Answer:
9x-4
Step-by-step explanation:
add 5x and 4x
9x-3-1
subtract 1 from -3
9x-4
Answer:
1 and 4 are correct. 2 and 3 are not.
Step-by-step explanation:
1.
When x = 0 where does the horse start?
y = 1.5*sin(0 + 0.5)*2*pi + 1.5
y = 1.5*sin(0.5*2pi) + 1.5
y = 1.5*sin(pi) + 1.5 But sin pi = 0
y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.
2.
This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.
3.
You can figure this one out by letting x = 0.01 When it does then the value of the function is
y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5
y = 1.5*sin(0.51*2*pi) + 1.5
y = 1.5*sin(3.204424) + 1.5
y = 1.5*(- .0623) + 1.5
y = -0.9418 + 1.5
y = 1.4058 so it is going downward The value is getting smaller.
4.
The horse starts out in the middle of the pole. What does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)
That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.
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Answer: Correct two digit number= 24
Step-by-step explanation:
Let
x= tens digit (wrong one)
and y= zeroes digit
and z= tens digit (right one)
Now according to the statement,
(10x+y)² - (10z+y)² = 2340
Simplifying this we get
(x-z)(5x+y+5z)= 117= 1 * 3 * 3 * 13
So it could either be
x-z=1 or x-z=3
If we take the x-z=1
then 5x+y+5z=117
which is not possible as maximum value we can get from this is 99.
This leaves us with x-z=3
so 5x+y+5z= 39
Put x=3+z
We get,
y+10z= 24
Now as y and z both are single digits so the only possible numbers to fit these are y=4 and z=2.
Put z=2 in x=3+z , we get x=5
So the numbers become 10x+y= 54
and 10z+y= 24
Their sum is 54+24=78
Check
54²-24²= 2340 so it is correct.
Answer:
a)P=0.42
b) 
Step-by-step explanation:
We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:
a) we have k=2, n=10 and p=0.01:
b) We have, 
, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.
