The recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.
What is a recurrence relation?
A recurrence relation is an equation that defines a sequence of values in terms of the preceding terms of the sequence. It is a mathematical tool used to define a sequence of numbers, functions, or other mathematical objects in a recursive manner.
To find a recurrence relation that counts the number of ways to climb n stairs if you can take either 1 star or 3 stairs at a time, we can use the following steps:
Identify the base cases. In this case, the base cases are the number of ways to climb 0 stairs (an = 1) and the number of ways to climb 1 stair (an = 1).
Determine the recurrence relation. For n > 1, the number of ways to climb n stairs is equal to the number of ways to climb n-1 stairs (taking 1 stair at a time) plus the number of ways to climb n-3 stairs (taking 3 stairs at a time). Therefore, the recurrence relation is:
an = an-1 + an-3
Use the base cases and the recurrence relation to determine the values of an for the desired range of n.
For example, to determine the values of an for n = 0, 1, 2, 3, 4, and 5, we can use the following table:
n | an
0 | 1
1 | 1
2 | an-1 + an-3 = 1 + 1 = 2
3 | an-1 + an-3 = 2 + 1 = 3
4 | an-1 + an-3 = 3 + 2 = 5
5 | an-1 + an-3 = 5 + 3 = 8
Hence, the recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.
To learn more about the recurrence relation, visit:
https://brainly.com/question/4082048
#SPJ4
At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was _______mg
At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.
A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.
The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:
r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr
If we integrate both sides of this equation with respect to t, we get:
A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt
This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:
A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt
The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:
A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt
The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:
A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)
Combining constants and simplifying gives:
A(t) = 25e^-0.1 t - 25e^-0.3 t
We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.
Taking the limit as t approaches 0 gives:
A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]
This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.
Learn more about limit, here https://brainly.com/question/8533149
#SPJ4
Ariel earns $8.00 per hour. Her benefits package is equal to 15% of her hourly wages.
Ariel works 40 hours each work week. How much does Ariel earn in a week WITH
benefits?
Answer:
$368 per week
Step-by-step explanation:
[tex]8 \times 40 \times 1.15 = 368[/tex]
how to solve probability of distribution
Answer:
Step-by-step explanation:
How to find the mean of the probability distribution: Steps
Step 1: Convert all the percentages to decimal probabilities. For example: ...
Step 2: Construct a probability distribution table. ...
Step 3: Multiply the values in each column. ...
Step 4: Add the results from step 3 together.
Here are the first 5 terms of a quadratic sequence.
2
10
24
44
Find an expression, in terms of n, for the nth term of this sequence.
70
The sequence is f(n)=3[tex]n^{2}[/tex]−n.
What is sequence?Sequences are ordered collections of numbers, often known as "terms," such as 2,5,8. There are some sequences that adhere to a particular pattern that allows for endless extension. For instance, 2,5,8 adheres to the "add 3" pattern, thus we may now continue the process. There are formulae for sequences that show us where to locate any given term.
We have 2 10 24 44 70 (which we refer to as the first column)
If we have 10 - 2 = 8, 24- 10 = 14, 44- 24 = 20, and 70- 44 = 26,
(this is second column)
The third column is now 14 - 8 = 6, 20 - 14 = 6, and 26 - 20 = 6.
First, create the second column sum formula.
Sum(x)
S(x)=8+6(x1)=6x+2 is the second digit of the phrase.
Next make the first column formula f(n)
f(n)= 2+[tex]sum_{n-1}[/tex]
=2+(n−1)[3(n−1)+5]
=2+(n−1)(3n−3+5)
=2+(n−1)(3n+2)
=2+3[tex]n^{2}[/tex]+2n−3n−2
=3[tex]n^{2}[/tex]−n
The sequence is f(n)=3[tex]n^{2}[/tex]−n.
To know more about sequence click the link:
brainly.com/question/21961097
#SPJ1
4 kilometer from house to the nearest mailbox. how far is it in meter?
Answer:
4 kilometers is equal to 4000 meters.
Step-by-step explanation:
1 kilometer is equal to 1000 meters, so 4 kilometers is equal to 4 x 1000 = 4000 meters. This is because the prefix "kilo" means 1000, so 1 kilometer is equivalent to 1000 meters.
differentiate of the following w.r.t.x
i mark u branlist if u give me right answer
The differentiation of y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x is cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
How to differentiate y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x?In mathematics, differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how the function changes as its input (or independent variable) change
Given: y = logx - cosecx + 5ˣ + 3/(x^(3/2))
Thus, the derivative will be:
d/dx [logx - cosecx + 5ˣ + 3/(x^(3/2))]
= d/dx [logx] - d/dx [logx] + d/dx [5ˣ] + 3d/dx[(x^(3/2))]
= 1/x - (-cotx)cosecx + log(5).5ˣ + 3(-3/2)x^((3/2) -1)
= cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
Learn more about differentiation on:
https://brainly.com/question/28822844
#SPJ1
Which of the following sets of numbers could not represent the three sides of a right
triangle?
O {48, 55, 73}
O {39, 80, 89}
O {42, 56, 70}
O {10, 23, 26}
Submit Answer
{48, 55, 73} and {10, 23, 26} do not represent a right angle triangle.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
Now,
48² + 53² = 73².
2304 + 2809 = 5329.
5113 ≠ 5329 so do not represents a right-angle triangle.
Similarly,
39² + 80² = 89² represents a right-angle triangle.
42² + 56² = 70² represents a right-angle triangle.
10² + 23² ≠ 26²so do not represent a right-angle triangle.
learn more about right-angle triangles here :
https://brainly.com/question/3770177
#SPJ1
consider a pair of integers (a b) the following operations can be performed on (a,b) in any order, zero or more times
If we consider a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.
How to carry out programming in Java?The program that carries out the required operations on the pair of integers is;
static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();
public static String isItPossible(Integer a, Integer b, Integer c, Integer d){
pairs.addLast(new Pair<Integer, Integer>(a,b));
while (!pairs.isEmpty()){
Pair<Integer,Integer> pair = pairs.poll();
Integer key = pair.getKey();
Integer value = pair.getValue();
if(key.equals(a) &&
value.equals(b)){
return "YES";
}
int sum=key+value;
if (sum<=c){
pairs.addLast(new Pair<Integer, Integer>(sum,value));
}
if (sum<=d){
pairs.addLast(new Pair<Integer, Integer>(key,sum));
}
}
return "NO";
}
Read more about Java Programming at; https://brainly.com/question/18554491
#SPJ1
Complete question is;
Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:
• (a, b)(a + b, b)
• (a, b) → (a, a + b)
Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example
(a, b) = (1, 1)
(c,d) = (5,2)
Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.
Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000
HELP QUICK!! Which set of side measurements could be used to form a right triangle?
Answer:
3, 4, 5
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')) OR ((w OR y') AND (x OR Y)') ? A) TRUE B) Not enough information.C) FALSE D) NULL
After solving the logical operations it can be determined that the correct answer is C) FALSE.
What are logical operations?Logical operations are phrases that connect expressions to test if they are true or not.
What does the complement sign mean?The complement (') sign means that the opposite value of the variable is needed. For example if y is false, y' means true.
Let False = 0 and True = 1
= ((0 OR 0') AND (1' AND 0')) OR ((0 OR 0') AND (1 OR 0)')
= ((0 OR 1) AND (0 AND 1)) OR ((0 OR 1) AND (1)')
= (1 AND 0) OR (1 AND 0)
= 0 OR 0
= 0
Hence, the answer is C) FALSE
To learn more about logical operations visit the link below
https://brainly.com/question/13092292
#SBJ4
Cast Iron Grills, Incorporated, manufactures premium gas barbecue grills. The
company reports inventory and cost of goods sold based on calculations from a LIFO
periodic inventory system. Cast Iron's December 31, 2024, fiscal year-end inventory
consisted of the following (listed in chronological order of acquisition):
Units. Unit cost
6,800. 600
4,900. 700
7,800. 800
The replacement cost of the grills throughout 2025 was $900. Cast Iron sold 36,000
grills during 2025. The company's selling price is set at 200% of the current
replacement cost.
Required:
1. & 2. Compute the gross profit (sales minus cost of goods sold) and the gross profit
ratio for 2025 under two different assumptions. First, that Cast Iron purchased 37,000
units and, second, that Cast Iron purchased 19,500 units during the year.
4. Compute the gross profit (sales minus cost of goods sold) and the gross profit ratio
for 2025 assuming that Cast Iron purchased 37,000 units (as per the first assumption)
and 19,500 units (as per the second assumption) during the year and uses the FIFO
inventory cost method rather than the LIFO method.
Answer:
a) ending inventory: 11,850,000
cost of goods sold: 25,200,000
gross profit 25,200,000
b)
ending inventory: 1,800,000
cost of goods sold: 23,100,000
gross profit 50,400,000 - 23,100,000 = 27,300,000
5,200 at $600
4,100 at $700
6,200 at $800
purchase 29,000 at $900
-sold 28,000 grills
As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account
ending inventory
5,200 at $ 600
4,100 at $ 700
6,200 at $ 800
1,000 at $ 900
Total $ 11,850,000
cost of good sold:
28,000 x $900 = $25,200,000
sales revenue
28,000 x 900 x 200% = $50,400,000
gross profit sales revenue less COGS
b) 5,200 at $600
4,100 at $700
6,200 at $800
purchase 15,500 at $900
-sold 28,000 grills
we check how many layer deep we go:
28,000 - 15,500 at 900= 12,500
12,500 - 6,200 at 800= 6,300
6,300 - 4,100 at 700 = 2,200 at 600
Ending Inventory
3,000 at $600 = $ 1,800,000
COGS:
15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000
Step-by-step explanation:
Rewrite the set U by listing its elements. Make sure to use the appropriate set
notation.
U= {x|x is an integer and -4
U =
The set U can be rewritten by listing its elements as follows:
U = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}
In this notation, the "..." symbol indicates that the set continues in both the negative and positive direction, and that all integers from negative infinity to positive infinity are included in the set. This notation is commonly used to represent sets of integers or other infinite sets in mathematics.
46. The table shows the temperature (in degrees) for eight consecutive days as well as the
respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature 68 77 83 85 89 94 96 99
Number of Cones 403 447 457 465 489 503 543 576
About how many ice cream cones would you expect the shop to sell if the temperature one day
is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
0579 cones
0585 cones
O 602 cones
(617 cones
A line of best fit for this problem is y = 5.08x + 46.59. The number of ice cream cones that you would expect the shop to sell if the temperature one day is 106 degrees is; 585 cones
How to find the line of best fit?A graph of the scatter plot and line of best fit is as shown in the attached file.
The temperature in this problem is the independent variable, or x. This is due to the fact that we are assuming that the particular number of ice cream cones sold will depend on the temperature. Therefore, we can say that the number of ice cream cones will be the dependent variable, or y.
Therefore in our graphing calculator, we will enter temperature in the first list and then the number of cones in the second.
Sequel to drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax + b:
a = 5.08
b = 46.59
Therefore, the equation is;
y = 5.08x + 46.59.
Entering our temperature of 106 degrees, for x gives;
y = 5.08(106) + 46.59
= 585.07
≈ 585
Read more about Line of best fit at; https://brainly.com/question/1441182
#SPJ1
evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are a1
The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
1. The integral is given as an area under a graph.
2. The graph has labeled regions.
3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.
4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
Learn more about integral here
https://brainly.com/question/18125359
#SPJ4
Use the given information to prove that ΔRST ≅ ΔVUT.
Given: ST ≅ UT
∠SRT ≅ ∠UVT
Prove: ΔRST ≅ ΔVUT
Based on the given information , the proof of triangle RST ≅ triangle VUT is shown below .
In the question ,
two triangles are given where ;
it is given that side ST ≅ UT
and ∠SRT ≅ ∠UVT .
we have to prove that ΔRST congruent ΔVUT .
In triangle RST and triangle VUT .
side ST = side UT .....given that ST ≅ UT ;
angle SRT = angle UVT ....given that ∠SRT ≅ ∠UVT ;
angle RTS = angle VTU .....because they are vertically opposite angles .
Hence by ASA congruence , triangle RST ≅ triangle VUT .
Therefore , it is proved that triangle RST ≅ triangle VUT .
Learn more about Congruence here
https://brainly.com/question/25827423
#SPJ4
Round 13.689 to the nearest hundredth
In triangle, HIJ, N is the centroid. If
HK = 10, find KI.
Answer:
4k because is right is the best answer
(easy) Jinsoul had 2 apples and Chaeyoung had 3 apples. Chaeyoung suggest they share, Jinsoul agrees. Together it makes 5 apples. BUT The apple tree they picked from has 20? 5+20=?
Answer:
Step-by-step explanation:
5+ 20= 25
Because when you set them up and add them properly you get 25
(Not sure if that was the question you wanted us to answer..)
Here is the preference schedule for a recent election among four candidates:
Number of voters 7 1 11 5 2 19 9
1st choice A X D A X A G
2nd choice X G G G A D X
3rd choice D D A X G X D
4th choice G A X D D G A
How many voters voted in this election?
How many first place votes are needed for a majority?
Which candidate/choice had the most first-place votes?
Which candidate/choice has the least first-place votes?
Which candidate/choice had the most last-place votes?
Which candidate/choice has the least last-place votes?
Answer:
There were a total of 7 + 1 + 11 + 5 + 2 + 19 + 9 = 44 voters in this election.
To get a majority, a candidate would need at least 44 / 2 + 1 = 23 first place votes.
The candidate with the most first-place votes is A, with a total of 7 + 1 + 5 = 13 first-place votes.
The candidate with the least first-place votes is X, with a total of 1 first-place vote.
The candidate with the most last-place votes is G, with a total of 9 + 2 + 9 = 20 last-place votes.
The candidate with the least last-place votes is X, with a total of 0 last-place votes.
Step-by-step explanation:
Score on last attempt: 2.5 out of 3 Score in gradebook 2.5 out of 3 For each of the following accounts, determine the growth factor and percent change for the account value over one compounding period a Account A has a 5% APR compounded monthly (12 times per year). Determine the account value's growth factor and percent change per compounding period Preview 1. Monthly Growth Factor: 1.0041667 ii. Monthly Percent Change: (1.0041667-1)-100 % Preview b. Account B has a 6.9% APR compounded quarterly (4 times per year). Determine the account value's growth factor and percent change per compounding period. i. Quarterly Growth Factor: 14(0.069/4) Preview 11. Quarterly Percent Change: (1.01725-1)*100 % Preview c. Account Chas a 3.4% APR compounded daily (365 times per year). Determine the account value's growth factor and percent change per compounding period i. Daily Growth Factor: 1+(0.034/100) Preview 11. Daily Percent Change: (1.00034.1) 100 N% Preview Submit
given rate r = 5% compounded monthly r = 0.05/12 = 0.0041667
(1) monthly growth factor = 1.0041667 (2) monthly percent change = (1.0041667-1)*100%= 0.0041667*100% monthly percent change = 0.41667%
(B) given rate r = 6.9% compounded quarterly
r = 0.069/4 = 0.01725
(1) Quarterly growth factor = 1.01725
(2) Quarterly percent change = (1.01725-1)*100%= 0.01725*100% monthly percent change =1.725%
(C) given rate r = 3.4% compounded quarterly
r = 0.034/365 = 9.315 * 10 ^ - 5
(1) daily growth factor = 1 + 9.315 * 10 ^ - 5 = 1.00009315
(2) daily percent change = (1.00009315-1)*100%= 0.00009315*100% monthly percent change =0.009315%
learn more about account here
https://brainly.com/question/25787382
#SPJ4
which phrase describes the variable expression 7 ÷ s?
a) 7 decreased by s
b) the product of 7 and s
c) 7 increased by s
d) the quotient of 7 and s
The phrase describes the variable expression 7 ÷ s is the quotient of 7 and s.
The correct option is (d).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 7 ÷ s
We know that the division results to quotient.
So, the expression shows the 7 is divided by s to give the quotient.
Hence, the answer is the quotient of 7 and s.
Learn more about Expression here:
https://brainly.com/question/14083225
#SPJ1
6. Write a linear equation with a slope of 1 and the y-intercept of -7
7. Identify the slope and y-intercept of the equation y=-3 x
8. Identify the slope and y-intercept of the equation 2 x+5 y=20
8. Identify the slope and y-intercept of the
9. Identify the slope and y-intercept of the equation 2 x+5 y=20 equation x-2 y=2
10. Write a linear equation given the graph.
11. Write a linear equation given the graph.
The line with a slope of 1 and y - intercept -7 will have an equation of y = x - 7
Given,
Slope of the line. m = 1
Y - intercept = -7
We have to determine the linear equation for the line;
Linear equation;-
A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here,
Equation of line in slope intercept form;
y = mx + b
Here,
-7 = 1x + b
Let b = y intercept (begins from 0)
Then,
y = x - 7
That is,
The linear equation is y = x - 7
Learn more about equation of line here;
https://brainly.com/question/13814739
#SPJ4
Given question is improper. Proper question is;
Write a linear equation with a slope of 1 and the y-intercept of -7
leg-leg (ll) congruence theorem if the legs of a right triangle are congruent to the legs of a second right triangle, then the triangles are congruent.
The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.
We know that two triangles are congruent if and only if they have three pairs of equal sides.
In the case of the LL congruence theorem,
the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).
Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.
Alternatively
If the legs are of equal length then
Their squares would be equal to
Hence, the sum of these squares too would be equal.
Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.
Hence, by SSS congruence criteria
the triangles would be congruent.
To learn more about congruency visit
https://brainly.com/question/12413243
#SPJ4
What improvement can we make?
In general, the improvements that we can make refer to optimizations that can be applied in a context.
¿What are the improvements?In a particular process or context, the best are optimizations that are done to make something more efficient or to improve the quality of an element.
For example, some improvements that we could make in our community are:
Establish more efficient containers to better collect garbage.Optimize public lighting. Improve solid waste management.¡Hope this helped!
If a line is tangent to a circle, then it is ___________ to the radius drawn to the point of tangency.
If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.
Given that the radius is drawn to the point of tangency of a tangent line.
We are required to fill the blank with the appropriate word.
Radius is basically the line segment which joins the center to any point on the circumference of the circle.
Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.
When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
Learn more about tangent at
brainly.com/question/11738604
#SPJ4
Jeff has two pieces of rope.the first piece of rope is 5/10 meter long. The second piece of rope is 52/100 meter long. The length of the third piece of rope is between the lengths of the first and second pieces of rope
Answer: 51/100
Step-by-step explanation:
I'm assuming that the numerator is supposed to be a whole number, because there is an infinite number of answers if it is not a whole number. 5/10 can be rewritten as 50/100 by multiplying the numerator and denominator by 10. The only fraction with a whole number numerator between 50/100 and 52/100 is 51/100. Hope this helped!
an assembly consists of two mechanical components. suppose that the probabilities that the firt and second components meet specfications are 0.81 and 0.84 respectfully. assume that the components are independent. x denotes the number of components in the assembly that meet specifications. obtain the cumulative distribution function (cdf)
The probability of the cumulative distribution function to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,
P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
As given in the question,
Let probability of the first component to meet the specification be P (M)
= 0.81
And probability of the second component to meet the specification be P (N)
= 0.84
Probability of the first component do not meet the specification be P ( M' )
= 1 - 0.81
= 0.19
Probability of second component do not meet the specification be P(N' )
= 1 - 0.84
= 0.16
X defined the number of components to the meet the specifications
Here X = 0, 1, 2
P( X = 0 ) represents components do not meet any specifications
= P( M' ∩ N' )
= P(M') P(N') ( Independent )
= 0.19 × 0.16
= 0.0304
P( X= 1) represents components meet only one specification
= P( M∩N') ∪ P( M'∩N)
= P( M∩N') + P( M'∩N)
= P(M) P(N') + P(M') P(N)
= 0.81(0.16) + (0.19)(0.84)
= 0.1296 + 0.1596
= 0.2892
P( X=2) represents components meet both the specification
= P( M ∩ N )
= P(M) P(N)
= 0.81(0.84)
= 0.6804
Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
does the object represented in (figure 1) have a positive or negative value of ayay ? explain. assume that yy -axis points upward.
Because the object is moving slowly toward the bottom and the positive y-direction points upward, the object has a positive value for ay.
Motion is the shift in an object's location with regard to time. Motion can be quick or slow, but motion is still present. Due to the significance of motion in the physical world, it is crucial that we pay proper attention to the study of motion. Generally speaking, the following phrases are used to describe motion
DistanceDisplacementSpeedTimeWith the use of equations and derivations, understanding the numerical of physics can be tedious, but with the aid of graphs, it is both entertaining and simple to understand what the answer is describing.
Since they are used in nearly all of the topics in physics, graphs are essential. Give us more information about various graphs in this article.
To learn more about graphs
brainly.com/question/11234618
#SPJ4
a clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $55, while 8000 shirts can be sold at a price of $47. give a linear equation in the form p
The linear relationship between the number of shirts, n ,it can sell and the price, p is p = (-1/250)x + 79
The linear equation is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here p is the total price
n is the number of shirts
The equation will be
p = mn + b
The price of 6000 shirts = $55
The price of 8000 shirts = $47
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line = (47-55) / (8000-6000)
= -8/2000
= - 1/250
Substitute the point (6000, 55) in the equation
55 = (-1/250)(6000) + b
55 = -24 + b
b = 55 + 24
b = 79
Substitute the values in the equation
p = (-1/250)x + 79
Therefore, the linear relation in the form of p is p = (-1/250)x + 79
Learn more about linear equation here
brainly.com/question/16926983
#SPJ4
Which equation has no solution?
0 14x-21=-6
012-x1=9
O 13x + 61 = 6
O 1-2x+81 = 0
Step-by-step explanation:
1 , 14x=-6+21
14x=15 , divide both sides by q4 to get the value of x
x=15/14
2 , x1=x
-x=9-12
-x=-3 , divide both side by -1
x=3
3, 13x=6_61
13x= 55 , divide both sides by 13
x=55/13
4, 1-2x+81=1+81_2x
82_2x=0
-2x=-82 , divide both sides by -2
x=41
So, all of them have a solution