A private clinic has two resident clinical psychologists, Sally and Morgan. For booking each day, Sally has six appointment slots and Morgan has three. The average number of demands for consultation with Sally is three on any weekday, and five on any weekend, while that with Morgan is two on any day of the week. Assuming these demands follow Poisson distributions and are independent.
(i) Compute the probability that all available slots for consultation with both Sally and Morgan are filled on a certain Saturday.

Answer:

B

Step-by-step explanation:

Triangle IJK is an isosceles triangle.

The slope of IJ is -2, the slope of JK is 1, and the slope of IK is 2. The length of IJ is 8, the length of JK is 4, and the length of IK is 6. Triangle IJK is an isosceles triangle.
√Correct

Learn more about isosceles trianlge

brainly.com/question/2456591

#SPJ11

a. 39 work sampling observations. b. By selecting a random time and a random employee to observe. c. The 95% confidence interval for the population standard is approximately 83.56 +/- (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

a. To determine the number of work sampling observations necessary to achieve a 95% confidence level with a margin of error of +10%, we need to use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (1.96 for 95% confidence level)

p = proportion of beak adjustments estimated from preliminary investigation (0.3)

E = margin of error (0.1)

Plugging in the values:

n = (1.96^2 * 0.3 * 0.7) / 0.1^2

n = 38.15

Rounding up, we need at least 39 work sampling observations.

b. The random observations should be made by selecting a random time of day, and then selecting a random employee to observe. This should be repeated until the required number of observations has been made. This method ensures that all employees have an equal chance of being observed and that the observations are not biased towards certain times or individuals.

c. To determine the standard in hours per hundred beak adjustments, we need to use the following formula:

Standard = (Total time worked / Total number of beak adjustments) * 100

For the six employees summarized in the table:

Granny:

Standard = (82 / 164) * 100

Standard = 50 hours per hundred beak adjustments

Tweety:

Standard = (80 / 161) * 100

Standard = 49.69 hours per hundred beak adjustments

Item:

Standard = (200 / 185) * 100

Standard = 108.11 hours per hundred beak adjustments

Total:

Standard = (82 + 80 + 200 + 121 + 161 + 185) / (164 + 161 + 185) * 100

Standard = 83.56 hours per hundred beak adjustments

The calculated error is the difference between the estimated standard and the true population standard. Since we do not have the population data, we cannot calculate the error. However, we can calculate the variability in the sample data using the following formula:

Standard Error = Standard Deviation / √(n)

Where:

Standard Deviation = √((Σ(x - x-bar)^2) / (n - 1))

n = sample size

Using the data provided in the table, we can calculate the standard deviation and standard error as follows:

Standard Deviation = √(((82-73.5)^2 + (80-73.5)^2 + (200-119)^2 + (121-82.5)^2 + (161-119)^2 + (185-82.5)^2) / (6-1))

Standard Deviation = 55.88

Standard Error = 55.88 / √(6)

Standard Error = 22.83

This means that there is a 95% chance that the true population standard falls within + or - 2 standard errors of the estimated sample standard. Therefore, the 95% confidence interval for the population standard is approximately 83.56 + or - (2 * 22.83), or 37.9 to 129.2 hours per hundred beak adjustments.

learn more about population standard: https://brainly.com/question/29942393

#SPJ1

The complete question goes thus:

ACME Corp has hired Daffy Duck to conduct a work sampling project to establish standards. 25 employees are part of the operations under scrutiny. The operations include scenery making, coloring, animation, joke writing, duck beak adjustment, and carrot sourcing. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent adjusting duck beaks (this is equal to 17,614 beak adjustments). a. How many work sampling observations would be necessary to conduct if a 95 percent confidence that the observed data were within a +10 percent of the population data? b. Describe how the random observations should be made and justify why (Assume that all random observations need to be conducted over a three-week period or 15 working days). c. The Following table illustrates summary data gathered from 6 out of the 25 employees. From this data, determine a standard in hours per hundred beak adjustments. What is the calculated error? Granny 82 164 Tweety 80 Item Total hours worked Total observations (all elements) Observations involving cataloguing Average rating Operators Speedy Taz Glez 78 76 200 121 Foghorn Leghorn 68 Yosemite Sam 81 161 185 144 51 57 29 42 47 55 78 95 120 85 95 99

Answer:

144

Step-by-step explanation:

The lengths of the two legs are 2 centimeters and 9 centimeters.

Let's call the shorter leg of the right triangle x and the other leg y. According to the given information, we can create the following equation:

x = y - 7

Since we know that the hypothenuse is 13 centimeters, we can use the Pythagorean theorem to create another equation:

x^2 + y^2 = 13^2

Substituting the first equation into the second equation, we get:

(y - 7)^2 + y^2 = 13^2

Simplifying and rearranging terms, we get:

2y^2 - 14y - 72 = 0

Using the quadratic formula, we can solve for y:

y = (14 ± √(14^2 - 4(2)(-72))) / (2(2))

y = (14 ± √484) / 4

y = (14 ± 22) / 4

y = 9 or y = -2

Since the length of a leg cannot be negative, we reject the negative solution and take y = 9 centimeters as the length of the other leg. Then, we can use the first equation to find the length of the shorter leg:

x = 9 - 7

x = 2 centimeters

Therefore, the lengths of the two legs are 2 centimeters and 9 centimeters.

Learn more about lengths

brainly.com/question/30100801

#SPJ11

Answer:

The second answer is correct

Step-by-step explanation:

The first image shows nuclear fusion, combining two lighter nuclei to make a helium and a heavy nucleus, and the second image shows nuclear fission, taking a large unstable nucleus and turning it into two lighter nuclei.

The asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 .

To find the asymptotes of a rational function, we need to analyze the degree of the numerator and denominator, and find the values of x that make the denominator equal to zero.

First, let's find the vertical asymptotes. Vertical asymptotes occur when the denominator of a rational function is equal to zero. In this case, the denominator is 3x+6. Setting this equal to zero, we get:

3x+6=0
3x=-6
x=-2

So, the vertical asymptote is x=-2.

Next, let's find the horizontal asymptotes. Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 0 and the degree of the denominator is 1, so there is a horizontal asymptote. To find the horizontal asymptote, we need to look at the leading coefficients of the numerator and denominator. The leading coefficient of the numerator is 5 and the leading coefficient of the denominator is 3. So, the horizontal asymptote is y=5/3.

Therefore, the asymptotes of the rational function f(x)=(5)/(3x+6) are x=-2 (vertical asymptote) and y=5/3 (horizontal asymptote).

To know more about asymptotes click here:

https://brainly.com/question/4084552

#SPJ11

The equation -7t-6=-7t has no solution.

Because when we try to isolate the variable t on one side of the equation, we end up with an equation that is not true.

Here's how we can do this:
-7t-6=-7t

First, we can add 7t to both sides of the equation:
-6=0

This equation is not true, so there are no values of t that will make this equation true. Therefore, the equation has no solution.

For more such questions on Equation & solutions.

https://brainly.com/question/545403#

#SPJ11

The equation is true, the point (-1,6) does indeed lie on the line (-3,5).

The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine whether or not the point (-1,6) lies on the line (-3,5), we need to plug in the x and y values of the point into the equation of the line and see if the equation is true.

First, we need to find the slope of the line. The slope is the difference in the y values divided by the difference in the x values:

m = (5 - 6)/(-3 - (-1)) = -1/-2 = 1/2

Next, we need to find the y-intercept of the line. We can do this by plugging in one of the points and solving for b:

5 = (1/2)(-3) + b

b = 5 + (3/2) = 13/2

Now we have the equation of the line: y = (1/2)x + 13/2

Finally, we can plug in the x and y values of the point (-1,6) to see if the equation is true:

6 = (1/2)(-1) + 13/2

6 = -1/2 + 13/2

6 = 12/2

6 = 6

To know more about equation of a line click on below link:

https://brainly.com/question/21511618#

#SPJ11

a. False
b. True
c. False
d. False

In order to answer this question, it is important to understand the definitions of each of the terms:
- True or False: this is a type of question that requires the student to choose between two possible answers, True or False.
- Normal Distribution: this is a type of data distribution in which the data is symmetrically distributed around the mean, and the probability of occurrence is equal for all values.
- Standard Deviation: this is a measure of how spread out a set of data is from the mean. It is calculated by taking the square root of the variance of the data set.
- Median: this is the middle value in a data set when the values are arranged in ascending or descending order.
- Quartile: this is a type of quartile division in which a data set is divided into four equal parts, each containing 25% of the data.
- Mode: this is the most frequently occurring value in a data set.
- Population Standard Deviation: this is a measure of the spread of the population, and it is calculated by taking the square root of the variance of the population.

Therefore, the correct answer to the given question is:
a. False
b. True
c. False
d. False

Learn more about variance

brainly.com/question/14116780

#SPJ11

The probabilities, using the binomial distribution, are given as follows:

a. P(X = 2) = 0.2109.

b. P(X = 3) = 0.0469.

c. P(X ≥ 2) = 0.2617.

d. P(X < 3) = 0.9492.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given by the equation presented as follows:

The parameters, and their meaning are listed as follows:

The parameter values for this problem are given as follows:

n = 4, p = 0.25.

Hence the relevant probabilities are given as follows:

Then:

P(x ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2109 + 0.0469 + 0.0039 = 0.2617.

P(x < 3) = 1 - (P(X = 3) + P(X = 4)) = 1 - (0.0469 + 0.0039) = 0.9492.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

The statements which can be assumed from the diagram are:

Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross.

Parallel curves are curves that do not touch each other or intersect and preserve a predetermined minimum distance

In simple geometry, two geometric objects are perpendicular if the intersection at the point of junction known as a foot results in right angles.

From the given image, it can be seen that

Read more about parallel lines here:

https://brainly.com/question/16742265

#SPJ1

The answer of another zero - polynomial function with real coefficient at 1+2i is 1-2i

The other zero of the polynomial function  with real coefficients and a zero at 1+2i is 1-2i.

This is because if a polynomial function with real coefficients has a complex zero,

then the conjugate of that zero is also a zero of the function. The conjugate of a complex number is obtained by changing the sign of the imaginary part.

Therefore, the conjugate of 1+2i is 1-2i. So, if 1+2i is a zero of the polynomial function, then 1-2i is also a zero of the function.

In summary, the other zero of the polynomial function with real coefficients and a zero at 1+2i is 1-2i.

To know more about polynomial function refer here:

https://brainly.com/question/12976257#

#SPJ11

Answer:

2400

Step-by-step explanation:

144 are seated

94% yet to arrive

6% = 144

Easy method Find the value of 1%

144/6 will be 1%

If 1% =24 then 100% will be 24x 100

Total tickets sold will be 2400

Check: 6% of 2400 is 144

As a result, the equation system has the following solution: x = -24/5, y = -9/5.

A mathematical assertion known as an equation is composed of a pair of expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of a quantity x is 7.

One of the best methods to solve the given system of equations is the elimination method.

To apply the elimination method, we need to multiply one or both equations by a suitable constant so that when we add or subtract the two equations, one of the variables is eliminated. In this case, if we multiply the first equation by 3, we get:

9x + 21y = -57

Now we can add this equation to the second equation to eliminate the x variable:

9x + 21y = -57

-3x + 4y = 12

25y = -45

Dividing both sides by 25, we get:

y = -45/25 = -9/5

Now we can substitute this value of y into one of the original equations to solve for x. Let's use the second equation:

-3x + 4y = 12

-3x + 4(-9/5) = 12

-3x - 36/5 = 12

-3x = 12 + 36/5

-3x = 72/5

x = -24/5

As a result, the following is the system of equations' solution:

x = -24/5, y = -9/5

So the best method to solve this system of equations is the elimination method.

To know more about Equation visit:

https://brainly.com/question/22688504

#SPJ9

To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.

The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:

1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)

Therefore, d/dx (csc(x)) = −csc(x)cot(x).

For more references on the principle of differentiation, click;

brainly.com/question/28492421

#SPJ11

The exact length of segment AB is equal to: D. √13 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - 2)² + (5 - 2)²]

Distance = √[(2)² + (3)²]

Distance = √(4 + 9)

Distance = √13 units.

Read more on distance here: brainly.com/question/12470464

#SPJ1

Answer:

3

Step-by-step explanation:

by the help of Prashant chettri

Answer:

1. Transitive

2. Reflexive

3. Symmetric

4. Reflexive

5. Symmetric

6. Transitive

Answer:

C, E

Step-by-step explanation:

Answer choice A implies that [tex]42 +22 \geq 50 + 27[/tex], which is false

Answer choice B implies that 50 is half of the population, however the population is 200, so it is false

Answer choice C implies that [tex]50 + 27\geq[/tex] all other combinations, which is true.

Answer choice D implies that [tex]33 + 22\leq 50[/tex], which is false

Answer choice E implies that [tex]42 \leq 22+22[/tex], which is true

So, C & E are correct

The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.

Let D = (x, y)

Now, We know that;

The midpoint of AC = Mid-point of BD

(-2 + 5)/2 = (x + 3)/2

3 = x + 3

x = 0

(- 3+3)/2 = (y + 2)/2

y = - 2

Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

Learn more about the parallelogram here:

brainly.com/question/1563728

#SPJ9

The equivalent percent of 1/5 is 20%.  

To find this answer, we can convert the fraction to a decimal and then multiply by 100 to find the percent. Here are the steps:

1. Convert the fraction to a decimal: 1/5 = 0.2
2. Multiply the decimal by 100 to find the percent: 0.2 * 100 = 20%

Therefore, 1/5 is equivalent to 20%.

In terms of the shaded grid, if we were to shade 1 out of 5 squares, we would be shading 20% of the grid.

To know more about grid refer to-

brainly.com/question/28586483#
#SPJ11

Answer:₹14.40

Step-by-step explanation:

36x2=72

24x2=48

72+48=120x12=1440/100 =14.40

x² - 7y - 4x²y + 8xy² is standard form of equation.

What are equations, and what different kinds are there?

Equations can be divided into two categories: identities and conditional equations. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.

                     When two expressions are joined together by the equals sign ("="), the result is an equation. A mathematical statement that demonstrates the equality of two mathematical expressions is the definition of an equation.

  8xy²+1x²-4x²y-7y

standard form = 8xy² + 1x² - 4x²y - 7y

                       =  x² - 7y - 4x²y + 8xy²

Learn more about equation

brainly.com/question/29657992

#SPJ1

The function that generates the sequence 1, 2, 4, 8, ... is:

Of(x) = 2^(x-1)

We can check this by plugging in the first few values of x:

Of(1) = 2^(1-1) = 1

Of(2) = 2^(2-1) = 2

Of(3) = 2^(3-1) = 4

Of(4) = 2^(4-1) = 8

Therefore, the answer is option B.

Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.

Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.

The arithmetic operations were used to arrive at the answer.

The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.

So, the total pounds of fruit bought = 0.5 + 3 = 3.5

Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits  = (x + y)

Hence, the required solution has been obtained.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ1

Answer: Your answer will be [tex]x=7[/tex]

If it's okay, I would like someone to talk to. My email address is jeremiah.mccrocklin06 at symbol g mail . com

Answer:

y= -1/4x+b

Step-by-step explanation:

see image

The expressions that are equivalent to 2x - 3y = 12 are B and D.

We can modify the equation algebraically and simplify 2x - 3y = 12 to find the expressions that are equal to that number:

2x - 3y = 12

2x - 12 = 3y (subtract 12 from both sides) (subtract 12 from both sides)

(2/3)x - 4 = y (divide both sides by 3) (divide both sides by 3)

As a result, the equation can also be written as y = (2/3)x – 4.

We can now determine which expressions have the same meaning as this form:

A. y = 4 - (2/3)x

This expression is simplified to give y = (-2/3)x + 4. This isn't the same as y = (2/3)x – 4.

B. y = (2/3)x - 4

This formula already equals y = (2/3)x - 4 in terms of value.

C. 2x - 3y = -12

2x - 3y + 12 = 0 is the result of adding 12 to both sides of the equation. y = (2/3)x - 4 is not the same form as this.

D. y = (3/2)x - 6

This expression can be simplified to y = (2/3)x - 4 by doing so. The formula for this is y = (2/3)x – 4.

Hence, the formulas B and D are the same as 2x - 3y = 12.

To know more about equivalent expressions visit:

https://brainly.com/question/28170201

#SPJ1

The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).

Given the solutions;

To have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.

Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):

Hence;

(x + 3)(2x - 5)(x + 5i)(x - 5i)

Multiplying out these factors gives:

(x + 3)(2x - 5)(x + 5i)(x - 5i)

(x + 3)(2x - 5)(x² + 25)

= (2x² + x - 15)(x² + 25)

= 2x⁴ + x³ - 15x² + 50x² + 25x - 375

= 2x⁴ + x³ + 35x² + 25x - 375

So the polynomial in factored form is:

= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)

= 2(x + 3)(2x - 5)(x² + 25)

Learn more about polynomials here: https://brainly.com/question/11536910

#SPJ1