Answer:


Step-by-step explanation:
Given

Required
Select equivalent expression





Start by solving the given expression (using a calculator)

Then we solve the given options (using a calculator)










The equivalent expressions are (a) and (e)
Answer:
Fast ball challenge
Step-by-step explanation:
Given
Slow Ball Challenge




Fast Ball Challenge




Required
Which should he choose?
To do this, we simply calculate the expected earnings of both.
Considering the slow ball challenge
First, we calculate the binomial probability that he hits all 7 pitches

Where
--- pitches
--- all hits
--- probability of hit
So, we have:




Using a calculator:
--- This is the probability that he wins
i.e.

The probability that he lose is:
---- Complement rule


The expected value is then calculated as:


Using a calculator, we have:
Considering the fast ball challenge
First, we calculate the binomial probability that he hits all 3 pitches

Where
--- pitches
--- all hits
--- probability of hit
So, we have:



Using a calculator:
--- This is the probability that he wins
i.e.

The probability that he lose is:
---- Complement rule


The expected value is then calculated as:


Using a calculator, we have:

So, we have:
-- Slow ball
--- Fast ball
<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>
35% off means that now it costs 100%-35%=65% of the original price
<span>£78 ---- 65%
x------100%
x=78*100/65=120</span>£<span>
or
part/whole=0.65
78/whole=0.65
whole =78/0.65 =120 </span>£
Answer:
x = 4, -2 1/2
Step-by-step explanation:
factors:
(2x + 5) (x - 4)
set each factor equal to zero:
2x + 5 = 0
2x = -5
x = -5/2
x - 4 = 0
x = 4
Answer:
I gave you most of the answer. I'll let you check my work and find the point using the solution.
Step-by-step explanation:
The first thing we do is we divide by negative one in the first equation to get
y = -x.
-3x + 3y = -36
Plug in y = -x and get
-3x + 3(-x) = -36
= -3x - 3x = -36
This equals -6x = -36
divide both sides by -6 and you get 6. 6 is your x value
Plug 6 back in to the second equation.
-3x + 3y = -36
-3(6) + 3y = -36
-18 + 3y = -36
3y = -18
y = -6