A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways
How to determine the number of ways?The selections are given as:
3 boys from 5 boys
3 girls from 4 girls
Each selection is calculated using:
[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]
So, we have:
[tex]Ways = ^5C_3 * ^4C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]
Expand
[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]
Simplify
Ways = 5 * 2 * 4
Evaluate
Ways =40
Hence, the number of ways is 40
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The figure shows a circle circumscribed around a triangle.
Triangle U T V is inscribed within a circle. A point is at the center of the triangle. Lines are drawn from the points of the triangle to the point in the middle. Lines are drawn from the point in the middle to the sides of the triangle to form right angles.
What is constructed first when creating the circle?
perpendicular segments to the vertices of the triangle
perpendicular bisectors of the sides of the triangle
angle bisectors of each angle of the triangle
the incenter of the triangle
Option B is right perpendicular bisectors of the sides of the triangle
What circumcircle?If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.
One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.
When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.
When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C
In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC
Therefore Option B is right perpendicular bisectors of the sides of the triangle.
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Write a paragraph proof to determine whether quadrilateral PQRS is a parallelogram.
Based on the vertices of quadrilateral PQRS, we can infer that quadrilateral PQRS is NOT a parallelogram.
Why is quadrilateral PQRS not a parallelogram?Quadrilateral PQRS would be a parallelogram if the sides have the same slope as this would prove that they are parallel.
The slope of PQ is:
= (6 - 5) / (6 - 4)
= 1/2
The slope of RS is:
= (2 - 4) / (7 - 9)
= -2 / -2
= 1
The slopes are not the same so quadrilateral PQRS is NOT a parallelogram.
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Answer: The quadrilateral is not a parallelogram.
Step-by-step explanation:
I am given that the vertices of quadrilateral PQRS are P(4,5), Q(6,6), R(9,4) and S(7,2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides:
slope of PQ= 1/2
slope of QR= -2/3
slope of RS= 1
slope of SP= -1
Since each side has a different slope, none of the sides are parallel. So quadrilateral PQRS is not a parallelogram.
4. Mr.X is thinking of two numbers. -The sum of the numbers is 212. -The difference between them is 88. Solve a system of equations to determine the value of each number.
Answer:
62 and 150
Step-by-step explanation:
let the 2 numbers be x and y , x > y , then
x + y = 212 → (1)
x - y = 88 → (2)
add the 2 equations term by term to eliminate y
2x + 0 = 300
2x = 300 ( divide both sides by 2 )
x = 150
substitute x = 150 into (1)
150 + y = 212 ( subtract 150 from both sides )
y = 62
the 2 numbers are 62 and 150
A teacher is decorating their classroom by placing posters in a row on one wall. The
teacher has 12 posters, of which 4 are colored and 8 are black & white.
a) If the teacher decides to only use 6 posters, determine how many arrangements
can be made? Describe 2 different ways to get an answer to this problem.
b) If the teacher uses all 12 posters, but wants to have a black & white poster at each
end, how many arrangements can be made? Justify your answer.
c) If the teacher uses all 12 posters, but wants all the colored posters to be side-by-
side, how many arrangements can be made? Justify your answer.
The permutation illustrates that when the teacher decides to only use 6 posters, the number of arrangements that can be made will be 665280 ways.
How to calculate the values?When the teacher decides to only use 6 posters, the number of arrangements will be:
= 12P6
= 12!/(12 - 6)!
= 12!/6!
= 665280 ways.
The fundamental principle will be:
= 12 × 11 × 10 × 9 × 8 × 7
= 665280 ways
When the teacher uses all 12 posters, but wants to have a black & white poster at each end, the number of arrangements will be 203212800 ways.
When the teacher uses all 12 posters, but wants all the colored posters to be side-by-side, the number of arrangements will be:
= 4!8!
= 4 × 3 × 2 × 1 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 967680 ways.
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HELP PLS I NEED 28 and 29 I DONT NEED THE WORK JUST THE ANSWERS FAST ILL MARK BRAINLIEST
Answer:
28) Y=1x+c
29)-2/3x+c
Step-by-step explanation:
A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3
The work required to pump the water out of the spout is 5000ft⋅lb
Given
The volume V=12(4ft)(5ft)(6ft)=60ft3,
Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.
Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.
Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.
In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.
We have to lift that slice 4ft−y, so work is
w = [tex]\int\limits^4_0[/tex] (62.5)(4 − y) (7.5y)
dy = (62.5)[15y2−2.5y3]40 = 5000ft⋅lb
The work required to pump the water out of the spout is 5000ft-lb
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Q={1,3,6,9,10,15} then rewrite in set builder method
Answer:
{x:x is a multiple of 3, x ≤ 15}
In set builder notation, the set Q is written as
Q = {x | x ∈ N, 1 ≤ x ≤ 15, x ∈ {1, 3, 6, 9, 10, 15}}
How to write in set builder in notationThe set Q can be rewritten using the set-builder notation as:
Q = {x | x ∈ N, 1 ≤ x ≤ 15, x ∈ {1, 3, 6, 9, 10, 15}}
In the set-builder notation, the expression "x |" indicates that x belongs to the set being defined.
The vertical bar (|) is read as "such that." The condition "x ∈ N" specifies that x is a natural number, and the condition "1 ≤ x ≤ 15" indicates that x must be greater than or equal to 1 and less than or equal to 15.
Finally, the expression "{1, 3, 6, 9, 10, 15}" specifies the specific elements that belong to the set Q.
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Please helpppppppppp
Answer:
1 4/5
Step-by-step explanation:
On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 [tex]\frac{4}{5}[/tex].
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:
Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C.
Part B: What are the initial value and slope of the graph, and what do they represent? (6 points) Please try to explain it as simply as possible
The answers are:
Part A: The slope of AB and BC are the same.Part B :The initial value is 60 m and the slope is 40 m/min.What is the triangles about?Note that the graph depict the depth, y, in meters, of a shark that moves from the surface of an ocean for a given amount of time, x, in minutes.
So:
Part A :
We look at the two right triangles: Δ ABD and Δ BCE, and where D(2,100) and E(1,60) points.
Since the triangle are the same and thus, the slope of line segment AB: tan θ = AD/BD
= 140 - 100 / 2 - 1
= 40
Since the the slopes of line segment BC will be:
tan a = BE/CE
= 100 - 6 / 1 - 0
= 40
So, θ = α and the slope of AB and BC are similar.
Part B :
Using the graph, one can see that the initial value of the graph is 60 m and it stands for the initial position of the shark
e.g. at point t = 0 min, the shark was seen at a depth of 60 m from the water surface.
So therefore, since the slope of the graph is 40 it implies that the rate of change of distance from the Ocean surface of the shark in regards to the time in minutes have to be 40 m per min.
Therefore, The answers are:
Part A: The slope of AB and BC are the same.
Part B :The initial value is 60 m and the slope is 40 m/min.
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HELP HELP HELP
HELP HELP HELP
Answer:
Step-by-step explanation:
Which scatter plot represents the data in the table?
Suppose cotangent (theta) = startfraction 5 over 12 endfraction, where pi less-than theta less-than startfraction 3 pi over 2 endfraction. what is sin(θ)?
sin(Q) = -(12/13)
What are trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively. It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.
cot(Q) = 5/12
sin(Q) = 1/cosec(Q)
[tex]sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}\\[/tex]
sin(Q) = ±12/13
Because, π < Q < (3/2)π
Therefore, sin(Q) = -12/13
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Answer:
A- -12/13
Step-by-step explanation:
i need help with this question guys i’ll give you brainly
Answer:
C
Step-by-step explanation:
C is most relevant to the question
A dependent means t-test determines if the differences between scores on the pretest and posttest measures differ significantly from:
A dependent means t-test determines if the differences between scores on the pretest and post-test measures differ significantly from Zero(0).
Benefits of pre-test measurements
This design is superior to the post-test-only control design because it adds pre-tests. Addition of pre-test: Improve your design ability to detect effects. You can investigate the impact of interventions on various sublevels of pretesting.
The design of the pre-test and post-test is similar to the in-subject experiment. In this experiment, each participant is first tested in control conditions and then in therapeutic conditions.
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In this circle, the area of sector COD is 50.24 square units.
The radius of the circle is ____ units, and mAB is ____ units.
Answer:
Radius = 8 units
Length of arc AB = 8.37758 units
Step-by-step explanation:
The sector COD is 1/4 the size of the circle.
the vertex angle is 90° and a circle has 360° at the center.
So the area of sector COD/area of Circle = 90/360 = 1/4
This means the area of the circle is 4 * 50.24 = 200.96 square units
Area of circle = πr² where r is the radius
πr² = 200.96
r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units
The circumference of the circle is 2πr = 16π units
arc AB has a vertex angle of 30°.
30°/360° = 1/6
So the length of the arc is 1/6th the circumference of the circle =
(1/6) * 16π = 2.67π units or 8.37758 units
more math i need help in
Answer:
It is B
Step-by-step explanation:
35/6 divided by 5/4 in ait simplest form
The simplest form of 35/6 ÷ 5/4 is 14/3
Given,
35/6 ÷ 5/4
hence it is written as= 35/6 ×4/5
= 7×2/3×1
= 14/3
The simplest form of fractions are determined by following the given steps:
List the denominator's and numerator's factors.Find the common factors between the denominator and numerator.The fraction obtained is in the reduced form when the numerator and denominator are divided by the common factors until they have no common factor but 1.This number can't be further subdivided. Hence we get the the simplest form of 35/6 ÷ 5/4 as 14/3.
If we get numbers which share common highest common factor then divide the number by both numerator and denominator to bring the simplest form of number.
Therefore we get the simplest form of number as 14/3.
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What is 16% of 750?
Answer:
120
Step-by-step explanation:
For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120
Replace variables with values and
evaluate using order of operations:
P = 2L+2w
L = 20
W=14
Step-by-step explanation:
p=2L+2w
factorise
p=2(L+w)
p=2(20+14)
p=2(34)
p=68
This is also a perimeter of a rectangle
Hello!
Here, the 2 mathematical operations involved are : multiplication and addition.
From the order of operations, we know multiplication is followed by addition.
⇒ P = 2(20) + 2(14)
⇒ P = 40 + 28
⇒ P = 68
∴ The answer will be [tex]\fbox {68}[/tex]
Alone LiZ can complete a project in 12 hours and Julia could do it alone in 24 hours. Liz worked on the project alone 2 hours before Julia joined her. How many hours did they work together to finish ?
Answer:
Julia and Liz worked 10 hours to finish the project.
Step-by-step explanation:
I don't know if I am 100% right, but I believe this is the answer.
If you take the 24 hours it will take Julia to finish the project on her own and subtract the time it would take Liz you would have 12 hours left then take the 2 hours Liz has already been working on the project you would have 10 hours for both of them to finish the project together.
24 -12 = 12
12 - 2 = 10
Enter the correct answer in the box.
Simplify the expression (6^2)4.
Answer:
1679616
Step-by-step explanation:
Answer:
it's 6^8 (6 to the 8th power)
Step-by-step explanation:
put 8 in the box
hope this helps :) <3
i need help with this page
Given △qrs ~ △xyz, what is the value of tan(q)? three-fifths three-fourths four-fifths four-thirds
The value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
According to the properties of similar triangle, the corresponding sides of similar triangles are in proportion.
In the question, we are given that ΔQRS ~ ΔXYZ.
By properties of similar triangles, we know that:
QR/XY = RS/YZ = SQ/ZX.
From this, we can show that:
RS/SQ = YZ/ZX ...(i).
We are asked to find the value of tan(Q).
By trigonometric ratios, we know that:
tan(Q) = Perpendicular/Base = RS/SQ.
From (i), we know that RS/SQ = YZ/ZX.
From figure, we know that YZ = 9, and ZX = 12.
Thus, YZ/ZX = 9/12 = 3/4.
Thus, tan(Q) = RS/SQ = YZ/ZX = 3/4.
Hence, the value of tan(Q) = 3/4, given that ΔQRS ~ ΔXYZ. Computed using properties of similar triangles. Hence, the second option is the best choice.
The question is incomplete. The complete question can be seen in the figure.
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A running track in the shape of an oval is shown. The ends of the track form semicircles.
A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 46 m and length of one straight edge 150 m.
What is the perimeter of the inside of the track?
The perimeter of the inside of the track is 444.44m
How to calculate the perimeter?Based on the information given, the length will be 150m and the width is 46m.
The circumference will be:
=2πr
= (2 × 3.14 × 46/2)
= 144.44
The length will be:
= 2 × 150
= 300
The perimeter of the oval will be:
= 300 + 144.44
= 444.44m
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Simplify the expression by combining like
terms:
4x² + 6x + 5x²-x
Enter the number that belongs in the green box.
[?]x² + [ ]x
Answer:
9x² + 5x
Step-by-step explanation:
4x² + 6x + 5x²-x
Combine like terms:-
4x² + 5x² = 9x²
6x - x = 5x
9x² + 5x
-----------------------------
If the center of the circle were moved from the origin to the point (h, k) and point p at (x, y) remains on the edge of the circle, which could represent the equation of the new circle? (h x)2 (k y)2 = r2 (x – h)2 (y – k)2 = r2 (k x)2 (h y)2 = r2 (x – k)2 (y – h)2 = r2
[tex]{(x-h)}^2 + {(y-k)}^2 = {r}^2[/tex] represent the equation of the new circle.
Given: (h,k) is center of circle
and (x,y) remains on edge of circle.
The distance formula is used to determine the distance, d, between two points. If the coordinates of the two points are (x1, y1) and (x2, y2), the distance equals the square root of x2 − x1 squared + y2 − y1 squared.
The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points.
In a Cartesian grid, to measure a line segment that is either vertical or horizontal is simple enough. You can count the distance either up and down the y-axis or across the x-axis
Using Distance formula which says,
[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r\\\sqrt{{(x - h)}^2 + {(y - k)}^2} = r\\\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]
Hence, the equation of the new circle will be [tex]\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]
Formula used:[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r[/tex]
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Answer: B
Step-by-step explanation:
A ferry traveling along the river at a constant rate covers of the distance between two ports in of
an hour. At this rate, what fraction of the distance between the two ports can the ferry travel in one
hour?
(A) 3/24 (B) 1/3 (C) 7/18 (D) 25/42
The formula speed = distance ÷ time can be rearranged, just like any other equation. The formula can be rearranged in three ways: speed = distance ÷ time , distance = speed × time.
Speed tells us how slow or fast an object moves. Distance refers to extent of space between two events. Time refers to an interval separating two events.
ASSUME a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports in 3.5 hours.
Distance that the ferry would be able to trave in 1 hour can be found out by :
unit rate=distance / time
=1/7÷3/5
Reciprocal:
=1/7×5/3
=5/21th of distance per hour
The distance that the ferry would be able to travel in 3.5 hours:
= (5/21 ) ×3.5
=(5/21)×(7/2)
Further solving:
=(5/3)×(1/2)
5/6th of the distance between two ports.
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Disclaimer:
Your question was incomplete. Please check below the full content.
Complete question could be a ferry travels 1/7th of the distance between two ports in 3/5 hours , then it will be able to cover 5/6th part of the distance between two ports in 3.5 hours.
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In the given figure CB ǁ QR, CA ǁ PR, AQ = 12cm, CB = CQ =15cm. Calculate PC and BR .
By applying basic proportionality theorem (BPT), the length of side PC and BR are 25 cm and 9 cm respectively.
How to calculate the length of side PC and BR?In order to determine the length of side PC and BR, we would apply basic proportionality theorem (BPT) as follows:
PC/CQ = AR/AQ
PC/15 = 20/12
Cross-multiplying, we have:
12PC = 20 × 15
PC = 300/12
PC = 25 cm.
For the length of side BR, we have:
PC/CQ = PB/BR
PC/15 = 15/BR
25/15 = 15/BR
25BR = 225
BR = 225/25
BR = 9 cm.
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Find the area and the perimeter of the shaded regions below. Give
your answer as a completely simplified exact value in terms of T (no
approximations). The figures below are based on semicircles or
quarter circles and problems b), c), and d) are involving portions of
a square.
Pls explain as best as you can i cant understand this stuff
Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.
How to find the area of the composite figure
The area of the composite figure is the sum of two areas, the area of a semicircle and the area of a right triangle. The formula for the area of the composite figure is described below:
A = (1/2) · AB · BC + (π/8) · BC² (1)
If we know that AB = 6 cm and BC = 6 cm, then the area of the composite figure is:
A = (1/2) · (6 cm)² + (π/8) · (6 cm)²
A ≈ 32.137 cm²
Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
x=0. The explanation is below.
Step-by-step explanation:
So, it is run 2 rise 6. We can fact-check that with 1 to 3 to 5 and 1 to 7 to 13. So, the slope is 3 because of rise over run. So, we can make an equation with y = mx + b. m = 3 because that is the slope. 1=3(1) + b. b=-2. So, the equation is y=3x-2. We can find any x using y and vice versa if we find the equation.
For this part, -2=3x-2. 3x=0. x=0.
Find equation of line
(1,1)(3,7)Slope
m=7-1/3-1m=6/2m=3Equation
y-1=3(x-1)y-1=3x-3y=3x-2Now
put y=-2
3x-2=-23x=0x=0