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pshichka [43]
3 years ago
14

Match the reasons with the statements in the proof.

Mathematics
2 answers:
bija089 [108]3 years ago
8 0

Answer:

Step-by-step explanation:

1. m∠6 = m∠8, b║c

Given

2. m∠7 = m∠8

It is given that b and c are parallel therefore, ∠7 and ∠8 are the corresponding angles.

3. m∠6 = m∠7

Since ∠6 = ∠8 and ∠7 = ∠8

Therefore, ∠6 = ∠7

Substitution

4. a║b

Since ∠6 = ∠7 (alternate interior angles) so lines a and b will be parallel.

natta225 [31]3 years ago
6 0
<span>1. m∠6=m∠8, b||c
Given

2. m∠7=m∠8
</span><span>If lines ||, corresponding angles =.
</span><span>
3. m∠6=m∠7
</span>Substitution 
<span>
4. a||b </span>
If alternate interior angles equal, then lines ||. 
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The blood platelet counts of a group of women have a boll-shaped distribution with a mean of 261.1 and a standard deviation of 6
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The variable is

X: blood platelet count of a woman

This variable has a bell shaped distribution (Normal)

With mean μ=261.1 and standard deviation σ=64.3

a.

The platelet count within 3 standard deviations of the mean can be calculated as

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You can symbolize it as

μ-3σ ≤ X ≤ μ+3σ

According to the empirical rule of the normal distribution you know that under any bell shaped distribution:

Between μ ± σ you'll find the 68% of the distribution

Between μ ± 2σ you'll find the 95% of the distribution

Between μ ± 3σ you'll find the 99% of the distribution

So following this rule you'll find 99% of the women with platelet count within 3 standard deviations of the mean.

b.

3% of the population is found between a vertain interval, the rest 97% is separated in equal tails around this interval.

Divide 0.97 by 2

0.97/2= 0.485

Each tail contains 0.485 of the distribtuion.

a and b represent the values within you'll find 3% of the population.

Until a you'll find 0.485 of the population and until b you'll find 0.485+0.03=0.515

To calculate both unknown values you have to use the standard normal distribution. This distribution is centered in zero, the left tail is negative and the right tail is positive.

a and b are at a equal distance from the mean but with different sign, so you only have to calculate on and then you invert the sign to get the other one.

I'll calculate the positive value:

Z= (X- μ )/σ~N(0,1)

P(Z≤ b)=0.515

Look in the body of the Z-table, rigth or positive entry and reach the margins for the value:

b= 0.038

Then using the values of the mean and the standard deviation you can calculate the corresponding valueof platelet count:

b= (X- μ )/σ

0.038= (X- 261.1 )/64.3

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X=263.5434=263.5

a=-b=-0.038

a= (X- μ )/σ

-0.038= (X- 261.1 )/64.3

-0.038*64.3=X-261.1

-2.4434+261.1=X

X=258.6566= 258.7

3% of the populations platelet count is between 258.7 and 263.5.

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