MATHEMATICS HIGH SCHOOL

Let the numbers m, n, p, and s be defined as: m = 0.1212121212... n = 0.1221221221... p = 0.1122112211... s = 0.1112221112... Which choice shows the correct ordering of these numbers?A) m < n < p < s
B) s < p < m < n
C) n < m < s < p
D) p < s < n < m
E) s < p < n < m

Answers

Answer 1
Answer: Short Answer: B
Comment
The < symbol means that the number on the left is smaller than the number on the right. When I was first stumbling through < or > the point goes to the smallest number and the open end goes to the most generous (largest) number. 

So in this question, the smallest number is on your left, and the largest number is on your right. 

Working it out
Method One
But which number is smallest and which way is biggest? You can get your calculator to tell you the answer. You can subtract one number from the other. Like m and p. Try m - p.
If you get a plus answer m>p
If you get a minus answer m<p
m = 0.12 p = 0.11
m - p = 0.12 - 0.11 = 0.01 and it is positive. 
Conclusion m>p   
Conclusion 2: A and C are both wrong.

Method Two
You can just scan the numbers with your eye and pick out the biggest one.
Start with m. 
It is 0.12 Is there anything bigger?
n is but you have to go to the third decimal place. n = 0.122 m = 0.121 n is bigger than m (and of course p).

So what does that do? Anything?
Yes it picks out the answer. B. Nothing is bigger than n so it should be on the far right. Only B shows that.

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At noon, the minute and hour hands overlap. In how many hours will they overlap again?
What is bigger 0.09 or 0.089
Remmi wrote the equation of the line y=1/3(x+2) He solved for x and got x=3y-2 Which of the following is an equivalent equation for x?a. x=y-11/3 b. x=y+7/3 c. x=3(y-2/3) d. x=3(y+2/3)
From his home, Albert would have to walk due north to get to his friend Donald's house and due east to get to his friend Zoe's house. It is 5 kilometers from Albert's house to Zoe's house and a straight-line distance of 9 kilometers from Donald's house to Zoe's house. How far is Albert's house from Donald's house? If necessary, round to the nearest tenth.

Natalie wants to measure the width of a river. She marks off two right angles, as shown in the figure. The base of the larger triangle has a length of 58m, and the base of the smaller triangle has a length of 26m. The height of the smaller triangle is 21.3m. How wide is the river? Round your answer to the nearest meter.

Answers

Given: 
Larger Triangle : base = 58 m ; height = x
Smaller Triangle: base = 26 m; height = 21.3 m

x:58 = 21.3:26
26x = 58*21.3
26x = 1,235.4
x = 1,235.4 / 26
x = 47.515

The river is 48 meters wide.

In a fruit cocktail, for every 18 ml of orange juice you need 3 ml of apple juice and 54 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?

Answers

Answer:

1:18:6

Step-by-step explanation:

3:54:18

This equals 1:18:6

The Hendersons have just bought a home that requires some monthly yard maintenance. They are trying to decide if they should hire a professional lawn care service to maintain the property or do it themselves. Below are the costs associated with both options:Professional Service Option Do-It-Yourself Option
$75 for the first month $250 lawnmower
$45 per month after initial visit $135 edger
Includes mowing and edging the $69 hedge trimmer
lawn, trimming the bushes, and $25 rake
raking the leaves.


How long would it take before the Hendersons would recover their costs if they chose to do it themselves over the professional service?
a.
5 months
b.
9 months
c.
10 months
d.
6 months

Answers

First, add together the costs for buying their own stuff. 250+135+69+25=479.

Then figure for the professional costs. Put it in perspective of a year. 45*11+75=570. 

Then subtract. Professional- DIY. 570-479=91. 

$91 is about 2 months worth of work. So a year has 12 months.

12-2=10

Answer:10 months

Professional Service Option Do-It-Yourself Option:

First month lawnmower = $250

Initial visit = $135

Price for mowing and edging = $69

Price for lawn and bushes trimming = $ 25

Hence, total cost becomes = 250+135+69+25 = $479

Professional service cost for 1 month lawnmower = $75

Professional cost for visit for 11 months (1st visit costs $135) = $45

Total cost for 11 months = 45*11 = $495

Total professional cost = 495+75 = $570

Now, subtracting the professional cost and do it yourself cost we get;

$570-$479=$91. 

This $91 is for 2 months worth of work. Hence, months needed to recover costs = 12-2 = 10 months

Hence, the answer is 10 months.

Multiply 2 1/2 x -4 3/5
Plz help

Answers

its -11.5 (or 1/2, you can write it like that too) if i'm not mistaken

Answer:

Step-by-step explanation:

2 1/2* -4 3/5=

5/2*-23/5

-23/2 or -11 1/2

ella bought some key chains and spent a total of 24 each key chain cost the same whole dollar amount she bought between 7 and 11 key chains how many key chains did ella buy?

Answers

Answer: there are 8 key chains Ella can buy.

Step-by-step explanation:

Since we have given that

Ella bought some key chain and spent a total of 24.

Each key chain cost the same whole dollar amount she bought between 7 and 11 key chains.

As we know that between 7 and 11, there is only 1 number which is factor of 24 i.e. 8

Hence, there are 8 key chains Ella can buy.
To solve this problem, you need to use a process of trial and error, and add up each number until you get 24 or above.  If you get above, it is wrong.  The only number that goes into 24 evenly is 8, so the answer is 8 keychains.

Can you solve (4x-3)/(x+2)+(15)/(x-3)

Answers

Please see the pic, I'd solved in it.
(4x-3)/(x+2) + (15)/(x-3) = 0
1st step: We need to have a common denominator.
So we do this:
((4x-3)*(x-3))/((x+2)*(x-3)) + ((15)*(x+2))/((x-3)*(x+2)) = 0
2nd step: Distribute them
(4x^(2)-3x-12x+9)/((x-3)(x+2)) + (15x+30)/((x+2)(x-3)) = 0
3rd step: Do the rest of the equation!
We can put it on one fraction, its fine.
(4x^2-15x+9+15x+30)/((x+2)(x-3)) = 0
(4x^2+39)/((x+2)(x-3)) = 0 (-15 and 15 cancels out)
4th step: take the denominator to the other side
4x²+39 = 0 (anything × 0 = 0)
5th step: Take 39 to the other side
4x² = -39
6th step: Divide by 4 on both sides
(4x^2)/(4) = -(39)/(4)
(4 and 4 cancels out)
x² = -(39)/(4)
7th step: Take the square root to keep x alone
x = -\sqrt(39)/(4)
It can also be written as:
x = -( √(39) )/( √(4) )
Final answer:
x = -( √(39) )/(2)
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