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3 years ago

A circle with radius 4 inches is inscribed in an equilateral triangle. Find the area of the triangle.

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

7 0

The inscribed circle has its center at the point of intersection of the angle bisectors, which also happen to be the medians. Hence the altitude of the triangle is 3 times the radius, or 12 inches.

The side length of this triangle is 2/√3 times the altitude, so the area is

... Area = (1/2)·b·h = (1/2)·(24/√3 in)·(12 in)

... Area = 48√3 in² ≈ 83.1384 in²

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Please help me !! find the missing sides

RoseWind [281]

Answer:

Step-by-step explanation:

Hello There!

That is a 45-45-90 special right triangle

so we use the same rules provided in the image

y is = to 10

x is = to $10\sqrt{2}$

so we can conclude that the answer is B

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3 years ago

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass

Setler [38]

Answer:

$\boxed{6.875 \text{\: grams}}$

Step-by-step explanation:

Half-lives are how long it takes for half of a substance to decay. If you start with a certain amount and it decays for a certain amount of half-lives, you are dividing by $2^{x}$ , where <em>x</em> is equal to the amount of half-lives.

In order to solve this question, simply divide the starting value by 2 raised to the value of half-lives.

$\large\boxed{\frac{220}{2^{5}}=6.875\text{\: grams}}$

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3 years ago

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Answer:

Budda Dawgggg

Step-by-step explanation:

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3 years ago

I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit numbers. What could my two numb

lawyer [7]

There 7 blocks of hundreds which means each such block is equivalent to 100.
There are 5 blocks of tens, which means each such block is equivalent to 10.
There are 8 blocks of ones, which means each such block is equivalent to 1.

The total of these blocks will be = 7(100) + 5(10) + 8(10) = 758

We can make several two 3-digit numbers from these blocks. An example is listed below:

Example:
Using 3 hundred block, 2 tens blocks and 4 ones block to make one number and remaining blocks to make the other number. The remaining blocks will be 4 hundred blocks, 3 tens blocks and 4 ones blocks
The two numbers we will make in this case are:

1st number = 3(100) + 2(10) + 4(1) = 324
2nd number = 4(100) + 3(10) + 4(1) = 434

The sum of these two numbers is = 324 + 434 = 758
i.e. equal to the original sum of all blocks.

This way changing the number of blocks in each place value, different 3 digit numbers can be generated.

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3 years ago

A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical trials, 200,0

CaHeK987 [17]

Answer:

1) No, there is not enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0$

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

$p_1=X_1/n_1=21/100000=0.0002$

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

$p_2=X_2/n_2=30/100000=0.0003$

The difference between proportions is (p1-p2)=-0.0001.

$p_d=p_1-p_2=0.0002-0.0003=-0.0001$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=P(z$

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the vaccine was effective.

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3 years ago