that arrive in the time interval [0, t], and let S₁, S₂, S₃, ... be the sequence of service times for each customer, where S_i is the time the i-th customer spends in the system (i.e., waiting and being served). Let Y(t) be the number of customers who have left the system by time t, and let X(t) be the number of customers who are still in the system at time t.

The joint distribution of X(t) and Y(t) can be written as:

P(X(t) = k, Y(t) = n) = P(N(t) = k + n) * P(sum of S_i for i = 1 to k + n > t) * P(sum of S_i for i = 1 to k + n - 1 <= t)

where the first term on the right-hand side represents the probability that k + n customers arrive in the time interval [0, t], the second term represents the probability that the sum of service times for the first k + n customers exceeds t (i.e., there are still k + n customers in the system at time t), and the third term represents the probability that the sum of service times for the first k + n - 1 customers is less than or equal to t (i.e., the first k + n - 1 customers have left the system by time t).

The distribution of X(t) and Y(t) can be quite complex, depending on the distribution of service times and the arrival rate of customers. However, in some special cases, closed-form expressions for the joint distribution can be derived. For example, if the service times have an exponential distribution and the arrival rate of customers is constant, then the joint distribution of X(t) and Y(t) is given by the following formula:

P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)

where μ is the rate parameter for the exponential distribution of service times.

Learn more about exponential distribution here https://brainly.com/question/22692312

#SPJ4

Answer:

Step-by-step explanation:

A graph shows Time in minutes along the x-axis and the Truck's distance from the factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins the ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3, and 5, 3, and the third straight line joins ordered pairs 5, 3 with the ordered pair 10, 0.

The measure of each angle is given below:

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The measure of angles {contd.} is:

Read more about angles here:

https://brainly.com/question/25716982

#SPJ1

The area of the trapezoid KELP is approximately 2285.47 square units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The formula to find the area of a trapezoid is -

A = (1/2) × h × (b1 + b2)

where -

A is the area of the trapezoid.

h is the height of the trapezoid.

b1 and b2 are the lengths of the parallel bases of the trapezoid.

Using the given values, we can substitute them into the formula and solve for the area -

A = (1/2) × h × (b1 + b2)

A = (1/2) × 52.6 × (47.8 + 39.1)

A = 2285.47

Therefore, the area value is 2285.47 square units.

To learn more about trapezoid from the given link

https://brainly.com/question/1410008

#SPJ1

Answer:

17

Step-by-step explanation:

jdjieieiieieieieieie

The number of tots Rew has = X and X∈[0,5] or X(10,∝).

What is a number line?

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Let the number of tots Rew has = X.

It is given that Rew has either no more than 5 tots or more than 10 tots.

This means that the number of tots is either less than 5 or greater than 10.

which mean that X≤5 or X>10.

X∈[0,5] or X(10,∝)

The graph of the number line is attached below.

To learn more about graphing on the number line, refer to the link below:

https://brainly.com/question/27848910

#SPJ1

what is even numbers and

True. A piece-wise function is composed of different functions that are joined together at certain points and each of these functions will either have an x-intercept or a y-intercept.

Yes, a piece-wise function will always have at least one x-intercept or at least one y-intercept. A piece-wise function is composed of different functions that are joined together at certain points. Each of these individual functions can either be linear, quadratic, or any other type of function, and each of these functions will either have an x-intercept or a y-intercept. For example, if a piece-wise function contains two linear equations, each of them will have one x-intercept and one y-intercept. The same is true for quadratic equations, and for any other type of equation. Therefore, since a piece-wise function is composed of these individual functions, it will always have at least one x-intercept or at least one y-intercept.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

Knowing the value of p tells one that option b. whether there is statistical significance.

The concept of probability, which is a measure of the likelihood of an event occurring. It is an essential tool in statistics, and it helps us make informed decisions based on data.

Now, let's dive into the answer to the question. Knowing the value of p tells us about the statistical significance of our results. In statistical analysis, we often conduct hypothesis tests to determine whether a particular effect is significant or just occurred by chance.

The p-value is the probability of observing the results we obtained under the null hypothesis, assuming that the null hypothesis is true. The null hypothesis is the default assumption that there is no significant difference between groups or means.

If the p-value is low, say less than 0.05, we reject the null hypothesis and conclude that there is a significant difference between groups or means. On the other hand, if the p-value is high, we fail to reject the null hypothesis, and we cannot claim that there is a significant difference between groups or means.

To give an example, suppose we conducted an experiment to test whether a new drug reduces blood pressure. We would have a control group that receives a placebo and a treatment group that receives the drug. We measure the blood pressure of both groups and compute the p-value. If the p-value is less than 0.05, we would conclude that the drug is effective in reducing blood pressure.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

The area of the picture is 144 square inches.

The area is a measurement of the extent of a two-dimensional surface or region. It is expressed in square units, such as square inches, square meters, or square feet. The area of a shape is the amount of space it occupies in a plane or on a flat surface. The calculation of area depends on the shape of the object. For example, the area of a circle is calculated by using the formula A = πr², where r is the radius of the circle.

The area of a square with side length s is given by the formula A = s². If the side length of the picture is 12 inches, then we can substitute s = 12 into the formula to get:

A = s² = 12² = 144

Therefore, the area of the picture is 144 square inches.

To know more about area visit:

https://brainly.com/question/27683633

#SPJ1

Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To maximize profit, Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative. The marginal profit is the difference between the expected value of retaining a customer and the cost of the promotion:

Marginal profit = [tex](0.7 * $60) - $15 = $33[/tex]

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below the point where the expected profit of retention becomes less than $33.

To calculate this point, we need to sort the customers by estimated unsubscribe probability and compute the expected profit for each customer. Let [tex]p_i[/tex] be the estimated unsubscribe probability for customer i, and let [tex]R_i[/tex] be the expected profit if we offer them a promotion:

[tex]R_i = 0.7 * $60 - $15 = $33[/tex]

If customer i unsubscribes, then the profit is -$15. Otherwise, the profit is $60 - $15 = $45. Thus, the expected profit is:

[tex]E(R_i) = (1 - p_i) * $45 - p_i * $15[/tex]

If we order the customers by decreasing [tex]p_i[/tex], we can compute the expected profit of retaining the top n customers:

[tex]E(profit_n) = ∑_{i=1}^n E(R_i)[/tex]

Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative, which means that:

[tex]E(R_{n+1})[/tex] < 33

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex](1 - p_{n+1}) * $45 - p_{n+1} * $15[/tex] < 33

Simplifying, we get:

[tex]p_{n+1} >[/tex] 0.6

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below 0.6. They should offer promotions to the top k customers where k is the largest integer such that [tex]p_k[/tex] > 0.6.

To compute the average profit from offering promotions to the top k customers, we can use the formula for [tex]E(profit_n)[/tex] and substitute k for n:

[tex]profit_k = ∑_{i=1}^k E(R_i)[/tex]

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex]profit_k = ∑_{i=1}^k [(1 - p_i) * $45 - p_i * $15][/tex]

Using the data provided, we can compute the estimated unsubscribe probability for each customer and sort them in descending order:

Customer Unsubscribe Probability

1                              1                 0.92

2                              1                0.85

3                              1                0.75

4                              0               0.68

5                              0               0.61

6                              0               0.54

7                              0               0.47

8                              0               0.39

9                              0               0.32

10                              0             0.25

We can see that the estimated unsubscribe probability drops below 0.6 after the top 5 customers. Therefore, Watershed should offer promotions to the top 5 customers.

Using the formula for [tex]profit_k[/tex], we get:

[tex]profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)*$45-0.\\profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)$45-0.75$15 + (1-0.68)$45-0.68$15 + (1-0.61)$45-0.61$15\\= $10.05[/tex]

Therefore, Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To know more about probability:

https://brainly.com/question/12844710

#SPJ4

The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.

Probability of dropouts next year being exactly 305: 0

Probability of dropouts next year being less than 305: 0.68

Probability of dropouts next year being greater than 305: 0.32

Probability of dropouts next year being within one standard deviation of 305: 0.95

The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.

The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

Learn more about median here

https://brainly.com/question/28060453

#SPJ4

The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.

In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:

5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)

the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

To learn more about divide:

https://brainly.com/question/9532881

#SPJ4

According to the given information the formula for f(x) in term of x is  f(x) = (4/5)x - 4.

A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.

When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.

4x - 5y = 20

Subtracting 4x from both sides

-5y = -4x + 20

Dividing 5 from the both sides

y = (4/5)x - 4

The formula for f(x) in terms of x is:

f(x) = (4/5)x - 4

To know more about function visit:

https://brainly.com/question/18959115

#SPJ1

The area and circumference of each circle are 78.5cm², 31.4cm, 113.04cm², 37.68cm, 28.26cm², 18.84cm and 153.86cm², 43.96cm respectively

Using the formula of area of a circle and circumference of a circle, we can solve for each circle as

a.

The area is given as;

A = πr²

A = 3.14 * 5²

A = 78.5cm²

The circumference = 2πr

C = 2 * 3.14 * 5 = 31.4cm

b

A = πr²

A = 3.14 * 6²

A = 113.04cm²

C = 2πr

C = 2 * 3.14 * 6

C = 37.68cm

c.

A = πr²

A = 3.14 * 3²

A = 28.26cm²

C = 2 * 3.14 * 3

C = 18.84cm

d.

A = πr²

A = 3.14 * 7²

A = 153.86cm²

C = 2πr

C = 2 * 3.14 * 7

C = 43.96cm

Learn more on area of circle here;

https://brainly.com/question/24375372

#SPJ1

The roots of the quadratic equation are -

{x} = 4 ± i(√2/2)

The  general form of a quadratic equation is -

y = f(x) = ax² + bx + c

Given is the quadratic equation as -

f(x) = x² - 8x + 17

We can write the roots of the equation as -

x = {- b ± √(b² - 4ac)}/2a

x = {8 ± √(64 - 68)}/2

x = {8 ± i√2}/2

x = 4 ± i(√2/2)

Therefore, the roots of the quadratic equation are -

{x} = 4 ± i(√2/2).

To solve more questions on quadratic equations, visit the link below

https://brainly.com/question/30098550

#SPJ9

Answer:

7

Step-by-step explanation:

The length, L (in miles), that is left to be paved after d days is given by the following function L = 205 - 9d.

In this function, 205 represents the total length of the road that needs to be paved, and 9 represents the number of miles that the crew paves each day. The variable d represents the number of days that the crew has been working on the road.

To find the length of the road that is left to be paved after a certain number of days, we can substitute the value of d into the function and solve for L. For example, if the crew has been working on the road for 10 days, we can find the length of the road that is left to be paved as follows:

L = 205 - 9d

L = 205 - 9(10)

L = 205 - 90

L = 115

Therefore, after 10 days, the crew still has 115 miles of road left to pave.

This function can be useful for the construction crew to keep track of their progress and plan their work accordingly. It can also be used by project managers and other stakeholders to monitor the project and ensure that it is on track to be completed within the desired timeframe.

To learn more about functions click on,

https://brainly.com/question/29184483

#SPJ4

[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]

Cross multiply...

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3} \\ [/tex]

x = 6

Answer:

it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.

The two statements that justifies step three and four in the congruency proof are;

Reason 3: SSS Congruency Postulate

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

The two column proof is as follows;

Statement 1: AB ≅ AD, BC ≅ DC

Reason 1: Given

Statement 2: AC ≅ AC

Reason 2: Reflexive Property of Congruence

Statement 3: ΔABC ≅ ΔADC

Reason 3: SSS Congruency Postulate

Statement 4: ∠ABC ≅ ∠ADC

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Read more about Congruency Proof at; https://brainly.com/question/17239468

#SPJ1

The exact value of sin V in simplest radical form is 0.813.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

Given;

Sin ratio √74:7

Now,

AB/sinA=BC/sinB

√74/sinA = 7/sinB

√74/sin90 = 7/sinB

sinB=7/√74

sinB=0.813

Therefore, the answer of sin V will be 0.813.

Learn more about law of sines here:

https://brainly.com/question/17289163

#SPJ9

The value of the house when it was purchased was $150,000, before the 38% discount was applied.

A discount is a reduction in price or value, typically given as an incentive to purchase or to compensate for a decline in value.

In this case, we know that the house has decreased in value by 38% since it was purchased. This means that the current value is only 62% of its original value (100% - 38% = 62%).

Now, we can use a proportion to determine the original value of the house. We can set up the equation:

Current value / Original value = 62% / 100%

Substituting the given values, we get:

$93,000 / Original value = 62 / 100

To solve for the original value, we can cross-multiply and simplify:

100 x $93,000 = 62 x Original value

$9,300,000 = 62 x Original value

Dividing both sides by 62, we get:

Original value = $150,000

To know more about discount here.

https://brainly.com/question/3541148

#SPJ4

Answer: that would be 5^4 = 625

Step-by-step explanation:

Answer:

544

Step-by-step explanation:

How many 4 letter words can be constructed from ABCDE  that would be 5^4 = 625

How many 4 letter words can be constructed using BCD      that would be 3^4 = 81

So the number of words that use at least one vowel would be  5^4 - 3^4  =  625-81 = 544

Answer:

None

Step-by-step explanation:

The reason is because none of them add up to at least 91°

62° would be your best bet but, even when you do the math 62*2= 124

124/6= 20 2/3°

62+20.66...= 82.666...

82.6666...<91°

The probability of the coin being the weighted one given that it returned heads is 0.8.

P(Weighted | Heads) = ( P(Heads | Weighted) * P(Weighted) ) / P(Heads)

                   = ( 0.8 * 0.5 ) / 0.5

                   = 0.8

The probability of the coin being the weighted one given that it returned heads can be calculated using Baye's Theorem. This theorem states that the probability of an event given a condition is equal to the probability of the condition given the event multiplied by the probability of the event divided by the probability of the condition. In this case, the event is the coin being weighted, the condition is the coin returning heads. Therefore, the probability of the coin being the weighted one given that it returned heads is equal to the probability of the coin returning heads given that it is weighted multiplied by the probability of the coin being weighted divided by the probability of the coin returning heads. The probability of the coin returning heads given that it is weighted is 0.8, the probability of the coin being weighted is 0.5, and the probability of the coin returning heads is 0.5. Thus, the probability of the coin being the weighted one given that it returned heads is 0.8.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

No, this sample of celebrities taken by Zach is not random.

A random sample is the one in which there is no predictability and it is totally instantaneous.

Hair in the human condition is as has served the first 45 celebrities to arrive at the movie premiere. Firstly it is a movie premiere show only a few selected celebrities who have been invited and above that people who are main cast in the movie must arrived early.

Because our condition is being implemented here we cannot say that this is random sample of celebrities.

To know more about sample space, visit,

https://brainly.com/question/10558496

#SPJ4

Answer: 219

Step-by-step explanation:

32 times 19= 608

608 minus 389=219

Answer:

It is 90

Step-by-step explanation:

I never copy the answer please mark me

Answer:

See below

Step-by-step explanation:

Sum of interior angles in a triangle = 180°

∴∠A° + ∠B° + ∠C° = 180°

= 2x° + 4x° + 6x° = 180°

= 12x° = 180°

= x = [tex]\frac{180}{12}[/tex]

∴ x = 15

Substitute this value of x in Angle C:

= 6x°

= 6(15)°

= 90°

This means AC is perpendicular to BC. Also triangle ABC is a right-angled triangle