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Nikolay [14]
3 years ago
13

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the ci

rcle area A = 9π cm2 and Θ = π/4 .
Mathematics
1 answer:
Luda [366]3 years ago
6 0
<h3>Answer:</h3>

arc length = 3π/4 cm

<h3>Explanation:</h3>

The appropriate relations are ...

... A = πr² . . . . area of a circle

so ...

... r = √(A/π)

and

... s = rθ . . . . . arc length

___

Combining these, we have

... s = θ√(A/π)

Filling in your numbers gives ...

... s = (π/4)√((9π cm²)/π)

... s = 3π/4 cm

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NeX [460]
Area of a square

A = s^2, where s = length of side

A = (12 mm)^2

A = 144 mm^2

The area if 144 mm^2.
5 0
3 years ago
The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.
Rom4ik [11]

Answer:

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u >= 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u/ (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = -0.22 / (0.41/4.2426)

t = -0.22/ 0.0966

t = -2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.

6 0
3 years ago
-8
nevsk [136]

Answer:

  take your pick. Each has its own reason.

Step-by-step explanation:

As with a lot of "doesn't belong" problems, the one that is different depends on your criteria. In the attached figure, each one "doesn't belong" for a different reason. Those reasons are listed below each number line.

__

I might choose the lower left: "addition, not subtraction", as it is the only one with arrows in the same direction. That makes its difference from the others more obvious, perhaps.

6 0
3 years ago
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
kow [346]

Answer: The triangles are not similar.

Step-by-step explanation:

Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.

<em>For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.</em>

Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.

\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24

Since we matched corresponding sides, we can now check whether they have the same ratio).

\frac{18}{14}=\frac{20}{15}=\frac{32}{24}

\frac{9}{7}=\frac{4}{3}=\frac{4}{3}

Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their

4 0
2 years ago
Select the correct answer from each drop-down menu.The center of the circle is at O. Segment AB is tangent to circle O at point
IRISSAK [1]

Based on the tangent theorem, m∡ADO = 90°.

Based on the angles of intersecting chords theorem, m∡CGF = 1/2(mCF + mDE).

What is the Angles of Intersecting Chords Theorem?

The angles of intersecting chords theorem states that when two chords in a circle intersect, the angle formed inside the circle at the point of intersection has a measure that is half of the sum of the measures of the intercepted arcs that are formed by the angle and its vertical angle.

<h3>What is the Tangent Theorem?</h3>

According to the tangent theorem, if a line is tangent to a circle, the segment forms a right angle at the point of tangency with the radius of the circle.

Since line AB is tangent to circle O at point D, therefore, based on the tangent theorem:

The measures of angle ADO = 90°

Chord CE and DF intersect in the circle, therefore, based on the angles of intersecting chords theorem:

The measure of CGF = 1/2(mCF + mDE).

Learn more about the tangent theorem on:

brainly.com/question/9892082

#SPJ1

4 0
1 year ago
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