The life, in years, of a certain type of electrical switch has an exponential distribution with an average life betaequals3. If 300 of these switches are installed in different systems, what is the probability that at most 70 fail during the first year?
Answers
The probability that at most 70 switches fail during the first year is low, at around 1.3%.
The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.
The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.
To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.
This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.
Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:
P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)
This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.
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Related Questions
Find the product
(4)(-11) =
Answers
Answer:
4 X -11
-44
plz mark as brainliest
Answer:
-44
Step-by-step explanation:
Basically It's like 4x11, but you put a negative sign.
Please show me 3+2 (2x - 4) and can you please show the work?
Answers
Answer:
4x -5
Step-by-step explanation:
3+2 (2x - 4)
Distribute
3 + 2*2x - 2*4
3+4x - 8
Combine like terms
4x +3-8
4x -5
Answer:
4x - 5
Step-by-step explanation:
3+ 2 (2x) + 2 (-4)
3+4x - 8
The diameter of a circle measures 26 mm. What is the circumference of the circle?
Answers
Answer:
81.68 mm
Step-by-step explanation:
C = πd = π · 26 ≈ 81.68141 mm
PLssssss HELPPPPPPP will GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Mr. Mayhood had 4½ pounds of sand in a bucket. He put 2¾ pounds
of sand around his flower bed. How much sand did he have left in the
bucket?
Answers
Answer:
For addition 7 1/4. For subtraction 1 3/4. For multiplication 12 2/8. For division 1 7/11.
Step-by-step explanation:
Find the number of terms in this polynomial.
-8f^2
Answers
Answer:
3 terms
Step-by-step explanation:
Which is the best average: 10 of 15 free throws, or 8 of 10 free throws?
Answers
Answer:
8 of 10 free throws
Step-by-step explanation:
10/15 is .6666667 or about 67%
But 8/10 is .8 or 80%
80% > 60%
what is the value of (-35) • (-5/7)
Answers
Answer:
56
Step-by-step explanation:
25
We'll start by getting rid of the negatives, because a negative times a negative equals a positive.
Multiply the whole number by the numerator first, then divide by the denominator.
35 x 5 = 175
175/7 = 25
CHALLENGE: L-Shaped Prism 2
Find the area of this L-Shaped Prism in .
Enter your solution without units below.
PLEASE HELPPP
Answers
Note that the area of the L-Shaped prism (which is a compound shape) is 10,250cm
How did we arrive at the above?
To get the area, we had to bread down the prism into simpler units of two cuboids A and B. See the attached.
Recall that the area of a Cuboid is
L x B x H
where
L = Length
B = Base
H = Height
For Cuboid A:
L = 50
B = 9 and
H = 15
Thus Area of Cuboid A =
50 x 9 x 15
= 6750
For Cuboid B we have
5 x 50 x 14
= 3500
Since A + B = the Area of the Full Prism, thus
6750 + 3500 = 10,250cm
Hence the area of the L-Shaped Prism is 10,250cm
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choose the table thst represents g(x) =-2•f(x) when f(x) = x +4
Answers
Answer:
c
Step-by-step explanation:
x=1 g(x)=-10
x=2 g(x)=-12
x=3 g(x)=-14
f(x)=x+4
=＞ g(x)=-2·(x+4)
An increase in the rate of inflation will: Multiple Choice increase the nominal interest rate while lowering the real interest rate. increase the real interest rate but not affect the nominal interest rate. decrease both the real and the nominal rate of interest. increase both the real and the nominal rate of interest. increase the nominal interest rate but will not affect the real interest rate.
Answers
An increase in the rate of inflation will increase the nominal interest rate while lowering the real interest rate.
When the rate of inflation rises, it affects both the nominal and real interest rates. The nominal interest rate is the stated or observed interest rate, while the real interest rate is adjusted for inflation and represents the purchasing power of the interest earned or paid. Inflation erodes the purchasing power of money over time.
As inflation increases, lenders and investors demand higher nominal interest rates to compensate for the expected loss in purchasing power. However, while the nominal interest rate rises, the real interest rate, which takes inflation into account, decreases because the purchasing power of the interest earned or paid is reduced.
In summary, an increase in the rate of inflation will result in an increase in the nominal interest rate but a decrease in the real interest rate due to the erosion of purchasing power caused by inflation.
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Katelynn is excited about her trip to Chicago with her orchestra. She needs to raise $500 in order to go. She decides to make and sell scarves in order to fund her trip. In order to make each scarf, she will need $3 worth of yarn. If she plans on making 100 scarves, how much must she charge for each scarf in order to be able to pay for her trip?
Answers
Answer:
$8 each scarf
Explanation:
Let the selling price for each scarf be x,
Formula:
unit amount(selling price - cost price) = total profit
Stepwise:
100(x - 3) = 500
100(x) - 100(3) = 500
100x - 300 = 500
100x = 500 + 300
100x = 800
x = 8
Nima collected 46 4 6 carton of eggs on Monday and 912 9 12 carton of eggs on Tuesday. How many cartons of eggs did Nima collect on these 2 days combined?
Answers
The total number of carton of egg is 1 5/12
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
If Noma collected 4/6 on Monday and 9/12 on Tuesday.
The total carton of egg is obtained by sum up the cartons collected on the two days.
= 4/6 + 9/12
=( 8 + 9)/12
= 17/12
= 1 5/12
therefore the total cartons of egg collected in the two days is 1 5/12
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Calcular x-y:
8 ; 7 ; 11 ; 10 ; 14; 13; x; y
Answers
First, we need to find the sum of the given numbers:
8 + 7 + 11 + 10 + 14 + 13 + x + y = 63 + x + y
Next, we can use the fact that the sum of the first six numbers is equal to twice the sum of x and y:
8 + 7 + 11 + 10 + 14 + 13 = 2(x + y)
63 = 2(x + y)
x + y = 31.5
Now we can substitute this expression into the first equation:
63 + x + y = 63 + 31.5
x + y = 31.5
Therefore, x-y = (x + y) - 2y = 31.5 - 2y
We cannot simplify this expression any further without knowing the values of x and y.
Answer:
To calculate x-y, we need to know the values of x and y. However, since we only have seven out of the eight values in the sequence, we cannot determine the values of x and y with certainty.
One approach to estimating x-y is to find the average value of the sequence and assume that x and y are close to this average.
The average of the given values is:
(8 + 7 + 11 + 10 + 14 + 13 + x + y) / 8 = (63 + x + y) / 8
If we assume that x and y are close to the average, we can set x = y = (63 + x + y) / 8, which gives:
x + y = 63 + x + y
x - y = 0
Therefore, an estimate for x-y based on this assumption is 0. However, without more information about the sequence, we cannot determine the actual value of x-y.
convert 20 mm into km
Answers
Answer:
Step-by-step explanation:
1 km = 1,000 m = 100,000 cm = 1,000,000 mm
1 mm is millionth part of 1 km
1 mm = 0.000001 km
20 mm = 0.00002 km
if you made a stack of nickles 100 inches tall how many nickles would you need
Answers
You would need approximately 1,283 nickels to make a stack that is 100 inches tall.
A nickel has a thickness of approximately 0.078 inches (or 1.98 mm).
To find out how many nickels you would need to make a stack 100 inches tall, you can divide 100 by 0.078:
100 inches / 0.078 inches per nickel = 1,282.05 nickels
Rounding up to the nearest whole number, you would need approximately 1,283 nickels to make a stack that is 100 inches tall.
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If you are good at science pls answer these questions (only 4 questions)
Answers
#19 - amphibians do not produce amniotic eggs. Therefore they must lay their eggs in water so they don't dry out
In a certain Algebra 2 class of 26 students, 6 of them play basketball and 15 of them play baseball. There are 9 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
The probability that a student chosen randomly from the class plays both basketball and baseball is 2/13.
What are outcomes?
An outcome is a potential outcome of an experiment or trial in probability theory. Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment).
Given that the total number of students in the class is 26. 6 of them play basketball and 15 of them play baseball. There are 9 students who play neither sport.
The number of students who play at least one sport is (26 - 9) = 17.
Assume that n(A) = 6
n(B) = 15.
n(A∪ B) = 17
n(A∪ B) = n(A) + n(B) - n(A∩B)
17 = 15 + 6 - n(A∩B)
n(A∩B) = 21 - 17
n(A∩B) = 4
Therefore 4 students plays both basketball and baseball.
The number of outcomes of favorable event is 4.
The number of total outcomes is 26.
Probability = The number of favorable outcomes/ Total number of outcomes
The probability is 4/26 = 2/13
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What is 2,047 × 508 step by step
Answers
Answer: 1039876
Step-by-step explanation:
Answer:
1,039,876
Step-by-step explanation:
2047
x 508
16376
+ 00000
1023500
1039876
find the two numbers such that the sum of the two numbers is 24 and the product of the two nuumbers is 143
Answers
11 and 13
Step-by-step explanation:
11 + 13 = 24
11 x 13 = 143
Answer:
119
Step-by-step explanation:
first you have to do 143-24 which is 119 and then just to double check you do 143-119 and you get 119
A box in the shape of a rectangular prism is shown below. The box is completely filled with 432 identical cubes. The edge length of each cube is inch long. What is the volume of the box?
Answers
The volume of the box is 432 cubic inches
Calculating the volume of the box?From the question, we have the following parameters that can be used in our computation:
Completely filled with 432 identical cubes. Edge length of each cube is 1 inch long.The volume of the box is calculated as
Volume = Number of cubes * Volume of each cube
Where
Volume of each cube = 1 * 1 * 1
Volume of each cube = 1
Substitute the known values in the above equation, so, we have the following representation
Volume = 432 * 1
Evaluate
Volume = 432
Hence, the volume of the box is 432 cubic inches
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A random sample is drawn from a population with mean u = 66 and standard deviation o=5.5. (You may find it useful to reference the z table.). a. What is the expected value and the standard error of the sampling distribution of the sample mean with n= 16 and n= 36. (Round the standard error to 3 decimal places.) n Expected Value Standard Error 16 36 b. Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes? O Yes, both the sample means will have a normal distribution
O No, both the sample means will not have a normal distribution O No, only the sample mean with n - 16 will have a normal distribution O No, only the sample mean with n= 36 will have a normal distribution
Answers
The sampling distribution of the sample suggests is about every day for each sample size of 16 and 36.
A. To calculate the predicted price and general errors of the sampling distribution of the pattern mean, we can use the subsequent formulation:
Expected Value (μx) = Population Mean (μ) = 66
Standard Error (SE) = Population Standard Deviation (σ) /\(\sqrt{n}\)
For n = 16:
SE = 5.5 / \(\sqrt{16}\) = 5.5 / 4 = 1.375
For n = 36:
SE = 5.5 / \(\sqrt{36}\) = 5.5 / 6 = 0.917
Therefore, the anticipated values and popular errors for the given pattern sizes are:
n = 16:
Expected Value = 66
Standard Error = 1.375
n = 36:
Expected Value = 66
Standard Error = 0.917
b. We can conclude that the sampling distribution of the sample mean is approximately usually disbursed for both pattern sizes. The Central Limit Theorem states that as the pattern size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the form of the population distribution.
Therefore, each sample manner with n = 16 and n = 36 can have a normal distribution.
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Margaret and Bethany have a lemonade stand for one week each summer.
Each day they spend $1.50 on the ingredients necessary to make 20 cups
of lemonade. They sell each cup of lemonade for $0.25. How much do the
girls, after expenses, earn on a day that they sell 18 cups of lemonade? *
$6.00
$4.50
$3.50
$3.00
Answers
Answer:
6.00
Step-by-step explanation:
Simplify. Rewrite the expression in the form a^na n a, start superscript, n, end superscript. a^{5}\cdot a^{-3}=a 5 ⋅a −3
Answers
Answer:
The expression simplified is a^2
Step-by-step explanation:
Here, we are interested in writing the product as a single value.
We have; a^5 • a^-3
This is same as a^5 * a^-3
We proceed here using the first law of indices;
It would result to a^5 * a^-3 = a^(5-3) = a^2
Answer:
Step-by-step explanation:
Ella earns $10.25 at her part-time job at the ice creak place downtown. If she worked 12 hours this week, how much money did she make?
Answers
Answer:
123$
Step-by-step explanation:
$10.25 × 12
Answer:
She made $123.
Step-by-step explanation:
10.25 times 12 = 123
How can I find the slope of a functional relationship?
Answers
Step-by-step explanation:
y2-y1/x2-x1
is how you can find the slope
In the drawing, >ℎ
. Which statement about the volumes of the two cylinders is true?
Answers
Answer: As the two cylinders have the same height, the cylinder with the greater radius will have the greater volume. Therefore, the statement "The cylinder with radius has a greater volume than the cylinder with radius /2" is true.
Step-by-step explanation:
Out of110110students,6666areabsentabsent. What percentage of the students areabsentabsent?
Answers
16.5
110110/6666=16.5
An isosceles trapezoid has perimeter of 70. Each of the congruent nonparallel sides has length 13, and the height of the trapezoid is 12. How long is the longest side?
Answers
The length of the longest side is 27 units, in the isosceles trapezoid.
What is isosceles trapezoid?
A four-sided shape called a trapezoid has two parallel lines on each side (normally the top and bottom sides). A trapezoid that has equal-length non-parallel sides (the legs) is said to be isosceles. Considering everything mentioned before, we may start learning how to calculate an isosceles trapezoid's perimeter.
Given, the congruent nonparallel sides has length 13.
he height of the trapezoid is 12.
the extra length of the larger side will be 2*x, as it will be extra portion in both side.
So x² = 13²-12²
x² = 169-144 = 25
x = √25 = 5
So the lentgh of the larger side is 10 unit larger than smaller side.
The perimer of the isosceles trapezoid will be P = sum of all sides
P = 2*13 + L + L+10
⇒70 = 26+10 +2L
⇒2L = 70 - 36
⇒2L = 34
⇒L = 17
The length of the larger side will be 17+10 = 27 units.
Hence the length of the longest side is 27 units.
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What is the inverse of f(x)=-3^x-3+4?
Answers
can some one help plz
