Answer:
281 different committees can be formed if the number of boys is more than the number of girls.
Step-by-step explanation:
The order in which the people are chosen to the committee is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Number of boys more than the number of girls:
3, 4 or 5 boys.
3 boys:
3 boys from a set of 6.
2 girls from a set of 5. So
[tex]C_{6,3}C_{5,2} = \frac{6!}{3!3!} \times \frac{5!}{2!3!} = 200[/tex]
4 boys:
4 boys from a set of 6.
1 girl from a set of 5. So
[tex]C_{6,4}C_{5,1} = \frac{6!}{4!2!} \times \frac{5!}{1!4!} = 75[/tex]
5 boys:
5 boys from a set of 6. So
[tex]C_{6,5} = \frac{6!}{5!1!} = 6[/tex]
Total:
200 + 75 + 6 = 281
281 different committees can be formed if the number of boys is more than the number of girls.
3. What is the volume of the regular pyramid?
Answer: 80 cubic meters (choice B)
==============================================================
Explanation:
The floor of the pyramid is a pentagon made of five congruent isosceles triangles as shown in the diagram below. Each triangle has a base of 6 meters and height 2 meters. The base and height are always perpendicular.
Each triangle mentioned therefore has area base*height/2 = 6*2/2 = 12/2 = 6 square meters. Five such triangles results in a total area of 6*5 = 30 square meters. This is the area of the pentagonal floor.
We'll multiply this area by the height of the pyramid (8 meters) and then take 1/3 of this to get the pyramid's volume
volume = (1/3)*(area of floor)*(height of pyramid)
volume = (1/3)*(30)*(8)
volume = 10*8
volume = 80 cubic meters
In a basketball game, Noli scored 3 points by shooting the ball at a horizontal distance of 7 feet from the 10-feet-high hoop. Noli threw the ball 6 feet above the ground and the ball went twice as high as its initial horizontal distance from the hoop. What was the horizontal distance of the ball from Noli when it reached its maximum height?
Answer:
The horizontal distance of the ball from Noli when it reached maximum height is approximately 4.1 feet
Step-by-step explanation:
The horizontal distance from the hoop at which Noli threw the ball, y₀ = 7 feet
The height of the hoop = 10 feet
The height from which the ball was thrown = 6 feet
The height to which the ball is thrown = 2 × The initial horizontal distance from the hoop
∴ The height to which the ball is thrown, [tex]y_{max}[/tex] = 2 × 7 feet = 14 feet
The coordinates of points on the path of the ball are;
(0, 6), (7, 10), (x, 14)
The projectile in vertex form is y = a·(x - h)² + k
Where;
(h, k) = The x, and y-coordinate of the maximum height
The y-coordinate of the maximum height reached = k = 14 feet
The x-coordinate of the maximum height = h = The horizontal distance of the ball from Noli when it reached maximum height
At y = 6, x = 0, therefore, we get;
6 = a·(0 - h)² + 14 = a·h² + 14
6 = a·h² + 14
a = -8/h²
At y = 10, x = 7, we get;
10 = a·(7 - h)² + 14 = (-8/h²)·(7 - h)² + 14
10·h² = -8·(7 - h)² + 14·h²
-4·h² = -8·(7 - h)²
4·h² - 8·(7 - h)² = 0
-4·h² + 112·h - 392 = 0
h = (-112 ± √(112² - 4 × (-4) × (-392)))/(2 × -4)
h ≈ 4.1, or h ≈ 23.9
We reject the value, h ≈ 23.9 feet given that the distance between the where the Noli threw the ball and the hoop = 7 feet
Therefore, the horizontal distance of the ball from Noli at which the ball reached its maximum height, h ≈ 4.1 feet
I need help ASAP!! PLEASE EXPLAIN YOUR ANSWER
Answer:
600
Step-by-step explanation:
Volume of cuboid = l x w x h
length = 12
width = 10
height = 5
12 x 10 x 5 = 600 yd^3
answered by g a u t h m a t h
Simplify:
6−4(3x−2)+4x
16x−2
−8x+14
−8x−2
Answer:
6 − 4(3x − 2) + 4x = 6 - 12x + 8 + 4x = x(-12 + 4) + 14 = -8x + 14[tex]\bf \large \longrightarrow \: \:6 \: - \: 4 \: (3x - 2) \: + \: 4x[/tex]
[tex]\bf \large \longrightarrow \: \:6 \: - \: 12x \: + \: 8 \: + \: 4x[/tex]
[tex]\bf \large \longrightarrow \: \:14 \: - \: 12x \: + \: 4x[/tex]
[tex]\bf \large \longrightarrow \: \:14 \: - \: 8x[/tex]
After rearranging[tex]\bf \large \longrightarrow \: \: - 8x \: + \: 14[/tex]
write in the form of p/q, 0.785 (bar on 85)
please to spam anything except answer....TOMORROW EXAM
The expression of 0.785 in the form p/q is 157/200
The ratio is defined as a way of dividing a variable by another variable.
For instance, p/q can be described as the ratio of p to q where p and q are integers.Given the decimal number 0.785, to convert to fraction, we will place divide 785 by 1000 (since the decimal is on thousandth)
0.785 = 785/1000
Express in its simplest form
785/1000 = 157/200
Hence 0.785 written in the form p/q is 157/200 where p = 157 and q = 200.
Learn more on ratio here: https://brainly.com/question/19473677
write as an inequality 9 is greater than or equal to w, and -7 is less than or equal to w
[tex]9 \geqslant w \\ \\ - 7 \leqslant w[/tex]
"9 is greater than or equal to w" translates to [tex]9 \ge w[/tex] which flips to [tex]w \le 9[/tex]. We swap both sides and flip the inequality sign as well.
"-7 is less than or equal to w" translates to [tex]-7 \le w[/tex]
We have [tex]-7 \le w[/tex] and [tex]w \le 9[/tex] which then ultimately combine into the compound inequality [tex]-7 \le w \le 9[/tex]
Final Answer: [tex]-7 \le w \le 9[/tex]PLEASE SOMEONE SOLVE B) I ALREADY KNOW 1. A) Is 75.875m^2
CAN YALL HELP ME WITH PYTHAGOREAN THEOREM
Answer:
c=82
Step-by-step explanation:
Answer:
The answer is 82!
Step-by-step explanation:
(18)^2 + (80)^2 is 6724, which has a square root of 82.
2.
Lucy shares 42 marbles between her and her 6 friends. How many does each child?
59,8x60,2 bằng bao nhiêu ạ
Answer:
3,6
Step-by-step explanation:
What is the domain of the square root function graphed below?
Answer:
D
Step-by-step explanation:
The graph clearly shows that x=>3
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
y = -2x + 5
[tex]\frac{risex}{run} = slope =[/tex]Δy/Δx = -8/4 = -2
Step-by-step explanation:
fin the slope of the line that is perpendicular to y=1/3x
1. 3
2. -3
3. -1/3
4. 12
Answer:
-3
Step-by-step explanation:
When a line is perpendicular, the slope becomes the opposite to the original. If the slope is 1/3, the perpendicular line's slope would be -3.
CORRECT ANSWER WILL GET BRAINLIEST
ANSWER PLEASE
Answer:
B and C
Step-by-step explanation:
A is actually 5 so it is an integer and 0 is considered and integer.
Help on this pls if you don’t mind
Answer:
(B) 3
Step-by-step explanation:
Remember that a parallel lines always have the same slope!
Help anyone can help me do this question,I will mark brainlest.
Answer:
22 mm
Step-by-step explanation:
căn bậc 2 của 5 là bao nhiêu
Answer:5
Step-by-step explanat[tex]\sqrt{5} = 5[/tex]
[tex]\sqrt{5}[/tex] = 2.23
Find a 101 of the sequence 5, 8, 11, ....
A. 302
B. 311
C. 305
D. 308
Answer:
305
Step-by-step explanation:
We are adding 3 each time
5+3 = 8
8+3 = 11
The formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = 5+3(n-1)
We want the 101 term
a101 = 5 +3(101-1)
= 5+3(100)
= 5+300
= 305
Find the area of the quadrilateral.
Answer:
12cm^2
Step-by-step explanation:
The first thing we want to do is find out what type of quadrilateral is shown so we can identify a formula we can use to solve for the area
The quadrilateral shown is a trapezoid
It's a trapezoid because it has four sides and one pair of parallel sides ( side AD and side BC are both formed vertically making them parallel as they can be extended an infinite length and will never intersect. ) This being the properties of a trapezoid
Now that we have identified the type of quadrilateral that the figure is, let's find the area.
Area of a trapezoid formula:
A = (a+b/2)h
Where a and b = bases and h = height
* Identify variable of quadrilateral shown*
( Note that each unit = 1cm )
The bases have lengths of 4 units (4cm) and 2 units (2cm)
The height can be represented by an imaginary line from a to c
From a to c is 4 units (4cm)
Now that we have identified the variables let's plug them into the formula
A = (a+b/2)h
a = 4
b = 2
h = 4
* Plug the variables into the formula *
A = (4+2)/(2)4
If you plug this into a calculator you get that the area is 12
If you need the work for evaluation here it is:
Evaluate using PEMDAS
Parenthesis
Exponents
Multiplication and Division ( left to right)
Addition and Subtraction ( left to right )
(4+2)/2 * 4
First step is to evaluate the operations inside of the parenthesis (4+2)
6/2 * 4
The next step is to evaluate exponents
There are no exponents so we move on to multiplication and division evaluate whatever come first going left to right
First comes division
3 * 4
Then multiplication
A = 12.
Plz help me out with this
Given,
HK is the perpendicular bisector of GJ. So, GK = KJ.GK = 2x + 10KJ = 3x - 15_______________
Find KJ .
_______________
First find the value of x
[tex] \sf \: GK \: = KJ \\\sf 2x + 10 = 3x - 15 \\\sf 2x - 3x = - 15 - 10 \\ \sf - x = - 25 \\ \sf \: - > \boxed{\bf \: x = 25}[/tex]
Now, find the value of KJ.
[tex]\sf3x - 15 \\ \sf= 3(25) - 15 \\ \sf=7 5 - 15 \\ = \boxed{\bf \: 60}[/tex]
-> The value of KJ is 60.
_______________
Hope it helps.
RainbowSalt2222
Answer:
KJ = 60
Step-by-step explanation:
In order to find the length of KJ we must find the value of x
Perpendicular bisectors split lines into two EQUAL parts.
If GJ is bisected then the two parts that make it up are equal to each other.
In other words GK = KJ
If GK = 2x + 10 and KJ = 3x - 15 then
2x + 10 = 3x -15
Solve for x
2x + 10 = 3x -15
Subtract 2x from both sides
10 = x - 15
Add 15 to both sides
x = 25
Now to find KJ we simply plug in the value of x into KJ's given expression
Expression given: 3x - 15
x = 25
KJ = 3(25) - 15
Multiply 3 and 25
KJ = 75 - 15
Subtract
KJ = 60
is -66 rational or irrational ?
Answer:
It's rational because it's not a decimal numbet
Select the false statement
A. Vertical angles are always congruent
B.Vertical angles are sometimes complimentary
C.Two right angles are always supplementary
D. Angles that form a linear pair are sometimes supplementary. Plz answer ASAP
Answer: D. Angles that form a linear pair are sometimes supplementary.
That is not true, linear pairs are always supplementary.
Answer:
D. Angles that form a linear pair are sometimes supplementary.
~OAmalOHopeO
Given 2 ||
m
|| n, find the value of x.
142°
m
(3x+8)°
n
PLSSSS HELP MEEEE
Answer:
x = 10Step-by-step explanation:
Given,
l || m
Therefore,
142° + (3x+8)° = 180° [Since Co-exterior angles]
=> 3x + 8 = 180 - 142
=> 3x + 8 = 38
=> 3x = 38 - 8
=> 3x = 30
[tex] = > x = \frac{30}{3} [/tex]
=> x = 10 (Ans)
Choose the inequality that represents the following graph.
Answer:
it's most most probably option d becoz I studied In different way so... as per me d ... figure is quite diff but d
HELP PLEASE
i would really appreciate if someone answered this correctly!
Answer:
n-32
Step-by-step explanation:
edmentum
Which point should Julio use to determine the amount of pizza sauce he needs to bring?
A
B
C
D
On a coordinate plane, a graph titled Pizza Recipe has Pizzas on the x-axis and Cups of Pizza Sauce on the y-axis. Point A is (3, 2), point B is (4, 2.6), point C is (4.5, 3), point D is (6, 4).
Answer:
The question is incomplete, but after a small search I've found that the complete question is something like:
To celebrate something, a teacher will make pizzas for the class.
There are 30 students in his class and each pizza serves 8
Julio will bring the pizza sauce. Which point should Julio use to determine the amount of pizza sauce he needs to bring?
In a graph, the vertical axis is represented with the variable y, which is defined as the dependent variable, while the horizontal axis represents the variable x, which is the independent variable.
The notation for a point in that graph is (x, y)
Here, we know that the x-axis represents the number of pizzas, and the y-axis represents the number of cups of pizza sauce needed for the x pizzas.
So, for example, the point (3, 2) means that:
for x = 3 pizzas, you need y = 2 cups of pizza sauce.
So, now let's find the number of pizzas that will feed the whole class.
There are 30 students, Each pizza serves for 8.
Then the number of pizzas needed is:
30/8 = 3.75 pizzas.
But we can round it to 4 pizzas because making a 0.75 of a pizza does not make a lot of sense.
Then we could use point B, which is (4, 2.6)
This means that, for 4 pizzas, they need 2.6 cups of pizza sauce.
So Julio should bring 2.6 cups of pizza sauce.
Which point should Julio use to determine the amount of pizza sauce he needs to bring?
(B 4,26)
Maya express charges 15 dollar for each person and great holiday charges fixed 84dollar and extra 12 dollar for a person. If the total amount charged by each company is same find the number of people going on holiday
Step-by-step explanation:
15 dollar for each
15*70*12
then 84*70
total amount. the above
Answer:
:>
Step-by-step explanation:
15 dollar for each
15*70*12
then 84*70
total amount. the above
Someone please help me!!!!!
Answer:
B is going to be half the intercepted arc
<ABC = 80
<CAB = 55
mARC(AB) = 90
mARC(BC) = 110
Step-by-step explanation:
at what rate of interest the sum of Rs 4000 amount to rs 6000 in 4 years
interest=4000
amount =6000
time =4yr
principal =6000-4000
=2000
interest=principal×time×rate/100
4000= 2000×4×r/100
4000=8000×r/100
r=8000-4000/100
r=2000/100
r=20
Answer:
12.5 %
Step-by-step explanation:
I = PRT
I is the interest, P is the Principle, R is the Rate and T is the time
The interest is 6000- 4000 = 2000
2000 = 4000* R *4
2000 = 16000R
Divide each side by 16000
2000/16000 = R
.125 = R
Changing to percent form
12.5 %
Help me asap im not good at math
Answer:
[tex] > [/tex]
Step-by-step explanation:
The denominators are the same so, you have to look at the numerator which is greater, - 1 is greater because it's close to 0
