9. Which lines are parallel if mZ4=mZ5? Justify your answer.
Answer:
r || s
Step-by-step explanation:
m∠4 = m∠5 Given.
These angles are called alternate interior angles and because you are given that they are = then there are two parallel lines. The converse of the theorem stated. If alternate interior angles are cut by a transverse and two lines and the alternate interior angles are equal, then you have a pair of parallel lines.
A computer programming team has 17 members. (For each answer, enter an exact number.) (a) How many ways can a group of nine be chosen to work on a project? 24310 Correct: Your answer is correct. (b) Suppose nine team members are women and eight are men. (i) How many groups of nine can be chosen that contain five women and four men? 1 Incorrect: Your answer is incorrect. (ii) How many groups of nine can be chosen that contain at least one man? 9 Incorrect: Your answer is incorrect. (iii) How many groups of nine can be chosen that contain at most three women? (c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project?
The number of groups that can be chosen from the team of 17 depends on
the given conditions of the selection.
The correct responses are;
(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.(ii) The number of groups of 9 that contain at least one man is 24,309 groups.(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.Reasons:
The combination of n objects taking r at a time is given as follows
[tex]_nC_r = \dbinom{n}{r}[/tex]
(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;
Number of ways of choosing groups of 9 = [tex]\dbinom{17}{9}[/tex] = 24,310 ways.
(b) (i) Number of women = 9
Number of men = 8
Number of groups of 9 containing 5 women and 4 men = [tex]\dbinom{9}{5} \times \dbinom{8}{4}[/tex]
[tex]\dbinom{9}{5} \times \dbinom{8}{4} = 126 \times 70 = 8,820[/tex]
Number of groups of 9 containing 5 women and 4 men = 8,820 groups.
(ii) The number of groups that contain at least one man is [tex]\dbinom{17}{9} - \dbinom{9}{9}[/tex]
[tex]\dbinom{17}{9} - \dbinom{9}{9} = 24,310 - 1 = 24,309[/tex]
The number of groups that contain at least one man are 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women if given as follows;
[tex]\dbinom{8}{8} \times \dbinom{9}{1} + \dbinom{8}{7} \times \dbinom{9}{2} + \dbinom{8}{6} \times \dbinom{9}{3} = 2,649[/tex]
The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are [tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8}[/tex]
[tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8} = 5,005 + 2 \times 6,435 = 17,875[/tex]
(d) Two team members must work together or not at all is [tex]\dbinom{15}{7} - \dbinom{15}{9}[/tex]
[tex]\dbinom{15}{7} - \dbinom{15}{9} = 6,435 - 5,005 = 1,430[/tex]
The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.
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Use your expression from #2 to answer the following question. If there are 6 $5 bills and 4 $10 bills, how much money is in the box
Answer:
70 dollars
Step-by-step explanation:
6 x 5 = 30, 4 x 10 = 40. Add them up, that's what you get.
Help me or I will steal your caprisun.
Answer:
C and DStep-by-step explanation:
A. Incorrect as the directions are not opposite.B. Incorrect as - 40 - 10 = -50 m ≠ 0.C. Correct as the same amount is added and subtracted, resulting in zero.D. Correct as protons and electrons have opposite charges, their sum is neutral.please help me with this sum
Answer:
1. 384
2. 180
3. 324
4. 648
5. 476
6. 528
7. 294
8. 384
9. 414
10. 80
11. 72
12. 301
13. 222
14. 146
15. 156
16. 270
17. 283
18. 300
19. 292
20. 58
21. 64
22. 138
23. 296
24. 170
Hope it helps you
Can you please Help me?
Answer:
D. 5i
Step-by-step explanation:
edge 2021
What is formed when the number of electrons is changed?
Question 2 options:
isotope
radioisotope
a new element
ion
Answer:
A New Element
Which of the following graphs represents a function?
Answer:
A and C
Step-by-step explanation:
A function has a unique y value for every unique x value
The vertical section disqualifies B
D has 2 y values for many x values.
solve pls brainliest
Answer:
53cm
Step-by-step explanation:
11+8+8+11+15=53cm
PLZ HURRY IM TIMEDDD
Sameer chose 12 different toppings for his frozen yogurt sundae, which was Three-fourths of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below.
Three-fourths = StartFraction x over 12 EndFraction. Three-fourths (12) = StartFraction x over 12 EndFraction (12). 9 = x.
Which best describes the error that Sameer made?
Sameer did not use the correct equation to model the given information.
Sameer should have multiplied both sides of the equation by Four-thirds instead of by 12.
The product of Three-fourths(12) is not equal to 9.
The product of Four-thirds and StartFraction 1 over 12 EndFraction should have been the value of x.
Answer:
B, second option: the product of three fourths is not equal to 9
The error made by Sameer while creating the algebraic equation: Sameer did not use the correct equation to model the given information.
What is algebraic equation?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other.
It is given that Three-fourths of the total number of different toppings available at the make-your-own sundae shop = 12
The algebraic equation given by Sameer is wrong, the correct equation will be:
Let the total number of toppings be x.
[tex]\frac{3}{4} x = 12\\ \\x = 12 (\frac{4}{3} ) = 16[/tex]
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The perimeter of a poster is 16 feet. The area is 15 square feet. What are the dimensions of the poster?
Find the percent of change from
10 yards to 15 yards
1. 5%
2. 33%
3. 15%
4. 50%
Answer:
option 4
Step-by-step explanation:
Percent change is calculated as
[tex]\frac{change}{original}[/tex] × 100%
change = 15 - 10 = 5 , then
percent change = [tex]\frac{5}{10}[/tex] × 100% = 5 × 10% = 50%
After two consecutive years of 5% rates of return, what rate of return in the third year will produce a cumulative gain of 16%?
Using decimal multipliers, it is found that a rate of return of 5.2% in the third year will produce a cumulative gain of 16%.
The decimal multiplier for a increase of a% is given by:
[tex]M = \frac{100 + a}{100}[/tex]
In this problem, two increases of 5%, thus:
[tex]M = \frac{100 + 5}{100} = 1.05[/tex]
Another of x, that we want to find, and the result is a increase of 16%, thus:
[tex]M = \frac{100 + 16}{100} = 1.16[/tex]
The three increases(5%, 5% and x%) result in a increase of 16%, thus:
[tex]1.05(1.05)(x) = 1.16[/tex]
[tex]x = \frac{1.16}{(1.05)^2}[/tex]
[tex]x = 1.052[/tex]
1.052 - 1 = 0.052
A rate of return of 5.2% in the third year will produce a cumulative gain of 16%.
A similar problem is given at https://brainly.com/question/21806362
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 100 m long and 60 m wide.
Find the area of the training field. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Step-by-step explanation:
given,
length = 100 m
breadth = 60 m
we know,
area = l × b
now,
100 × 60 = 6000 m
therefore, area of rectangular field is 6,000 m.
and for both the semicircle if we add both the semicircle we will get a complete circle.
as the width of the rectangle is the diameter of circle so the radius of the circle is 60/2 = 30m
we know,
Area = πr²
now,
→ 3.14 × 30²
→ 3.14 × 900
→ 2826 m
so,
area of rectangle + area of circle = area of the training field.
→ 6000 + 2826 = 8826.
therefore, area of training field is 8,826 m.
hope this answer helps you dear...take care and may u have a great day ahead!
Answer:
8826 m²
Step-by-step explanation:
The field is composed of a rectangle and a circle .( the 2 semicircles form a complete circle when placed together )
area = area of rectangle + area of circle
= lb + πr² ( r = 60 ÷ 2 = 30 )
= (100 × 60) + (3.14 × 30²)
= 6000 + (3.14 × 900)
= 6000 + 2826
= 8826 m²
Help very urgent, . . .
Answer: 3.1
Step-by-step explanation:
Consider these four number lines of solutions.
4 number lines going from negative 5 to positive 5. Graph A: a point is at negative 4. Everything to the left of the point is shaded. Graph B: a point is at negative 4. Everything to the right of the point is shaded. Graph C: Points are at negative 4 and positive 4. Everything to the left of negative 4 and to the right of positive 4 is shaded. Graph D: points are at negative 4 and positive 4. Everything between the points is shaded.
Which graph represents the solution to the inequality |k|StartAbsoluteValue k EndAbsoluteValue greater-than-or-equal-to 4?
graph A
graph B
graph C
graph D
Answer:
its graph c
Step-by-step explanation:
Gus wrote the following riddle: I am a number between 30 and 60. My ones digit is three less than my tens digit. I am a prime number.
What number does Gus’ riddle describe?
Answer: 41
Step-by-step explanation:
Darren’s taxable income is $27,481. He is filing as head of household, and he has already paid $3847 in federal taxes.
What will he receive or pay after he figures his taxes for the year?
Tax table of wages
He will receive a refund of $161.
He will receive a refund of $346.
He will pay $161.
He will pay $346.
Answer:
If Darren's taxable income is $27,481 and he is the head of household, he will be exempted from tax deductions. If he has already paid $3,847 in federal taxes, he will receive an equivalent amount in return if his tax deduction exceeds his collectible tax. Therefore, his money at the end of the year will total to $31,328.
Step-by-step explanation:
Answer:
Step-by-step explanation:
he will receive a refund of 346 dollars
i just took the test
A Matrix of 1xM is called as ______.
Answer:
row matrix
Step-by-step explanation:
A matrix with only 1xmis called a ______ matrix
Plot the following and their opposites on the number line.
Step-by-step explanation:
Is there a image or any numbers because I can't see any
Answer:
If you are doing it thru edmentum the answer would be -2, 7, 1, 0, -5, 4, -3
Step-by-step explanation:
Hope this helps!!
The model below represents an equation. IN Which represent like terms in the model of the equation? and and T Save and Exit Next Mark this and return Ei O Type here to search NEWD HELP ASAP PLSSS
Answer:
x x x and 1 1 1
Step-by-step explanation:
3rd option is the correct answer.
A department store sells shoes with an 70% markdown. If one pair of shoes is originally $148, then with the markdown, what is the new selling price for those shoes?
Answer:
$44.40
Step-by-step explanation:
100%-70%=30%
30/100x148=44.40 (discounted price)
Appreciate to be marked brainliest. Hope this helps!
Last year Kaitlin opened an investment account with $7600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of the year
The increase was: 494
need help plz help for math class
-8/27
Step-by-step explanation:
Just multiply this fraction by itself 3 times and you will get the answer then simplify.
Find the mass of 250 ml of water. The density of water is 1 g/ml.
D= Density
M=
Volume - 10ml
What is the Mass?
V=
Mass - 70
Density
Alaalam
Answer:
250g
Step-by-step explanation :
250ml x 250g/ml = 250 g
To get the mass (in grams), you need to divide the ml's off and get the g alone.
a bit hard. thank you if u can do it for me? <3
The triangle shown is a right triangle shown by the little square inside of it.
Area of a triangle is 1/2 x height x base
Rotating the shown triangle so the square is at a bottom corner the height is 6 and the base is 6
Area = 1/2 x 6 x 6 = 18 square cm
I'll give Brainliest, I need this now. :D
Answer:
I think it's 6:3=18:9=54:27
Step-by-step explanation:
I hope this helps!
Hurry please What is the equation of this line
A. Y=1/4x-6
B. Y=6x-4
C. Y=6x-1/4
D. Y=4x-6
Find the value of x. 2x – 15 – 7x + 24 = -36
Answer:
9
Step-by-step explanation:
hlo!! dear!! glad to help u!
2x – 15 – 7x + 24 = -36
2x -7x -15 +24= -36
-5 x + 9= -36
-5 x = -36-9
-5 x =-45
x = -45/-5
x = 8
thank u!!!
If y varies directly with x which equation describes x = 72 and y = 36?
Answer:
k = 1/2
Step-by-step explanation:
direct variation equation is y = kx where 'k' is the constant of variation
substitute 36 for 'y' and 72 for 'x' to get:
36 = 72k
solve for 'k' to get:
k = 36/72 or k = 1/2