Which of the adhering to numbers is farthest from the number 1 on the number line?

0510

Explanation

Circling each of the answer options in a sketch of the number line (Figure 4) mirrors that of the given numbers,

is the biggest distance from 1.

You are watching: The following figure is an example of:

Figure 4

Another way to answer the question is to remember that the distance in between two numbers on the number line is equal to the absolute value of the difference of the two numbers. For example, the distance between

and also 1 is
and the distance between 10 and 1 is
The correct answer is Choice A,

Figure 5

The figure over mirrors the graph of the feature f, characterized by

for all numbers x. For which of the adhering to functions g, identified for all numbers x, does the graph of g intersect the graph of f ?

Explanation

You deserve to watch that all five choices are straight features whose graphs are lines via various slopes and also y-intercepts. The graph of Choice A is a line with slope 1 and also y-intercept

presented in Figure 6.

Figure 6

It is clear that this line will not intersect the graph of f to the left of the y-axis. To the appropriate of the y-axis, the graph of f is a line via slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y rises faster for f than for g, and therefore the graphs perform not intersect to the right of the y-axis. Choice B is similarly ruled out. Keep in mind that if the y-intercept of either of the lines in Choices A and also B were greater than or equal to 4 instead of less than 4, they would certainly intersect the graph of f.

Choices C and D are lines with slope 2 and y-intercepts much less than 4. Hence, they are parallel to the graph of f (to the ideal of the y-axis) and therefore will certainly not intersect it. Any line via a slope better than 2 and a y-intercept much less than 4, choose the line in Choice E, will certainly intersect the graph of f (to the best of the y-axis). The correct answer is Choice E,

A automobile got 33 miles per gallon utilizing gasoline that price \$2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline offered in driving the car 350 miles?

\$10\$20\$30\$40\$50

Explanation

Scanning the answer choices shows that you deserve to do at leastern some estimation and also still answer confidently. The car provided

gallons of gasoline, so the expense was
dollars. You can estimate the product
by estimating
a small low, 10, and also estimating 2.95 a little high, 3, to obtain approximately
dollars. You have the right to likewise use the calculator to compute a more specific answer and then round the answer to the nearemainder 10 dollars, as said by the answer selections. The calculator yields the decimal
which rounds to 30 dollars. Hence the correct answer is Choice C, \$30.

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A specific jar contains 60 jelly beans — 22 white, 18 green, 11 yellow, 5 red, and 4 purple. If a jelly bean is to be liked at random, what is the probcapability that the jelly bean will be neither red nor purple?

Explanation

Since tright here are 5 red and also 4 purple jelly beans in the jar, tbelow are 51 that are neither red nor purple and the probcapacity of choosing one of these is

Because all of the answer choices are decimals, you need to convert the fractivity to its decimal tantamount, 0.85. Hence the correct answer is Choice D, 0.85.