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3 years ago

Use the arc length formula and the given information to find r. s = 16 cm, θ= 48°; r = ? (1 point)

Mathematics

2 answers:

rodikova [14]3 years ago

6 0

Solution:

The value of r is 19.1 cm

Explanation:

We know the arc length formulas which is shown below.

$\theta= \frac{s}{r} \\\\r=\frac{s}{\theta}$

Here the angle is in radian.

We have been given that

s = 16 cm, θ= 48°

We know that 1 degree = 0.0174533 radian

Hence, 48° = 0.837758 radian

On substituting these values in the formula, we get

$r=\frac{16}{0.837758} \\\\r=19.1 \text{ cm}$

Therefore, the value of r is r=19.1 cm

LenKa [72]3 years ago

3 0

I converted θ to radians, then put that and the length of the arc into the formula shown.

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A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

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3 years ago

A company’s sales increased 17% this year, to $8267. What were their sales last year?

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eekk im not shure sorry but it might be 8156 i no no

Step-by-step explanation:

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3 years ago

This is what I am supposed to do, I’m confused on what to do on 3,4, and 5. PLEASE HELP ASAP!!!!!! 30 POINTS!!!!!

max2010maxim [7]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

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m = (y₂ - y₁ ) / (x₂ - x₁ )

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3 years ago

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liq [111]

Answer:

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Same steps for the last shape, another rectangular prism:

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= 2·2·x·x·x·x·x

= 4·x⁵

= 4x⁵

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2 years ago

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