. Let ????1 be the function that assigns to each nonnegative integer its last digit. Note: The nonnegative integers is the set o
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A linear function is a function that has constant average rate of change;
Also, a relation that represents a function must have unique input and output values.
<h3>Question 11: Relations and Functions</h3>A relation may or may not represent a function.
When the domain and the range of a relation are unique, then the relation is a function.
So, the true option is (b) function
<h3>Question 12: Relations and Functions</h3>A one-to-many relation is not a function.
This is so because the domain and the range of the function are not unique
So, the true option is (c) figure 3: one-to-many.
<h3>Question 13: Variables</h3>A dependent variable is a variable that depends on other variables for its value.
In this case, the dependent variable is (b) boosts the immune system.
<h3>Question 14 and 15: Domain and Range</h3>The domain is the set of input values (i.e. the x values), while the range is the set of output values (i.e. the y values)
This means that:
- The domain of the function is: (a) {2,3,4,5,6}
- The range of the function is: (b) {4,6,8,10,12}
The graph of a linear function is represented by a straight line, and it has a constant slope or rate.
This means that:
- Graph C is a linear function
- Table B is a linear function
The fare of 3 km and 5 km are given as 35 pesos and 55 pesos, respectively.
This means that:
Table (b) represents the information
<h3>Question 19: The linear equation</h3>Start by calculating the slope (m) using:
So, we have:
The linear equation is then calculated as:
This gives
This means that:
The linear equation that describes the relationship is (c) ;
This means that x = 4.
So, we have:
Hence, the fare will be (a) 45 pesos
Read more about linear functions at:
(C) fraction of the marbles now in the bag is blue.
- A fraction is a portion of a whole or, more broadly, any number of equal parts.
- In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
- A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line.
- Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
To find what fraction of the marbles now in the bag is blue:
- Important information is that immediately before the last step blue marbles formed
from the marble in the bag.
- That means that there were
blue and
other marbles, for some
- When we double the number of blue marbles, there will be
blue and
- Hence, blue marbles now form
all marbles in the bag.
Therefore, (C) fraction of the marbles now in the bag is blue.
Know more about fractions here:
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Complete question:
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/5
(E) 1/2