The number of groups that can be chosen from the team of 17 depends on
the given conditions of the selection.
The correct responses are;
(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.(ii) The number of groups of 9 that contain at least one man is 24,309 groups.(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.Reasons:
The combination of n objects taking r at a time is given as follows
[tex]_nC_r = \dbinom{n}{r}[/tex]
(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;
Number of ways of choosing groups of 9 = [tex]\dbinom{17}{9}[/tex] = 24,310 ways.
(b) (i) Number of women = 9
Number of men = 8
Number of groups of 9 containing 5 women and 4 men = [tex]\dbinom{9}{5} \times \dbinom{8}{4}[/tex]
[tex]\dbinom{9}{5} \times \dbinom{8}{4} = 126 \times 70 = 8,820[/tex]
Number of groups of 9 containing 5 women and 4 men = 8,820 groups.
(ii) The number of groups that contain at least one man is [tex]\dbinom{17}{9} - \dbinom{9}{9}[/tex]
[tex]\dbinom{17}{9} - \dbinom{9}{9} = 24,310 - 1 = 24,309[/tex]
The number of groups that contain at least one man are 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women if given as follows;
[tex]\dbinom{8}{8} \times \dbinom{9}{1} + \dbinom{8}{7} \times \dbinom{9}{2} + \dbinom{8}{6} \times \dbinom{9}{3} = 2,649[/tex]
The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are [tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8}[/tex]
[tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8} = 5,005 + 2 \times 6,435 = 17,875[/tex]
(d) Two team members must work together or not at all is [tex]\dbinom{15}{7} - \dbinom{15}{9}[/tex]
[tex]\dbinom{15}{7} - \dbinom{15}{9} = 6,435 - 5,005 = 1,430[/tex]
The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.
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Circle A has a circumference of 25 centimeters.
Circle B's diameter is 3 times as long as circle A's
diameter.
What is the circumference of circle B?
The circumference of circle B would be; 74.98 cm.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We have been given that Circle A has a circumference of 25 centimeters.
And Circle B's diameter is 3 times as long as circle A's diameter.
Thus, the Diameter of Circle B = 3 x the Diameter of Circle A
Since The circumference of the circle A = 2πr = 25
2πr = 25
r = 25/ 2π
r = 3.98 cm
The Diameter of Circle A = 2 x 3.98 = 7.96 cm
Since Diameter of Circle B = 3 x the Diameter of Circle A
Diameter of Circle B = 3 x 7.96 cm
= 23.88 cm
Radius = 23.88 / 2
Hence, the circumference of circle B = 2πr
= 2 x 22/7 x 23.88 / 2
= 74.98 cm
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solve pls brainliest
Solve what
I think ym forgot to add the question or sth
Which pair of angles are supplementary?
Answer:
1 and 7
Step-by-step explanation:
supplementary means that they add up to 180º
1,3 5,6 1,7
2,4 7,8 2,8
1,2 5,7 3,5
3,4 6,8 4,6
There are still some more but my hands are tired of typing.
Answer:
A: 1 and 7
Step-by-step explanation:
when 2 angles are put next to each other on a straight line with a line going through the middle those two angles always add to 180 since 180 is equal to a straight line.
supplementary angles are 2 angles that together make 180.
out of the options given, all of them except 1 and 7 are equal angles and as a result would not add to 180. if you put angles 1 and 7 on a straight line together, they do, thus the answer is A, aka 1 and 7.
step 1: find the factors of ac that add up to b. ac=6(−10)=−60 b=−11 the factors of −60 that add up to −11 are and . step 2: rewrite the trinomial with the x-term expanded, using the two factors from step 1. 6x2−11x−10 (6x2− )+( −10) step 3: group the first two and second two terms together, find the gcf and factor again. (2x−5)+ (2x−5
Answer:
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅−10=−60 and whose sum is b=−11
.
6x2+4x−15x−10
Factor out the greatest common factor from each group.
2x(3x+2)−5(3x+2)
Factor the polynomial by factoring out the greatest common factor, 3x+2
.
(3x+2)(2x−5)
Solve for in terms of A and w. A=w
Answer:
Step-by-step explanation:
Given A = w:
w in terms of A is w = A, and
A in terms of w is A = w
Can someone answer this please I need it ASAP
Answer:
Frank scored 10 runs
B) the mean is 20
Step-by-step explanation:
PLEASE HELP ILL MARK BRAINLIEST
Find the zeros of the function write as ordered pairs
Answer:
Step-by-step explanation:
You can do nothing more than just write the ordered pairs.
(1,0)
(-1.5,0)
(-3.75,0)
Not yet answered Tharu bought a refrigerator and paid Rs. 40,000 as a down payment. On delivery, she paid another Rs. 80,000 and owed 60% of the purchased price. What was the price of the refrigerator?
Rs. 250000 was the price of the refrigerator.
Let x represent the price of the refrigerator.
Since she made a Rs. 40,000 down payment. On delivery paid another Rs. 80,000 and owed 60% of the purchased price. Hence:
Total Money paid = 100% - 60% = 40% of purchased price
40000 + 60000 = 40% of x
100000 = 0.4x
x = Rs. 250000
Hence, Rs. 250000 was the price of the refrigerator.
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[tex]\frac{8}{22} + \frac{3}{22} [/tex]
SOLVE It
NO G.OOGLE
Answer:
[tex]\sf\huge\longmapsto \: \frac{11}{22} [/tex]
Step-by-step explanation:
[tex]\sf\huge\longmapsto \frac{8}{22} + \frac{3}{22} [/tex]
[tex]\sf\huge\longmapsto \: \frac{8 + 3}{22} [/tex]
[tex]\sf\huge\longmapsto \: \frac{11}{22} [/tex]
−2/9−(−1/3÷3/5)
PLZZZZ ANSWER TEST
Answer:
The answer should be 1/3 Also known as 0.3333
Help help please please
Step-by-step explanation:
=2(20)+2(14)
=2⋅20+2(14)
=40+2(14)
=40+2⋅14
=40+28
=40+28
=68
Answer:
P = 68Step-by-step explanation:
P = 2L + 2W
P = 2(20) + 2(14)
P = 40 + 28
P = 68//
Dakota worked 55 hours over the last two weeks and his paycheck was $572.00. how much does he earn per hour
Answer:
572/55 = $10.4
or
(572 * 2)/ 55 = $20.8
Step-by-step explanation:
You divide the amount earned over the number of hours worked.
Or
if the paycheck is given monthly, the second option fits. Because $572 is half what they earned that month.
Margo borrows $1100, agreeing to pay it back with 6% annual interest after 6 months. How much interest will she pay?
Answer:
I'm guessing you mean 1% annual interest per month, so she would have to pay 11 dollars each month meaning she will pay 66 dollars in interest.
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Solve pls brainliest
Answer:
In order: 7.5, 7.5061, 7.56, 9.213
Step-by-step explanation:
Show your solution follow the steps need an answer, please need an answer, please.
Answer:
Step-by-step explanation:
27 ) 2x² - x - 1 = 0
2x² - 2x + x - 1 = 0
2x ( x - 1) + (x - 1) = 0
(x - 1)(2x + 1) = 0
x - 1 = 0 ; 2x + 1 = 0
x = 1 ; 2x = -1
x = -1/2
x = 1 ; -1/2
Option b
28) Area of a rectangle = 24 cm²
length * width = 24
(3x +2 )(2x -1) = 24
3x(2x -1) + 2(2x - 1) = 24
3x *2x - 3x *1 + 2*2x - 2*1 = 24
6x² -3x + 4x - 2= 24
6x² + x - 2 -24 = 0
6x² + x - 26 = 0
6x² -12x + 13x - 26 = 0
6x(x - 2) + 13(x - 2) = 0
(x -2)(6x +13) = 0
x = 2 {Ignore 6x + 13 as it gives negative value}
length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm
Width = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm
29) Area of square = 900 cm²
Side² = 900
(5x)² = 900
25x² = 900
x² = 900/25
x² = 36
x = √36 = √6*6
x = 6 cm
30) base = b cm
height = b + 2
Area of triangle = 24 cm²
[tex]\dfrac{1}{2}base*height = 24\\\\\dfrac{1}{2}*b*(b+2) = 24\\[/tex]
b(b + 2) = 24*2
b² + 2b = 48
b² + 2b - 48 = 0
b² - 6b + 8b - 48 = 0
b(b - 6) + 8(b - 6) = 0
(b - 6) (b + 8) = 0
b - 6 = 0 {Ignore b +8 = 0 as it gives negative value}
b = 6 cm
height = 6+ 2 = 8 cm
Given the cost function, C(x), and the revenue function, R(x), more than how many units must be produced and sold for the business to make money?
C(x)= 2,000x + 60,000
R(x)= 8,000x
Answer:
x= 10
Step-by-step explanation:
C(x) = 2,000x + 60,000
R(x) = 8,000x
Set the solution to zero.
R(x) - C(x) = 0
8,000x - (2,000x + 60,000) = 0
6,000x - 60,000 = 0
x=10
Find the total future amount for $500 invested at 2.02% for 5 years
compounded monthly.
State your answer in terms of dollars rounded to the nearest cent
(hundredth).
Do not include a $ sign with your response.
Correct Answer is but explain how
553.09
solve for x. round to the nearest tenth. 37 48
Answer:
1776
Step-by-step explanation:
Eight less than the product of a number and three (algebraic expression)
Express as a trinomial.
(x-5)(3x-6)
(x−5)(3x−6)
The polynomial expressed as trinomial is 3x² - 21x + 30
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
Polynomials can be classified based on the number of terms as binomial, trinomial.
Trinomial is a polynomial with 3 terms.
Given the polynomial:
(x - 5)(3x - 6)
= 3x² - 15x - 6x + 30
= 3x² - 21x + 30
The polynomial expressed as trinomial is 3x² - 21x + 30
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Someone help plz tyyyy!
Answer:
When y=7,9 the answer is yes when it = -10,-8 the answer is no.
Step-by-step explanation:
Simple substitution gets us the resulting values. for y=7 we get [tex]15\geq 15[/tex] which is true. For y=9 we get [tex]19\geq 15[/tex] which is also true. For the other values we get a negative number which is not a solution.
write the first four terms of the sequence defined by the given rule f (1) = 3, f(n) = [ f(n - 1)] ^2
Answer:
3, 9, 81, 6561
Step-by-step explanation:
previous term × itself
[tex]\\ \sf\longmapsto f(n)=[f(n-1)]^2[/tex]
f(1)=3[tex]\\ \sf\longmapsto f(2)=(f(1))^2=3^2=9[/tex]
[tex]\\ \sf\longmapsto f(3)=(f(2))^2=(9)^2=81[/tex]
[tex]\\ \sf\longmapsto f(4)=(f(3))^2=(81)^2=6561[/tex]
Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.
Using a line of best fit with the equation y = -3x + 21 to predict the value of y when x = 10 is an example of Choose...
causation
interpolation
extrapolation
correlation
Answer:
Step-by-step explanation:
D
20 points fast plzz!!! Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
6 in.
12 in.
72 in.
144 in.
Answer:
The width of the rectangular yard is 72 inches
Step-by-step explanation:
Let
L -----> the length of the yard
W ----> the width of the yard
we know that
The perimeter is equal to
we have
substitute in the formula and solve for W
Divide by 2 both sides
Subtract 5 both sides
Convert feet to inches
Remember that
1 ft= 12 in
Step-by-step explanation:
The width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
What is rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
Perimeter of the rectangle :
P = 2L + 2W
L = 5 feet
22 = 2(5) + 2W
After calculating:
W = 6 feet
1 feet = 12 inches
6 feet = 72 inches
Thus, the width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
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HELP PLSSSSSSSSSSSSSSSSSSSS
Step-by-step explanation:
I need help in that too :(
Answer:
1 true
2true
3 false
4 false
Step-by-step explanation:
Write an equation of the line that passes through (0,4) and (0,-3).
Answer:
It is a vertical line at x = 0
Step-by-step explanation:
An equation of a line in a slope-intercept form is y=mx+b
So with the coordinates given, we must find the slope (m), and the y-intercept (b).
In order to find the slope using these coordinates,
we have to use the formula (y2-y1)/(x2-x2).
So the slope would be -3 - 4 / 0.
Because the denominator is 0, the slope would be undefined.
It is easier to see the equation/graph by graphing the coordinates on the coordinate plane. You will see that it is a straight vertical line down x=0.
Hello there! :)
We can use the formula:
[tex]\frac{y2-y1}{x2-x1} \\[/tex]
First, let's take a look at the x-coordinates. They are the same, aren't they?
If the x-coordinates are the same, then the slope is undefined.
Put the x-coordinates into the formula. It turns out that we divide by 0, and division by 0 is undefined.
Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature[/tex]
HELPPP THIS IS SO HARD Keegan and Jeff did some research and found that there are approximately 7,492,000,000,000,000,000 grains of sand on Earth. Jeff says that it is about 7 × 10(15) grains of sand. Keegan says that this is about 7 × 10(18) grains of sand.
Guys please add the step by step so they dont know im cheating
Answer:
Keegan is correct.
Step-by-step explanation:
Keegan is correct.
Put a decimal point after the first digit which is 7. Count decimal places there are after the 7, this will be your power of 10. There are 18 decimal places after the 7. This means the answer would be 7 x 10^18.
Basically, Keegan is right
when you present 7,492,000,000,000,000,000 in standard form, it is indeed, 7×10¹⁸, the reason Jeff is wrong is because he only counted Os and not the numbers 492 which Keegan rounded to Os. Ok, to simply this 7×10¹⁵ equals 7 000 000 000 000 000, and 7×10¹⁸ is 7 000 000 000 000 000 000 while is closer to thee original answer than Jeff's response.
Please mark BRAINLIEST if you're satisfied with this explanations.
Paloma decided to divide 1,292 by 31 using partial quotients. She uses 30 as her first partial quotient. Which are the partial quotients Paloma should show in her work
A 20, 10
B 30, 10,1
C 10,10,10,1
D 10,10,10,10,1
−a^3 b^5 is a polynomial or not
Answer:
notStep-by-step explanation:
HOPE IT HELPS YOUBTW GOOD DAY TO YOUOrder these numbers from least to greatest:
4[tex]\pi[/tex] , v18, 14, 9
Answer:
18,14,9
Step-by-step explanation:
enjoy