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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The angles of a triangle are A, B and C.
Angle A is three times as big as angle B.
Angle B is half the size of angle C.
What is the size of angle A?
Answer:
∠A = 90°
Step-by-step explanation:
∠A = 3∠B
∠B = 1/2 × (∠C), this can also be written as ∠C = 2∠B
∠A + ∠B + ∠C = 180, because there are 180° inside a triangle
Write angle A, B and C in terms of angle B:
3 ∠B + ∠B + 2 ∠B = 180
Simplify:
6 ∠B = 180
∠B = 180 ÷ 6 = 30°
Work out angle A:
∠A = 3∠B = 3 × 30°
∠A = 90°
What is six hundred seventy-eight and thirty-four hundredths written in standard form?
6,870.34
6,087.34
687.34
678.34
Answer: 678.34
Step-by-step explanation:
600 + 78 and 34 hundredths
678.34
Oliver incorrectly states that the expression tan(3pi/4 + x) can be simplified as -1. Review Oliver’s work. Which statement explains why Oliver is incorrect?
Keyword gibberish:
The expression does not simplify not have a value if simplified to not equivalent to not
tan startfraction 3 pi over 4 endfraction + x
We want to see where Oliver is making a mistake in his claim.
The correct option is the first one, the simplification on the last step is wrong.
We start with the expression:
[tex]tan( \frac{3*pi}{4} + x)[/tex]
Now, by looking at Olvier's work, we can see that on the last step he writes:
[tex]\frac{-1 + tan(x)}{1 + tan(x)} = -1[/tex]
This is clearly wrong, as the numerator and the denominator are dont simplify to -1 (this only happens if the numerator is -1 times the denominator), so the left side can't be equal to -1, it actually would be simplified to:
[tex]\frac{-1 + tan(x)}{1 + tan(x)} = \frac{-1 +1 - 1 tan(x)}{1 + tan(x)} = \frac{-2 + 1 + tan(x)}{1 + tan(x)} \\\\\frac{-2 + (1 + tan(x))}{1 + tan(x)} = \frac{-2 }{1 + tan(x)} + \frac{ 1 + tan(x)}{1 + tan(x)} = \frac{-2 }{1 + tan(x)} + 1[/tex]
Then the correct option is the first option.
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Can someone please help me?
The derivative of:
[tex]f(x) = ( {3x}^{2} + 2x - 1) 6[/tex]
is....
[tex]6( {3x}^{2} + 2x - 1)5(6x + 2)[/tex]
Hope this helped you- have a good day bro cya)
Fractions
9/4 = ?/28 can u help me solve this explination please
A right triangle is shown below.
45°
3 units
What is the tan of x?
Answer:
Tan x = 1
Step-by-step explanation:
As a tangent of 90° is impossible, x must be the measure of both of the 45° angles.
If we assume 3 is the length of one of the shorter legs, it is also the length of the other of the shorter leg
Tangent x = Opposite/Adjacent = 3/3 = 1
Evaluate.
plz help
12⋅(14+13)2+23
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
52
Step-by-step explanation:
14+13= 27+2=29+23=52
The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 12 ⋅ (14 + 13)² + 23
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.
⇒ 12 ⋅ (14 + 13)² + 23
⇒ 12 ⋅ (27)² + 23
⇒ 12 ⋅ 729 + 23
⇒ 8748 + 23
⇒ 8771
The value of the numerical expression 12 ⋅ (14 + 13)² + 23 will be 8771.
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janet obtained 32% for her statistics test, which was out of a total of 300 marks. how much should she score in the computer science test that is out of 200 marks in total if she is to get proportionally weighted average of 46%
Her score in computer to get a proportionally weighted average of 46% will be 134.
The total score for both subjects = 200 + 300 = 500
Since the proportionally weighted average is 46%, then her score will be:
= 46% × 500
= 0.46 × 500
= 230
Since she had 32% for her statistics test, which was out of a total of 300. Her score will be:
= 32% × 300
= 0.32 × 300
= 96
Therefore, her score in computer will be:
= 230 - 96
= 134
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What is the answer X=-2(6+4)
Answer:
X = -20
Step-by-step explanation:
X = -2(6+4)
^ add 6 and 4 together first because they are in parentheses
-2(10)
^ this parenthesis means you want to multiply -2 and 10
because 2 x 10 = 20
that must mean -2 x 10 = -20
therefore, the value of X is -20
X= -20
help please its hard
Answer:
11
Step-by-step explanation:
Rewrite expression using given information:
20 - 3a + 2b = 20 - 3*7 + 2*6
20 - 21 + 12 = 11
2x^3+128 factor polynomials
Answer:
2(x−4)(x^2+4x+16)
Step-by-step explanation:
2(x^3-4^3)
b=4
2(x-4) (x^2+x*4+4^2)
= 2(x-4) (x^2 +4x+ 16
Hope this helps :)
Evaluate the expression 6^2-(8–4^2+7
please mark this answer as brainlist
The value of given expression is 27.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6²-(8-4)²+7.
Here, 6²-(8-4)²+7
= 6²-(4)²+7
= 36-16+7
= 20+7
= 27
Therefore, the value of given expression is 27.
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A landowner recently sold a large plot of land. The sale decreased his total acreage by 12%. Let v be the original acreage.
a. Write two equivalent expressions that represent the new acreage.
Answer:
.88v or [tex]\frac{22}{50}[/tex]v
Step-by-step explanation:
Answer:
Step-by-step explanation:
Link is needed
What is the common ratio between
1,-5, 25, -125
Answer:
1/5
Step-by-step explanation:
hope this helps!
no links please
Suppose you took out a $120,000 loan to go to med school. Your loan has a 6.9% APR to be paid in 30 years. You make monthly payments of $790.32 – to date, you have made 180 payments. What is the total amount you have left to pay if you simply make payments for the next 180 months?
The total amount left to pay is $ 745,945.74.
Supposing you took out a $ 120,000 loan to go to med school. Your loan has a 6.9% APR to be paid in 30 years, and you make monthly payments of $ 790.32, and to date, you have made 180 payments, to determine what is the total amount you have left to pay if you simply make payments for the next 180 months the following calculation must be performed:
(120,000 x 1,069 ^ 30) - (790.32 x 180) = X (120,000 x 7.40) - 142,257.6 = X 888,203.34 - 142,257.6 = X 745,945.74 = X
Therefore, the total amount left to pay is $ 745,945.74.
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Maths Question - Topic Pythagoras
Please answer the question. Awarding 20 points
So for this you use a formula which is
a2 + b2 = c2
You name the highest one c, the rest are you choice
so now it will be - x2 + 7 2 = 14 2
you now square them,
now they will be x2 + 49 = 196
now it will be easy to solve it.
if A=(-2,-4) and B=(-8, 4) what is the length of AB?
the length of AB is 10 cm..........
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Length of AB is equal to :
[tex]10 \: \: units[/tex]Refer to the attachment for solution ~
What is the median number of this data set 15,33,51,75,51?
Answer:
51
Step-by-step explanation:
1. The median of a data set is the quantity that's in the middle of the data points. Before looking what number is in the middle, you have to order them from least to greatest.
15, 33, 51, 51, 752. Now, when crossing from left to right then left to right again, you end up with 51 in the middle.
Therefore, the median number is 51.
If 6 spiders can spin 6 webs in 6 minutes how long will it take 100 spiders to spin 200 webs
Answer:
200 minutes
Step-by-step explanation:
if six spiders can spin 6 webs in 6 min then 100 spiders can spin 100 webs in 100 min then multipy by 2 and you get 200
The amount of time that 100 spiders can spin 200 webs will be 12 minutes.
What is Algebra?Algebra is the study of graphic formulas, while logic is the manipulation of those signs.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.
If 6 spiders can spin 6 webs in 6 minutes. Then the 1 spider can sin one web in six minutes. So, the 100 spiders can spin 100 webs in 6 minutes.
Then the 100 spiders can spin 200 webs in 12 minutes.
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Which is the label of the ordered pair (1,3)?
1. V
2.W
3.X
4. Y
5. Z
Answer:
dude. its 4.Y
A class is selling magazines as a fund raiser. of the 500 magazines sold, allie sold 1/7 of them. Gary sold 0.085 of the magazines. rob sold 9/100 of the magazines, and felisha sold 0.185 of the magazines. who sold the most magazines?
PLS ANSWER QUICKLY THANK YOU :)
Answer:
Felisha
Step-by-step explanation:
9.65180 to the nearest tenth
Answer:
9.7
Step-by-step explanation:
4. As Jody dives below the water, its temperature decreases by 0.3 degrees Fahrenheit per foot that he dives. If
Jody is diving at a rate of 2.5 feet per second and the water at the surface is at a temperature of 68 degrees
Fahrenheit then what is the temperature of the water Jody is in after diving for 20 seconds?
(1) 48
(3) 57
(2) 53
(4) 83
Answer:
83
Step-by-step explanation:
The temperature of the water Jody is in after diving for 20 seconds is 53.
Given that,
The temperature should be decreased by 0.3 degrees.The rate should be 2.5 feet per second and the temperature of 68 degrees.And, the time taken is 20 seconds.Based on the above information, the calculation is as follows:
[tex]= 68 - (2.5\times 20\times 0.3)[/tex]
= 68 - 15
= 53
Therefore we can conclude that the temperature of the water Jody is in after diving for 20 seconds is 53.
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Question 7 of 10
Which statement best describes an example of a short-term investment
strategy?
A. Mariam buys an IRA that she can't withdraw from without penalty
until she's 59.5.
B. Mariam invests $4,000 in a mutual fund to create a new income
stream.
O C. Mariam buys a certificate of deposit to set aside money for a
down payment on a car.
D. Mariam buys 100 shares of stock in a proven company known for
solid, dependable performance over time.
SUBMIT
Answer:
C
Step-by-step explanation:
Its not A because she can't withdraw it for however many years.
Its not B because creating a new income stream is a long term investment.
Its not D because it says she buys stock of a long-term performing company
WHat is the solution of x^2 + x-6 / x-7 < 0
Answer:
x≤-3 or 2≤x∠7
Step-by-step explanation:
It would be the first answer on the paper
Answer:
A
Step-by-step explanation:
[tex]\frac{x^2+x-6}{x-7} \leq 0\\[/tex]
hence numerator and denominator are of opposite sign.
case1 .
let x²+x-6≥ 0
and x-7<0
x²+x≥6
x²+x+1/4≥6+1/4
(x+1/2)²≥25/4
(x+1/2)²≥(5/2)²
|x+1/2|≥5/2
x+1/2≥5/2
x≥5/2-1/2
x≥2
or
x+1/2≤-5/2
x≤-5/2-1/2
x≤-3
also x-7<0
x<7
combining
x≤-3 or 2≤x<7
case 2.
x²+x-6<0
and x-7≥0
x²+x<6
x²+x+1/4<6+1/4
(x+1/2)²<25/4
|x+1/2|<5/2
so -5/2 <x+1/2<5/2
-5/2-1/2<x<5/2-1/2
-3<x<2
also x-7≥0
so x≥7
combining
we get no vlaue satisfying both the values.
Hence rejected.
Carpenter Chalberg is building a new wall in his house. The wall is 8 feet long and 8 feet tall. The wall will be framed with wood and also have studs (vertical supports) at least every 18 inches. The wall has no doors or windows. He is looking to purchase enough 8 foot boards of wood to make the wall’s frame. How many boards will Carpenter Chalberg need?
9514 1404 393
Answer:
9
Step-by-step explanation:
For studs 16" O.C., Chalberg will need 9: one at the beginning of each of the 16" spaces in the 96" width of the wall, and one at the end. That's a total of 6+1 = 7 studs.
The top and bottom edges of the wall are each 8', so will require 1 more board each.
The total number of boards Chalberg needs is 9.
Write an equation for the line that passes through the given point and is parallel/perpendicular to the graph of the given point.
Parallel: Y=3x-2; (3,2)
Perpendicular: Y= -2x-1; (2,-1)
Also I will mark brainly to who explain what they did step by step
Answer:
Parallel: The slope is the same as in the previous equation. So, y=3x+b. To find the value of b, you plug in the given point, 2=3(3)+b, b=-7. So the equation is y=3x-7.
Perpendicular: The slope is the negative reciprocal when an equation is perpendicular. The negative reciprocal of -2 is 1/2. So, y=1/2x+b. To find the value of b, you plug in the given point, -1=1/2(2)+b, -1=1+b, b=-2. So the equation is y=1/2x-2.
:)
9514 1404 393
Answer:
parallel: y = 3x -7perpendicular: y = 1/2x -2Step-by-step explanation:
The given line equations are written in "slope-intercept" form.
y = mx + b . . . . . . . . . m is the slope; b is the y-intercept
If we solve this equation for b, we find ...
b = y - mx
This is useful for completing the equation of the line through a given point when the slope is known.
ParallelA parallel line will have the same slope as the given line. The given line has a slope (x-coefficient) of 3. We can find the "b" of the line through the desired point as ...
b = y -3x
b = 2 -(3)(3) = -7
The equation of the parallel line is ...
y = 3x -7
__
PerpendicularA perpendicular line will have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to. Here, the given line has a slope of -2, so the perpendicular line will have a slope of ...
-1/(-2) = 1/2
Then the y-intercept is ...
b = y -(1/2)x
b = -1 -(1/2)(2) = -2
And the equation of the perpendicular line is ...
y = 1/2x -2
__
The attached graph shows the original lines as dashed lines, and the corresponding desired lines as solid lines in the same color.
Karen paints her house in 10 1/2 days working 7 1/2 hours per day. How long would it take Karen to do the job if she worked 9 hours a day?
Answer:
8. 75 days
Step-by-step explanation:
You work for 10.5 days 7.5 hrs each day painting the house = it takes 78.75 hours to paint the house.
If you work 9 hours a day: 78.75/9 = 8.75 days
If she does the same job for 9 hours. Then the number of days will be 8.75 days.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Karen paints her house in ten and a half days, working seven and a half hours every day.
If she does the same job for 9 hours. Then the number of days is given as,
D x 9 = 10.5 x 7.5
9D = 78.75
D = 78.75 / 9
D = 8.75 days
If she does the same job for 9 hours. Then the number of days will be 8.75 days.
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y=4x+2 and y=-x-3. Graph
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
(Credit: M a t h w a y )
Select the correct answer.
Select the simplification that accurately explains the following statement.
Answer:
option B
Step-by-step explanation:
[tex]\left(2^{\frac{1}{4}}\right)^{4} = 2^{\frac{1}{4}} * 2^{\frac{1}{4}} *2^{\frac{1}{4}}*2^{\frac{1}{4}} =2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}\\\\=2^{\frac{4}{4}} = 2^{1}=2[/tex]
Answer:
B
Step-by-step explanation:
It was right for me
