There are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have the total number of students = 18
The number of ways the club send 4 students to the next debate is:
= C(18, 4)
[tex]= \rm \dfrac{18!}{4!(18-4)!}[/tex]
= 3060
Thus, there are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
Learn more about permutation and combination here:
https://brainly.com/question/2295036
#SPJ1
Solve below functions word problem ASAP
The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)
The assumed valuesTicket price = $60 per ticketPeople = 250Increase in price = 8Decrease in people = 30The revenue functionLet the number of people be x, and the revenue function be F(x).
Using the assumed values, the revenue function is:
F(x) = (60 + 8x)(250 - 30x)
The maximum fundsWe have:
F(x) = (60 + 8x)(250 - 30x)
Expand
F(x) = 15000 - 1800x + 2000x - 240x²
Differentiate the function
F'(x) = -1800 + 2000 - 480x
Evaluate
F'(x) = 200 - 480x
Set to 0
200 - 480x = 0
This gives
480x = 200
Divide both sides by 480
x = 0.42
Substitute x = 0.42 in F(x)
F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)
Evaluate
F(x) = 18210
Hence, the maximum revenue is $18210, at a rate of $0.42 per person.
Would they raise $5000?We start by setting F(x) to 5000.
So, we have:
15000 - 1800x + 2000x - 240x² = 5000
Evaluate the like terms
10000 + 200x - 240x² = 0
Using a graphing tool, we have:
x = 6.89
Hence, they would reach their goal at a rate of $6.89 per ticket.
The cost function
We have:
People = x
Cost per person = 20
So, the cost function is:
C(x) = 20x
The profit functionProfit is calculated using:
P(x) = F(x) - C(x)
So, we have:
P(x) = 15000 - 1800x + 2000x - 240x² - 20x
Evaluate
P(x) = 15000 + 180x - 240x²
The break even priceThis is the point where P(x) = 0.
So, we have:
15000 + 180x - 240x² = 0
Using a graphing tool, we have:
x = 8.29
Hence, the break even price is $8.29
Read more about profit, cost and revenue at:
https://brainly.com/question/25623677
#SPJ1
Given f(x) = -x + 5, find f(-3).
Answer:
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Given f(x)=-x+5, find f(-3).
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
We have the function
[tex]\longmapsto\sf{f(x)=-x+5}[/tex]
We need to find
[tex]\longmapsto\sf{f(-3)=}[/tex]
What we need to do:-Replace x with -3:-[tex]\longmapsto\sf{f(x)=-(-3)+5}[/tex]
Simplifying,
[tex]\longmapsto\sf{f(x)=3+5}[/tex]
(which is the exact same thing as 5-3)
Henceforth, We conclude that the answer is
[tex]\longmapsto\sf{f(-3)=8}[/tex]
Good luck with your studies. [tex]\ddot\smile[/tex]#TogetherWeGoFar ~
[tex]\rule{300}{1}[/tex]
Hey there!
Find f(-3) :
Answer :f(-3) = 8 ✅
Explanation :f(x) = -x + 5
>> Substitute -3 for x in f(x) :
f(-3) = -(-3) + 5
f(-3) = 3 + 5
f(-3) = 8
Therefore, your answer is f(-3) = 8
Similar question :
↣ https://brainly.com/question/20922457
a scientist notes that the number of bacteria in a colony is 50.3 hours later, she notes that the number of bacteria has increased to 80. if this rate of growth continues, how much more time will it take for the number of bacteria to reach 1119?
Answer:
16.8 hours
Step-by-step explanation:
An exponential population increase can be modeled by the function ...
p(t) = a·b^(t/p)
where 'a' is the initial value (at t=0), b is the multiplier in time period p.
__
setupThe colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.
p(t) = 80·1.6^(t/3)
1119 = 80·1.6^(t/3)
__
solutionSolving this for t, we find ...
1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80
log(1119/80) = (t/3)log(1.6) . . . . . take logarithms
t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t
t ≈ 16.8 . . . . hours
It will take about 16.8 more hours for the population to increase from 80 to 1119.
Find the values of the six trig functions for theta on each triangle.
Step-by-step explanation:
Select four types of data demographers study to make predictions.
birth rate
death rate
employment
income
marriage
migration
pushpa Rajkgf chapter 2VOLINCE VOLINCE VOLINCERRRAn artist is designing a website to showcase his 15-inch-wide paintings. The website will include scaled-down images of the paintings called thumbnails. For ease of viewing and to keep the thumbnail images large enough to show some detail, the artist decides to put three thumbnail images in a row so that any two adjacent images are separated by a space of 40 pixels, as shown in the figure above. If the website is 800 pixels wide, what should be the scaled size (in pixels per inch of painting) of the thumbnails?
The scaled size of the thumbnails is 16 pixels per inch of painting
How to determine the scaled size?The given parameters are:
Width = 15 inchesWebsite = 800 pixelsThe space between adjacent images is 40 inches.
Given that there are two spaces, the remaining space is:
Remaining = 800 - 2 * 40
Remaining = 720
Given that there are three samples of image, the width of each image is:
Image = 720/3
Divide
Image = 240 pixels
The scaled size is then calculated using:
Scale = Image scale width/actual width
This gives
Scale = 240/15
Evaluate
Scale = 16
Hence, the scaled size of the thumbnails is 16 pixels per inch of painting
Read more about dilation at:
https://brainly.com/question/3457976
#SPJ1
Sketch the graph of y= (x-3)2 - 25, then select the graph that corresponds
to your sketch.
The graph of the given quadratic equation is graph C.
How to sketch the quadratic equation?
Remember that for a quadratic equation with a vertex (h, k), the vertex form is given by:
[tex]y = a*(x - h)^2 + k[/tex]
Where a is the leading coefficient, in this case we have a = 1.
Here we have:
[tex]y = (x - 3)^2 - 25[/tex]
So the vertex is at (3, -25).
From that function we can also get the y-intercept, that is given by evaluating the function in x = 0, so we get:
[tex]y = (-3)^2 - 25 = -16[/tex]
So this function passes through (3, -25) and (0, -16). The sketch can be seen below.
Notice that from the given options only the third graph intercepts the y-axis on the negative region, so from that, we conclude that the third graph is the correct option.
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
what is three and 2 fourths and minus two and three fourths
Answer:
The answer is 0.75
Hope this helps!
Perform the indicated operation
Answer:
Step-by-step explanation:
Determine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of rectangle ABCD with side 6 unit by 8 units is 48 unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
From the rectangle ABCD:
AB = 6 units, BC = 8 units
Hence:
Area of ABCD = 6 units * 8 units = 48 unit²
The area of rectangle ABCD with side 6 unit by 8 units is 48 unit²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
HELP ASAP ILL MAKE YOU THE BRAINIEST
find the value of c
Work Shown:
tan(angle) = opposite/adjacent
tan(61) = x/9
x = 9*tan(61)
x = 16.2364298 approximately
Your calculator needs to be in degree mode. One quick way to check is to type in something like tan(45) and the result should be 1.
HELP ON 1 & 2 THANK YOU
[1] n = -2
We will convert the words given into a mathematical equation and then solve by isolating the variable. Let n be "a number"
19 decreased by four times a number is 17
19 - four times a number is 17
19 - 4 n is 17
9 - 4n = 17
-
9 - 4n = 17
- 4n = 8
n = -2
[2] x = -1, y = 3, or (-1, 3)
I will plug the first equation into the second from the system of equations given to us because it already has an isolated variable, y.
2y - 2x = 8
2(2x + 5) - 2x = 8
4x + 10 - 2x = 8
2x = -2
x = -1
Now, I will plug this value back into the equation and solve for y.
y = 2x + 5
y = 2(-1) + 5
y = -2 + 5
y = 3
In circle B below, diameter RT, radius BE, and chord RE are drawn.
If m2TRE = 15° and BE = 9, then the area of sector EBR is
The area of sector EBR in the given diagram attached below is: 33.75π units².
What is the Area of a Sector?Area = θ/360º × πr²
Given the following:
m∠TRE = 15° BE = 9Measure of arc TE = 2(m∠TRE) = 2(15) [inscribed angle theorem]
Measure of arc TE = 30°
Arc RE = 180 - arc TE = 180 - 30 [semicircle]
Arc RE = 150°
m∠EBR = Arc RE = 150°
Area of sector EBR = m∠EBR/360 × π(BE²)
Area of sector EBR = 150/360 × π(9²)
Area of sector EBR = 33.75π units²
Learn more about the area of sector on:
https://brainly.com/question/22972014
#SPJ1
(5√3-√27)^3
how do you prove that this is an integer?
Keys:
[tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]Step-by-step explanation:
[tex]\left(5\sqrt{3}-\sqrt{27}\right)^3\\\5\sqrt{3}-\sqrt{27}^3=\left(2\sqrt{3}\right)^3\\= 2\sqrt{3}\\\left(2\sqrt{3}\right)^3=2^3\left(\sqrt{3}\right)^3\\=2^3\left(\sqrt{3}\right)^3\\2^3=8\\=8\left(\sqrt{3}\right)^3\\=8\cdot \:3\sqrt{3}\\8\cdot \:3=24\\=24\sqrt{3}[/tex]
Answer:
It is not an integer.
Step-by-step explanation:
[tex](5\sqrt{3} -\sqrt{27} )^3\\\\=(\sqrt{3} *(5-3))^3\\\\=8*3*\sqrt{3} \\\\=24\sqrt{3} \\[/tex]
Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
Parville surveys every 15th person in the
town to see if there is support for a new
library and there are 40,161. How many people are surveyed?
Answer:
2677.4
Step-by-step explanation:
40161/15
If you draw all of the diagonals from one vertex of a regular hexagon, how
many triangles do you make?
If you draw all of the diagonals from one vertex of a regular hexagon we make 5 triangles. This is further explained below.
What is a hexagon?Generally, the hexagon is simply defined as the hexagon is a polygon with six sides. to be considered a hexagon, the form must have six sides, all of which must be closed.
In conclusion, We get five triangles if we draw the diagonals of a regular hexagon starting at a single vertex.
Read more about Trigonometry
https://brainly.com/question/8120556
#SPJ1
find the length for point a to point
b
What is the sum of the interior angles of a regular polygon with 12 sides?
A. 1260
B. 1800
C. 2160
OD. 360
The sum of the interior angles of a regular polygon of 12 sides is 1800°
What is a polygon?A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of the all the interior angles of a polygon with 'n' number of sides is given by the formula,
Sum of all the angles = (n-2) × 180°
Since the number of sides in the polygon is 12, the sum of the angles will be,
Sum = (12-2) × 180° = 10 × 180° = 1800°
Hence, the sum of the interior angles of a regular polygon of 12 sides is 1800°.
Learn more about Polygon:
https://brainly.com/question/10441863
#SPJ1
What is the purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aeronautics (pilot), engineers, landscapers, and architects?
The purpose of knowing the angle of elevation and depression in relation to the field of surveyor, military/police, aeronautics (pilot), engineers, landscapers, and architects is discussed below
What is angle of elevation and depression?If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object. If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.
If the pilot looks straight out, that line of sight is horizontal (focused on the distant horizon). The pilot might see the airport's runway, distant buildings, or even mountains in her field of view.
If the pilot looks down at the ground, the one will see the ground crew. The angle of depression is the angle that is formed between the horizontal and the downward looking angle. It is always a downward view, an angle below the horizon.
For the ground crewmember, looking down would not be much help in communicating with the pilot in her cockpit seat. The crewmember will look up, above the horizontal line, to see the pilot. The ground crewmember's angle of vision if an angle of elevation, the angle above the horizon.
Angle of elevation or depression in a survey can be defined as the angle subtended between the line of sight passing through the scope and the horizontal axis of the instrument.
Engineers, landscapers, architects all use trigonometry in their everyday life to help them efficiently and safely create or design something new.
Learn more about angle of elevation and depression here:
https://brainly.com/question/18652056
#SPJ1
Help me I’m confused
The properties used is [tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]
the correct option is (A).
What is exponents and power?
power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.
Given:
[tex]4^{\frac{5}{3} } = \sqrt[3]{4^{5} }[/tex]
We can use the following property
[tex]\sqrt[3]{4^{5} } = (4^{5})^{\frac{1}{3} } = 4^{\frac{5}{3} }[/tex]
By using the property we can find the answer.
Learn more about exponents and power here:
https://brainly.com/question/15722035
#SPJ1
Express cos K as a fraction in simplest terms.
9
M
15
Answer: cos K=
K
Submit Answer
Answer:
4/5
Step-by-step explanation:
In a right triangle such as this one
cos (angle) = adjacent leg / hypotenuse
cos(k) = KL / 15
You will need to find the leg length KL using Pythagorean Theorem
15^2 = 9^2 + (KL)^2 KL = 12
then cos k = 12/15 = 4/5
Do these two statements contradict
each other?
aurt is scalene
and aurt is obtuse.
yes
no
What is the approximate length of minor arc JH? Round to the nearest tenth of a centimeter.
3.5 cm
6.9 cm
21.6 cm
46.8 cm
The length of the arc is 3.5 cm
How to determine the arc length?The attached image completes the question
The given parameters are:
Diameter, d = 16Central angle, x = 25The length of the arc is calculated as:
[tex]L = \frac{x}{360} * \pi d[/tex]
So, we have:
[tex]L = \frac{25}{360} * 3.14 * 16[/tex]
Evaluate the product
L = 3.5cm
Hence, the length of the arc is 3.5 cm
Read more about arc lengths at:
https://brainly.com/question/2005046
#SPJ1
Answer:3.5
Step-by-step explanation:
Solve the equation by completing the square.
0 = 4x2 − 64x + 192
A.
x = -12, -4
B.
x = 4, 12
C.
x = -8, 24
D.
x = -24, 8
Answer:
A
Step-by-step explanation:
Given the following f(x) = 3x² + 7x³ + 8x^4; g(x) = -3x + 12x² - 5x³; and h(x) = 12x +
6
Complete the following: (f.h)(x)
96x5 +132x4+78x³ + 18x²
96x +132x4+78x³ + 18x²
96x5 + 122x + 78x³ + 18x²
96x5 +132x4+84x³ + 18x²
The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²
How to solve function?f(x) = 3x² + 4x³ + 8x⁴
g(x) = -3x + 12x² - 5x³
h(x) = 12x + 6
Therefore,
(f.h)(x) = f(x).h(x)
Hence,
f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)
f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴
(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ + 36x³ + 42x³ + 18x²
(f.h)(x) = 96x⁵ + 132x⁴ + 78x³ + 18x²
learn more on function here: https://brainly.com/question/7783704
#SPJ1
Help me out please….
Answer:
There two images below,
one is the final product and one of how it was reflected
i can figure out
12 is greater than four times a number g
Answer:
"Find g to make this statement true".
12 > 4 • g
The answer of the given expression is 1 & 2.
Concept:Firstly, convert word form into numerical expression.Then Simplify the given expression.How to solve the given question?Convert word form into numerical expression.Thus, the answer of the given expression is 1 & 2.
Learn more about expressions here:
https://brainly.com/question/723406
#SPJ2
Select the correct solution method below, where x represents Kendall’s money
The correct solution method of Kendall's money is 7x = 98. Divide both sides by 7. Kendall had $14
How to write equation?x = Kendall's money
Mateo's money = $98
= 7 × x
The equation:
7 × x = 98
7x = 98
x = 98/7
x = $14
Therefore, the correct answer is option B
Learn more about equation:
https://brainly.com/question/2972832
#SPJ1
answer this fully! i need to know what x equals
answer this fully! i need to know what x equals
X equal minus 0.5
Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. how many quarts of paint did mieko use in the living room?
The number of quarts of paint did mieko use in the living room is A = 3 quarts
Given data ,
Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room
Now , on simplifying the equation , we get
Two gallons of paint is equal to 8 quarts (2 x 4 = 8)
Mieko used 1/4 of the paint on her bedroom, which is equal to 2 quarts (1/4 x 8 = 2)
She used 3 quarts of paint on the hallway
Thus, Mieko used a total of 2 + 3 = 5 quarts of paint on the bedroom and hallway
Therefore , she used 8 - 5 = 3 quarts of paint in the living room
Hence , the number of quarts is A = 3 quarts
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1