All Answers 355934 Answers

susy: x

mary: y

x=2/3y

x+1/2y=210

therefore

2/3y+1/2y=210

4/6y+3/6y=210

7/6y=210

y=180 (Mary)

x=180*2/3=120 (Susy)

easy peazy

so write like this:

20 people -> 4800 @36min

9 people   -> 3600

now we have to find efficiency of each person

20*36min*efficiency = 4800

efficiency = 6.66667

therefore, 9 people * 6.6667 * time = 3600

time = 60 minutes

Easy peazy

um the picture is blocked on my browser. You might have to screenshot it.

On my PC the picture is clear enough. What part do you not understand? Let me know.

In number 3, can you use a calculator?

If so:                               cos(5°)  =  sin(25°)  + sin(X)

                        cos(5°) - sin(25°)  =  sin(X)

Using inv(sin):

     --->        =  35°             

Sorry that I couldn't answer all of these fully or properly I assume, still getting the hang of it. 

I'll try #!:

Using the formula:  cos(X) + cos(Y)  =  2·cos( (X + Y)/2 ) ·cos( (X -Y)/2 ):

Let  ax = 4x  and  bx  =  4x:  cos(ax) + cos(bx)  =  cos(4x) + cos(4x)   2 · cos( (4x + 4x)/2 ) · cos( (4x - 4x)/2 )

                                                                           =  2 · cos( 8x/2 ) · cos( 0/2 )

                                                                           =  2 · cos(4x) · cos(0)

                                                                           =  2 · cos(4x) · 1

                                                                           =  2 · cos(4x)

Let  cx = 3x  and  dx  =  1x:  cos(ax) + cos(bx)  =  cos(3x) + cos(x)   2 · cos( (3x + x)/2 ) · cos( (3x - x)/2 )

                                                                          =  2 · cos( 4x/2 ) · cos( 2x/2 )

                                                                          =  2 · cos(2x) · cos(x)

So we have:  2 · cos(4x) · 2 · cos(2x) · cos(x)  =  4 · cos(4x) · cos(2x) · cos(x)

Choose  cos(4x) + cos(4x) + cos(3x) + cos(1x)

Let John's hourly rate =j
Sarah's hourly rate      =j + 6
1/j + 1/(j+6) = 1/4, solve for j
j = 6 hours - time that John needs to paint the room by himself.
6 + 6 = 12 hours - time that Sarah needs to paint the room by herself.

Paper rectangle ABCD is folded in such a way that the fold passes through point B, and so A coincides with point H where H ∈ CD. BK is the folding line where K ∈ AD. m∠BKD = 120°. If BK = 28 cm, find BC.

BK = 28 cm

AK = sin(30°) * 28 = 14cm

AN = cos(30°) * 14 = 12.125cm

AH = 2 * AN  = 24.25cm

AD = cos(30°) * 24.25 = 21cm

AD = BC = 21 cm            

We need a better description or a picture Dragan.  

THANKS!

You can track the probabilities using different case, i.e. Anty gets to 0 after 1 steps, 2 steps, 3 steps, and so on.  This gives us e_1 = 1/2*1 + 1/4*2 + 1/8*3 + 1/16*4 + ... By arithmetico-geometric series, e_1 = 2.  Similarly, e_2 = 1/2*2 + 1/4*3 + 1/8*4 + 1/16*5 + ... = 3, so (e_1,e_2) = (2,3).

The x^y  button right next to '7'

I also need help with these problems, ASAP!

6) If the centre of the circle passing through the origin is $(3,4)$,then the intercepts cut off by the circle on the x-axis and y-axis respectively are what?

7) Let $ABC$ be an acute angled triangle. The circle $L$ with $BC$ as diameter intersects $AC$ again at $P$ and $Q$, respectively. Determine angle $BAC$ (in degrees) given that the orthocentre of triangle $APQ$ lies on $L$.

8) Given the circle with center at $L$, $MRST$ quadrilateral with vertices on the circle $L$, and a circle $O$ inscribed in the quadrilateral, such that
\[ \overline { RM } =17, \ \overline { MT } =19, \ \overline { TS } = 23 \]
What is the value of $ \overline{RT} \times \overline{MS} $? 

9) If the area between three tangent circles of equal radii is $144-\pi^{4} $ and a circle tangent to all three of these circles  has an area A. What is $ \lceil A\rceil$. 

10) If the circle passing through distinct points $(1,t), (t,1),(t,t)\ \forall\ t\in R$ also passes through a fixed point $(a,b)$, then calculate argument of complex number $a+ib$ in radians.

11) In the fig. given below, $O$ is the center of the circle. If $PA = 12$cm, $PC = 15$cm and $CD = 7$cm. Find length of $AB$.

12) Let circle $A$ be a circle with radius $\sqrt{5}$ centered at $(2,0)$ and circle $B$ be a circle with radius $2$ centered at $(-1,0)$ Let the center of circle $A$ be $A_C$ and the center of circle $B$ be $B_C$. The two circles $A$ and $B$ intersect at points $X$ and $Y$. When the area of quadrilateral $X A_C Y B_C$ is expressed in the form $a \sqrt{b} $ where $b$ is nor divisible by the square of any prime, find $a+b$ 

From a sigma calculator:

https://web2.0calc.com/questions/can-anyone-please-solve-this-mathematics-question

https://web2.0calc.com/questions/maths-question_22

https://web2.0calc.com/questions/can-anyone-please-solve-this-mathematics-question

Yes you are right. Excellent spotting!

I have edited my answer acordingly.

Count the total number of possibilities:  36

Count the number which are red and have a number less than 5:  4

Count the number which are yellow and have a number less than 5: 4

Add these together (=8) and divide by the total number of possibilities (=36).

Probability  =  8/36

This is an arithmetic series, first term = 0.30, last term = 0.50, with the number of terms = 21.

A formula for the sum of an arithmetic series is:  Sum  =  [ number · (first + last) ] / 2

                                                                             Sum  =  [ 21 · (0.30 + 0.50) ] / 2

                                                                             Sum  =  8.40

This can be checked by summing all the individual terms.

The angle  QPR = 28°