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2 years ago

What is the area of the figure below? Use 3.14 for pi. Round your answer to the nearest hundredth.

Mathematics

1 answer:

sammy [17]2 years ago

8 0

Answer:

area of the figure ≈61.23 cm² to the nearest hundredth

Step-by-step explanation:

To find the area of the figure, we will follow the steps below;

Looking at the figure, we will see that the figure comprises of both semi-circle and a parallelogram

area of figure = area of semicircle + area of parallelogram

first, we will find the area of the semi-circle

area of a semi-circle = πr² /2

from the diagram given, diameter = 7cm

but diameter = 2r, this implies that radius r = d/2, hence radius r = 7/2 = 3.5 cm

π = 3.14

Lets insert the values into the formula

area of a semi-circle = πr² /2

=3.14×3.5² /2

=3.14×12.25 /2

=19.2325 cm²

Area of a parallelogram = b×h

where b = base and h = height

from the figure given, base b = 7cm and height h = 6 cm

Lets insert the values into the formula

Area of a parallelogram = b×h

= 7×6

=42 cm²

area of the figure = area of semicircle + area of parallelogram

=19.2325 cm² + 42 cm²

=61.2325 cm²

≈61.23 cm² to the nearest hundredth

area of the figure ≈61.23 cm² to the nearest hundredth

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Answer:

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Step-by-step explanation:

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where,

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3 years ago

The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approxi

True [87]

Answer:

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.

Step-by-step explanation:

The circumference ( $s$ ), in centimeters, and the surface area ( $A_{s}$ ), in square centimeters, of a sphere are represented by following formulas:

$A_{s} = 4\pi\cdot r^{2}$ (1)

$s = 2\pi\cdot r$ (2)

Where $r$ is the radius of the sphere, in centimeters.

By applying (2) in (1), we derive this expression:

$A_{s} = 4\pi\cdot \left(\frac{s}{2\pi} \right)^{2}$

$A_{s} = \frac{s^{2}}{\pi^{2}}$ (3)

By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ( $\Delta A_{s}$ ), in square centimeters:

$\Delta A_{s} = \frac{\partial A_{s}}{\partial s} \cdot \Delta s$

$\Delta A_{s} = \frac{2\cdot s\cdot \Delta s}{\pi^{2}}$ (4)

Where:

$s$ - Measure circumference, in centimeters.

$\Delta s$ - Possible error in circumference, in centimeters.

If we know that $s = 82\,cm$ and $\Delta s = 0.5\,cm$ , then the maximum error is:

$\Delta A_{s} \approx 8.3083\,cm^{2}$

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.

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2 years ago

Find the four arithmetic means between -21 and -36.

lara31 [8.8K]

The numbers given in the problem above are part of an arithmetic sequence with first and sixth terms equal to -21 and -36, respectively. Firstly, calculate for the common difference (d).

d = (-36 - -21) / (6 - 1) = -3

The arithmetic mean is calculated by adding -3 to the term prior to it.

a2 = -21 + -3 = -24 a3 = -24 + -3 = -27
a4 = -27 + -3 = -30 a5 = -30 + -3 = -33

Thus the four arithmetic means are -24, -27, -30, and -33.

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3 years ago

Bobbie has 100 more followers than Debora. Write an expression that

alukav5142 [94]

Answer: x + 100

Step-by-step explanation:

From the question, we are told that Bobbie has 100 more followers than Debora and x is used to represent the number of followers that Debora has.

The expression that shows the number of followers Bobbie has will be the number of followers that Debora has plus 100. This will be :

= x + 100

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3 years ago

Suppose a local manufacturing company claims their production line has a variance of less than 9.0. A quality control engineer d

Alexxx [7]

Answer:

$\chi^2 =\frac{35-1}{9} 2.12^2 =16.979$

$p_v =P(\chi^2$

If we compare the p value and the significance level provided we see that $p_v$ so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly lower than 9

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=35$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s =2.12$ represent the sample deviation obtained

$\sigma_0 =3$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is lower than 9 and the deviation lower than 3, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \geq 9$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{35-1}{9} 2.12^2 =16.979$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df= n-1= 35-1=34. And since is a left tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(16.979,34,TRUE)"

Conclusion

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3 years ago