Answer:
a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two
e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
One in four people in the US owns individual stocks.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
You randomly select 12 people and ask them if they own individual stocks.
This means that [tex]n = 12[/tex]
a. Find the mean, variance, and standard deviation of the resulting probability distribution.
The mean of the binomial distribution is:
[tex]E(X) = np[/tex]
So
[tex]E(X) = 12(0.25) = 3[/tex]
The variance is:
[tex]V(X) = np(1-p)[/tex]
So
[tex]V(X) = 12(0.25)(0.75) = 2.25[/tex]
Standard deviation is the square root of the variance, so:
[tex]\sqrt{V(X)} = \sqrt{2.25} = 1.5[/tex]
The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. Find the probability that the number of people who own individual stocks is exactly six.
This is P(X = 6). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401[/tex]
0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. Find probability that the number of people who say they own individual stocks is at least two.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584[/tex]
0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. Find the probability that the number of people who say they own individual stocks is at most two.
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907[/tex]
0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.
e. Are the events in part c. and in part d. mutually exclusive
Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
Please help NO LINKS
Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
5
,
about the
y
-axis.
V
=
Answer:
[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 5
Step 2: Identify
Find other information from graph.
See Attachment.
Bounds of Integration: [0, 5]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^5_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^5_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{625}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{625 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.8 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 8% and the bottom 8%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
5.70 < X < 5.89
Step-by-step explanation:
Z = ±1.40507156
z = (x - μ)/σ
1.40507156 = (x - 5.8)/.07
5.70 < X < 5.89
A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation 0. a. Show that satisfies the equation for any constant A. b. Show that satisfies the equation for any constant B. c. Show that satisfies the equation for any constants A and B.
Answer: hi your question is poorly written below is the correct question
answer :
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y = Asint + B cost satisfies the differential equation for any constant A and B
Step-by-step explanation:
y" + y = 0
Proves
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y3 = y1 + y2 , y'3 = y'1 + y'2, y"3 = y"1 + y"2
∴ y"1 + y1 = -Asint + Asint
y"2 + y2 = -Bcost + Bcost
y"3 - y3 = y"1 + y"2 - ( y1 + y2 )
= y"1 - y1 + y"2 - y2
= -Asint - Asint + ( - Bcost - Bcost ) = 0
Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B
Which of the following sets of points are NOT coplanar?
admins, pls delete this, I messed up and don't know how
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answer:
-5 it is
Step-by-step explanation:
PLEASE HELP :) I will give all points
answer choice a
x^2 - 5x - 1 = 0
a=1, b=-5, and c=-1
next you plug in the numbers into the quadratic formula
-(-5) plus or minus the square root of (-5)^2 - 4(1)(-1)/ 2(1)
after you simply, you should get 5 plus or minus the square root of 29, which is answer choice a
What is the range of the given set of ordered pairs?
(9,-2) (4,3) ( 8, 10) (-4, 8)
Answer:
(-2,3,10,8)
Step-by-step explanation:
eg
(x,y)=(domain,range)
x components are domain and y components are range in the given set of ordered pairs
express the ratio as a fraction in it's lowest terms.3kg to 800g
Answer:
15 / 4
Step-by-step explanation:
1 kg = 1000 g
3 kg
= 3 x 1000
= 3000 g
3kg to 800g
= 3kg : 800g
= 3000 : 800
= 30 : 8
= 30 / 8
= 15 / 4
15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.
To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.
we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:
3 kg = 3 * 1000 g = 3000 g
Now, we have the quantities in the same unit, and the ratio becomes:
3000 g to 800 g
To express this ratio as a fraction, we place the quantities over each other:
3000 g
-------
800 g
Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.
The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:
3000 ÷ 200 = 15
800 ÷ 200 = 4
Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.
In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.
To know more about Fraction here
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Write an equation that represents the line.
Use exact numbers
3x is 18 what value is x
Answer:
6
Step-by-step explanation:
We have the expression "3x is 18" and we want to find out x, so the easiest way is to isolate x. The way to do this is by dividing both 3x and 18 by 3, leaving us with 6. This means that our answer for x is 6. I hope this helped and please don't hesitate to reach out for clarification!
Answer:
6
Step-by-step explanation:
3x = 18
Divide both sides by 3
3x / 3 ( the 3s cancel out and we're left with x )
18/3 = 6
We get that x = 6
We can then plug in 6 to x in 3x = 18 to check if our answer is correct
3x = 18
Replace x with 6
3(6) = 18
3(6) = 18
18 = 18
This is true hence we can confirm that x = 6
By recognizing the series as a Taylor series evaluated at a particular value of x, find the sum of each of the following convergent series
1 + 3 + 9/2! + 27/3! + 81/4! + .....
Answer:
the answer should be e^3
Step-by-step explanation:
i hope it helps you
Question:
which is a y-intercept of the graphed function?
Answers:
A. (-9,0)
B. (-3,0)
C. (0,-9)
D. (0,-3)
Answer:
(0, -9)
Step-by-step explanation:
The y intercept is the y value when x =0
(0, -9)
find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2 Step 1 The Maclaurin series formula is f(0) + f '(0)x + f ''(0) 2! x2 + f '''(0) 3! x3 + f (4)(0) 4! x4 + .
Answer:
= ∑ 6*n*x^n-1
Radius of convergence = 1
Step-by-step explanation:
f(x) = 6(1-x)^-2
Maclaurin series can be expressed using the formula
f(x) = f(0) + f '(0)x + f ''(0)/ 2! (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .
attached below is the detailed solution
Radius of convergence = 1
The Maclaurin series for f(x) = 6 / (1 - x )^2 = ∑ 6*n*x^n-1 ( boundary ; ∞ and n = 1 )
Math pweasee 15 points
Answer:
Step-by-step explanation:
a = 5
b = 15
c = ?
c^2 = a^2 + b^2
c^2 = 5^2 + 15^2
c^2 = 25 + 125
c^2 = 250
sqrt(c^2) = sqrt(250)
c = sqrt(250)
GED Academy Practice Test
What is the value of the expression?
4+(-2)
-3+3
Answer:
The first one is 2
The second one is 0
I hope this helps!
Answer:
First:
[tex]{ \tt{ = 4 + ( - 2)}} \\ = 4 - 2 \\ = 2[/tex]
Second:
[tex] - 3 + 3 \\ = 0[/tex]
Jamal opens a savings account with a starting balance of $200 and plans to
deposit $75 each week after opening the account. His savings over time is
represented by the graph below. How would this graph change if Jamal
decided to deposit $100 each week instead?
the graph would steeper, meaning more savings over time
HELP! AAHHHHH SOMEBODY HELP!
If each square of the grid below is $0.5\text{ cm}$ by $0.5\text{ cm}$, how many square centimeters are in the area of the blue figure?
Answer:
8.50 cm²
Step-by-step explanation:
The dimension of each square is given as 0.5cm by 0.5cm
The area of the a square is, a²
Where, a = side length
Area of each square = 0.5² = 0.25cm
The number of blue colored squares = 34
The total area of the blue colored squares is :
34 * 0.25 = 8.50cm²
Find the volume of the box. The box shows the length is 6 feet, the width is 5 feet, and the height is 3 feet. The volume of the box is blank cubic feet. The solution is
Answer:
[tex]90[/tex] [tex]ft^3[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the volume of a rectangular prism is [tex]V=lwh[/tex]
Let's substitute the number for the length, width, and height now.
[tex]V=(6)(5)(3)[/tex]
[tex]V=(30)(3)[/tex]
[tex]V=90[/tex]
--------------------
Hope this is helpful.
what is the answer to 10% of 900
Answer:
90 cause 90 times 10 is 900 and 10% times 10 is 100%
Step-by-step explanation:
Answer: 90
Step-by-step explanation: 900 × .10 = 90
What is the measure of L?
A. 390
B. 25°
C. Cannot be determined
D. 32°
Answer:
∠L = 25°
Step-by-step explanation:
Two sides are equal. so , it is an isosceles triangle.
Angles opposite to equal sides are equal.
∠L = 25
Which of the following best describes the number below square root of -7
A. Perfect square
B.composite
C.imaginary
D.positive
Answer: The ans is imaginary . option c
what graph shows the solution to the equation below log3(x+2)=1
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
Explain relationship between ≠2 and the factor x – 2.
Answer:
It has a difference of x=2 of -4
Step-by-step explanation:
It has a difference of x=2 of -4
What is factor ?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.Given ,
x ≠ 2 ,
x - 2 =0
So, we put x = -2 because in question x ≠ 2 .
Then, x - 2 = 0
-2 -2 = 0
- 4 =0
Therefore, it has a difference of x= -2 of -4.
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The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle
9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
Please help with this
Answer:
i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds
Are the triangles similar ? If they are identify the similarity ratio.
Answer:
C
Step-by-step explanation:
The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3
Write the range of the function using interval notation.
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range [tex]=\{y|-2<y\leq 2\}[/tex]
The interval notation is:
Range [tex]=(-2,2][/tex]
Therefore, the range of the given function is (-2,2].
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:
[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)
Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.
If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:
[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]
[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]
The area of the square is increasing at a rate of 40 square centimeters per second.
NEED HELP ASAP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth:
Exponential Decay:
y = 1700(1.25)^t
y =240(1/2)^t
y = 4000(1.0825)^t
y = 1.5(10)^t
y = 12,000(0.72)^t
y = 8000(0.97)^t
Answer:
Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t
Decay: y =240(1/2)^t, y = 12,000(0.72)^t, y = 8000(0.97)^t
Step-by-step explanation:
In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.
!PLEASE HELP WILL GIVE BRAINLIEST!
An internet service charges $34 per month for internet access. Write an equation to represent the total cost based on the number of months of internet access.
Answer:
34m = c
Step-by-step explanation:
For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).
Answer:
[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]