Answer:
Step-by-step explanation:
<h3><u>Question 6</u></h3>
To find the greatest common factor (GCF), first list the prime factors of each number:
- 42 = 2 × 3 × 7
- 60 = 2 × 2 × 3 × 5
42 and 60 share one 2 and one 3 in common.
Multiply them together to get the GCF: 2 × 3 = 6.
Therefore, 6 is the GCF of 42 and 60.
Divide the numerator and the denominator by the found GCF:
<h3><u>Question 7</u></h3>
To find the greatest common factor (GCF), first list the prime factors of each number:
- 80 = 2 × 2 × 2 × 2 × 5
- 272 = 2 × 2 × 2 × 2 × 17
80 and 272 share four 2s in common.
Multiply them together to get the GCF: 2 × 2 × 2 × 2 = 16.
Therefore, 16 is the GCF of 80 and 272.
Divide the numerator and the denominator by the found GCF:
Step-by-step explanation:
first you find the volume of a bin.
that is multiplication of 3 dimensions given.
4*4*4=64 cubic feet...
now volume of books..
0.75*0.75.0.25=0.14 cubic feet
now the number of books that will fit the bin=volume of bin/volume of books
64/0.14=455
455 books
The information given about the probability shows that the cardinality of D is 18.
<h3>How to calculate the probability?</h3>
From the complete information, the number of red-colored cards is 26.
Also, the number of red-colored number cards will be 18.
The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.
Here, the cardinality of set D is 18.
Here is the complete question:
Take a deck of playing cards. Form following sets out of those:
A = Set of Face Cards
B = Set of Red Coloured Face cards
C = Set of Black Coloured Face Cards
D = Set of Red Coloured Number Cards
Find the Cardinality of set D
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P-0.40p = 0.60p
C. Decrease by 40% is the same as multiply by 60%.
Assume that p = 10
10 - 0.40(10) = 0.60(10)
10 - 4 = 6
6 = 6
Based on the above assumption. 40% of 10 is 4 ; and 60% of 10 is 6. So, 10 less 4(40% of 10) is equal to 6 (60% of 10).
Percentage is used because 0.40 and 0.60 will be multiplied with 100% to get the equivalent percentage 0.40 x 100% = 40% ; 0.60 x 100% = 60%
Option 2: 
is the correct answer.
Step-by-step explanation:
The radical expressions like these are simplified by using fractional exponents
given
![\frac{\sqrt{4}}{\sqrt[3]{4} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B4%7D%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D)
Converting radicals into exponents
When there is no base the exponent is 1/2 and as the base is 3, the exponent will be 1/3
So
As the bases of numerator and denominator is same, the exponents can be subtracted
Hence,
Option 2: is the correct answer.
Keywords: Exponents, radicals
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