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2 years ago

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The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

the circle circumscribed about this triangle.
Answer in CM, please. Thanks!

1 answer:

Svetllana [295]2 years ago

4 0

Answer:

16cm

Step-by-step explanation:

To find the diameter we must first find the radius and multiply by 2.

The isosceles triangle that has the length of a leg to be 8cm and a vertex angle of $120\degree$ that has been circumscribed is shown in the attachment.

We draw a line from the vertex of the isosceles triangle that bisects the base through the center O of the circle.

This implies that $m\angle OAC=60\degree$ .

Based on this $m\angle ACO=60\degree$ because the two radii are equal.

It follows that: $m\angle AOC=60\degree$ because sum of angles in a triangle must be 180 degrees.

This means that, triangle AOC is an equilateral triangle, hence all sides are equal.

One side of this equilateral triangle happens to be the side of the leg of the isosceles triangle which is 8cm.

It follows that, the radius of the circle is 8cm.

Therefore the diameter of the circle is 16cm

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Write 0.00658 in standard form

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Answer:

0.00658 = 6.58 * 10^-3

Step-by-step explanation:

The standard form is a way of writing numbers easily in powers of 10.

To write a number in standard form, we have to move the decimal point to the front of the first non zero number.

Depending on the position of the decimal point to the first non zero number, movement can be towards the right or towards the left. When we move towards the right, our power of 10 will be negative, when we move in the left direction, our power of 10 will be positive

In this question, we shall be moving towards the right. Thus, our power of 10 is negative. We shall be moving towards the right 3 three times

Thus our power would be 10^-3

Thus our standard form will be 6.58 * 10^-3

Kindly note that another pointer is, if the value of our number to be written in standard form is less than zero, then the standard form will come in negative powers of 10. If the value of the number is greater or equal to 1 at least, then then the standard form will be in positive powers of 10

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Solution:

we are given that

Nathan takes 42 minutes to thread a distance of 4.5 miles on a threadmill.

we have been asked to find the average distance covered in one minute.

Using the concept of unity we can write

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Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

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Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.

Then we have $n_{1} = 25$ , $\bar{x}_{1} = 2.04$ , $\sigma_{1} = 0.010$ and $n_{2} = 20$ , $\bar{x}_{2} = 2.07$ , $\sigma_{2} = 0.015$ . The pooled estimate is given by

$\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552$

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative).

The test statistic is $T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}}$ and the observed value is $t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257$ . T has a Student's t distribution with 20 + 25 - 2 = 43 df.

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$-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}$

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$-0.03\pm(2.0167)(0.012459)(0.3)$ , i.e.,

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