the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.
What is the difference between permutation and combination in probability?For a list of data, where the order of the data is important, a permutation is used, while for a group of data, where the order of the data is irrelevant, a combination is used.Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!the possible outcomes are
BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG
wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.
We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities
P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)
=[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]
= 3/8.
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A committee has fourteen members. There are two members that currently serve as the board's chairman
and ranking member. Each member is equally likely to serve in any of the positions. Two members are
randomly selected and assigned to be the new chairman and ranking member. What is the probability of
randomly selecting the two members who currently hold the positions of chairman and ranking member and
reassigning them to their current positions?
...
Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
As given,
Total members in the committee=14
Number of members serve as chairman and ranking member=2
Total number of ways to assigned new position
=¹⁴P₂
=(14!) / (14-2)!
=(14 × 13 × 12!) / 12!
=14 ×13
=182
Each member is equally likely to serve in any of positions.
Each position there is only one way to reassign position.
Probability of randomly selecting two members = 1 /182
Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
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how do i do this problem.
ANSWER
[tex]g(5x)=75x^2\text{ + 5}[/tex]STEP-BY-STEP EXPLANATION:
Given information
[tex]g(x)=3x^2\text{ + 5}[/tex]Find g(5x)?
Step 1: make x = 5x
[tex]\begin{gathered} g(x)=3x^2\text{ + 5} \\ g(5x)=3(5x)^2\text{ + 5} \\ g(5x)=3(25x^2)+5^{} \\ g(5x)=75x^2\text{ + 5} \end{gathered}[/tex]4 = 4(k − 15) hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
distribute the 4 to the k and -15 so you get 4=4k-60 then add the 60 to the other 4 so its 64=4k then divide 4 to 64 and your answer is 16
Step-by-step explanation:
[tex]4=4k-60\\4k-60=4\\4k=4+60\\4k=64\\\frac{4k}{4} =\frac{64}{4} \\k=16[/tex]
As solved above k=16
Jeremy invests $8,500 into an account with a 2.4% interest rate that is compounded quarterly. How much money will be in this account after 6 years?
Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.
Answer:
9812.29
Step-by-step explanation:
Using the compound interest formula,
[tex]8500 \left(1+\frac{0.024}{4} \right)^{(6)(4)} \approx 9812.29[/tex]
If y = 2cos(lnx). + 3sin(Inx) then Select one: 0 dy a 22 dy +r +y = 0 dx dx2 d'y x2 dy +2 dr2 dr y=0 o x2d²y dy dx + y To dx2 day 22 dy dr -y=0 dr2
Solution
Given
[tex]y=2\cos(\ln x)+3\sin(\ln x)[/tex][tex]\begin{gathered} \frac{dy}{dx}=\frac{-2}{x}\sin(\ln x)+\frac{3}{x}\cos(\ln x) \\ \\ \end{gathered}[/tex]Determine a bank account balance if the account starts with $300 has a annual rate of %4 what is the money in the account after 10 years
Answer:420
Step-by-step explanation: multiply 300 times 4% =12. Then multiply 12 times 10=120. Then add 300 and 120=420
59 + 43.6 estimate the sum or difference
Answer:
Step-by-step explanation:
59+ 43.6
43.6=44.0
59+44
59+43.6
=103.0
4.
908 ÷ 10 Power of 5
0.908
90.800,000
9.08
0.00908
Answer:
0.00908 is the answer...
3. Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven,
respectively.
A numeral exists a sign, combination of symbols, or figure that represents a number.
142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47
11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π
39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550
What is meant by numeral?A numeral is a sign, combination of symbols, or figure that represents a number. It can be a mathematical numbering system.
A numeral's value is determined by the number it represents. All modern numbers cannot be represented by all number systems; Roman numerals, for instance, do not have a zero. A numeral system should, in theory, be able to: Represent a useful set of numbers (e.g. all integers, or rational numbers).
The correct answer is as follows:
142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47
11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π
39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550
The complete question is:
Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively.
Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten andeleven, respectively.
a. 142five
b. 11011two
c. 39Ttwelth
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You have a combination lock
with 3 secret digits. Find the 3
correct digits using the
following clues and enter your
answer below.
127 One digit is right and in its place
138 One digit is right, but in the wrong place
791
Two digits are right but both are in the
wrong place
452 All digits are wrong
8
529 One digit is right, but in the wrong place
Answer:
987
Step-by-step explanation:
You want to determine a three-digit combination based on clues about which digits are right and/or correctly placed.
Clue 1This tells you one of digits 1, 2, or 7 is correct and correctly placed.
Clue 2 tells you that digit is not 1. Clue 4 tells you that digit is not 2.
7 is correctly placed as the 3rd digit
Clue 2We already know that 1 is not the correct digit. This means 3 must be the first digit, or 8 must be the first or second digit.
Clue 3We already know that 7 is a correct digit, properly placed as the 3rd digit. Since 1 is not a correct digit, 9 must be a correct digit, properly placed as the 1st digit.
9 is correctly placed as the 1st digit
Combining this fact with Clue 2 means ...
8 is correctly placed as the 2nd digit
The combination is 987.
__
Check
Clues 4 and 5 are consistent with this combination.
If 1 x 10^a + 2 x 10^b + 3 x 10^c + 4 x 10^d = 24130 and a≠b≠c≠d, then what does a/2 + b/4 + c/8 + d/16 equal?
Question 1
Using scientific notation, we know a=2, b=4, c=1, and d=3. So,
[tex]\frac{a}{2}+\frac{b}{4}+\frac{c}{8}+\frac{d}{16}=1+1+\frac{1}{8}+\frac{3}{16}=37/16[/tex]
Question 2
[tex]a+13b=3(3a-b)\\\\a+13b=9a-3b\\\\16b=8a\\\\a=2b\\\\\therefore \frac{a^3}{b^3}=\frac{(2b)^3}{b^3}=\frac{8b^3}{b^3}=8[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
The functions f and g are defined as follows.
f (x) = 4x - 3 g (x) = -3x^2 - 2
Find f (-4) and g (3)/
Simplify your answers as much as possible.
Answer: [tex]f(-4)=-19, g(3)=-29[/tex]
Step-by-step explanation:
[tex]f(-4)=4(-4)-3=-19\\\\g(3)=-3(3)^2 -2=-29[/tex]
Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may
apply.)
square root of -9
Select all descriptions that may apply.
A. Nonreal complex
B. Real
C. Pure imaginary
D. Complex
Answer:
acxdddhdhxhhh sax skskskkkkkddffffffrrkel sssddjeeeeerrjrrjtjjj
What is the value of x9+(12−y), when x = 2 and y = –5?
Answer: 35
Step-by-step explanation:
1) Substitute the x's and y's
(2)9+(12−(-5))
2) Simplify the numbers inside the equation
18+(12-(-5)
= 18+(17)
= 35
3) Solved.
35
Find the first four terms of the binomial series for the function (1+2x)^1/2
The first four terms of the binomial series are 1, x, - x²/2 and - 1/32x³ respectively.
The binomial provided to us is [tex](1+2x)^{1/2}[/tex]
To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.
(1+x)^n = 1 + nx + [n(n - 1)/2!] x² + [n(n - 1)(n - 2)/3!] x³ +...
As we can see here,
The value of x = 2x,
The value of n = 1/2.
We get,
(1+2x)^1/2 = 1 + 1/2(2x) + [1/2(1/2-1)/2!]x² + [1/2(1/2-1)(1/2-2)/3!]x³ +
(1+2x)^1/2 = 1 + x - x²/2 - 9/4x³ + .....
From the expansion, we can see,
First term = 1
Second term = x
Third term = -x²/2
Fourth term = -1/32x³.
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a gear reduction drive has three separate stages with ratio of 3:1,2.38:1 and 4.2:1. the total ratio of the drive is?
The total ratio of the drive is 9.58:1.
What are ratios?A relationship between two quantities that are typically stated as the product of their respective quotients is known as a ratio.The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.Given ratios of the three separate stages of a gear reduction drive are 3:1,2.38:1 and 4.2:1.
To find the total ratio of the drive we have to add the respective ratios.
When the denominator of the ratios are same, as in this case we just have to add the numerators to obtain the result.
Total ratio of the drive = 3:1 + 2.38:1 + 4.2:1 = 9.58:1
So, the total ratio of the drive is 9.58:1.
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equation of the line that passes through the point (1, -1) & is parallel to the graph of y = 3/5x + 2?
Equation is 5y = 3x + 8.
What is slope?Slope is the inclination of a line with respect to the horizontal is measured numerically. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Given Data
line that passes through the point (1, -1) &
is parallel to the graph of y = 3/5x + 2
y = mx + c
y = [tex]\frac{3}{5}[/tex]x + 2
m = [tex]\frac{3}{5}[/tex]
Equating points,
-1 = [tex]\frac{3}{5}[/tex](1) + c
-1 = [tex]\frac{3}{5}[/tex] + c
-1 - [tex]\frac{3}{5}[/tex] = c
[tex]\frac{-5-3}{5}[/tex] = c
[tex]\frac{-8}{5}[/tex]
Equation-
y = [tex]\frac{3}{5}[/tex]x + [tex]\frac{8}{5}[/tex]
5y = 3x + 8
Equation is 5y = 3x + 8.
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1&4/5 on a number line
Write an expression that is equivalent to 8 using each of the following numbers and symbols once in the expression.
optionsWe want to obtain an expression equivalent to 8 using these symbols and numbers.
The option that exactly matches this is,
[tex](7\text{ }\frac{.}{.}7)^2+7[/tex]That is because,
7 divided by 7 is 1.
1 squared is still one, and;
1 added to 7 is 8.
So one answer is option D.
We also have another answer.
Which is;
[tex](7+7^2)\frac{.}{.}7[/tex]That's because 7 squared is 49, and 7 + 49 is 56.
56 divided by 7 is 8.
So our answers are option C and option D
A passbook savings account has a rate of 10% Find the effective annual yield if the interest is compounded daily.
The effective annual yield if the interest is compounded daily is 10.5155 %.
The annual interest rate or rate of return that an investor is entitled to over a particular time period is known as effective annual yield.
In the case of daily, there are 360 days in a year.
Therefore, making n = 360.
Therefore, the effective annual yield if the interest of 10% is compounded daily when r = 10 % and n = 360 will be:
Y = ( 1 + r/n )ⁿ - 1
Y = ( 1 + 0.1 / 360 )³⁶⁰ - 1
Y = ( 1 + 0.000277 )³⁶⁰ - 1
y = 1.105155 - 1
Y = 0.105155
However, since it is in decimal form, we must first multiply it by 100 before adding the symbol "%" after the last digit of the value.
Therefore,
Y = 0.105155 × 100%
Y = 10.5155 %
Therefore, the effective Annual Yield is 10.5155 %
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What is (-5,2); m=2/5 in standard form?
The standard form of the straight line is given by 5y - 2x = 20 .
Ax + By = C is the standard form for two-variable linear equations.
Standard form is used, for instance, in the linear equation 6x+5y=11. This method makes finding an equation's two intercepts very simple (x and y) .Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient of the line and c denotes the location of its y-axis intersection.An infinitely long object without any width, depth, or curvature is a line. Since they can exist in two, three, or higher dimensions, lines are one-dimensional objects.We know that when a straight line passes through (a,b) with slope m then the equation of the line is given by:
y - b = m ( x - a )
putting the values in the respective places we get:
y - 2 = 2/5 × ( x + 5 )
or, 5y - 10 = 2x + 10
or , 5y - 2x = 20
Hence the standard form of the straight line is given by
5y - 2x = 20 .
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Which function, g or h, is the inverse function for function f? CHECK PHOTO
Answer: The function g because the graphs of f and g are symmetrical about the line y=x.
Answer:
A. The function g because the graphs of f and g are symmetrical about the line y=x.
Step-by-step explanation:
Pls help with this !!!
The given graph shown in the image is a function, Option b is correct.
Given that,
A graph is shown, and we have to determine whether the graph shown is a function or not.
The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
The graph shows of a curve representing an exponential function,
There is why the graph shown is a function, and also the graph is continuous and as well as differentiable.
Thus, the given graph shown in the image is a function, Option b is correct.
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The Pythagorean Identity is sin^2x+cos^2x=1. Write this equation two other ways.
[tex]\sin^2 x=1-\cos^2 x \\ \\ \cos^2 x=1-\sin^2 x[/tex]
In a lottery game, a player picks six numbers from 1 to 21. if the player matches all six numbers they win 50,000 dollars otherwise they lose $1
Your best option is to simply choose six distinct numbers, in any sequence. You would win if those six numbers matched the six that the lottery officials chose (again, in any sequence).
The likelihood of selecting the correct six numbers is one in
[tex]\frac{23}{6}[/tex] = [tex]\frac{23}{6(23-6)}[/tex] = [tex]\frac{23.22.21.20.19.18}{1.2.3.4.5.6}[/tex] = 100974
Therefore, 100946/100947, or a probability of losing, is very near to 1.
The total of your payouts multiplied by the probability that each scenario will occur is the anticipated value of the game. which is
(50,000) [tex]\frac{1}{100947}[/tex] + (-1) [tex]\frac{100946}{100947}[/tex] = [tex]\frac{50000-100946}{100947}[/tex] = -0.5046
You will typically break even if its value is 0. You should play the game if it is more than zero because you will typically win, and you shouldn't play it if it is less than zero because you will typically lose. The payoff is decently substantial for this, however the typical player loses just over 70 cents per round. Almost every player loses a complete dollar.
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T 4 Account 1 point Which trig function should Sharlot use to find the measure of angle A ? C Pashboard 5 Courses 1 1 A B 12 Calendar 2 O sine 49 cosine Inbox 3 tangent O History 4 pythagorean theorem o
In the given triangle we have :
Base line with angle A, and the Hypotenuse of angle A
Since the ratio of Base to the hypotenuse is the Cosine trignometric ratio:
[tex]\text{Cos}\theta=\frac{Base}{Hypotenuse}[/tex]Answer : Cosine
Translate this sentence into an equation.
Carlos's height decreased by 7 is 62
Use the variable c to represent Carlos's height
after school, a group of students decides to have a snowball fight. with 2 students on a team, they can make 6 snowballs per minute. with 10 students on a team, they can make 30 snowballs per minute. what is the slope in this situation?
Based on the calculations using the given points, the slope in this situation is equal to 5.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (30 - 10)/6 - 2)
Slope = 20/4
Slope = 5.
In conclusion, the slope of the line that passes through the given points is equal to 5.
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Given m/8= 86° and m/4= (4x + 2)°, what is the value of x ?
X =
Bring the variable to the left and the remaining values to the right to define the value of x. If m/8 = 86° and m/4 = (4x + 2)° then value of x = 21.
How to find the value of x?Any of the algebraic expressions, including addition, subtraction, multiplication, and division, should be used. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
Let the m/8 = 86° and m/4 = (4x + 2)°
m ∠4 = m ∠8 (Corresponding angles are equal)
To estimate the value of x
4x + 2 = 86
Substracting both sides of the equation by 2, we get
4x + 2 - 2 = 86 - 2
simplifying the above equation,
4x = 86 - 2
4x = 84
Dividing both sides of the equation by 4, we get
4x / 4 = 84 / 4
x = 21
Therefore, the value of x = 21.
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