Answer:
Explained below.
Step-by-step explanation:
The random variable X is defined as the number of stars in a given volume of space.
[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]
The probability mass function of X is:
[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
(7)
Compute the probability of exactly two stars in 16 cubic light-years as follows:
[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]
(8)
Compute the probability of three or more stars in 16 cubic light-years as follows:
[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]
(9)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.
(10)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in t cubic light years there will be, [t × (1/16)] stars.
which is the product of 7/9 and 6 in a fraction number
Answer:
4 2/3
Step-by-step explanation:
7/9 multiplied by 6/1 = 42/9
Simplify: 14/3
Turn it into a mixed number: 4 2/3
Use the information given to answer the question
An artist prints T shirts to sell at a fair for $14 each
• The artist has some initial T shirts ready to sell and works for h hours more, printing a constant number of T-shirts every
hour
• The expression 14(12h + 30) represents the amount, in dollars, the artist will earn selling all the T-shirts.
Part A
How many T shirts did the artist have initially?
Find the equation of the line
passing through the points. (5, 2) and (10, 6).??
Guys I need help I'm giving brainlist also show your work for me please this is my last math problem help
Answer:
.
Step-by-step explanation:
Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = p(1 - p)n-1 (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents
Answer:
(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.
(c) The probability that n ≥ 4 is 0.018.
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.
Step-by-step explanation:
We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.
Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,
Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
So, the probability distribution of the geometric distribution is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
where, p = probability that the residents are of Hawaiian ancestry = 74%
(b) The probabilities that n = 1, n = 2, and n = 3 is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]
P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74
P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192
P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050
(c) The probability that n ≥ 4 is given by = P(n ≥ 4)
P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)
= 1 - 0.74 - 0.192 - 0.050
= 0.018
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)
We know that the mean of the geometric distribution is given by;
Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]
= [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).
Graph the line y=−3x+b if it is known that the graph goes through point:
b
B(5, 2)
Answer: y=-3x+17
b = 17
Plssssss answer thjs quet
Answer:
I’m. Not really good at math but I think its b
Step-by-step explanation:
Which expression is the result of factoring the expression below by taking out its greatest common factor?
4x^2+ 16x – 4 = ?
Answer:
[tex]4(x^2+4x-1)[/tex]
Step-by-step explanation:
The greatest common factor is 4
[tex]4(x^2+4x-1)[/tex]
Tyrell filled his 290
gallon pool with water
in 5 hours. How many
gallons per hour did
he use?
Which is bigger 0.78 or 0.708
Answer:
0.78
Step-by-step explanation:
Answer:
0.78
Step-by-step explanation:
because...
0.78 = 0.780
so,
0.780 > 0.708
have a nice day! <3
pls help me!!! i can’t get it right
Answer:
24√3 square units
Step-by-step explanation:
The side length of a regular hexagon is 2/√3 times the length of the apothem. For an apothem of 2√3, the side length is ...
s = (2/√3)(2√3) = 4
The perimeter P of the hexagon is 6 times the side length, so is 6×4 = 24.
The area is given by ...
A = 1/2Pa
where P is the perimeter and 'a' is the apothem.
A = 1/2(24)(2√3) = 24√3
The area of the hexagon is 24√3 square units.
_____
A hexagon can be divided into 6 congruent equilateral triangles. The apothem will be the altitude of one of those, so will divide the triangle into two triangles with angles 30°, 60°, and 90°. The ratios of the side lengths of such a triangle is something you might want to remember: 1 : √3 : 2. The altitude corresponds to the "√3" side, and the side length of the equilateral triangle corresponds to the "2" side. That is, we have the proportion ...
apothem : hexagon side = √3 : 2
Multiplying by 2 gives the actual values in the hexagon of this problem:
apothem : hexagon side = 2√3 : 4
Sophia has fabric to make banners for school she needs 1 and 1/4 yards of fabric for each Banner she has made 4 banners and has 2 and a 1/2 yards of fabric left over how much fabric did she begin with
Answer: 7 and a 1/2
Step-by-step explanation: 1 and 1/4 times4 = 5 plus 2 and a 1/2 = 7 and a 1/2
what are the domain and range for each of the following functions
Answer:
a.) DomainL: -2 ≥ x < 1 Range: 1 ≥ y < 2
b.) DomainL: -2 > x < 2 Range: -2 > y < 2
Step-by-step explanation:
look up what the open and closed dots mean
understand how to determine values on the y or x axis
how to solve this problem 3x+5=2x+1
Answer:
Step-by-step explanation:
Simplifying
3x + 5 = 2x + 1
Reorder the terms:
5 + 3x = 2x + 1
Reorder the terms:
5 + 3x = 1 + 2x
Solving
5 + 3x = 1 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
5 + 3x + -2x = 1 + 2x + -2x
Combine like terms: 3x + -2x = 1x
5 + 1x = 1 + 2x + -2x
Combine like terms: 2x + -2x = 0
5 + 1x = 1 + 0
5 + 1x = 1
Add '-5' to each side of the equation.
5 + -5 + 1x = 1 + -5
Combine like terms: 5 + -5 = 0
0 + 1x = 1 + -5
1x = 1 + -5
Combine like terms: 1 + -5 = -4
1x = -4
Divide each side by '1'.
x = -4
Simplifying
x = -4
Answer:
x = -4
Step-by-step explanation:
To solve the given equation, we must find a value of x that satisfies the equation.
3x + 5 = 2x + 1
Subtract 2x from both sides.
x + 5 = 1
Subtract 5 from both sides.
x = -4
So the value of x that satisfies the equation is -4. So the solution to the equation would be x = -4.
I hope you find my answer and explanation to be helpful. Happy studying.
Eqiuvelent Ratio for 23:37
Lisa paid 45.30 for 15.9 gallons of gasoline.what was the cost per gallon, rounded to the nearest hundreath
Answer:
About $2.85 per gallon
Step-by-step explanation:
We can set up a proportion [tex]\frac{45.3}{15.9}[/tex]=[tex]\frac{x}{1}[/tex] we can then cross multiply, getting 15.9x=45.3. When you divide you get about $2.85
50 apples cost $25.how much would 75 apples cost
Answer:
150
Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150
3. The average rate of change of the function f(x) on the interval -2 is less than or equal to X which is less than or equal to 4 is -3.5. If f (4)=11 then which
of the following is the value of f(-2)?
(1) -11
(3) 21
(2) -21
(4) 32
The value of the function f(x) at x = - 2 is equivalent to 32.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is that the average rate of change of the function f(x) on the interval -2 is less than or equal to [x] which is less than or equal to 4 is -3.5.
In the range of {- 2 ≤ x ≤ 4}, the rate of change of f(x) is -3.5. This means we can write -
r = {f(4) - f(-2)}/(4 + 2)
f(4) = 11 and [r] = - 3.5. So, we can write -
- 3.5 = {11 - f(-2)}/6
11 - f(-2) = -3.5 x 6
11 - f(-2) = - 21
f(-2) = 11 + 21
f(-2) = 32
Therefore, the value of the function f(x) at x = - 2 is equivalent to 32.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
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Please help me with this geometry homework
Answer:
18
Step-by-step explanation:
We know that line FH total length is 49. We also know that the length of line GH is 31.
To find FG, all we need to do is subtract 49-31 to find the length of FG.
Line FG total length is 18.
Marco spent $85.43 on a new pair of
shoes, $21 on a t-shirt, and $7.84 on a
pair of socks. If he gave the sales clerk
$120, how much change should he
receive?
Answer:
5.73
Step-by-step explanation:
Answer:
He should have $5.73 as change
Step-by-step explanation:
First add 85.43 with 21 and 7.84 and then do 120 - 114.27.
Help please it’s urgent
Answer:
D
Step-by-step explanation:
We can use d to find out how much x equals which therefore would solve the rest of the equation. We also know that half of a parallelogram= 180 degrees so we know that it wouldn't be c and it wouldn't be any of the others either.
Hope this helps!
what is the least common denominator of 5/12 and 4/18
Answer:
36
Step-by-step explanation:
Write an equation for the description.
Tanmayi wants to raise $150 for a school fundraiser. She has raised $120 so far. How much more does she
need to reach her goal? Let m be how much more is needed.
Plzzzz hellpppp
Tanmayi will need $30 more to reach her goal.
$120 + n = $150
$150 - $120 = 30
n = 30
The perimeter of a rectangular room is 60 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Select all of the equations below that could model this situation.
2(x+y)=60
2x+2y=60
x+2y=60
2x+y=60
x+y=60
Answer:
Step-by-step explanation:
2(x+y)=60
2x+2y=60
The second is the same as the 1st but with the distribution
perimeter formula: P=2(W+L)
We can distribute .Then P = 2W+2L
i’ll mark brainliest!!
The answer is 50
Hope this helps!
The ratio of girls to boys in a school simplifies to 2:3. How many boys are there if there are 345 students in the school?
Answer:
230
Step-by-step explanation:
You should multiply 345 by 2/3 or you can divide 345 by 3, which equaks 115 and then multiply 115 by 2 which equals 230.
The number of boys in the school is 207.
Given
The ratio of girls to boys in a school simplifies to 2:3.
We need to find out how many boys are there if there are 345 students in the school.
What are ratios?The ratio gives us an idea between two quantities.
It is denoted by a:b
Example:
The ratio of apple and mango in the basket is 1:2.
The total number of fruits is 12.
Apple = [ 1 / (1+2) ] x 12 = (1/3) x 12 = 4
Mango = [ 2/(1+2) ] x 12 = (2/3) x 12 = 2 x 4 = 8
We have,
Total number of students = 345
The ratio of girls to boys = 2:3
The number of boys :
= [ 3 / (2+3) ] x 345
= [ 3/5 ] x 345
= 3 x 69
= 207
Thus the number of boys in the. school is 207.
Learn more about ratios here:
https://brainly.com/question/1504221
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Solve the following system of equations.
(15 Points)
x + 3y = -5 & 5y - 10 = -20x
Answer:
( 1 ; -2 )
Step-by-step explanation:
x + 3y = -5..............1
5y - 10 = -20x........2
x = -5 - 3y..............3
5y - 10 = -20( -5 - 3y)
5y - 10 = 100 + 60y
-55y = 110
y = -2
x = 1
what statement makes the open sentences 12+3x= 30 true hurry!!!!
Answer: X=6
you would do 30 - 12 witch equals 18
than you would do 18 divided by 3 witch is 6 so it is x = 6
Felix decides to establish a budget. He will spend $700 for rent, $325 for food, $420 for child care,
$182 for transportation, $300 for other expenses, and he will put the remainder in savings. If his
monthly take-home pay is $2025, find his savings.
Answer:
98$ in savings
Step-by-step explanation:
If you do all the spending combined you would do $700+$325=$1025 $420+$182=$602 add those = $1627+$300=$1927 if his monthly take-home pay is $2025 you would have to do $2025-$1927=$98 remanding.
average cost,average
revenue, average profit
