Grade Eleven Answers
Grade Eleven Answers
Answer:
5 tires 5000kms
4 at each time
4 * 5000km = 20,000km travelled by 4 tires.
20,000/5 = 4000km each
START OUT:
Distance |
Travelled | #1 #2 #3 #4 #5
------------+-------------------------------------------
1000 | x x x x
|
2000 | x x x x
|
3000 | x x x x
|
4000 | x x x x
|
5000 | x x x x
|
Answer:
Area of the region = (3Pi-24)/4
Answer:
A_i=5/8*B_iA_e=1/2*B_e
0.4*(5/8*B_i)=5/8*B_i - 1/2**B_e
0.375*B_i=1/2*B_i
B_e=0.75B_i Therefore Basil saves 25% of his income.
Answer:
Angle D = 40 degrees
Let angle DFE = X
Angle FBC = X
Angle BCF = 180 - 2X
Angle DEF = 180 - 40 - X = 140 - X
Angle EAC = 140 - X
Angle ACE = 180 - 2 (140 - X)
= 180 - 280 + 2X
= -100 + 2X
180 - (-100 +2X + 180 - 2X) = Angle ACB
100 Degrees = angle ACB
Answer:
Length of ladder =[72+x2]1/2
Length of ladder = x+1
Therefore
(x+1)2=72 + x2
x2 + 2x + 1 = 49 + x2
2x + 1 = 49
2x = 48
x = 24
Therefore the ladder is originally 24 m from the wall. It is 25m long (x+1)
Answer:
Volume of 1/2 the tank
= 100cm * 40cm * 60cm
= 240000cm3
1/4 (240000) = 60000cm3
d * 100cm * 60cm = 60000
d = 10cm
Answer:
4.5 min 45r/min = 202.5 revolutions
202.5rev/33.3 r/m = 6.075 minutes.
Answer:
Area = 800m2
Todd must mow 400m2
length and width reduce by 2m
Time around the lawn Area remaining
start 20*40=800 m2
1 time 18*38=684 m2
2 times 16*36=576 m2
3 times 14*34=476 m2
4 times 12*32=384 m2
About 3 and 1/2 times he would have to go around the lawn to
do his share!!
Answer:
AB = ED = x meters
CD = BC = (15 -x)
Area of deck -> A(x) = x (15-x) + x(15-2x)
= -3x2 + 30x
= -3(x2 - 10x + 25) + 75
= -3(x-5)2 + 75
Maximum value of A(x) is 75 and occurs when x =5
The dimensions of the deck are 5m * 10m * 10m * 5m
Answer:
(x+4)2 + (x-3)2 = (2x-5)2
x2 + 8X + 16 + X2 - 6X + 9 = 4X2 - 20X + 25
2X2 - 22X = 0
2X (X-11) = 0
2X = 0 X-11 = 0
X=0 X=11
X cannot = 0, therefore X = 11
y2 = (11-3)2 + (11-5)2 z2 = 112 + 82
y = (64+36)1/2 = 10 z = (121+64)1/2 = (185)1/2
Answer:
6/h=sin2*theta
h=2sin theta*cos theta
h=3/(sin theta* cos theta)
L/h=1/cos theta=sec theta
L=3*sec2 theta* csc theta
Answer:
Let x = the number of jumps taken
3x = 45 + 2x
x=45
45 jumps he will have caught up with the rabbit
Answer:
(ac + bd)2 + (ad-bc)2 =
(ac)2 + 2acbd + (bd)2 + (ad)2 - 2adbc (+bc)2 =
(ac)2 + (bd)2 + (ad)2 + (bc)2 =
(a2 + b2) (c2 +d2)
Similarly (ac - bd)2 + (ad +bc)2 = (a2 + b2)(c2 + d2)
a=2 b=3 c=1 d=6
481 = (13)(37)
=(4+9) (1+36)
481 = (22 + 32)(12 + 62)
= (2(1) + 3(6)2 + (2(6) - (3)(1))2
= 202 + 92
or 481 = (22 + 32)(12 +62)
=(2(1) - (3(6))2 + ((2)(6) + (3)(4))2
= (-16)2 + 152
Answer:
300 Sheets * 12cm = 3600cm of sheets length
Thickness of one sheet 40.72cm2/3600cm = .011cm
6 - 4.8 = 1.2 cm
In 1.2cm of radii and .011cm thickness
.011(1.21/2)cm = 106 times
Answer:
k= 11.25
k-5.00 entering casino
2(k-5.00) -> leaving casino
2(k-5.00)-5.00 (after paying for parking)
(2k - 10) -10.00 = 2k - 20(after paying asmission to the second casino)
2(2k - 20) = 4k -40
4k - 40 -5 = 0
4k - 45 = 0
k = 11.25
Answer: BC=12.06 km
Answer:
(a) y = 16 + 15sin(Pi/60*750) = 31
(b) T = 2*Pi/(Pi/60) = 120
Maximum height:
sin(Pi/60)*x = 1 ==> x=30 ==> max height = y = 31 meters.
Answer: d = 2 *(7)1/2
Answer:
NOTE: All logs in this answer are in base 3.
40 = 20 + 5 log3(x+3) 120= 20 - 5 log3(x+3)
20 = 5 log3(x+3) 100= 5 log3(x+3)
4 = log(x+3) 20 + log3(x+3)
320 = x+3
X + 3 = 34 = 81
a) x = 78 b) 320 - 3 = x
Answer:
distance from (0,0) to y=2x-3
d=|-3|/[(222+(-1)2)]1/2=3*[(5)/5]1/2
r >= 3*[(5)/5]1/2 so the line and the
circle intersect.
Mike was wrong!
Answer:
n + m = $42.50/$.50 n = # of odd numbered digits
n + m = 85 M = # of even numbered digits
n - m = $5.50/$.50
n - m = 11
n + m = 85/ 2n = 96
n = 48 48 - m = 11
37 = m
n = 48 -> odd digits
3, 5, 7, 9 -> 4 single digit houses
1. 13, 15.....44/2 = 22 double digit houses.
22+4=26 houses in all.
The last number on the odd numbered side is 53.
Even numbered side needs an additional 11 digits to be equivalent to
the other side.
Trial and error should show that these are the missing numbers:
8, 10, 12, 14, 16, 18 <- 11 digits.
Answer:
abc 100a + 10b + c
a + b + c = 12
a - b = b - c
a > b + c
a + b + c = 12
-a + 2b -/+ c = 0/3b = 12
b = 4
a + c = 8
8 - c > 4 + c
4 > 2c
c < 2
abc is odd numbered so the digit "c" must be odd.
Hence c = 1, a = 7 and b = 4
DIGIT IS NUMBER 741
Answer:
Let y = Freshman class
Let x = Freshmen not from Dr. J.H.G. or Guysborough
300 + 1/2(400) + x = Freshman Class
500 + x = y
1/2 y = 300
y = 600
500 + x = 600
x = 100
100 must be coming from neither.
Answer:
m + n = 11 + 5 = 16
Answer:
1/2
TRICKY -> For those people who went through the problem to
answer the question, what is the probability of getting eleven
heads in a row with a fair coin?
1/2 * 1/2... = (1/2)11 = 1/2048
11 times
Answer:
21.5% of the field is not watered.
Answer:
Alf and Bert are guilty. If Bert is innocent, then Bash is
innocent and Alf if guilty; but Alf never works alone.
Therefore, no one is guilty. Therefore, Bert cannot be
innocent; he must be guilty. If Bert is guilty, then Cash
is innocent and Alf if guilty.
Answer:
Area of the circles= 3*Pi/2
DC=AB=3
DA=CB=31/2+1
Area of rectangle =3(31/2+1)
Area not covered = 3*31/2+3-3*Pi/2
Answer:
3 + 4 = 7
32 = 27 34 = 81
54 + 43 = 625 + 64 = 689
b)
2 @ 8 = -2
A possible rule: 3 times the first number minus the second
number.
Answer:
10 (3,6,6) (6,6,3)
(4,5,6) (6,5,4)
(4,6,5) (6,4,5)
(5,4,6) (6,3,6)
(5,6,4)
(5,5,5)
Answer:
The family keeps the small cupboard (s) for daily access to
wine. When s becomes empty, they transfer the bottles from
the main stock in the large cupboard (l).
More than 1 times - s or l cannot be opened.
n bottles of wine were bought
they drink one immediately
put 11 into s for consumption during the next 11 days
n-12 -> in l.
When l is exposed the second time only 10 bottles can be
transferred into s.
Family takes 11 from l, drink 1, that day and put 10 into s
for use for next 10 days, leaving n-12-11 bottles in l. The
next time l is opened only 9 can be put into s and 1 drunk
immediately leaving n-12-11-10 bottles in l, exposed 3
times.
n - 12 - 11 - .....-3 - 2 bottles exposed 11 times.
Now when l is opened, only one bottle must remain to be
drunk right away as it has been exposed 12 times.
n - 12 - 11 - ..... - 3 - 2 = 1 Chateau family buy every
78 days.
Answer:
How much is left unpainted?
Original area = A
1color 1st square - leaving 8/9 A
2 8 squares - leaving 8/9 x 8/9 A unpainted
3 8 x 8 squares - 8/9 x 8/9 x 8/9 A unpainted
4 83 - (8/9)4 A unpainted
5 84 (8/9)5 = .555 A
6 85 (8/9)6 = .493 A remains
So after 6 colors are used, over half the canvas is covered.
TOTAL number of squares painted:
1 + 8 + 82 + 83 + 84 + 85 = 37449
Answer:
Volume = 2x x y/2 x 1 = xy cm3
Answer:
Line perpendicular to a, has slope - m
and equation p = -mx + b
o = -mx + b
+b = mx
+b/m = x (b/m,0)
a2 = mx + f <- line a2
0 = m(b/m) + f
-b = f
The y intercept of y2 is -b
Answer:
a)
x = log103 / log2 3
x = log102
b)
0 - because the cot 90 degrees = 0 !!!
Answer:
Player | Weight | Cumulative Number | | Average ----------+--------------+-------------- | | 1 | x | x 2 | x+2 | x+1 3 | (x+1)+3 | x+2 4 | (x+2)+4 | x+3 5 | (x+3)+5 | x+4 Fifth player weighs 8 more kilograms than the first! When difference is 2 lbs ->5th player weighs 16 more kilograms.
Answer:
n = # of coins in her purse.
15n + 10 = 14(n+1)
n=4
4 coins totalling 60 cents are two nickels and two
quarters.
Answer:
"A" denotes the value of a unit of money at a given time, then 9A denotes
its value a year later and (.9)n A is its value n years later.
(.9)n A =< A/10
(9/10)n =< 1/10
log10(9/10)n =< log10 (1/10)
n(2 log10 3 - 1) =< -1
n >= 1/1-2 log10 3 = 21.7
Answer:
Let n be the last number on the board. The largest possible
average is obtained if the digit 1 is erased; the average is
then
(2+3+...+n)/(n-1)=((n+1)n/2-1)(n-1)=(n+2)/2
The smallest average possible is obtained when n is erased the
average then:
n(n-1)/2(n-1) = n/2 1+2+.......n-1/n-1
Thus
n/2 <= 35 7/17 <= n+2/2
n <= 70 14/17 <= n+2
68 14/17 <= n <= 70 14/17
Therefore
n = 69 pr 70. Since 35 7/17 is the average of (n-1)
integers (35 7/17)(n-1) must be an integer and n is 69.
If x is the number erased.
1/2(69)(70)-x/68 = 35 7/17
69 ??? 35 - x = 35 (7/17) 68
x = 7
Answer:
All multiples of 8 fall into the second column.
So 1000 must fall here!
Answer:
Extend BN past N and meets AC at E
Triangle BNA = Triangle ENA
congruent
Since angle BAN = angle EAN
AN = AN
Angle ANB = angle ANE
Therefore N is the midpoint of BE
and AB = AE = 14
Therefore EC = 5
MN is the line joining the midpoints of sides BC and BE of
triangle CBE, its length is 1/2(EC) = 5/2
Answer:
Let W, X, Y, Z be amounts paid by Mark, Mike, Lawrence and
Joshua respectively.
w+x+y+z = 60
w=1/2(x+y+z) = 1/2(60-w) w=20
x=1/3(w+x+z) = 1/4(60-y) y=12
1/4(20+15+z) = 12
20+15+z= 48
z=48-35 = 13
Joshua paid $13.00 for the motorbike!
Answer:
Assume it come to rest with one end against the rim at the
bottom of the pan and the other end touching the side at point A.
y = (262 - 242)1/2
= 10cm
The minimum depth = 10cm
Radius of pan = 12cm
V = ((12)2 * 10)Pi = 4523.9cm2
Answer:
Jerome rides x km at 12 km/hr
" walks 16-x km at 5 km/hr
Total time Jerome = x/12 + (16-x)/5
Meanwhile...
4 km/hr walks x to the bike
10 km/hr rides 16-x km to home
Total time Fred = (16-x)/10 + x/4
(16-x)/10 + x/4 = x/12 + (16-x)/5
x = 6 km
They take 2 1/2 hours to get home.
Jerome should ride for 1/2 hour.
Answer:
m = k and m = n-k stars are of identical shapes.
Ex: n = 7, M=1, and m=6 produce the same star.
m=2, m=5, m=3, and m=4. When m and n share a common factor > 1, the
other star can be split into two or more smaller ones.
If m = n/2, the figure produced is not a star but two coincident
straight lines.
| M | Total number
| | of Stars
-------+-----------------------+----------------
7 | 1 2 3 | 3
| |
8 | 1 3 | 2
| |
9 | 1 2 4 | 3
| |
10 | 1 3 | 2
| |
15 | 1 2 4 | 4
Answer:
Area = 2 + 8 + 32 = 42
Area of triangle = 1/2 (4 + 2 + 8) -4 = 28
Area of shaded region = 14 units2
Answer:
29
The enemy will count the number of troops in the corner position twice.
30th
5 5 5 6 4 5 6 4 5 8 7
5 5 -> 4 5 -> 4 4 ->....
5 5 5 5 3 5 5 4 6 7 8
When the general
jumps into the
corner.
When the reinforcements arrive the enemy are about to charge
so there are 29 active defenders left.
Answer:
_ _
Porche travels (x+15km/hr) * (1.3 hours) = 1.3x + 20km
_ _
Chevette x km/hr * 1.3 hours = 1.3x km
_ _
(100km)2 = (1.3x)2 + (1.3x + 20)2
_ _ _
1002 = 1.3x2 + 1.3x2 + 53.3x + 400
_ _
1002 = 3.5x2 + 53.3x + 400
_ _
0 = 3.5x2 + 53.3x - 9600
_ _ _ _
x = [-53.3 +/- [(53.3)2 - 4(3.5)(-9600)]1/2] / 2(3.5)
_ _
= [-53.3 +/- 373.3] / 7.111
x = 45 km/hr
Chevette was travelling at 45 km/hr
Porche was travelling at 60 km/hr
Answer:
10x + 15Y = 360
10(x-2) + 15 (y/2) = 220
10x + 15y = 360
-20(x-2) - 15y = - 440 / 10x - 20x + 40 = -80
-10X = -120
X = 12 CATS
10(12) + 15Y = 360
15Y = 240
Y = 16
12 Cats
16 Canaries
Answer:
NOT POSSIBLE POSSIBLE
Father 36 49
Mother 18 36
Daughter 9 9
51)
Answer:
The thief stole 36 diamonds originally!!