MATHEMATICS HIGH SCHOOL

You pick a card at random. Without putting the first card back, you pick a second card at random. [1] [2] [3]

What is P(3, greater than 2)? Write your answer as a percentage.

Answers

Answer 1
Answer: Probability of first getting a  3 = 4/52 = 1/13
The p(getting >2)  =   probability of getting  one of the remaining 3's or 40 other cards ( Im taking the aces to be low value)  = 43/51

Required probability = 1/13 * 43/51 =  43/663

If aces are counted high it will be 1/13 *  47/51 =   47/531

=  

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After lunch, you need to buy new shoes. You bought a pair last year and they cost $79.00. Now, the same shoes cost $86.00. By what percent has the price increased? Write your answer to 2 decimal places. *

Answers

Answer:

The main answer: $4.84

Step-by-step explanation:

County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

$75 * 0.0725 = $5.4375

Add the original price and the sales tax.

$75 + $5.4375 = $80.4375

County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

$70 * 0.08 = $5.6

Add the original price and the sales tax.

$70 + $5.6 = $75.6

Then take the difference.

80.4375 – 75.6 = 4.8375

Round to the nearest hundredth: $4.84

What is the y value of the y-intercept of the line that contains the points (-8,-5) and (10,67)?

Answers

(67)-(-5)<br />-------------= 72/18<br />(10)-(-8) reduce down 72/18=4

Rationalise:
(1)              4/(2+root3+root7)
(2)              4/(2root3+root5)

Answers

(4)/(2+\sqrt3+\sqrt7)\cdot(2-(\sqrt3+\sqrt7))/(2-(\sqrt3+\sqrt7))=(8-4\sqrt3-4\sqrt7)/(2^2-(\sqrt3+\sqrt7)^2)=(8-4\sqrt3-4\sqrt7)/(4-3-2√(3\cdot7)-7)\n\n=(8-4\sqrt3-4\sqrt7)/(-6-2√(21))=(-2(2\sqrt3+2\sqrt7-4))/(-2(3+√(21)))=(2\sqrt3+2\sqrt7-4)/(3+√(21))\cdot(3-√(21))/(3-√(21))\n\n=(6\sqrt3-2√(63)+6\sqrt7-2√(147)-12+4√(21))/(3^2-(√(21))^2)=(6\sqrt3-2√(9\cdot7)+6\sqrt7-2√(49\cdot3)-12+4√(21))/(9-21)

=(6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4√(21))/(-12)=(-8\sqrt3+4√(21)-12)/(-12)=(-4(2\sqrt3-√(21)+3))/(-12)\n\n=(2\sqrt3-√(21)+3)/(3)

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(4)/(2\sqrt3+\sqrt5)\cdot(2\sqrt3-\sqrt5)/(2\sqrt3-\sqrt5)=(8\sqrt3-4\sqrt5)/((2\sqrt3)^2-(\sqrt5)^2)=(8\sqrt3-4\sqrt5)/(4\cdot3-5)=(8\sqrt3-4\sqrt5)/(12-5)\n\n=(8\sqrt3-4\sqrt5)/(7)
(1) (4)/(2+√(3) +√(7)) \n \n or, (4)/(2+√(3) +√(7)) * (2 - √(3) -√(7))/(2-√(3)-√(7)) \n \n => \frac{ \sqrt[2]{3} - √(21)+3}{3} \n \n \n (2) \frac{4}{\sqrt[2]{3} + √(5)} \n \n or, \frac{4}{\sqrt[2]{3} + √(5)} * \frac{\sqrt[2]{3}-√(5)}{\sqrt[2]{3}-√(5)} \n \n => \frac{\sqrt[8]{3}-\sqrt[4]{5}}{7}

What is 10^0 + 10^1 + 10^2 equal to? A. 10,201 B. 120 C. 111 D. 110 E. 100

Answers

Answer:

111

Step-by-step explanation:

10^0 + 10^1 + 10^2

1 + 10 + 100

111

Answer:

111

Step-by-step explanation:

1+10+100=111

What does -4x + 9x equals

Answers

5x
just think of it as -4 + 9 because the variables are the same

Jim goes canoeing on a local stream that has been measured to flow at 2 mph. If he can go 9 miles upstream in the same time it takes him to go 15 miles downstream, find how fast he can go in still waters.

Answers

Answer: This is a problem of solving a system of linear equations. Let x be the speed of Jim in still waters, and y be the speed of the stream. Then we have:

{x+y=15/tx−y=9/t​

where t is the time it takes Jim to go upstream or downstream. We can solve this system by adding the two equations and eliminating y:

2x=24/tx=12/t

Then we can substitute x into one of the equations and solve for y:

y=15/t−12/ty=3/t

Since we know that the speed of the stream is 2 mph, we can equate y to 2 and solve for t:

3/t=2t=3/2

Finally, we can plug in t into the expression for x and find the speed of Jim in still waters:

x=12/tx=12/(3/2)x=8

Therefore, Jim can go 8 mph in still waters.

Answer:

Time taken to go downstream = 4 / ( 2 + S) where S is the speed of the river

TIme taken to go upstream = 1 / ( 2 - S )

Since the time taken is the same in each case we can equate both of them

1 / ( 2 - S) = 4 / ( 2 + S )

2 + S = 8 - 4S

5 S = 6

S = 6 / 5

= 1.2 mph
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