Choose the number sentence that illustrates the distributive property of multiplication over addition.
1 answer:
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Answer:
Possible values of dimensions are (24,16,2) or (24,8,4)
Step-by-step explanation:
We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.
Let us say that the width is x and height is y
Length = 24
Volume of a cuboid = length * width * height
Volume = 768
768=24*x*y
xy=32
Now the possible factors of 32
32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can not be more length)
32=2*16
32=4*8
Hence the possible values width are 8, 16 and that of height 4 and 2
Hence the possible values of dimensions are (24,16,2) or (24,8,4)
This situation has two outcomes: either an invoice is discounted or not. This two outcomes satisfy what we call a binomial distribution (note "bi" in binomial).
The binomial distribution tells us the probability that a randomly selected sample will have the outcome of success. In this case, we consider receiving the discount as the "success" outcome while not receiving it means "failure". The distribution takes the form:
where n is the total number of samples, x is the number of samples you'll expect to have a success outcome, p is the probability of success, q is the probability of failure, and nCx is the combination of n samples taken x at a time.
You have an inconsistency regarding the total number of samples by the way, but I will take the first mentioned sample of 15 as I answer (you can just follow through the same process for another value).
For the next step, let's digest the problem to get the needed variables.
The total number of samples, n, is equal to 15. The probability of success (receiving a discount), p, is 10% or 0.1, and the probability of failure (not receiving a discount) is 90% or 0.9.
For P(X=x), we need to find the probability that less than two of the samples have success outcomes therefore we need to find the probability that NO invoice will receive the discount plus the probability that ONE invoice will receive the discount. This is equivalent to saying
Calculating these probabilities we'll get:
ANSWER: The probability that fewer than 2 sampled invoices will receive the discount is 0.549 or 54.9%.
The binomial distribution tells us the probability that a randomly selected sample will have the outcome of success. In this case, we consider receiving the discount as the "success" outcome while not receiving it means "failure". The distribution takes the form:
where n is the total number of samples, x is the number of samples you'll expect to have a success outcome, p is the probability of success, q is the probability of failure, and nCx is the combination of n samples taken x at a time.
You have an inconsistency regarding the total number of samples by the way, but I will take the first mentioned sample of 15 as I answer (you can just follow through the same process for another value).
For the next step, let's digest the problem to get the needed variables.
The total number of samples, n, is equal to 15. The probability of success (receiving a discount), p, is 10% or 0.1, and the probability of failure (not receiving a discount) is 90% or 0.9.
For P(X=x), we need to find the probability that less than two of the samples have success outcomes therefore we need to find the probability that NO invoice will receive the discount plus the probability that ONE invoice will receive the discount. This is equivalent to saying
Calculating these probabilities we'll get:
ANSWER: The probability that fewer than 2 sampled invoices will receive the discount is 0.549 or 54.9%.
Answer:
After solve the equations we get value of k=3
Step-by-step explanation:
We need to find value of k for which the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent.
If the lines are concurrent, they pass through same point.
Let:
First solving equation 1 and 2 to find values of x and y
From eq(1) we find value of x and put it in eq(2)
After solving we get value of y=-1
Now putting in eq(1) to get value of x
So, Value of x= 2
Now put value of x=2 and y=-1 into eq(3) to find value of k
So, After solve the equations we get value of k=3