In a batch of 960 calculators, 8 were found to be defective. What is a probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary.

Answer:

The correct answer is yes, we can draw an isosceles triangle with only one 80° angle. NO this is not the only possibility.

Step-by-step explanation:

A triangle is a three sided figure. There are three types of triangles: Equilateral, Isosceles and Scalene triangle. The sum of angles in a triangle is 180°.

If all sides have equal length then it is an equilateral triangle. All angles of this triangle are equal.

If two sides are equal then it is an isosceles triangle. Two opposite angles are equal.

If none of the angles and sides are equal then we call it a scalene triangle.

Given one angle of the triangle is 80°.

There exists two possibilities. One, 80° is the equal angle and 80° is not the equal angle.

Required Case : 80° is not the equal angle, i.e. only one 80° angle.

We are to draw an isosceles triangle (say ABC) with one angle say ∠A as 80°.

Other two angles (∠B and ∠C) are 50° each as the other two angles are supposed to be equal. (°).

Now let us consider side AB and AC be of length say a. These two sides are equal.

Thus now we have successfully constructed an isosceles triangle with only one 80° angle.

We can get infinitely many isosceles triangle by just varying the length of the equal side.

The only batch of paint that will create the same colors as the first batch is Batch 5. Therefore, the correct answer is D. Batch 5

The first batch of paint has the following proportions of blue, white, and yellow:

Blue: 2 parts

White: 1.5 parts

Yellow: 1 part

In order for another batch of paint to create the same colors, it must have the same proportions of blue, white, and yellow.

Batch 2:

Blue: 5 parts

White: 7 parts

Yellow: 3.5 parts

The proportions of blue, white, and yellow in Batch 2 are not the same as the proportions in the first batch, so Batch 2 will not create the same colors.

Batch 3:

Blue: 2.5 parts

White: 3.5 parts

Yellow: 5.5 parts

The proportions of blue, white, and yellow in Batch 3 are also not the same as the proportions in the first batch, so Batch 3 will not create the same colors.

Batch 4:

Blue: 4.5 parts

White: 32 parts

Yellow: 5 parts

The proportions of blue, white, and yellow in Batch 4 are not the same as the proportions in the first batch, so Batch 4 will not create the same colors.

Batch 5:

Blue: 4 parts

White: 3 parts

Yellow: 2 parts

The proportions of blue, white, and yellow in Batch 5 are the same as the proportions in the first batch, so Batch 5 will create the same colors.

Batch 6:

Blue: 432 parts

White: 1.5 parts

Yellow: 34 parts

The proportions of blue, white, and yellow in Batch 6 are not the same as the proportions in the first batch, so Batch 6 will not create the same colors.

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Answer:

D. Batch 5.

Step-by-step explanation:

The batch should have the same proportion of blue to white to yellow.

In Batch 1, there are two parts of blue, 1.5 parts of white, and 1 part of yellow.

In Batch 5, there are four parts of blue, 3 parts of white, and 2 parts of yellow.

4 / 2 = 2

3 / 2 = 1.5

2 / 2 = 1

Since the proportions are equal to those found in Batch 1, D. Batch 5 will create the same colors as the first batch.

Hope this helps!

If A central angle has a measure of 2. 3 radians and the subtended arc length is 12 cm, then the radius of the circle is approximately 5.2 cm.

The formula relating the central angle, radius, and arc length of a circle is:

arc length = radius × central angle

We can use this formula to find the radius of the circle, given the central angle and arc length.

Substituting the given values, we get:

12 cm = r × 2.3 rad

Solving for r, we divide both sides by 2.3 rad:

r = 12 cm / 2.3 rad

Using a calculator, we get:

r ≈ 5.2174 cm

Rounding to the nearest tenth, we get:

r ≈ 5.2 cm

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