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Fiesta28 [93]
4 years ago
7

Mr. Stewart bought a new battery for his car. The battery cost $72. Since batteries are a taxable item, he had to pay a sales ta

x of 7.5%. What was the total cost of the battery in dollars and cents?
Mr. Stewart spent $77.40 on his new car battery.
Mathematics
1 answer:
Sladkaya [172]4 years ago
7 0

Answer: $77.40

Step-by-step explanation:

First you take the 7.5% and turn it into a decimal and to do that you have to divide 7.5 by 100 which gives you .075. You then multiply 72 by .075 to know how much money you will pay with tax and you get $5.40. then you add $5.40 to $72 to get the total coast of the battery, which is $77.40.

The total cost of the battery was $77.40.

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AlexFokin [52]

Answer:

  1. \huge{x =  -  \frac{5}{4}  +  \frac{7}{4} y}
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Step-by-step explanation:

1. 4x - 7y =  - 5

4x =  - 5 + 7y

\boxed{\green{x =  -  \frac{5}{4}  +  \frac{7}{4} y}}

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2. 3x - 2y =  - 7

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3 years ago
Design specifications require that a key dimension on a product measure 105 ± 12 units. A process being considered for producing
marta [7]

Answer:

Cpk = Cpu = Cpl = 0.4785

Step-by-step explanation:

Solution:-

- The capability of a process is determined using the capability index ( Cpk ). The index helps in determining the output of the process lies within the specification limits.

- The key dimension on a product measure is:

                                 105 ± 12 units

- Process is producing this product at a 6-sigma quality standards i.e ( process is producing this product has a standard deviation (σ) of three units.)

Where,         Standard Error in measured value = 12 units.

- The process capability (Cpu) is defined based on the Upper Specification Limit of the process (USL):

                             Cpu = (USL - u) / 3σ

- The process capability (Cpl) is defined based on the Lower Specification Limit of the process (LSL):

                             Cpl = ( u - LSL) / 3σ

- Assume that the process is centered with respect to specifications, then the given absolute value of u = 105 units.

Where the specification limits are defined as:

                             LSL = u - SE = 105 - 12

                             LSL = 93 units

                             USL = u + SE = 105 + 12

                             USL = 117 units

- Now evaluate the Process capability on each of the two limits specification limits:

                           Cpu = (USL - u) / 3σ

                           Cpu = (117 - 105) / 3σ

                           Cpu = 4 / σ

                           Cpl = ( u - LSL) / 3σ

                           Cpl = ( 105 - 99 ) / 3σ

                          Cpl = 4 / σ    

- The minimum of Cpu and Cpl is denoted as the Cpk value:

                           Cpk = min ( Cpu , Cpl )

                           Cpk = Cpu = Cpl = 4 / 8.36

                           Cpk = Cpu = Cpl = 4 / 8.36 = 0.4785          

               

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Answer:

2(x²-8+15)

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So the answer is C. 2(x-3)(x-5)

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