The possible number of ways of selection by using combination formula is 3060.
What is combination?
A grouping of items where the order in which they were chosen is irrelevant is known as combination.
Given that the number of people in the group is 18. Only 4 people will be member of the council.
The formula of combination is [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex] , where r number of objects are selected from n objects.
In the given question the value of n is 18 and the value of r is 2.
Substitute the value of n and r in [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex].
[tex]^{18}C_{4}=\frac{18!}{4!(18-4)!}[/tex]
Solve the above expression:
18^C_4 = 18x17x16x15x14/4x14
18^C_4 = 18x17x16x15/4x3x2x1
3060 18^C_4 = 3060
The number of ways such selection is 3060.
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Use the information on the diagonal to find: a. the length ACb. the length ABc. the perimeter of quadrilateral ABCDd. the area of quadrilateral ABCD
A) To find the length AC, we must use the trigonometric ratio
[tex]\cos \text{ 31 =}\frac{adjacent}{hypothenuse}[/tex]adjacent = 5cm
hypothenuse = AC
[tex]\begin{gathered} \cos 31\text{ = }\frac{5}{AC} \\ AC\text{ = }\frac{5}{\cos 31} \\ AC\text{ =}5.8332\operatorname{cm} \end{gathered}[/tex]B) To find the length AB, we will use the value of AC just obtained to get it
since triangle ABC is a right-angled triangle, we will use Pythagoras theorem
so that
|AC|^2 = |AB|^2 +|BC|^2
AC = 5.8332cm
BC = 4cm
|AB|^2 = |AC|^2 - |BC|^2
[tex]\begin{gathered} AB\text{ = }\sqrt[]{5.8332^2-4^2} \\ AB\text{ = }\sqrt[]{18.0262224} \\ AB\text{ = 4.245729883cm} \end{gathered}[/tex]C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.
Perimeter = AD +CD + BC + AB
We do not have CD and we must find CD
[tex]\begin{gathered} CD\text{ = }\sqrt[]{|AC|^2-|AD|^2} \\ CD\text{ =}\sqrt[]{5.8332^2-5^2} \\ CD\text{ =}\sqrt[]{9.02622224} \\ CD\text{ = 3.004366195cm} \end{gathered}[/tex]Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm
D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.
Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter
Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter
Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter
Factor Pairs (MAJOR POINTS!)
Answer:
3rd option
Step-by-step explanation:
the factors of 48 are
1 , 2, 3, 4, 6, 8, 12, 16 , 24 , 48
the factor pairs are
1 × 48 , 2 × 24 , 3 × 16 , 4 × 12 , 6 × 8
(-25)^(/3) =?-125 1 O A. -25 B. 5 or -5 C. -15 D. -5
We will have that the expression has the solution of:
[tex]\sqrt[3]{-125}=-5[/tex]Therefore the solution is D. -5.
When we elevate to the power of 3 -5 will be equal to -125.
Which inequality represents the graph?
y less than negative one-fourth (x minus 10) squared + 4
y greater than negative 4 (x + 10) squared + 4
y greater than one-fourth (x minus 10) squared + 4
y greater than 4 (x + 10) squared + 4
Answer: 1st option!
Step-by-step explanation:
Just did it on edg
Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
negative 2 and 19 over 48
negative 24 and 8 over 15
negative 21 and 2 over 15
negative 3 and 19 over 93
Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of negative 2 and 19 over 48
How to determine the quotient of 7 and 2 over 3 ÷ negative 3 and 1 over 5information gotten from the question include
Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
Division is a basic mathematical operator that performs the function of sharing
division of fraction is done as follows
7 and 2 over 3
= 7 2/3
= 23/3
negative 3 and 1 over 5.
= -3 1/5
= -16/5
= 23/3 ÷ -16/5
= 23/3 * -5/16
= -115/48
= -2 19/48
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A line passes through the points (-18, -2) and (9, 10). Find this line's equation in point-slope form. Using the point (-18, -2), this line's point-slope form equation is [ ]Using the point (9, 10), this line's point-slope form equation is [ ]
We know that the point-slope formula is given by:
y − y₁=m(x − x₁)
where the terms: m, y₁ and x₁ are numbers.
Given that the line passes through a given points we have that:
m is the slope of the line
y₁ is the y value of that given point
x₁ is the x value of that given point
Finding the slopeWe want to find the slope m, having that
(x₁, y₁) = (-18, -2)
(x₂, y₂) = (9, 10)
The slope is always a rate of change. It is:
m = Δy/Δx,
where Δ means "change"
Step 1: finding the change of each term x and y
Δy = change of y = y₂ - y₁
Δy = 10 - (-2) = 12
Δx = change of x = x₂ - x₁
Δx = 9 - (-18) = 27
Step 2: dividing the found quantities
Then
m = Δy/Δx = 12/27
m = 4/9
Step 3: replacing in the equation
Using the equation, we have that
y − y₁ = m(x − x₁)
replacing m:
y − y₁= 4/9(x − x₁)
Step 4: replacing each pointFor the first point: (-18, -2)
We have that (x₁, y₁) = (-18, -2)
since the equation is
y − y₁ = 4/9(x − x₁)
replacing each term for each number of the given coordinate
y − (-2) = 4/9(x − (-18))
y + 2 = 4/9(x + 18)
Equation: y + 2 = 4/9(x + 18)
For the second point: (9, 10)
We have that (x₂, y₂) = (9, 10)
since the equation is
y − y₂ = 4/9(x − x₂)
replacing each term for each number of the given coordinate
y − (10) = 4/9(x − (9))
y - 10 = 4/9(x - 9)
Equation: y - 10 = 4/9(x - 9)
Does anybody know the answer to this question?
The values of x and y after solving the given system of equations are respectively.
According to the question,
We have the following two equations:
y = 2x+3 ....(1)
y = 4x-1 .....(2)
Now, we can put the value of y from equation 1 in equation 2:
2x+3 = 4x-1
Now, we can change sides as it will not affect the result.
4x-1 = 2x+3
Moving 2x from the right hand side to the left hand side will result in the change of sign from plus to minus:
4x-2x-1 = 3
2x-1 = 3
2x = 3+1
2x = 4
x = 4/2
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
y = 2x+3
y = 2*2+3
y = 4+3
y = 7
Hence, the value of x is 2 and the value of y is 7 after solving the equations.
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a boat traveled 27miles in 2hours at this rate how many miles will the boat travel in 1/2 hours?
Answer:
6.75 miles
Step-by-step explanation:
27/2 = 13.5
27/4 = 6.75
27 miles in 2 hours
13.5 in 1 hour
6.75 in half an hour :)
Answer: 6.75 miles
Step-by-step explanation:27/4=6.75, I divided by 4 to get the half hour
Mamadou spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7325 feet. Mamadou initially measures an angle of elevation of 15 degrees to the plane at point A. At some later time, he measures an angle of elevation of 42 degrees to the plane at point BB. Find the distance the plane traveled from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance between points A and B will be 19201.93 feet.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Mamadou notices an airplane arriving in a straight line and flying directly overhead on the radar. The plane stays at the same height of 7325 feet. Mamadou initially measures a 15-degree angle of inclination to the plane at point A. Later, he detects a 42-degree angle of elevation to the plane at point B.
The distance between points A and B will be given as,
D = 7325 / tan 15° - 7325 / tan 42°
D = 27337.27 - 8135.34
D = 19201.93 feet
The distance between points A and B will be 19201.93 feet.
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Answer:
19202 feet
Step-by-step explanation:
I got the same problem and got it right with that answer.
Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-6,-5) and (-4,-4) ,
So , the slope(m) is = (-4 -(-5)/(-4 -(-6))
= (-4+5)/(-4+6)
= 1/2
the equation of the line passing through (-4,-4) and slope as 1/2 is
(y -(-4)) = (1/2)(x -(-4))
y + 4 = (x+4)/2
2y + 8 = x + 4
x - 2y = 8-4
x - 2y = 4
Therefore , The equation of line that passes through the points (-6,-5) and (-4,-4) is x - 2y = 4 .
The given question is incomplete , the complete question is
Complete the equation of line that passes through the points (-6,-5) and (-4,-4) .
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can you help mw with my work?
In this problem the function that models the hight is:
[tex]h(t)=-5t^2+14t+3[/tex]So when the water hits the grownd h=0 so we replace that and solve for t so:
[tex]0=-5t^2+4t+3[/tex]To solve this expression we can use the cuadratic equation:
[tex]x=\frac{-4\pm\sqrt[]{16-4(-5)(3)}}{-10}[/tex]and we operate so:
[tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{76}}{-10} \\ x=\frac{-4\pm8.7}{-10} \end{gathered}[/tex]Now we solve bout of the equation so:
[tex]\begin{gathered} x_1=\frac{-4+8.7}{-10}=-0.47 \\ x_2=\frac{-4-8.7}{-10}=1.27_{} \end{gathered}[/tex]So the answer that have sense is the secon one so the water hits the ground after 1.27 seconds
Solve the given linear equation.14x + 4 = 8x + 23x =
We have to solve this linear equation for x:
[tex]\begin{gathered} 14x+4=8x+23 \\ 14x-8x+4-4=8x-8x+23-4 \\ 6x+0=0x+19 \\ 6x=19 \\ x=\frac{19}{6} \\ x\approx3.16\ldots \end{gathered}[/tex]The answer is x=19/6
Help really need it
.........................................
Answer:
you wmekekd
Step-by-step explanation:
What two numbers multiplied give you 100 and added give you 21?
Answer: [tex]\frac{21}{2}+\frac{\sqrt{41}}{2}, \frac{21}{2}-\frac{\sqrt{41}}{2}[/tex]
Step-by-step explanation:
Let the two numbers be x and y.
[tex]x+y=21 \implies y=21-x\\\\xy=100\\\\\therefore x(21-x)=100\\\\21x-x^2 =100\\\\x^2 -21x+100=0\\\\x=\frac{21 \pm \sqrt{21^2 -400}}{2}=\frac{21}{2} \pm \frac{\sqrt{41}}{2}[/tex]
six distinct positive integers are randomly chosen between and , inclusive. what is the probability that some pair of these integers has a difference that is a multiple of ?
Answer:
So the probability of this happening is exactly 1 - it must be true
Step-by-step explanation:
If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.
By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.
So the probability of this happening is exactly 1 - it must be true
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
The equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)
How to determine the equation of f(x)?From the question, we have the following parameters:
Roots = -4 and 2
Point = (1, -5)
Rewrite the given parameters as
Roots: x = -4 and x = 2
Point: (x, y) = (1, -5)
Recall that:
x = -4 and x = 2
This gives
x + 4 = 0 and x - 2 = 0
Multiply the equations
So, we have
y = a(x + 4)(x - 2)
When (x, y) = (1, -5), we have
-5 = a(1 + 4)(1 - 2)
This gives
a = 1
Substitute a = 1 in y = a(x + 4)(x - 2)
y = (x + 4)(x - 2)
Hence, the equation of f(x) = (x + 4)(x - 2)
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Answer:
f(x) = (x − 2)(x + 4)
Hope this helps you
P(x) = x³- 2x² + 5x.
factor p completely
Answer:
P(x) = x (x²- 2x + 5)
Step-by-step explanation:
First factor x out:
P(x) = x (x²- 2x + 5)
Then, try to simplify (x²- 2x + 5):
However, there is no way to further simplify.
So, the answer should be x (x²- 2x + 5).
Sheila can wash her car in 15 minutes. It takes Bob twice as long to wash the same
car. How long does it take them to wash the car working together
Both Sheila and Bob together can wash the car in 10 minutes
Calculating work :
The formulas to find work and time is given by
Time Taken = 1 / Rate of Work
Rate of Work = 1 / Time Taken
If a work can be done in x number of days, then the work can be done in one day = 1/x
Total Work done = Number of Days × Efficiency ( of the person or machine )
Given that,
Sheila can wash her car in 15 minutes
Let us consider washing the car is 1 unit of work
Then the work can done by Sheila in 1 minute = 1/15
Bob take twice as long as Sheila to wash the same
Bob can wash the same car in 30 minutes
Then the work can done by Bob in 1 minute = 1/30
From above calculation,
The work can be done by Sheila and Bob = (1/15 + 1/30)
= (2+1) /30 = 3/30 = 1/10
So the efficiency of Both Sheila and Bob per minute = 1/10
Let Both can complete the work in x minutes
As we know Total Work done = time × Efficiency
⇒ 1 = x × 1/10
⇒ x = 1 × 10
⇒ x = 10 minutes
Therefore,
Both Sheila and Bob together can wash the car in 10 minutes
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Write an exponential expression equivalent to 8^3 that has a base of 2.
Answer:
2^9
Step-by-step explanation:
8 is [tex]2^3\\[/tex], so we can replace [tex]8^3[/tex] for [tex](2^3)^3[/tex]
Exponents separated by parenthesis, multiply.
So [tex](2^3)^3=2^9[/tex]
Currently Madeline makes $28,800 a year. Based on the following list ofmonthly expenses, find Madeline's adjusted monthly income (AMI).Student Loan:$250 (5 years remaining)Car Loan:$180 (6 months remaining)Personal Loan:$150 (30 months remaining)Apartment Lease: $425 (4 months remaining)>Gas/Electric:~$115 each month
Given:
yearly salary=28,800
Required:
To calculate adjusted monthly income
Explanation:
student loan
250 dollar
if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<4= ?
According to the theorem, the corresponding angles, formed by a transversal on a pair of parallel sides, are always equal.
Also, the sum of angles on a straight line is 180 degree.
The angles 5 and 7 constitute a pair of corresponding angles, formed by the transversal 'r' on the pair of parallel sides 'p' and 'q'. So they must be equal,
[tex]\begin{gathered} \angle5=\angle7 \\ \angle5=131^{\circ} \end{gathered}[/tex]The angles 4 and 5 constitute a straight line, so they must add up to be 180 degrees,
[tex]\begin{gathered} \angle4+\angle5=180^{\circ} \\ \angle4+131^{\circ}=180^{\circ} \\ \angle4=180^{\circ}-131^{\circ} \\ \angle4=49^{\circ} \end{gathered}[/tex]Thus, the angle 4 measures 49 degrees.
The opposite of the opposite by of 2 is to the_of zero and is written as _
Recall that the opposite of 2 is
[tex]-2.[/tex]Therefore, the opposite of the opposite of 2 is
[tex]-(-2)=2.[/tex]Now, recall that a horizontal number line is of the form:
Therefore, 2 is to the right of zero.
Answer:
On a horizontal number line, the opposite of the opposite of 2 is to the right of zero and is written as 2.
I need this answer asap!! Taylor earned $338.00 at her job when she worked for 20 hours. What was her hourly wage, in dollars per hour?
Answer:
$16.90 per hour
Step-by-step explanation:
You want the hourly wage Taylor earned when she worked 20 hours for $338.00.
Hourly wageTo find dollars per hour, divide dollars by hours:
$338.00/(20 h) = $16.90/h
Taylor earned $16.90 per hour.
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what is 1.025 as a fraction?
The decimal number 1.025 is 41/40 in fractions.
What is Number system?A number system is defined as a system of writing to express numbers.
A fraction is a part of a whole
The decimal number one point zero two five should be converted to fraction.
The conversion of 1.025 to fraction is 41/40.
If we calculate 41/40 we get the value 1.025.
Hence 1.025 is 41/40 in fractions.
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please help with the question below (please add an explanation)
In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.
First, let's calculate the volume of the upper part.
The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.
[tex]V_{upper}=7cm\times3cm\times3cm=63cm^3[/tex]Hence, the volume of the upper figure is 63 cm³.
Let's now calculate the volume of the lower figure.
The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.
[tex]V_{lower}=5cm\times4cm\times3cm=60cm^3[/tex]The volume of the lower figure is 60 cm³.
Let's add the volume of the two figures to get the volume of the entire irregular figure.
[tex]V_{irregular}=V_{upper}+V_{lower}[/tex][tex]V_{irregular}=63cm^3+60cm^3=123cm^3[/tex]Therefore, the entire volume of the given irregular figure is 123 cm³.
Part A Write the multiplication expression shown by the model. Do not solve the problem.
Explain the expression written in Part B. Include the final product and how it is shown with the model.
The multiplication model represented by the image is given as follows:
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
What is a multiplication operation?A multiplication operation is equivalent to consecutive additions.
For the green squares, the following addition is obtained:
10 + 10 + 10 + 10 + 6.
(which is the number of squares painted green).
Considering a multiplication with consecutive additions, it is written as follows:
4 x 10 + 6.
For the red squares, the expression is:
4 + 4 x 10 + 2 = 4 x 10 + 6.
For the blue squares, the expression is:
8 + 3 x 10 + 8
3 x 10 + 16
For the white squares, the expression is:
2 + 6 x 10
Hence the total model is calculated as follows:
4 x 10 + 6 + 4 x 10 + 6 + 3 x 10 + 16 + 2 + 6 x 10
(4 x 10)(6 + 6) + (3 x 10) + (6 x 10) + 18.
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
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Quadrilateral ABCD is dilated with center
( 0, 0 ), taling B to B' . Draw A' B' C' D' .
Answer:
See the picture below
Step-by-step explanation:
Lana and raul are participating in a walk-a-thon at the local community college track to raise money. lana can walk around the track in 4 minutes. raul can walk around the track in 6 minutes. lana and raul started walking at the same time. question: how many minutes will it be until they complete a lap at the same time?
The minutes will it be until they complete a lap at the same time is 2.4 minutes
How to calculate the time?From the information, Lana can walk around the track in 4 minutes and Raul can walk around the track in 6 minutes.
Lana will cover a distance of 1/4 while Raul will be represented as 1/6.
This will be illustrated as:
1/4 + 1/6 = 1
3/12 + 2/12 = 1
5x/12 = 1
Cross multiply
5x = 12
x = 12/5
x = 2.4 minutes
Note that x = number of minutes
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which of the following expressions does not represent 7 + 7 + 7 + 7 + 7
7 + 7 + 7 + 7 + 7 means 7 is added 5 times
It could be written as
5(7)
7 x 5 and
7 . 5
But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7
Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7
This makes the correct option to be the third option. That is 7^5
a researcher counted the hours a brand of batteries could power different devices. the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. what percentage of devices ran on the batteries for fewer than
the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So 10.2% of gadgets were powered by batteries for fewer than 63 hours.
Given that,
Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.
The standard deviation is defined as ?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]
From standard deviation,
[tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]
a certain percentage of gadgets have battery life of less than 63 hours.
X= 63 hours
Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%
Therefore, 10.2% of electronic devices had battery life of less than 63 hours
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