Answer:
Step-by-step explanation:
The given line is y = 5x + 2. We know that any line perpendicular to this line will have a slope that is negative reciprocal of 5. The negative reciprocal of 5 is -1/5.
Line A is perpendicular to y = 5x + 2, so it has a slope of -1/5. We also know that the y-intercept of line A is 3. Therefore, the equation of line A can be written as:
y = (-1/5)x + 3
or in the form y = mx + c, where m = -1/5 and c = 3.
Kate plans to save 5% of her income. She just earned 80.Howmuchmoneyshouldsheputintosavings?
$4
Multiply 80 by 0.05 to get the answer of $4
Answer:
4 (insert the currency needed)
Step-by-step explanation:
To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!
5 ÷ 100 = 0.0580 × 0.05 = 4This means she has to put £4 into her savings!
Hope this helps, have a lovely day! :)
A simplified carbon cycle with aerobic and anaerobic processes is depicted here. Although much of the emphasis on global climate change has been on increasing carbon dioxide levels, methane is also a greenhouse gas whose levels are increasing due to human and other activity. Which of these actions would increase methane levels in the atmosphere and potentially affect global climate change? Select ALL that apply.
--------------------------------------------------------------------------------------------------------------------------------
A Agricultural practices in rice cultivation releases methane.Agricultural practices in rice cultivation releases methane.
B Anaerobic digestion of cellulose by cows produces methane.Anaerobic digestion of cellulose by cows produces methane.
C Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.Photosynthesis by phytoplankton converts carbon dioxide into the atmosphere.
D Industrial combustion of fossil fuels releases methane into the atmosphere.Industrial combustion of fossil fuels releases methane into the atmosphere.
E Anaerobic decomposition of landfill material releases methane into the atmosphere.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
what is equation ?A mathematical equation is a claim that two expressions are equal, typically represented with an equal sign (=) between them. The terms "left hand side" (LHS) and "right hand side" (RHS) of the equation, respectively, refer to the expressions on either side of the equal sign. Equations are a common tool for problem solving because they may be used to depict relationships between variables or quantities and to determine the value(s) of the unknown variable(s) that satisfies the equation. For instance, the link between the variables x and the integers 2, 5, and 11 is represented by the equation 2x + 5 = 11. Finding the value of x that makes the left and right sides of the equation equal is necessary to solve this equation.
given
A) Rice farming operations release methane into the atmosphere.
B) Methane is created when cows break down cellulose anaerobically.
E) Methane is released into the atmosphere when landfill material decomposes anaerobically.
Any of the aforementioned behaviours would raise the atmospheric methane concentrations and may have an impact on climate change globally.
Methane is a greenhouse gas that causes the atmosphere of the Earth to warm.
It is produced by both natural and artificial processes. Examples of human activities that contribute to methane emissions into the atmosphere include the production of rice, cattle digestion, and landfill decomposition.
In attempts to reduce greenhouse gas emissions and the effects of climate change, these sources must be taken into account.
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In order to make the same amount of money, they would have to each sell ______ bicycles. They would both make $______.
In order to make the same amount of money, they would have to each sell 5 bicycles. They would both make $500
How many bicycle would they sell to make the same amount of money?To find the number of bicycles they would need to sell to make the same amount of money,
We can set Jim's and Tom's weekly earnings equal to each other and solve for the number of bicycles:
250 + 50x = 400 + 20x
30x = 150
x = 5
So they would need to sell 5 bicycles to make the same amount of money.
How much would they make for selling that amountTo find out how much money they would make for selling 5 bicycles, we can substitute x = 5 into either equation.
Let's use Jim's equation:
250 + 50(5) = 500
So they would make $500 for selling 5 bicycles.
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What’s -9.1 times 3.75
How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
How much was one movie ticket in 2008
Answer: 7 dollars 18 cents.
Step-by-step explanation:
A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
A coffee maker is on sale for 45$. If the sales tax is 7%, how much will the buyer spend altogether?
Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at
Step-by-step explanation:
Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested
The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.
To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:
A = $4,000.00(1 + 0.045/365)^(365*4)
A = $4,000.00(1.0001234)^1460
A = $4,889.68
The final amount is $4,889.68, which means that the interest earned is:
Interest = $4,889.68 - $4,000.00 = $889.68
We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:
$1.197204 / $1.00 = 1.197204
Interest earned = $889.68 x 1.197204 = $1,064.08
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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
Work out the fraction and ratio that
complete the equations below.
Give each answer in its simplest form.
a) h:k=5:6
h =
k
b) 2x=9y
x:y
=
:
The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.
What is the fraction and ratio that complete the equations?h : k = 5 : 6
h/k = 5/6
cross product
h × 6 = k × 5
6h = 5k
divide both sides by 6
h = 5/6k
Then,
2x = 9y
2/9 = x/y
2 : 9 = x : y
Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.
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Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
Complete the recursive formula of the arithmetic sequence -16, -33, -50, -67,. −16,−33,−50,−67,. Minus, 16, comma, minus, 33, comma, minus, 50, comma, minus, 67, comma, point, point, point. C(1)=c(1)=c, left parenthesis, 1, right parenthesis, equals
c(n)=c(n-1)+c(n)=c(n−1)+c, left parenthesis, n, right parenthesis, equals, c, left parenthesis, n, minus, 1, right parenthesis, plus
The following is the recursive formula for the arithmetic sequence in this issue:
c(1) = -16.
c(n) = c(n - 1) - 17.
An arithmetic sequence is a series of numbers where each term is obtained by adding a fixed constant, known as the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, 14, 17, each term is obtained by adding 3 to the previous term.
The formula for finding the nth term of an arithmetic sequence is: a(n) = a(1) + (n-1)d, where a(1) is the first term, d is the common difference, and n is the term number. For example, to find the 10th term of the sequence 2, 5, 8, 11, 14, 17, we would use the formula a(10) = 2 + (10-1)3 = 29. Arithmetic sequences have many practical applications, such as in finance, where they can be used to calculate the interest earned on an investment over time.
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a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 32.083. what is the value of the additional data point?
The value of the additional data point is [tex]$19.17$[/tex].
What is the value of the additional data point?Let us first find the mean of the given data:
[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]
Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is
[tex]$(39+45+43+42+44+x)$[/tex].
Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:
[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]
Multiplying both sides of the equation by 6 we get:
[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]
We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].
Therefore, substituting all the values, we get:
[tex]193.83 + x = 213[/tex]
On subtracting [tex]$193.83$[/tex] from both sides, we get the value of
[tex]x. x = 213 - 193.83 = 19.17[/tex]
Therefore, the value of the additional data point is [tex]$19.17$[/tex]
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.
Part 1: Calculation of probability of getting 5 questions correct
(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:
P(k) = (nCk)pk(q(n−k))
Where, n = total number of questions
(10)k = number of questions that are answered correctly
p = probability of getting any question right = 1/4
q = probability of getting any question wrong = 3/4
P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058
Part 2: Calculation of probability of getting more than 3 questions correct
(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)
P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02
P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058
P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012
P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002
P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001
P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000
P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0
P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093
Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.
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What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
LetR=[0, 4]×[−1, 2]R=[0, 4]×[−1, 2]. Create a Riemann sum by subdividing [0, 4][0, 4] into m=2m=2 intervals, and [−1, 2][−1, 2] into n=3n=3 subintervals then use it to estimate the value of ∬R (3−xy2) dA∬R (3−xy2) dA.Take the sample points to be the upper left corner of each rectangle
The Riemann sum is:Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
We can create a Riemann sum to estimate the value of the double integral ∬R (3-xy²) dA over the rectangular region R=[0, 4]×[-1, 2] by subdividing [0, 4] into m=2 intervals and [-1, 2] into n=3 intervals. Then we can evaluate the function at the upper left corner of each subrectangle, multiply by the area of the rectangle, and sum all the results.
The width of each subinterval in the x-direction is Δx=(4-0)/2=2, and the width of each subinterval in the y-direction is Δy=(2-(-1))/3=1. The area of each subrectangle is ΔA=ΔxΔy=2*1=2.
Therefore, the Riemann sum is:
Σ(3-xᵢₖ*yᵢₖ²)ΔA, where i=1,2 and k=1,2,3.
Evaluating the function at the upper left corner of each subrectangle, we get:
(3-0*(-1)²)2 + (3-20²)2 + (3-21²)2 + (3-41²)*2 = 2 + 6 + 2 + (-22) = -12.
Thus, the estimate for the double integral is -12.
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
Use the following circle to solve for x
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
Guidance Missile System A missile guidance system has seven fail-safe components. The probability of each failing is 0.2. Assume the variable is binomial. Find the following probabilities. Do not round intermediate values. Round the final answer to three decimal places, Part: 0 / 4 Part 1 of 4 (a) Exactly two will fail. Plexactly two will fail) = Part: 1/4 Part 2 of 4 (b) More than two will fail. P(more than two will fail) = Part: 214 Part: 2/4 Part 3 of 4 (c) All will fail. P(all will fail) = Part: 3/4 Part 4 of 4 (d) Compare the answers for parts a, b, and c, and explain why these results are reasonable. Since the probability of each event becomes less likely, the probabilities become (Choose one smaller larger Х 5
The probability of all will fail is the lowest.
The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:
(a) Exactly two will fail.
(b) More than two will fail.
(c) All will fail.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
(a) Exactly two will fail.
The probability of exactly two will fail is given by;
P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713
Therefore, the probability of exactly two will fail is 0.2713.
(b) More than two will fail.
The probability of more than two will fail is given by;
P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967
Therefore, the probability of more than two will fail is 0.1967.
(c) All will fail.
The probability of all will fail is given by;
P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002
Therefore, the probability of all will fail is 0.00002.
(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.
The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.
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