Explain why it is necessary to rename 4 1/4 if you subtract 3/4 from it

1 answer:

8 0

You would rename four and one fourth when subtracted from three fourths because when you subtract the fractions you get a different fraction for your answer.
$4 \frac{1}{4}- \frac{3}{4}= 3 \frac{1}{2}$
so you would said three and one half instead of four and one fourth.
Hope I helped!

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A bookcase contains 2 statistics books and 5 biology books. if 2 books are chosen at random, the chance that both are statistics

xenn [34]

Answer:

The chance that both are statistics books is $\frac{1}{21}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{total number of possible cases}$

Combination of n elements taken from k to k is called each of the ways of choosing k different elements from the n of the original set. That is, it is called combinations of m elements taken from k to k to all the possible groupings that can be made with the m elements. It is expressed as:

$Cn,k=\frac{n!}{k!*(n-k)!}$

Remember that the factorial of a positive integer n is defined as the product of all the natural numbers before or equal to it.

A bookcase contains 2 statistics books and 5 biology books. The total number of book is 7.

2 books are chosen at random. The total outcomes can be obtained by selection of two books from seven books which is represented as follows:

$C7,2=\frac{7!}{2!*(7-2)!}=\frac{7!}{2!*5!}=\frac{5040}{2*120} =\frac{5040}{240} =21$

The selection of two statistics book from two statistics book is represented as follows:

$C2,2=\frac{2!}{2!*(2-2)!}=\frac{2!}{2!*0!}=\frac{2}{2*1} =\frac{2}{2} =1$

Then, the probability is:

$P(A)=\frac{C2,2}{C7,2}$

$P(A)=\frac{1}{21}$

The chance that both are statistics books is $\frac{1}{21}$

7 0

2 years ago

Using the identity ( x+a) 9x+b) = x2 + (a+b)x +ab, find the following product: (4p+3q)(4p+7q)

Aleks [24]

Answer:

$(4p+3q)(4p+7q)=x^2+40pq+21q^2$

Step-by-step explanation:

$Given\ (x+a)(x+b)=x^2+(a+b)x+ab\ ...............................(1)\\\\We\ have\ to \find\ (4p+3q)(4p+7q)\\\\Compare\ (4p+3q)(4p+7q)\ with\ (x+a)(x+b)\\\\x=4p\\\\a=3q\\\\b=7q\\\\Substitute\ these\ values\ in\ eq(1)\\\\(4p+3q)(4p+7q)=x^2+(3q+7q)\times 4p+3q\times 7q\\\\(4p+3q)(4p+7q)=x^2+10q\times 4p+21q^2\\\\(4p+3q)(4p+7q)=x^2+40pq+21q^2$