12x + 4y = 10
4x - 8y > 8
Answer:
Step-by-step explanation:
Answer:
36
Step-by-step explanation
9x4=36
12x3=36
Answer:
The smallest possible number Megan is thinking, is 36.
Step-by-step explanation:
In order to answer this question, you have to find the LCM of 9 and 12.
9 = 3 x 3 (simplified)
12 = 3 x 4 (simplified)
This means that 3 and 4 are both common factors in these two numbers.
Now, multiply the common factors with the uncommon factor.
3 is an common factor, and 4 is an uncommon factor
Hence, we do 3 x 3 x 4 which is equal to 36
2x² – 5x + 3 = m(x)
Answer:
Step-by-step explanation:
For quadratic ax² +bx +c, the axis of symmetry is x = -b/(2a). For your function, a=2, b=-5, c=3 and the axis of symmetry is ...
x = -(-5)/(2(2)) = 5/4 = 1.25
The vertex is on the axis of symmetry. The y-value there is ...
m(5/4) = (2(5/4) -5)(5/4) +3 = (-5/2)(5/4) +3 = -25/8 +24/8 = -1/8
The vertex is (5/4, -1/8).
The axis of symmetry is x = 5/4.
The leading coefficient is positive, so the parabola opens upward. The vertex is a minimum.
The minimum is -1/8.
The function is defined for all values of x, so ...
the domain is all real numbers.
Values of y can only be -1/8 or greater, so ...
the range is y ≥ -1/8.
There are
the seats are chosen
ways that 4 seats can be left empty in the auditorium. This is a
important.
Answer:
5773185
Step-by-step explanation:
There are 110 seats
110 ways to choose the first empty seat
Now there are 109 seats
109 ways to choose the next empty seat
Now there are 108 seats
108 ways to choose the next empty seat
Now there are 107 seats
110*109*108*107=138556440
Now the order of the empty seats doesn't matter so we need to divide by 4!
138556440/ 4!
138556440/ 24
5773185
In this mathematics problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. We can use the concept of combinations to solve this.
In this problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. To solve this, we can use the concept of combinations. The total number of ways to choose 4 seats out of 110 is represented by the combination formula: C(110, 4). To calculate this, we can use the formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of seats and r is the number of seats left empty. Plugging in the values, we have C(110, 4) = 110! / (4!(110 - 4)!).
Using a calculator, we can simplify this expression and calculate the answer.
#SPJ12
Answer:
And replacing we got:
Step-by-step explanation:
Previous concepts
A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Solution to the problem
For this case our random variable is given by:
For this case we want this probability:
And replacing we got:
In this binomial distribution scenario, the parameter 'p', representing the probability of success on each trial, is the probability of the pitcher throwing a strike, which is 0.721.
In the binomial distribution scenario you described, the softball pitcher throwing a pitch is the independent trial with two possible outcomes: throwing a strike (success) or a ball (failure). The parameter p represents the probability of success on each independent trial. From the question, we can see that the probability, or p, of the pitcher throwing a strike (success) is 0.721. Therefore, p = 0.721.
Please note that the binomial distribution model can be used when all trials are independent, the outcome of a trial is success or failure, and the probability of success remains the same for each trial. It doesn't appear that we need the number 'n' of independent trials or the random variable 'X' representing the number of successes (strikes in this case) for your question, as we were only asked for the value of 'p'.
#SPJ12
Answer:
k < -2
Step-by-step explanation:
Step 1: Write inequality
4k + 2(3k + 8) < 3k + 10 - 8
Step 2: Solve for k
Answer:
10k+16<3k+2
10k-3k+16<2
7k<2-16
k<-2