To determine the number of ways to form a committee of 6 students from 30 council members, we use the combination formula C(30, 6), which yields 593,775 different combinations.
Explanation:The question asks how many possible committees of 6 students can be formed from a group of 30 students on the student council. This is a combinatorial problem and can be solved using the combination formula which is given by C(n, k) = n! / (k! * (n - k)!), where C(n, k) is the number of combinations, n is the total number of items, and k is the number of items to choose. So to answer the question, we must calculate C(30, 6).
Calculating C(30, 6), we have:
C(30, 6) = 30! / (6! * (30 - 6)!)
C(30, 6) = 30! / (6! * 24!)
C(30, 6) = (30 × 29 × 28 × 27 × 26 × 25) / (6 × 5 × 4 × 3 × 2 × 1)
C(30, 6) = 593,775
There are 593,775 different ways to form a committee of 6 students from a student council of 30 members.
apply the distributive property to create an equivalent expression to 6(a+2b+3c)
Answer:
6a+12b+18c
Step-by-step explanation:
Multiply 6 with the numbers inside the parentheses.
Linda shoots an arrow at a target in an archery competition. The arc of the arrow can be modeled by the equation y = −0.02x2 + 0.65x + 4, where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow. How far from Linda does the arrow hit the ground? Round to the nearest tenth.
Answer:
Linda was 37.8 m away when the arrow hit the ground
Step-by-step explanation:
We are given that The arc of the arrow can be modeled by the equation :
[tex]y = -0.02x^2 + 0.65x + 4[/tex]
Where x is the horizontal distance (in meters) from Linda
y is the height (in meters) of the arrow.
Now we are supposed to find How far from Linda does the arrow hit the ground
So, y must be 0 when the arrow hits the ground
So, Substitute y = 0 in the equation :
[tex]y = -0.02x^2 + 0.65x + 4\\0 = -0.02x^2 + 0.65x + 4\\0.02x^2-0.65x-4=0\\0.02(x-37.79)(x+5.29)=0\\x=37.79,-5.29[/tex]
Since distance cannot be negative
So,Linda was 37.8 m away when the arrow hit the ground
In a game of luck, a turn consists of a player rolling 12 fair 6-sided dice. Let X = the number of dice that
land showing "l"in a turn.
Find the mean and standard deviation of X.
You may round your answers to the nearest tenth.
Answer:
The mean of X, μₓ is 2
The standard deviation of X, σₓ is 1.3
Step-by-step explanation:
Here we have the expected value given by the following relation
Expected value = P(x) × n
Where:
P(x) = Probability that the event occurs
n = Number of times the event occurs
The probability of the dice showing 1 = 1/6
The number dice rolled = 12
Therefore, out of 12, the expected number of dice that show 1 in a turn = 12×1/6 = 2
The proportion, p of dice that show 1 = 1/6, hence the mean, μx = np
Standard deviation of a proportion, [tex]\sigma _x =\sqrt{np{(1 - p)} }[/tex]
Where:
p = 1/6
n = 12
Hence;
μx = 12 × 1/6 = 2
[tex]\sigma _x =\sqrt{np{(1 - p)} } = \sqrt{12 \times \frac{1}{6} (1 - \frac{1}{6}) } = \sqrt{\frac{5}{3} } = 1.29099 \approx 1.3 \ to \ the \ nearest \ tenth[/tex]
Hence the mean and standard deviation of X are presented as follows;
The mean of X, μₓ = 2
The standard deviation of X, σₓ = 1.3.
Complete the statement about figures on the graph. Parts A and create a figure on the coordinate plane that has point symmetry about the origin.
Answer:C
Step-by-step explanation:
The answer is "Parts A and C create a figure on the coordinate plane that has point symmetry about the origin" on Edge 2020
To find the area of the regular hexagon, a classmate uses 12m for the perimeter. What is your classmates error?
Answer:
Required was area, they provided the perimeter
Area = 6sqrt(3) m²
Step-by-step explanation:
Perimeter = 6s
6s = 12
s = 12/6 = 2m
Area = 3sqrt(3)/2 × 2²
Area = 6sqrt(3) m²
sqrt: square root
Can someone please help me with this problem?
Answer:
f'(1) = 2
Step-by-step explanation:
f(x) = 2x^2 -2x +3
Take the derivative
f'(x) = 2 * 2x - 2 * 1
f'(x) = 4x -2
f'(1) = 4(1) -2
=4-2
=2
jo triangles.
The base of the rectangle is 7 inches, and the height is
6 inches.
The area of one triangle is
square inches.
13
21
42
84
Answer:
21
Step-by-step explanation:
Area = 1/2 (Base x Height)
Area = 1/2 (7 x 6)
Area = 1/2 (42)
Area = 21
Answer:
Answer is B.21
Step-by-step explanation:
what is 1/3 + 14 =26
Answer:
False
Step-by-step explanation:
If x =-4 and y= 3 , what is the value of x - 3y^2 ?
A. -13
B. -23
C. -31
D. -85
Answer:
-31
Step-by-step explanation:
= x - 3y^2
= -4 - 3 × 3^2
= -4 - 27
= -31
hope it helps!
Easy Question, Easy points
Topic: Volume
Use the other attached paper to help u find formula
Focus on question Scenario 2
Answer:
20,000 cm³
Step-by-step explanation:
The shape is a triangular prism
Base area × height
½ × 20 × 25 × 80
20,000 cm³
The sum of three consecutive numbers is greater than 40. The inequality that represents this is x + x + 1 + x + 2 > 40. Which values of x hold true for the inequality?
Answer:
All integers greater than 12 (13 onwards) satisfy the inequality
Step-by-step explanation:
x + x + 1 + x + 2 > 40.
3x + 3 > 40
3x > 37
x > 12.3333
All integers greater than 12 (13 onwards) satisfy the inequality
The ratio 36:60 is equivalent to what other ratios? ( list at least 2)
b) make the ratio 36:60 equivalent to _:50 ( show proof)
Answer:
1.) 12:20
6:10
2.) 30:50
6*5=30 and 10*5=50
(6:5 is the proportional relationship)
Step-by-step explanation:
Part A: Since the base numbers are 6:5, you can multiply any number like 5 on both sides. They only have to be the same number.
Part B: Divide the numbers until you cannot any more. I divided them both by 6.
Easy Question, Easy Points
Topic: Volume
Answer:
a 125600 cm^3
b 327910.2 m^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
a = 3.14 (20)^2 100
=125600 cm^3
b We know the diameter r =d/2 = 118/2 =59
V = pi r^2 h
3.14 (59)^2 *30
327910.2 m^3
Answer:
1) 125,600 cm³
2) 327,910.2 m³
Step-by-step explanation:
Volume of cylinder: pi × r² × h
1) 3.14 × 20² × 100
125,600 cm³
2) 3.14 × (118/2)² × 30
327,910.2 m²
Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 6 people. Hudson booked a total of 19 rooms which can accommodate 87 guests altogether. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system.
Answer:
Our system is : S + L = 19, and 3S + 6L = 87
Let # of small rooms = S
# of Large rooms = L
10 Large rooms and 9 Small rooms
Step-by-step explanation:
Let # of small rooms = S
# of Large rooms = L
S + L = 19
3*S + 6*L = 87
Our system is : S + L = 19, and 3S + 6L = 87
solve.
S = 19 - L
3*(19 - L) + 6L = 87
57 - 3L + 6L = 87
57 + 3L = 87
3L = 30
L = 10
S = 19 - 10 = 9
Answer:
Step-by-step explanation:
Let the number of smaller rooms be x
Total rooms are 19. So, number of larger rooms = 19 - x
Total guests = 87
3x + (19-x)6 = 87
Find the volume of a rectangular prism that is 16 cm in length, 12 cm in height, and 10 cm in width.
the largest number which divides 60 and 75 leaving remainders 8 and 10 respectively is
Final answer:
To find the largest number that divides 60 and 75 and leaves remainders of 8 and 10 respectively, the GCD (greatest common divisor) can be used. The GCD between 60 and 8 is 4, and the GCD between 75 and 10 is 5. Thus, the largest number that satisfies the conditions is 4.
Explanation:
To find the largest number that divides 60 and 75 and leaves remainders of 8 and 10 respectively, we can use the concept of the greatest common divisor (GCD). The GCD is the largest number that divides two or more numbers without leaving a remainder. To find the GCD, we can use the Euclidean algorithm.
First, we divide 60 by 8. The quotient is 7 and the remainder is 4. Then, we divide 8 by 4. The quotient is 2 and the remainder is 0. Since the remainder is 0, we stop here. Therefore, the GCD of 60 and 8 is 4.
Next, we divide 75 by 10. The quotient is 7 and the remainder is 5. Then, we divide 10 by 5. The quotient is 2 and the remainder is 0. Again, since the remainder is 0, we stop here. Therefore, the GCD of 75 and 10 is 5.
Therefore, the largest number that divides 60 and 75 and leaves remainders of 8 and 10 respectively is 4.
From the top of a lighthouse 55 feet above sea level, the angle of depression to a small boat is 11.3*. How far is the boat from the base of the lighthouse? *
Answer:
275.248 ft
Step-by-step explanation:
this is a trigonometry question, so we first draw a triangle with height 55 and angles 11.3 (degrees) and 78.7 (degrees). tan(11.3)=55/base, so the base would be 275.248 ft.
Solve a triangle when A = 27.3°, B = 55.9°, and a = 8.6.
Answer:
The correct answer is A.
Step-by-step explanation:
i just did the test on edge and got it right, it’s not D, it’s A.
Answer:
A=
Step-by-step explanation:
Explain.
log2x = log2(3x + 5) + 4
It’s no solution but I need to explain how
How long would it take for a snail (average speed of 0.029) to travel 2,800 miles ?
Answer:
5 days 12 hours = 7920 minutes. x = 5280 feet = 1 mile.
Step-by-step explanation:
Answer:
answer is 5 days and 12 hours
Step-by-step explanation:
hope we can be friends
can i please get brainliest
Slope of 0 3 and 4 1
Answer:
m = [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
The slope of (0,3) (4,1) =
[tex]\frac{-1}{2}[/tex]
Hope this helps :)
During a recent football season, the relationship between the number of points a team scored and the number of wins a team had is modeled by the equation w equals zero point zero three one p minus three point eight one, where w is the number of wins and p is the number of points scored. One team in the league scored 444 points and had 12 wins.
What is the residual of that team’s win total?
a. -2.046
b. -1.764
c. 1.764
d. 2.046
Answer:A
Step-by-step explanation:
The solution is, the number that the residual of that team’s win total is, -2.046, i.e. option a. -2.046.
What is equation?An equation can be stated as a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
During a recent football season, the relationship between the number of points a team scored and the number of wins a team had is modeled by the equation w equals zero point zero three one p minus three point eight one,
i.e. w = 0.031p - 3.81
where w is the number of wins and p is the number of points scored.
now, we have,
One team in the league scored 444 points and had 12 wins.
i.e. p = 444
w = 12
so, we get,
LHS = 12
and, RHS = 9.954
so, the residual of that team’s win total is,
9.954 - 12
= -2.046
Hence, The solution is, the number that the residual of that team’s win total is, -2.046, i.e. option a. -2.046.
To learn more on equation click:
brainly.com/question/24169758
#SPJ6
Solve the quadratic equation: -x^2+8x=7
Answer:
Step-by-step explanation:
To solve the quadratic equation [tex]-x^2 + 8x = 7[/tex], we first convert it to standard form and identify the coefficients. Using the quadratic formula, we find the solutions to be x = -1 and x = 7.
To solve the given quadratic equation, [tex]-x^2 + 8x = 7[/tex], we first need to bring the equation to the standard form of a quadratic equation, which is [tex]ax^2 + bx + c = 0[/tex]. We can do this by subtracting 7 from both sides, resulting in [tex]-x^2 + 8x - 7 = 0[/tex].
Now the equation is in standard form, we identify the coefficients: a = -1, b = 8, and c = -7. Applying these to the quadratic formula, x = [-b ± [tex]\sqrt(b^2 - 4ac)[/tex]] / (2a), we get:
x = [-8 ± [tex]\sqrt((8)^2[/tex] - 4(-1)(-7))] / [2(-1)]
x = [-8 ± [tex]\sqrt(64 - 28)[/tex]] / -2
x = [-8 ± [tex]\sqrt(36)[/tex]] / -2
x = [-8 ± 6] / -2
Now, solving for x, we get two solutions:
x = (-8 + 6) / -2 = -1
x = (-8 - 6) / -2 = 7
Therefore, the solutions to the quadratic equation are x = -1 and x = 7.
What is the image of (-1,-6) after a reflection over the y-axis?
Answer:
your answer is (1,-6)
Step-by-step explanation:
when a point is reflected in y-axis, then the y-co-ordinate remains same and then x-co-ordinate becomes the opposite of that number.
When you reflect a point across the y-axis, only the x-coordinate changes while the y-coordinate stays the same. For example:
(-x, -y) -> (x, -y)
So:
(-1, -6) -> (1, -6)
Best of Luck!
The Zamoras rent a storage room that is 10 feet wide, 12 feet long, and
8 feet high. How many cube-shaped boxes 1 foot on each edge can the
Zamoras store in the room?
Answer:
960 cubes
Step-by-step explanation:
To find how many cubes of side 1 foot can be contained in the room, we have to find the volume of the storage room and then, divide by the volume of the cube.
The storage room is in the shape of a rectangular prism, hence, its volume is:
[tex]V = L * W * H[/tex]
where L = length
W = width
H = height
The dimensions of the storage room are:
10 feet wide, 12 feet long, and 8 feet high
Hence, its volume is:
[tex]V = 10 * 12 * 8 = 960 ft^3[/tex]
The volume of the cube of side 1 foot is:
[tex]V = S^3\\\\V = 1^3 = 1 ft^3[/tex]
Hence, the number of cubes that can be contained in the storage room is:
960 / 1 = 960 cubes
960 cubes can be stored in the storage room.
FP!!!!!!!!!!!!
(10 x 5 ) + 50 =
read comment plz
Answer:
(10 x 5) + 50 =
(50) + 50 = 100
Step-by-step explanation:
1. do parenthesis first
2. add them together
Answer:
(10*5)+50
50+50=100
Step-by-step explanation:
Hope I helped
Solve the equation. 5x + 8 − 3x = −10 x = −9 x = −1 x = 1 x = 9
Answer:
[tex]x=-9[/tex]
Step-by-step explanation:
[tex]5x+8-3x=-10[/tex]
Simplify to get [tex]2x+8=-10[/tex]
Find what [tex]2x[/tex] equals to by taking away 8, [tex]2x = -18[/tex].
Divide by 2 to find x, [tex]x = -9[/tex]
Answer:
X = -9
Step-by-step explanation:
Which values are within the range of the piecewise-defined function? f(x) = StartLayout enlarged left-brace 1st Row 1st column 2 x + 2, 2nd column x less-than negative 3 2nd row 1st column x, 2nd column x greater-than negative 3 3rd Row 1st column negative x minus 2, 2nd column x greater-than negative 3 EndLayout y = –6 y = –4 y = –3 y = 0 y = 1 y = 3
Answer:
the answer is below frum ed
Step-by-step explanation:
y= -6
Y= -4
Y= -3
Y= 0
Ross has a spinner that is split into eight equal sections numbered 1 through 8. He spun the spinner 1,104 times. Which of the following would be a good estimate of the number of times the spinner landed on number 6?
A.
291
B.
117
C.
209
D.
127
Answer:
D. 127
Step-by-step explanation:
Because our spinner is split up evenly 8 ways, we a have a 1/8th chance of getting 6 with any given spin. We will want to pick the number that is the closest to one 1/8th of 1104 from our options at the right.
Let's check them one by one. Note that 1/8 as a decimal is .125, if you are using a calculator to do this problem, decimals will be fastest and we'll work with those here.
A) 291/1104 = .264
B) 117/1104 = .106
C) 209/1104 = .189
D) 127/ 1104 = .115
Our closest number to .125 (ie, 1/8th) is .115. or 127 out of 1,104 spins.
Answer:
D, 127
Step-by-step explanation:
it would be d because if the spinners each have equal spots then you can divide it by 8. which gets you 138, but that isn't an option and its probability so its always around a number. so the closest one is 127 or D
what is the slope of a line that goes through the points (3, -2) and (2, 3)
Answer:
-5
Step-by-step explanation:
To find the slope between two points we use
m = (y2-y1)/(x2-x1)
= (3 - -2)/(2 - 3)
= (3+2)/(2-3)
= 5/ -1
- 5
Answer:
M=-5
Step-by-step explanation:
y2-y1 over x2-x1
3+2 divided by 2-3
5/-1
-5