Answer:
8820 ways
Step-by-step explanation:
Given that :
Selecting 4 pairs of pant from 8 available and selecting 5 shirts from 9 available
Using combination :
4 pants from 8 = 8C4
5 shirts from 9 = 9C5
Recall:
nCr = n! / (n-r)! r!
8C4 * 9C5 = [8! /(8-4)!4!] * [9! /(9-5)!5!]
8C4 * 9C5 = (8! /4!4!) * (9! /4!5!)
8C4 * 9C5 = 70 * 126
8C4 * 9C5 = 8820 ways
an island has three towns located at points with the coordinates a (15,3) b (25,10) and c (0,20) where the coordinates have units of Km the government wants to locate a toxic waste dump at a position as far as possible away from each town you may assume that this location is not on the edge of the island find the coordinates at the point where the toxic waste dump should be located
9514 1404 393
Answer:
(13.06, 16.41)
Step-by-step explanation:
Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.
The midpoint of AB is ...
(A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)
The midpoint of AC is ...
(A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)
__
The differences between points are ...
B -A = (25, 10) -(15, 3) = (10, 7)
C -A = (0, 20) -(15, 3) = (-15, 17)
Then the perpendicular bisector equations can be written as ...
bisector of AB ⇒ 10(x -20) +7(y -6.5) = 0
10x +7x -245.5 = 0
bisector of AC ⇒ -15(x -7.5) +17(y -11.5) = 0
-15x +17y -83 = 0
These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...
x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06
y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41
The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).
_____
Further detail regarding the solution
Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...
R -S = (∆x, ∆y)
The midpoint of segment RS can be called ...
(R +S)/2 = (h, k)
Then the line that is a perpendicular bisector of RS can be written as ...
∆x(x -h) +∆y(y -k) = 0
This is the form that is used above.
__
The "cross multiplication method" for solving a pair of general-form linear equations ...
ax +by +c = 0
dx +ey +g = 0
will give the solution as ...
1/(ae -db) = x/(bg -ec) = y/(cd -ga)
If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.
[tex]\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right][/tex]
In the diagram below, AB is parallel to CD. What is the value of x?
A. 120
В. 80
с. 100
D. 60
Answer:
120
Step-by-step explanation:
By the rule of opposite angles, we can determine that x=120 because:
AB is parallel to CD
120 degree angle (let's call it Y) is on AB
X (we can see that it is obtuse) is on CD
So, Y is congruent to X, vice versa, so x=120
hope this helps! :)
ibrahim
A school is having a canned food drive. Each class is challenged to collect 220 cans. If there are x classes in the school, which equation could be used to find the total number of cans, y, the school will collect if each class meets the challenge?
A. y = 20x
B. y = 220x
C. y = 220/x
D. y = 220 + x
Answer:
B)
Step-by-step explanation:
no. of Classes = x
cans = 220
220×x = 220x
no.of classes × cans = total number of cans
Identify the Y intercept of the equation 5x+8y=120
Answer:
120
Step-by-step explanation:
baqhBajBjabajabqj
What is the probability
Answer:
Probability = the number of ways of achieving success. the total number of possible outcomes.
Step-by-step explanation:
For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
Which of these is an example of typing at a rate of 42 words per minute?
A
typing 21 words in 2 minutes
B
typing 84 words in 3 minutes
С
typing 210 words in 5 minutes
D
typing 400 words in 10 minutes
Answer:
C. typing 210 words in 5 minutes
Step-by-step explanation:
Because 210 divided by 5 equals 42 over 1. :)
Answer:
C. Typing 210 words in 5 minutes
Step-by-step explanation:
42 words per minute, so think about this. 42 plus 42 is 84, so it is not A cause a to less than 84. And it is not Ba either cause 84 words is 2 minutes. 42×5=210
please help help help
Answer:
?
Step-by-step explanation:
Kiesha and her classmates wrote proportions for the reduction of a triangle,
height
height
base
base
Which proportions are set up correctly? Select three options.
Answer:
1,2,4
Step-by-step explanation:
Answer:
Trust the person above me, they're correct it's A,B,D
Step-by-step explanation:
(9x+29)+(93-5x)+(10x+2)
Answer:
14x + 124
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Expression
(9x + 29) + (93 - 5x) + (10x + 2)
Step 2: Simplify
Combine like terms (x): 14x + 29 + 93 + 2Combine like terms (Z): 14x + 124Step-by-step explanation:
1, Rearrange the problem.
(9+29)+(9−5)+(10+2)
(9x+29)+(93−5x)+(10x+2)
(9+9)+(−5+93)+(10+2)
2, Solve.
14x+124
Answer:14x+124
Lukas graphed the system of equations shown.
2x + 3y = 2
y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3
A coordinate grid with 2 lines. The first line passes through the points labeled (negative 2, 2), (0, 0.67) and (1, 0). The second line passes through the points labeled (negative 2, 2) and (0, 3).
What is the solution to the system of equations?
The solution to the system of equations is A. (-2, 2)
How to calculate the value?The system of equation was:
2x + 3y = 2 ..... i
y = 1/2x + 3 ...... ii
Substitute equation ii into i
2x + 3/2x + 9 = 2
Multiply through by 2.
7x + 18 = 4
7x = -14
Divide
x = 14/7
x = -2
Also, y = 1/2x + 3
y = 1/2(-2) + 3
y = -1 + 3
y = 2
Therefore, the solution to the system of equations is (-2, 2).
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Lukas graphed the system of equations shown. 2x + 3y = 2 y = A system of equations. 2 x plus 3 y equals 2. y equals StartFraction one-half EndFraction x plus 3.x + 3 A coordinate grid with 2 lines. The first line passes through the points labeled (negative 2, 2), (0, 0.67) and (1, 0). The second line passes through the points labeled (negative 2, 2) and (0, 3). What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)
Will the standard form of 8.5 × 10–3 be more or less than 1? Explain what effect the negative exponent has.
The value is less than 1 and the impact of the negative exponent is that it moves the decimal point to the left
What is standard form?Standard form can be defined as a mathematical way of writing large or too small numbers in a defined manner.
Given the standard form;
8.5 × 10–3
The negative exponent (-3) indicates an addition of three zeros ruled out from the start.
It could be written as;
0. 0085
This is 0. 9915 less than the value of 1
The impact of the negative value is that it moves the decimal point to the left.
Thus, the value is less than 1 and the impact of the negative exponent is that it moves the decimal point to the left
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How many 5 minute intervals are between 4:35 pm and 5:00 pm
Answer: There are 5 five minute intervals.
I hope this helps, and Happy Holidays! :)
Answer:
25, 5 minute intervals.
Step-by-step explanation:
Hope this helps and you have a great day!
1.What is the solution to this system of linear equations?x + y = 4 x − y = 6
Answer:
If x+y=4×-y =6 then what is the question
Im very confuzed by this plz help me!
Answer: 2.339
Step-by-step explanation:
Make sure that you align your decimal points. The 1 shouldn't line up with the 7.
Instead, write your equation like:
2.37
- 0.031
The numbers don't match up, but instead, the decimals do.
I hope this helps! :)
Norma made 16 braided bracelets. She split them evenly among g gift boxes. Write an expression that shows how many bracelets were in each box.
Answer:
16/g
Step-by-step explanation:
Answer:
the correct answer is 16÷g
Step-by-step explanation:
why 16÷g because the explanation said 16 braided bracelets. and the gift boxes was g so i think its 16÷g
Solve for x in the triangle above
Answer:
x = 30
Step-by-step explanation:
The interior angles of a triangle must always add up to 180.
2x + 2x + 3x - 30 = 180
Add 30 to both sides to seperate variables.
2x + 2x + 3x = 210
Combine like terms.
7x = 210
Divide by 7 to isolate x.
x = 30
plz help. an airplane flies 1,600 miles in four hours. how far will it fly in half a day?
Answer:
4800
Step-by-step explanation:
A day consist of 24 hours. Half of 24 is 12. 4 x 13 = 12 so 1600 x 3 = 4800.
(a) Work out the value of (16/81)^3/4
Answer: 8/27
Step-by-step explanation:
Just evaluate the equation.
Do it in this order: Parenthesis, Exponents, Multiply/Divide, Add/Subtract.
So:
16/81 = 16/81
16/81 To the Power of 3/4 = 0.2^0.75 = 8/27
can ya'll help me with this 7r+8>64-r
Answer:
r > 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define inequality
7r + 8 > 64 - r
Step 2: Solve for r
Add r to both sides: 8r + 8 > 64Subtract 8 on both sides: 8r > 56Divide 8 on both sides: r > 7Here we see that any value r greater than 7 would work as a solution to the inequality.
Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes. If he has 20 blueberries and 30 grapes, what is the maximum number of bags of snacks that he can pack so that each bag has the same number of blueberries and grapes?
5 bags
10 bags
50 bags
60 bags
Answer:
10bags
Step-by-step explanation:
Answer:
10 bags.
Step-by-step explanation:
I got it right on my quiz- Edge2020
2. Aashvi is making garlic naan. The recipe calls for 2 cups of flour, but Aashvi only has teaspoons. If 24 teaspoons are equal to 1/2 cup, how many teaspoons will Aashvi use to measure 2 cups of flour? *
Answer:
98 teaspoons
Step-by-step explanation:
Aashvi is making garlic naan. The recipe calls for 2 cups of flour, but Aashvi only has teaspoons. If 24 teaspoons are equal to 1/2 cup, how many teaspoons will Aashvi use to measure 2 cups of flour? *
From the above question, we understand that:
1/2 cup of flour = 24 teaspoons
2 cups of flour = x teaspoons
Cross Multiply
1/2x = 24 × 2
x = 48 ÷ 1/2
x = 48 × 2
x = 98 tea spoons
Therefore, Aashvi will use 98 teaspoons to measure 2 cups of flour.
Function g(x) has a removable discontinuity at x = c, where g(c) is undefined. Which statement describes the one-sided limits at x = c?
Answer:
B
Step-by-step explanation:
The function that describes the one-sided limits at x = c.
[tex]\lim_{x \to c^-} g(x) = a\\\\ \lim_{x \to c^-} g(x) = a[/tex] ( for some value of a).
What is removable discontinuity?A discontinuity is removable if the limit of the function at the point of discontinuity exists and the value of the function exists but they aren't equal to each other.
We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.
Function g(x) has a removable discontinuity at x = c,
where g(c) is undefined.
In this case, the statement that's is true for g(x) is that you can remove the discontinuity at x = c by defining g(c) = a.
The function that describes the one-sided limits at x = c.
[tex]\lim_{x \to c^-} g(x) = a\\\\ \lim_{x \to c^-} g(x) = a[/tex] ( for some value of a).
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Blake practices the piano 420 minutes in 4 weeks. assuming he practices the same amount every week, how many minutes would he practice in 1 weeks?
139 students choose to attend one of three after school activities: football, tennis or running.
There are 66 boys.
56 students choose football, of which 28 are girls.
54 students choose tennis.
18 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
(NEED HELP)
Your friend made $324 babysitting last year.This year she made 296% of what she made last year.How much more did your friend make this year?
Answer:
$635
Step-by-step explanation:
She made a total of $959 anad last year she made $324 so you then subtract the ammounts because the problem wants to know how much MORE she made.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The more amount made this year is $635.04
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Your friend made $324 babysitting last year.
This year she made 296% of what she made last year.
This means,
The amount this year.
= 296/100 x 324
= $959.04
The difference in the amount.
= $959.04 - $324
= $635.04
The difference in the amount can also be calculated as,
= 296% - 100%
= 196% more this year.
So,
196% of $324
= 196/100 x 324
= $635.04
Thus,
The more amount made this year is $635.04
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I NEEEEEEEEEEEEEEEEEEEED HELLLLLLLLLP
Answer:
go to jesus
Step-by-step explanation:
put both hands together and pray we know your struggling
who is good at math?! IM GIVING BRAINLIEST! comment or answer on the question so we can talk cuz i need help!!
Answer:
Wheres the question then i'll help
Step-by-step explanation:
Find the slope of the line
Answer:
1/5th
Step-by-step explanation:
trust me. ik how to do slopes
The discriminant of a quadratic equation is negative. One solution is 2 +3i.
What is the other solution?
A. 3-2i
B. 2-3i
C. -2+3i
D. 3+2i
Answer: B
Step-by-step explanation:
For their history project, students case to either write a report or give a presentation. Two fifth of the students wrote a report and 0.6 of the students gave a presentation. Dominic said that more students gave a presentation. Do you agree with Dominic? Use numbers and words to support your answer. *
Answer: Yes. Dominic is correct
Step-by-step explanation:
We are informed that Two fifth of the students wrote a report. This also means that (2/5 × 100) = 40% = 0.4 wrote a report and 0.6 of the students gave a presentation.
From the decimals gotten, we can see that 0.6 is more than 0.4. Therefore, more students gave a presentation. This implies that Dominic is correct.