The number of ways of selecting a committees of 5 members from a group of 10 people will be 252
Combination is a method to calculate different ways to select items from a set / group regardless of the order.
ⁿCₓ = n! / (n-x)! x!
Total number of people in group is 10
Number of people require to form committee is 5
By using Combination ,
¹⁰C₅ = 10! / (10 - 5 )! 5!
= 10×9×8×7×6×5! / 5! × 5!
Cancelling 5! from numerator and denominator
= 10×9×8×7×6 / 5!
expanding the factorial
= 10×9×8×7×6 / 5×4×3×2×1
= 252
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Tarak wants to find the value of a so that the line that passes through (10, a) and (-2, -8) has a slope of value of 1/4.
Explain how Tarak can find the a.
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{a})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{a}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{10}}} ~~ = ~~\stackrel{\textit{\LARGE m}}{\cfrac{1}{4}} \\\\\\ \cfrac{8-a}{-12}=\cfrac{1}{4}\implies 32-4a=-12\implies 44-4a=0 \\\\\\ 44=4a\implies \cfrac{44}{4}=a\implies \boxed{11=a}[/tex]
Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the
tarting line.
06 miles
√6 miles
O√12 miles
√20 miles
hello hope you are having a good day
the answer to your question would be A 6 miles i took the test and got an 100% also asked the teacher.
Water Glasses on a shelf are broken and must be replaced.
The replacement cost can be cut in half if you can figure out how many glasses were broken.
Here are your clues:
There were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
The total number of water glasses on the shelf may be 39, 63 or 87.
Given, that there were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
Let the number of glasses be x,
So, x = 6k1 + 3
=> (x - 3) is a multiple of 6
x = 8k2 + 7
=> (x - 7) is a multiple of 8
Now, the numbers that can satisfy the given conditions are,
39 , 63 & 87.
So, the total number of glasses may be 39, 63 or 87.
Hence, the total number of water glasses on the shelf may be 39, 63 or 87.
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HELP!!!!!!!!!!!!!!!!!!
Answer:-1/3
Step-by-step explanation: the point goes right one and down three making the slope negative
What is (5,-3) & (4,0) in slope intercept form?
The slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.
The slope intercept form is simply writing an equation of a line so that the slope or steepness and y-intercept i.e. where the line crosses the vertical y-axis are immediately apparent.
The slope-intercept equation is y = mx + c, where x and y are two variables, and m is slope.
Slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Let,
(x1, y1) = (5, -3)
(x2, y2) = (4, 0)
Slope (m) = [tex]\frac{0 - (-3) }{4 - 5}[/tex]
= [tex]\frac{3}{-1}[/tex]
= -3
By substituting x, y, and m values in the equation we can get the value of c.
Consider x = 4 , y = 0, m = -3
y = mx + c => 0 = (-3)4 + c
c = 12
Therefore, the slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.
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someone please help asap! 50 points + brainliest. this is the only question im stuck on
(about galaxies)
Match the galaxy type to its correct description.
column A
1. ___ elliptical
2. ___ spiral
3. ___ irregular
column B
a. defined central bulge; dusty cloud around the bulge.
b. no defined shape, the central bulge, or arms.
c. defined central bulge; dusty arms extending from the bulge.
Answer:1=a, 2=b, 3=c
Step-by-step explanation:
just smart like that
HELP ASPPP PLEASE SHOW UR WORKKKK
Step-by-step explanation:
when we have an equation
y = ax + b
then "a" is the slope.
in our equation we see
1/2(6x ...) = 6/2 x ... = 3x ...
so, the slope is 3.
In a scene from a television show, a van rolls down an incline and off a vertical cliff, falling into a valley below. The van starts from rest and rolls down the incline, which makes an angle of 18.0° below the horizontal, with a constant acceleration of 2.90 m/s2. After rolling down the incline a distance of 40.0 m, it reaches the edge of the cliff, which is 45.0 m above ground level.
(a) How much time (in s) does it take the van to fall from the edge of the cliff to the landing point?
(b)
At the point where the van crashes into the ground, how far is it horizontally from the edge of the cliff (in m)?
Answer:
its A
Step-by-step explanation:
A
Answer:50
Step-by-step explanation:i said so
Devon and Albert are shelving books at a public library. Devon shelves 6 books at a time, whereas Albert shelves 9 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?
What is the radical form of each of the given expressions?
Drag the answer into the box to correctly match each expression.
Answer:
The answer is displayed in the attached image.
Step-by-step explanation:
To find the radical form of an expression, first determine what is in the denominator of the fractional exponent. That number will determine the order of the root you will take. The numerator will be the power of your original number
EXAMPLE:
[tex]5^{\frac{3}{4} }[/tex] = [tex]\sqrt[4]{5^3}[/tex]
Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)?
O Focus (2, -0.5); directrix x = 0
O Focus (2,-0.5); directrix y = -1.5
O Focus (0, -0.5); directrix y = -1.5
O Focus (0, -0.5); directrix x = 0
The first option Focus(2,-0.5); directrix x=0 of the parabola is the correct answer.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
The general equation of a parabola is as follows:
[tex](y-k)^2=4a(x-h)[/tex]
Now, consider the given equation.
[tex](y+0.5)^2=4(x-1)[/tex]
Now, compare with the standered equation.
a=1, k=-0.5 and h=1
Here, a is positive hence, the parbola opens right side.
Focus is given by the following coordinate:
[tex](h+a,k)=(1+1,-0.5)\\=(2,-0.5)[/tex]
Now, equation of diretrix is given by the following expression:
[tex]x=h-a\\x=1-1\\x=0[/tex]
Hence, the first option Focus(2,-0.5); directrix x=0 is the correct answer.
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Find the total surface area of this prism where
the cross-section is an isosceles triangle.
Marks
5 cm
13 cm
24 cm
10 cm
The total surface area of this prism is: 620 cm².
How to find the total surface area?First step it to find the Area of isosceles triangles:
Area of isosceles triangles = [(24 × 5) ÷ 2]
Area of isosceles triangles (120 ÷ 2)
Area of isosceles triangles = 60 cm²
Second step is to find the area of 2 triangles
Area of 2 triangles = 60 cm² × 2
Area of 2 triangles = 120 cm²
Third step is to find the Area of 2 identical rectangles
Area of 2 identical rectangles= (10 × 13 ) × 2
Area of 2 identical rectangles= 260 cm²
Fourth step is to find the bottom area of rectangle
Area of rectangle = 24 × 10
Area of rectangle = 240²
Now let find the total surface area
Total surface area =120 + 260 + 240
Total surface area = 620 cm²
Therefore the surface area is 620 cm².
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I need help asap. Given the equation 14.25y = 99.75, determine the value of y.
114.00
85.50
7.00
1421.44
Answer: Answer is 7.00
Step-by-step explanation: i did this i got right answer... please likes, 5 star have great day :)
46+(-4) pLeAsE SoLVe
Answer:
42
Step-by-step explanation:
Answer:
+ - = -
Step-by-step explanation:
46 - 4 = 42
hope this helps
The math dept is buying pizza for the students from either Papa Johns or
Cicis. The equation for Papa Johns can be represented as C=12p+15 which
includes a one time delivery charge. The equation for Cicis can be presented
as C=10p+12 which includes a one time delivery charge.
How much more does Papa Johns charge PER PIZZA than Cicis?
answer
Papa Johns charges 2 more per pizza plus 3 more for the delivery charge so 5 total
Factorize 6pq-3rs-3ps+6qr
with solutions
3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.
What is Factor?A factor is a number that divides another number, leaving no remainder
The given expression is 6pq-3rs-3ps+6qr
We need to factorize the expression.
6pq-3rs-3ps+6qr
= 3 (2pq - rs - ps + 2qr)
= 3 (2pq + 2qr -ps - rs)
= 3 (2q(p + r) -s(p + r))
= 3 (2q - s)(p + r)
Hence, 3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.
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K
Find the production matrix for the following input-output and demand matrices
using the open model.
A =
0.3 0.2
0.35 0.4
3
-[³]
6
D=
The production matrix is
(Round the final answer to the nearest hundredth as needed. Round all
intermediate values to four decimal places as needed.)
[tex]\displaystyle\\Answer:\ \left [ {{\boxed{2.1}} \atop {\boxed{3.45}}} \right][/tex]
Step-by-step explanation:
[tex]\displaystyle\\A=\left [ {0.3\ \ \ \ 0.2} \atop {0.35\ \ \ 0.4}} \right]\ \ \ \ \ D=\left [ {{3} \atop {6}} \right]\\\\A*D=\left [ {{c_{11}} \atop {c_{21}}} \right] \\\\c_{11}=a_{11}*b_{11}+a_{12}*b_{21}\\\\c_{11}=0.3*3+0.2*6\\\\c_{11}=0.9+1.2\\\\c_{11}=2.1\\\\c_{21}=a_{21}*b_{11}+a_{22}*b_{21}\\\\c_{21}=0,35*3+0,4*6\\\\c_{21}=1.05+2.4\\\\c_{21}=3.45\\\\Thus,\ A*D=\left [ {{2.1} \atop {3.45}} \right][/tex]
The triangle below will be reflected across the line x = 5, then translated to
the left 12 units to form an image. A reflection over which line would result
in the same image?
Reflecting over the y-axis and then translating to the right 10 units
Step-by-step explanation:
Reflection over the line x=5 gives you the transformation ...
(x, y) ⇒ (2·5 -x, y) = (-x +10, y)
This is precisely the same transformation you get by reflection over the y-axis:
(x, y) ⇒ (-x, y)
followed by translation to the right 10 units:
(-x, y) ⇒ (-x +10, y)
__
Reflection over x=5 is the same as reflection over y and translation right 10.
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Given the Quadratic equation y = 2x²- 9x - 13, what is the y intercept?
(0,0)
(0,-13)
(0,2)
(0,-9)
Help please
Answer: (0,-13)
Step-by-step explanation:
The y intercept is x=0
Hence,
y=2(0²)-9*(0)-13
y=2(0)-0-13
y=0-13
y=-13
Thus, (0,-13)
Help please. 20 pts WILL MARK BRAINLIEST
Answer:
Subtract 6 from both sides
Please help
me answer both of them ASAP!! and submit it like this. Example: 1=b and 2=d
8. -a+b-7
9. m=(y-b)/x
Answer:
first one: C
second one: A
Step-by-step explanation:
4a - 5 + 3b - 2 - 2b - 5a
combine a terms:
-a - 5 + 3b - 2 - 2b
combine b terms:
-a - 5 + b - 2
combine numbers:
-a + b - 7 (this is option c)
_____________________
y = mx + b, solve for m
subtract b from both sides:
y - b = mx + b - b
y - b = mx
divide both sides by x:
(y - b)/x = mx/x
m = (y - b)/x (this is option a)
what is - 8/15 - 3 4/5
-4 1/3
I hope this helps
When subtracting or adding fractions make sure that the denomators are the same.
jake brought a bike that cost 65 when it was new if he eventually sold it for 20% of the original cost how much he sold it for
Answer:
$13
Step-by-step explanation:
$65 x 0.20 = 13
Answer: 20% off 65 is $52.00 so it was $13 saved
Sarah can text 91 words in 14 minutes. At
this rate, how many minutes would it take
her to text 65 words?
If Sarah can text 91 words in 14 minutes, then at this rate she will type 65 words in 10 minutes
Number of minutes to types 91 words = 14 minutes
Here we have to use the unitary method to solve the problem
Time taken to type 1 word = Number of minutes to types 91 words / 91
Substitute the values in the equation
= 14 / 91
= 2 / 13
Time taken to type 65 words = Time taken to type 1 word × 65
Substitute the values in the equation
= (2/13) × 65
= 10 minutes
Hence, if Sarah can text 91 words in 14 minutes, then at this rate she will type 65 words in 10 minutes
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State the coordinates of the point.
5. What is the independent variable in the following function?
f(c) = 2c + 9
09
Of
0:
Answer:
C
Step-by-step explanation:
C is the input. The input is the independent variable. The output would be the dependent variable.
Which of the expressions below has a 7 in the
tenths place of the sum? Select all that apply.
A) 12.35 + 19.38
B) 9.89 + 4.9
C) 8.135 + 2. 644
D) 3.445 +2.382
Pls tell me!
is it true that the discriminant of f(x)=2x^2-10x+8 equals -36? (algebra 2)
The discriminant of the equation f(x) = 2x^2-10x+8 [tex]\neq[/tex] 36
To find out the discriminant of f(x)=2x^2-10x+8
The formula for the discriminant is represented by b²-4ac.
This equation is in general form, which is ax² + bx + c = 0.
So, lets assume the values to be
a = 2
b = -10
c = 8
The discriminate that we need to find out in the equation below is
D = b²-4ac
[tex]D = -10^{2} - 4(2)(8)[/tex]
D = -100 - 64
D = -164 which is not a nice number
As the discriminant had a negative value of -164.
This means there are no real solutions to the equation, because the discriminant is negative.
Hence the discriminant of the equation f(x) = 2x^2-10x+8 [tex]\neq[/tex] 36
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A school is arranging a field trip to the zoo. The school spends 651.21 dollars on passes for 46 students and 3 teachers. The school also spends 396.98 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Cost of 14 apples is Rs. 120, find the cost of 20 apples
Answer:
Rs 171.40
Step-by-step explanation:
For 1 apple we have to divide 120 by 14 which is 8.57 to 2d.p.
So 20 * 8.57 = 171.4
to 2d.p. = Rs 171.40
Pls could you give me brainliest
pls:(