Answer:
If the relationship is proportional, we can use the proportionality constant, k, to relate the cost and number of climbs. The equation would be:
t = kc
We can find the value of k by using the given information that 5 climbs cost $52.50:
52.50 = k(5)
Solving for k, we get:
k = 10.50
Therefore, the equation that represents the total cost, t, of c climbs is:
t = 10.50c
pls answer this :))
due in 10 mins
Step-by-step explanation:
a=55 because
75+50+a=180 (Sum of angle in a stratight line)
or, 125+a=180
or, a=180-125
a=55
b=75 because they are alternate angles
c=50 because they are alternate angles
d=50 Because d=c(vertically opposite angle) and c=50
Please help ASAP!!!!!!!! :)
Answer:
12(a) 4(x+19)=752 (b) 169
Step-by-step explanation:
12(a) 4(x+19)=752
(b) 4(x+19)=752
4x+76=752
4x=676
x=169
a. The equation representing the situation is 4(x+19)=752
b. The price of one ticket is $169
How to determine the valueIt is important to note that algebraic expressions are defined as expressions consisting of terms, coefficients, constants, factors and variables
They are also made up of mathematical operations are;
SubtractionAdditionMultiplicationBracketParenthesesDivisionFrom the information given, we have that;
Let x be the price ticket
This is then represented as;
4(x+19)=752
expand
4x + 76 = 752
collect the like terms
4x = 676
Divide by the coefficient
x = $169
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In a raffle, there are winners drawn of the first, second, and third prizes. Three sisters are participating along with 9 other people. What is the exact probability that the first sister wins the first prize, the second sister wins the second prize, and the third sister wins the third prize?
The probability that the first sister wins the first prize, the second sister wins the second prize, and the third sister wins the third prize is given as follows:
1/1320.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The probabilities for each sister are given as follows:
First sister wins the first prize: 1/12 -> there are 12 people.Second sister wins the second prize: 1/11 -> there are 11 people.Third sister wins the third prize: 1/10 -> there are 10 people.Hence the probability is given as follows:
1/12 x 1/11 x 1/10 = 1/(12 x 11 x 10) = 1/1320.
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Here is another triangle similar to DEF.
•What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”?
•What are cos(D”), sin(D”), and tan(D”)
(Triangle DEF has coordinates D(0,0) E(12,0) F(12,5)
And pictured is triangle D”E”F”
The scale factor from triangle DEF to triangle D”E”F” is the ratio of the corresponding sides in the two triangles.
The coordinates of F” can be calculated using the scale factor.
The value of cos(D”) would be equal to 0.707. Similarly, the value of sin(D”) would be 0.707 and the value of tan(D”) would be 1.
What is a scale factor?Scale factor is a number which is used to describe the relationship between two objects or two measurements. It is used to compare two objects of different sizes in order to calculate the ratio of their size. It is also used to express a proportional relationship between two different measurements, such as their lengths, widths, heights or angles.
The corresponding sides are DE and D”E”, and EF and E”F”. We can calculate the ratio of the two sides by dividing the lengths of the two corresponding sides. For example, the ratio of DE to D”E” would be 12/16. We can do this for all three corresponding sides, and then take the average of the three ratios to get the scale factor from triangle DEF to triangle D”E”F”.
Since we know that the coordinates of F are (12,5), we can multiply the x-coordinate (12) by the scale factor and the y-coordinate (5) by the scale factor to get the coordinates of F”.
The angle D” can be used to calculate the values of cos(D”), sin(D”), and tan(D”). Since we know the angle D”, we can use the trigonometric functions to calculate the values of the trigonometric functions for that angle. For example, if the angle D” is 45 degrees, then the value of cos(D”) would be equal to 0.707. Similarly, the value of sin(D”) would be 0.707 and the value of tan(D”) would be 1.
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how do i turn 7/4 into a mixer number
Answer:
1 3/4
Step-by-step explanation:
To turn 7/4 into a mixed number, you have to look at the numerator and the denominator. 4 can go into 7 once (with 3 left over), so it would be 1 and 3/4
Focus group probabilities. A focus group of 15 consumers has been selected to view a new TV commercial. Even though all of the participants will provide their opinion, two members of the focus group will be randomly selected and asked to answer even more detailed questions about the commercial. The group contains seven men and eight women. What is the probability that the two chosen to answer questions will both be women?
Therefore , the solution of the given problem of probability comes out to be roughly 0.2667, or 26.67%.
What is probability exactly?The primary goal of the schemes within a technique known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any figure between 0 and 1, with 0 typically signifying probability and 1 typically signifying a degree of certainty, can represent chance. A probability diagram shows the chance that a specific event will occur.
Here,
We can use combinations and probability to fix this issue.
First, we can determine how many different methods there are to choose 2 individuals from a group of 15:
=> C(15,2) = 105 is the total number of options.
Next, we can determine how many options there are to choose two women from a group of eight women:
There are 28 different methods to choose 2 women, or
=> C(8,2).
The likelihood that the two selected to respond to queries will both be women is as follows:
P(both women) equals the variety of methods to choose two women (total number of ways)
=> P(all females) = 28/105
=> P(all females) = 0.2667
The likelihood that both of the two people selected to respond to questions are women is therefore roughly 0.2667, or 26.67%.
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Find the exact value of s in the given interval that has the given circular function value Do not use a calculator.
[????, 3????/2] tan s = √3
To find the exact value of s in the given interval that has the given circular function value, we can use the properties of the tangent function and the unit circle.
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. In the unit circle, the opposite side is the y-coordinate and the adjacent side is the x-coordinate. Therefore, we can write:
tan s = y/x
Given that tan s = √3, we can write:
√3 = y/x
Cross-multiplying and simplifying, we get:
y = √3x
Now, we can use the Pythagorean theorem to find the value of x:
x^2 + y^2 = 1
Substituting y = √3x, we get:
x^2 + ( √3x)^2 = 1
Simplifying, we get:
4x^2 = 1
Dividing by 4, we get:
x^2 = 1/4
Taking the square root of both sides, we get:
x = ±1/2
Since we are looking for the value of s in the interval [????, 3????/2], we need to find the corresponding value of y for x = 1/2. Substituting x = 1/2 into y = √3x, we get:
y = √3(1/2)
Simplifying, we get:
y = √3/2
Therefore, the point on the unit circle that corresponds to the given value of the tangent function is (1/2, √3/2).
Now, we can use the properties of the unit circle to find the value of s. The angle s is the angle between the positive x-axis and the line connecting the origin and the point (1/2, √3/2). Since the point (1/2, √3/2) is in the first quadrant and the angle is measured counterclockwise, the value of s is:
s = π/3
Therefore, the exact value of s in the given interval that has the given circular function value is π/3.
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Which description matches the translation of the equation: y = |x - 5| + 2
Moves 5 units left and 2 units up
Moves 2 units right and 5 units down
Moves 5 units right and 2 units up
Moves 2 units left and 5 units right
Answer:
The description that matches the translation of the equation y = |x - 5| + 2 is "Moves 5 units to the right and 2 units up".
This is because the equation involves the absolute value of the quantity (x - 5), which means that the expression inside the absolute value bars will always be positive or zero. This means that the graph of the equation will be a "V" shape, centered at x = 5, and opening upwards. The "+2" outside the absolute value bars indicates that the entire graph will be shifted upward by 2 units.
Therefore, the graph of the equation y = |x - 5| + 2 will be obtained by taking the graph of y = |x|, shifting it 5 units to the right to obtain y = |x - 5|, and then shifting it 2 units up to obtain y = |x - 5| + 2.
Step-by-step explanation:
pa brainliest pls
A teacher buys a binder for $1. 75 and a monthly planner for $9. 50 for each student in their classroom. The teacher spends a total of $393. 75 for all of the binders and monthly planners. How many students are in the teacher's class?
write a multiplication expression to represent this problem 9 1/3
The multiplication expression will be (9*3+1)/3.
What exactly are expressions?
In mathematics, an expression is a combination of one or more numbers, variables, and/or mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and logarithms) that can be evaluated to produce a single numerical or algebraic value.
Expressions can be very simple, such as a single number or variable, or they can be more complex, involving multiple variables and operations. They can also include mathematical functions and constants, such as pi or the square root of a number.
Here are some examples of expressions in mathematics:
Now,
We have expression 9 1/3
and to change it to simple fraction
we do this 9*3+1/3
=27+1/3
=28/3
Hence,
The multiplication expression will be (9*3+1)/3.
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Solve the following system of equations. Write your answer in
the form of an ordered pair (x,y).
{10x+5y20x−10y==−60−80
Enter your answer as an ordered pair (x,y).
The answer is an ordered pair (x,y)=(-7,2).
To solve the system of equations, we can use the elimination method to eliminate one of the variables and solve for the other.
First, let's multiply the first equation by 2 so that we can eliminate the y variable:
{20x+10y=−120
Next, let's subtract the second equation from the first:
{20x+10y−(20x−10y)==−120−(−80)
Simplifying the equation gives us:
{20y=40
Dividing both sides by 20 gives us:
{y=2
Now, let's plug this value of y back into the first equation to solve for x:
{10x+5(2)==−60
Simplifying the equation gives us:
{10x+10=−60
Subtracting 10 from both sides gives us:
{10x=−70
Dividing both sides by 10 gives us:
{x=−7
So, the solution to the system of equations is the ordered pair (x,y)=(−7,2).
Therefore, the answer is an ordered pair (x,y)=(-7,2).
I hope this helps! Let me know if you have any further questions.
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Which of the following is the quotient of x^2 + 4 x – 32 when divided by x + 8?
To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:
x - 4
____________
To find the quotient of x^2 + 4x - 32 when divided by x + 8, we can use polynomial long division or synthetic division. Here's how to do it using polynomial long division:
markdown
Copy code
x - 4
____________
x + 8 | x^2 + 4x - 32
- (x^2 + 8x)
____________
-4x - 32
- ( -4x - 32 )
____________
0
Therefore, the quotient is x - 4.
brainly wouldn't let me type the question for some reason, so i had to attach a pic
The correct answer is for the equation is C, "minimizes the sum of the squared distances from the actual y-value to the predicted y-value," as explained below.
What is a least-squares regression line?The least-squares regression line is a line that best fits the given data by minimizing the sum of the squared distances between the predicted y-value (ŷ) and the actual y-value (y) for each data point. In other words, the line is chosen so that the sum of the squares of the vertical distances between the data points and the line is as small as possible.
In this case, the equation provided represents the least-squares regression line for the given data, which suggests that for every unit increase in x, y increases by 0.5 units.
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One angle of a triangle measures 50°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
The measure of the two angles is x = 69 degrees and y = 70 degrees.
How many angles total there in a triangle?In every triangle, the total of the angles is 180 degrees. The Triangle Sum Theorem.
For triangle ABC it is given as follows:
Angle A + Angle B + Angle C = 180.
Let us suppose the measure of two angles as x and y.
According to the ratio we can write as follows:
x = 6k and y = 7k
The sum of the angles in a triangle is 180°, so we can write:
50° + 6k + 7k = 180°
13k + 50° = 180°
13k = 130°
k = 10°
Substituting the value of k in x and y we have:
x = 6k = 6(10°) = 60°
y = 7k = 7(10°) = 70°
Hence, the measure of the two angles is x = 69 degrees and y = 70 degrees.
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What is a number between 1-100
Whoever is closest gets brainliest
Answer:
56
Step-by-step explanation:
Twenty Six, perhaps?
The size of the civilian labor force (in millions) for selected years from 1950 and projected to 2050 can be modeled by y = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7, where x is the number of years after 1950. What does this model project the civilian labor force to be in 2013? In what year does the model project the civilian labor force to be 152 million?
In 2013 the model project the civilian labor force to be ___ million?
Using a graphing calculator or algebraic methods, we can find that x ≈ 71.6. Therefore, the model projects the civilian labor force to be 152 million in the year 1950 + 71.6 = 2021.6, or approximately in the year 2022.
According to the given model, the size of the civilian labor force (in millions) for selected years from 1950 and projected to 2050 can be modeled by y = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7, where x is the number of years after 1950.
To find the projected civilian labor force in 2013, we need to plug in the value of x as 2013-1950 = 63 into the given model:
y = - 0.0001 (63)^3 + 0.0058 (63)^2 + 1.43(63) + 56.7
y = - 0.0001 (250047) + 0.0058 (3969) + 90.09 + 56.7
y = - 25.0047 + 23.0002 + 90.09 + 56.7
y = 144.7855
Therefore, the model projects the civilian labor force to be approximately 144.7855 million in 2013.
To find the year when the model projects the civilian labor force to be 152 million, we need to set y = 152 and solve for x:
152 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7
0 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x - 95.3
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Can someone PLEASE help me with this three part question? It’s due today!! I need help ASAP
1. The Formula used SA = 2w (l +h) + lh
2. The box is 0.37125 inch deep.
3. The SA of box with lid is 294.7972 inch².
What is Surface Area?The area is the territory covered by a shape or figure, whereas the perimeter is the distance covered by the shape's outside boundary. The unit of area is the square unit or unit², while the unit of perimeter is the unit.
Given:
length = 13.2 inch
Height = 10.5 inch
And, Surface Area used = 295.02 inch²
Using the Formula
SA = 2lw + 2wh + lh
SA = 2w (l +h) + lh
295. 02 = 2w ( 13.2 + 10.5) + (13.2)(10.5)
147.51 = w x 24 + 138.6
8.91 = 24w
w = 0.37125 inch
SA of box with lid
= 2( lw+ wh + lh)
= 2( 13.2 x 10.5 + 10.5 x 0.37125 + 0.37125 x 13.2)
= 2(138.6 + 3.8981 + 4.9005)
= 2 x 147.3986
= 294.7972 inch²
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if you have $4 in quarter and dimes and 34 coins how many quarter and dimes are there
What is the area of this figure?
find the cosine of
I dont know what else it wants me to say because it says that its to short to ask.
well, for the cosine of G we'll need the hypotenuse GH, so let's get it, Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{GH}\\ a=\stackrel{adjacent}{\sqrt{6}}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ GH=\sqrt{ (\sqrt{6})^2 + 1^2}\implies GH=\sqrt{ 6 + 1 } \implies GH=\sqrt{ 7 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cos(G )=\cfrac{\stackrel{adjacent}{\sqrt{6}}}{\underset{hypotenuse}{\sqrt{7}}}\implies \cos(G )=\cfrac{\sqrt{6}}{\sqrt{7}}\cdot \cfrac{\sqrt{7}}{\sqrt{7}}\implies \cos(G )=\cfrac{\sqrt{42}}{7}[/tex]
50 Points!!! Use triangle PQR for questions 2-4. What are the values of the trigonometric ratios for R in this triangle?
2. What is the value for sin R? Enter your answer as a fraction.
3. What is the value for cos R? Enter your answer as a fraction.
4. What is the value for tan R? Enter your answer as a fraction
Answer:
こんにちは
Step-by-step explanation:
2. 答えは2.5
次の番号 3 の場合は 6.9 次の番号は 4 の場合は 5.6
Moving to another question will save uestion 12 Solve the system by the addition meth -2x-7y=22 7x-4y=-20
The solution to the system of equations is (5.56, -4.73).
To solve the system of equations by the addition method, we need to follow these steps:
Step 1: Multiply one or both of the equations by a constant to make the coefficients of one of the variables the same in both equations.
Step 2: Add the two equations together to eliminate one of the variables.
Step 3: Solve for the remaining variable.
Step 4: Substitute the value of the variable back into one of the original equations to find the value of the other variable.
Let's apply these steps to the given system:
-2x - 7y = 22
7x - 4y = -20
Step 1: Multiply the first equation by 7 and the second equation by -2 to make the coefficients of x the same:
-14x - 49y = 154
-14x + 8y = 40
Step 2: Add the two equations together to eliminate x:
-41y = 194
Step 3: Solve for y:
y = 194/(-41)
y = -4.73
Step 4: Substitute the value of y back into one of the original equations to find the value of x:
-2x - 7(-4.73) = 22
-2x + 33.11 = 22
-2x = -11.11
x = 5.56
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an airplane 3,000 ft above the ground begin descending at a rate of 2,000 ft per minute
The height of the plane is modeled by the linear equation:
height = 3000ft - 2000ft*t
How to get the plane height equation?If the rate at which the plane descends is constant, then the height is modeled by a linear equation.
We can write:
height = initial height - rate*time
We know that the initial height is 3000ft, and that the plane descends at ar ate of 2,000ft per minute, then we can write the linear equation:
height = 3000ft - 2000ft*t
Where t is the time in minutes.
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Complete question:
"an airplane 3,000 ft above the ground begin descending at a rate of 2,000 ft per minute, which will be the height of the plane after t minutes?"
Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet
SA = 2π(1.6)2 + 3.2π(3.8) square feet
SA = 2π(1.6)2 + 1.6π(3.8) square feet
SA = 2π(3.2)2 + 3.2π(3.8) square feet
SA = 2π(3.2)2 + 1.6π(3.8) square feet
The surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.
Option (A) is correct.
What is the surface area of the cylinder?
The surface area of a cylinder can be calculated using the following formula:
SA = 2πr² + 2πrh
where r is the radius of the circular base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi, approximately equal to 3.14159.
The surface area of a cylinder is the sum of the areas of its top and bottom circles, plus the area of its lateral surface (the curved surface that connects the two circles). The lateral surface area of a cylinder is found by multiplying the height of the cylinder by the circumference of one of its circular bases. Therefore, the correct method to calculate the surface area of the cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet is:
SA = 2π(1.6)² + 3.2π(3.8)
So, the correct answer is:
SA = 2π(1.6)² + 3.2π(3.8) square feet
Hence, the surface area of the cylinder would be SA = 2π(1.6)² + 3.2π(3.8) square feet.
Option (A) is correct.
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Ryan, a consumer electronics salesperson, earns a base salary of $ 1300 per month and a commission of 7% on the amount of sales he makes. One month Ryan received a $1622 paycheck. Find the amount of his sales for the month.
Ryan, a consumer electronics salesperson, earns a base wage of $ 1300 per month and a commission of 7% on the amount of sales he makes. One month Ryan received a $1622 paycheck, which made his sales for the month $4600.
To find the amount of Ryan's sales for the month, we can use the equation:
Total paycheck = Base salary + (Commission rate × Sales)
We can plug in the given values and solve for the amount of sales:
$1622 = $1300 + (0.07 × Sales)
$322 = 0.07 × Sales
Sales = $322 ÷ 0.07
Sales = $4600
Therefore, Ryan's sales for the month were $4600.
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Seven Subjects S1, S2, S3, ...,S7 Are To Be Scheduled In An Examination. The Following Pairs Of Subjects Have Common Students: 2 1 a. {S1, S2}, {S1, S3},{S1, S4},{Sı, S7} b. {S2, S3}, {S2, Sa}, {S2, S5}, {S2, S7}, c. {S3, S4}, {S3, S6},{S3, S7},{S4, S5}, {S4, Sc}, d. {S5,S6},{S5, St}, And {S6, S7} How Can The Examination Be Scheduled So That No Student Has Two examination at same day?
To schedule the examination so that no student has two examinations on the same day, we can use graph coloring. Graph coloring is the process of assigning colors to the vertices of a graph in such a way that no two adjacent vertices have the same color.
1. First, we can create a graph with the seven subjects as vertices and the pairs of subjects with common students as edges.
2. Next, we can assign a color to each vertex, starting with S1 and moving clockwise around the graph. We can use the smallest available color for each vertex, making sure that no two adjacent vertices have the same color.
3. Once we have assigned a color to each vertex, we can use the colors to schedule the examinations. Each color represents a different day, and all of the subjects with the same color can be scheduled on the same day.
The resulting schedule would look something like this:
Day 1: S1, S5
Day 2: S2, S4
Day 3: S3, S6
Day 4: S7
This schedule ensures that no student has two examinations on the same day, since no two adjacent vertices in the graph have the same color.
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Please help asap -
Answer choices are
75 ft
80 ft
78 ft
62 ft
78 ft is the value of x in Triangles.
What is a triangle and what are its types?
Triangles are three-sided shapes. The various triangle varieties go under various names. The size of the angles and side lengths determine what kind of triangle it is (corners).
According on how long their sides are, triangles can be classified as equilateral, isosceles, or scalene.
Sin45° = x/110
1/√2 = x/110
√2 x = 110
x = 110/√2
x = 77.78
x = 78 ft
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A pharmacy store sells hand sanitizer, which is supplied by a chemical manufacturer in
a nearby city. The lead time is 16 days. The daily demand for hand sanitizer is normally
distributed. The mean of daily demand is 20 bottles with the variance of 36 bottles2. The
pharmacy store wants to keep its stock-out probability as low as 2.5%.
Question 1 – 3
The pharmacy store is using the latest inventory tracking system, which allows it to track
inventory all the time.
Q1: Based on the given stock-out level, what is the corresponding Z-value?
Q2: What is the safety stock level? (Reminder: round UP to the next whole number)
Q3: When should the pharmacy store place orders? When the inventory level drops to
___ bottles. (Reminder: round UP to the next whole number)
Q4. The pharmacy store now wants to change the stock-out probability to 4%, when
should the pharmacy store place orders? When the inventory level drops to ___ bottles.
(Reminder: round UP to the next whole number)
1. Based on the given stock-out level, the corresponding Z-value is 1.96. 2. The safety stock level is 12. 3. The pharmacy store should place orders when the inventory level drops to 332 bottles. 4. The pharmacy store changing the stock-out probability to 4%, should place orders when the inventory level drops to 331 bottles.
1. The corresponding Z-value for a stock-out level of 2.5% is 1.96. This can be found by looking at a standard normal table or using a Z-value calculator.
2. The safety stock level can be calculated using the formula:
Safety stock = Z-value * standard deviation of lead time demand.
In this case, the standard deviation of lead time demand is the square root of the variance, or 6 bottles. So the safety stock level is:
= 1.96 * 6 = 11.76
which should be rounded up to the next whole number, or 12 bottles.
3. The pharmacy store should place orders when the inventory level drops to the reorder point, which is calculated using the formula:
Reorder point = Lead time demand + Safety stock.
In this case, the lead time demand is 16 days * 20 bottles/day = 320 bottles.
So the reorder point is 320 + 12 = 332 bottles.
Therefore, the pharmacy store should place orders when the inventory level drops to 332 bottles.
4. If the pharmacy store wants to change the stock-out probability to 4%, the corresponding Z-value is 1.75. Using the same formula as before, the safety stock level is:
= 1.75 * 6 = 10.5, which should be rounded up to the next whole number, or 11 bottles.
The reorder point is then 320 + 11 = 331 bottles. Therefore, the pharmacy store should place orders when the inventory level drops to 331 bottles.
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Modular Arithmetic: Please solve the following questions. (1) 42mod11
The answer to the question "(1) 42mod11" is 9.
The answer to the question "Modular Arithmetic: Please solve the following questions. (1) 42mod11" is:
The concept of "Modular Arithmetic" is a system of arithmetic that involves only integers. In modular arithmetic, numbers "wrap around" after they reach a certain value called the modulus.
To solve the given question, we can use the following steps:
Step 1: Find the modulus of the given number. In this case, the modulus is 11.
Step 2: Divide the given number by the modulus. In this case, 42/11 = 3 with a remainder of 9.
Step 3: The remainder is the answer to the question. So, 42mod11 = 9.
Therefore, the answer to the question "(1) 42mod11" is 9.
I hope this answer helps you! If you have any further questions, feel free to ask.
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If X ~N (0,2) Find the probability distribution function of Y
=|X| . Hence, on otherwise Find
1.E(|X| )
2. Var(|X|)
Solve it fast
The probability distribution function of Y = |X| is given by:
P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y) = P(X ≤ y) - P(X < -y)
Since X ~ N(0, 2), we can use the standard normal distribution to find the probabilities:
P(X ≤ y) = Φ(y/√2)
P(X < -y) = Φ(-y/√2)
Therefore, the probability distribution function of Y is:
P(Y ≤ y) = Φ(y/√2) - Φ(-y/√2)
To find E(|X|) and Var(|X|), we can use the properties of the absolute value function:
E(|X|) = ∫_(-∞)^(∞) |x| f(x) dx = 2 ∫_(0)^(∞) x f(x) dx
Var(|X|) = E(|X|^2) - (E(|X|))^2 = 2 ∫_(0)^(∞) x^2 f(x) dx - (2 ∫_(0)^(∞) x f(x) dx)^2
Since f(x) is the probability density function of X, we can substitute it with the standard normal distribution:
f(x) = (1/√(2π)) e^(-(x^2)/4)
Therefore, E(|X|) and Var(|X|) can be found by evaluating the integrals:
E(|X|) = 2 ∫_(0)^(∞) x (1/√(2π)) e^(-(x^2)/4) dx = √(2/π)
Var(|X|) = 2 ∫_(0)^(∞) x^2 (1/√(2π)) e^(-(x^2)/4) dx - (√(2/π))^2 = 2 - (2/π)
So the final answers are:
1. E(|X|) = √(2/π)
2. Var(|X|) = 2 - (2/π)
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