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2 years ago

Use the change of base formula to compute log1/4 6. Round your answer to the nearest thousandth.

Mathematics

1 answer:

Arte-miy333 [17]2 years ago

8 0

Answer:

$-1.292$

Step-by-step explanation:

The change of base formula is $log_b(a)=\frac{log(a)}{log(b)}$ , therefore:

$log_{\frac{1}{4}}(6)=\frac{log(6)}{log(\frac{1}{4})}\approx-1.292$

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Answer:

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2 years ago

The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at ea

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Answer:

The distance around the inside is 199.44 m.

Step-by-step explanation:

Given that,

Length = 84.39 m

Width = 9.76 m

Suppose, all the way around and 73 m wide.

We know that,

Perimeter of half circle is

$perimeter = \pi r$

We need to calculate the inner radius of the circle

Using formula of radius

$r=\dfrac{D}{2}$

Put the value into the formula

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We need to calculate the distance around the inside

Using formula of distance

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Put the value into the formula

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3 years ago

Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need

Mars2501 [29]

Answer:

$\text{Average diameter is 1.65 mm and we decide that it is not 1.65 mm.}$

Step-by-step explanation:

We are given the following in the question:

The needle size should not be too big and too small.

The diameter of the needle should be 1.65 mm.

We design the null and the alternate hypothesis

$H_{0}: \mu = 1.65\text{ mm}\\H_A: \mu \neq 1.65\text{ mm}$

Sample size, n = 35

Sample mean, $\bar{x}$ = 1.64 mm

Sample standard deviation, s = 0.07 mm

Type I error:

It is the error of rejecting the null hypothesis when it is true.
It is also known as false positive error.
It is the rejecting of a true null hypothesis.

Thus, type I error in this study would mean we reject the null hypothesis that the average diameter is 1.65 mm but actually the average diameters of the needle is 1.65 mm.

Thus, average diameter is 1.65 mm and we decide that it is not 1.65 mm.

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3 years ago

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