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2 years ago

The side length of an equilateral triangle is 6 cm. What is the height of the triangle?

Mathematics

2 answers:

soldi70 [24.7K]2 years ago

4 0

Answer:

$3\sqrt{3}$

Step-by-step explanation:

We are asked to find the height of an equilateral triangle, whose side length is 6 cm.

We know that all sides of an equilateral triangle are equal.

We can find height of an equilateral triangle using formula $\frac{\sqrt{3}}{2}a$ , where 'a' represents side length of equilateral triangle.

$\frac{\sqrt{3}}{2}\cdot 6$

$\sqrt{3}\cdot 3$

$3\sqrt{3}$

Therefore, the height of the equilateral triangle is $3\sqrt{3}$ .

solniwko [45]2 years ago

3 0

Correct me if I am wrong but an equilateral has the same length on each side so wouldn’t it be 6 cm?

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Is the number 17 a prime or composite number?

Alborosie

Answer:

It is a prime number.

Step-by-step explanation:

A prime number is a number that can only be the product of 1 and itself. 17 can only be multiplied by 1 and 17, so it is prime.

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3 years ago

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The number of subjects needed to estima

Ludmilka [50]

Answer:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous 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 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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Assuming that the deviation is known we can express the margin of error is given by this formula:

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

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

Replacing into formula (b) we got:

$n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65$

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

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3 years ago

Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her tota

SVETLANKA909090 [29]

Based on the calculations, the amount of money she invested is equal to $3,520.

<h3>How to determine the amount invested?</h3>

First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:

Let x be the amount of money she invested at 11%.

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Since Lydia invested the same amount of money in both stocks, we have:

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Solving the equations simultaneously, we have:

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Read more on interest rates here: brainly.com/question/16793428

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8 0

1 year ago

Help please!!!!!!!!!!!

kvasek [131]

Answer:

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Step-by-step explanation:

To solve this we have to take into account this axioms:

- The total probability is always equal to 1.

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Then, if the probabilities are proportional to the area, we have 1/3 probability of selecting a point inside a circle and (1-1/3)=2/3 probability of selecting a point that is outside the circle.

Then, the probabilty that a random selected point inside the square (the total probability space) and outside the circle is 2/3.

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9514 1404 393

Answer:

Step-by-step explanation:

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