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3 years ago

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

2013). Assume rainfall is normally distributed. How many yearly mm of rainfall would there be in the top 15%? Round answer to 2 decimal places.

1 answer:

svetlana [45]3 years ago

5 0

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%.

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Graph the line that represents a proportional relationship between yyy and xxx where the unit rate of change of yyy with respect

My name is Ann [436]

Answer:

$y=\frac{4}{3}x$

The graph in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m or unit rate of the line and the line passes through the origin

so

In this problem we have

$k=\frac{4}{3}$

substitute

$y=\frac{4}{3}x$

using a graphing tool

The graph in the attached figure

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Name the ray rhat angle PQR and angle SQR share

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<span>Ray Q is the ray that angle PQR and SQR shares. Because both angles has the ray of Q.
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HELP ME ASAP FOR BRANETEST I MEAN IT >_

Julli [10]

Answer:1 1/6

Step-by-step explanation:

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9. Determine how long it takes for 80% of the material to decay.

Vilka [71]

Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

$A(t) = A(0)e^{-kt}$

In which:

k is the decay rate, as a decimal.

A(0) is the initial amount.

The half-life is of 8 days, hence $A(8) = 0.5A(0)$ , and this is used to find k.

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-8k}$

$e^{-8k} = 0.5$

$\ln{e^{-8k}} = \ln{0.5}$

$-8k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{8}$

$k = 0.08664339757$

Hence:

$A(t) = A(0)e^{-0.08664339757t}$

The time it takes for 80% of the material to decay it t for which $A(t) = 0.2A(0)$ , hence:

$0.2A(0) = A(0)e^{-0.08664339757t}$

$e^{-0.08664339757t} = 0.2$

$\ln{e^{-0.08664339757t}} = \ln{0.2}$

$-0.08664339757t = \ln{0.2}$

$t = -\frac{\ln{0.2}}{0.08664339757}$

$t = 18.6$

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

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3 years ago

Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

so

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

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3 years ago