A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. if the geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis, what is the pmf of the number of basalt specimens selected for analysis? what is the probability that all specimens of one of the two types of rock are selected for analysis?
The PMF of the number of selecting basalt specimen is [tex]\boxed{\bf P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex] and the probability of selecting all specimen of one of two type of rocks is [tex]\boxed{\bf 0.0325}[/tex].
Further explanation:
Concept used:
The probability of an event [tex]E[/tex] can be calculated as follpws:
[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]
Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].
The probability mass function of getting exactly [tex]r[/tex] success in [tex]n[/tex] independent trial in an experiment can be expresses as follows:
[tex]\boxed{P=^nC_{r}p^{r}q^{n-r}}[/tex]
Here, [tex]p[/tex] is the success probability and [tex]q[/tex] is the failure probability of an event.
Calculation:
A geologist has collected [tex]10[/tex] specimens of ballistic rock and geologist collected [tex]10[/tex] specimens of granite.
The total number of specimens is [tex]20[/tex].
The sample space is the collection of all possible outcomes in an experiment.
Therefore, the total possible outcomes are [tex]20[/tex].
The probability of selecting ballistic rock can be calculated as follows:
[tex]\begin{aligned}P_{b}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]
The probability of selecting granite can be calculated as follows:
[tex]\begin{aligned}P_{g}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]
The PMF of selecting exactly [tex]x[/tex] basalt specimen for analysis can be calculated as follows:
[tex]\boxed{P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex]
Consider [tex]A[/tex] as an event that all rocks are selecting from one rock and [tex]n(A)[/tex] as the number of favorable outcomes in an event [tex]A[/tex].
The number of favorable outcomes in an event [tex]A[/tex] can be calculated as follows:
[tex]\begin{aligned}n(A)&=\left(^{10}C_{10}\cdot ^{10}C_{5}\right)+\left(^{10}C_{10}\cdot ^{10}C_{5}\right)\\&=\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)+\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)\\&=\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}+\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=252+252\\&=504\end{aligned}[/tex]
The total possible outcomes of selecting [tex]15[/tex] rocks in [tex]20[/tex] rocks can be calculated as follows:
[tex]\begin{aligned}n(S)&=^{20}C_{15}\\&=\dfrac{20!}{15!\cdot (20-15)!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15!}{15!\cdot 5!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=19\cdot 3\cdot 17\cdot 16\\&=15504\end{aligned}[/tex]
The probability [tex]P(A)[/tex] of selecting all specimen of one of two type of rocks can be calculated as follows:
[tex]\begin{aligned}P(A)&=\dfrac{504}{15504}\\&=0.0325\end{aligned}[/tex]
Thus, the probability that all specimens of one of the two types of rock are selected for analysis is [tex]\boxed{\bf 0.0325}[/tex].
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Answer details:
Grade: College school
Subject: Mathematics
Chapter: Probability
Keywords: Basalt specimen, geologist, rock, granite, PMF, probability mass function, exactly, probability, possible outcomes, favorable, failure success, , event, experiment, trial, P=n(E)/n(S).
The PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.
To solve this problem, we need to find the probability mass function (PMF) of the number of basalt specimens selected for analysis and the probability of selecting all specimens of either basalt or granite.
Given information:
- There are 10 specimens of basaltic rock and 10 specimens of granite.
- The laboratory assistant will randomly select 15 specimens for analysis.
Step 1: Find the PMF of the number of basalt specimens selected for analysis.
Let X be the random variable representing the number of basalt specimens selected for analysis.
The possible values of X range from 0 to 10 (since there are 10 basalt specimens).
The PMF of X can be calculated using the binomial probability formula:
P(X = k) = (C(n, k) [tex]\times[/tex] ([tex]p^k[/tex]) [tex]\times[/tex] [tex](1-p)^{(n-k)}[/tex])
where:
n = total number of trials (selecting 15 specimens)
k = number of successes (number of basalt specimens selected)
p = probability of success (selecting a basalt specimen) = 10/20 = 1/2
q = probability of failure (selecting a granite specimen) = 1 - p = 1/2
The PMF of X for different values of k is as follows:
P(X = 0) = C(15, 0) [tex]\times[/tex] [tex](1/2)^0[/tex] [tex]\times[/tex] [tex](1/2)^15[/tex] = 0.000030518
P(X = 1) = C(15, 1) [tex]\times[/tex] [tex](1/2)^1[/tex] [tex]\times[/tex] [tex](1/2)^14[/tex] = 0.001525879
P(X = 2) = C(15, 2) [tex]\times[/tex] [tex](1/2)^2[/tex] [tex]\times[/tex] [tex](1/2)^13[/tex] = 0.030517578
Step 2: Find the probability of selecting all specimens of one type of rock.
The probability of selecting all 10 basalt specimens = P(X = 10) = C(15, 10) [tex]\times[/tex] (1/2)^10 [tex]\times[/tex] (1/2)^5 = 0.000030518
The probability of selecting all 10 granite specimens = P(X = 0) = 0.000030518
Therefore, the probability of selecting all specimens of one type of rock (either basalt or granite) is:
P(X = 10) + P(X = 0) = 0.000030518 + 0.000030518 = 0.000061036
In summary, the PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.
estimate the product. choose a method. 81×38
(a) determine a linear function for the percent of hardwood trees y at 2600 ft in terms of the year x.
At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale?
Answer:
A. 569(0.18)
Step-by-step explanation:
sorry for the like 3 years late answer- but I hope this helps someone. <3
- EDGE 2020
Final answer:
To calculate the commission, multiply the commission rate by the sale price.
Explanation:
To calculate the commission she will receive from the sale, we can use the expression: commission = (commission rate) * (sale price).
In this case, the commission rate is 18 percent, which can be written as 0.18 in decimal form.
Therefore, the expression for the commission is: commission = 0.18 * $569 = $102.42.
So, the salesperson will receive approximately $102.42 in commission from the sale.
Using the numbers 8, 6, 4, and 2 write an expression that equals 7.
( You can not change the order of the numbers and you can only use: parentheses, divided by, multiplication, addition, and subtraction).
Explain how rays AB and AC form both a line and an angle.
Answer:
An angle is defined as two rays with a common endpoint, so CAB (or BAC) is an angle. A line is described as an infinite set of points that extend forever in either direction, which these rays also do.
What did you include in your response? Check all that apply. (You should have all of these)
Angles are rays with a shared endpoint.
Lines extend forever in either direction.
Rays AB and AC extend forever in either direction.
in a recent year, there were approximately 125 million moviegoers in a certain country. Of these, about 12/25 were ages 27-37. Find the approximate number of people ages 27-37 who attended the movies that year.
what is the interval notation for -3<x<4
The inequality is , -3<x<4. Thus, the correct interval notation for the given inequality is (-3, 4),
The question concerns how to express the inequality -3<x<4 in interval notation. Interval notation is a way to denote a range of numbers on the real line where certain numbers are included or excluded in the set.
The notation uses brackets and parentheses to indicate closed or open intervals, respectively. A closed interval means the endpoint is included, while an open interval means the endpoint is not part of the set.
In this instance, the inequality suggests that x can take any value between -3 and 4, but cannot equal -3 or 4.
Thus, we use parentheses to denote that both -3 and 4 are not contained within the interval.
Therefore, the correct interval notation for the given inequality is (-3, 4), where the round parentheses indicate that -3 and 4 are not included in the solution set.
Compute a · (b ✕ c), where a = i − 3j + k, b = 4i + j + k and c = 9i − j + 3k.
We need to find the answer of the expression [tex]a\cdot (b\times c)[/tex]
The required expression is [tex]a\cdot (b\times c)=0[/tex]
The vectors are
[tex]a=\hat{i}-3\hat{j}+1\hat{k}[/tex]
[tex]b=4\hat{i}+\hat{j}+\hat{k}[/tex]
[tex]c=9\hat{i}-\hat{j}+3\hat{k}[/tex]
Solving the term in the bracket
[tex]b\times c=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\ 4 & 1 & 1 \\ 9 & -1 & 3 \end{vmatrix}\\ =\hat{i}(3+1)-\hat{j}(4\times3-9\times1)+\hat{k}(4\times-1-9\times 1)\\ =4\hat{i}-3\hat{j}-13\hat{k}[/tex]
[tex]a\cdot (b\times c)=(\hat{i}-3\hat{j}+1\hat{k})(4\hat{i}-3\hat{j}-13\hat{k})\\ =1\cdot 4+(-3)\cdot (-3)+1\cdot (-13)\\ =4+9-13\\ =13-13=0[/tex]
So, [tex]a\cdot (b\times c)=0[/tex]
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When she subtracts 4 from both sides, 1/2x = –1/2x results. What is the value of x?
Answer: The value of x is 0.
Explanation:
Since we have given that
[tex]\frac{1x}{2}=\frac{-1x}{2}[/tex]
According to question,
If she subtracts 4 from both sides, our equation becomes,
[tex]\frac{1x}{2}-4=\frac{-1x}{2}-4\\\\\text{ by transposing the like terms on the both sides, we get}\\\\\frac{1}{2}+\frac{1x}{2}=-4+4\\\\x=0[/tex]
Hence, the value of x is 0.
A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water. 1. Solve for the y-variable. y – 12 = –3(x – 1) y – 12 = –3x + 3 y = –3x +15 2. Write the equation using function notation. f(x) = –3x +15 The tub started with ____ gallons of water.
The number of gallons of water initially present in the tub will be 15 gallons.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A tub of water is discharged at a pace of 3 gallons each moment. The condition y - 12 = - 3(x - 1) models how much water remaining, where x is time (in minutes) and y is how much water is left (in gallons).
Simplify the equation into a slope intercept form, then we have
y - 12 = - 3(x - 1)
y - 12 = - 3x + 3
y = - 3x + 15
The number of gallons of water initially present in the tub will be 15 gallons.
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If l is a line whose equation is y=5x-3, find the equation of the image of l under each of the following translations a. (x,y) --> (x, y-6) b. (x,y) --> (x+2,y)
how to solve the proportion 2/7=x/42
2/7 = x/42
multiply 42 *2 = 84
then divide by 7
84 /7 =12
x = 12
Which of the following best explains how a single nucleotide substitution can cause hemoglobin molecules to chain together instead of forming the appropriate protein product?
The mutation causes the removal of an amino acid, which results in a different protein product
. The mutation causes the same amino acid to be repeated multiple times in the protein product, which results in a linear protein structure.
The mutation causes the wrong amino acid to be incorporated into the protein product, which results in improper protein folding.
The mutation causes the protein product to be lengthened due to an increased number of amino acids being incorporated.
Cynthia ran 4 laps in 40 min. What is the rate of number of laps to minutes?
The answer is 1:10 because 4 to 40,
there is 1 for every 10.
So in fractional form your answer is 1/10.
The rate is 0.1 laps in 1 minute, or 1//10, 1 lap in 10 minutes.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
It is possible to simplify mathematical formulas by merging and grouping related terms. This makes the term understandable.
Given,
Cynthia ran 4 laps in 40 min.
ratio of laps to minutes is
4:40 = 1:10
1/10 = 0.1/1
so 0.1 laps in 1 minute or 1 lap in 10 minutes.
Hence the rate is 1 lap in 10 minutes: 1/10;
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The stock market decreased by 135 points during a 5 day week.
What was the average daily change in the market for that week?
0.006 is greater than 0.1
Is this true?
Which is the larger unit, a degree or a radian? Are they very close in size, or very different
Hector is competing in a 42 mile bicycle race. He has already completed 18 miles of the race and is traveling at a constant speed of 12 miles per hour when Wanda starts the race. Wanda is traveling at a constant speed of 16 miles per hour.
Write and solve an equation to find when Wanda will catch up to hector
Answer:
Step-by-step explanation:
Alarm for 20 yards of fencing he used fit 5.9 yards to surround one flower garden and 10.3 yards to surround another garden write the amount remaining as a fraction in. Simplest form
what is 22119 rounded to the nearest hundredth
Answer:
22119 to the nearest hundred is 22100
Step-by-step explanation:
When rounding the number to the nearest hundred. Follow the given rules:
When rounding to the nearest hundred, look at the TENS DIGIT of the number.
If that digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.In other words if the number at the tenth position is less than 5 then we will convert all the digits after the hundred to zeros
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.In other words if the number at the tenth position is greater than or equals to 5 then we will add one to the hundred and convert all digits after the hundred to zeros.Now look at the given number which is: 22119
The number at the hundredth position is 1.
And the number at the tenth position is also 1.
Then according to the defined rule if the number at the tenth position is less than 5 then we will convert all the digits after the hundred to zeros.
So, for the given number (22119) we just convert all digits after the hundred to zeros
Therefore, 22119 to the nearest hundred is 22100...
Suppose that 18 red beads, 12 yellow beads, eight blue beads, and 12 black beads are to be strung in a row. how many different arrangements of the colors can be formed
The number of different arrangements of the colors that can be formed will be 5.13498 x 10²⁶.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
Assume that 18 red globules, 12 yellow dabs, eight blue dots, and 12 dark dots are to be hung in succession.
The total number of bread will be calculated as,
Total bread = 18 + 12 + 8 + 12
Total bread = 50
Then the number of different arrangements of the colors that can be formed will be given as,
⇒ 50! / (18! x 12! x 8! x 12!)
Simplify the expression, then we have
⇒ 50! / (18! x 12! x 8! x 12!)
⇒ 5.13498 x 10²⁶
The number of different arrangements of the colors that can be formed will be 5.13498 x 10²⁶.
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The number of arrangements is: [tex]\(\frac{{50!}}{{18!12!8!12!}}\)[/tex]
To calculate the number of different arrangements of the beads, we can use the formula for permutations of multiset:
[tex]\(\frac{{n!}}{{n_1!n_2!n_3!n_4!}}\)[/tex]
where:
n is the total number of items to arrange,
n_1, n_2, n_3, n_4 are the numbers of indistinguishable items of each type.
For our beads, we have:
Total beads n = 18 (red) + 12 (yellow) + 8 (blue) + 12 (black) = 50 beads,
n_1 = 18 (red),
n_2 = 12 (yellow),
n_3 = 8 (blue),
n_4 = 12 (black).
So, the number of arrangements is: [tex]\(\frac{{50!}}{{18!12!8!12!}}\)[/tex]
This value gives us the total number of different color arrangements possible when stringing these beads in a row.
The table below shows two equations:
Equation 1 |2x − 3| + 5 = 4
Equation 2 |5x + 3| − 10 = 3
Which statement is true about the solution to the two equations? (1 point)
Equation 1 and equation 2 have no solutions.
Equation 1 has no solution and equation 2 has solutions x = 2, −3.2.
The solutions to equation 1 are x = 1, 2 and equation 2 has no solution.
The solutions to equation 1 are x = 1, 2 and equation 2 has solutions x = 2, −3.2.
Middle school has 450 students vanlue school has 600 students which school has a greater percent of girls explain
PLEASE ANSWER THIS QUICKLY! THANK YOU!
Which equation is an identity?
7m – 5 = 8m + 7 – m
3w + 8 – w = 4w – 2(w – 4)
9 – (2v + 3) = –2v – 6
–3y + 3 = –3y – 6
Please explain your answer.
Jennifer is playing with a die that has six faces. What is the likelihood that she will roll a four?
A) Certain
B) Likely
C) Unlikely
D) neither likely nor unlikely
I know 100% that isnt right I did a test it is NOT D
Given three collinear points, which of the following is true?a.. There is exactly one plane that contains all three points. b..They form a triangle. c.They are not coplanar. d.They are contained in multiple planes.
Option: d is the correct answer
d. They are contained in multiple planes.
Step-by-step explanation:Since, the three points are collinear.
This means that there is a line which pass through these three given points and as we know that a line always lie in a plane so all the three points will be coplanar and there may be multiple planes which contain a line.
Also, a triangle is formed with the help of three non-collinear points.
Hence, the correct option is:
Option: d
How many up/down runs are there in this data? observations 1 2 3 4 5 6 7 8 9 10 # of defects 5 2 3 5 4 3 2 1 2 4?
A 20 inch flat panel computer moniter is on sale for 249.99.it was reduced $80.00 from the original price. find the percent reduction in price
The percent reduction in the price was approximately 32%.
What are percentages?Percentages are similar to fractions, but the whole part of the fraction is always set as constant, which is always 100.
To convert a fraction to a percentage, we multiply it by 100.
To convert a percentage to a fraction, we divide it by 100.
How to solve the question?In the question, we are given that a 20-inch flat panel computer monitor is on sale for 249.99., and it was reduced by $80.00 from the original price.
We are asked to find the percent reduction in price.
The price reduction = $80.00.
The original price = $249.99.
Therefore, the fraction of reduction in the price can be shown as the ratio of the reduction in the price to the original price, that is, the
Fraction = $80.00/$249.99 = 0.320013.
To convert a fraction to a percentage, we multiply it by 100.
Therefore, the percentage of reduction = 0.320013 * 100% = 32.0013% ≈ 32%.
Therefore, the percent reduction in the price was approximately 32%.
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