The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
How to find the number of ways to pick a panel of 2 men and 2 women
Given data
number on men = 5
number of women = 8
The number of ways of picking a panel of 2 men and 2 women
= 5 combination 2 * 8 combination 2
= 5 C 2 * 8 C 2
= 5! / ( 2! ( 5 - 2 )! * 8! / ( 2! ( 8 - 2 )!
= 5! / ( 2! 3! ) * 8! / ( 2! 6! )
= 5 * 4 * 3! / ( 2! * 3! ) * 8 * 7 * 6! / ( 2! * 6! )
= 20 / 2 * 56 / 2
= 10 * 28
= 280 ways
The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
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Solve for x.
A. 8
B. 4.8
C. 4
D. 7.2
Answer: x=8 ==> A
Step-by-step explanation:
15x-6=114 ==> both angles are congruent angles, so they're equal
15x-6+6=114+6
15x=114+6
15x=120
15x/15=120/15
x=120/15
x=8 ==> A
Anyone know how to solve please
If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;
B' = (0, -5)
K' = (-3, 0)
U' = (2, -2)
Y' = (-3, 4)
Rotation of coordinate pointWhen a coordinate (x, y) is rotated 90 degrees clockwise around the origin is (-y, x)
Given the coordinates points
B = (5, 0)
K = (0, 3)
U = (2, -2)
Y = (4, 3)
If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;
B' = (0, -5)
K' = (-3, 0)
U' = (2, -2)
Y' = (-3, 4)
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PLS HELP RIGHT ANSWER ONLY ill give 500 points
Determine the value of x in the diagram below.
Question 1 options:
A. 4
B. -6
C. 10
D. 12
By applying the triangle midpoint theorem to the triangle, the value of x is equal to: D. 12.
The properties of similar triangles.In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Corresponding parts of two congruent figures.In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the triangle, we have:
8x = 2(2x + 24)
8x = 4x + 48
8x - 4x = 48
4x = 48
x = 48/4
x = 12.
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Determine the values of m in the equation m2 = 36.
please helppp
Answer:
m = 6
Step-by-step explanation:
➟ m² = 36
in order to find the value of m take square root from both side
➟ [tex] \sf \: \sqrt{ {m}^{2} } = \sqrt{36} [/tex]
Calculate the values
➟ m = 6
∴ the value of m is 6
Below is the relationship for miles per hour for 3 different people and their car speeds. Which "Will" has a greater slope? Identify EACH slope for all THREE graphs to come to a conclusion.
Answer:
Step-by-step explanation:
A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. The steeper the slope of the line the greater the acceleration.
A school playground is in the shape of a rectangle 800 feet long and 700 feet wide. If fencing costs $18 per yard, what will it cost to place fencing around the playground?
Answer:
pomogło dzięki xxxxxxxxxx
) What happens if both bags weigh over 50 pounds when the passenger approaches the check in counter? Think. This is real life.
When both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.
How to illustrate the information?It should be noted that one will pay for an excess luggage when the luggage is heavier than the allowance when the person checks in.
It should be noted that every airline has a restriction on how heavy the luggage can be.
Therefore, when both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.
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Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Measures less than m∠ 5
The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
What is meant by Exterior Angle Inequality Theorem?According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .
Therefore, the correct answer is ∠ 7 and ∠ 8.
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Leah is deciding between two truck rental companies. Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Leah drives xx miles, and let BB represent the amount Company B would charge if Leah drives xx miles. Write an equation for each situation, in terms of x,x, and determine the number miles driven, x,x, that would make the cost of each company the same.
AA=60+1.50x and BB=30+2.50x are the two required situations and the number miles driven, x,x, that would make the cost of each company the same is 30.
What is Equation?Two expressions with equal sign is called as Equation.
Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven= 60+1.50x
Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven=30+2.50x.
60+1.50x=30+2.50x
60-30=2.50x-1.50x
30=x
Therefore, AA=60+1.50x and BB=30+2.50x are the two required situations and the number miles driven, x,x, that would make the cost of each company the same is 30.
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Is the solution shown below correct? Explain.
9x+2=8x²+6x
Answer:
The solution below is wrong. The correct solution is [tex]x = \frac{-b (+-)\sqrt{73} }{16}[/tex]
Step-by-step explanation:
Rearrange the numerals :
[tex]9x + 2 = 8x^2 + 6x\\8x^2 + 6x - 9x - 2 = 0\\8x^2 - 3x - 2 = 0\\[/tex]
Use quadratic formula :
Solution 1: (Note: the -b"+".... is actually "±" as the system has some problem of adding "±" symbol)
[tex]x = \frac{-b+\sqrt{b^2 - 4ac}}{2a} \\x = \frac{-(-3)+\sqrt{(-3)^2 - 4(8)(-2)}}{2(8)} \\x= \frac{3+\sqrt{9 + 64 }}{16} \\\\x= \frac{3+\sqrt{73 }}{16} \\\\[/tex]
Hope this helps, it would really help me if u mark me as the brainliest.
The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking
The problem statement provides information about the Vasquez Family, who pay visits to their grandmother every three weeks and host a neighborhood party every eight weeks.
The number of weeks combined when the Vasquez Family visits their grandmother and hosts the neighborhood party is 24 weeks.
The total number of weeks with all the three events occurring together (visit, neighborhood party, hiking) is 48 weeks.
Now we concluded that the number of weeks is 24 because we know that the Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks.
Therefore, we will look for a least common factor of both 3 (visit) and 8 (party) and that LCM (least Common Factor) is 24.
Therefore, the number of weeks when the Vasquez family visits their grandmother and hosts the neighborhood party is 24.
Complete Problem Statement:
The Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks. Every 16 weeks, the Vazquez family takes a day to go hiking. After how many weeks will the Vasquez family visit their grandmother and host the neighborhood party? After how many weeks will all three events occur?
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i thought of a number added 6 divided the results by 4 i got 13 if x is my number what's the equation
Answer:
x+6/4=13
Step-by-step explanation:
the result is 11.5
Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
15,36,39
The following set of numbers, 15, 36, and 39, can be the measures of the sides of a right triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 15, b = 36, and c = 39
a + b > c 15 + 36 > 39 51 > 39 True
a + c > b 15 + 39 > 36 54 > 36 True
b + c > a 36 + 39 > 15 75 > 15 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
15^2 + 36^2 = 1521
2. Compare it to the square of the largest side.
39^2 = 1521
1521 = 1521
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 15, 36, and 39 can be the measure of the sides of a right triangle.
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Prove the following.
If SC ≅ HR and HR ≅ AB , then SC ≅ AB.
The congruent segments, [tex] SC \cong HR [/tex] and [tex] HR \cong AB[/tex], according to the substitution property of equality, gives; [tex] SC \cong AB [/tex]
How can the definition of congruency and equality property prove [tex] SC \cong AB [/tex]?The given parameters are;
[tex] SC \cong HR [/tex] [tex] HR \cong AB[/tex]Required;
To prove;
[tex] SC \cong AB[/tex]
Solution;
From the given parameters, and the definition of congruency, we have;
SC = HRHR = ABAccording to the symmetric property of equality, we have;
SC = HR
Therefore;
HR = SCAccording to the substitution property of equality, we have;
If a = b and a = c, therefore;
b = c
Which gives;
HR = SC
HR = AB
Therefore;
SC = AB
Which gives;
[tex] SC \cong AB [/tex] (Inverse of the definition of congruency)
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8x1,000=8x_____=_____ i need help btw thanks last person by the way who helped me on my last question
The value of the expression 8 x `1000 is 8000
How to evaluate the expression?The expression is given as
8 x `1000
The above expression implies that we multiply 8 by 1000
This can be done directly using a calculator, and it can be solved step by step
The step by step procedure is as follows
Express 1000 as 10 x 100
So, we have
8 x `1000 = 8 x `10 x 100
Evaluate 8 x 10
8 x `1000 = 80 x 100
Evaluate 80 x 100
8 x `1000 = 8000
Hence, the value of the expression 8 x `1000 is 8000
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A rental car company charges $48 per day to rent a car and $0.08 for every mile
driven. Bilquis wants to rent a car, knowing that:
. She plans to drive 175 miles.
. She has at most $110 to spend.
Write and solve an inequality which can be used to determine x, the number of days Bilquis can afford to rent while staying within her budget.
The number of days Bilquis can afford to rent while staying within her budget is 2 days.
How to solve the inequalityThe question has the following data
amount charged = $48
Rent per mile = $0.08
The mile to drive = 175 miles.
Amount to spend = 110 dollars
The inequality would be written as
48x + 0.08(175) ≤ 110
we are to solve for the value of x
this would be
48x + 14 ≤ 110
48x ≤ 110 - 14
48x ≤ 96
We have to divide through by 48
x ≤ 96 / 48
x ≤ 2
Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.
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5. For f(x) = 5x + 1, find f-4). (1 point)
O-19
01
O-21
021
Answer: 19 ==> 1st option
Step-by-step explanation:
f(x) = 5x + 1
f(-4)=5(-4) + 1
f(-4)=-20 + 1
f(-4)=-19 ==> 1st option
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if a polynomial f(x) has a remainder of 8 qhen divided by x-3 what is f(x)
The value of f(x)= (x-3).g(x)+8
A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division.
dividend= divisor x quotient+ remainder
given that, f(x) has remainder 8 and divided by x-3
as per division algorithm we can say that
dividend= divisor x quotient+ remainder
f(x)= (x-3).g(x)+ 8
if we need to find f(3) then put 3 in the place of x
that gives you f(3) = (3-3).g(x)+ 8
f(3)= 8
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The answer to f(x)= (x-3). g(x)+8
An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm.
Dividend equals Divisor x Quotient plus Remainder.
Given that, f(x) is divided by x-3 and has a remainder of 8.
The division algorithm allows us to state that
Dividend equals Divisor x Quotient plus Remainder.
f(x)= (x-3) (x-3).
g(x)+ 8
If we need to find f(3), we should substitute 3 for x.
giving you f(3) = (3-3).
g(x)+ 8
f(3)= 8
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f(x)=x², g(x)=2x²
The points (-1, 1), (0, 0), and (1, 1) of f(x) translate to the points ‘blank’ of g(x).
The coordinate points of g(x) are (-1, 2), (0, 0), (1, 2).
Which are the coordinates of the new points?
We know that the points (-1, 1), (0, 0), and (1, 1) belong to f(x) graph, where:
f(x) = x^2
Notice that the inputs in these points are x = -1, x = 0, x = 1.
Function g(x) is:
g(x) = 2x^2
Using the given inputs, we have:
g( -1) = 2*(-1)^2 = 2
g(0) = 2*0^2 = 0
g(1) = 2*(1)^2 = 2
Then the coordinate points of g(x) are (-1, 2), (0, 0), (1, 2).
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Trigonometry question
Answer:
[tex]\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]
Step-by-step explanation:
In triangle ABD,
[tex]\sin 72^{\circ}=\frac{BD}{8} \implies BD=8 \sin72^{\circ} [/tex]
In triangle BCD,
∠CBD=34° (isosceles triangle)
∠DCB=116° (sum of angles in a triangle)
[tex]\frac{BC}{\sin 34^{\circ}}=\frac{8\sin 72^{\circ}}{\sin 116^{\circ}} \\ \\ BC=\frac{8\sin 72^{\circ}\sin 34^{\circ}}{\sin 116^{\circ}}[/tex]
Answer:
4.59 cm to nearest hundredth.
Step-by-step explanation:
Consider triangle ABD.
sin 72 = DB / 8
DB = 8 sin 72
= 7.608 cm.
Imagine a line from point C perpendicular to DB at point E.
As triangle CDB is isosceles ( DC = BC), this line will cut DB in 2
so, DE = 1/2 * 7.608 = 3.804.
Now consider triangle DCE which is a right-angled triangle at E.
cos 34 = 3.804 / DC
DC = 3.804 / cos 34
= 4.588 cm
BC = DC = 4.588.
(3-x/2)-(1-x/3)=7-(x-x/2)
(3-[tex]\frac{x}{2}[/tex])-(1-[tex]\frac{x}{3}[/tex])=7-(x-[tex]\frac{x}{2}[/tex])
The value of x is 15.
(3 - x/2) - (1 - x/3) = 7 - (x - x/2)
(6 - x/2) - (3 - x/3) = 7 - (2x - x/2)
(6 - x/2) - (3 - x/3) =14 - 2x +x /2
by solving these equations we get ,
18 - x -6 = 42 - 3x
12 - 42 = - 2x
where, x = 15 .
therefore the value of x is 15.
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
There are three major forms of linear equations ; point-slope form, standard form, and slope-intercept form.examples of equation and expression.
For example, 3x - 2 is an expression. While on the other hand, an equation means that two different expressions are connected to each other by an equal to sign in between, For example, 3x - 2 = 5 + x is an equation.to know more about mathematical equations;
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Maria is going for a run. She runs for 4 hours at a speed of 6.4 miles per hour. For how many miles does she run?
The number of miles that Maria ran is 25.6 mile.
How to calculate the value?From the information given, she runs for 4 hours at a speed of 6.4 miles per hour.
It should be noted that distance is calculated as the speed multiplied by the time taken.
In this case,the distance will be:
= Speed × Time
= 6.4 × 4
= 25.6 miles
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the temperature in sudbury was 4c. what was the temperature after a rise of 5c followed by a fall of 10c
By the use of arithmethic, the final temperature in Sudbury is - 1 °C.
What is the final temperature of Sudbury?
In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:
T = T' + ΔT₁ + ΔT₂
T = 4 °C + 5 °C - 10 °C
T = 9 °C - 10 °C
T = - 1 °C
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Kendra and Ann shared 200 apples such that Kendra received 50 apples more than Ann I)calculate their share Ii)find the ratio of their share
pls help Asap
Step-by-step explanation:
this is the solution above
HELPPP ASAPPPP
which expression is equivalent to 5(2.47y − 2.03)?
A.)12.35y + 10.15
B.)12.35y − 10.15
C.) 12.35y + 2.03
D.) 12.35y − 2.03
Answer:
5(2.47y−2.03)
Use the distributive property to multiply 5 by 2.47y−2.03.
12.35y−10.15
Step-by-step explanation:
The diagrams below show two cereal boxes of different sizes and prices. (a) big box 500 g $8.00 small box 300 g $5.40 Which of the boxes is better value for money? Show your workings.
Answer: Small box has the lowest amount when divided, that box has the best value.
Step-by-step explanation:
Given data,
Big box = 500 g
It cost is $8.00
Small box = 300 g
It cost is $ 5.40
First switch the box that's in kilograms into grams.
One kilogram=1000 grams.
Then, Big box = 500 g = $ 8.00
Small box = 300 g = $ 5.40
Next divide the amount in each box by the cost of each box.
Big box = 500/8
Big box = 62.5
Small box = 300/540
Small box = 0.5555
Therefore,
So, since small box has the lowest amount when divided, that box has the best value.
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bisects ∠PQT.
7. If m∠PQT = 60 and m∠PQS =
4x + 14, find the value of x.
The value of x in the question is 4
How to find the value of x?The given parameters are
PQT = 60
PQS = 4x + 14
The line bisects PQT
So, we have
PQS = 1/2 * PQT
This gives
4x + 14 = 1/2 * 60
Evaluate
4x + 14 = 30
Evaluate the like terms
4x = 16
Divide by 4
x = 4
Hence, the value of x in the question is 4
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Find the distance between pair of parallel lines with the given equations.
y=x+2 y=x-4
The distance between pair of parallel lines with the following equation
y=x+2 y=x-4 is [tex]3{\sqrt 2 }[/tex]
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The slope of a line which is perpendicular to both the lines will be -1. Check what are the y-intercept of any of the two lines and write the equation of the perpendicular line through it.
The y-intercept of the line y = x − 4 is (0,−4).
So, the equation of a line with slope −1 and a y-intercept of −4 is y = −x −4.
The perpendicular intersects or meets the line y = x - 4 at (0, 4).
Now, to find the point of intersection of the perpendicular & the other line, solve the two equations. Solve the right sides & solve for x.
x + 26 = -x - 6
2x = -6 (combine them like terms)
x = -3 (divide both the side by 2)
Find y:
y = -3 - 4
= -7
So, the point of intersection is (−3,−7).
Use the Distance Formula to find the distance between the points (-3, -7) and (0,−4).
[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]
[tex]={\sqrt {\left(0-(-3\right)^{2}+\left(-4-(-7\right))^{2}}}[/tex]
[tex]={\sqrt {3^2 +3^2}}[/tex]
[tex]=3{\sqrt 2 }[/tex]
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For every 21 litres of petrol a car can run for 80 km.
How much petrol do you need (to 1 DP) to ensure the car has enough petrol of a trip that is 224 km?
A= h(b+c) solve for b
Answer:
A=h(b+c) solve for c
First, multiply h to b and c
A = hb + hc
Then, transfer hb to the other side and change its sign from positive to negative.
A – hb = hc
To get c, Divide both sides by h
(A – hb)/h = hc/h
(A - hb)/h = c OR c = (A – hb)/h
Example. Let us assume the following. A = 500 ; h= 10;b= 20; c= ?
c = (A – hb)/h
c = (500 – (10*20))/10
c = (500 – 200)/10
c = 300/10
c = 30
To check; use the original equation given.
A = h(b+c)
A = 10(20+30)
A = 200 + 300
A = 500. same as the figure given in the example.
[tex]\displaystyle\\Answer:\ b=\frac{A-hc}{h}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\A=h(b+c)\\A=hb+hc\\A-hc=hb+hc-hc\\A-hc=hb\\Divide\ both\ parts\ of\ the\ equation\ by\ h(h\neq 0):\\\frac{A-hc}{h}=b\\ Hence,\\b=\frac{A-hc}{h}[/tex]
