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SpyIntel [72]
2 years ago
10

Diesel Inc. is making frames for a new product being launched at the end of the year. To keep the weight down, the area of the f

rame should be 18 cm2. The inside of the frame has to be 11 cm by 6 cm. What should the width of the frame be?
Mathematics
1 answer:
tresset_1 [31]2 years ago
7 0
To answer, allow the width of the frame to be represented by x. The dimensions of the frame should then be, 11+2x and 6+2x. Subtracting the area of the inside of the frame from the area of the outside should be able to give us 18 cm². The equation,
                              (11 + 2x)(6 + 2x) - (11)(6) = 18
The value of x from the equation is equal to  0.5. Thus, the width of the frame should be 0.5 cm. 
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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is
Dahasolnce [82]

Answer:

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given the mean of the Population(μ)  = 419 grams

The sample size 'n' =19

Given mean of the sample x⁻ = 412

Given variance of the sample S² = 784

                                                 S = √784 = 28

<u><em>Step(ii)</em></u>:-

<u><em>Null hypothesis: H₀</em></u>: There is no sufficient evidence to support the claim that the bags are underfilled.

<u><em>Alternative hypothesis: H₁:</em></u>

There is sufficient evidence to support the claim that the bags are underfilled.

Test statistic

                     t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }

                    t = \frac{412 -419}{\frac{28}{\sqrt{19} } }

                   t = -1.09

                 |t| = |-1.09|

<em>Degrees of freedom   ν = n-1 = 19-1 =18</em>

<em>t₀.₀₂₅ =  3.19</em>

<u><em>Final answer:</em></u><em>-</em>

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

                   

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