The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².
What is the area of the triangle ?The area of triangle can be determined using the equation;
Area = 1/2 × base × height.
The angle described forms a right-triangle.
Height of the triangle = XZ = 15cmBase of the triangle = XY = 12cmAngle X = 90°Area A = ?Area = 1/2 × base × height
Area = 1/2 × 12cm × 15cm
Area = 6cm × 15cm
Area = 90 cm²
Therefore, the area of the triangle is 90 cm².
Learn more about area of triangles here: brainly.com/question/19305981
#SPJ1
solve the problem and then click on the correct answer choice. jane must select 3 different items for each dinner she will serve. the items are to be chosen from among 5 different vegetarian and 4 different meat selections. if at least one of the selections must be vegetarian, how many different dinners can jane create?
Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.
For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]
A combination is a way of selecting items from a collection where the order of selection does not matter.
We will have to apply the formula separately for vegetarian and meat items.
Combinations available
A. 1 vegetarian item and 2 meat items
[tex]^{5} C_{1} and ^{4} C_{2}[/tex] (In combination "and" means to multiply)
= [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]
= [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]
= [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]
= 5.3.2
= 5.6
= 30
B. 2 vegetarian items and 1 meat item
[tex]^{5} C_{2} and ^{4} C_{1}[/tex]
= [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]
= [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]
= [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]
= 5.2.4
= 10.4
= 40
C. 3 vegetarian items and no meat item
= [tex]^{5} C_{3} and ^{4} C_{0}[/tex]
= [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]
= [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]
= 5.2
= 10
Now, we will add all the different combination
Total combinations = 30+40+10
= 80 different type of dinners
To know more about combination
https://brainly.com/question/13387529
#SPJ4
Which ordered pair is a solution of the inequality y≤1/3x−6
The ordered pair of the inequality will be (9,-3).
What is inequality?The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
Given that inequality is given as y ≤ 1/3x−6.
The ordered pair can be calculated as:-
y ≤ 1/3x−6
Substitute the value of x equal to 9 and get the value of y,
y ≤ 1/3(9) - 6
y ≤ 3 - 6
y ≤ -3
Hence, the ordered pair will be (9,-3).
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ9
A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 19 meters above the ground?
Rounded to the nearest minute, the answer is 12 minutes.
What do you mean by equation?The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.
The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.
To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:
h(t) = 10 sin(2πt/10) + 11
To find out when h(t) is greater than 19, we solve the inequality:
10 sin(2πt/10) + 11 > 19
Subtracting 11 from both sides, we get:
10 sin(2πt/10) > 8
Dividing by 10, we get:
sin(2πt/10) > 0.8
The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:
sin(2πt/10) = 0.8
sin(2πt/10) = -0.8
Using a calculator, we find that these equations have solutions at:
t = 1.167, 8.833, 3.5, 6.5
These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.
Therefore, the total time spent higher than 19 meters is:
(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes
Rounded to the nearest minute, the answer is 12 minutes.
To know more about time visit:
https://brainly.com/question/28050940
#SPJ1
Heeeeeloepepepelelelelelelelelelloeoepeoepwp
Answer:
C) E = 118°; T = 118°
-----------------------------------
The given figure is a kite since it has two pairs of congruent sides as marked.
Its one pair of opposite angles are congruent. That is:
∠E ≅ ∠TSum of all interior angles of a quadrilateral is 360°:
m∠W + m∠E + m∠S + m∠T = 36029 + x + 95 + x = 3602x + 124 = 3602x = 360 - 1242x = 236x = 118Both the missing angles are 118°.
use the rule to complete the table below Multiply by 2 and then add 3
The values in the table are 7, 11, 15, and 19.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We are assuming the table to be:
x value
2 2x2 + 3 = 7
4 4x2 + 3 = 11
6 6x2 + 3 = 15
8 8x2 + 3 = 19
Thus,
The values in the table are 7, 11, 15, and 19.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ9
The measure of an angle is 84°. What is the measure of its complementary angle?
Answer:
6°
Step-by-step explanation:
Two angles are called complementary if the sum of their measures equals to 90°:
The complementary angle of 84° = 90° - 84°
= 6°
Answer: 6
Step-by-step explanation:
The complementary angle means the sum of two angles equal to 90. Let x be the other angle.
x + 84 = 90
x = 6
Explain why the comparison is either reasonable are unreasonable
Answer:
Reasonable
Step-by-step explanation:
The comparison 3.84 > 3.8 is reasonable.
In this comparison, 3.84 is a larger number than 3.8, so it makes sense to say that 3.84 is greater than 3.8. When comparing decimal numbers, we can simply compare the values to the right of the decimal point. In this case, both 3.84 and 3.8 have two digits to the right of the decimal point, so we can compare those digits directly. Since 4 is greater than 8, it follows that 3.84 is greater than 3.8.
The comparison is reasonable because it is based on a correct understanding of the relative sizes of the numbers involved.
Find the product of 3√2 and 4√/18 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.
Result:
√
The result i
because it
integers and its decimal expansion
be written as the ratio of two
At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys
After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.
We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets
4n + b = 20 (Lin spends $20 on necklaces and bracelets)
where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:
n + 1b = 5
4n + 1b = 20
We can use the first equation to solve for n in terms of b: n = 5 - b
Substitute this expression for n into the second equation: 4(5 - b) + b = 20
Simplifying this equation, we get: 20 - 4b + b = 20
Solving for b, we get: b = 4
Substituting this value of b back into n = 5 - b, we get: n = 1
Therefore, Lin bought 1 necklace and 4 bracelets
To learn more about equations click here
brainly.com/question/22277991
#SPJ4
Complete Question
At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.
Mona was comparing two linear functions. Function 1 has the equation y= −2x −4y The graph below shows function 2.
The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.
What is a linear equation?The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
Function 1 is given as,
y = - 2x - 4
The slope is -2 and the y-intercept is -4.
From the graph, the equation of function 2 is given as,
x / 2 + y / 4 = 1
2x + y = 4
y = - 2x + 4
The slope is -2 and the y-intercept is 4.
The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ9
The missing graph is attached below.
Write an equivalent expression by combining like terms. 8b - 4b b =5
The equivalent expression for 8b-4b is 4b.
What are like terms?In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.
Given 8b-4b. b=5
We have to combine the like terms to get an equivalent expressions.
Like terms containing variables with same power.
When combining like terms, we have to add or subtract their coefficients.
Coefficients are the numbers which are placed with variable.
Then, 8b-4b=4b.
When b=5⇒4*5=20
Hence, the equivalent expression for 8b-4b is 4b.
Complete question:
Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.
Learn more about like terms here:
https://brainly.com/question/29085383
#SPJ9
What is the area of KELP, h = 52.6, b1 = 47.8, 62 = 39.1 *
A diagram with Trapezoid KELP and Circle C is shown. Given the dimensions, find the
area of each figure and complete the table. Round to the nearest hundredth if
necessary.
O
O
156.61
12443.11
476.26
14.62
25.15
O 13565.51
161.88
36.89
419.78
2285.47
The area of the trapezoid is A = 2285.47 units²
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the area of the trapezoid be represented as A
Now , the value of A is
Let the height of the trapezium be h = 52.6
Let the length of the shorter base a = 39.1
Let the length of the longer base b = 47.8
Now , Area of Trapezoid = ( ( a + b ) h ) / 2
On simplifying , we get
Area of trapezoid A = ( ( 47.8 + 39.1 ) 52.6 ) / 2
Area of trapezoid A = ( 86.9 x 52.6 ) / 2
Area of trapezoid A = 4,570.94 / 2
Area of trapezoid A = 2285.47 units²
Hence , the area of the trapezoid is 2285.47 units²
To learn more about trapezoid click :
https://brainly.com/question/12221769
#SPJ1
Let a function f A B be defined by f(x) 11 B-1-2, 1, 0,2- 4¹5) 0. can you make it one to one and onto both? x-1 F x*-2 with A = {-1, 0, 1, 2, 3, 4) and x+2 find the range off. Is the function one to one and onto both? If not, how a whother each of the functions below is one to one, onto both?
Answer:
The function f: A -> B is defined by:
f(x) = { 11, if x = -1 or x = 2,
-1, if x = 0,
-2, if x = 1,
0, if x = 3 or x = 4 }
The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.
To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.
To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.
Therefore, the function f is one-to-one and onto both.
The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.
a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%
Complete the table using the given function Then plot the dots on the
graph Use the line tool to draw a line connecting the dots for each
line
Point of Solution:ixy)
Y = 3x
y
x
-1
03
1
Y = -2x + 5
X
y
-1
0
1
7
3456
The complete tables for the given equations is:-
For y = 3x
X Y
1 3
2 6
3 9
For y = -2x + 5
X Y
1 3
2 1
3 -1
What is an equation?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The given two equations are;-
y = 3x
y = -2x +5
The different points passing through the line y =3x are:-
X Y
1 3
2 6
3 9
The different points passing through the line y =-2x + 5 are:-
X Y
1 3
2 1
3 -1
The graph of the points and the line as is attached with the answer below.
To know more about an equation follow
https://brainly.com/question/25798491
#SPJ9
f(x) = 3x + 5
g(x) = 4x² - 2
h(x)=x²-3x+1
Find f(x) - g(x) — h(x).
The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x² - 3x + 1
Now,
f(x) - g(x) - h(x)
= 3x + 5 - (4x² - 2) - (x² - 3x + 1)
= 3x + 5 - 4x² + 2 - x² + 3x - 1
= 6x - 5x² + 6
Thus,
6x - 5x² + 6 is the expression.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ9
The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
plsss help
By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.
Which bird is closer to the ground after 8 minutes?We know that the height of the hawk is modeled by:
y=−20x+350
And the height of the eagle is modeled by:
y=−10x+400
Now we need to evaluate both equations in x = 8.
hawk:
y = -20*8 + 350 = 190
For the Eagle:
y = -10*8 + 400 = 320
We can see that the hawk is closer to the ground.
Learn more about evaluating equations at:
https://brainly.com/question/4344214
#SPJ1
7. A polygon has vertices at F(-5, 2), G(-3, 2), H(-3, 4), J(1, 4), K(1, 1), L(4, 1), M(4, -2), N(6, -2), P(6, -3), and Q(-5, -3). Graph the figure on the coordinate plane. Then find the area and perimeter of the figure.
The area of the figure is 52 square units
The perimeter of the figure is 36 units
The graph is attached
How to the perimeterThe perimeter of the figure is found by summing the length of the sides
F(-5, 2) - G(-3, 2) = 2 units
G(-3, 2) - H(-3, 4) = 2 units
H(-3, 4) - J(1, 4) = 4 units
J(1, 4) - K(1, 1) = 2 units
K(1, 1) - L(4, 1) = 3 units
L(4, 1) - M(4, -2) = 3 units
M(4, -2) - N(6, -2) = 2 units
N(6, -2) - P(6, -3) = 1 units
P(6, -3) - Q(-5, -3) = 11 units
Q(-5, -3) - F(-5, 2) = 5 units
The perimeter = 2 + 2 + 4 + 2 + 3 + 3 + 2 + 1 + 11 + 5 = 36 units
Learn more about perimeter of irregular figure at:
https://brainly.com/question/29301703
#SPJ1
Which expression would NOT be equivalent to 4(10+5)?
Answer:
Not Possible
Step-by-step explanation:
No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.
Here are some that are equivalent:
20(2+1)
2(20+10)
40+20
60
Mr. Herman compare his students score for two class periods for a social studies final
Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.
How to identify the median?The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.
The median for period 1: 84
The median for period 2: 82
Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.
Learn more about the median in https://brainly.com/question/28060453
#SPJ1
I WILL GIVE BRAINLY
Part A: Given the function g(x) = |x − 7|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answer:
Part A:
The graph of g(x) = |x - 7| is a V-shaped graph that opens upward, with a vertex at x = 7 and y = 0. The graph of the function is symmetrical about the vertical line x = 7. The domain of the function is all real numbers, and the range is all non-negative real numbers, including zero.
Part B:
The transformation from f(x) to h(x) is a vertical shift upward by 2 units. The vertex of the parent function f(x) = |x| is at (0, 0), and the vertex of the transformed function h(x) = |x| + 2 is at (0, 2). The range of the parent function f(x) is all non-negative real numbers, including zero. The range of the transformed function h(x) is all non-negative real numbers greater than or equal to 2. The transformation shifts the entire graph of the parent function upward, increasing the y-values of all points on the graph by 2 units.
Which value of x makes the equation
5(x - 2) - 4 = 6 true?
A. 2
B. 3
C. 4
D. 5
Answer:
Step-by-step explanation:
5x - 10 - 4 = 6
5x - 14 = 6
5x = 20
x = 4
Option C is the solution
a certain bacteria population obeys the population growth law. it is observed that the doubling time for the population is 4 hours. the length of time it will take for the population to increase to 3-times its original population is
According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:
[tex]P = P_0 * 2^{t/t_d)}[/tex]
where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.
To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:
[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]
Dividing both sides by [tex]P_0[/tex] gives:
[tex]3 = 2^{t/t_d}[/tex]
Taking the logarithm of both sides (using any base) gives:
[tex]log(3) = log(2^{t/t_d} )[/tex]
Using the logarithmic identity
[tex]log(a^b) = b*log(a),[/tex]
we can rewrite this as:
[tex]log(3) = (t/t_d)*log(2)[/tex]
Solving for t, we get:
[tex]t = t_d * (log(3)/log(2))[/tex]
Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:
[tex]t = 6 * (log(3)/log(2)) hours[/tex]
Simplifying using the change of base formula
[tex](log(a)/log(b) = log_b(a))[/tex], we get:
[tex]t = 6 * log_2(3)[/tex] hours
Therefore, the answer is (f) None of the above.
For more question on exponentially click on
https://brainly.com/question/29166359
#SPJ4
Correct question should be
Click on image for question
7. Mark starts out the week with $8. Every day he gives sister $2. Write an equation and
graph the situation. What is the meaning of the values when x is greater than 4?
Answer:
y = -2x + 8
When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.
Step-by-step explanation:
[tex]-11+6x+25-3x[/tex]
Answer:
If you want it simplified, it is 3x + 14!
Hope it helps!
Triangle QRS triangle TUV.
Q
117⁰
V
30°
R
S
What is the measure of LQ and the measure of LS?
U
T
Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.
In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.
In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.
The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
The measure of LQ is equal to the sum of the measures of angles R and T:
LQ = 63 + 150 = 213 degrees
The measure of LS is equal to the sum of the measures of angles Q and U:
LS = 117 + 30 = 147 degrees
So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.
Step-by-step explanation:
watershed is a media services company that provides online streaming movie and television content. as a result of the competitive market of streaming service providers, watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. for a test set of customers, the file watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. in an effort to prevent customer churn, watershed wishes to offer promotions to customers who may unsubscribe. it costs watershed $15 to offer a promotion to a customer. if offered a promotion, it successfully persuades a customer to remain a watershed customer with probability 0.7, and the retaining the customer is worth $60 to watershed. click on the datafile logo to reference the data. assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers watershed should offer the promotion to maximize the profit of the intervention campaign. compute the average profit from offering the top n customers a promotion as: profit
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
Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
5. What is the experimental probability of selecting the name Alex? * O Option 1 O Option 3 406 = 27/35 10 טחת O Option 2 Option 4 23 25 10 points
The experimental probability of selecting the name Alex would be 40 % or 2 / 5
How to find experimental probability ?The experimental probability of selecting the name Alex can be found by the formula :
= Number of times Alex is drawn / Number of total draws x 100 %
Number of times Alex is drawn = 4 times
Number of total draws = 10 draws
The experimental probability of selecting Alex would therefore be :
= 4 / 10 x 100 %
= 0. 4 x 100 %
= 40 % or 2 / 5
Find out more on experimental probability at https://brainly.com/question/14395891
#SPJ1
what is the measure of the angle of one slice of pizza if the length of the crust (arc) is 4.9 in and the length of one side of the slice is 6.2 in?
The correct answer is 45.28°
In order to get that answer, you must set up the arc length formula.
l = m/360 • 2πr
4.9 = m/360 • 12.4π
We are trying to find the angle measure; therefore, we are going to divide.
4.9 = 0.10821m
Flip the equation
0.10821m = 4.9
0.10821m/0.10821 = 4.9/0.10821
m = 45.28°
We can use the formula angle = (arc length / radius) or an online calculator to find the angle of the slice, which is approximately 47 degrees in this case.
To find the measure of the angle of one slice of pizza, we can use the formula:
angle = (arc length / radius)
However, we are not given the radius of the pizza, so we first need to find it. One way to do this is to use the length of one side of the slice and the central angle of the slice. We know that the central angle of the slice is twice the angle at the center of the pizza that the slice occupies, so we can find this angle by:
angle at center = (angle of slice) / 2
We can then use the law of cosines to find the length of the radius:
radius² = (side length / 2)^2 + (side length / 2)² - 2 * (side length / 2) * (side length / 2) * cos(angle at center)
Once we have the radius, we can use the formula above to find the angle of the slice. However, since this calculation can be quite involved, it may be simpler to use an online pizza slice angle calculator. Using this tool with the given values, we find that the angle of one slice of pizza is approximately 47 degrees.
Learn more about mathematics here: brainly.com/question/24600056
#SPJ4
