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2 years ago

What property was used on 14k+2(3k+5)-5=10 to obtain 14k+6k+10-5=10

1 answer:

3 0

The difference between

i) 14k+2(3k+5)-5=10 and

ii) 14k+6k+10-5=10

is the equality 2(3k+5)=6k+10

The property used here, can be described for any numbers a, b and c as:

$a \cdot (b+c)=a \cdot b +a \cdot c$

This is called the DISTRIBUTIVE PROPERTY

Answer: DISTRIBUTIVE PROPERTY

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A survey of 2690 musicians showed that 368 of them are left-handed. Find a point estimate for p, the population proportion of mu

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Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690 [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: $\hat{p}=\dfrac{368}{2690}\approx0.137$

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

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2 years ago

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquariu

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Answer:

Workdone = 2450Joules

Step-by-step explanation:

Let the top of the aquarium be at height 0.

Let the bottom of the aquarium be at height 1

F = mg = 2p◇x × g

F= 2000◇x × 9.8

F = 19600◇x

Workdone = 19600xdx

Total workdone = Integral (limits 0.5 -0)19600×dx

Total work = [9800x^2]^0.5

Total work= 9800× 0.5^2 = 2450 Joules

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2 years ago

Before the distribution of certain statistical software, every fourth compact disk (CD) is tested for accuracy. The testing proc

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Answer:

a) For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

$P(R) =\frac{1}{4} =0.25$

The failure probability for each program are given by:

$P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01$

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

$P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932$

So then the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

And if we use the fact that we have 4 possible test the true probability of interest would be:

$P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017$

b) $p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))$

And replacing we got:

$p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484$

c) From part a we now that the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

So then if we have 100 CDs the expected number of rejected Cd's are:

$100*0.068= 6.8 \approx 7$

Step-by-step explanation:

Part a

For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

$P(R) =\frac{1}{4} =0.25$

The failure probability for each program are given by:

$P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01$

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

$P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932$

So then the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

And if we use the fact that we have 4 possible test the true probability of interest would be:

$P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017$

Part b

For this case we want the probability that it failed program 2 or 3

So then we can find this probability like this:

$p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))$

And replacing we got:

$p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484$

Part c

From part a we now that the probability that any program fails would be given by:

$P(F) = 1- 0.932= 0.068$

So then if we have 100 CDs the expected number of rejected Cd's are:

$100*0.068= 6.8 \approx 7$

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2 years ago

. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal

Phantasy [73]

Answer:

x = $\frac{\sqrt{3} }{3}$

Step-by-step explanation:

You can either use the unit circle to find your values and then solve for x or plug it into the calc directly to find your answer (don't forget to put your mode on deg!). It is much faster to plug it into your calc. Simply just divide both sides by tan45°cos30° and you should isolate x and find your answer.

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2 years ago

Draw a diagram in which segment AB intersects segment CD equals segment CB

Contact [7]

The correct diagram is attached.

Explanation:

Using technology (such as Geogebra), first construct a line segment. Name the endpoints C and D.

Construct the perpendicular bisector of this segment. Label the intersection point with CD as B, and create another point A above it.

Measure the distance from C to B and from B to D. They will be the same.

Measure the distance from A to B. If it is not the same as that from C to B, slide A along line AB until the distance is the same.

Using a compass and straightedge:

First construct segment CD, being sure to label the endpoints.

Set your compass a little more than halfway from C to D. With your compass set on C, draw an arc above segment CD.

With your compass set on D (the same distance as before) draw an arc above segment CD to intersect your first arc. Mark this intersection point as E.

Connect E to CD using a straightedge; mark the intersection point as B.

Set your compass the distance from C to B. With your compass on B, mark an arc on EB. Mark this intersection point as A.

AB will be the same distance as CB and BD.

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2 years ago

Read 2 more answers