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stellarik [79]
2 years ago
15

Twice the difference of a number and 16 is the same as three times a number less than 18

Mathematics
1 answer:
Maksim231197 [3]2 years ago
4 0

Answer:

Step-by-step explanation:

Let x be the "number."

"twice the difference of a number and 16" can be written as:  

2(x-16)

"is the same as three times a number less than 18" can be written as:

= 3(x<18)

I wonder if this was meant to say "is the same as three times a number less  18," instead of "less than 18."  If so, we would have:

=3(x-18)

1.  Using the sentence as written:  2(x-16) = 3(x<18)

2.  Using the sentence as amended:  2(x-16) = =3(x-18)

 Going with this interpretation:  

 2(x-16) = 3(x-18)

2x - 32 = 3x - 54

x = 22

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The measure of an angle is 28 greater than its complement. Find the measure of each angle.
deff fn [24]
A complement means both angles sum to 90 degrees. We can use x to represent the angle that is greater. (X-28)+x=90.
2x-28=90
2x=118
X=59 degrees
6 0
3 years ago
You have a summer job that pays time and a half for overtime. that is if you work more than 40 hours per week,your hourly wage f
Nataliya [291]
Your pay is described by a piecewise function p(t) where t is hours worked.
p(t)=\left\{\begin{array}{rcl}7t&\mbox{for}&t\leq40\\10.5t-140&\mbox{for}&t>40\end{array}\right.

The domain of this function is the number of hours you can work in a week—zero to 168. The range is the set of values p(t) can take on, which we have said is p(0) to p(168). This problem, however, is asking for the range for a typical 40-hour week. That will be p(0) to p(40): the interval [0, 280].
8 0
3 years ago
Which ordered pairs are solutions to the inequality 2x - y &gt; -4? Check all that apply.
JulsSmile [24]

Answer:

(1,-6)

(-2,-5)

(8,2)

(4,0)

4 0
3 years ago
A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far
defon

Answer: The addition of the new point alters the previous standard deviation greatly

Step-by-step explanation:

Let the initial five points be : 2 3 4 5 and 6. In order to calculate the standard deviation for this data, we will need to calculate the mean first.

Mean = summation of scores/number of scores.

The mean is therefore: (2+3+4+5+6)/5 = 20/5 = 4.

We'll also need the sum of the squares of the deviations of the mean from all the scores.

Since mean = 4, deviation of the mean from the score "2" = score(2) - mean (4)

For score 3, it is -1

For 4, it's 0

For 5 it's 1

For 6 it's 2.

The squares for -2, -1, 0, 1, and 2 respectively will be 4, 1 , 0, 1, 4. Summing them up we have 10 i.e (4+1+0+1+4=10).

Calculating the standard deviation, we apply the formula:

√(summation of (x - deviation of mean)^2)/N

Where N means the number of scores.

The standard deviation = √(10/5) = 1.4142

If we add another score or point that is far away from the original points, say 40, what happens to the standard deviation. Let's calculate to find out.

i.e we now have scores: 2, 3, 4, 5, 6 and 40

We calculate by undergoing same steps.

Firstly mean. The new mean = (2+3+4+5+6+40)/6 = 60/6 = 10.

The mean deviations for the scores : 2, 3, 4, 5, 6 and 40 are -8, -7, -6, -5, -4 and 30 respectively. The squares of these deviations are also 64, 49, 36, 25, 16 and 900 respectively as well. Their sum will then be 1090. i.e. (64+49+36+25+16+900 = 1090).

The new standard deviation is then=

√(1090/6)

= √181.67

= 13.478.

It's clear that the addition of a point that's far away from the original points greatly alters the size of the standard deviation as seen /witnessed in this particular instance where the standard deviation rises from 1.412 to 13.478

7 0
2 years ago
Lin runs 5 laps around a track in 6 minutes.
Paladinen [302]

Answer:

25.2

Step-by-step explanation:

6/5 is 1.2, so it takes 1.2 minutes to run one lap.

This means 21 x 1.2 = the minutes it takes to run 21 laps around the track.

Therefore it takes 25.2 minutes to run around the track 21 times.

3 0
2 years ago
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