Answer:
a) 0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.
b) 3 backup systems are needed.
Step-by-step explanation:
For each system, there are only two possible outcomes. Either it works, or is does not. Systems are independent. 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.
Three separate computer control systems
This means that [tex]n = 3[/tex]
The probability of failure for any one system on any one mission is known to be 0.01.
So the probability of working is:
[tex]p = 1 - 0.01 = 0.99[/tex]
(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)
This is [tex]P(X = 0)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.99)^{0}.(0.01)^{3} = 0.000001[/tex]
0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.
(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be 1 over one hundred thousand
This is n for which:
[tex]P(X = 0) < \frac{1}{100000} = 0.00001[/tex]
With 2 backup systems, the probability is lower than this, so lets see if with only two is possible.
We find [tex]P(X = 0)[/tex] when [tex]n = 2[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.99)^{0}.(0.01)^{2} = 0.0001 > 0.00001[/tex]
So 3 backup systems are needed.
17, 25, 23, 200, 14
Mean
Median
Mode
Answer:mean- 55.8
Median-23
Mode:none
Step-by-step explanation:
Please help I don’t know these questions
Write 1 3/8 as an improper fraction.
Answer:
[tex] \frac{11}{8} [/tex]
Step-by-step explanation:
[tex] \frac{1 \times 8 + 3}{8} [/tex]
Answer:
11/8
Step-by-step explanation:
Is c2−6c+9 a perfect square?
Answer:
yes it's a perfect square
More trig questions! Given that sin(C) = cos(B)Find the measure of ∠C if m∠C=10x+4 and the m∠B = 4x+2
Answer:
angle C = 64 degrees
Step-by-step explanation:
sin C = cos B
angle C = 10x+4
angle B = 4x+2
angle C + angle B = 90 degrees
10x+4 + 4x+2 = 90
simplify:
14x+6 = 90
14x = 84
x = 6
angle C = 64 degrees
what is the remainder
Use each number in the box once to complete the division
5÷6,206
Answer:
i believe it is 1,241.2
Step-by-step explanation:
well you use long division.
5/8+1/4 plz help me
I need help with that one anyone can help me please
Answer:
11: 1 tens, 1 ones 17: 1 tens, 7 ones 17 is greater number, it is greater by 6
State if the pair of triangles are similar. If so, state how you know they are similar and
complete the similarity statement
How many miles will Mrs. Garcia drive in eight hours if she is traveling 65 mph? _ miles
Answer:
520 miles
Step-by-step explanation:
65 mph * 8 hours = 520 miles
I hope this helps :)
how many do they have
Answer:
333
335
355
555
533
553
353
535
so I think 8
factor this quadratic polynomial -8x^2+8
Answer:
This is my answer
Step-by-step explanation:
-8×12+8
-96+8
-88____so this is the answer I solved it properly
PLEASE HELP ME I NEED THE ANSWER FAST.
Answer:
126
Step-by-step explanation:
9 by 10 is 90
9 by 4 is 36
90+36= 126
Hope this helps <3
The Property where if the order of addends changes, the sum stays the change
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Upper H Subscript 0 Baseline colon mu equals 175 millimeters versus Upper H Subscript 1 Baseline colon mu greater-than 175 millimeters, using the results of n equals 4 samples. Calculate the P-value if the observed statistic is
Answer:
The p-value of the observed statistic is 0.15866
Step-by-step explanation:
The given parameters of the system are;
The standard deviation of the foam height, σ = 20 mm
The null hypothesis, H₀; μ = 175 mm
The alternative hypothesis, Hₐ; μ > 175 mm
The number of observations that make the sample, n = 4
The observed statistic, [tex]\overline x[/tex] = 185
The test statistic is given as follows;
[tex]Z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Therefore, we get;
[tex]Z=\dfrac{185-175 }{\dfrac{20}{\sqrt{4}}} = 1[/tex]
P(Z > 1) = 1 - P(Z < 1) = 1 - 0.84134 = 0.15866
The p-value of the observed statistic = 0.15866
Phillip writes the following equation to show how many hours h he needs to work to earn $108 at $12 per hour: h12=108. Is his equation correct? Explain.
Answer:
Yes
Step-by-step explanation:
He is correct because h which is how many hours he needs to work times $12 will give you $108 which is the total cost.
Find the slope of the line that passes through (10, 6) and (7, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-1 1/3 - Proper Fraction
-4/3 - Improper Fraction
Step-by-step explanation:
(10,6) (7,10)
m = [tex]\frac{rise}{run}[/tex]
your "equation" should look like this: [tex]\frac{10-6}{7-10} =\frac{4}{-3} = -1\frac{1}{3}[/tex]
I hope this helped!!!!
in the following figure, the value of x is ____
Answer:
it should be 20 i hope it helps but im nt 100% sure
Step-by-step explanation:
Select the correct answer.
Consider this absolute value function.
f(x) = [ x + 3 ]
If function f is written as a piecewise function, which piece will it include?
A. x + 3, x > 3
B. x + 3, x > -3
C. -x + 3, x < -3
D. -x - 3, x < 3
Answer:
B) x + 3, x > -3
Step-by-step explanation:
I just took a test with this question on it and got it right.
Hope this helps! :)
If function f is written as a piecewise function, it will include x + 3, x > -3
The absolute value function is given as:
f(x) = | x + 3 |
Given that the function is an absolute value function, this means that:
|x + 3| > 0
Remove the absolute sign
x + 3 > 0
Subtract 3 from both sides
x > -3
Hence, if function f is written as a piecewise function, it will include x + 3, x > -3
Read more about absolute value functions at:
https://brainly.com/question/10538556
Of the 800 people at a concert, 42% of them were teenagers. How many teenagers were at the concert
Answer:
336 of them were teenagers
Answer:
There are 336 teenagers at the concert.
Step-by-step explanation:
You are welcome
please help me !! find the missing sides
Answer:
B
Step-by-step explanation:
Hello There!
That is a 45-45-90 special right triangle
so we use the same rules provided in the image
y is = to 10
x is = to [tex]10\sqrt{2}[/tex]
so we can conclude that the answer is B
WILL MARK BRAINLYIST
ou are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 96%, how many citizens should be included in your sample
Answer:
[tex](\frac{4\sigma}{2.056})^2[/tex], rounded up, if needed, citizens should be included in the sample, in which [tex]\sigma[/tex] is the standard deviation of the population.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.056.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Within 4 years of the actual mean
We have to find n for which M = 4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 2.056\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2.056\sqrt{n} = 4\sigma[/tex]
[tex]\sqrt{n} = \frac{4\sigma}{2.056}[/tex]
[tex](\sqrt{n})^2 = (\frac{4\sigma}{2.056})^2[/tex]
[tex]n = (\frac{4\sigma}{2.056})^2[/tex]
[tex](\frac{4\sigma}{2.056})^2[/tex], rounded up, if needed, citizens should be included in the sample, in which [tex]\sigma[/tex] is the standard deviation of the population.
Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles
will he need?
7 cm
14 cm
Dmitri will need
23 cm
glass tiles.
Answer:
372
Step-by-step explanation:
We are given that the dimensions of the box are,
Length = 15 cm, Width = 20 cm and Height = 9 cm.
We know that the box represents a cuboid.
Since, surface area of a cuboid = L×W + 2×L×H + 2×W×H
Thus, the surface area of the box = 15×20 + 2×15×9 + 2×20×9
i.e. Surface area = 300 + 270 + 360
i.e. Surface area = 930.
Thus, the surface area of the box is 930 cm² i.e. 9300 mm².
Further, the sides of the tiles are 5 mm and the tile represents a square.
So, the surface area of the tile = 5 × 5 = 25 mm².
This gives us that,
Number of tiles required to cover the box = = 372.
Hence, Dmitri requires 372 tiles to cover the box.
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer:
Step-by-step explanation:
Yes
Answer:
it's no
Step-by-step explanation:
6 = 5(2) - 4
7 = -1/2(2) + 8
they don't meet at (2,6)
The length of ZX is 2 units.
What is the perimeter of triangle XYZ?
Answer:
5+3 square root of 5 units
Mick paid $2.94 in sales tax on an item that cost $42.00 before tax. At that percent rate, how much would he pay in sales tax for an item that costs $58.00 before tax?
Answer:
4.06
Step-by-step explanation:
Answer:
34
Step-by-step explanation:
qsSDASD
THE TEACHER WONT HELP ☺️ pls
answer:
2/5=0.4
2/5=40%
step-by-step explanation:
to get 2/5 as a decimal you can simply just divide 2÷5 which is 0.4
and from there you can use 0.4 to find the percentage multiply 0.4 x 100 which is 40
good luck :)
hopefully, this helps
have a great day !!
I need help I dont quite understand it