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2 years ago

Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate Pi.

Mathematics

1 answer:

taurus [48]2 years ago

6 0

Answer:

$26.13ft^2$

Step-by-step explanation:

Step 1 - As both triangles have lengths the same size, they both add together to equal a rectangle. Therefore:

4 x 3 = 12

Which is the area of the triangles.

Step 2 - Calculating the area of a circle uses the formula:

$\pi r^2$

Where r is the radius of the circle.

Plug the known variables in:

$\pi \cdot 3^2\\\pi \cdot 9\\3.14 \cdot 9 = 28.26\\$

However, this is the area of a full circle. The figure is only half a circle so we must divide this by two:

28.26 ÷ 2 = 14.13

Now, add the area of the semi-circle to the area of the triangles:

14.13 + 12 = 26.13

Therefore, the area of the figure is $26.13ft^2$ .

Hope this helps!

You might be interested in

The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili

Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that $\mu = 74, \sigma = 15$

Question a:

Sample of 36 means that $n = 36, s = \frac{15}{\sqrt{36}} = 2.5$

This probability is 1 subtracted by the pvalue of Z when X = 78. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{78 - 74}{2.5}$

$Z = 1.6$

$Z = 1.6$ has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that $n = 150, s = \frac{15}{\sqrt{150}} = 1.2247$

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

$Z = \frac{X - \mu}{s}$

$Z = \frac{77 - 74}{1.2274}$

$Z = 2.45$

$Z = 2.45$ has a pvalue of 0.9929

X = 71

$Z = \frac{X - \mu}{s}$

$Z = \frac{71 - 74}{1.2274}$

$Z = -2.45$

$Z = -2.45$ has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that $n = 219, s = \frac{15}{\sqrt{219}} = 1.0136$

This probability is the pvalue of Z when X = 74.2. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{74.2 - 74}{1.0136}$

$Z = 0.2$

$Z = 0.2$ has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0

3 years ago

Papa john is 50 years old. His age is 2 years more than 3 times the age of jimmy John

kakasveta [241]

Jimmy John is sixteen

7 0

3 years ago

Read 2 more answers

Please help Evaluate this equation!!

lozanna [386]

Answer:

1.)-8

2.)-5

3.)4

Step-by-step explanation:

So, the function f(x)=3x-5

The questions say "If you were to substitute these numbers what answer would you get?"

Understanding this,

First question is with x=-1

f(-1)=3(-1)-5

f(-1)=-3-5=-8

_____________________________________

f(0)=3(0)-5

f(0)=0-5=-5

_____________________________________

f(3)=3(3)-5

f(3)=9-5=4

6 0

3 years ago

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a product

djyliett [7]

The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.

<h3>How to calculate the value?</h3>

The different ways that are there to cast Fantine from the 28 women will be:

= 28!/(28 - 1)!

= 28!/27!

= 28

When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:

= 27!(27 - 1)!

= 27!/26!

= 26

When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:

= (28 - 2)!/(28 - 2 - 1)!

= 26!/25!

= 25

Learn more about permutations on:

brainly.com/question/4658834

#SPJ1

6 0

2 years ago

PLZ HELP WILL GIVE BRAINLIEST!!!!

Natalka [10]

3 i think here is the brainly link where i found tht brainly.com/question/472442 if i helped would you mark me brainiest if i helped?

7 0

3 years ago