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scZoUnD [109]
3 years ago
12

Vicki currently earns $35.00 an hour at her job. Thanks to her hard work, her boss is going to give her a 15% raise. How much wi

ll she earn each hour after the raise?
Mathematics
1 answer:
saveliy_v [14]3 years ago
7 0

Answer:

$40.25 per hour

Step-by-step explanation:

If you multiply 35 by 15% you get 5.25. You can either add this on, or you can multiply by 1.15 instead of .15.

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Building a is 271 meters taller than building
kvv77 [185]

Let a and b represent the heights of the corresponding buildings (in meters).

... a = b +271 . . . . . . . a is 271 meters taller than b

... 2b -a = 211 . . . . . . if a is subtracted from twice b, the result is 211

Use the expression for a in the first equation to substitute for a in the second.

... 2b - (b+271) = 211

... b = 482 . . . . . . . . . . . simplify and add 271

... a = b +271 = 753

Building a is 753 meters tall; building b is 482 meters tall.

4 0
3 years ago
A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How
Mazyrski [523]
Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:


In the year 1985 the worker earned <span>$10,500. 

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

                                            $10,500(1+0.06).



In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]=$10,500(1.06)^2.


Similarly we can check that in the year 1987 the worker earned $10,500(1.06)^3, which makes the pattern clear. 


We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}.

Factorizing, we have

=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r}) (where a is the first term and r is the common ratio) we have:

\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17.



Finally, multiplying 10,500 by 59.17 we have 621.285 ($).


The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating (1.06)^{26}.


Answer: D



4 0
3 years ago
Two families are saving up for a summer trip. The Smith family originally has $1000 and will save $50 every week. The Jones fami
gizmo_the_mogwai [7]
Hello. the answer is 20 weeks
4 0
3 years ago
Using the GCF factor the given expression: 21xy + 14y
MArishka [77]

Answer:

7y(3x+2)

you take out the 7y from both sides

3 0
3 years ago
Please help with 22. and 23.
kirill115 [55]

Answer:

22) y=1/4x-3/4

23) y=-1/3x-9

Step-by-step explanation:

22 ) Using the rise/run strategy, we can find the slope. From (-1,-1) you go up 1 unit to reach the same level as (3,0), and go right 4 to reach (3,0). This means your rise/run is 1/4, which is also your slope. Now to find the y-intercept, we can use the equation format y=mx+b. m is your slope, which we have, and b is the y intercept. With y and x, we can substitute in a point we already know, for example (-1,-1) as (x,y). When everything we know is substituted in, we get -1=(1/4)(-1)+b. According to PEMDAS, we should now multiply 1/4 and -1 to get (-1/4). Now our equation is -1=-1/4+b. To isolate B, we need to add 1/4 on both sides. As a result, you'll get -3/4. Your y intercept is -3/4. Thus, the final equation is y=1/4x-3/4.

23) This question is a lot more straight forward than question 22. In this question, you're already given everything in the equation to substitute everything in. Like I said before, the format for a linear equation is y=mx+b where m is your slope and b is your y intercept. This question already gives you both the slope and y intercept, so you can just fill it in. (m = -1/3, b= -9) Thus, you'll get y=-1/3x-9.

8 0
3 years ago
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