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3 years ago

A drink coaster in the shape of a circle has

Mathematics

1 answer:

egoroff_w [7]3 years ago

5 0

The diameter of the coaster is 5 cm.

Step-by-step explanation:

Given,

The area of the circle = 19.63 sq inch

To find the diameter, we need to find the radius

Formula

The area of a circle with radius(r) = π $r^{2}$ sq cm

According to the problem,

π $r^{2}$ = 19.63

or, $r^{2}$ = $\frac{7 X 19.63}{22}$

= 6.2459

or, r = $\sqrt{6.2459}$ = 2.499 (approx)

= 2.5 cm

Hence the diameter of the circle = 2 × 2.5 cm = 5 cm

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To estimate the length of the lake, caleb starts at one end of the lake and walk 95m. He then turns a 60° angle and walks on a n

aivan3 [116]

Answer:

Length of the lake is 97.30 m

Step-by-step explanation:

We have given Caleb starts at one end of the lake and walk 95 m

So $d_1=95m$

And then he turns at an angle of 60°

So $\Theta =60^{\circ}$ and then again walk 8 m

So $d_2=8m$

We have to fond the total length of the lake , that is d

Total length of the lake is given by $d=\sqrt{d_1^2+d_2^2+2d_1d_2cos\Theta }=\sqrt{95^2+8^2+2\times 95\times 8\times cos60^{\circ}}=97.30m$

So length of the lake is 97.30 m

3 0

3 years ago

Find the missing length of the triangle. Round to the nearest tenth. a = _____, b = 7, c = 9

kogti [31]

Answer: Maybe 5.7

Step-by-step explanation: To solve this we are going to need to understand the pythagorean theorem. we can use it as a way to find this certain side. if we put these numbers in the theorem, we get a^2+49=81 (7^2=49 and 9^2=81), we can subtract 49 on both sides and get 32. We would also need to take out the power of 2 on the side of the a^2, so you would do the square root of a^2, which would just become a and the square root of 32, which if you crunch the numbers on a calculator. You would get 5.656..... then you round it to the nearest tenth and get 5.7.

5 0

3 years ago

Read 2 more answers

Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb

Maksim231197 [3]

Answer:

$n=(\frac{1.64(4)}{0.25})^2 =688.537 \approx 689$

So the answer for this case would be n=689 rounded up to the nearest integer

Step-by-step explanation:

Assuming this complete question: "Suppose that the minimum and maximum ages for typical textbooks currently used in college courses are 0 and 8 years. Use the range rule of thumb to estimate the standard deviation.

Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb to estimate the standard deviation. Next, find the size of the sample required to estimate the mean age (in years) of textbooks currently used in college courses. Use a 90% confidence level and assume that the sample mean will be in error by no more than 0.25 year."

Solution for the problem

First we need ti find the estimation for the standard deviation using the Rule of thumb, with the following formula:

$s \approx \frac{R}{4}$

Where R is the range defined as :

$R = Max - Min = 8-0 = 8$

So then the deviation would be approximately:

$s \approx 4$

Important concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error (ME) is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that $ME =\pm 0.25$ and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

We can assume that the estimator for the population deviation from the rule of thumb is $\hat \sigma = s= 4$

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got $z_{\alpha/2}=1.64$ , replacing into formula (2) we got: