Answer: LIKLEY
Step-by-step explanation:
Formula : Probability [tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
A standard cube has six numbers on it (1,2,3,4,5 and 6).
P( NOT 6) =[tex]\dfrac{\text{Numbers that are not 6}}{\text{Total numbers}}[/tex]
[tex]=\dfrac{5}{6}=0.8333[/tex]
We know that when the probability of any event lies between 0.5 and 1then the event is said to be likely to happen.
Since , P(not 6)=0.8333 which lies between 0 and 0.5.
That means, it is likely to happen.
Note :
When probability of having A = 0 , we call A as uncertain event.
When probability of having A = 1 , we call A as certain event.
When probability of having A = 0.5 , we call A as equally likely event.
When probability of having A lies between 0 and 0.5 , we call A as unlikely event.
When probability of having A lies between 0.5 and 1 , we call A as likely event.
A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
We have,
Given:
Total number of components (n) = 1000
Number of defective components (d) = 350
a.
P(A) is the probability that the first component drawn is defective:
P(A) = d/n = 350/1000 = 0.35
b.
P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:
Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.
P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349
c.
P(A ∩ B) is the probability that both the first and second components drawn are defective:
P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122
d.
P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:
[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:
[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65
Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.
P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228
e.
P(B) is the probability that the second component drawn is defective:
P(B) = Number of defective components / Total number of components
= 350/1000
= 0.35
f.
P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:
P(A|B) = P(A ∩ B) / P(B)
= (0.35 * 0.349) / 0.35
= 0.349
g.
To determine if A and B are independent, we need to compare
P(A) * P(B) with P(A ∩ B).
P(A) * P(B) = 0.35 * 0.35 = 0.1225
P(A ∩ B) = 0.122
Since P(A) * P(B) = P(A ∩ B), A and B are independent events.
It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.
The occurrence or non-occurrence of A does not impact the probability of B.
Thus,
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ4
Solve the inequality for x
Answer:
see below
Step-by-step explanation:
[tex]\frac{x-c}{d} > y[/tex]
x - c > dy
x > dy + c
The results of a linear regression are shown below.
y= ax + b
a = -1.15785
b= 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship between x and y?
1)Strong Postive Correlation
2)Strong Negative Correlation
3)Weak Positive Correlation
4)Weak Negative Correlation
Answer:
2) Strong Negative Correlation
Step-by-step explanation:
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
Find the area of the circle
Answer:
615.44
Step-by-step explanation:
The area in terms of π is 196π
196 * 3.14 = 615.44
Answer:
615.75
Step-by-step explanation:
Area equals pi times r times 2
A equals 3.14 times 14 times 2
Para cubrir un tejado rectangular de 29,7 m de largo ,se gastaron 24 552 locetas de 25cm x19 cm las cuales pierden al colocarse la 1/5 parte de su extensión eficaz . ¿ Qué ancho tenía el tejado ?
Answer:
El tejado tenía un ancho de 31.4 m.
Step-by-step explanation:
Tenemos un techo rectangular, con un largo de 29.7 m y un ancho x, que debemos calcular.
Entonces, la superficie del tejado es:
[tex]S=29.7x\;\,\text{[m}^2\text{]}[/tex]
Las locetas tienen una superficie de 25x19 cm, de las cuales 1/5 se pierde en la colocación. La superficie eficaz que ocupa cada loceta una vez colocada es:
[tex]S_L=(25\cdot19)\cdot(1-1/5)=475\cdot(0.8)=380\;\text{cm}^2[/tex]
Entonces, si se utilizaron 24552 locetas para cubrir todo el techo, podemos expresar la superfice del techo como:
[tex]S=24552\;\text{locetas}\;\cdot380\dfrac{\text{cm2}}{\text{loceta}}\cdot \left(\dfrac{1\text{m}}{100\text{cm}}\right)^2=\dfrac{24552\cdot380}{10000}\;\text{m2}=932.976\;\text{m2}[/tex]
Podemos calcular x igualando este último resultado con la primer ecuación:
[tex]S=29.7x=932.976\\\\x=932.976/29.7=31.413\approx31.4[/tex]
Which inequality is represented by this graph?
Answer:
its probably a. x>-53
my appolgies if it's wrong
Can someone help me with this I don’t know if I’m right so
A sample consists of 80 separate events that are equally likely what is the probability of each?
Answer:
1/80Step-by-step explanation:
This problem brothers is the probability of mutually exclusive events,
Given the sample space of 80 separate events, the probability of of one event happening is
Pr(each event)= [tex]\frac{1}{80}[/tex]
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
(4,1)
Step-by-step explanation:
(1+7)/2 = 4
(9+(-7))/2 = 1
Solve the system of equations by using substitution
Y=2x+3
Y=x+2
Since our first equation reads y = 2x + 3, we can substitute a 2x + 3
in for y in our second equation and then solve from there.
So we have 2x + 3 = x + 2.
Now subtract x from both sides to get x + 3 = 2.
Now subtract 3 from both sides to get x = -1.
To find y, plug -1 back into either equation.
I have chosen to plug it into the second.
So we have y = (-1) + 2 which simplifies to 1.
So our solution to this system is (-1, 1).
what does a obtuse angle measure between
Answer:
90° and 180°
Step-by-step explanation:
An obtuse angle is any angle larger than 90° and smaller than 180°
What is the missing number in the pattern? Please Help. Been stuck on this for hours.
Answer:
8
Step-by-step explanation:
The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).
So, 2 x 4 = 8
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
Solve 5(2x-3a)+2b=3ax-4, for x
Answer:
10x-15a
Step-by-step explanation:
lled a 12:3:112:3:1 ratio. Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is
Here is the full question:
When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.
Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?
The null hypothesis for the chi-square goodness-of-fit test is
Answer:
The null hypothesis for the chi-square goodness-of-fit test is :
[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]
Step-by-step explanation:
The objective of this question is to state the null hypothesis for the chi-square goodness-of-fit test.
Given that:
There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1
The total number of these color traits associated with this model = 12 + 3 + 1 = 16
Thus ;
The null hypothesis for the chi-square goodness-of-fit test is :
[tex]\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }[/tex]
What is the point-slope form of a line with slope 3 that contains the point
(2, 1)?
Answer:
y-1 = 3(x-2)
Step-by-step explanation:
The point slope form of a line is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-1 = 3(x-2)
Which of the lists of letters all have rotational symmetry?
a. C, H, N, X
b. N, O, S, Z
c. H, J, N, S
d. F, H, X, Z
Answer:
So C doesn't have symmetry so that rules out a
b does though
J doesn't work so that rules out c
F doesn't work so that rules out d
B is answer
Answer:
B. is the rotational symmetry
Step-by-step explanation:
Mrs. Brown has 16 children in her first-grade class, and Mr. Lopez has 23 children in his second-grade class. The principal has been asked to select 1 student from one of the classes to appear at a PTA meeting. How many ways can the selection be made?
Answer: 368 ways
Step-by-step explanation: To find the total number of probabilities, you multiply all the factors together to get total outcome. 16 * 23 = 368
The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?
Answer:
13.53% probability that no customers arrive in a five-minute period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
They arrive at a rate of two every five minutes
This means that [tex]\mu = 2[/tex]
What is the probability that no customers arrive in a five-minute period?
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
13.53% probability that no customers arrive in a five-minute period
please help me... I'm confused
Answer:
a=5
b=15
Step-by-step explanation:
By following the pattern on the table we can see that the x is increasing by 1 and the y is increasing by 3 each time. Therefore, the next set of numbers would be (5,15).
Which one of the following numbers is an irrational number?
Question 20 options:
A)
134∕675
B)
3.
C)
7.676767…
D)
8.12131415…
Answer:
B
Step-by-step explanation:
rational number means comparison between two numbers
eg: 1:3 or 1/3 or 0.333
irritional number does not
The one of the numbers is an irrational number that is A) 134 / 675
What are rational numbers, and irrational numbers?Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Irrational numbers are those real numbers which are not rational numbers.
Noted that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
For example
: 1:3 or 1/3
or 0.333
But irrational number does not.
The rational number means the comparison between two numbers
A) 134 / 675 = 0.19
B) 3.
C) 7.676767…
D) 8.12131415…
So, A) 134 / 675
This is an irrational number
Learn more about numbers here;
https://brainly.com/question/3151755
#SPJ2
Which flight has the fastest average speed
Answer:
Fastest wind speed ever recorded
That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976
Step-by-step explanation:
Complete the transformation on the rectangle ABCD shown and choose the resulting vector: Use [ABCD]
edgen.
last option
The previous transformation could be classified as a
✔ reflection across the y–axis
.
Step-by-step explanation:
Answer:
D. [3, -1, -1, 3, 4, 4, 1, 1]
Reflection across the y–axis
Step-by-step explanation:
Please mark as Brainliest!
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice
Answer:
A 16 inches diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let r be the radius and [tex]\theta[/tex] be the angle of a circle.
According with the graph, the area of the sector is given by
[tex]A=\frac{1}{2}r^2\theta[/tex]
The arc length of a circle with radius r and angle [tex]\theta[/tex] is r [tex]\theta[/tex]
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
[tex]2r+r\theta=32 \:in[/tex]
We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]
[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]
Next, we substitute this equation into the area equation
[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]
The domain of the area is
[tex]0<r<12[/tex]
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]
To check if r=8 is a maximum we use the Second Derivative test
if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.
The second derivative is
[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]
Because [tex]A''(r)=-2 <0[/tex] the largest slice is when r = 8 in.
The diameter of the pizza is given by
[tex]D=2r=2\cdot 8=16 \:in[/tex]
A 16 inches diameter will reward you with the largest slice of pizza.
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
44.70 US dollars
73.06 US dollars
136.87 US dollars
140.41 US dollars
Answer:
Step-by-step explanation:
€150 ($1.3687 / €1) = $205.30
$250 − $205.30 = $44.70
Answer:
A: 44.70 US dollars
Step-by-step explanation:
What are the next two numbers in the pattern of numbers 45,15,44,17,40,20,31,25
Answer:
14, 32
Step-by-step explanation:
45,15,44,17,40,20,31,25
this is combination of 2 series:
45-44-40-31- ?15-17-20-25-?In the first series we can see the pattern as:
-1, -4, -9 = -1², -2², -3² so next difference must be -4², which is 31- 16= 14In the second series we can see the pattern as:
2, 3, 5 prime numbers, so next difference must be 7, which is 25+7=32The series will continue as:
45, 15, 44, 17, 40, 20, 31, 25, 14, 32What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
1/2r = 2π/Cb
Please help me with this math problem
Answer:
[tex]7x^2-2x-2[/tex]
Step-by-step explanation:
[tex]-3x^2+9+10x^2-11-2x[/tex]
Combine like terms:
[tex]10x^2-3x^2-2x+9-11[/tex]
Simplify:
[tex]7x^2-2x-2[/tex]
Hope this helps!
Answer: 7x^2 - 2x - 2
Step-by-step explanation:
in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.
-3x^2 + 9 + 10x^2 - 11 - 2x rearrange to make easier
-3x^2 + 10x^2 - 2x + 9 - 11 combine like-terms
7x^2 - 2x - 2
Solve for y
A)16
B)18
C)22
D) 30
Omg help me I need help, please help me I’m so nice and funny, I can make u laugh, help me freaks I’m big baller
Answer:
30
Step-by-step explanation:
It is an equalateral triangle
a business owes $8,000 on a loan. every month, the business pays half of the amount remaining on the loan. how much will the business pay in the six-month?
Answer:
$7875
Step-by-step explanation:
1 Month 4000 Paid
2 Months 2000 Paid
3 Months 1000 Paid
4 Months 500 Paid
5 Months 250 Paid
6 Months 125 paid
Total = $7875 Paid
Hope this helped ;)
