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Virty [35]
3 years ago
9

Noah is buying a pair of jeans and using a coupon for 10%off. The total price is $56.70 which includes $2.70 in sales tax. Noah’

s purchase can be modelled by the equation
x-0.1x+2.70=56.70
what does the solution to the equation mean in this situation?
How can you verify that 70 is not a solution but 60 is the solution?
Mathematics
2 answers:
lora16 [44]3 years ago
8 0

Answer:

See below.

Step-by-step explanation:

So, we know that Noah's purchase can be modeled by the equation:

x-0.1x+2.70=56.70

Part 1)

The solution to the equation will be the value of x.

In this case, x will represent the original price of the jeans.

We know that Noah has a coupon for 10% off the <em>original price of the jeans</em>.

So, 0.1x will represent how much of the original price Noah gets a a discount on.

Therefore, (x - 0.1x) represents the total cost of the jeans <em>after</em> the coupon.

So, x is our original price of the jeans.

Part 2)

To verify that 70 is <em>not</em> a solution, we can simply substitute 70 for x and check whether or not the equation is true. So:

(70)-0.1(70)+2.7\stackrel{?}{=}56.70

Multiply:

70-7+2.7\stackrel{?}{=}56.7

Subtract:

63+2.7\stackrel{?}{=}56.7

Add:

65.7\neq56.7

However, we <em>can</em> verify that 60 <em>is</em> the solution by substituting. So, substitute 60 for every x:

(60)-0.1(60)+2.7\stackrel{?}{=}5.7

Multiply:

60-6+2.7\stackrel{?}{=}56.7

Subtract:

54+2.7\stackrel{?}{=}56.7

Add:

56.7\stackrel{\checkmark}{=}56.7

So, 60 is indeed the solution and is the value of x.

So, this means that $60 was the original price of the jeans.

IgorLugansk [536]3 years ago
4 0

Answer:

$60

Step-by-step explanation:

i did it on paper

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From left to right, the sides measure 15, 12, and 20 units.

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The accompanying data contains the depth​ (in kilometers) and​ magnitude, measured using the Richter​ Scale, of all earthquakes
Sunny_sXe [5.5K]

Answer:

Depth:

μ =20.2025 km

M = 15.625 km

Range = 47.15 km

σ ≈ 15.92 km

Q₁ = 5.7375 km

Q₃ =  34.6675 km

Magnitude:

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M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

Step-by-step explanation:

The given data are;

Depth {}                                 Magnitude

0.76 {}                                    0.84

4.93 {}                                    0.47

8.16 {}                                     0.35

33.58 {}                                  1.32

21.2 {}                                     1.61

35.03 {}                                  4.57

10.05 {}                                   5.52

47.91 {}                                    1.99

For the Depth, we have;

The mean, μ = (0.76+4.93+8.16+33.58+21.2+35.03+10.05+47.91)/8 =20.2025 km

The median, M = The (n + 1)/2th term after arranging the term in increasing order as follows;

0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 , the median is therefore;

(8 + 1)/2th term or the 4.5th term which is 10.05 + (21.2 - 10.05)/2 = 15.625 km

The Range = The highest - The lowest value = 47.91 - 0.76 = 47.15 km

The Standard deviation of, σ, is given as follows;

\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu  \right )^{2} }{N}}

Where;

x_i = The individual data point = (0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 )

N = The total number of data point = 8

Substituting, (using Microsoft Excel) we get;

\sigma =\sqrt{\dfrac{\sum \left (x_i-20.2025  \right )^{2} }{8}} \approx 15.92 \ km

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Q₁ = The (8 + 1)/4th term = The 2.25th term = 4.93 + (8.16 - 4.93)×0.25) = 5.7375 km

Q₃ = The first quartile = The 3×(n + 1)/4th =  term arranged in increasing order

Q₃ = The 3×(8 + 1)/4th term = The 6.75th term = 33.58 + 3×(35.03 - 33.58)×0.25) = 34.6675 km

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μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

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