The radius and height, in two decimal places are mathematically given as
r=10.60
What is the radius and height, in two decimal places?Generally, the equation for the volume is mathematically given as
[tex]V=\pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]
Therefore
[tex]5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}[/tex]
[tex]V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\[/tex]
[tex]\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle[/tex]
Using Lagrange method
[tex]$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$[/tex]
[tex]$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$[/tex]
[tex]$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\[/tex]
[tex]$400 \pi r-300 \pi r=150 \pi h$[/tex]
[tex]$160 \pi r=150 \pi h \quad \\\\\\[/tex]
with
[tex]h=\frac{2}{3} r $[/tex]
[tex]$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$[/tex]
[tex]\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$[/tex]
[tex]$\frac{4 \pi \gamma^{3}}{3}=5000 \quad[/tex]
[tex]r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$[/tex]
r=10.60
In conclusion, the radius and height, in two decimal places is
r=10.60
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What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=|x|:
a) Stretch vertically by a factor of 2;
b) Compress horizontally by a factor of 2
if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x| and a horizontal compression by a factor of 2, the resulting function will be 1/2|x|
Transformation of functionsTransformation is a technique used to change the position of an image on an xy-plane.
If the function f(x)is vertically stretched by "a" units, the resulting function will be f(x) = a|x|.
Hence if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x|
For a horizontal compression by a factor of 2, the resulting function will be 1/2|x|
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A survey was conducted to determine which type of lunch was more popular among the school’s football team. For this purpose, the number of each type of lunch sold to the players was tracked. How many more pizza lunches than hot dog lunches were sold? A. 3 B. 4 C. 7 D. 5
The number of pizza lunches sold more based on the survey is 5.
How to compute the value?The information is incomplete and an overview will be given.
Let the number of pizza lunches sold be 24.
Let the number of hot dog lunches be 19.
Therefore, the number of pizza lunches sold more will be:
= 24 - 19
= 5
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Answer: C, 7
Step-by-step explanation:
PLEASE HELP THIS IS TIMEDDDD PLS DONT GUESS
What is the sum of f° + g°?
360°
120°
180°
110°
Answer: 180
Step-by-step explanation:
i got you!!!!!!! Hope u pass
Answer:
180
Step-by-step explanation:
<f and <g are on a straight line and they are supplementary angles which means their sum is equal to 180.
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas.During
one particular week, the two cars went a combined total of 1400 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week
20 gallons is consumed from the first car and 25 gallons is consumed from the second car.
What is an Equation ?A mathematical statement that relates two algebraic expression using an equal sign is called an equation.
It is given that
Fuel Efficiency of the first car is 20 miles per gallon of gas
Fuel Efficiency of the second car is 40 miles per gallon of gas
Total miles travelled = 1400 miles
Total gas consumption = 45 gallons
Let the gallons consumed from the first car is x
then the gallons consumed by the second car is (45 - x)
The equation formed will be
20* x + 40 * (45 -x) = 1400
20x +1800 - 40x = 1400
-20x = -400
x = 20
Therefore 20 gallons is consumed from the first car and
45-20 = 25 gallons is consumed from the second car.
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189 divided by 7 please get a long division answer
Using long division, 189 divided by 7 is 27
How to use long division technique?The picture below represent how to use long division.
Firstly, we divided 1 by 7, it can't go. Therefore, it zero. we put zero at the quotient space.
Multiply zero by 7 and subtract from 189.
We use 18 to divide 7. It will give us 2 remainder 4. we put the 2 at the quotient side and multiply it by 7 to get 14.
Then we subtract 14 from 18. And so on. This is done till we get 0.
Therefore, using long division, 189 divided by 7 is 27
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What is 88=10y + 30 - 4y?
Answer:
y = [tex]\frac{29}{3}[/tex]
Step-by-step explanation:
88 = 10y + 30 - 4y , that is
88 = 6y + 30 ( subtract 30 from both sides )
58 = 6y ( divide both sides by 6 )
[tex]\frac{58}{6}[/tex] = y , that is
y = [tex]\frac{29}{3}[/tex]
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps used to solve the quadratic equation are
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to determine the stepsGiven the equation;
8x² + 16x + 3 = 0
Collect like terms
8x² + 16x = -3
Take the common factors, we have
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation in the right side
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square
[tex]8(x + 1)^2} = 5[/tex]
Make 'x' subject
[tex](x + 1)^2= \frac{5}{8}[/tex]
[tex](x + 1) =[/tex] ±[tex]\sqrt{\frac{5}{8} }[/tex]
[tex]x =[/tex] -1 ±[tex]\sqrt{\frac{5}{8} } }[/tex]
Thus, we can clearly see the steps used to solve the quadratic equation are
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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Michael has never taken a foreign language class, but is doing a story on them for the school newspaper. The school offers French and Spanish. Michael has a list of all 25 kids in the school enrolled in at least one foreign language class. He also knows that 18 kids are in the French class and 21 kids are in the Spanish class. If Michael chooses two kids at random off his list and interviews them, what is the probability that he will be able to write something about both the French and Spanish classes after he is finished with the interviews
The probability that kids will be able to write something about both the French and Spanish classes after he is finished with the interviews is 91/100.
Given 25 kids has enrolled in atleast one foreign language class. 18 kids are in French class and 21 kids are in Spanish class.
We have to find the probability that kids will be able to write something about both the French and Spanish classes after Michael is finished with the interviews.
Let F is a set showing students knowing French,
S be a set showing students knowing Spanish ,
FS= Showing students both enrolled in one languages.
FS=F+S-(F∪S)
=18+21-25
=14
F-18-14=4
S=21-14
=7
4 outcomes lead to Michael being able to write both the languages are (F,S),(FS,S)(FS,F)(FS,FS)
Required probability is the sum of all the probabilities of (F,)(FS,S)(FS,F)(FS,FS)
P(F,S)=[tex]4C_{1}*7C_{1}/25C_{2}[/tex]
=(4*7)/300
=28/300
P(FS,S)=[tex](14C_{1}*7C_{1} )/25C_{2}[/tex]
=14*7/300
=98/300
P(FS,F)=[tex](14C_{1}*4C_{1} )/25C_{2}[/tex]
=14*4/300
=56/300
P(FS,FS)=[tex]14C_{2}/25C_{2}[/tex]
=91/300
Required probability=28/300+98/300+56/300+91/300
=(28+98+56+91)/300
=273/300
=91/100
Hence the probability that kids will be able to write both the languages is 0.91.
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asap! find the length of the arc
Answer:
A. [tex]\frac{21}{4} \pi\ \space\ in[/tex]
Step-by-step explanation:
The formula for arc length is:
arc length = rθ
where:
r is the radius = 7 in
θ is the central angle in radians = 135 × [tex]\frac{ \space\ \pi\ }{180}[/tex] = 3/4 π
Substituting these values into the formula:
arc length = 7 in × 3/4 π
= [tex]\frac{21}{4} \pi\ \space\ in[/tex]
Can some one put the answers out
Step-by-step explanation:
1. -5(a - 9) = -5a + 45
2. [tex]\frac{-8.3-(+2.7)}{\frac{1}{5} } = \frac{-8.3-2.7}{0.2} =\frac{-11}{0.2}=-55[/tex]
3.13p + 13 - p = (13p - p) + 13 = 12p + 13
4. -11b - 3(-4b + 1) = -11b + 12b - 3 = b - 3
5.
[tex]-2n+\frac{1}{6}-4\frac{1}{2}n = (-2n-4\frac{1}{2}n)+\frac{1}{6} = [-\frac{4}{2} n-(\frac{8}{2}+\frac{1}{2} )n]+\frac{1}{6} = -\frac{4}{2} n- \frac{9}{2} n+\frac{1}{6} =-\frac{13}{2}n\\+ \frac{1}{6}[/tex]
6. It didn't show all the information on the question.
7. [tex]-\frac{3}{5}(20r-5)-(-6r) =-12r+3+6r = (-12r+6r)+3=-6r+3[/tex]
8. [tex]-\frac{5}{6}x+\frac{4}{9}+\frac{2}{3}x+\frac{1}{3}=(-\frac{5}{6}x+\frac{2}{3}x)+(\frac{4}{9}+\frac{1}{3})=(-\frac{5}{6}x+\frac{4}{6}x)+(\frac{4}{9}+\frac{3}{9})=-\frac{1}{6}x+\frac{7}{9}[/tex]
9.It didn't show all the information on the question.
What is the gradient of the graph shown?
Answer:
1
Step-by-step explanation:
t14= 46, and t19= 100, find t3, t7, and tn
The terms are as follows:
t₃ = -62
t₇ = -29.6
tₙ = 10.8n - 105.2
How to find terms of an arithmetic sequence?t₁₄ = 46
t₁₉ = 100
Therefore,
tₙ = a + (n - 1)d
where
a = first termd = common differenceHence,
46 = a + 13d
100 = a + 18d
5d = 54
d = 10.8
46 - 13(10.8) = a
a = 46 - 140.4
a = - 94.4
t₃ = a + 3d = - 94.4 + 3(10.8) = -62
t₇ = a + 6d = - 94.4 + 6(10.8) = -29.6
tₙ = -94.4 + 10.8n - 10.8 = 10.8n - 105.2
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Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
34 feet
27 feet
Answer: [tex]52.6^{\circ}[/tex]
Step-by-step explanation:
Let the angle of depression be x.
[tex]\sin x=\frac{27}{34}\\\\x=\sin^{-1} \left(\frac{27}{34} \right) \approx 52.6^{\circ}[/tex]
Could you guys help meee
1. y= 2x
2. (0, 5)
3. y = 3x + 12
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
1. let us take (0,0) and (1, 2)
m= 2-0/1-0
m= 2
So equation of line
y- 0 = 2(x-0)
b
2. y= 3x+5
passes through (0, 5)
3. y= 3x+5
m = 3
We need the equation of a line with slope 3 that passes through point (0, 12).
y - y1 = m(x - x1)
y - 12 = 3(x - 0)
y - 12 = 3x
y = 3x + 12
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Given a line segment that contains the points A,B, & C in order, and given B is the midpoint of AC, if AB = 4x - 3, and BC = 2x + 7, find x.
Answer:
x = 5
Step-by-step explanation:
given B is the midpoint of AC , then
AB = BC ( substitute values )
4x - 3 = 2x + 7 ( subtract 2x from both sides )
2x - 3 = 7 ( add 3 to both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Come up with two examples of ratio relationships that are interesting to you.
In mathematics a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
Let's take an mathematical example
Let's find the ratio of volume of a cone and cylinder if radius and height are same for both .
See
V for cone=1/3πr²hV for cylinder=πr²hThe ratio is 1:3
#Example 1
Gems Ram has=3Gems Kane has=4Ratio of gems=3:4
#Example 2
Total continents in world=7Total oceans in world=5Ratio of ocean to continents=5:7
Note:-
Two examples are already provided on your another question .You may refer there
expand and simplify(2x-3)(3x-5)
Answer:
6[tex]x^{2}[/tex] - 19x + 15
Step-by-step explanation:
(2x - 3) (3x - 5)
2x(3x-5) - 3 (3x-5)
6[tex]x^{2}[/tex] - 10x - 3 (3x - 5)
6[tex]x^{2}[/tex] - 10x - 9x + 15
6[tex]x^{2}[/tex] - 19x + 15
Answer:
6x² - 19x + 15
Step-by-step explanation:
(2x - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
2x(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 6x² - 10x - 9x + 15 ← collect like terms
= 6x² - 19x + 15
Triangle abc is a right triangle with leg lengths of 5 and 12 inches. find the length of the hypotenuse. round answer to the nearest hundredth if necessary. 4.12 in 10.91 in 13 in 17 in
The hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.
The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.
If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:
a² = b² + c².
In the question, we are given that the right triangle ABC, has legs of lengths 5 and 12 inches each, and we are asked to find the length of the hypotenuse.
Thus, taking b = 5 and c = 12, in the above equation, we get:
a² = 5² + 12²,
or, a² = 25 + 144,
or, a² = 169,
or, a² = 13²,
or, a = 13.
Thus, the hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.
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-6. The area of trapezium in cm² is A. 276 C. 207 B. 240 D. 225
Answer:
276 cm²
Step-by-step explanation:
Area of trapezium:Construct a line DE parallel to AB.
DE = 13 cm
So, ABED is a parallelogram
In ΔDEC,
DE = a = 13 cm
EC = AB - BE
= 30 - 16
EC = b = 14 cm
DC = c = 15 cm
Use Heron's formula to find the area of triangle.
[tex]\sf s = \dfrac{a+b+c}{2}\\\\=\dfrac{13+15+14}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]
s-a = 21 - 13 = 8
s - b = 21 - 14 = 7
s - c = 21 - 15 = 6
[tex]\sf \boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }[/tex]
[tex]\sf = \sqrt{21 * 8 * 7* 6}\\\\=\sqrt{3 * 7 * 2* 2 * 2 * 7 * 2 * 3}\\\\= 3 * 7 * 2 * 2\\\\= 84 \ cm^2[/tex]
Area of ΔDEC = 84 cm²
[tex]\sf \dfrac{1}{2}*base * height = 84\\\\ \dfrac{1}{2}*14*height = 84[/tex]
[tex]\sf height =\dfrac{84*2}{14}\\\\[/tex]
= 6 *2
height = 12 cm
Now we know the height of the trapezium. h = 12 cm
The length of the parallel sides are a = 30 cm & b =16 cm
[tex]\sf \boxed{Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]
[tex]\sf =\dfrac{(30+16)*12}{2}\\\\=\dfrac{46*12}{2}\\\\= 23 * 12\\\\= 276 \ cm^2[/tex]
If The Area Of Triangle MNO Is 24cm2 Find The Area Of Triangle PNO
Answer:
24 cm^2
Step-by-step explanation:
The three sides are equal (SSS: side, side, side) so the triangles are congruent.
Can you help me find the answer to it pls and ty <3 .
The expression that represent the area of the cut off part is 81π / 4
How to find area?The area of the cut off part can be found as follows:
Area of a circle = πr²
where
r = radiusTherefore, the cut off part is like 1 / 4th of a circle.
Hence,
area of the cut off region = πr² / 4
r = 9 inches
area of the cut off region = π9² / 4
area of the cut off region = 81π / 4
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7. License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we consider passenger cars and commercial trucks. Among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates (based on samples collected by the author). A reasonable hypothesis is that passenger car owners violate license plate laws at a higher rate than owners of commercial trucks. Use a 0.05 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval
Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.
Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.
let [tex]p_{1}[/tex] be the probability that commercial cars have rear license plates and [tex]p_{2}[/tex] be the probability that connected trucks have rear license plates.
Cars Trucks Total
Total 2049 334 2383
x 239 45 284
p 0.1166 0.1347 0.1191
α=0.05
Hypothesis will be :
[tex]H_{0}:p_{1} =p_{2}[/tex]
[tex]H_{1} :p_{1} < p_{2}[/tex]
It is a left tailed test at 0.05 significance.
Standard errors of p=[tex]\sqrt{p(1-p)/n}[/tex]
=[tex]\sqrt{(0.1191*0.8809)/2383}[/tex]
=[tex]\sqrt{0.1049/2383}[/tex]
=0.0066
Test statistic Z=p difference/standard error
=(0.1166-0.1347)/0.0066
=-0.0181/0.0061
=-2.967
p value=0.001505<5%
Since p is less than 5% we reject null hypothesis.
We cannot calculate standard deviation so we cannot calculate confidence interval.
Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
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Which exponential equation with base of 2, has been reflected on y -axis, vertically compressed by a factor of 1/3 and vertically translated up 2 units:
*
By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
How to derive a function by using rigid transformations
Rigid transformations are transformations applied on functions such that their Euclidean distance is conserved. In this problem we must use the following rigid transformations to determine an expression based on f(x) = 2ˣ.
Reflection on y-axis
f'(x) = f(-x) (1)
f'(x) = 2⁻ˣ
Vertical compression
f''(x) = k · f'(x) (2)
f''(x) = (1/3) · 2⁻ˣ
Vertical translation
f'''(x) = f''(x) + c (3)
f''(x) = (1/3) · 2⁻ˣ + 2
By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
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The perimeter of a rectangular book is 16.84 cm. find the length of the rectangular book (in decimals) whose width is 18/7 cm. estimate to the nearest tenths place.
The length of the rectangular book is 5.8cm
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.
The perimeter of a rectangle is found by adding up the length of all four sides. The formula for the perimeter of a rectangle is,
P = length + breadth + length + breadth. Or, P = 2(length + breadth)
Given:
Perimeter = 16.84 cm.
length = 18/7 cm
substituting in the formula we get
16.84 = 2( 18/7 + width)
8.42 = 18/7 + width
5.8 cm = width
Thus the length of the rectangular book is 5.8cm.
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A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. what is the plane’s drift angle?
Lets simplify the given problem,
The speed with which the plane flies = 350 mph
The direction of flight of the plane = N 40° E
The speed with which the wind blows = 40 mph
The direction in which the wind blows = S 40° E
Therefore, we have;
The resolution of the components of the motion of the plane, given as follows;
= 350 × sin(40°)·i + 350 × cos(40°)·j
The resolution of the components of the motion of the wind, given as follows;
= 40 × sin(40°)·i - 40 × cos(40°)·j
The resultant motion of the plane is given as follows;
= 262.563·i + 254.435·j
The direction of motion of the plane = tan⁻¹(262.563/254.435) ≈ N 45.9° E
Therefore, the plane's drift = Plane's Track - Plane's Heading = N 45.9° E - N 40° E ≈ 5.9° ≈ 5.89°
Drift Angle of the plane is 5.89 degree.
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Answer: A 5.9
Step-by-step explanation:
cuz i said so
Find the length of the 40 degree arc shown in red. Round your
answer to the nearest whole number. (Enter only a number as your
answer.)
The radius or any additional information related to the circle to assist in calculating the length of the 40-degree arc.
To find the length of a 40-degree arc, to know the radius or diameter of the circle to which the arc belongs. Once you have that information, use the formula to find the arc length:
Arc Length = (θ / 360) × 2 ×π ×r
Where:
θ = Central angle in degrees (40 degrees in this case)
r = Radius of the circle
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Pls, can someone help me with this problem?
Answer:
1 ÷ 3
Step-by-step explanation:
You want 1/3 written as a quotient.
QuotientThe quotient of A and B is "A divided by B." There are two ways to write this using math symbols:
A/B
A÷B
The fraction 1/3 is already written as a quotient. This set of symbols can be read as either of ...
"one-third""one divided by three".The other way to write the quotient is ...
1 ÷ 3
__
Additional comment
When you learn about exponents, you learn another way to write the quotient of A and B is ...
A·B⁻¹
<95141404393>
given: AB is congruent to CD and BC is congruent to AD Prove: AB ll CD and BC ll AD
We'll prove first the triangles formed by diagonal are congruent then we'll prove the angles on either side of diagonal are congruent.
The steps are:
Step ⇒ Statement ⇒ Reason=============================================================
1 ⇒ AB ≅ CD and BC ≅ AD ⇒ Given2 ⇒ AC = CA ⇒ Common side3 ⇒ ΔABC ≅ ΔCDA ⇒ Side-side-side congruence4 ⇒ ∠BAC ≅ ∠DCA ⇒ Corresponding angles of congruent triangles5 ⇒ ∠BAC and ∠DCA are alternate interior angles ⇒ Definition of alternate interior angles6 ⇒ AB║CD ⇒ The converse of alternate interior angles theorem 7 ⇒ ∠BCA ≅ ∠DAC ⇒ Corresponding angles of congruent triangles8 ⇒ ∠BCA & ∠DAC are alternate interior angles ⇒ Definition of alternate interior angles9 ⇒ BC║AD ⇒ The converse of alternate interior angles theoremWork out the mean for the data set below: 3 , 5 , 4 , 3 , 5
Answer:
4
Step-by-step explanation:
The mean is the average of the numbers.
if you rearrange the data, you will get the order, 3,3,4,5,5.
you add all of them together to get the number twenty, then you divide 20 by the total number of data plots which is five. Then you get the number 4 which is your answer
3+3+4+5+5 = 20
20/5 = 4
Ten friends want to play a game. They must be divided into three teams with three people in each team and one field judge. In how many ways can they do it?
Using the combination formula, it is found that there are 16,800 ways for them to do it.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
For the judge, one is taken from a set of 10.For the first team, 3 are taken from a set of 9.For the second team, 3 are taken from a set of 6.For the third team, 3 are taken from a set of 3.Hence the number of ways is:
[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
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