The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:
[tex]E(X) = 5.25, Var(X) = 0.5966[/tex]P(X < 6) = 0.9545P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.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]
The mean and the variance are:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]
We have that:
5 + 7 = 12 rocks, which means that [tex]N = 12[/tex]
9 are chosen, which means that [tex]n = 9[/tex]
7 are granite, which means that [tex]k = 7[/tex]
Question a:
[tex]E(X) = \mu = \frac{9\times7}{12} = 5.25[/tex]
[tex]Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966[/tex]
Thus:
[tex]E(X) = 5.25, Var(X) = 0.5966[/tex]
Question b:
Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:
[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)[/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 = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591[/tex]
[tex]P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773[/tex]
[tex]P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181[/tex]
Thus
[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545[/tex]
So P(X < 6) = 0.9545.
Question c:
5 of basaltic and 4 of granite: 0.1591 probability.
7 of granite is P(X = 7), in which
[tex]P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455[/tex]
0.1591 + 0.0455 = 0.2046, thus:
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
A similar question is found at https://brainly.com/question/24008577
find the measure of the indicated angle
Answer:
Step-by-step explanation:
36°
gordan is twice as old as tony was when gordan was as old as tony is now. combined age of gordan and tony is 112 years. how old are gordan and tony now?
Answer:
Answer
Tony:48
Gordan :64
Step-by-step explanation:
[tex]\begin{array}{c|c|c}Age&Gordon&Tony\\------------------&-------&-------\\now&g&t\\when\ gordan\ was\ as\ old\ as\ tony\ is\ now&t(=g-g+t)&t-g+t=2t-g\\\end{array}\\\\\\\\\left\{\begin{array}{ccc}g&=&2*(2t-g)\\g+t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}3g&=&4t\\g+t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}g&=&\dfrac{4}{3}\\\dfrac{7}{3} t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}t&=&48\\g&=&64\\\end {array}\right.\\[/tex]
Proof:
16 years ago, Gordan was 48 and Tony 32.
64=2*32
64+48=112
for the vector (-9,3), find 1/2V, -V, and 4V
9514 1404 393
Answer:
1/2V = <-9/2, 3/2>-V = <9, -3>4V = <-36, 12>Step-by-step explanation:
The scalar multiplier multiplies each of the components.
1/2V = <-9×1/2, 3×1/2> = <-9/2, 3/2>
-V = <(-9)(-1), (3)(-1)> = <9, -3>
4V = <-9×4, 3×4> = <-36, 12>
Solve each equation for the given variable
1.3(2x+4)=54
2.4+(5x+5)54
Please
Answer:
1. x = 7
2. 270x+274
Explanation:
see attached filed for step by step reasoning
Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2
are : 30 / 120 / 150 / 330
and
45 / 60 / 105 / 135
What are the correct solutions?
Answer:
henc X = 30°
Step-by-step explanation:
here is the proof
when X=30° then
sin2x = sin2×30
=sin 60°
= √3/2
or else,
putting value of X = 30° then
sin2x= 2sinxcosx
= 2×sin30°×cos30°
=2×1/2×√3/2
= 2√3/4
= √3/2
hence proved sin2x= √3/2.
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
What’s the distance between (4,-9) and (5,3)
Answer: Distance = √145
Concept:
Here, we need to know the concept of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Given information
(x₁, y₁) = (4, -9)
(x₂, y₂) = (5, 3)
Given formula
[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the formula
[tex]Distance = \sqrt{(5-4)^2+(3+9)^2}[/tex]
Simplify values in the parentheses
[tex]Distance = \sqrt{(1)^2+(12)^2}[/tex]
Simplify exponents
[tex]Distance = \sqrt{1+144}[/tex]
Simplify by addition
[tex]Distance = \sqrt{145}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\boxed {\boxed {\sf \sqrt {145} \ or \ 12.04}}[/tex]
Step-by-step explanation:
The distance between 2 points is calculated using the following formula.
[tex]d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2)[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
We know the two points are (4, -9) and (5,3). If we match the values of the points and the coordinating variable, we see that:
x₁ = 4y₁= -9 x₂ = 5 y₂ = 3Substitute the values into the formula.
[tex]d= \sqrt { ( 5 -4)^2 + ( 3 --9)^2[/tex]
Solve inside the parentheses.
(5-4)= 1 (3 --9) = (3+9) = 12[tex]d= \sqrt {(1)^2 + (12)^2}[/tex]
Solve the exponents.
(1)² = 1 *1 = 1 (12)² = 12 * 12 = 144[tex]d= \sqrt{ 1+144}[/tex]
Add.
[tex]d= \sqrt{145[/tex]
Take the square root.
[tex]d=12.04159458[/tex]
Let's round to the nearest hundredth. The 1 in the thousandth place tells us to leave the 4 in the hundredth place.
[tex]d \approx 12.04[/tex]
The distance between the 2 points is √145 or approximately 12.04.
I need help with this question please
Answer:
Step-by-step explanation:
30t - 5t² = 10
5t² - 30t + 10 = 0
t = [30 ± √(30² - 4 ⋅ 5 ⋅ 10)] / [2 ⋅ 5]
= [30 ± √700] / 10
= [30 ± 10√7] / 10
= 3 ± √7
≈ 0.35 seconds and 5.65 seconds
5. Determine the formula for the following arithmetic sequence: 4, 7, 10, 13, ...
Answer:
[tex]a_{n}[/tex] = n + 3Step-by-step explanation:
Each number increases by 3. Therefore, n+3.
Malika is 1.45 meters tall. At 10 a.m., she measures the length of a tree's shadow to be 32.25 meters. She stands 27.5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
If the length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m
Given:
Malika height=1.45 meters
Length =32.25 meters
Width =27.5 meters
Height of the tree=x
Proportion:
1.45 : 32.25 :: x : 27.5
Now let determine the height of the tree
32.25-27.5/1.45=32.25/x
4.75/1.45=32.25/x
Cross multiply
4.75x=32.25×1.45
4.75x=46.7625
Divide both side
x=46.7625/4.75
x=9.84m
Inconclusion if the length of a tree's shadow is 32.25 meters. The height of the tree to the nearest hundredth of a meter will be : 9.84m
Learn more here:
https://brainly.com/question/23966984
Solve each equation.
1) -133 = 7(-3 + 4v)
Answer:
-4
Step-by-step explanation:
-133 = -21 + 28v
-133 + 21 = 28v
-112 = 28v
v = -4
What is the value of log,1252
PERE
3
5
Ο ΟΟΟ
15
Mark this and return
Save and Exit
Next
look at the image for the question
Volume = l × b × h
Length = 7m
Breadth = 7m
Height = 9m
Volume = 7×7×9
441m³
Must click thanks and mark brainliest
*Will Give Brainliest* Find the length of side xx in simplest radical form with a rational denominator.
Answer:
10√2 = x
Step-by-step explanation:
Since the figure is a square, all angles of the square are equal to 90 degrees
The diagonal also bisects the 90 degrees into 2 45 degrees
So you can use special triangles to find x
Ratio of sides of a 45-45-90 triangle is 1: 1: √2
10: 10: 10√2
you can also use pythagorean theorem
10^2 + 10^2 = x^2
100 + 100 = x^2
200 = x^2
10√2 = x
Answer:
12
Step-by-step explanation:
12=12
IM DOING THIS TO GIVE OTHER GUY BRAINLIEST CUZ HE ALSO HELPED ME GET IT RIGHT
PLEASE HELP!! WHOEVER HELPS FIRST AND GETS IT CORRECT GETS BRAILIEST!!
Answer:
16 rotations
Step-by-step explanation:
500/32 = 15.625
15.625 rounded = 16
hope it helps!
Need help answer plz help
Answer:
BONANA MY NANA
Step-by-step explanation:
Approximately how many times greater is
7.4 x 10^8
than
2.5 x 10^7
0.3
3
30
300
Answer:
30
Step-by-step explanation:
To compare the numbers, divide the first number by the second number.
(7.4 x 10^8)/(2.5 x 10^7) = (74 x 10^7)/(2.5 x 10^7) = 74/2.5 = 29.6
Answer: 30
Which polynomial expressions are in standard form?
x2 - x - 72
(x + 3)(x - 7)
-8x + 56
05
5x(2x)
Answer:
PLATO ANSWER
Step-by-step explanation:
x2 − x − 72
-8x + 56
5
those are the correct answers
rewrite the following statements into algebraic expression
the sum of x and y
5 is subtracted from y
How to calculate pvalue
Answer:
If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.
Answer:
The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). The p-value for: a lower-tailed test is specified by: p-value = P(TS ts | H 0 is true) = cdf(ts)
Step-by-step explanation:
May this answer is helpful for you
Find a formula for a function f that satisfies the following conditions. lim x→±∞ f(x) = 0, lim x→0 f(x) = −∞, f(2) = 0 lim x→7− f(x) = ∞, lim x→7+ f(x) = −∞
9514 1404 393
Answer:
f(x) = (x -2)/(x²(7-x))
Step-by-step explanation:
The horizontal asymptotes of zero mean the denominator degree needs to be greater than the numerator degree. The zero at x=2 means (x-2) will be a factor in the numerator. The limit at x=0 means there will be a factor of x² in the denominator. Since the numerator term is negative at x=0, the signs of the terms so far do not need modification.
The vertical asymptote at x=7 means there will be a factor of (x-7) in the denominator. In order for the limits to be correct, it must have a negative sign:
-(x -7) = (7 -x)
Then the function with these characteristics can be written ...
f(x) = (x -2)/(x²(7 -x))
A rectangular prism has volume 1,088 ft3 and height 8 ft. What is the area of the base of the prism?
a. 146 ft2
c. 136 ft2
b. 1,080 ft2
d. 1,096 ft2
We know
[tex]\boxed{\sf Volume=Area\:of\:Base\times Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{Volume}{Height}[/tex]
[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{1088}{8}[/tex]
[tex]\\ \sf\longmapsto Area\;of\:base=136ft^2[/tex]
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
What’s the answer to this?
Answer:
[tex]f(3x)=9x^2-3[/tex]
Step-by-step explanation:
One is given the following function:
[tex]f(x)=x^2-3[/tex]
One is asked to evaluate the function for ([tex]f(3x)[/tex]). Substitute ([tex]3x[/tex]) in place of ([tex]x[/tex]) then simplify. Remember that a number raised to an exponent is the same as that number times itself the number of times that the exponent indicates. One can apply this logic here while simplifying,
[tex]f(x)=x^2-3[/tex]
[tex]f(3x)=(3x)^2-3[/tex]
[tex]f(3x)=(3x*3x)-3[/tex]
[tex]f(3x)=(9x^2)-3[/tex]
[tex]f(3x)=9x^2-3[/tex]
Which of the following is an example of a sample that would NOT be random?
A. Going through the list and choosing the first 25 names on the list.
B. Writing each student’s name on a card and then drawing out 25 names without looking.
C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.
D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Answer: D
"Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group."
Step-by-step explanation:
You are sampling an equal amount of boys and girls since your getting an equal sample of each gender. (Not random)
The option that is not a random sample is:
Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Option D is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a population given.
Each item has an equal probability of being chosen.
We have,
We will see which option is a sample that is not random.
A. Going through the list and choosing the first 25 names on the list.
Going through the list means every name has an equal chance of getting chosen.
This is a random sample.
B. Writing each student’s name on a card and then drawing out 25 names without looking.
Since we are drawing out 25 names without looking, all the students' names have an equal chance of getting drawn.
This is a random sample.
C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names.
Choosing one student at random means every student has an equal chance of getting chosen.
This is a random sampling.
D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
The students are separated into boys and girls and the sample is chosen from each group so we are selecting the sample from the separated group.
This can not be a random sampling.
Thus,
The option that is not a random sample is:
Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Option D is the correct answer.
Learn more about random sampling here:
https://brainly.com/question/12719656
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A/An is a type of blood cell that's also called a red blood cell. a) Jeukocyte O b) thrombocyte c) plasma d) erythrocyte
Answer:
opt. (d)
Step-by-step explanation:
red blood cell, also called erythrocyte, cellular component of blood, millions of which in the circulation of vertebrates give the blood its characteristic colour and carry oxygen from the lungs to the tissues.
What is the conjugate of 3 + 6i?
A -3 - 61
B 3 - 6i
C 3 + 6i
D 9i
Answer:
C.3-6
Step-by-step explanation:
Every complex number has a complex conjugate.
Examples is a+bi the conjugate is a-bi,if your adding the two conjugate its going to be 2a and if your subtracting the result is 2bi.And if multiplied it is seen as complex number which are a²+b²
The sum of a number and its inverse is 3 29 / 52. Find the number?
Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
1) How much money does mila take as loan from the bank?
a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000
Answer:
Scheme a 45000 is the answer
12/1,000 into decimal
0.012 is the answer!
I hope this helps you out! :D
[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]
1000 has 3zeros hence decimal will go 3 points left[tex]\\ \sf\longmapsto 0.012[/tex]
More:-
[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]
