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Aleks [24]
3 years ago
13

A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.

Mathematics
2 answers:
GrogVix [38]3 years ago
7 0
Using the Pythagorean theorem we can solve for the radius

see attached picture: 

nika2105 [10]3 years ago
7 0

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

l=\sqrt{d^{2}-(r_{1}-r_{2})^{2}}

19=\sqrt{20^{2}-(11-r_{2})^{2}}

Square both sides.

361=400-(11-r_{2})^{2}

(11-r_{2})^{2}=400-361

(11-r_{2})^{2}=39

Tnking square root both sides.

11-r=\sqrt{39}

11-6.245=r

4.775=r

r\approx 4.8

Therefore the radius of second circle is 4.8 inches and option 3 is correct.

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The length of the red line segment is 6, and the length of the blue line segment is 4. how long is the major axis of the ellipse
juin [17]

An ellipse is divided into two axes, the longer axis is the major axis and the shorter axis is the minor axis. The length of the major axis of an ellipse is equal to the sum of two distance: the distance between any point on the ellipse and one on focus and the distance between the same point and the other focus. The focus is the point that helps define an ellipse and every ellipse has two foci. These two distance are also called the red line segment and blue line segment. Given 6 for red line segment and 4 for blue line segment therefore, the length of the major axis of the ellipse is 10.

3 0
3 years ago
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Match each equation to its equivalent equation in slope-intercept form.
Bumek [7]
1.) y+6=3(x+2)    C
     y+6=3x+6
     y=3x+6-6
     y=3x+6
2.) y=1/2(x+8)-2    B
     y=1/2x+4-2
     y=1/2x+2
3.) y+1=1(x-3)    E
     y+1=x-3
     y=x-3-1
     y=x-4
4.) -4x+y=-2    A
     y=-4x-2
5.) 2x-4y=-4     F
     -4y=-2x-4
     y=-2/-4x-4/-4
     y=2/4x+4/4
     y=1/2x+1
6.) 2x+4y=8     D
     4y=-2x+8
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6 0
3 years ago
Do students that are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student governme
balu736 [363]

Answer:

Option B is correct.

The alternative hypothesis is given Mathematically as

Ha: pA - pB > 0

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup.

For this question, we want to test if students who are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek" by checking the proportion of each group of students that turn out to vote in the student government elections.

If the proportion of Greek students that turn out to vote in the student government elections = pA

And

The proportion of non-Greek students that turn out to vote in the student government elections = pB

And the difference between them is given as

μ₀ = pA - pB

The theory to be tested that pA > pB, would constitute the alternative hypothesis and the null hypothesis would say that either the proportions are equal or proportion of non-greek students that turn out to vote is more than the proportion of Greek students that turn out to vote in the student government elections.

Mathematically,

The null hypothesis would be that

H₀: μ₀ = pA - pB ≤ 0

or

H₀: pA = pB

And the alternative hypothesis would be that

Hₐ: μ₀ = pA - pB > 0

or

Hₐ: pA > pB

Thereby, confirming the theory to be tested.

Hope this Helps!!!

3 0
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Andreas93 [3]

Answer:

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Answer:

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