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3 years ago

Could someone please explain how to solve for the area?

Mathematics

2 answers:

sladkih [1.3K]3 years ago

8 0

9514 1404 393

Answer:

6.9 m²

Step-by-step explanation:

All of the sides are the same length. The altitude meets the base at its midpoint, so the altitude (h) of the triangle can be found using the Pythagorean theorem.

h² + 2² = 4²

h² = 12

h = 2√3

Then the area is ...

A = 1/2bh

A = (1/2)(4 m)(2√3 m) = 4√3 m² ≈ 6.9 m²

___

If you work through the above area formula in generic terms, you find the area of an equilateral triangle to be ...

A = (s²/4)√3 . . . . . where s is the side length

Another approach is to treat the figure as a 3-gon and use the n-gon area formula that uses the perimeter. That formula is derived here brainly.com/question/22386162

It is ...

A = P²/(4n·tan(180°/n))

For a triangle with side length s, this is ...

A = (3s)²/(4·3·tan(60°) = (s²/4)√3 . . . . same as above

Ipatiy [6.2K]3 years ago

6 0

Answer:

area of equilateral TRAINGLE =√3/4 A²=√3/4×4²=6.9mi² is your answer

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Suppose that 16% of the population of the U.S. is left-handed. If a random sample of 170 people from the U.S. is chosen, approxi

Shalnov [3]

Answer:

0.6064 = 60.64% probability that fewer than 29 are left-handed.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

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

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

16% of the population of the U.S. is left-handed.

This means that $p = 0.16$

Sample of 170 people

This means that $n = 170$

Mean and standard deviation:

$\mu = E(X) = np = 170*0.16 = 27.2$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{170*0.16*0.84} = 4.78$

Probability that fewer than 29 are left-handed.

Using continuity correction, this is P(X < 29 - 0.5) = P(X < 28.5), which is the pvalue of Z when X = 28.5. So

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

$Z = \frac{28.5 - 27.2}{4.78}$

$Z = 0.27$

$Z = 0.27$ has a pvalue of 0.6064

0.6064 = 60.64% probability that fewer than 29 are left-handed.

6 0

3 years ago

What is the answer 333

harkovskaia [24]

Answer:

Option A wilk be the correct answer.

6 0

3 years ago

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Mario has 3.875 liters of juice at the beginning of the day he drinks 2.79 liters during the day how much juice is left over st

katen-ka-za [31]

Answer:

The juice left at the end of the day is 1.085 liters.

Step-by-step explanation:

Juice at the beginning of the day: 3.875 liters

Juice drink by Mario during the day: 2.79 liters

Juice left at the end of the day = Juice at the beginning of the day - Juice drink by Mario during the day

= 3.875 - 2.79

= 1.085 liters

7 0

4 years ago

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If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc?

a_sh-v [17]

I guess what you are asking is what is the measure of the central angle?

arc length = radius * central angle (in radians)

central angle (in radians) = arc length / radius

central angle (in radians) = 12 / 10

central angle (in radians) = 1.2 radians = 68.7549 degrees

3 0

3 years ago

A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a pili

Dimas [21]

Answer:

x = 225.16 feet

Step-by-step explanation:

Given that,

The angle between the piling and the pier is 60°.

A surveyor has set up his transit on one side of the lake 130 feet from a piling that is directly across from a pier on the other side of the lake.

We need to find the distance between the piling and the pier. Let the distance be d. Using the trigonometry to find it as follows :

$\tan(60)=\dfrac{x}{130}\\\\x=\tan(60)\times 130\\\\x=225.16\ feet$

So, the required distance is 225.16 feet.

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3 years ago