By looking up formulas on how to solve questions involving circles, and input numbers, such as pi, circumference, radius, and diameter of a circle, thank you
I have to rewrite the expressions because they look very confusing.
1) The given fractions to add are:
4p² + 6 2p - 2
------------ + ------------
4p² 10p²
2) The statements to asses are:
<span>A) The least common denominator is 20p
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²
C) The second fraction rewritten with the LCD is (4p - 4) / 20p
D) The sum is (24p² -4p +30 ) / 20p² = (12p-2p+15) / 10p^2
E) The sum is a rational expression.
This is the result for each statement.
</span>
<span>A) The least common denominator is 20p
FALSE: THE LCD IS 20p², because it the least expression that contains all the prime factors of both denominators: 4p² and 10p.
See that you cannot divide 20p by 4p² but you can divide 20p² by 4p² and 10 p. So, 20p is not a common denominator.
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²
TRUE: you get this expression from the first fraction by multiplying both numerator and denominator by 20p² / 4p² = 5:
(4p² + 6)×5 = 20p² + 30
(4p²)×5 = 20p²
=>
20p² + 30
--------------
20p²
C) The second fraction rewritten with the LCD is (4p - 4) / 20p
FALSE: you have to multiply both numerator an denominator by 20p² / 10p = 2p
(2p - 2) × 2p = 4p² - 4p
10p × 2p = 20p²
So, the second fraction rewritten with the LCD is:
4p² - 4p
-----------
20p²
D) The sum is (24p² - 4p +30 ) / 20p² = (12p-2p+15) / 10p²
TRUE
</span>
<span><span> 20p² + 30 4p² - 4p 24p² - 4p + 30
-------------- + --------------- = ----------------------
20p² 20p² 20p²</span>
And when you simplify the last fraction dividing by 2 you get:
12p² - 2p + 15
-----------------------
10p²
E) The sum is a rational expression.
TRUE:
The sum of rational number has the closure property which means that by adding rational expression you will always ge a rational expression.
</span>
Answer:
The fourth one
Step-by-step explanation:
Surface area of a cylinder: 
where r = radius and h = height
We have a given height of 14cm and a given diameter of 6cm
We need the radius, not the diameter
To convert diameter to radius we simply divide by 2
6 / 2 = 3
so R = 3
We now plug in the given values into the formula
This equation matches with answer choice D
5*3=15 10+5=15 11=4=15 13+2=15 14=1=15 9+5+1=15
<u>Question Completion</u>
(a)In this region, are the events "silver" and "black" mutually exclusive:? Choose 1 answer
(A) Yes (B) No
(b) Find the probability that a randomly selected car from this region is mainly silver OR mainly black. P (silver OR black)=
Answer:
(a)Yes
(b)0.41
Step-by-step explanation:
(a) The events silver and black are mutually exclusive. Although a car's color can consist of both silver and black, its main color can only be either silver or black. It cannot be both
(b)In probability theory, given two mutually exclusive events A and B.
P(A or B)=P(A)+(B)
Therefore:
P (silver OR black)= P(silver) + P(black)
= 0.22 + 0.19
= 0.41
