1) Since there are 20 students, and each committee is formed by 4 people.
The order does not matter, and there can't be repetition. Just one person can be, let's say president, VP, secretary, and treasurer.
2) So we can write, the possibilities on the numerator of people filling in and on the denominator the number of vacancies for that committee, we can set this Combination simply as:
[tex]\frac{20}{4}\times\frac{19}{3}\times\frac{18}{2}\times\frac{17}{1}=4845[/tex]3) So there are 4845 possibilities to form a Committee with 20 people for 4 vacant lots.
I need help ASAP please can you help you help
OPTION C
A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.
From our question, it was easy to
The following table is a function.х15725354 9у-3 27-4 5971 0
a For any relation to be a function, an independent variable x cannot produce different dependent varible y
From the table,
when x = 5, y = 2
Also, when x = 5, y = 5
and when x = 5, y = 7
We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function
Hence, the table is not a function
The answer is False
Write each equation in slope intercept form. Then graph .
ANSWER
EXPLANATION
Given;
[tex]y=-\frac{5}{6}x+4[/tex]Recall, the general formula for slope - intercept form is;
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]comparing the given equation with the standard slope intercept form formula;
[tex]\begin{gathered} y=mx+c \\ y=-\frac{5}{6}x+4 \\ m=-\frac{5}{6} \\ c=4 \end{gathered}[/tex]Hence, the graph of the given equation is;
how to write this on a number line1 plus x less than 5
We are given the following inequality
[tex]1+x<5[/tex]Let us first solve the inequality for x.
Subtract 1 from both sides of the inequality
[tex]\begin{gathered} -1+1+x<5-1 \\ x<4 \end{gathered}[/tex]So the solution of the inequality is all the values of x less than 4
Now let us graph this solution on a number line.
"The distributive Property"
Using the distributive property, the maximum number of players that can be in the NBA is; 450 players
How to use distributive property?The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;
a(b + c) = ab + ac
Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;
Number of players on each team = (12 + 3)
Now, for the 30 teams;
Total number of players for the teams = 30(12 + 3)
Applying distributive property, we have;
(30*12 + 30*3) = 450
Read more about distributive property at; https://brainly.com/question/2807928
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I need the answer but i also need to check my answer after
we have the following:
[tex]\begin{gathered} 7=\frac{x-8}{3} \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} x-8=7\cdot3 \\ x=21-8 \\ x=13 \end{gathered}[/tex]please need a answer
Answer:
ok you can ask
Step-by-step explanation:
don't forget to follow rate like
What is the multiplicity of each of the roots of this graph?2
SOLUTIONS
What is the multiplicity of each of the roots of this graph?
[tex]f(x)=2x^4+12x^3+16x^2-12x-18[/tex]Factorise f(x) by the options
(a) According to the option we have -3 is a root of so x+3 is a factor
[tex]\frac{2x^4+12x^3+16x^2-12x-18}{x+3}=2x^3+6x^2-2x-6[/tex](b) 1 is a root too so x - 1 is a factor
[tex]\frac{2x^3+6x^2-2x-6}{x-1}=2x^2+8x+6[/tex][tex]\begin{gathered} 2x^2+8x+6=2(x+3)(x+1) \\ f(x)=2(x+3)^2(x+1)(x-1) \end{gathered}[/tex]Therefore the correct answer = Option A
which is the best description of the data in the scatter plot
Types of correlation:
Based on the types of correlation, we can see that the best description of the data given is a positive correlation.
Answer: A positive correlation.
please help. due today! will mark as brainliest!
Answer:
which question you want to be answered
Answer:
[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]
[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]
Step-by-step explanation:
Question 13The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:
[tex]\boxed{P=0.5 \pi d+d}[/tex]
Part (a)
To express d in terms of P, rearrange the equation to isolate d.
Factor out the common term d from the right side of the equation:
[tex]\implies P=d(0.5 \pi +1)[/tex]
Divide both sides by (0.5π + 1):
[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]
[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]
[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]
Part (b)
Given:
Perimeter = 36 in[tex]\pi \approx \dfrac{22}{7}[/tex]Substitute the given values into the equation derived in part (a) and solve for d:
[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]
[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]
[tex]\implies d=36 \times \dfrac{7}{18}[/tex]
[tex]\implies d=\dfrac{252}{18}[/tex]
[tex]\implies d=14[/tex]
Therefore, the diameter is 14 inches.
Where x is the horizontal distance in feet from the point at which the ball is thrown.How far from the child does the ball strike the ground?
To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:
[tex]\begin{gathered} y=-\frac{1}{14}x^2+4x+3 \\ \Rightarrow y^{\prime}=-\frac{2}{14}x+4=-\frac{1}{7}x+4 \\ \Rightarrow y^{\doubleprime}=-\frac{1}{7} \end{gathered}[/tex]Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow-\frac{1}{7}x+4=0 \\ \Rightarrow\frac{1}{7}x=4 \\ \Rightarrow x=7\cdot4=28 \\ x=28 \end{gathered}[/tex]Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:
[tex]\begin{gathered} y=-\frac{1}{14}(28)^2+4(28)+3 \\ \Rightarrow y=-\frac{1}{14}(784)+112+3 \\ \Rightarrow y=-56+112+3=59 \\ y=59 \end{gathered}[/tex]Finally, we have that the ball will go 59 feet from the child
the corporate team building event will cost $30 if it has 6 attendees. How many attendees can there be, at most, if the budget for the corporate team building event is $50? Assume the relationship is directly proportional.
Let the number of attendees be a.
ak=c , where k=constant of variation.
6k=30
k=30/6
k=5
Find a when c=$50
5a=50
a=50/5
a=10
There will be 10 attendees for a bu
y= 4/3 x-1 graph the line the top to right is 10 8 6 4 2 and at the left to bottom is -10 -8 -6 -4 -2
the graph of this equation is:
Let us make part of the table corresponding to this graph
Find the coordinates of the missing vertex of rectangle ABCD with A(-3, 3),B(5, 3), and D(-3, -1).O (5, -1)© (-11, 7)O (5,3)O (1, -1)
Given:
The given vertex of a rectangle ABCD are A=(-3,3), B=(5,3) and D=(-3,-1)
To find: Missing vertex, that means vertex C
The graph is as follows:
From the above graph, the coordinates of point C are (5,-1).
Hence, the required answer is (5,-1).
A hose for the hot tub at a rate of 3.61 gallons per minute. How many hours will it take to fill a 345 gallon hot tub?
We have a 345 gallon hot tub that fills at a rate of 3.61 gallons/min.
To calculate filling time, we need to divide as it follows:
[tex]t=\frac{345\text{gal}}{3.61\frac{\text{gal}}{\min }}[/tex]in that way we can find how much time does it take in minutes
[tex]t=\frac{345}{3.61}=95.56786[/tex]now, if we want to determine time in hours, we must divide by 60, because there are 60 min. in one hour.
[tex]t=\frac{345}{3.61}\cdot\frac{1}{60}=1.59279[/tex]Then, it would take approximately 1.59 hours to fill the hot tub.
Question 3 Olivia is making pancakes for breakfast. The recipe calls for 0.5 quart of milk and 2.5 cups of flour. She has quart of 3/8 quart of milk and 18/8 cups of flour. Olivia makes the recipe with the milk and flour she has. Explain her error. Hint: Convert all of them to either decimal or fraction so that you can compare the values. Challenge: How much more or less milk does Olivia need? How much more or less flour does Olivia need?
ANSWER and EXPLANATION
The recipe calls for 0.5 quart of milk and 2.5 cups of flour.
She has 3/8 quart of milk and 18/8 cups of flour.
To know the error she made, we have to find the ratio of milk to flour in the recipe and the ratio of milk to flour that she used and see if the ratios are the same.
RECIPE
Ratio of milk to flour is:
[tex]\begin{gathered} 0.5\text{ : 2.5} \\ \Rightarrow\text{ 1 : 5} \end{gathered}[/tex]That is the ratio of milk to flour.
USED BY OLIVIA
Ratio of milk and flour that she used is:
[tex]\begin{gathered} \frac{3}{8}\text{ : }\frac{18}{8} \\ =>\text{ 3 : 18} \\ \Rightarrow\text{ 1 : 6} \end{gathered}[/tex]We can already see that the ratios are not the same.
By comparing the ratios, we see that she actually used more flour than she was supposed to.
Which of the following represents the factorization of the trinomial below?x2 – X-20A. (x-4)(x-5)B. (X + 4)(x-5)oC. (x-2)(x-10)0D. (x+2)(x-10)
Answer:
(x+4)(x-5)
Step-by-step explanation:
Second order polynomial in the following format:
ax² + bx + c = 0
Has roots x¹ and x².
Can be factored as:
(x - x¹)(x - x²)
So, we have to find the roots.
Finding the roots:
Bhaskara formula, which is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In the polynomial given in this question:
a = 1, b = -1, c = -20
So
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]The roots are:
[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]The factored form is:
(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)
What is the LCM of 10 and 4?
One way to find the least common multiple of two numbers is to first list the prime factors of each number.
[tex]\begin{gathered} 10=2\cdot5 \\ 4=2\cdot2 \end{gathered}[/tex]Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.
[tex]undefined[/tex]Can you pls help with 7 I need to do 8 more packets like these by tomoghy
The daily rate can be found by dividing the total number of books over the number of calendar days.
15,260 / 28 = 545
545 books per day
triangle W quadrilateral hexagon pentagon 2 + please help me out with thisWhat is a name for this shapetrianglequadrilateralhexagonpentagon
To determine the name of the shape you have to count its sides.
If it has 3 sides is a triangle, if it has 4 sides is a quadrilateral, if it has 5 sides is a pentagon and if it has 6 sides is a hexagon,
The shape has 6 sides so it is a hexagon.
Find the derivative of the trigonometric function using the Chain Rule.[tex]y = \cos \sqrt{x} [/tex]
is rational or irrational v2
The square root of 2 is irrational
Here, we want to check if the square root of 2 is rational or not
When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers
Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd
Which number is the same as (4-1)20-4-2), A - 2 B. 1/8C 2 D. 32 E. 512
Hi I need help bad on this I have a report card Wednesday and my birthday is in 13 days
3)
- 18/(- 6)
This can be written as
- 18/- 6
Recall, if a negative number divides a negative number, the result is positive. Thus, the answer is 3
y=-x^2-4x-8Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of the parabola.
Here we have the following parabola:
[tex]y=-x^2-4x-8[/tex]To find the vertex, we could use the following formula:
[tex]V(x,y)=V(\frac{-b}{2a},\frac{-b^2}{4a}+c)[/tex]Where a, b and c are the coefficients of the quadratic function:
[tex]y=ax^2+bx+c[/tex]As you can see, in this problem a = -1 , b = -4 and c = -8. Thus,
[tex]V(x,y)=V(\frac{-(-4)}{2(-1)},\frac{-(-4)^2}{4(-1)}-8)[/tex]This is:
[tex]V(-2,-4)[/tex]Then, the vertex of the parabola is (-2,-4)
The axis of symmetry of the parabola is the line x=-2. Since the vertex is situated at the coordinates (-2,-4), that means that the parabola is symmetrical around this line.
The vertex is maximum point of the parabola.
The range, is defined as all the values that the y-axis could take. If we notice, that is:
[tex](-\infty,-4\rbrack[/tex]I'm going to upload a picture of the parabola:
Questionf(2)Find R(2) where f(2)g(2)x² – a- 2 - 3010x + 100and g(2)-22 – 5x + 6611x + 110(Simplify your answer.)Provide your answer below:
Answer:
Given that,
To find,
[tex]R(x)=\frac{f(x)}{g(x)}[/tex]where,
[tex]f(x)=\frac{x^2-x-30}{10x+100}[/tex][tex]g(x)=\frac{-x^2-5x+66}{11x+110}[/tex]Simplifing f(x) and g(x), we get
[tex]f(x)=\frac{x^2-x-30}{10x+10)}=\frac{x^2-6x+5x-30}{10(x+10)}[/tex][tex]=\frac{x(x-6)+5(x-6)}{10(x+10)}=\frac{(x-6)(x+5)}{10(x+10)}[/tex][tex]f(x)=\frac{(x-6)(x+5)}{10(x+10)}-----(1)[/tex]This is the simplified form of f(x).
For g(x) we get,
[tex]g(x)=\frac{-x^2-5x+66}{11x+110}=\frac{x^2+5x-66}{-11(x+10)}[/tex][tex]=\frac{x^2+11x-6x-66}{-11(x+10)}=\frac{x(x+11)-6(x+11)}{-11(x+10)}[/tex][tex]g(x)=\frac{(x+11)(x-6)}{-11(x+10)}------(2)[/tex][tex]\frac{i}{g(x)}=\frac{-11(x+10)}{(x+11)(x-6)}[/tex]Now To find R(x), we get
[tex]R(x)=\frac{f(x)}{g(x)}=f(x)\times\frac{1}{g(x)}[/tex][tex]=\frac{(x-6)(x+5)}{10(x+10)}\times\frac{-11(x+10)}{(x+11)(x-6)}[/tex][tex]=\frac{-11(x+5)}{10(x+11)}[/tex]we get,
[tex]R(x)=\frac{-11(x+5)}{10(x+11)}[/tex]Answer is:
[tex]R(x)=\frac{-11(x+5)}{10(x+11)}[/tex]The local bike shop rents bikes for $18 plus $6per hour. Bill paid $36 to rent a bike. For howmany hours did he rent the bike for?
we have:
h = hour
the equation is
[tex]\begin{gathered} 18+6h=36 \\ 18+6h-18=36-18 \\ 6h=18 \\ \frac{6h}{6}=\frac{18}{6} \\ h=3 \end{gathered}[/tex]answer: 3 hours
how would I graph 3x + 4y = -4
Answer:
To graph a line you have to find two points on the line, one way of doing this is first setting x=0 and solving for y, as follows:
[tex]\begin{gathered} 3(0)+4y=-4, \\ 4y=-4, \\ y=-1. \end{gathered}[/tex]With the above calculations, we got that the point (0,-1) is on the line.
Now, to find another point on the line we set y=0 and solve for x:
[tex]\begin{gathered} 3x+4(0)=-4, \\ 3x=-4, \\ x=-\frac{4}{3}\text{.} \end{gathered}[/tex]With the above calculations, we got that the point (-4/3,0) is on the line.
Once we have those points we draw the line that passes through those points.
The graph of the given equation is:
11.Solve the given equation over the interval [0, 271): 2 sin x++3 = 0.117and x=64757X=- and x=332лx= -- and x=3T57x= -- and x=6and x3
Question:
Solution:
Let the following trigonometric equation:
[tex]2\sin (x)+\sqrt[]{3}=\text{ 0}[/tex]Subtract the root of 3 from both sides of the equation:
[tex]2\sin (x)=-\sqrt[]{3}[/tex]solve for sin(x):
[tex]\sin (x)=\text{ -}\frac{\sqrt[]{3}}{2}[/tex]Applying the trigonometric circle on the given interval, we obtain that the correct answer is:
[tex]x\text{ = }\frac{4\pi}{3}\text{ , x = }\frac{5\pi}{3}[/tex]
1. Which of the following have the same domain and range? I. y = 2x - 1 II. y = -x + 2 x = 2 (A) I and III only (B) I and II only (C) II and III only (D) I, II and III
The I and II are linear function, so those have the same domain and the same range always. So the answer is B