Answer: correct answer is S + L = 95 and 2S + L = 120
Step-by-step explanation:
A group consists of 6 men and 5 women. five people are selected to attend a conference. in how many ways can 5 people be selected from this group of 11? in how many ways can 5 men be selected from the 6 men? find the probability that the selected group will consist of all men.
To compute for combinations, we will use the method nCr = n! / r! * (n - r)!
Where: n signifies the number of items, and r signifies the number of items being selected at a time.
Solution
1. 11C5 = 11!/ 5! * (11-5)! = 462 ways
2. 6C5 = 6!/ 5! * (6-5)! = 6 ways
3. 6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.
The calculation involves using combinations to find the total number of ways to select 5 people from 11, and then to find the probability of selecting 5 men by dividing the number of ways to select 5 men from 6 by the total number of selections.
Explanation:The student's question deals with the topic of combinatorics, specifically the selection of groups and calculation of probabilities using the hypergeometric distribution. To find how many ways 5 people can be selected from a group of 11 (6 men and 5 women), we use the combination formula [tex]C(n, k) = n! / (k!(n-k)!).[/tex]
For the first part of the question, selecting 5 people out of 11, the calculation is C(11, 5). To calculate the number of ways 5 men can be selected from 6 men, we use C(6,5).
Lastly, to find the probability that the selected group will consist of all men, we divide the number of ways to select 5 men by the total number of ways to select 5 people from the whole group:
Calculate the number of ways to choose 5 people from 11 (C(11, 5)).Calculate the number of ways to choose 5 men from 6 (C(6,5)).Divide the number of ways to choose 5 men by the total number of ways to choose 5 people to get the probability of selecting all men.Learn more about hypergeometric distribution here:https://brainly.com/question/35126689
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A minivan can hold up to 7 people how many minivans are needed to take 45 people to a baseball game
Use slopes to determine if the triangle whose vertices are left parenthesis negative 4 comma 4 right parenthesis(−4,4), left parenthesis 1 comma 5 right parenthesis(1,5), and left parenthesis 2 comma 0 right parenthesis(2,0) is a right triangle. find the slope for the side of the triangle between the vertices left parenthesis negative 4 comma 4 right parenthesis(−4,4) and left parenthesis 1 comma 5 right parenthesis(1,5). mequals= one fifth 1 5 (type an integer or a simplified fraction.) find the slope for the side of the triangle between the vertices left parenthesis 1 comma 5 right parenthesis(1,5) and left parenthesis 2 comma 0 right parenthesis(2,0). mequals= negative 5−5 (type an integer or a simplified fraction.) find the slope for the side of the triangle between the vertices left parenthesis negative 4 comma 4 right parenthesis(−4,4) and left parenthesis 2 comma 0 right parenthesis(2,0). mequals= negative two thirds− 2 3 (type an integer or a simplified fraction.) is the triangle a right triangle?
Final answer:
By calculating slopes of the triangle's sides and identifying that two of them are negative reciprocals of each other, it's confirmed that the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle.
Explanation:
To determine if the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle, we calculate the slopes of all three sides. The slope of the line between points (-4, 4) and (1, 5) is calculated using the slope formula m = (y2 - y1) / (x2 - x1). Using the coordinates, the slope is (5 - 4) / (1 - (-4)) = 1 / 5. Similarly, the slope between points (1, 5) and (2, 0) is (0 - 5) / (2 - 1) = -5. Lastly, the slope of the line between (-4, 4) and (2, 0) is (0 - 4) / (2 - (-4)) = -4 / 6, which simplifies to -2 / 3. A right triangle has one 90-degree angle, and the slopes of perpendicular lines are negative reciprocals of each other. Therefore, if two of these slopes are negative reciprocals, the triangle is a right triangle. In this case, the slopes -5 and 1/5 are negative reciprocals, confirming that the triangle is a right triangle.
The quotient of the number of students and 3
Answer:
This can be written as x/3, in which x is the number of students.
Step-by-step explanation:
The term quotient means to find what happens when you divide the first by the second. Then we need to pick a variable for the unknown number of students.
which container holds more a half gallon milk jug or a 2 L juice bottle
Helpppppppppppppppppppppppppppppppppp
The vertices of ΔABC are (-2,0), (-2, 3), and (-5, 1). T(x,y) = (x + 1, 3y) represents the transformation of the triangle. What are the coordinates of the vertices for ΔA'B'C'? Are the pre-image and image congruent? Justify your answer.
using the equation for the transformation:
(x+1, 3y)
add 1 to very X and multiply y by 3
so (-2,0) becomes (-1,0)
(-2,3) becomes (-1,9)
(-5,1) becomes (-4,3)
new coordinates are (-1,0) (-1,9) (-4,3)
you don't have an image attached, so to see if they are congruent, the sides need to stay the same lengths and the angles need to stay the same, from the coordinates of the new triangle, I would say they are not congruent
N a triangle, the measure of the first angle is twicetwice the measure of the second angle. the measure of the third angle is 68 degrees68° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
If n people are seated in a random manner in a row containing 2n seats, what is the probability that no two people will occupy adjacent seats? 10. a box contains 24 light bulbs, o
To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n).
Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :
The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].
Explanation:To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.
Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:
_ A _ A _A _ A __ A _ ASo, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.
Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].
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The function shown is reflected across the y-axis to create a new function.
Which is true about the domain and range of each function?
A.Both the domain and range change.
B.Both the range and domain stay the same.
C.The domain stays the same, but the range changes.
D.The range stays the same, but the domain changes
Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.
Explanation:When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.
The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.
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Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.
The correct option is A. Both the domain and range change.
When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.
The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.
The correct option is A. Both the domain and range change.
Which postulate or theorem proves that these two triangles are congruent?
ASA Congruence Postulate
SAS Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
Answer:
AAS Congruence Theorem
Step-by-step explanation:
i dont know bro
Answer: AAS Congruence Theorem
Step-by-step explanation:
In the given picture , we have given two triangles ΔFGJ and ΔHJG with one common edge i.e. GJ
Now, in the given triangles ΔFGJ and ΔHJG we have
∠F=∠H [given]
and ∠FGJ=∠HJG [given]
Also, GJ=GJ [Reflexive property]
Therefore, by AAS Congruence Theorem,
ΔFGJ ≅ ΔHJG
AAS Congruence Theorem says that if any two angles and a side one triangle are congruent to any two angles and a side of another triangle, then these two triangles are congruent.Multiply 5 4/7 × -2 2/5
A) -10 8/35
B) 10 8/35
C) -13 13/35
D) 13 13/35
Suppose that b>0 and that the average value of f(x)=5x−5 on [0,b] is 14. find the value of
b.
The value of b is [tex]\dfrac{38}{5}[/tex].
Linear equation
In this, the power of x is 1. And it consists of the variable and/or constant term only.
Given
f(x)=5x−5
The average of that is 14 for the [0, b]
To find
The value of b.
How to get the value of b?For the x = 0, the value of f(x) will be
f(0) = -5
For the x = b, the value of f(x) will be
f(b) = 5b - 5
The average of that is 14.
[tex]\begin{aligned} \rm Average &= \dfrac{f(0)+f(b)}{2} \\14 &= \dfrac{(-5)+(5b-5)}{2} \\28 &= 5b -5 -5\\28 +5 + 5 &= 5b\\5b &= 38\\b &= \frac{38}{5} \\\end{aligned}[/tex]
Thus, the value of b is [tex]\dfrac{38}{5}[/tex].
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Mrs. Williams is knitting a blanket for her newborn granddaughter. The blanket is 2.25 meters long and 1.8 meters wide. What is the area of the blanket? Write the anwser in centimeters.
Solve the inequality -×/7+4>3×.
What’s the derivative of 3g(x)
Is it just 3g’(x)
Final answer:
The derivative of 3g(x) is 3g'(x), obtained by taking the derivative of the function and multiplying it by the constant.
Explanation:
Derivative of 3g(x):
Yes, the derivative of 3g(x) is indeed **3g'(x)**.
When you have a constant multiplied by a function, you can simply take the derivative of the function and multiply it by the constant to find the derivative of the entire expression. In this case, the derivative of 3g(x) would be 3 times the derivative of g(x), which is 3g'(x).
A recipe calls for 40 ounces of meat. How many pounds of meat does the recipe require?
The recipe requires 2.5 pounds of meat.
we have,
To convert ounces to pounds, we use the conversion factor that 16 ounces is equal to 1 pound.
This means that every pound is made up of 16 ounces.
Given that the recipe calls for 40 ounces of meat, we can divide this quantity by the conversion factor of 16 ounces per pound to find the equivalent in pounds.
Dividing 40 by 16 gives us 2.5. So, the recipe requires 2.5 pounds of meat.
This conversion is based on the relationship between ounces and pounds, where each pound consists of 16 ounces.
So,
When converting from ounces to pounds, we divide the number of ounces by 16 to find the equivalent number of pounds.
Therefore,
The recipe requires 2.5 pounds of meat.
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what is 2 1/3 divided by 2/5
Is the product of two positive mixed numbers ever less than 1?
Bill is 6 years younger than amy.the sum of their ages is 22.how old will each of them be in 8 years
The organizers of a drama club wanted to sell 350 tickets to their show.The actual sales were no more than 35 tickets from his goal.Write an d solve an absolute value inequality to find the range of the number of tickets that could have been sold
Select the function that represents the transformation of the parent function three units to the left and up two.
f(x) = |x - 3| - 2
f(x) = -|x - 3| + 2
f(x) = |x + 3| + 2
f(x) = -|x + 3| + 2
Answer:
The correct option is C. f(x) = |x + 3| + 2
Step-by-step explanation:
The parent function in this case is : mod x = |x|
Let the parent function be f(x) = |x|
Now, The parent function is transformed 3 units to the left
⇒ f (x) = f(x + 3)
⇒ f(x) = |x + 3|
Also, The parent function is transformed up by 2 units
⇒ f(x) = f(x) + 2
⇒ f(x) = |x + 3| + 2
Therefore, The correct option is C. f(x) = |x + 3| + 2
WILL BE AWARDED 68 POINTS. Solve for x. Round your answer to 2 decimal places. (5 points)
to find x divide 16 by the sin of 30
16 / sin(30) = 32
if you need 2 decimal places it would be 32.00
Answer:
16 sin30 = 32
Step-by-step explanation:
Four balls of wool will make 8 knitted caps. How many balls of wool will Malcolm need if he wants to make 6 cups
Factor the quadratic function f(x) = 4x2 – x – 5 to determine the zeros of the function.
To find the zeros of the function f(x) = 4x2 – x – 5, we first set the equation to zero, factor it to find (4x - 5)(x + 1) = 0, and solve for x, finding the zeros to be 5/4 and -1.
Explanation:The first step in factoring the quadratic function f(x) = 4x2 – x – 5 is to set the equation to zero.
The factored form of a quadratic equation is generally represented as (ax + b)(cx + d) = 0, where x is the zeros of the function. So, the equation we have is 4x² - x - 5 = 0.
Now, we need to look for two numbers that multiply to (a*c) = -20 (4*-5) and add up to -1 which are -5 and 4. Hence, the middle expression -x can be expressed as -5x + 4x, so the equation becomes:
4x² - 5x + 4x - 5 = 0.
Factoring, we get the following:
x(4x - 5) + 1(4x - 5) = 0.
Or we could write as:
(4x - 5)(x + 1) = 0.
Now, to find zeros of the function, we set each factor equal to zero and solve for x:
4x - 5 = 0 implies, x = 5/4.
x + 1 = 0 implies, x = -1.
So, the zeros of the function are 5/4 and -1.
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How many rectangles are needed to draw the net of this object?
There's an image of the problem that I'm asking about attached.
Answer with explanation:
If you will count the faces of this three dimensional geometrical shape , there are 5 faces in which there are 2 triangles and 3 Quadrilaterals.
So,to draw the net of this solid , you need
⇒As there are 3 Quadrilaterals which is in the shape of parallelogram,
You need three rectangles ,to draw the net of this object.
Option C: 3
Consider the sequence of steps to solve the equation: x - 3 3 = x + 3 Step 1 ⇒ x - 3 = 3(x + 3) Step 2 ⇒ x - 3 = 3x + 9 Step 3 ⇒ x = 3x + 12 Step 4 ⇒ -2x = 12 Step 5 ⇒ x = -6 Identify the property of equality which yields Step 5. A) Division Property B) Addition Property C) Subtraction Property D) Multiplication Propert
In May, there were 157 people living in Kristin's neighborhood. By August, the population had increased 21%. How many people were in Kristin's neighborhood by August?
A.330
B.190
C.33
D.1900
Reduce fractions expressing probability to lowest terms. in 3,000 repetitions of an experiment, a random event occurred in 500 cases. the expected probability of this event is? 1/6 5/5 1/3 2/3
From the statement select the related given statement. If B is between A and C, then AB + BC = AC
A.) Plane R is parallel to plane S; Plane T cuts planes R and S.
B.) △ABC with ∠1 = ∠2.
C.) Point B is between points A and C.
D.) Line l; point P not on l.
E.) △ABC with midpoints M and N.
Answer:
C.) Point B is between points A and C.
Step-by-step explanation:
The simplest way to analyze this is as a line.
This line goes from A to C and somewhere in the middle, is B.
But they tell you that AB + BC = AC.
The distance from A to B plus the distance from B to C is the same as the distance from A to C.
Option A about planes is not the correct one because there's no mention of planes.
Option B about angles is not correct because they only talk about some points of a line. You don't know if there's some angle in between.
The same happed with options D and E.