Which statement must be true to be able to use the AAS Congruence Theorem to prove triangle LMN is congruent to triangle PON?

The South Coast Air Basin (Los Angeles, Orange, and San Bernardino counties) does not meet the air quality standards for carbon

Archy [21]

Answer:

0.2225 gr/mile

Step-by-step explanation:

Let's work out first the amount of CO sent out in 1990.

The population we estimated in 12.5 million people with a total of driven miles per year of about

12.5 million*8,700 = 108,750 million miles.

With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams

Now, we must estimate the population for 2020.

Since we are assuming an exponential growth, the population in year t is given by a function

$\bf P(t)= Ce^{kt}$

where C and k are constants to be determined.

We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.

So P(0) = 10.3 and C=10.3

So far we have

$\bf P(t)= 10.3e^{kt}$

Given that P(10)=12.5

$\bf 10.3e^{k*10}=12.5\rightarrow e^{10k}=\frac{12.5}{10.3}=1.21359\rightarrow \\10k=log(1.21359)\rightarrow k=0.01936$

And the function that models the population growth is

$\bf P(t)= 10.3e^{0.01936t}$

We need P(20)

$\bf P(20)= 10.3e^{0.01936*20}=10.3e^{0.38717}=15.17\;million$

If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of

15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.

The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.

We must reduce 118,781.1 down to 29,362.5

Hence the new CO emission factor would be

29,362.5/131,979 = 0.2225 gr/mile

6 0

2 years ago

What is the answer step by step

vesna_86 [32]

2 ≤ 2w +4 ≤ 12

Subtract 4 from all 3 terms:

-2 ≤ 2w ≤ 8

Divide all 3 terms by 2:

-1 ≤ w ≤4

7 0

2 years ago

Two events A and B are independent with Upper P left-parenthesis Upper A right-parenthesis equals Upper P left-parenthesis Upper

soldi70 [24.7K]

Answer:

The value of P (A ∩ B) is 0.25.

Step-by-step explanation:

Independent events are those events that do not effect the occurrence of each other, i.e. if event X and Y are independent then the occurrence of X and Y are not influenced by each other.

For independent events X and Y the joint probability of X and Y is:

$P (X\cap Y)=P(X)\times P(Y)$

It is provided that events A and B are independent of each other.

And P (A) = P (B) = 0.50.

Compute the value of P (A ∩ B) as follows:

$P (A\cap B)=P(A)\times P(B) \\= 0.50\times0.50\\=0.25$

Thus, the value of P (A ∩ B) is 0.25.

3 0

2 years ago

What is m Any answers?

Likurg_2 [28]

Answer:

B. 68°

Step-by-step explanation:

Since, opposite sides of the quadrilateral MNPQ are parallel.

Therefore, it is a parallelogram.

Measures of the opposite angles of a parallelogram are equal.

So,

(6x - 2)° = (4x + 36)°

6x - 2 = 4x + 36

6x - 4x = 36 + 2

2x = 38

x = 38/2

x = 19

$m\angle M = (6x - 2)\degree \\ \\ m\angle M = (6 \times 19- 2)\degree \\ \\ m\angle M = (114- 2)\degree \\ \\ m\angle M =112\degree \\ \\ \because m\angle M + m\angle N = 180\degree \\ (adjacent \: angles) \\ \\ \therefore m\angle N = 180\degree - m\angle M \\ \\ \therefore m\angle N = 180\degree - 112 \degree \\ \\ \therefore m \angle N = 68\degree$

8 0

2 years ago

Write y=-3x^2+12x-21 in vertex form

riadik2000 [5.3K]

Complete the square:
y = 3x^2 - 12x + 4 
y = 3(x^2 - 4x) + 4 
y = 3(x^2 - 4x + 4 - 4) + 4 
y = 3(x^2 - 4x + 4) - 12 + 4 
y = 3(x - 2)^2 - 8

5 0

2 years ago

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