Answer:
-6x+3
Step-by-step explanation:
Astronomers treat the number of stars X in a given volume of space as Poisson random variable. The density of stars in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years, on average. NOTE: Light-years is a distance measure. 7. What is the probability of exactly two stars in 16 cubic light-years? 8. What is the probability of three or more stars in 16 cubic light-years? 9. How many stars would be expected in 4 cubic light years? 10. How many stars would be expected in t cubic light years? 11. How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95? HINT: let `t' represent the unknown region of space, then nd the `t' that gives you the relevant probability.
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.
7.5 more than the quotient of h and 3 is w
Answer: h/3 + 7.5 = w
An AutoCAD drawing has a scale of inches to 3 ft. If a piece of a bridge measures 17 feet, how long is that piece in the AutoCAD printout?
Answer:
D
Step-by-step explanation:
Answer:
2.83 inches
Step-by-step explanation:
Let y equal the length of the drawing in inches. Use a proportion to solve for the missing length.
What is the expanded form of (a + b)^2?
Answer:
[tex] {a}^{2} + 2ab + {b}^{2} [/tex]
Answer:
(a + b) × (a + b)
Step-by-step explanation:
(a + b)²
(a + b) × (a + b)
A jar that contains quarters and dimes is worth $7.15. If there are a total of 40 coins,
how many of each type of coin is there?
Answer:
21 quarters and 19 dimes
Step-by-step explanation:
Create a system of equations where q is the number of quarters and d is the number of dimes.
0.25q + 0.1d = 7.15
q + d = 40
Solve by elimination by multiplying the bottom equation by -0.25
0.25q + 0.1d = 7.15
-0.25q - 0.25d = -10
Add them together and solve for d:
-0.15d = -2.85
d = 19
Then, plug in 19 as d into the second equation to solve for q:
q + d = 40
q + 19 = 40
q = 21
So, there are 21 quarters and 19 dimes
Answer:
21 Quarters, 19 Dimes.
Step-by-step explanation:
21 x .25 = 5.25
19 x .10 = 1.90
5.25 + 1.90 = 7.15
If a 25 kg car Accelerates at a speed of 100ms what will the force of the car be
Answer:
force = 100 m/s/25 s = 4 m/s^2
multiply express your anwser in simplest form
Answer:
1/6
Step-by-step explanation:
9: 9,18,27,36,45,54,63,72,81,90
10: 10,20,30,40,50,60,70,80,90,100
Since, 90 is the LCM of 9 and 10 that turns into your denominater then your equation turns into this...
5/90 x 3/90
The denomineter stays the same so you get 90 then 5 x 3 equals 15 so you get 15 and in total that gives you 15/90. Divide the top and bottom by the greatest number that will divide both numbers exactly which gives you 1/6
HOPE THIS HELPED :D
12x ÷ 4y (if x = -8 and y = 3)
Answer:
- 8
Step-by-step explanation:
Step 1:
12x ÷ 4y Equation
Step 2:
12 ( - 8 ) ÷ 4 ( 3 ) Input x and y
Step 3:
- 96 ÷ 12 Multiply
Answer:
- 8 Divide
Hope This Helps :)
Solve.
2x + 4 3
B) x < 3
B) x 1/3
D) x < 1/3
Answer:
c
Step-by-step explanation:
what is -1 as a decimal
Answer:
-1.0
Step-by-step explanation:
The total sales tax in a certain city is 8.75%. The state sales tax rate is 7.25%, and the county adds an additional sales tax of 0.5%. How much in sales tax is added by the city?
a.) 0.1%
b.) 0.25%
c.) 1%
d.) 2.5%
Answer:
C.1%
Step-by-step explanation:
some helps plssss i need help
Answer:
Yess
Step-by-step explanation:
If you multiply all the numbers together you get 39690000. And the square root of that number is 6300. So it is a perfect square. If you did 6300² = 39690000.
What is the slope of the line through the points (-4, 2) and (-16, -6)
Answer:
[tex]m = \frac{2}{3}[/tex]
Step-by-step explanation:
Use the following equation:
slope [tex](m) = \frac{y^2 - y^1}{x^2 - x^1}[/tex]
Set the variables with the points:
[tex](x_1 , y_1) = (-16 , -6)\\(x_2 , y_2) = (-4 , 2)\\[/tex]
Plug in the corresponding numbers to the corresponding variables in the equation:
[tex]m = \frac{2 - (-6)}{-4 - (-16)}[/tex]
[tex]m = \frac{2 - (-6)}{- 4 - (-16)} = \frac{2 + 6}{16 - 4} = \frac{8}{12}[/tex]
slope [tex]m = \frac{8}{12}[/tex] [tex]= \frac{2}{3}[/tex] (simplified)
~
Answer:
2/3
Step-by-step explanation:
The area of a rectangle is x²-4x-21
Write down an expression for the width and the length of
the rectangle.
Answer:
Step-by-step explanation:
Area of rectangle= Length x Width
and the given Area is a quadratic expression
A=[tex]x^{2} -4x-21[/tex]
We use the factorization method so,
we need 2 numbers that when multiplied we get -21 and when we add/subtract we get -4 so,
A=[tex]x^{2} -7x+3x-21[/tex]
now we simplify,
A=[tex]x(x-7)+3(x-7)[/tex]
A=[tex](x-7)(x+3)[/tex]
This looks familiar doesn't it, when we write the formula for the area of rectangle its
A= Length x Width and the equation here shows that
A= [tex](x-7)(x+3)[/tex]
So the expression for the length is x-7 and
the expression for the width is x+3 i think u have missed maybe some information on the question as such that the perimeter might be missing because length could be either x-7 or even x+3 same goes for width maybe someone can correct me if im wrong
Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.
Answer:
x= 6, -7
Step-by-step explanation:
Question 9 of 10 What is the scale factor of ABC to DEF?
9x6=9x(4+ )
=( X4)+(9x )
= +
=
idkStep-by-step explanation:
Joseph and Wendy were catching tadpoles. At first Wendy caught nine times three more than Joseph caught. Joseph was upset and released half of Wendy ’s tadpoles, and then six times as many as Joseph caught swam away. After all of this, Wendy only had three tadpoles left. How many tadpoles did Joseph catch?
Answer:
7
Step-by-step explanation:
Step 1: translate the given word problem into solvable algebraic equation.
Let "t" represent the number of tadpoles Joseph caught.
"Wendy caught nine times three more than Joseph caught" can be expressed as 9(t + 3)
Number of Wendy's tadpole = [tex] 9(t + 3) [/tex]
Given that half of Wendy's tadpole and also 6 times Joseph's tadpoles swarm away leaving Wendy with only 3, the following equation can be written:
[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]
Step 2: solve for t using the equation created.
[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]
Add 6t to both sides
[tex] \frac{9(t + 3)}{2} - 6t + 6t = 3 + 6t [/tex]
[tex] \frac{9(t + 3)}{2} = 3 + 6t [/tex]
Multiply both sides by 2
[tex] \frac{9(t + 3)}{2}*2 = (3 + 6t)*2 [/tex]
[tex] 9(t + 3) = 2(3 + 6t) [/tex]
[tex] 9t + 27 = 6 + 12t [/tex]
Collect like terms
[tex] 9t - 12t = 6 - 27 [/tex]
[tex] -3t = -21 [/tex]
Divide both sides by -3
[tex] t = 7 [/tex]
Joseph caught 7 tadpoles
i need help on this stuck on it
Answer:
5=148 and 8=32
Step-by-step explanation:
For this equation we know since the lines are parelle that they will produce the same angle degrees.
so 2,4,6,and 8 are all 32
if we subtract 180 (the dregree of a stright line) from 32 we get 148
so 148 is for 1,3,5, and 7
Is this a function or not a function? (Picture)
At sunrise on monday the temperature in new haven, ct is -5f. By noon the temperature is 14 degrees warker and by sunset the temperature is 9 degrees colder than it was noon
Answer:
0 degrees faranhiet
Step-by-step explanation:
when you add 14 and -5 you get 9 then the question says 9 degrees cooler so that would translate to the problem 9 - 9 which you get zero.
Odd number between 3 and 19
Answer:
11, there both 8 away so its right in ze middle :D
Step-by-step explanation:
Finding Decimal Products Which statements are true for the product of 0.2 and 0.2? Check all that apply. The product will be smaller than both the factors. ✓ There will be a zero in the tenths place, There will be a zero in the hundredths place. The answer is 0.4. ✓ The answer is 0.04.
Answer:
0 The product will be smaller than both the factors.
0 There will be a zero in the tenths place.
0 The answer is 0.04.
find the original price given the total amount and the tip rate if the total amount is $51.84 and the tip is 20%
Answer: $41.472 or $41.50
Step by step solving: First convert 20% to a decimal which is .20 now multiply that by $51.84 which equals 10.368 now subtract that number from 51.84 which equals 41.472
If you are allowed to round to the nearest hundreth then that would be $41.50 before the tip.
HELP ASAP!!!! simplify 3^2-4/5
Answer:
9-4/5
5/5 = 1
Step-by-step explanation:
Answer:
1
9-4/5 is equal to 5/5 which is equal to 1
Is Triangle B a rotation of Triangle A?
Explain How u know
Answer:
No, triangle B is a reflection of triangle A.
Step-by-step explanation:
The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.
Answer:
No
Step-by-step explanation:
Its a reflection because even if you did rotate it it would never be in that orientation.
Which of the following is the value or PQ
Answer:
B. 61
Step-by-step explanation:
Given:
∆PQR ≅ ∆PQS
PQ = 2x + 41
QS = 7x - 24
QR = 3x + 16
Required:
Numerical value of PQ
SOLUTION:
First, create an equation to find the value of x as follows:
Since both triangles are congruent, therefore:
QS = QR
7x - 24 = 3x + 16 (Substitution)
Collect like terms
7x - 3x = 24 + 16
4x = 40
Divide both sides by 4
4x/4 = 40/4
x = 10
Find PQ by plugging x = 10 into PQ = 2x + 41
PQ = 2(10) + 41
PQ = 20 + 41
PQ = 61
Simplify. 863x14y9−−−−−−√
Answer: 1
Step-by-step explanation: 863x14ysqrt9= 3 simplified is 1
Please help being timed for test !
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (F)
4 10 6 9
Low Temperatures
Last Week (OF)
13 9 5 8
6
5
Which measures of center or variability are greater than 5 degrees? Select three choices
the mean of this week's temperatures
the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
Answer:
I think it B or C but hope I can help :)
Step-by-step explanation:
Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?
Answer:
- 1/2
Step-by-step explanation:
Just took the test
The value of cot (b) using trigonometry is -1/2 when tan b = -2.
Since we are given that tan(b) = -2 and the terminal side of angle b is in quadrant II, determine the value of cot(b).
In quadrant II, the sine and cosine values are positive, while the tangent and cotangent values are negative.
Given:
tan(b) = -2
The cotangent (cot) of an angle is the reciprocal of the tangent:
cot(b) = 1 / tan(b)
Now, substituting the given value of tan(b):
cot(b) = 1 / (-2)
cot(b) = -1/2
So, the value of cot(b) is -1/2.
Learn more about Trigonometry here:
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