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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7. The ratio of the base to height of a triangle is 3:5. If the area of this triangle is 30, find the lengths of the base and height.
Answer:
Base= 6
Height= 10
Step-by-step explanation:
Area of triangle= ½ ×base ×height
Let the base be 3x and the height be 5x.
Given that the area is 30,
½ ×base ×height= 30
½(3x)(5x)= 30
Multiply both sides by 2:
3x(5x)= 60
15x²= 60
x²= 60 ÷15
x²= 4
Square root both sides:
[tex]x = \sqrt{4} [/tex]
x= 2
(reject x= -2 since length has a positive value)
Length of base
= 3x
= 3(2)
= 6
Length of height
= 5x
= 5(2)
= 10
Can someone please help me on this problem I’m struggling
Answer:
No pictures so can't help ya.
Which number is not in scientific notation? (5 points)
11 ⋅ 1021
5.7 ⋅ 109
3.1 ⋅ 10−12
1.67 ⋅ 10−5
9514 1404 393
Answer:
(a) 11·10^21
Step-by-step explanation:
"Scientific notation" has a mantissa that has one digit to the left of the decimal point. The number 11·10^21 has two digits to the left of the decimal point, so is not in the form required by scientific notation.
11·10^21 is not in scientific notation
_____
It would be correctly written in scientific notation as as 1.1·10^22.
Answer:
A) 11 ⋅ 10^21
3 to the power of 1/7
Answer: 0.42857142857
Step-by-step explanation:
given that 2x+y= y+x+1 and y
=2x+2y solve for x and y
Answer:
x=1,y=-2
Step-by-step explanation:
What single percentage change is equivalent to a 14% increase followed by a 11% decrease?
Options:
4.54% decrease
26.54% increase
4.54% increase
1.46% decrease
26.54% decrease
1.46% increase
Answer:
1.46%
Step-by-step explanation:
Pretend you have a number as a test dummy. We'll go with 100 for simplicity. A 14% increase to 100 would be 114. Then we can decrease 114 by 11%. We can find 11% of 114 with an equation like so: x/114 = 11/100. We can then cross multiply to get this" 100x = 1254, which can be simplified to x=12.54. Now, we can subtract 12.54 from 114, which will get us 101.46. Because percentage is based on 100, we can simply subtract 100 from 101.46, which gives us 1.46. So, the answer is 1.46%.
Sorry its blurry but please hurry!!!!!!! Answer 9 and 10 please!!!!
Answer:
9. 31/2 or 15.5( I think that's the answer)
10. B
Step-by-step explanation:
The lines graphed below are parallel. The slope of the red line is - What is
.
the slope of the green line?
X
-5
5
m =
O A. -
ОВ.
Rlო
4
3
O c. -
O c c
O D.
O
3
4
Answer:
C. -4/3
Step-by-step explanation:
Parallel lines have the same gradient (steepness) and this means that they will never intersect.
Hope this helps!
The slope of the red line will be {m} = - 4/3.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
{m} is the slope of the line.
{c} is the {y} - intercept.
Given is that the straight lines graphed below are parallel.
The slope of the red line could be calculated from the points through which the line passes. The points are : (- 3, 0) and (0, 4).
{m} = (- 4 - 0)/(0 + 3)
{m} = - 4/3
Since the lines are parallel, we can write the slope of the green line as same as that of the red line.
Therefore, the slope of the red line will be {m} = - 4/3.
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right please no link or bot
Answer:
3^18
Step-by-step explanation:
Hope it helps
Answer:
3^3
Step-by-step explanation:
a 2) Choose the correct name for the set of numbers. . {4 4. 256, 0.888, 26, – 4.0, 81 1.0, 781 4 O natural numbers O irrational numbers integers O whole numbers real numbers O rational numbers
Answer:
irrational numbers integers
2. In our country today, what do you think are the possible application of pattern and sequence in the field of engineering? How?
Engineering has many applications in our country focused on the construction and development of new technological devices.
Engineering is a term that refers to the set of scientific principles necessary to design and build machines, structures, and others such as:
BridgesTunnelsRoadsVehiclesBuildingsSystemsProcesses.Engineering is characterized by:
Innovation and invention.Development and improvement of techniques and instruments.According to the above, engineering has many applications in the country such as:
Construction of new and more technological buildingsManufacture of tools and devices for different applications such as education, medicine, construction, among others.Learn more in: https://brainly.com/question/18564178
A baker packed 24 cupcakes into each box. After he had packed 37 boxes of cupcakes, there were 248 cupcakes left. How many cupcakes were there altogether?
Hope this helps have a great day!!!!!
A number that has more than two factors is a
Composite number? I’m not sure if that’s what you’re working on but it’s a true statement.
the 10th term of an arithmetic sequence is 57 and the seventh term is 447 find the common difference and the first term
Answer:
232
Step-by-step explanation:
I need it asap fast and I give brainliest to a right answer.
Answer:
hiik
Step-by-step explanation:
rvnlgsudffstdrestdftuisffjhigyhoffyxhcccdfidsudjifg
What is the opposite of V3?
i will give brainliest to the best answer.
Answer:
Step-by-step explanation:
The slope intercept form is like so:
y = mx + b
mx is the slope
b is the y-intercept
Now in your equation:
y = 0.25x + 2
0.25x is the slope
2 is the y-intercept
Use the Quadratic Formula to solve for x and then determine whether your solution is real or
complex.
y = x2 - 4x + 9
**Remember y = 0**
O Real
o Complex
Answer:
[tex] {x}^{2} - 4x + 9 = 0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-( - 4)\pm\sqrt{( - 4)^2-4(1)(9)}}{2(1)} \\x=\frac{ 4\pm\sqrt{ 16-36}}{2} \\ x=\frac{ 4\pm\sqrt{ - 20}}{2} \\ x=\frac{ 4\pm2i\sqrt{ 5}}{2} \\ x = 2\pm \: i\sqrt{ 5} \\ D = {b^2-4ac} \\D = { 16-36} \\ = - 20 < 0 \rightarrow \: x \in \: \mathbb{C} \: \\ x \: is \: complex [/tex]
Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4
y=
Correct answer: y = [tex]\frac{1}{3}[/tex]x + 2
To find out the slope, you would need to remember this slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as [tex]x_{1}[/tex] and [tex]y_{1}[/tex], and (0, 2) as [tex]x_{2}[/tex] and [tex]y_{2}[/tex]. Now we can plug these numbers into the slope formula to find out the slope:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] → [tex]\frac{2-3}{0-3}[/tex] → [tex]\frac{-1}{-3}[/tex] → [tex]\frac{1}{3}[/tex]
To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.
y = mx + b
(3) = [tex]\frac{1}{3}[/tex](3) + b
3 = 1 + b
2 = b
You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.
Now we know that m = [tex]\frac{1}{3}[/tex] and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = [tex]\frac{1}{3}[/tex]x + 2.
Hope this helps you! Let me know if you have any more questions related to this problem.
I think of a number Then multiply it by 3 then add 4 then divide by 4 my final answer is 3 less than the number is the number i thought of the beginning.
Write it as an equation and solve.
Pleas help me out here.
Answer:
A and E
Step-by-step explanation:
The given problem shows a graph of a vertical line with an undefined slope, in which its equation is x = 3 (which matches Option A).
It is not considered a function because it has the same input for every given output. This means that regardless of its y-coordinate, its corresponding x-coordinate will always be x = 3.
The Vertical Line Test allows us to know whether or not a graph is actually a function. Remember that a function can only take on one output for each input. We cannot plug in a value and produce two output values. Since the graph represents a vertical line, it automatically fails the vertical line test. Therefore, it is not a function.
Because it is not a function, Options B, C, and D are invalid answers.
Hence, the correct answers are Options A and E.
In a group of 97 students, the number of students taking programming is twice the number of students taking math. There are 53 students taking exactly one of these subjects, and 15 are taking neither of these subjects. How many students are taking math? How many students are taking programming? In a group of 97 students, the number of students taking programming is twice the number of students taking math. There are 53 students taking exactly one of these subjects, and 15 are taking neither of these subjects. How many students are taking math? How many students are taking programming?
The number of student taking math is 37 while the number of students taking programming is 74
Universal set = 97
let
The number taking math = x
The number taking programming = 2x
The number of students that take exactly one subject = 53
The student taking neither of the subject = 15
The number of students taking only maths will be
x - n(m ∩ p)The number of students taking only programming will be
2x - n(m ∩ p)let
n(m ∩ p) = y
Therefore,
x - y + 2x - y = 53
3x - 2y = 53
Also,
97 = x + 2x - y + 15
3x - y = 82
Therefore,
3x - 2y = 53
3x - y = 82
-y -(-2y) = 82 - 53
y = 29
3x - 29 = 82
3x = 82 + 29
3x = 111
x = 111/3
x = 37
Finally,
number of students taking maths = 37
number of student taking programming = 37×2 = 74
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Use the graph below to find the indicated expression: f(3)-f(-3)
Answer:
f×3-f×(-3)
3f+3f
solution:
6f
Step-by-step explanation:
hope it's can help
Estimate and then solve 6,699 ÷ 72 = ___.
92 r 4
93 r 3
93 r 4
94 r 3
Answer:
It would be 93 remainder 3/the second one.
758 rounded of to the nearest hundred
Answer:
800
Step-by-step explanation:
Hope this helps
Answer:
800, if it's higher than 50 you can round it to the next hundred
PLS HURRY WILL GIVE BRAINLIEST & 20 PTSS!!!!
Answer:
(0,2) x (3,-2)
Step-by-step explanation:
How many combinations are possible? Assume the items are distinct.
10 items chosen 10 at a time
Find the circumference of a circle with a radius of 7 centimeters. Use 3.14 as an approximation for pi . Round your answer to the nearest whole centimeter. Enter only the number.
Hi this is the answer and explaination
I'm sorry if it's incorrect
hope's it's help
The circumcenter of a circle with a radius of 7 cm is, 44cm.
What is circumference?Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.
The formula for the circumference of a circle is given by: C = 2πr,
Given that,
The radius of circle = 7 cm
Substituting the given value of radius as 7 and using pi = 3.14,
we get:
Circumference = 2 × 3.14 × 7
= 43.96
Rounding this to the nearest whole centimeter, we get:
Circumference ≈ 44
Therefore, the circumference of the circle with a radius of 7 centimeters is approximately 44 centimeters.
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needing help with fraction problem
4/11 - 10/8 equals?
having trouble breaking it down to get the answer
Answer:
71/44
Step-by-step explanation:
Here the LCD is the product of the two denominators given: 11*8 = 88.
We rewrite 4/11 as 32/88 and 10/8 as 110/88. Now the denominators are the same.
Combine 32/88 and 110/88. We get the sum 142/88, which reduces to 71/44.
Answer:
-39/44.
Step-by-step explanation:
We need to find the lowest common multiple of 11 and 8.
This is 88.
Now to convert the 2 fractions to denominator 88 we multiply first by
8/8 and the second by 11/11:
4/11 - 10/8
= 32/88 - 110/88
= -78/88
= -39/44
what is the length of segment XZ?
192
12
8
144
Answer:
12 is the length of XZStep-by-step explanation:
Pythagorean Theorem Formula: a² + b² = hypotenuse²
x² + 5² = 13²
x² + 25 = 169
x² + 25 - 25 = 169 - 25 (subtract 25 in both sides)
x² = 169 - 25
√x² = √144
x = 12