VCE Maths questions help (4 Viewers)

[boredsatan]

in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
draw a venn diagram
how do you work out how many people speak both french and german, given that it's not stated above?

 

[boredsatan]

bump

 

[boredsatan]

solve cos(x) = 0.5, (-4pi to 4pi)
base = pi/3,
+ve rotation
x = pi/3, 2pi-pi/3 = 5pi/3
pi/3 + 2pi = 7pi/3
5pi/3 + 2pi = 11pi/3

-ve rotation
x = -pi/3, x = -2pi + pi/3 = -5pi/3
-2pi - (-pi/3) = -5pi/3
-2pi - (-5pi/3) = -pi/3

are these answers right?

 

[1729]

solve cos(x) = 0.5, (-4pi to 4pi)
base = pi/3,
+ve rotation
x = pi/3, 2pi-pi/3 = 5pi/3
pi/3 + 2pi = 7pi/3
5pi/3 + 2pi = 11pi/3

-ve rotation
x = -pi/3, x = -2pi + pi/3 = -5pi/3
-2pi - (-pi/3) = -5pi/3
-2pi - (-5pi/3) = -pi/3

are these answers right?

cos(x) is an even function so cos(x) = cos(-x). If you have 7pi/3 and 11pi/3, you must also have -7pi/3 and -11pi/3.

 

[1729]

in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
draw a venn diagram
how do you work out how many people speak both french and german, given that it's not stated above?

10,000 people
7,500 German
4,500 French
1,000 Neither

If N people speak both,
(7500 - N) + (4500 - N) + N + 1000 = 10000
N = 3000 people

 

[boredsatan]

A is a matrix of order (3*5) and the order of the matrix product AB is (3*1) then what is the order of matrix B? How would you work it out?

 

[InteGrand]

A is a matrix of order (3*5) and the order of the matrix product AB is (3*1) then what is the order of matrix B? How would you work it out?

Remember, the general rule is if A is (m x n) and B is (n x p), then AB is (m x p).

Since A is (3 x 5) and AB is (3 x 1), we must have that B is (5 x 1). (No. of rows of B must be 5 in order for B to be compatible with A in the product AB, and no. of columns of B must be 1 in order that the no. of columns in the result AB is 1.)

 

[BenHowe]

If pr(A) = 0.45, pr(B) = 0.35, and pr(A inverted u B) = 0.25, how would you find Pr (A' inverted u B')

It helps if you draw a venn diagram or you can alternatively use de Morgan's Laws

 

[boredsatan]

It helps if you draw a venn diagram or you can alternatively use de Morgan's Laws

Thanks for replying to my post which was over a month ago!

 

[boredsatan]

2^x = 7
How would you solve for x without a calculator using logarithms?

 

[jathu123]

2^x = 7
How would you solve for x without a calculator using logarithms?

if you want the exact value of x;
take the log of both sides to get log(2^x)=log(7)
now apply the rule log(a^b)=blog(a) on the LHS to get xlog(2)=log(7)
hence x=log(7)/log(2)
put this on the calc if you want an approximation

 

[boredsatan]

if you want the exact value of x;
take the log of both sides to get log(2^x)=log(7)
now apply the rule log(a^b)=blog(a) on the LHS to get xlog(2)=log(7)
hence x=log(7)/log(2)
put this on the calc if you want an approximation

It's a tech free question though

 

[jazz519]

It's a tech free question though

He gave you the answer and working without using a calculator (they aren't going to ask you to approximate the value of x without a calc, i.e the exact value which is in the 2nd last line of working)

 

[pikachu975]

It's a tech free question though

Then the answer is x = ln7/ln2

 

[boredsatan]

10^x = 2
Would x = log(2)/log(10)?

 

[boredofstudiesuser1]

10^x = 2
Would x = log(2)/log(10)?

yes

 

[boredsatan]

yes

thanks

 

[boredsatan]

A carpenter charges 68$ per hour of service (10% of gst included)
calculate the amount of gst
10% of 68 = $6.8 of gst
Someone said you had to divide by 11 instead of 10
If the hourly rate was increased by 8.5%, calculate the new hourly rate (with gst included)
Is the answer $73.8?

I didn't have a calculator on me

 

[boredsatan]

A carpenter charges 68$ per hour of service (10% of gst included)
calculate the amount of gst
10% of 68 = $6.8 of gst
Someone said you had to divide by 11 instead of 10
If the hourly rate was increased by 8.5%, calculate the new hourly rate (with gst included)
Is the answer $73.8?

I didn't have a calculator on me

Anyone?

 

[BLIT2014]

Anyone?

I think GST would be 6 and 2/11 or $6.1818...

To work out GST if it is included, the formula is gst inclusive price * 1/11

To work out amount without GST 10/11 * gst inclusive price.