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Paul [167]
2 years ago
15

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or und

erfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is _____.
Mathematics
1 answer:
KengaRu [80]2 years ago
4 0

Answer:

\mathbf{H_o : \mu = 12}  \\ \\ \\  \mathbf{H_a: \mu \ne 12}

Step-by-step explanation:

Given that:

The population mean μ =  12

By computing the null and alternative hypotheses, the correct set of hypotheses for this test is:

\mathbf{H_o : \mu = 12}  \\ \\ \\  \mathbf{H_a: \mu \ne 12}

This is a two-tailed test.

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Answer:

\\ \gamma= \frac{a\cdot b}{b\cdot b}

Step-by-step explanation:

The question to be solved is the following :

Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if b \neq 0. Recall that given two vectors a,b  a⊥ b if and only if a\cdot b =0 where \cdot is the dot product defined in \mathbb{R}^n. Suposse that b\neq 0. We want to find γ such that (a-\gamma b)\cdot b=0. Given that the dot product can be distributed and that it is linear, the following equation is obtained

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\gamma= \frac{a\cdot b}{b\cdot b}

By construction, this γ is unique if b\neq 0, since if there was a \gamma_2 such that (a-\gamma_2b)\cdot b = 0, then

\gamma_2 = \frac{a\cdot b}{b\cdot b}= \gamma

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Step-by-step explanation:

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