Find the sum or difference in -8+13=

The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

BartSMP [9]

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

5 0

3 years ago

In a study of the accuracy of fast food drive-through orders, one restaurant had orders that were not accurate among orders obs

Lesechka [4]

Complete Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

Step-by-step explanation:

Generally from the question we are told that

The sample size is n = 367

The number of orders that were not accurate is $k = 32$

The population proportion for rate of inaccurate orders is p = 0.10

The null hypothesis is $H_o : p = 0.10$

The alternative hypothesis is $H_a : p \ne 0.10$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{32}{367}$

=> $\^ p = 0.0872$

Generally the test statistics is mathematically represented as

$z= \frac{ \^ p - p }{ \sqrt{ \frac{ p(1 - p)}{ n} } }$

=> $z= \frac{ 0.0872 - 0.10 }{ \sqrt{ \frac{ 0.10 (1 - 0.10 )}{367} } }$

=> $z= -0.8174$

From the z table the area under the normal curve to the left corresponding to -0.8174 is

$P(z < -0.8173 ) = 0.20688$

Generally the p-value is mathematically represented as

$p- value = 2 * 0.20688$

=> $p- value = 0.4138$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%

4 0

3 years ago

Find the value of x.

DanielleElmas [232]

Answer:

x = -7

Step-by-step explanation:

Make an equation:

3x + 33 = 12

3x = -21

x = -7

7 0

3 years ago

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Please help me in this question.Tell me if it is good. And if it is not good then do it for me please.

Orlov [11]

Answer:

Y = 170, Z = 64.

Step-by-step explanation:

Since y is the external angle to x, which you got right, it is in fact, 180-10, = 170 degrees. And since z is the external to our unknown angle, that means it is equal to the sum of the other two angles in the triangle. That means z is 54 + 10, which is 64.

6 0

3 years ago

Calculate the value of y

Reika [66]

157 degrees ... set 4x-5 = x+16 then solve, you should get x=7, plug in 7 for one of the equations and you'll get 23. subtract 23 from 180 and get 157. hope that helped :)

4 0

3 years ago

Read 2 more answers