Answer:
D
Step-by-step explanation:
Let x be Bill’s scores.
Let y be Theo’s scores.
x + y = 90
x² = y
Solve for x in the second equation.
x = √y
Put x as √y in the first equation and solve for y.
√y + y = 90
√y = 90 - y
y = (90 - y)²
y = - y² - 180y - 8100
0 = -y² - 181y - 8100
0 = (-y+81)(y-100)
-y+81=0
y = 81
y - 100 = 0
y = 100
100 does not work if we plug in to check, so y is 81.
y = 81
Put y as 81 in the first equation and solve for x.
x + 81 = 90
x = 9
Bill scored 9 goals and Theo scored 81.
Answer:
you should play the game with the probability of winning is one tenth
Step-by-step explanation:
If the probability of winning an instant prize game is one tenth, <u>then the odds in the game can be described as 1:9</u> . The odds are clearly better than the game with odds 1:10.
In other words,
If the odds of winning a instant prize game are 1:10, <u>then the probability of winning the game is one eleventh</u>. This is a lower probability than the game which has the probability of winning one tenth.
9514 1404 393
Answer:
7×10⁻¹ +6×10⁻² +5×10⁻³
Step-by-step explanation:
Place value in any place-value number system increases by a factor of the base for each place to the left of the "decimal" point. It is reduced by a factor of the base for each place to the right of the "decimal" point.
For base-10 numbers, the powers of 10 are -1, -2, -3, ... as you go to the right of the decimal point. Hence the number 0.765 decomposes as ...
7×10⁻¹ +6×10⁻² +5×10⁻³
Answer:
12 boys
Step-by-step explanation:
From the above question:
Number of boys = 3
Number of girls = 2
Boys: Girls
3:2
Let :
a = boys
b = girls
Hence, a : b = 3 : 2
a/b = 3/2
Cross Multiply
2a = 3b .......... Equation 1
a = 3b/2
If four more girls join the class, there will be the same number of boys and girls
Hence,
a: b + 4 = 3 : 3
a/b + 4 = 3/3
Cross Multiply
3a = 3(b + 4)
3a = 3b + 12 ........ Equation (2)
From Equation 1: a = 3b/2
Substitute 3b/2 for a in Equation 2 we have:
3a = 3b + 12 .........Equation 2
3(3b/2) = 3b + 12
9b/2 = 3b + 12
Cross Multiply
9b = 2(3b + 12)
9b= 6b + 24
9b - 6b = 24
3b = 24
b = 8
Substitute 8 for b in Equation 1
a = 3b/2
a = 3 × 8/2
a = 24/2
a = 12
Therefore, the number of boys in the class is 12
