The probability of getting exactly one face card is 0.72.
According to the questions two cards are drawn from a deck.
Since, we know that
Total number of cards in a deck = 52
Total number of face cards = 3 × 4 = 12
So, the number of ways of selecting 2 cards from a deck = [tex]^{52} C_{2}[/tex]
And, the total number of ways of getting exactly one face cards
= [tex]^{12} C_{1} \times ^{40} C_{1}[/tex] + [tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
= 2[tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
Therefore, the probability of getting exactly one face card
= [tex]\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }[/tex]
[tex]= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }[/tex]
[tex]= \frac{2(40\times 12)}{26\times 51}[/tex]
[tex]=\frac{2\times 480}{1326}[/tex]
= 0.72
Hence, the probability of getting exactly one face card is 0.72.
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A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. if a marble is randomly selected from the bag, what is the probability that it is blue?
3/12, or 1/4 is the probability that it is blue.
What is probability?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .Probability = number of successes / total number of outcomes
Total marbels in bag = 4+ 3 + 5 = 12
A total of 12 marbles are in the bag.
3 blue marbles are in the bag.
Therefore, the probability of picking a blue is 3/12, or 1/4.
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3. What is the greatest common factor for the two expressions? Use ^ to mean an exponent (use Shift +6 key). For example, 3x2 would be written as 3x^2. 15v³ and 12v² Write your response on the line below. Do not use any spaces or words.
The greatest common factor of the two expressions given as in the task content is; 3v².
What is the greatest common factor of the two expressions given?It follows from the task content that the terms whose greatest common factor are to be determined are: 15v³ and 12 v².
15v³ and 12v²
= 3v²(5v) and 3v²(4)
= 3v²(5v) and (4)
Consequently, in a bid to factorise the two expressions by means of their greatest Common factor, the greatest common factor can be determined as; 3v².
The correct answer choice which therefore represents the greatest common factor as required in the task content is; 3v².
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Pls help I’ll brainlest
Asap
Answer:
C. slope
Greetings !
The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).
Answer: slope.
Step-by-step explanation:
THE FIRST PERSON TO ANSWER GETS BRAINLIEST!!! A student traveled to a foreign country on an airplane. It took 18 hours to arrive at his destination, and the plane was traveling 900 kilometers per hour. When returning home, the same trip took only 15 hours going at a speed of 1,080 kilometers per hour. If t represents time and s represents the speed of the plane, which statement is true about this relationship?
(answer choices are below)
Answer:
4
Step-by-step explanation:
the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200
A toy store retailer charges $26.88 for a board game. He marks up his goods by 25% before selling them. What was the cost of the game before the markup?
The price of the board game before the markup is $21.50.
What is the cost before the markup?
Percentage can be described as a fraction an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
When the price of an item is marked up, it means that the price of the item has been increased by a predetermined percentage. In this question, the price of the board game is increased by 25%.
Price of the item before the mark up = price the retailer sells / ( 1 + percentage)
$26.88 / 1.25 = $21.50
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Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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How to answer this problem
Answer:
m<C = 12.0 °
Step-by-step explanation:
Since we know that this is a non-right triangle, we must use either the law of sines or law of cosines to find m<C.
The information we now have only allows us to use the law of sines, which focuses on proportions:
[tex]\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}[/tex]
Thus, we can use:
[tex]\frac{sin(98)}{19}=\frac{sinC}{4}\\ 4*sin(98)=19*sinC\\ \frac{4*sin(98)}{19}=sinC\\ sin^-1\frac{4*sin98}{19}=12.033=12.0[/tex]
The sin^-1 represents the sin inverse, which you must use to find angle measures.
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=10
There is a maximum value of 7/6 located at (x, y) = (5/6, 7).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 10.
Rearranging the constraint, we get:
6x + y = 10,
or, y = 10 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(10 - 6x) = 10x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 10 - 12x ... (i)
Equating to 0, we get:
10 - 12x = 0,
or, 12x = 10,
or, x = 5/6.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 5/6.
The value of y, when x = 5/6 is,
y = 12 - 6x,
or, y = 12 - 6*(5/6) = 7.
The value of f(x, y) when (x, y) = (5/6, 7) is,
f(x, y) = xy,
or, f(x, y) = (5/6)*7 = 7/6.
Thus, there is a maximum value of 7/6 located at (x, y) = (5/6, 7).
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Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 7x 1, [0, 9], f(c) = 19 c =
we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
According to the given question.
We have a function.
f(x) = x^2 + 7x + 1
As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".
Now, we will apply the theorem for the given function f(x).
So,
f(0) = 0^2 +7(0) + 1 = 1
And,
f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145
Here, f(0) = 1< 19< 145 = f(9).
So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.
To find, c,
We have to solve the quadratic equation f(c) =19.
This equation is
c² + 7c + 1 = 19.
Rearranging, c²+ 7c - 18=0.
Factor the expression to get
c² + 9c - 2c -18 = 0
⇒ c(c + 9) - 2( c + 9) = 0
⇒ (c - 2)(c + 9) = 0
⇒ c = 2 or -9
c = -9 is not possible beacuse it is not in the interval [0, 9].
So, the value of c is 2.
⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19
Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
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neeed help more more please uwu
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
a = 2b = 17 c = 10[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
Get every whole number from 0-10 using exactly five 3's, and any arithmetic operations and parentheses
See below for the combination of the arithmetic operations and exactly five 3's
How to determine the operations?The conditions are given as:
Exactly five 3'sAny arithmetic operation or combination of operationsThere are no direct rules to this, except by trial and error.
After several trials, we have the following operations:
(3 * 3 - 3 * 3)/3 = 0
3 - 3/3 - 3/3 = 1
(3 + 3 - 3 / 3)-3 = 2
(3 * 3 - 3 + 3)/3 = 3
3 *3/3 + 3/3 = 4
3 +3/3 + 3/3= 5
3 + 3 + (3 - 3)/3 = 6
(3^3 - 3 - 3)/3 = 7
3 + 3 + (3 + 3)/3 = 8
3 + 3 + 3+ 3 -3 =9
3 + 3 + 3 + 3/3 = 10
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Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
The number of views on a viral video can be modeled by the function p(t)=590(5)^3t . Write an equivalent function of the form p(t)=ab^t
Answer:
p(t) = 2950^3t
Step-by-step explanation:
I’m not sure if this is exactly what you wanted or not. Please let me know more info and I’ll write any more answers for this question in the comments. Have a great day!!
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
Simultaneous equationSimultaneous equation is an equation which involves the solving for two unknown values at the same time.
number of contemporary titles = xnumber of classic titles = yx + y = 3,500
x – y = 2,342
Add both be equation
x + x = 3,500 + 2,342
2x = 5,842
x = 5,842 ÷ 2
x = 2,921
Substitute x = 2,921 into
x – y = 2,342
2,921 - y = 2, 342
-y = 2,342 - 2,921
-y = -579
y = 579
Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
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Find the missing length.
= √ [?]
C =
C
6
2
Pythagorean Theorem: a² + b² = c²
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{Formula: a^2 + b^2 = c^2}[/tex]
[tex]\textsf{Solving:}[/tex]
[tex]\mathsf{2^2 + 6^2 = c^2}[/tex]
[tex]\mathsf{2 \times 2 + 6 \times6 = c^2}[/tex]
[tex]\mathsf{4 + 36 = c^2}[/tex]
[tex]\mathsf{40 = c^2}[/tex]
[tex]\large\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\sqrt{40}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In △ABC, AB = 13, AC = 20, BC = 21. Find the length of the altitude AD
The length of the altitude AD is 12 units.
How to find the height of a triangle?The height of the triangle can be found as follows:
We have to find an angle using cosine law before we can find the height.
Therefore,
20² = 13² + 21² - 2 × 21 × 13 cos B
400 = 169 + 441 - 546 cos B
400 - 610 = - 546 cos B
-210 = - 546 cos B
cos B = -210 / -546
cos B = 0.38461538461
B = cos⁻¹ 0.38461538461
B = 67.3810899783
B = 67.38°
Hence,
sin 67.38° = opposite / hypotenuse
sin 67.38° = AD / 13
cross multiply
AD = 13 sin 67.38°
AD = 11.9999882145
AD = 12 units
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Define the geometric sequence as a recursive function, if the first term is 1/5 and the common ratio is 5 .
The geometric sequence when the first term is 1/5 and the common ratio is 5 is; f(n) = f(n-1) . 5.
What is the geometric sequence described?The geometric sequence described in the task content is one whose first term is; f(1) = 1/5.
Additionally, it follows from convention that the recursive function for a geometric sequence is; a product of a previous term and the common ratio.
Hence, we have; f(n) = f(n-1) . 5.
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The points A(-3, 4), B(3, 2), C(1,4), and D(-5, -2) form quadrilateral ABCDin the coordinate plane. What condition verifies that the
diagonals are perpendicular?
PLEASED HELP
The diagonals of the qudrilateral will not be perpendicular to each other.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.
The slope of a coordinate pair is given by the change in y divided by the change in x, that is:
For the diagonal AD the slope will be:-
Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )
For the diagonal BC, the slope will be:-
Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1
The multiplication of the two slopes will be,
M = ( 1 / 3 ) x -1 = ( - 1 / 3 )
Therefore, the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.
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Answer:
The product of the slopes of the diagonals is -1.
Step-by-step explanation:
I had the question and got it right.
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?
Answer:
100 miles
Cost = $63
Step-by-step explanation:
Let us assume that the distance driven for both plans when they both equal in cost is X miles
Plan 1
Cost = 48 + 0.15X
Plan2
Cost = 53 + 0.1X
If they are both equal then
48 + 0.15X = 53 + 0.10X
Collecting like terms
0.15X - 0.10X = 53 - 48
0.05X = 5
X 5/0.05 = 100 miles
Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63
Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63
PLS HELP!What is the difference of
Answer:
Option 3
Step-by-step explanation:
Since the denominators are the same, you can just subtract the numerators.
HElp meee mwa mwa mwa
Answer:
[tex]a = 1, \ - 3[/tex]
Explanation:
[tex](a-6)(a+8) = -45[/tex]
distribute
[tex]a^2 + 8a - 6a - 48 = -45[/tex]
collect terms
[tex]a^2 + 8a - 6a - 48 + 45=0[/tex]
simplify
[tex]a^2 + 2a - 3=0[/tex]
factor
[tex](a - 1)(a + 3)= 0[/tex]
set to zero
[tex]a = 1, \ - 3[/tex]
Answer:
a = 1, -3
Step-by-step explanation:
Given equation:
[tex](a-6)(a+8)=-45[/tex]
Expand the brackets:
[tex]\implies a^2+8a-6a-48=-45[/tex]
[tex]\implies a^2+2a-48=-45[/tex]
Add 45 to both sides:
[tex]\implies a^2+2a-48+45=-45+45[/tex]
[tex]\implies a^2+2a-3=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
Two numbers that multiply to -3 and sum to 2 are: 3 and -1.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies a^2+3a-a-3=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies a(a+3)-1(a+3)=0[/tex]
Factor out the common term (a + 3):
[tex]\implies (a-1)(a+3)=0[/tex]
Apply the zero product property:
[tex]\implies (a-1)=0 \implies a=1[/tex]
[tex]\implies (a+3)=0 \implies a=-3[/tex]
Verify the solutions by inputting the found values of a into the original equation:
[tex]a=1 \implies (1-6)(1+8) & =-5 \cdot 9 = -45[/tex]
[tex]a=-3 \implies (-3-6)(-3+8) & =-9 \cdot 5 = -45[/tex]
Hence both found values of a are solutions of the given equation.
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Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5.
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexes of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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Enter the correct answer in the box. jackson needs to determine the value of x in this equation. rewrite the expression as a logarithmic quotient that he could enter in his calculator.
A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.
What is a logarithmic equation?A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.
Given: [tex]$1.13^x = 2.97[/tex]
Taking log on both sides, we get
log [tex]$1.13^x[/tex] = log 2.97
x log 1.13 = log 2.97
x = log 2.97/log 1.13
Therefore, the value of logarithmic equation x = log 2.97/log 1.13.
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A bowl holds Fraction 3 over 10 cups of oil when it is Fraction 2 over 5 full. Which statement best describes the quotient of 3 over 10 division sign2 over 5?
1. The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.
2. The amount of oil that can be still poured in the bowl is Fraction 3 over 4 cup.
The statement that describes the quotient of 3 over 10 division sign2 over 5 is A. The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.
How to illustrate the fraction?From the information given, we are told that a bowl holds fraction 3 over 10 cups of oil when it is Fraction 2 over 5 full.
Therefore, the statement that best describes the quotient of 3 over 10 division sign2 over 5 will be that the maximum amount of oil the bowl can hold is fraction 3 over 4 cup.
In conclusion, the correct option is A.
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Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x² + 2
a = 0
b= 6
6 intervals
Answer:
67 square units
Step-by-step explanation:
The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.
AreaThe attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.
The approximate area is 67 square units.
Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]
where the left endpoint of the [tex]i[/tex]-th interval is
[tex]\ell_i = i - 1[/tex]
with [tex]i\in\{1,2,3,4,5,6\}[/tex].
The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,
[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]
where we use the well-known sums,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
PLEASE HELP IM STUCK
Answer:
23
Step-by-step explanation:
The question gives the first equation:
0.05N + 0.10D = 2.20
It can be rewritten as:
0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.
Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.
The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.
Therefore...
N+D = 23
Solve the following systems of equations algebraically:
[tex]\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.[/tex]
The value of x in the system of equation is 6
How to solve the system of equations?The system of equations is given as:
y = 1/2 * 2^x
y = 5x + 2
Substitute y = 1/2 * 2^x in y = 5x + 2
1/2 * 2^x = 5x + 2
Multiply through by 2
2^x = 10x + 4
Next, we use the trial by error.
Set x = 6
This gives
2^6 = 10 * 6 + 4
Evaluate the product and the exponent
64 = 60 + 4
Evaluate the sum
64 = 64
Hence, the value of x in the system of equation is 6
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30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Using the binomial distribution, we have that you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 0.2308, as of the 52 cards, there are 12 faces, hence 12/52 = 0.2308.Then the expected value is found as follows:
E(X) = np = 35 x 0.2308 = 8
You would expected to draw a face card 8 times.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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4. Joe has five times as much money as Bill. However, Joe pays Bill $5 he owes him, after which Joe has just twice the amount Bill now has. How much money did each have in the beginning?
Answer:
Bill starts with $5 and Joe starts with $25Step-by-step explanation:Let Ji and Bi represent the initial amounts that Joe and Bill have at the start. Number after J and B will be used to indicate subsequent steps in the problem.
We are told that "Joe has five times as much money as Bill," which we can write as:
1) Ji = 5Bi
We learn that "Joe pays Bill $5," which we can represent as:
2) J1 = Ji - 5
This would mean that Bill has added $5:
3) B1 = Bi + 5
We are then told that "Joe has just twice the amount Bill now has," which we can write as:
4) J1 = 2B1
===
We can rearrnage and substitute the above relationships to eliminate one of the two variables (B1 or J1)
J1 = Ji - 5 [from 2]
2B1 = Ji - 5 [Substitute 4 to eliminate J1]
Ji = 5Bi [from 1]
2B1 = 5Bi - 5 [Substitute 1 to eliminate Ji]
B1 = Bi + 5 [Rearrange]
2(Bi + 5) = 5Bi - 5 [Use the above expression in the previous equation to eliminate B1]
2Bi + 10 = 5Bi - 5 [Simplify]
-3Bi = -15 [Simplify]
Bi = $5 [Solve]
Ji = 5Bi [from 1]
Ji = 5*(5) [Since Bi = $5]
Ji = $25 [Solve]
Bi = $5 and Ji = $25===
CHECK:
Does Joe has five times as much money as Bill?
Ji = $25 and Bi = $5 YES
When Joe pays Bill $5 he owes him, does Joe has just twice the amount Bill now has?
J1 = $25 - $5 = $20
B1 = $5 + $5 = $10 YES
suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth
In quadrant I, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}[/tex]