The lines are parallel.

In order to figure this out, let's start off by simplifying both equations as much as we can:
2y = 16 + 4x
Divide by 2
y = 2x + 8

Remember that the slope of that equation is '2' since 'm' in the equation y = mx + b represents slope.

Simplify the next equation:
6y - 30 = 12 x
6y = 12x + 30
Divide by 6:
y = 2x + 5

As you can tell, this line also has a slope of 2.
Parallel lines is defined as two lines that have the same slope. Knowing this, we can infer that these two lines are parallel.

-T.B.

7 0

2 years ago

The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of,"

svetlana [45]

Answer:

At least 202.44 mm in the top 15%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 134, \sigma = 66$

How many yearly mm of rainfall would there be in the top 15%?

At least X mm.

X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

$Z = \frac{X - \mu}{\sigma}$

$1.037 = \frac{X - 134}{66}$

$X - 134 = 66*1.037$

$X = 202.44$

At least 202.44 mm in the top 15%.

5 0

2 years ago

Find x please help me

Mrac [35]

X = 30 I think as angle on straight line = 180 so 180-103 = 77 , 30+43 = 73 , 77+73 = 150 , 180-150= 30 , then opposite angles are the same so therefore x = 30 degrees

8 0

2 years ago

Evaluate the expression for = −3 and = 5. r^{-4} s^2

Butoxors [25]

If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81

If r = 5 and s = -3:
(r^-4)(s^2) = (5^-4)(3^2) = (1/625)(9) = 9/625

5 0

2 years ago

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