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saw5 [17]
2 years ago
8

A music player was marked down by 1/4 of the original price. If the sales price is $128, what is the original price? If the musi

c player was marked up by ½ before it was placed on the sales floor, what was the price that the store paid for the player? What is the difference between the discount price and the price that the store paid for the music player?
Mathematics
1 answer:
Sedaia [141]2 years ago
3 0

Answer:

Step-by-step explanation:

Let the original price be represented by x.

1. \frac{1}{4} of x = x - 128

\frac{x}{4} = x - 128

x - \frac{x}{4} = 128

4x - x = 4 x 128

3x = 512

x = \frac{512}{3}

  = 170.67

x = 170.67

The original price is $170.67.

2. If the price of the music player was marked up by ½ of its original price, its new price would be;

170.67 + (170.67 x ½)   = 170.67 +85.335

                                     = 256.005

                                     ≅ $ 256.0

The price paid by the store for the music player is still the original price i.e $170.67.

3. The difference between the discounted price and the price paid by the store can be determined by;

price paid by the store - the discounted price of the music player

= $170.67 - $128

= $42.67

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Answer:

\frac{1}{16}

Step-by-step explanation:

With a negative fractional exponent place a 1 over the positive value

\frac{1}{ {8}^{ \frac{4}{3} } }

rewrite 8 as

( {2}^{3} ) ^{ \frac{4}{3} }

apply the power rule and multiply the exponents.

cancel the common factor of 3

rewrite the expression

\frac{1}{ {2}^{4} }

raise 2 to the power of 4 which =16

so the answer is

\frac{1}{16}

5 0
3 years ago
The simple interest on $15,000 for 4 years<br>is $8, 100. Calculate the rate percent per annum.​
insens350 [35]

Answer:

13.5%

Step-by-step explanation:

8100 interest/4 years=2,025 interest per year

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15000 x interest rate=2025

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4 0
3 years ago
A stainless steel patio heater is a square pyramid. The length of one side of the base is 89.6 The slant height of the pyramid i
Temka [501]

Answer:

9.48

Step-by-step explanation:

Complete question

<em>A stainless steel patio heater is a square pyramid. The length of one side of the base is 89.6 The slant height of the pyramid 90.1. What is the height of the​ pyramid?</em>

To get the height of the pyramid, we will use pythagoras theorem.

slant height l is the hypotenuse

length of the base is the adjacent

height of the pyramid is the opposite

According to the theorem;

l² = h² + b²

90.1² = h² + 89.6²

8,118.01 = <em>h²+</em>8,028.16

h²= 8,118.01 - 8,028.16

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h =√89.85

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3 0
2 years ago
In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump for women was 70.0 in
sveta [45]

Answer: year 2194



Explanation:



1) Model the jump of the women:


i) initial jump = 70.0 in


ii) increase rate = 0.48% per year


iii) equation: h = 70.0(1 +0.0048)ⁿ


2) Model the jump of the men:


i) initial jump 86.5 inches.


ii) increase rate, 0.4%.


iii) equation: h = 86.5 (1 + 0.004)ⁿ


3) Equal the two equations (h = h) to find when the jumps will be equal:


i) 70.0(1 +0.0048)ⁿ = 86.5 (1 + 0.004)ⁿ


ii) 70.0(1.0048)ⁿ = 86.5 (1.004)ⁿ


ii) [1.0048ⁿ / 1.004ⁿ] = 86.5/70.0


iii) [1.0048/ 1.0040]ⁿ = 86.5/70.0


iv) n log (1.0048 / 1.0040) = log ( 86.5/70)


v) n = log (86.5/70) / log (1.0048/1.0040) ≈ 266


3) year = 1928 + 266 = 2194


That is in the year 2194

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