Answer: 210 secs (3 mins, 30 secs)
Step-by-step explanation:
No of minutes gained every 10 days = 5 mins
No of minutes gained every day = 5 ÷ 10
= 0.5 min (30 secs)
Amount of time gained in 7 days = 30 secs × 7
= 210 secs (3 mins, 30 secs)
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Answer:
The right answer is:
(a) 0.1456
(b) 18.125, 69.1202, 8.3139
Step-by-step explanation:
Given:
N = 24
n = 5
r = 7
The improperly drilled gearboxes "X".
then,
⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]
(a)
P (all gearboxes fit properly) = [tex]P(x=0)[/tex]
= [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]
= [tex]0.1456[/tex]
(b)
According to the question,
[tex]X = 91+5[/tex]
Mean will be:
⇒ [tex]\mu = E(x)[/tex]
[tex]=E(91+5)[/tex]
[tex]=9E(1)+5[/tex]
[tex]=9.\frac{nr}{N}+5[/tex]
[tex]=9.\frac{5.7}{24} +5[/tex]
[tex]=18.125[/tex]
Variance will be:
⇒ [tex]\sigma^2=Var(X)[/tex]
[tex]=V(9Y+5)[/tex]
[tex]=81.V(Y)[/tex]
[tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]
[tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]
[tex]=69.1202[/tex]
Standard deviation will be:
⇒ [tex]\sigma = \sqrt{69.1202}[/tex]
[tex]=8.3139[/tex]
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
The average score of all golfers for a particular course has a mean of 65 and a standard deviation of 4.5 . Suppose 81 golfers played the course today. Find the probability that the average score of the golfers exceeded 66 . Round to four decimal places.
Answer:
Answer:
The probability that the average score of the 49 golfers exceeded 62 is 0.3897
Step-by-step explanation:
1. Given the line of best fit y = 6.2x + 13, what is the residual for the point (10,80)? (1 pt)
A. 75
B. 5
C. 499
D. 55
Answer:
c
Step-by-step explanation:
The residual for the point line (10,80) is option A 75. at the given line which best fits y = 6.2x + 13.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
solving the equation:-
y = 6.2x + 13
putting value of X = 10
Y = 6.2 * 10 + 13
Y = 62 + 13
Y = 75
Hence the line best fit = 75.
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Find the missing length indicated
Answer:
x = 960
Step-by-step explanation:
x=√{576×(576+1024)}
or, x = √(576×1600)
or, x = √576×√1600
or, x = 24×40
or, x = 960
Answered by GAUTHMATH
Answer:
Step-by-step explanation:
resolver utilizando la regla de clamer
Answer:
pordondede donde eres?
Step-by-step explanation:
........................
Two angles of a triangle have the same measure.
If two sides have lengths 15 and 20, what is the
greatest possible value of the perimeter of the
triangle?
9514 1404 393
Answer:
55 units
Step-by-step explanation:
If two angles have the same measure, the triangle is isosceles. That means two sides have the same measure. Since the two given sides are different measures, the remaining side must be one of those. The perimeter will be greatest if the congruent sides are the longest. The greatest perimeter is ...
15 + 20 + 20 = 55 . . . units
A physicist examines 10 water samples for iron concentration. The mean iron concentration for the sample data is 0.711 cc/cubic meter with a standard deviation of 0.0816. Determine the 90% confidence interval for the population mean iron concentration. Assume the population is approximately normal.
Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2 of 2: Construct the 90% confidence interval. Round your answer to three decimal places. Lower endpoint? Upper endpoint?
Answer:
Poggers
Step-by-step explanation:
Suppose the variable x is represented by a standard normal distribution. What is the probability of x > 0.3 ? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Answer: 0.38
Step-by-step explanation:
Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:
P(x > 0.3)
Then, we will use a standard normal table
P(z > 0.3)
= 1 - p(z < 0.3)
= 1 - 0.62
= 0.38
Therefore, p(x > 0.3) = 0.38
The probability of x > 0.3 is 0.38.
Marnie just finished setting herself up at a cozy spot at the airport. Her laptop is ready, phone within reach, and her papers are organized, but now, she's hungry. What should she do? a) Take her phone and laptop with her to get something to eat b) Leave her stuff, but get a snack really quickly O c) Put her coat over her laptop to hide it and go get a snack O d) Ask the person next to her to watch her stuff
Answer:
a) someone will steal her stuff in any other situation even if a stranger watches it
If the probability that an event occurs is 0.5 , the probability that the event does not occur is
Answer:
0.5
Step-by-step explanation:
P(that an event occurs) = 0.5
P(that an event does not occur) = 1 - P(that an event occurs)
= 1 - 0.5
= 0.5
Answer:
It is also 0.5
Step-by-step explanation:
From independent events:
[tex]{ \bf{p + q = 1}}[/tex]
p is probability for an event to occur (success).
q is probability for an event not to occur (failure).
[tex]{ \tt{0.5 + q = 1}} \\ { \tt{q = 1 - 0.5}} \\ { \tt{q = 0.5}}[/tex]
Naval intelligence reports that 99 enemy vessels in a fleet of 1818 are carrying nuclear weapons. If 99 vessels are randomly targeted and destroyed, what is the probability that no more than 11 vessel transporting nuclear weapons was destroyed
Answer:
0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.
Step-by-step explanation:
The vessels are destroyed and then not replaced, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
In this question:
Fleet of 18 means that [tex]N = 18[/tex]
9 are carrying nuclear weapons, which means that [tex]k = 9[/tex]
9 are destroyed, which means that [tex]n = 9[/tex]
What is the probability that no more than 1 vessel transporting nuclear weapons was destroyed?
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,18,9,9) = \frac{C_{9,0}*C_{9,9}}{C_{18,9}} = 0.000021[/tex]
[tex]P(X = 1) = h(1,18,9,9) = \frac{C_{9,1}*C_{9,8}}{C_{18,9}} = 0.001666[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.000021 + 0.001666 = 0.001687[/tex]
0.001687 = 0.1687% probability that no more than 1 vessel transporting nuclear weapons was destroyed.
if you run 250 ft of cable and lose rate 3.6 dB how much rate you lose at 100 ft
Answer:
99
Step-by-step explanation:
99
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have 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 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
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.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
the figure below is made up of a square, a quadrant and a semicircle. the length of the square is 12cm. find the area of the shaded parts.
Answer:
P=2pi×r
P=2×12pi=24pi
24pi÷4=6pi
6pi÷2=3pi
p=2×6×pi
p=12pi
12pi÷2=6pi
permiter=3pi+6pi+12=40.27
that is for part a
Present value takes ____________.
A. Compounding rate.
B. Discounting rate.
C. Inflation rate.
D. Deflation rate
I need help answering this question asap
Answer:
Step-by-step explanation:
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11? The graph of y = f(x) will shift up 11 units. The graph of y = f(x) will shift right 11 units. The graph of y = f(x) will shift left 11 units. The graph of y = f(x) will shift down 11 units.
Answer:
The graph of y = f(x) will shift down 11 units
Step-by-step explanation:
is the sequence 1/6, 1/2, 3/2,9/2 arithmetic, or geometric
Answer:
geometric
Step-by-step explanation:
What is the slope of the line that passes through the points (-9, 8) and (–21, 10)?
Write your answer in simplest form.
Answer:
-1/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-8)/(-21 - -9)
= ( 10-8)/(-21 +9)
= 2 /-12
= -1/6
These two cones are similar. What is the value of x?
Answer:
A
Step-by-step explanation:
Given that the cones are similar then corresponding dimensions are in proportion, that is
[tex]\frac{12}{2}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
12x = 6 ( divide both sides by 12 )
x = 0.5 → A
A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there
Answer:
[tex]T=812[/tex]
Step-by-step explanation:
From the question we are told that:
No. Committee Members [tex]n=6[/tex]
Pool of : 5 students and 7 faculty members
At least 2 student members and at least 1 faculty member
Generally the committee is mathematically given by
The Total Events are
[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]
[tex]T=350+350+105+7[/tex]
[tex]T=812[/tex]
Joe nas to take two quizzes tomorrow. He nas only enough time to study one of them. • The science quiz has 7 true-or-false questions. • The English quiz has 3 multiple-choice questions. Joe calculates the probability that he will get each question correct by guessing. ?
Answer:
C.
Step-by-step explanation:
Science questions are T/F. That's .5 or [tex]\frac{1}{2}[/tex] chance to get it right.
7 questions. Each with a [tex]\frac{1}{2}[/tex].
That's [tex](\frac{1}{2})^{7}[/tex]
[tex](\frac{1}{2})^{7}[/tex] = [tex]\frac{1}{128}[/tex] = .0078 = .008 rounded
English questions are multiple choice. 4 choices. That's .25 or [tex]\frac{1}{4}[/tex]
3 questions. Each [tex]\frac{1}{4}[/tex]
That's [tex](\frac{1}{4})^{3}[/tex]
[tex](\frac{1}{4})^{3}[/tex] = [tex]\frac{1}{64}[/tex] = .0156 = .016 rounded
The probability of getting all questions correct is 0.004 which is lower than for science (0.016).
Science questions are said to have a 6 out of 6 correct answer range and a 0.5 chance of being answered properly.
So, P(6) = 0.5⁶
P(6) = 0.016
We are informed that there are 4 out of 4 correct answers for English, with a 0.25 chance of getting it right.
Thus; P(4) = 0.25⁴ = 0.004
Thus, we conclude that they will have to study English.
Learn more about Probability here:
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Please find the missing ? Explanation need it
Answer:
the answer is 3.162
Step-by-step explanation:
Simplify |3 − 11| − (15 ÷ 3 + 2) 2
35 POINTS HELP in the figure above the circle has center O and radius 6 what is the length of arc acb
Answer:
9.425 or 3π
Step-by-step explanation:
arc length = 2πr(θ/360)
The angle is 90˚ as indicated by the square symbol.
ABC = 2π6(90/360) = 9.425 or 3π
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Spinning an American roulette wheel 8282 times and recording the number the ball lands on.
Answer:
No, binomial distribution cannot be applied.
Step-by-step explanation:
We known that a Binomial Distribution depends on provided experiment , a binomial distribution have only 2 outcomes. For example, when we flip a coin in the air, then the possible outcomes are Head and Tail.
But in the context, an American roulette wheel has [tex]37[/tex] outcomes. It means when we spin the American Roulette wheel, ball may lend on any of the numbers between 0 to 36. So there are more than [tex]2[/tex] outcomes.
Therefore, binomial distribution can not be applied here.
Round to the nearest whole number.
6.4
Answer:
6
Step-by-step explanation:
Therefore, the number 6.4 rounded to the nearest whole number is 6. * If the number you are rounding off is followed by 0,1,2,3,4, round the number down. To find 6.4 rounded to the nearest whole number.
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HELP OR IM GONNA FAIL pleasee!!!! Last one
What is the solution to the system of equations graphed below?
10
X= - x+2
y = 5x + 28
-10
Answer:
(-4,8)
Step-by-step explanation:
The solution to the system is where the lines intersect
The lines intersect at x=-4 , y = 8
(-4,8)
2x+3=60 thì x băng bao nhieu
Answer:
x=57/2
Step-by-step explanation:
2x+3=60
<=> 2x=57
=> x=57/2
