the prom committee is made up of 8 boys and girls. If there are 12 boys and 15 girls in the group to pick the committee from, how many ways can the committee be organized?
1). 1860 ways
2). 3185325 ways
3). 2220075 ways
4). 675675 ways
Thanks guys!!
The number of ways can the committee be organized will be 2220075. Then the correct option is 3.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
The prom committee is made up of 8 boys and girls.
If there are 12 boys and 15 girls in the group to pick the committee from.
Then the number of ways can the committee be organized will be
Then the number of ways is given by the combination formula. Then we have
Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀
Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495
Number of ways = 2220075
Thus, the correct option is 3.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ1
Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a hypotenuse = 24?
√2, √2, 24
24√2, 24√2, 12
24, 24, 24√2
12√2, 12√2, 24
The sides of the triangle are (d) 12√2, 12√2, 24
How to determine the side lengths?The given parameters are:
Hypotenuse = 24Angle = 45-45-90 degree anglesIn a 45-45-90 degree angle triangle, we have:
Hypotenuse = Opposite√2 and Hypotenuse = Adjacent√2
This means that:
Opposite =Adjacent
So, we have:
24 = Adjacent√2
Divide both sides by √2
Adjacent = 24/√2
Evaluate
Adjacent = 12√2
This means that:
Opposite = 12√2
Hence, the sides of the triangle are (d) 12√2, 12√2, 24
Read more about right triangles at:
https://brainly.com/question/2437195
#SPJ1
In a lab, a substance was cooled by 6 degrees celsius each hour for 12 hours.
The total change in temperature was what?
Answer:
72 degrees 72° Celsius. It changed by 72 degrees.
Step-by-step explanation:
6 * 12 because it changed 6 degrees each hour for 12 hours
6 *
12
—-
72
Answer:
72 degree Celsius
Step-by-step explanation:
Since every hour the temperature is cooled by 6⁰C and the total time spent was 12 hour we can do a simple multiplication shown:
6 * 12 = 72
use decomposition to find the area of the figure
If you wanted to make the graph of y=3x+1 steeper which equation could you use
Answer:
Increase the slope
Step-by-step explanation:
The slope of this line is '3' ......a steeper line has a higher number than '3' in front of the 'x' like y = 4x+3 or y = 7x + 12
In the diagram below, GH is parallel to DE . If GH is 3 more than EH FH=10, and DE=12 find the length of EH. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answer: 5
Step-by-step explanation:
Since [tex]\overline{GH} \parallel \overline{DE}[/tex], by the corresponding angles theorem, [tex]\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED[/tex]. This means [tex]\triangle FGH \sim \triangle FDE[/tex] by AA.
As corresponding sides of similar triangles are proportional,
[tex]\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5[/tex]
However, as distance must be positive, we consider the positive solution, x=5.
Therefore, the answer is 5
i like cheese burger do u liek cheese burgers 2+2+12-21+492
In a city, the distance between the library and the police station is 3 miles less than twice the distance between the
police station and the fire station. The distance between the library and the police station is 5 miles. How far apart
are the police station and the fire station?
O 1 mile
O 3 miles
O4 miles
O6 miles
Answer:
C. 4 milesStep-by-step explanation:
Let the distance between police station and the fire station be x.
According to question we have:
the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station,the distance between the library and the police station is 5 miles.It can be expressed as:
5 = 2x - 3Solve the equation for x:
2x = 5 + 32x = 8x = 4Correct choice is C
7. The perimeter of a circle of diameter 10 cm is-
(a) 30.4 cm. (b) 30.14 cm
(c) 31.4 cm. (d) 30.01 cm.
(Take π = 3.14)
[tex]\qquad\qquad\qquad\boxed{\bf\:\:{(c) \: 31.4 \: cm \: ans \: }}[/tex]
Explanation -:
The diameter is = 10 cm
( Take π = 3.14 )
[tex] \\ \: \tt :\implies \: 10 \: \times 3.14 \\ \\ 31.4 \: ans[/tex]
More Information -:
Area of circle= πr² Circumference= 2 πr π = 22/7 or 3.14 ( approx )Annulas = π(R² - r ²)The Question is in the picture because I could not type it out correctly for some reason.
Step-by-step explanation:
the circumference of a complete circle (360°) is
2×pi×r
in our case
2×pi×3 = 6pi (= 18.84955592... ft)
5 ft is now what fraction of the whole circumference ?
because the corresponding arc angle is the same fraction of 360°.
5 ft are 5/(6pi) of the whole circumference.
so, the arc angle AB is
5/(6pi) × 360 = 5×60/pi = 300/pi = 95.49296586...°
but maybe you need the angle in radians instead of degrees ?
then remember, 360° = 2pi radians.
and then the arc angle AB is
5/(6pi) × 2pi = 10/6 = 5/3 = 1.666666... radians.
A baseball is thrown into the air from a height of 5 feet. the ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. which equation models the height of the baseball? assume that acceleration due to gravity is –16 ft/s2. h(t) = 16t2 49.64t 5 h(t) = -16t2 5t 49.64 h(t) = -16t2 49.64t 5 h(t) = 16t2 5t 49.64
The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².
Maximum height reached by the base ball
The maximum height reached by the baseball is calculated as follows;
H = y₀ + v₀yt + ¹/₂gt²
Assuming negative direction for upward motion
H = y₀ + v₀yt - ¹/₂gt²
0 = y₀ + vt -16(t)²
0 = 5 + 3.2v - 16(3.2)²
0 = 5 + 3.2v - 163.84
3.2v = 158.84
v = 158.84/3.2
v = 49.64
Required equation modelH(t) = 5 + 49.64t -16(t)²
Learn more about maximum height here: https://brainly.com/question/12446886
#SPJ1
Answer:C?
Step-by-step explanation:
edge
The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2). determine the lengths of the outside edges of the garden. write your answer in
simplest form.
The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
What is the scale factor?In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.
Given that:-
The outside edges of the walkway form a rectangle whose length and width are proportional to the sides of the garden, increased by a scale factor of 3. the sides of the garden are (2x+4) and (3x+2)The length and width of the outside edge will be:-
The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-
Length = 3 ( 2x+4 ) = 6x + 12
Width = 3 ( 3x+2 ) = 9x + 6
Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.
To know more bout scale factors follow
https://brainly.com/question/25722260
#SPJ1
(Refer to the attached image)
===========================================
Work Shown:
side a = 8side b = 5angle C = 88 degreesApplying the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 8^2 + 5^2 - 2*8*5*cos(88)
c^2 = 64 + 25 - 80*cos(88)
c^2 = 86.2080403
c = sqrt(86.2080403)
c = 9.2848285
c = 9
Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.
A die has six sides, with the numbers 1, 2, 3, 4, 5, and 6. What is the probability of rolling a number greater than 2?
Answer:
1/2
Step-by-step explanation:
There are 3 numbers greater than 2: 3, 4, 5, and 6. There are 6 numbers, so it is 3/6=1/2.
A researcher wishes her patients to try a new medicine for depression. how many different ways can she select 5 patients from 50 patients?
There are 2118760 ways to select 5 patients from 50 patients.
What is Combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Here, Total patients= 50
Number of selection is to made = 5
So, total ways of selection = ⁵⁰C₅
= (50X49X48X47X46) / (5X4X3X2X1)
= 2118760 ways
Thus, There are 2118760 ways to select 5 patients from 50 patients.
Learn more about Combinations from:
https://brainly.com/question/19692242
#SPJ1
Answer:
2118760
Step-by-step explanation:
She can select 5 patients from 50 patients in :
[tex]50c_{5}[/tex]
= [tex]\frac{50!}{5! (50-5)!}[/tex]
= [tex]\frac{50!}{5! 45!}[/tex]
= 50 x 49 x48 x47 x46 x45!
= 2118760
Don’t know how to solve
Answer:
Θ ≈11.31°
Step-by-step explanation:
the model is a right triangle with side opposite being the height and side adjacent the horizontal length , in relation to angle Θ , then
using the tangent ration
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4}{20}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{20}[/tex] ) ≈ 11.31° ( to 2 dec. places )
you deposit a check for $254.67 into your savings account. Your account has a balance of $419.33 after the deposit. Find the balance of your savings account before the deposit.
Answer:
$164.66
Step-by-step explanation:
Just subtract them from each other
Hello i need help ASAP i cant figure this out its just like part A
and i i have 1 hour
Number of unmarked wolves: 928 - 232 = 696
probability of next wolf being unmarked = 696 / 928 = 0.75
0.75 x 100 = 75%
Answer: 75%
Does the table below represent a function? Why or Why Not?
Answer:
A.
Step-by-step explanation:
For the x value (6) there are two different output values(y) 5 and 6.
If it's a function then there must be one output value for every input.
It cost Makayla $2.80 to send 28 text messages. How much would it cost to send 163 text messages?
Answer:
$16.30
Step-by-step explanation:
Hope this helps! Have a great day!!
The cost of 163 text messages is $16.3
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.Given:
price for 28 text messages = 2.80
So, price for 1 text messages = 2.80/ 28
= $ 0.1
Now, the price for 163 messages = 163 * 0.1
= $16.3
Hence, the price for 163 text messages be $16.30.
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
(04.01 MC)
The tables show some input and output values:
Table A
Table B
Input Output
Input Output
1
7
6
1
2
9
7
3
3
7
2
4
5
8
5
Which tables represent functions?
O Only A
O Only B
O Both A and B
ONeither A nor B
Answer:
table a represents functions table b does not
The number scale used on this map is 1:10 000 000 explain what this scale means?
Answer:
1 unit on the map is equivalent to 10 000 on the ground or reality
What are two possible measures of the angle below?
Construction This section of a concrete skateboard ramp has the shape of a triangular prism. Find the volume
of the triangular prism. Find the value of the concrete used in the ramp if the cost of concrete is $4.00 per cubic
foot.
Answer:
volume = 73.3ft³
value = $194.4
Step-by-step explanation:
volume of prism = (½bh)l
=(½×4×4)×9.2
=73.6ft³
value of concrete
1ft³ : $4.00
73 .6ft³ : X
X : (73.6ft³ × $4.00) ÷ 1ft³
X : $294.4
Solve for the value of s.
(s+1)°
(2S-1)°
Answer
90*
Step-by-step explanation:
Answer:
s = 30
Step-by-step explanation:
The three angles lie on a line.
The sum of angles on a line are supplementary, meaning they add up to 180 degrees.
s + 1 + 90 + 2s - 1 = 1803s = 90s = 30If a line has a slope of 2 and contains the point (-2, 1), what is its equation in
point-slope form?
A. y +2=-2(x-1)
B. y-2 =-2(x-1)
C. y-1=2(x-2)
D. y- 1 = 2(x+ 2)
Answer:
D
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 2 and (a, b ) = (- 2, 1 ) , then
y - 1 = 2(x - (- 2)) , that is
y - 1 = 2(x + 2)
I need help please answer fast!!!
Answer:
2 and -4 :) because -2×4=-8, and 4+(-2)=2. Solve x-2=0 and x+4=0, you get the answer I previously mentioned!
The nth term of a different sequence is 2^n+5 show that 36 is not part of the sequence
Answer:
It is not a term of the sequence
Step-by-step explanation:
See attached image
Rachel rides her bike due east at 9 miles per hour. Amos rides his bicycle due north at 12 miles per hour. If they left from the same point at the same time, how far apart will they be in 1 hour? Geometry and measurement :))) help please.
They will be 15 miles apart after one hour if they left the same point at the same time.
How do we measure and calculate the distance in Geometry?The distance between two points in geometry can be calculated by using the Pythagoras theorem.
Mathematically, the Pythagoras theorem can be expressed as:
[tex]\mathbf{d = \sqrt{x^2 +y^2}}[/tex]
where;
x and y are opposite and adjacent sides respectively.[tex]\mathbf{d = \sqrt{(9)^2 +(12)^2}}[/tex]
[tex]\mathbf{d = \sqrt{81+144}}[/tex]
[tex]\mathbf{d = \sqrt{225}}[/tex]
d = 15 miles
Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.
Learn more about calculating the distance between two points here:
https://brainly.com/question/7243416
#SPJ1
A school had a lot of problems with
student absences and wanted to try a
intervention program to see if it
encouraged students to come to school
more often. As a trial, 20 students were
split into two equal size groups. Group 1
would get the new intervention and
Group 2 got no intervention. The mean-
number of absences was calculated after
one month for each group, as shown in
the table below. What inference can be
made about the results?
The inference is that the results of the study are statistically significant.
How to make the inference about the results?For group 1, we have:
Mean = 1.7
For group 2, we have:
Mean = 3.3
The mean of group 2 is greater than group 1, and the mean difference is:
Difference = 3.3 - 1.7
Evaluate
Difference = 1.6
Based on the sample values, the mean difference of 1.6 is significant.
Hence, the inference is that the results of the study are statistically significant.
Read more about inference at:
https://brainly.com/question/24261687
#SPJ1