Using the hypergeometric distribution, the probabilities are given as follows:
a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]
b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]
c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
Parameter x is the number of successes.Parameter N is the size of the population.Parameter n is the size of the sample.Parameter k is the total number of desired outcomes.The general parameters in this problem are given as follows:
N = 52, as a standard deck has 52 cards.n = 13, as 13 cards will be chosen.In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]
For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:
[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]
For item iii, we want:
Seven spades from a set of 13.Six clubs from a set of 13.Hence the probability is given as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]
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Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne's shadow is feet long and Dixon's shadow is feet long. If Ariadne is feet tall, how tall is Dixon?
Using the similar triangle principle, the height of Dixon in feet is 6 feet.
How to find the side of similar triangle?Ariadne's shadow is 15 feet long and Dixon's shadow is 18 feet long.
Ariadne is 5 feet tall.
The height of Dixon can be found using similar triangle principle.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, using the similar triangle theory,
Let
x = height of Dixon
Hence,
shadow length of Ariadne / Ariadne height = Dixon shadow length / Dixon height
shadow length of Ariadne = 15 ft
Ariadne height = 5 feet
Dixon shadow length = 18 feet
15 / 5 = 18 / x
cross multiply
15 × x = 18 × 5
15x = 90
divide both sides by 15
15x / 15 = 90 / 15
x = 6 ft
Therefore, Dixon height is 6 feet.
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Select the relation that is a function
cos 20-2 cos0=-1
Find all solutions of the equation in the interval [0,2pie).
The solutions for the trigonometric cosine equation are [0, 90,2pi].
What is trigonometric cosine function?
Trigonometric is one of the branch in mathematics which is used to study the relationship between the length and angles. Its angle is categorized into six form depending upon their sides.
To calculate the solution of the given equation in the interval of [0, 2 pi].
Therefore, the given equation in the form of the trigonometric function is as written below:
[tex]cos^{2} 0 - 2cos0 +1 = 0\\(cos0-1)^{2} =0[/tex]
Hence, the solutions for the trigonometric cosine equation are [0, 90,2pi].
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the digits 3,4,5,6,7 and 8 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 800.
The probability of getting an even number greater than 800 is 0.08
Total outcomes possible when a three-digit number is formed without repetition:
Using the digits 3,4,5,6,7 and 8:
The first digit can be filled in using any of the 6 options
The second digit can be filled using the remaining 5 options
The third digit can be filled in using the remaining 4 options
So, total outcomes possible = 6*5*4 = 120 possibilities
Now, finding even number greater than 800:
The first digit can only be filled by 8 for a number to be greater than 800 which means there is only one option for the first digit
The second digit can be filled using any of the remaining options except 8 which means there are 5 options
The last digit can be filled using 4 and 6 because these are the only even numbers which mean 2 options
Total possible outcomes = 1*5*2 = 10 possibilities
The probability that the number is even and greater than 800:
= 10/120 = 0.08
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A factory produces sweatshirts for a sports team, and packages the sweatshirts in boxes of 20. Every
hour, the factory produces 9,284 sweatshirts.
How many full boxes of sweatshirts are packaged in 1 hour?
Answer:
464 remainder 2
Step-by-step explanation:
9284÷20
Please answer Part A and B
Answer:
a 47 b 34
Step-by-step explanation:
so basically its very easy im just trying to do a task so this is most probabilly noot correct
Answer: Part A: Figure D I Part B 3 Units to the left...
Step-by-step explanation: Because they are the same, but in different locations... : )
Find the area of the triangle:
Answer:30
Step-by-step explanation:
Sentences to Algebraic EquationsTranslate the following sentence into equations and solve them.1. The quotient of a number and six is five. Find the number.
1. The quotient of a number and six is five.
he algebraic expression ifor the previous sentence is:
x/6 = 5
multiply by 6 to solve for x:
x = 5(6)
x = 30
. Eight decreased by twice a number is four.
- 2x = 4 subtract 8 both sides
-2x = 4 - 8
2x = -4 divide by -2 both sides
x = 2
3. Three less than the division of a number to seven is one.
3 - x/7 = 1 subtract 3 both sidesa
-x/7 = 1 - 3
x/7 = -2 multiply by -7 both sides
x = 2
4. Seven times the difference of 15 and a number equals - 56.
7(15 - x) = -56 a
7(15) - 7x = -56
105 - 7x = -56 subtract 105 both sides
-7x = -56 - 105
7x = -161 divide by -7 both sides
x = 23
Jacob ran 10 miles in 80 minutes at that rate how far would he run in 21/2 hours? (*hint - 1 hour = 60 minutes)
If Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours
Number of miles that Jacob will run in 80 minutes = 10 miles
Number of miles that Jacob will run in 1 minutes = Number of miles that Jacob will run in 80 minutes/ 80
= 10/80
= 0.125 miles
We know,
1 hour = 60 minutes
[tex]2\frac{1}{2}[/tex] hours = 2.5×60
= 150 minutes
Number of of miles that Jacob will run in 150 minutes = Number of miles that Jacob will run in 1 minutes × 150
= 0.125×150
= 18.75 miles
Hence, if Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours .
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The angle measures in a triangle are 25 degrees, 135 degrees, and 20 degrees. what type of triangle is it. isosceles triangleobtuse triangle right triangle acute triangle
25 degrees, 135 degrees, and 20 degrees
no 90 degree angle, so not a right triangle
all three angles are different, so not an isosceles triangle
135 > 90, so not an acute triangle
must be an obtuse triangle
please help im not sure how this works
Answer:
b i nthink
Step-by-step explanation:
B. maybe?
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If √6 is the geometric mean between 4 and another number, then the number is
A. 9
B. 24
C. 1.5
Answer: THE ANSWER TO THAT IS C
Step-by-step explanation:
Patrick lost his lunch money on the way to
school. If he can get thirteen of his friends
to each give him a quarter, he can buy a
school lunch. How much does a school
lunch cost?
$_
Answer:
$3.25
Step-by-step explanation:
Each quarter is 25¢
13 quarters will be worth 13 x 25 = 325¢
Since 1$ = 100¢
divide 325¢ by 100 to get amount in $
= 325/100 = $3.25
What in the world how do you solve this?
Answer:
B
Step-by-step explanation:
using the rule of radicals
• [tex]\sqrt[n]{x}[/tex] ÷ [tex]\sqrt[n]{y}[/tex] = [tex]\sqrt[n]{\frac{x}{y} }[/tex], then
32[tex]\sqrt[8]{18y}[/tex] ÷ 8[tex]\sqrt[8]{3y}[/tex]
= [tex]\frac{32}{8}[/tex] ×[tex]\sqrt[8]{\frac{18y}{3y} }[/tex] ( cancel 18y and 3y by 3y )
= 4 × [tex]\sqrt[8]{6}[/tex]
= 4[tex]\sqrt[8]{6}[/tex]
Match each slope and y-intercept with the appropriate linear equation.
m = 3, b=4
m = 5, b = -2
m = 4, b=3
m = -2, b=5
Intro
↑
↑
y = 4x +3
y = 3x + 4
y = 5x-2
y = -2x + 5
Done
Answer:
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
y = 1.5x - 7 m = 1.5 b = -7
(y = (1.5)x + (-7) ----> y = 1.5x - 7)
y = -1.5x - 4 m = -1.5 b = -4
y = -3x + 4 m = -3 b = 4
y = 3x m = 3 b = 0
y = 7 m = 0 b = 7
(y = (0)x + 7 ---> y = 7)
Step-by-step explanation:
Your uncle wants to buy a monthly garage parking pass that costs $49.75.
He has five $10 bills, one $5 bill, five $1 bills, and 3 quarters. Use the table
to show three different ways your uncle could pay for the pass and the
change that he receives.
Answer:
See below
Step-by-step explanation:
Answer
Denomination
10 5 1 0.75 Change
5 0 0 0 0.25
4 1 4 0.75
These are the only 2 ways I see of paying the parking pass. The tens can't drop down to 3 because the rest will never add up to 19.95
Noah has collected $50 by selling lemonade and muffins. He sold $10 worth of muffins. He sold each cup of
lemonade for $2. How many cups of lemonade did he sell?
Choose the correct equation.
a. 2x-10-50
b. 2x+10=50
c. 2x+50=10
d. 10x+2=50
Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
The equation of the line will be y = -2x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Given that the equation of the line that passes through the points (0,3) and (2,-1).
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
First calculate the slope of the line:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -1 - 3 ) / ( 2 - 0 )
Slope = -2
The y-intercept will be:-
y = mx + c
3 = 0 + c
c = 3
Equation of the line:-
y = mx + c
y = -2x + 3
Therefore, the equation of the line will be y = -2x + 3.
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The change in the value of a stock is represented by the rational number -6.50 describe in words what this means
The rational number given in words mean that the value of the stock has declined or decreased by 6.50.
What is a negative number?A rational number is a number that can be expressed as a fraction of two integers. Rational numbers can be positive or negative.
A negative number is a number that is smaller than zero. A negative number usually has this sign, -, preceding it. An example of a negative number is -6.50.
When a stock's value is represented by a negative number, it means that the value of the stock has declined or fallen.
On the other hand, if the stock's value is represented by a positive number, it means that the value of the stock has increased.
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select 3 statements one for Cosine one for Tangent and one for sine
From the unit circle, we can deduce the 3 correct statements.
1. The first correct sine statement is;
[tex]\sin 45=\frac{\sqrt[]{2}}{2}[/tex]2. The correct cosine statement is;
[tex]\cos 45=\frac{\sqrt[]{2}}{2}[/tex]3. The correct tangent statement is;
[tex]\tan 45=1[/tex]Here's a diagram to show why
The stemplot displays 26 students' scores on a 90-point
statistics test. The lowest possible passing grade on the test was a 54 out of 90. What percentage of students passed this test ?
A. 23%
B. 54%
C. 77%
D. 96%
Answer:
C. 77%
Step-by-step explanation:
20 out of 26 people passed so
20 divided by 26 equals 76.9 so 77 percent
Send the answer's please.
Answer:
A 573308928
B. 124176266400000000000000000
Tell whether the ordered pair is a solution to the system of equations. You must show work to support your answer.a) (5,2)2x-3y=42x+8y=11
Replace x by 5 and y by 2 on both equations, and check if the equalities remain:
2x-3y=4
2(5)-3(2) =4
10-6= 4
4=4 EQUAL
2x+8y= 11
2(5) + 8(2)=11
10 + 16 = 11
26=11
26 is not equal to 11
The ordered pair is NOT a solution to the system of equations.
Two numbers have a difference of 1,200 and a total of 6,484
What are the two numbers
3842 and 2642 are the two numbers.
What is linear equations?
Linear equations are a subset of first order equations. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
How to Solve?
Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. There are six main ways to resolve linear equations. For the purpose of solving linear equations, these methods include the Graphical Method, Elimination Method, Substitution Method, Cross Multiplication Method, Matrix Method, and Determinants Method.
Let the greater of the two numbers be "x" and the smaller one be "y".
Given, x - y = 1200 --(i) & x + y = 6484 --(ii)
Adding (i) and (ii), we get, 2x = 7684 ⇒ x = 3842
Subtracting (i) from (ii), we get, 2y = 5284 ⇒ y = 2642
Thus, the greater number of the two numbers is 3842 and the smaller number is 2641.
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Let sets A and B be defined as follows. A is the set of integers greater than -8 and less than -4.B={b,h,i,l,r,s}
A
Concept
The cardinality of a set is a measure of the "number of elements" of the set. For example, the set contains 3 elements, and therefore. has a cardinality of 3.
Set A is the set of integers greater than -8 and less than -4.
Therefore set A = {-7, -6, -5,}
-7 is greater than -8 and -5 is less than -4 from the number line.
Therefore, set A = { -7, -6, -5 }
B = {b, h, i, l. r, s }
Cardinalities of
n(A) = 3 n(B) = 6
B
[tex]\begin{gathered} -5\text{ }E\text{ A = true} \\ -12\text{ E A = false} \\ b\text{ E B = true} \\ t\text{ }\notin\text{ B = true} \end{gathered}[/tex]
Please help with this
Explanation
Given the function
[tex]y=arctanx[/tex]The domain of the function is given as
[tex]-\inftyAnswer: Option 3Find each of the numbers below.
Simplify your answers as much as possible.
The opposite of 0:
The opposite of 7:0
The opposite of the opposite of 6:
The opposite of 0 is 0, the opposite of 7 is -7 and the opposite of 6 is -6.
If we consider a number x, then the opposite of the number x will be equal to -x. In a number line the opposite of a number lying on the positive side always lies on the negative side of number line. Also, the opposite of a number -x is the x that is the number itself. It is given in the question that we need to find opposite of 0, 7 and 6.
Let x = 0, opposite of x is -x.
=> -x = -0
=> -x = 0
Now, let x = 7, opposite of x is -x
=> -x = -7
Now, let x = 6, opposite of x is -x
=>-x = -6
Thus, the opposite of the numbers 0, 7 and 6 are 0, -7 and -6 respectively.
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Given the function f(x) in red, write the equation for the transformed function g(x)in green
Subtract these equations.
INFORMATION:
We have the next subtraction
And we must solve it
STEP BY STEP EXPLANATION:
To solve a subtraction of two expressions, we must multiply the second expression by -1 and then add up the first expression and the result of the multiplication.
1. Multiply the second expression by -1
[tex]\begin{gathered} -1(3x+2y=3) \\ -3x-2y=-3 \end{gathered}[/tex]2. Add up the first expression and the result of the multiplication. We must add similar terms
[tex]\begin{gathered} 3x+4y=17 \\ -3x-2y=-3 \\ -------- \\ 0x+2y=14 \\ →2y=14 \end{gathered}[/tex]Finally, the result of the subtraction is 2y = 14
ANSWER:
aA. 2y = 14
TRUE OR FALSE?
The Transitive property on N states that: For any two natural numbers a and b, either a > b or a = b or b> a.
Answer:
False a=b
Step-by-step explanation: