Answer:
The Substitution Property of Equality allows you to say that if 7j + 14k = 28, and j = 2, then k = 1 .
Step-by-step explanation:
As the expression is given in the question be as follow .
7j + 14k = 28
As given the value of j = 2 .
Put the value of j in the equation 7j + 14k = 28 .
7 × 2 + 14k = 28
14 + 14k = 28
14k = 28 - 14
14k = 14
k = 1
Therefore the Substitution Property of Equality allows you to say that if 7j + 14k = 28, and j = 2, then k = 1 .
We are given
The value -2 is a lower bound for the zeros of the function shown below f(x)=4x^3-12x^2-x+15
So, firstly, we will find value of f(x) at x=-2
we will plug x=-2 into f(x)
we get
we will plug x=-2
now, we can simplify it
so,
we know that any zeros always lies between positive and negative value
Here , we got f(-3)=-63 ...which is negative value
so, this is lower bound
Hence , this is TRUE
Answer: a) 146 units used b) the cost of the number of units used is 3136 p.
Step-by-step explanation:
Since we have given that
First 100 units = 24 p per unit
Remaining units = 16 p per unit
New reading = 7143 units
Old reading = 6997 units
Difference between the readings would be
So, there are 146 units used.
(B) Calculate the cost of the number of units used
There are 146 units
For the first 100 units = 24 p per unit
For the remaining i.e. 146-1400 = 46 units , cost = 16 p per unit
Total cost of the number of units used is given by
Hence, a) 146 units used b) the cost of the number of units used is 3136 p.
Answer:
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 assuming numbers (0,1,2,3,4,5,6,7,8,9) so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
Step-by-step explanation:
Previous concepts
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".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The conditions to apply this distribution is that we have the parameters fixed n and p.
Let's analyze one by one the possible solutions:
a. The number of traffic tickets written by each police officer in a large city during one month.
False, the number of traffic tickets written by each police is not a fixed amount always, so then the value of n change and we can't apply a binomial model for this case.
b. The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled.
False, not all the hands of size 5 are equal and since we can't ensure this condition then the binomial model not apply for this case
c. The number of 7's in a randomly selected set of five random digits from a table of random digits.
True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.
d. The number of phone calls received in a one-hour period.
False, the number of phone calls change by the hour and is not always fixed so then we don't have a valu for n, and the binomial model not applies for this case.
e. All of the above.
False option C is correct.