There can be 2184 ways in which three posts can be selected using permutation.
What is permutation?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.
Main Body:
Total members =14
total posts =3
As one person can not hold more than 1 post ,
total ways are = ¹⁴P₃
Therefore total ways = 14!/11!
= (14*13*12*11!)/11!
= 14*13*12
= 2184 ways
Hence answer is 2184 ways to select 3 members out of 14.
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The radius of the circle below is 27 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d.p.
27 m
84.78 mm² is area of circle .
What is a circle ?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center.Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry.radius of the circle = 27 mm
area of the circle = πr²
= 3.14 * 27
= 84.78 mm²
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If tan 8 = 3 and 8 lies in the second quadrant. Use a Pythagorean identity to find
the exact value of cos 6.
The exact value of Cosθ is -1/√10 .
In the question ,
it is given that ,
the value of tanθ = 3/1 ,
that means the perpendicular = 3x
and the base of the triangle is = 1x,
So ,By Pythagoras Theorem
hypotnuse² = perpendicular² + base²
hypotnuse² = (3x)² + (1x)²
hypotnuse² = 9x² + 1x²
hypotnuse² = 10x²
hypotnuse = (√10)x
So , Cosθ = base / hypotnuse
Cosθ = 1x/(√10)x
Cosθ = 1/√10
Since , [tex]\theta[/tex] lies in the second quadrant ,
and in second quadrant Cos is negative ,
So , Cosθ = -1/√10
Therefore , The exact value of Cosθ is -1/√10 .
The given question is incomplete , the complete question is
If Tanθ = 3 , θ lies in the second quadrant. Use a Pythagorean identity to find the exact value of Cosθ ?
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What is the largest multiple of 30 which is less than 520?
The largest multiple of 30 that is less than the number, 520, can be found to be 510.
How to find the multiple?To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:
= 520 / 30
= 17.333
Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.
The multiple of 30 that is the largest and below 520 is then:
= 30 x Rounded down result of division of 520
= 30 x 17
= 510
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Find the coordinates of the point which divide the lines joining the following pairs of points in the given ratio
a. (5,8) and (-1,3) 2:3
b.(4,7) and (3,-2) 4:5
The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then
(x,y)=( (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n )
Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3
Therefore, we have
P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))
P(x,y)=(2.6,6)
Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
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Fine the slope of the line and use rise/run to fill in the blanks
Answer: Rise is 5 and run is 1 and now that is equal 5
Step-by-step explanation:
why are 0.8 and 0.80 are equivalent?
0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.
The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.
It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.
Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
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A business started the year with a net worth of $4,873. During the first six months of the year, the business
recovered and increased its net worth to a value of $15,866. Find the average monthly increase in net worth for the 6-month period.
The average monthly increase in net worth for the 6-month period is $1832.16.
Given:
A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.
Six months net worth = 15,866 - 4873
= 10,993
Average monthly increase in net worth = six month net worth / 6
= 10,993/6
= $1832.16.
Therefore The average monthly increase in net worth for the 6-month period is $1832.16.
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Solve the system by back substitution.
- 2x - 4y - z- 3w = -5
-2y - 12z - 4w = - 16
5z +5w=10
4w =12
Answer:
y=8 x=-19.5
Step-by-step explanation:
Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8
Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:
2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5
The sum of two numbers is 14 and the difference between the numbers is 20. What could one of the numbers be?
The number will x=17 and y=-3 as the sum of two numbers is 14 and the difference between the numbers is 20.
What is arithmetic operation?The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators. One operand is added to the other in addition. On the provided operands, the operator is accustomed to performing mathematical operations like addition, subtraction, multiplication, division, modulus, etc. Examples of arithmetic operators include: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.
Here,
x+y=14
x-y=20
subtract equation,
2y=-6
y=-3
x+y=14
x-3=14
x=17
The result will be x=17 and y=-3 because the sum of the two numbers is 14 and their difference is 20.
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Everyone at Colin's school wore either brown or red for school spirit day. 126 out of the 600 students at the school wore brown. What percentage of the students wore brown?
Write your answer using a percent sign (%).
Answer:
21%
Step-by-step explanation:
126 out of 600=126/600
=0.21 *100 for
21%
help, please !!!!!!!! **50points**
Answer:Answer: SAS
Step-by-step explanation:
The meteorologist at Channel 8 News predicted that a snowstorm would drop 7 inches of
snow. After the storm, she reported that the actual snowfall was 4 inches. What is the
percent error for the meteorologist's prediction?
If necessary, round your answer to the nearest tenth of a percent.
%
THE percent error is, 5
what is percent error?Percent error calculates the difference between an estimate and a right value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual number. It is also referred to as % error and percentage error.The estimate and accurate values in this situation might be any of the following:a measurement, an approximation, a value obtained experimentally, or a guess.Correct Value: A number that has been established or is widely regarded as accurate. It might serve as a standard measurement for something tested as a measurement system. Or a value that is theoretically valid and is known, like a circle's circumference.hence,THE percent error is, 5
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Please help me find the slope on the lined graphed below??
Answer:
2/3
Step-by-step explanation:
The gradient is found by doing rise/run. If you go to a point on the line you can then rise 2 squares and run 3 to the right. This means that the gradient is 2/3. It is not negative as the line is going up.
I NEED HEEEEELP!!
There are 5 cockroaches crawling on each square meter of the front of this building. How many cockroaches are crawling on the front of the building?
Please, show your work and explain. TYSM!! ^^
There are 855 cockroaches crawling on the front of the building
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The population density is given as:
Population density = total animals / area occupied
Given that, the population density of the cockroaches is 5 cockroaches per square meter.
The area of the building = area of triangle + area of square
Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²
Population density = total animals / area occupied
5 cockroaches per square meter = Total cockroaches / 171 m²
Total cockroaches = 855
There are 855 cockroaches
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For how many values of x is h(x) = 0? Justify you answer.
Answer:
the answer for x when h(x) is 2.9
48 - (3 c+4)=4(c+5)+3 c=???
Answer in multiple forms depending on what needed
Answer:
c = 3
Step-by-step explanation:
48- (3c+4)=4(c+5)+3
48-3c-4=4(c+5)+3 Distributed the - sign
48 -3c -4= 4c+20 +3 Distributed the 4
44-3c =4c+23 Combined like terms
21-3c=4c Subtract 23 from both sides
21=7c Add 3c to both sides
3=c
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, what was the change in the altitude of the missile?
The required change in height of the missile is 16100 feet.
Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.
Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.
here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.
Thus, the required a change in height of the missile is 16100 feet.
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Let a=2 b=5 c= -3
8b-4b=4b Please help quick!!!!!
Answer:
40-20= 20
Step-by-step explanation:
8(5)- 4(5)= 4(5)
40-20=20
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Determine whether the ratios are equivalent.
85: 210 and 340: 735
These are equivalent. I hope this helps a ton. I had this question on a test. Tell me if its wrong or not. <:
the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.
Answer:
L = 6 feet ; W = 4 feet
Step-by-step explanation:
l = 2 + w
perimeter/2 = 8
l + w > 8
2 + w + w > 8
2 + 2w > 8
2w > 8-2
2w > 6
2/2 w > 6/2
w > 3
smallest integer > 3 = 4
W= 4
L = 4 + 2 = 6
A school is arranging a field trip to the zoo. The school spends 643.34 dollars on passes for 36 students and 2 teachers. The school also spends 339.48 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
$
40 POINTS
By taking some simple quotients, we will see that the cost per student is:
$26.36
How much money was spent on a pass and lunch for each student?First, we know that the school spends $643.34 on passes for 38 people, then the cost of each pass is given by the quotient:
p = $643.34/38 = $16.93
Then there is also lunch for the 36 students, which costed $339.48, then the cost in lunch per student is.
l = $339.48/36 = $9.43
The total cost per student is:
$16.93 + $9.43 = $26.36
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Select all of the descriptions which describe a transformation of the graph of f(x) = x that could result in the graph of g(x) = 7x.
A: The graph is translated 7 units to the right.
B: The graph is rotated about (0, 0), becoming steeper.
C: The graph is reflected across the x−axis.
D: The graph is vertically shrunk.
E: The graph is translated 7 units up.
F: The graph is vertically stretched.
Answer:
A,C,D
Step-by-step explanation:
Find the slope using points: (0, - 3) and (- 4, 2)
Answer:
-5/4
Step-by-step explanation:
slope
[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]
How to solve: 24 - (5 + 3)^2 + 4 × 2^3 step by step.
The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value given will be expressed thus:
= 24 - (5 + 3)^2 + 4 × 2^3
= 24 - (8)² + 4 × 8
= 24 - 64 + 32
= -8
The value is -8.
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Please Help 2
Find (fxg)(x) if f(x)=x2+2+4 and g (x)=x-2
Answer:
x³ - 8
Step-by-step explanation:
Find the values of x and y.
Answer: The correct answer is x = 50
Step-by-step explanation:
The sum of angles in a triangle = 180 degrees
This is a right-angled triangle, so one of the angles is 90 degrees + x +y
Therefore: 90 + y + x = 180
Substitute the variables:
90 + 40 + x = 180
130 + x =180
Subtract 130 from each side:
(-130) 130 + x =180 (-130)
x = 50
3/5 of a fruit punch is orange juice.
What percentage of the fruit punch is orange juice?
60% of the fruit punch is orange juice.
In this question, we have been given 3/5 of a fruit punch is orange juice.
We need to find the percentage of the fruit punch is orange juice.
3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.
Using the percentage formula,
3/5 * 100
= 0.6 * 100
= 60%
Therefore, 60% of the fruit punch is orange juice.
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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
As given in the question,
Ratio of orange juice in the given fruit juice = 3/5
From the given ratio it indicates out of 5 fruits 3 are orange
Percentage of fruit punch is orange juice in the given juice is equal to
= ( 3 / 5 ) × 100
= ( 3 × 100 ) / 5
= 300 / 5
= 60%
60% of the fruit punch is orange juice.
Therefore, for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.
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Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt. $69 $90 $420 $1,080
The simple interest that Oliver needs to pay is $ 90
Calculating Simple interest:Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below
Simple interest, I = ptr
where p = principal amount
t = time period in years
r = rate of interest in decimals
Here we have
Oliver borrowed $1,500 to purchase a riding lawn mower
The rate of interest r = 12%
=> 12/100 = 0.12 (in decimals )
The time period given = 6 months = 0.5 years [ 6/12 = 0.5 ]
From the above formula,
The simple interest, I = ptr
=> I = $1,500(0.12) (0.5) = $ 90
Therefore,
The simple interest that Oliver needs to pay is $ 90
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Simplify 5^3 x 5 please
Answer:
5^4
Step-by-step explanation:
5^3x5
5x5x5x5
5^4
Hopes this helps please mark brainliest
The simplified form of the expression, 5³.5 will be 625.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that the expression is, 5³.5
=5³.5
The base should remain constant and the exponents added when multiplying like bases. Keep the base constant when raising a base with power to another power, and multiply the exponents instead. Keep the base constant and deduct the exponents in the denominator and numerator when dividing like bases.
Apply the law of exponent as
xᵃ × xᵇ = xᵃ⁺ᵇ
=5³⁺¹
=5⁴
=5x5x5x5
=625
Thus, the simplified form of the expression, 5³.5 will be 625.
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