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vichka [17]
3 years ago
9

You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is th

e original price?
Mathematics
2 answers:
schepotkina [342]3 years ago
8 0
Final cost/1.06 = sale price

\frac{22.26}{1.06} = 21.06

The sales price is $21.06

Sales price/.70 (70% of the original price) = original price

\frac{21.06}{.70} = 30.09

The original price of the helmet was $30.09
Korvikt [17]3 years ago
7 0
6% de 22,26 = 
6*22,26/100 = 
1,3356
22,26 - 1,3356 = 20,9244
70% de 20,9244 = 
70*20,9244/100 = 
14,64708 ~ 14,64
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The expression 3P2 can also be read as "permutation of 3 taken 2". This represents the number of ways in which the 3 items are arranged with the emphasis on the arrangement of the first two other items. 
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See attached graph for the first part

Answer to second part: The end part of the graph show the slowest increase

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The attached picture represents the number of infected people, starting with a relatively small number at the origin of the horizontal axis (x=0, or time=0) then increasing abruptly in the center of the graph with steep slope. and then infection slowing down (although still slowly increasing) in the region highlighted in yellow to the right of the graph.

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Usain Bolt ran the 2012 Olympic 100-meter race in 9.63 seconds. If he runs at this rate on a road with a speed limit of 25 miles
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You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0
3 years ago
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