Answer:
21
Step-by-step explanation:
asdawda
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components act independently.a) Find the probability that exactly two of the four components last longer than 1000 hours.b) Find the probability that the subsystem operates longer than 1000 hours.
Answer:
a) 0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.
b) 0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The probability of a component failing in less than 1000 hours is independent of any other component. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours.
Four components means that [tex]n = 4[/tex]
Probability of 0.2 of failling means that 1 - 0.2 = 0.8 probability of not failling, so [tex]p = 0.8[/tex]
a) Find the probability that exactly two of the four components last longer than 1000 hours.
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]
0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.
b) Find the probability that the subsystem operates longer than 1000 hours.
It will operate if at least two compoents last longer than 1000 hours. So
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]
[tex]P(X = 3) = C_{4,3}.(0.8)^{3}.(0.2)^{1} = 0.4096[/tex]
[tex]P(X = 4) = C_{4,4}.(0.8)^{4}.(0.2)^{0} = 0.4096[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.1536 + 0.4096 + 0.4096 = 0.9728[/tex]
0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.
The sum of two numbers is 58. Twice the second
number subtracted to four times the first number is
28. Find the two numbers.
Answer:
Step-by-step explanation:
a+b=58 and 4a-2b=28 is the system of equations
solving the first for a, a=58-b, using this value for b in second equation is
4(58-b)-2b=28
232-4b-2b=28
232-6b=28
-6b=-204
b=34, and since a=58-b
a=58-34
a=24
So the two numbers are 24 and 34
What is the value of a?
Answer:
your answer will be option B
Step-by-step explanation:
[tex]\frac{10}{12} =\frac{a}{38} \\\\a=\frac{(10) (38)}{12} \\\\=31.6[/tex]
The picture shows the top view of a piece of glass. A rectangular piece of glass is shown. The length is measured as 4 feet. The width is measured as 2 and one-half feet. Which equations can be used to find the area, in square feet, of the piece of glass? Select all that apply. A. A = 2 1 2 × 4 B. A = 5 2 + 4 C. A = ( 2 1 2 + 2 1 2 ) + ( 4 + 4 ) D. A = 5 2 × 4 E. A = ( 2 × 2 1 2 ) + ( 2 × 4 ) F. A = 2 1 2 + 4 answer and u get brainlyest
Answer:
d. and e.
Step-by-step explanation:
i did the test
Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that A rectangular piece of glass is shown.
The length is measured as 4 feet.
The width is measured as 2 and one-half feet.
We have to find the equations can be used to find the area of the piece of glass.
Area=Length×width
Area=4 feet × 2 and one-half feet
=4×[tex]2\frac{1}{2}[/tex]
=4×5/2
Hence, Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.
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What is the difference of the polynomials:
(3x2 + 4x + 8) - (2x2 + 2x + 5)
a x^2 + 2x + 3
b x^2 + 6x + 3
c x^4 + 2x^2 + 3
d x^4 + 6x^2 + 13
Answer:
(6+4x+8)-4-2x-5
6-4+4x-2x+8-5
2+2x+3.
suppose that grade point averages of undergraduate students at one university bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.4 describe where approximately 99.7% of a grade point averages lie
Answer:
2.57-0.4-0.4-0.4=1.37
2.57-0.4-0.4=1.77
so the answer is 1.37 between 3.77
Step-by-step explanation:
plzz help me solve this question i need correct question i will mark you as a brainliest and I will give 5.0 rating anf thanks if ur answer will be correct
Answer:
I. p = 7
II. 17 litres
Step-by-step explanation:
I. Determination of the value of p
Mean = 17.7
p =.?
Let the number of litre be L
Let the number of motorist be M
Mean = summation LM / summation M
Summation of LM = (16×11) + (17×10) + (18×p) + (19×4) + (20×8)
= 176 + 170 + 18p + 76 + 160
= 582 + 18p
summation M = 11 + 10 + P + 4 + 8
= 33 + p
Mean = summation LM / summation M
17.7 = 582 + 18p / 33 + p
Cross multiply
17.7(33 + p) = 582 + 18p
584.1 + 17.7p = 582 + 18p
Collect like terms
584.1 – 582 = 18p – 17.7p
2.1 = 0.3p
Divide both side by 0.3
p = 2.1 / 0.3
p = 7
II. Determination of the median number of litre.
Let the number of motorist be M (i.e the frequency)
summation M = 11 + 10 + P + 4 + 8
p = 7
summation M = 11 + 10 + 7 + 4 + 8
summation M = 40
The median is the middle term i.e
Median = (summation M / 2)ᵀʰ motorist
Median = (40 / 2)ᵀʰ motorist
Median = 20ᵀʰ motorist
Considering the table in the question above, the 20ᵀʰ motorist has 17 litres.
Therefore, the median number of litres is 17 litres.
Can someone help me with these questions and show work please and thank you
Answer:
11. 78
12. 4x² - 3x - 1
Step-by-step explanation:
11. Sum of n whole numbers = ½(n² + n)
Multiply
½*n² + ½*n
= n²/2 + n/2
To find the sum of the first 12 whole number, substitute 12 for n into the equation.
= 12²/2 + 12/2
= 144/2 + 12/2
= 72 + 6
= 78
12. Area of trapezoid = ½(a + b)*h
Where,
a = 5x - 4
b = 3x + 2
h = x + 1
Area = ½(5x - 4 + 3x + 2)*(x + 1)
Area = ½(8x - 2)*(x + 1)
Area = ½[8x(x + 1) -2(x + 1)]
= ½[8x² + 8x - 2x - 2]
Add like terms
= ½(8x² - 6x - 2)
= ½(8x²) - ½(6x) - ½(2)
= 4x² - 3x - 1
Combine like terms to simplify; (5x + 2) + (4x + 5). 1 point 9x - 7 9x + 7 -9x - 11 X + 7
(5x + 2) + (4x + 5)
= 5x + 2 + 4x + 5
= 5x + 4x + 5 + 2
= 9x + 7
If Figure F is rotated 180° and dilated by a factor of , which new figure could be produced?
Hurry please!
Answer:
2nd answer choice :)
Step-by-step explanation:
The new figure produced is given below.
Option C is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
Let the figure be in the first quadrant.
Now,
Rotation of 180-degree means,
The figure will be in the third quadrant.
Now,
Dilation with a factor of 1/2.
This means,
The figure will shrink by 1/2.
Thus,
The new figure is given below.
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If m = 27 and n = 4, what is the value of the following expression?
Answer:
2
Step-by-step explanation:
m - 5 • n + 5
plug it in
27- 5 * 4+5
well, we gotta follow PEMDAS (there are no parentheses)
5*4
20
now we have
27-20+5
20+5
25
27-25
2
A satellite television company charges a one-time installation fee of $55 and a monthly service charge of $46. Elizabeth was installed this year and has spent a total of $285.00 on her satellite connection. The equation 55 + 46x = 285 can be used to represent her expenses so far. What does the variable x represent in this situation?
Answer:
The monthly service charge
Step-by-step explanation:.
Students picked 144 ounces of strawberries to make strawberry jam. How many pounds of strawberries did they pick
Answer:
9 pounds
Step-by-step explanation:
I converted it
Please answer and explain I’ll mark brainliest!!!!!!!!!!!!
Answer:
A. x^2−x+6
B. 2x^2−11x+12
C. x^2−4
Step-by-step explanation:
Hope it helps
A. Distribute:
=(x)(x)+(x)(−3)+(2)(x)+(2)(−3)
=x2+−3x+2x+−6
Combine Like Terms:
=x2+−3x+2x+−6
=(x2)+(−3x+2x)+(−6)
=x2+−x+−6
B. I can't find an explanation
C. I can't find an explanation
Answer:
So we apply the distributive property to get
a) x^2 - 3x + 2x - 6
b) 2x^2 - 8x - 3x + 12
c) x^2 - 2x + 2x - 4
then we add like terms to get
a) x^2 - x - 6
b) 2x^2 - 11x + 12
c) x^2 - 4
brainliest please?
You go to Trader Joes with your older sister to pick up avocados to make guacamole. Trader Joes sells 4 avocados for $3.50 or 6 avocados for $5.00. Which is a better deal?
I got 18 can someone double check me please?
Answer:
It's correct, it is 18 because ur adding
Answer:
28!
Step-by-step explanation:
this is because its 8 + 8 + 6 + 6 = 28. They're asking to add the outline of the perimeter.The perimeter is the length of the outline of a shape.
What is the answer
7(2m+5)
Answer:
14m+35 is your answer ☺️☺️☺️
Answer:
14m+35
Step-by-step explanation:
7(2m+5)
7(2m)+7(5)
14m+35
If ABCD is a parallelogram, m
A
B
(3x + 4)º
D
xº
C
Equation:
X=
(PLEASE HELP)
Answer:
x is 44 because
3x+4+x=180
4x=180-4
4x=176
x=44
Solve the inequality:
8+4x≥12
Select one:
x≤1
x≥5
x≥1
x≤5
Answer:
x≥1
Step-by-step explanation:
HELP QUESTION IS IN THE PHOTO ILL GIVE YOU EXTRA POINTS
A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?
w2 = 3(243)
3w2 = 243
4w2 = 243
3w2 = 3(243)
Answer:
the second option because it's three times the width so it would be time the W
Step-by-step explanation:
Answer:
the guy above me is correct
Step-by-step explanation:
just did the test got a 100%
Plzzz help. Giving everything.
Answer:
d. 260. is the answer.
The table shows the number of hours spent practicing
singing each week in three samples of 10 randomly
selected chorus members.
Time spent practicing singing each week (hours)
Sample 1 12 13 11 8 9 7 4
8 9 10 Mean = 9.1
Sample 2 7 12 11 8 9 8 12 8 9 10 Mean = 9.4
Sample 3 11 9 8 12 8 10 7 8 7 9 Mean = 8.9
Which statement is most accurate based on the data?
A. A prediction based on the data is reliable, because the means of
the samples are close together.
OB. A prediction based on the data is reliable, because each sample
has 10 data points.
O C. A prediction based on the data is not completely reliable, because
the means are not the same.
D. A ediction based on the data is not completely reliable, because
the means of samples 1 and 2 are greater than 9 and the mean of
sample 3 is less than 9.
PREVIOUS
Answer:
A prediction based on the data is reliable, because the means of the samples are close together.
Step-by-step explanation:
Test approved
The most accurate statement is A. A prediction based on the data is reliable, because the means of the samples are close together.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given three data sets.
All the samples have 10 data points.
Number of data points = 10
Mean of sample 1 = 9.1
Mean of sample 2 = 9.4
Mean of sample 3 = 8.9
We can see that the mean of the three samples is so close to each other.
So the data is reliable.
Hence the option is A.
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WILL GIVE BRAINLEST !
hAVE A GOOD DAy :)!
PLEASE HELP WILL MARK BRAINLIEST
Answer:
D
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf D. \ 64x^{12}y^6z^2}}[/tex]
Step-by-step explanation:
This is an example of a power to a power. The exponents inside the parentheses are being raised to another power outside the parentheses. We multiply the exponents and take the coefficients (number in front of the variables) to the power.
[tex](8x^6y^3z)^2[/tex]
Remember that a variable without an exponent has an implied exponent of 1.
[tex]8^2x^{6*2}y^{3*2}z^{1*2}[/tex]
Solve the coefficient's exponent.
8²= 8*8= 64[tex]64x^{6*2}y^{3*2}z^{1*2}[/tex]
Multiply the exponents.
[tex]64x^{12}y^{6}z^{2}[/tex]
So, the expression given is equal to Choice D: 64x¹²y⁶z²
Can someone help me with these two for brilliant please
Answer:
its A
Step-by-step explanation:
Answer:
A. y=5.50x
Step-by-step explanation:
Brainlist plz
Find the slope of the line that passes through (9, 6) and (6, 2).
Answer:
4/3 not sure
i hope its hepls
Answer:
y2 - y1/ x2 - x1
6 - 6/2 - 6 = 0/-4 = 0
Step-by-step explanation:
Convert the following angle from degrees to radians. Express your answer in simplest form. 435^
Answer:
29π/12.
Step-by-step explanation:
Multiply by π/180
= 435π/180
= 29π/12 radians.
Which one is greater?
4 yd or 144 in.
Answer:
4yd
144
Step-by-step explanation:
because 4yd is greater than 144
Which model shows 1/4 divided by 3 ? A B C D
Answer:
You didn't attach a picture of the models?
Answer:
b or d
Step-by-step explanation: