Which of the following graphs represents the solution set for the inequali -35-2x +1 <11
1 answer:
Answer:
You did not give the options, so i just will graph it.
The inequality is:
-35 - 2*x + 1 < 11.
Now we would want to isolate the x in one side, so we can start by adding 35 in both sides.
(-35 -2*x + 1) + 35 < 11 + 35
-2x + 1 < 46
now we can subtract 1 in both sides:
-2x + 1 - 1 < 46 - 1
-2x < 45
Now we can divide by -2, remember that if we multiply or divide by a negative number, then the "direction" of the sign changes.
(-2x)/-2 > 45/-2
x > -22.5
Then the graph of the set is an open dot at the point x = -22.5 (this means that the set does not include this point) and a line that extends to the right. (Extends to the right because x is larger than -22.5)
Below is an example of how to draw the graph that represents the set of solutions.
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Answer:
So, equation for 7 more than a number is 10 is
Step-by-step explanation:
We need to write equation for 7 more than a number is 10.
For writing the equation, we first consider a number. Let the number be x
7 More than a number in mathematical form is translated as :
So, equation for 7 more than a number is 10 is
Answer:
a) 2¹³
b) 0.0873
c) 0.9983
d) 0.9538
Step-by-step explanation:
a) How many different outcomes are possible?
For every toss, there are two possible outcomes (heads or tails), so if we toss the coin 13 times the total of outcomes possible is 2¹³
b) What is the probability of getting exactly 4 heads?
The definition of probability is an event is: number of favourable events/ number of total events.
When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by
where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.
So we have to know how many different ways we can get exactly 4 heads.
let's name p = probability of getting heads = 0.5
1 -p = probability of getting tails = 0.5
We are going to toss the coin 13 different times and we want to get heads 4 times and tails 9 times.
So, by the Binomial Distribution we would have:
P(X=4) = 13C4 (0.5)⁴(0.5)⁹ = 715 (0.5)¹³ = 0.0873
Thus, the probability of getting exactly 4 heads is 0.0873.
c) What is the probability of getting at least 2 heads?
We are going to use the same binomial distribution but now we need at least to heads, this can be written as <u>1 - (P(X=0) + P(X=1))</u>
P(X=0) + P(X=1) = 13C0 (0.5)⁰(0.5)¹³ + 13C1 (0.5)¹(0.5)¹² = 0.0001220703125 + 0.0015869140625 = 0.001708984375
1 - 0.001708984375 = 0.998291015625
The probability of getting at least 2 heads is 0.9983
d) What is the probability of getting at most 9 heads?
We are going to use the same binomial distribution but now we need at most 9 heads. This can be written as <u>1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13))</u>
1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13)) =1 -(13C10(0.5)¹⁰(0.5)³ + 13C11(0.5)¹¹(0.5)²+ 13C12(0.5)¹²(0.5)¹ + 13C13(0.5)¹³(0.5)⁰) = 0.95385742188
The probability of getting at most 9 heads is 0.9538