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Aleks [24]
2 years ago
9

8. Two competing companies are having sales on projectors. Projector #MD375 has a retail price of $1,550. The Office Spot is adv

ertising #MD375 for 15% off, while Office & Beyond has stated they will match any competitor’s advertised special and take an additional 10% off of the advertised price. How much money is saved by purchasing the projector from Office & Beyond instead of the Office Spot?
Mathematics
1 answer:
shtirl [24]2 years ago
6 0

Answer:

  $131.75

Step-by-step explanation:

The advertised price is 1 -15% = 85% of $1550, so is ...

  0.85×$1550 = $1317.50

The savings obtained by purchasing from O&B is 10% of this value, so is ...

  0.10×$1317.50 = $131.75 . . . . savings at O&B

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The area of a room is 396 square feet. The length is x+3, and the width is x+7 feet. Find the dimensions of the room
Marrrta [24]
This is an odd problem. The length and width look like they should be interchanged. Anyway I'll solve it and we'll talk about the results.
(x +7) (x + 3) = 396
x^2 + 7x + 3x + 21 = 396
x^2 + 10x + 21 = 396 Subtract 21 from both sides.
x^2 + 10x = 396 - 21
x^2 + 10x = 375
x^2 + 10x - 375 = 0 This probably factors.
(x + 25)(x - 15)
x + 25 = 0
x = - 25 which makes no sense. Negatives do not describe room dimensions.
x - 15= 0
x = 15. this is fine.

x+3 = 15 + 3 = 18
x + 7 = 15 + 7= 22

Check
=====
Area = L * W = 18 * 22 = 496. It does check.
22 should be the length

18 should be the width.
3 0
2 years ago
Estimate the diameter of the supergiant star Betelgeuse, using its angular diameter of about 0.05 arcsecond and distance of abou
8090 [49]

<span>0.05 arc-second = 1 degree/72000 = (pi radians)/(180*72000) = 2.424 x 10^(-7) radians</span>

<span>The distance is roughly: </span>

<span>R*(theta) = (600 light-years)*2.424 x 10^(-7) = 0.00014544 light-years = 1.275 light-hours = (3600 seconds)*(3 x 10^8 m/s)*(1.275) = 1.38 x 10^12 meters.</span>

7 0
2 years ago
Read 2 more answers
Mikhael and hema want to hire a professional dj to play music during the event. Dj kay-cee charges $100 plus $50 per hour . Dj f
11Alexandr11 [23.1K]

Dj kay-cee: 50x+100

Dj fav fred: 30x+150

So, setting up the equation, you get that 50x+100=30x+150

So, 20x=50, and x=\frac{5}{2}

So after 2.5 hours, dj kay-kee and dj fab fred would charge the same amount.

6 0
2 years ago
If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21
Ilya [14]
This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34  + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\&#10;a_n=a_1+(n-1)d\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;d=\textit{common difference}\\&#10;----------\\&#10;n=7\\&#10;d=5\\&#10;a_7=34&#10;\end{cases}&#10;\\\\\\&#10;a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5&#10;\\\\\\&#10;34=a_1+30\implies \boxed{4=a_1}

and now let's use those 2 found folks, to get the 21st term,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\&#10;a_n=a_1+(n-1)d\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;d=\textit{common difference}\\&#10;----------\\&#10;a_1=4\\&#10;d=5\\&#10;n=21&#10;\end{cases}&#10;\\\\\\&#10;a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104
3 0
2 years ago
According to the manufacturer, about 26% of sour candy in a package of Sandy's Sours are grape. What is the probability that the
Leto [7]

Answer:


Step-by-step explanation:

We assume that there are 100 sour candies, Thus-  

26 % of candy are grape implies that 26% of 100 candies are grape that is equal to 26

Now remaing candies that are not grape are 100-26 = 74

Based on the rule of multiplication:

P(A ∩ B) = P(A)/ P(B|A)  

 In the beginning, there are 26grape candies, probability of choosing first grape candy =  26C1 = 26

 After the first selection, we replace the selected grape candy so there are still 100 candies in the bag P(B|A) =  100C3 = 100 x 99 x 98 x 97!/3! X 97!

= 50 x 33 x 98

So probability =1/ 50 x 33 x 98 x 26

= 1/4204200



8 0
2 years ago
Read 2 more answers
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