Answer: The Numbers are 15 and 39
Step-by-step explanation: 2(15) + 9 = 39
A committee of 3 is to be formed from 5 men and 6 women. (a) What is the probability that a random committee is made up of 2 women and 1 man? (b) Suppose now that the committee consists of different positions: Chairperson, Vice-Chairperson, and Treasurer. What is the probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man?
Answer:
a) 0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.
b) 0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
If the order of the people chosen is important, we use the permutations formula. If the order is not important, we use the combinations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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]
(a) What is the probability that a random committee is made up of 2 women and 1 man?
Order is not important, so we use the combinations formula.
Desired outcomes:
2 women from a set of 6, and a men from a set of 5. So
[tex]D = C_{6,2}*C_{5,1} = \frac{6!}{2!4!}*\frac{5!}{1!4!} = 15*5 = 75[/tex]
Total outcomes:
3 people from a set of 6 + 5 = 11. So
[tex]T = C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{75}{165} = 0.4545[/tex]
0.4545 = 45.45% probability that a random committee is made up of 2 women and 1 man.
(b) Suppose now that the committee consists of different positions: Chairperson, Vice-Chairperson, and Treasurer. What is the probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man?
Now, the order is important, which means that we use the permutations formula.
Desired outcomes:
2 women from a set of 6, and a men from a set of 5. So
[tex]D = P_{6,2}*P_{5,1} = \frac{6!}{4!}*\frac{5!}{4!} = 30*5 = 150[/tex]
Total outcomes:
3 people from a set of 11. So
[tex]T = P_{11,3} = \frac{11!}{8!} = 990[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{150}{990} = 0.1515[/tex]
0.1515 = 15.15% probability that the Chairperson and Vice Chairperson are both women and the Treasurer is a man
t/3 > Solve > 15. Graph the solution 3 The solution is
Answer:
[tex]T > 45[/tex]
Step-by-step explanation:
Given
[tex]\frac{T}{3} > 15[/tex]
Required
Graph the solution
[tex]\frac{T}{3} > 15[/tex]
Multiply both sides by 3
[tex]3 * \frac{T}{3} > 15*3[/tex]
[tex]T > 15*3[/tex]
[tex]T > 45[/tex]
See attachment for graph (Assume T is on the x-axis)
When a system of linear equations has no solution the graph will
a - have parallel lines
b- be the same line
c- have intersecting lines
Answer:
A
Step-by-step explanation:
there is no intersection which means no solution...i dont knwo how to explain sorry
Melanie purchases 6 basketballs and 2 volleyballs for $114. A volleyball cost her $3 less than a basketball. How much did each volleyball cost?
Answer:
a volleyball is $16.5
Step-by-step explanation:
6b+2v= 114
v=b-3
6b+2(b-3)= 114
6b + 2b - 6
8b - 6 = 114
8b = 108
b= 13.5
substitute b in
6(13.5) + 2v = 114
81 + 2v = 114
2v = 33
v= 16.5
Bob has a total of 60 adventure cards for a game. The table shows the number of cards, c, distributed to p players. Which equation describes the
paltem in the table?
Does anyone know the answer for this ?
Answer:
A. c = 60 / p
Step-by-step explanation:
If p=2, the equation would read... c = 60 / 2, which mean c = 30. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.
if x=2, y=3 and z=1 then find the value of
1/2 x + 3/4 y
I need help please.
Answer:
b
Step-by-step explanation:
beacause 2x+60 thats the answer
3x – 4y = 31
y = -2x + 6
Answer:
x = 5
Step-by-step explanation:
3x – 4y = 31
y = -2x + 6
Plug in Y
3x – 4(-2x + 6) = 31
Distribute
3x +8x-24= 31
Add like terms
11x - 24 = 31
Add 24 on both sides
11x = 55
Divide both sides by 11
x = 5
write the supplement of : (x+ 35)^0.
please tell fast
Answer:
179
Step-by-step explanation:
(x+35)^0=1
supplement=
180-1
179
what is the value of x in the equation 6x + 3 +4x= 1/2 (9+10x)
Answer:
x=0.3
Step-by-step explanation:
6x+3+4x=1/2(9+10x)
10x+3=4.5+5x
5x=1.5
x=0.3
Answer:
x=0.3
Step-by-step explanation:
6x+3+4x=1/2(9+10x)
10x+3=4.5+5x
subtract 5x and 3 from both sides
5x=1.5
x=0.3
(5x³-7x²+3x-4)-(8x³+2x²+3x-7)
Answer: =−3x^3−9x^2+3
Step-by-step explanation:
Distribute the Negative Sign:
=5x^3−7x^2+3x−4+−1(8x^3+2x^2+3x−7)
=5x^3+−7x^2+3x+−4+−1(8x^3)+−1(2x^2)+−1(3x)+(−1)(−7)
=5x^3+−7x^2+3x+−4+−8x^3+−2x^2+−3x+7
Combine Like Terms:
=5x^3+−7x^2+3x+−4+−8x^3+−2x^2+−3x+7
=(5x^3+−8x^3)+(−7x^2+−2x^2)+(3x+−3x)+(−4+7)
=−3x^3+−9x^2+3
Ali spent a total of $65 at the grocery store. Of this amount, he spent $39 on fruit. What percentage of the total did he spend on fruit?
Answer:
He spent 60% on fruit
Step-by-step explanation:
Answer:
Step-by-step explanation:
65-39=26
26/100=0.26
Substitute w = 1 and w = 3 to determine if the two expressions are equivalent.
Answer:
mineeeeeeeeeeee
Step-by-step explanation:
ILL MARK U BRAINLEST Find the circumference of the circle. Use 3.14 for 1. Round to the nearest hundredth, if necessary.
is
9 in.
The circumference of the circle is about
inches.
1
Answer:
The answer is either 56.55in or 28.27
Step-by-step explanation:
This is the formula that I used
C=2πr
Circumference = 2·π·4.5 ≈ 28.27433 or
Circumference = 2·π·9 ≈ 56.54867
The answer can be either one. It depends on if 9 is the radius or the diameter of this circle. If 9 is the radius, then the answer would be 56.55in. If the radius isn't 9 but 9 is the diameter, then your radius would be 4.5 and the answer would be 28.27in.
Hope that helps :)
The circumference of the circle will be 56.52 inches.
The circumference of a circle can be found using the formula:
Circumference = 2πr
Where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.
If the radius of the circle is 9 inches, then we can substitute this value into the formula to find the circumference:
Circumference = 2π(9 inches)
Circumference = 18π inches
We can leave the answer in terms of π or approximate it using a decimal approximation for π. Using the value of π rounded to 3.14, we have:
Circumference ≈ 56.52 inches
Therefore, the circumference of a circle with a radius of 9 inches is approximately 56.52 inches or exactly 18π inches.
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Ryan made a $3180 down payment on a car. The total cost of the car was $7500. He made 36 equal monthly payments to pay the car in full. How much did Ryan pay per month?
Write an equation for the line in slope-intercept
form.
(Use integers or fractions for any numbers in the
equation.)
Answer:
y = 3x + 5Step-by-step explanation:
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptTake two points from the graph:
(-2, -1) and (0, 5)Find the slope:
m = (5 - (-1))/(0 - (-2)) = 6/2 = 3The y-intercept is b = 5
The line is:
y = 3x + 5let x = -11/8 and y = -11/4 Which expression has a negative value? A. x + y B. x - y C. x . y D. x/y
Can I get some help I don’t get this
Answer: 3 1/30
Step-by-step explanation:
Hi, IReady sucks. So I am gonna help you. I got 3 1/30 when you add them together. I would also recommend using a Fraction Calculator online. ;) it helps a lot!
Please help me???.....
Answer:
40_ page 302
Step-by-step explanation:
mathematics teacher and she said that to me and happy holidays so we can get the text on
Answer:
im sry
Step-by-step explanation:
ss of
3. In a class of 50 students, 40 % are girls. Find the number of girls and
number of boys in the class?
Solution:
Answer:
20 boys in the class
Step-by-step explanation:
40% of 50 is 20
what is the solution set of x+4/2x-1 <0
Answer: x=1/3
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
3x−1<0
Step 2: Add 1 to both sides.
3x−1+1<0+1
3x<1
Step 3: Divide both sides by 3.
3x/3 <1/3
x/1/3
The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A. Two sides of each of the regular pentagons and two side of A meet at the pint P. Calculate the value of n.
Answer:
n=10
Step-by-step explanation:
For a regular polygon with n sides, each interior angle, x, is given by
[tex]x=180\frac{n-2}{n}[/tex]
This can be solved for n
[tex]n=\frac{360}{180-x}[/tex]
For the pentagons
x(5)=180(3/5)=108 degrees.
The angles around P sum to 360, so
2(x(5))+x(A)=360
x(A)=360-2(108)=144.
Substitue in the equation for n.
n=360/(180-144)=10
The number of sides in this polygon is 10.
For any polygon, the sum of interior angles is given as,
[tex]\bold{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
where,
n = number of sides,
We know that for a pentagon, the number of sides is 5.
thus, substituting the values in the sum of interior angle formula we get,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
[tex]{Sum\ of\ interior\ angles= {5-2}\times{180^o}}\\= 3 \times {180^o} = 540^o[/tex]
therfore, each angle in a regular pentagon,
[tex]\dfrac{Sum\ of\ interior\ angles}{Number\ of\ Sides} = \dfrac{540^o}{5} = 108^o[/tex],
Let's assume that polygon A is having x number of sides.
At point P, the sum of the angles must be 360°.
The sum of the angles at point P
= interior angle of the first pentagon
+ interior angle of the second pentagon
+ interior angle of the polygon A with x sides
Substituting the values,
360° = 108° + 108° + z
z = 360° - 108° - 108°
z = 144°
Thus, the interior angle of the x sided polygon is z = 144°.
For a regular polygon, all the interior angles are equal,
so, for a polygon with sides x.
the sum of interior angle = measure of interior angle x Number of sides
= [tex]144^o \times x[/tex]
Also, we know
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]
Substituting, the values for an x number of side polygon,
[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}\\{144^o \times x = {(x-2)}\times {180^o}}\\144x = 180x - 360\\360 = 180x- 144x\\x = \dfrac{360}{36}\\x = 10[/tex]
Hence, the number of sides in this polygon is 10.
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True or false: 30% of 750 Km=225 km
It's True True True True True True True
Someone plz help been stuck on this question for the last 2 hours
Paul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?
7% interest =$?
13% interest =$?
Answer:
7% interest = $10,00013% interest = $20,000Step-by-step explanation:
First find out what an 11% return on $30,000 is.
= 11% * 30,000
= $3,300
Use simultaneous equations.
Assume the amount to be invested in to make a 7% interest is x and the amount for a 13% interest is y.
0.07x + 0.13y = 3,300
x + y = 30,000
y = 30,000 - x
0.07x + 0.13 (30,000 - x) = 3,300
0.07x + 3,900 - 0.13x = 3,300
0.07x - 0.13x = 3,300 - 3,900
-0.06x = -600
x = -600 / -0.06
x = $10,000
y = 30,000 - x
= 30,000 - 10,000
y = $20,000
4. The speed limit is 45 miles per hour. Choose the metric speed limit that is higher than 45 miles per hour. 0 91 km per hour 64.1 km per hour O 64.1 per hour
PLSS I NEED IT NOW
Answer:
91 km per hour
Step-by-step explanation:
45 miles per hour is the same as 72 kilometers per hour (metric), so pick any value greater than 72 km per hour.
1.- Sea y = 2x + 1 ¿Cuál es el valor de "y cuando"x" es igual a 7?
a) 15
b)3
c) 5
2.- Sea y = 3x? - 7 ¿Cuál es el valor de y cuando"x" es igual a 7?
a) 150
b) 140
c) 130
el área de un rectángulo es 6 x al cuadrado más 2x en cm Determine su base y altura
Answer:
Tres respuestas posibles son:
2 y 3x^2 + x
2x y 3x + 2
x y 6x + 2
y hay muchas mas.
Step-by-step explanation:
Hay muchas respuestas posibles.
6x^2 + 2x = 2(3x^2 + x) = 2x(3x + 2) = x(6x + 2)
2x +5y = -7
7x + y = -8
Solve by substitution SHOW WORK!
Answer:
x = 1, y = -15
Step-by-step explanation:
7x + y = -8 ⇒ y = -7x-8
2x + 5y = -7
substitute -7x-8 for y:
2x + 5(-7x-8) = -7
2x - 35x - 40 = -7
-33x - 40 = -7
-33x = -33
x = 1
y = -7x-8 = -15
14000.00 rate 8% 60 days simple interest
Answer:186.66is answer
p=14000
r=8%
time=60days=2month/12=1/6year
Step-by-step explanation:
simple interest=ptr/100=14000×8×1/600=186.666
If a sprinkler waters 1/20 of a lawn in 1/5 of an hour how much time will it take to water the entire lawn?
• 3/20 hour
• 1/4 hour
• 4 hours
• 5 hours
Answer:
4 hours
Step-by-step explanation:
