Hello! First, let's write some important information contained in the exercise:
committee = 6 students
class: 28 students:
- 10 males
- 18 females
Let's consider the rule: At least three females must be on the committee, so we have some cases, look:
_F_ * _F_ * _F_ * __ * __ * __
1st option:
3 females and 3 males
_F_ * _F_ * _F_ * _M_ * _M_ * _M_
2nd option:4 females and 2 males
_F_ * _F_ * _F_ * _F_ * _M_ * _M_
3rd option:5 females and 1 male
_F_ * _F_ * _F_ * _F_ * _F_ * _M_
4th option:6 females and 0 male
_F_ * _F_ * _F_ * _F_ * _F_ * _F_
Now, we have to use the formula below and find the number of possible combinations:
[tex]C_{n,p}=\frac{n!}{p!\cdot(n-p)!}[/tex]Let's calculate each option below:
1st:3 females:
[tex]C_{18,3}=\frac{18!}{3!\cdot(18-3)!}=\frac{18\cdot17\cdot16\cdot15!}{3\cdot2\cdot1\cdot15!}=\frac{4896}{6}=816[/tex]3 males:
[tex]C_{10,3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10\cdot9\cdot8\cdot7!}{3\cdot2\cdot1\cdot7!}=\frac{720}{6}=120[/tex]3 females and 3 males: 816 * 120 = 97920
2nd option:4 females:
[tex]C_{18,4}=\frac{18!}{4!\cdot(18-4)!}=\frac{18\cdot17\cdot16\cdot15\cdot14!}{4\cdot3\cdot2\cdot1\cdot14!}=\frac{73440}{24}=3060[/tex]2 males:
[tex]C2=\frac{10!}{2!\cdot(10-2)!}=\frac{10\cdot9\cdot8!}{2\cdot1\cdot8!}=\frac{90}{2}=45[/tex]4 females and 2 males: 3060* 45 = 137700
3rd option:5 females:
[tex]C_{18,5}=\frac{18!}{5!\cdot(18-5)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13!}{5\cdot4\cdot3\cdot2\cdot1\cdot13!}=\frac{1028160}{120}=8568[/tex]1 male:
[tex]C_{10,1}=\frac{10!}{1!\cdot(10-1)!}=\frac{10!}{1\cdot9!}=\frac{3628800}{362880}=10[/tex]5 females and 1 male = 8568 * 10 = 85680
4th option:6 females and 0 male:
[tex]C_{18,6}=\frac{18!}{6!\cdot(18-6)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12!}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot12!}=\frac{13366080}{720}=18564[/tex][tex]C_{10,0}=\frac{10!}{0!\cdot(10-0)!}=\frac{10!}{10!}=1[/tex]6 females and 0 male: 18564 * 1 = 18564
To finish the exercise, we have to sum the four options:
97920 + 137700 + 85680 + 18564 = 339864
So, right answer A: 339864.
An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 245ft. Use the formula s=24d−−−√ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.
The vehicle speed is 53 units if s = 24d and d = 245ft
Given the formula for speed is = √24 d
s denotes the vehicle's speed.
d = the length of the skid marks
We need to find the speed of the vehicle.
We know that the displacement d is 117 ft
d = 117 ft
And also it is mentioned in the question to use the below-given formula.
s = √24d
Now substituting the value of displacement in the formula we get
=> s = √24 x 117
=> s = √2808
=> s = 52.99
Now approximating to the nearest value of the decimal, we get.
=> s = 53
Therefore the speed of the vehicle is 53 units.
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Juan took out a $5000 loan for 292 days and was charged simple interest.
The total interest he paid on the loan was $336 As a percentage, what was the annual interest rate of Juan's loan?
Assume that there are 365 days in a year
Since the total interest he paid on the loan was $336. Then, The annual interest rate of Juan's loan if there are 365 days in a year will be as at 8.4%.
What is Simple Interest?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.
The formula of simple interest is given as:
S.I = PRT
Where:
P = principalR = rateT = timeSubstituting the values and solving for the rate on the loan
r = {A} {PT}\r
= {5336} {5000*292}
r = 8.4 %
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please Solve for brainliest and 20 points
Answer:
g=30
Step-by-step explanation:
Answer:
g = 28
Step-by-step explanation:
( n - 2 ) × 180
( 30 - 2 ) × 180
( 28 ) × 180 = 5040
6g × 30 = 180g
5040 = 180g
÷180 ÷180
--------------------
28 = g
I hope this helps!
2) The Allen's rectangular backyard has a
perimeter of 144 feet. If the backyard is 40
feet wide, what is the area of their yard?
Answer:
1280 ft²
Step-by-step explanation:
Perimeter is the addition of all sides of the shape added together. Therefore, if the backyard is the rectangular shape you know that two of the sides are 40 feet wide. By adding both sides you get a total of 80 feet. Subtract the total from the perimeter in order to get the total of the unknown sides. 144 minus 80 is equivalent to 64. Now that you have the total of the unknown sides, divide by two in order to get the single unknown length. So, 64 divided by 2 is equal to 32. The area is the multiplication of two sides with quadrilaterals. Therefore, 40 times 32 equals an area of 1280 feet squared.
64x power 9 as a cube of a monomial
Answer:21
Step-by-step explanation:
What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answer:
C. 64 units squared
Step-by-step explanation:
do 4•4•4 so 4 • 4 = 16 then 16 • 4 = 64 and since its surface area square it. so the answer would actually be 4096 units
A machine used to paint white lines on a road uses 250 litres of paint for
each 8km of road marked. Calculate:
a how many litres of paint would be needed for 200km of road
b what length of road could be marked with 4000 litres of paint.
a) Amount of paint needed for 200 km road = 6250 litres
b) Length of road that can be painted by using 4000 litres of paint = 128 km
Amount of paint used for painting white lines on road= 250 litres
Length which was painted = 8 km
By using unitary method;
Thus for 1 km amount of paint required = 250/8
= 31.25 litres
a) Amount of paint needed for 200 km road = 31.25 × 200
= 6250 litres.
therefore, Amount of paint needed for 200 km road = 6250 litres
b) Since for 1 km 31.25 liters paint is required this implies with 1 liter = 1/ 31.25 = 0.032 km can be covered.
Length of road that can be painted by using 4000 litres of paint = 4000× 0.032
= 128 km
Thus, Length of road that can be painted by using 4000 litres of paint = 128 km
What is unitary method?A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
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How many ways can you arrange 4 books on a shelf?
In order to find the number of ways, we must simply calculate:
4! = 4*3*2*1 = 24
24 possible ways.
Write the equation of the line, with the given properties, in slope intercept form. Slope = -7, through (-6,8)
Given:
The slopr of line is m = -7.
The line passes through point (-6,8).
Explanation:
The equation of line in slope-intercept form is,
[tex]y=mx+c[/tex]Substitute the valus in the equation to determine the value of c.
[tex]\begin{gathered} 8=-7\cdot(-6)+c \\ c=8-42 \\ =-34 \end{gathered}[/tex]So equation of line is y = -7x - 34.
Determine if the function below is continuous.A. not continuous, >2 holesOB. not continuous, 1 holeOC. not continuous, 2 holesOD. continuousReset Selection
Given:
A graph
To determine if the given function is continuous, we first note that the given function has gaps or holes. As we can see, the function has two holes.
We must also remember that a function that has any hole or break in its graph is known as a discontinuous function.
Therefore, the answer is:
[tex]C.\text{ not continuous, 2 holes}[/tex]
Given the right △△DEF, DE = 30, EF = 72 and DF = 78. Find the cos F=
see the figure below to better understand the problem
cos(F)=EF/DF --------> by CAH
substitute given values
cos(F)=72/78
simplify
cos(F)=12/13Option C1 ptsQuestion 22The point A(8,-6) has been transformed using the composition T-15) • r(180,0). Where is A?0 (71)o 17, -1)0 (-7,1)0 (-7, -1)+ Previous
You have to perform two transformations the first one is a 180º rotation with respect to the origin r(180º,O) and the second one is a translation of one unit left and 5 units up T(-1,5)
Given point A(8,-6)
To make a 180º rotation you have to invert the signs of both coordinates, following the rule:
[tex](x,y)\to(-x,-y)[/tex]For point A, the rotation is the following:
[tex]A(8,-6)\to A^{\prime}(-8,--6)=(-8,6)[/tex]Once you rotate the point, you have to perform the translation T(-1,5). The rule for the translation can be expressed as follows
[tex](x,y)\to(x-1,y+5)[/tex]So, the translation of point (-8,6) is:
[tex]A^{\prime}(-8,6)\to A^{\doubleprime}(-8-1,6+5)=(-9,11)[/tex]Ronny is selling coffee mugs for $4.00. So far, he has earned $344.00. Ronny needs to earn more than $392.00 in order to meet his sales goal. How many more coffee mugs, x, does Ronny need to sell in order to reach his sales goal?
Answer:
25 more cups
Step-by-step explanation:
1. You need more than $636.00, but you already have $492.00. To find the needed amount of cups needed to sell, you need to find the difference of the two prices first. In other words, you need to subtract the total needed by the amount already raised.
2. You can get the equation, 636 - 492 = 144
3. Now that you have the amount needed, you can divide the number that you got (144) by 6. You divide it by 6 because that is the amount each cup costs.
4. After dividing 144 by 6, you should get 24. This gives your answer for getting EXACTLY 636. However, in this case, you need more to reach your goal. Since you cannot sell fractions of a cup, just raising it by one can reach your goal. We can add one to 24, making it 25.
In conclusion, you need to sell 25 more cups to reach your goal.
daryl has 1/4 of a pound of chocolate he wants to divide it into 2 equal parts for his siblings how much will each sibling get
To divide the 1/4 of a pound into two equal parts, it is necessary to divide 1/4 by 2, as follow:
(1/4)/2
if 2 is written as 2/1, the previous quotient can be written as a product:
(1/4) (1/2) = 1/8
Now, to write a general expression that takes into account the number of siblings, you name the number of siblings as x. Thus, you have:
(1/4)/(x) = 1/(4x)
WILL MARK BRAINLIEST. Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it
Answer:
The axis of symmetry is -4 because the axis of symmetry is equal to h, in the vertex form!
The height, h (in meters above ground), of a projectile at any time, t (in seconds), after the launch is defined by the function h(t) = −5t2 + 13t + 6. The graph of this function is shown below. When rounded to the nearest tenth, what is the maximum height reached by the projectile, how long did it take to reach its maximum height, and when did the projectile hit the ground?
As we can se from the graph, the maximum value of the function is almost 15 meters, it is reached between t=1s and t=2s, and the height is 0 again when the time is approximately 3 seconds.
We can find the exact values by using the equation.
First, find the zeroes of the function by setting h(t)=0 and solving the quadratic equation for t:
[tex]\begin{gathered} h(t)=-5t^2+13t+6=0 \\ \Rightarrow t=\frac{-13\pm\sqrt[]{13^2-4(6)(-5)}}{2(-5)} \\ \Rightarrow t_1=-0.4;t_2=3 \end{gathered}[/tex]Then, the projectile hits the ground at t=3s.
To find the time at which the projectile reaches its maximum height, find the average between both zeroes:
[tex]t_{\max }=\frac{t_1+t_2}{2}=\frac{-0.4s+3s}{2}=1.3s[/tex]To find the maximum height, evaluate h at t=1.3s:
[tex]h(1.3s)=-5(1.3)^2+13(1.3)+6=14.45[/tex]Therefore, to the nearest tenth, the projectile reached a maximum height of 14.5 meters in 1.3 seconds and it took 3.0 seconds for it to hit the ground.
The correct option is the second one.
Translate the following sentence into an equation.
Twelve minus three times x equals fourteen.
Answer:
12-3x=14
Step-by-step explanation:
Find a solution for the equation. x^2-6x-8=0
Given:
[tex]x^2-6x-8=0[/tex]Required:
To find the solution of the given equation.
Explanation:
From the given equation,
[tex]\begin{gathered} a=1 \\ b=-6 \\ c=-8 \end{gathered}[/tex]Now
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Therefore,
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-8)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt{36+32}}{2} \\ \\ =\frac{6\pm\sqrt{68}}{2} \\ \\ =\frac{6\pm2\sqrt{17}}{2} \\ \\ =\frac{2(3\pm\sqrt{17)}}{2} \\ \\ =3\pm\sqrt{17} \end{gathered}[/tex]Final Answer:
The solutions are
[tex]x=3+\sqrt{17},3-\sqrt{17}[/tex]6+4×2+11+10÷2 order
To solve the following calculation
[tex]6+4\cdot2+11+10\div2[/tex]You have to keep in mind the order of operations. Which states that multiplications and divisions are to be solved before additions or subtractions.
So the first step is to solve the multiplication "4*2" and the division "10÷2"
[tex]6+8+11+5[/tex]Now all that is left is to add the numbers when you have to perform the same operation several times, you have to solve them from lef
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
Slope: 0
Ordered Pair: (-9,7)
The equation of the line woth slope 0 and passing through (-9,7) in slope-intercept form is y = 7.
If a line L has a slope M and it has the intercept c, then the equation of the line L can be written in the point slope form as,
L : y = Mx + c
This above equation of line is known as slope-intercept form of line.
Here, we have to find the equation of line which has slope m equal to zero and passing through (-9,7).
putting the known values in y = mx+c
y = (0)x+ c
y = c
Putting the value of y = 7
c = 7
Here, we have,
y = 7
So, the equation of the required line is y=7.
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Four years after paying $2700 for shares in a startup company, you sell the shares for $1300 (at a loss).
Based on the amount you paid for the shares and the selling price as well as the number of years, the total return would be -51.9%
The annual return would be -16.7%
How to find the total return?The total return on the stock can be found by finding the difference in stock prices for the 4 years and dividing by the buying price:
= (1,300 - 2,700) / 2,700 x 100%
= -1,400 / 2,700 x 100%
= 0.51851851851851851851851851851852 x 100%
= -51.9%
The annual return can be found as:
= ((1,300 / 2,700) ^ 1/4 - 1) x 100%
= -16.7%
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What is the square root of 225As I am new to thisPlease answer step by step in the easiest form possible
Given:
[tex]225[/tex]To Determine: The square root of the given number
Solution
Step 1: Express 225 as the product pf its prime factors of 225
[tex]\begin{gathered} 225=3\times3\times5\times5 \\ 225=3^2\times5^2 \end{gathered}[/tex]Step 2: Separate the factors into their own square root
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2\times5^2} \\ \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \end{gathered}[/tex]Step 3: Solve the individual's squares
[tex]\begin{gathered} \sqrt{225}=\sqrt{3^2}\times\sqrt{5^2} \\ \sqrt{225}=3\times5=15 \end{gathered}[/tex]Hence, the square root of 225 is 15
how can i find x and y in a triangle?
Using the sine formula;
sin 60 / x = sin 90 / 16
cross-multiply
x sin 90 = 16 sin 60
Divide both-side of the equation by sin 90
x = 16 sin 60 /sin 90
x= 13.86
To find y, we can simply use the Pythagoras theorem
opp² + adj² = hyp²
13.86² + y² = 16²
192.0996 + y² =256
subtract 192.0996 from both-side of the equation
y² = 256 - 192.0996
y² = 63.9004
Take the square root of both-side
y = 7.99
Gross Income 3 Ted gets paid a monthly salary of $5,000 and receives 6% commission on all sales over $8000. 1 point Which of the following is an equation that can be gross income? y = 5000+ 6(x - 8000) y = 5000+.06 (x - 8000) y = 8000 +.06 (x - 5000) O y = 5000+.06 (8000 - 2) Previous 3 4
Given that,
base salary = b = 5000$
Comission rate = 6% = 0.06
Let's say, the sales are = x
As given in the question, he receives 6% commission on all sales over $8000.
Hence, the commissionable amount is (x - 8000) '.' x - 8000 shows the amount greater than 8000, which receives a commission.
hence, gross income will be
base salary + commission * (commisonable amount)
=> 5000 + 0.06 * (x - 8000)
Where X in the age of the baby in months according to this model what is the weight in pounds of a baby At age 5 months
The given function is:
f(x) = 1.5x + 7
Then, since x represents the age of the baby, in months, in order to find its weight with 5 months, that is, f(5), we need to replace x by 5 in the above equation:
f(5) = 1.5 * 5 + 7 = 7.5 + 7 = 14.5
Therefore, the last option is correct.
Can you teach me how to divide fractions?
We illustrate the division of fractions by taking the example below.
[tex]\frac{5}{7}\div\frac{25}{14}[/tex]The first step is to change the division sign to multiplication by changing the fraction after the division sign.
[tex]=\frac{5}{7}\times\frac{14}{25}[/tex]Next, we multiply the numerators together and the denominators together.
[tex]=\frac{5\times14}{7\times25}[/tex]You then simplify by dividing common factors.
[tex]\begin{gathered} \\ =\frac{5}{25}\times\frac{14}{7} \\ =\frac{1}{5}\times2 \\ =\frac{2}{5} \end{gathered}[/tex]Rewrite the decimal fraction as a decimal number.
14 25
100
The decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25
The given mixed fraction = [tex]14\frac{25}{100}[/tex]
The mixed fraction is the fraction that consist of one whole number and the simple fraction.
The simple fraction is the fraction that consist of numerator and denominator as whole number. The top term of the simple fraction is called numerator and bottom term is called denominator
The decimal number is a number that consist of one whole number and the fractional part. The fractional parts are separated by a decimal point.
The number is [tex]14\frac{25}{100}[/tex]
Convert the mixed fraction to simple fraction
[tex]14\frac{25}{100}[/tex] = (100×14+25)/100
= 57/4
Convert the simple fraction to decimal number
57/4 = 14.25
Hence, the decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25
The complete question is:
Rewrite the decimal fraction as a decimal number.
[tex]14\frac{25}{100}[/tex]
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Speed is calculated by the equation S = d/t, where S = speed, d = distance, and t = time travelled. For what amount of time (in hours) did a car travel if its speed was 75 miles per hour and it travelled a distance of 187.5 miles?
We get from the question the following equation:
S = d/t
We have the following informations:
Speed(S) = 75 miles /h
Distance(d) = 187.5 miles
If you plug those informations into the formula, you'll get the following:
75 miles/h = 185.5 miles/ t
Now, you just have to solve for "t". If you invert the equation, you'll get(I'm going to omit the units, to make it clearer, but don't forget about them!)
1/75 = t / 185.5
If you multiply both sides by 185.5, you'll get
185.5/75 = t
Solving this calculation, we get the final solution!
t = 185.5/75 hours = 2.47 hours
What bearing and airspeed are required for a plane to fly 360 miles due north in 2.0 hours if the wind is blowing from a direction of 331 degrees at 15 mph?
Using the vector form of velocity, it is possible to calculate the airspeed and bearing, which are 165.33 mph and 0.7 degrees respectively.
Given:
A plane may go 360 miles straight north in 2.0 hours if the wind is blowing at 15 mph and 331 degrees from the north.
You can use the following formula to calculate airspeed.
[tex]V^{2} =V_{x} ^{2} + V_{y} ^{2}- 2v_{x} v_{y}cos\beta \\[/tex] ...........equation (1)
[tex]v_{x}[/tex] is the velocity of the wind and [tex]v_{y}[/tex] is the velocity of the plane.
[tex]\beta = 331-180 = 151 degree[/tex]
Putting [tex]v_{x}, v_{y} , \beta[/tex] in equation (1)
[tex]V^{2}= 15^{2} +180^{2} -2*15*180*cos151\\ V^{2} = 225 + 32400 - 5400*cos151\\V^{2} = 27336.49\\V = 165.33[/tex]
Hence, The airspeed of the plane is 165.33 mph
Now,
[tex]\frac{sin\alpha }{v_{x} } =\frac{sin\beta }{V} \\\frac{sin\alpha }{15 } =\frac{sin151 }{165.33} \\\\sin\alpha = 10*0.00122\\\alpha = 0.7[/tex]
Hence bearing required is 0.7 degrees.
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PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
THIS IS MY LAST QUESTION!!
Answer:
Step-by-step explanation:
statement:
1 = 2
reason:
since 1 and 4 are equal to each other and because lines AB and CD are parallel, any line crossing both lines will create the same angles in the same areas, thus connecting 4 and 2 together. And since 4 is equal to 1, it is also equal to 2.
I hope this helps!
Answer:
statement is 1=2
reason: since 1 and 4 are eqaul to eachothers and beacause lines AB CD are parelle, any line crossing both lines will create the same angels and same area