12. Phil invests $5000 in a high-interest savings account and earns 3.5% simple

What does a trapezium look like

sasho [114]

This is a trapezium with congruent unparallel lines.

5 0

3 years ago

Birds arrive at a birdfeeder according to a Poisson process at a rate of six per hour.

m_a_m_a [10]

Answer:

a) time= $10 \frac{1}{6}=\frac{10}{6}=1.67 hours$

b) $P(T\geq 0.25h)=e^{-(6)0.25}=0.22313$

c) $P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347$

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

$P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}$

And the parameter $\lambda$ represent the average ocurrence rate per unit of time.

The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

$P(T>t)= e^{-\lambda t}$

a. What is the expected time you would have to wait to see ten birds arrive?

The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:

time= $10 \frac{1}{6}=\frac{10}{6}=1.67 hours$

b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?

Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:

$P(T\geq 0.25h)$

And we can use the result obtained from the definitions and we have this:

$P(T\geq 0.25h)=e^{-(6)0.25}=0.22313$

c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?

First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :

$P(T \leq a +t |T>t)=P(T\leq a)$

Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:

$P(T\leq 0.0833+0.0833| T>0.0833)$

$P(T\leq 0.1667| T>0.0833)$

And using the Markovian property we have this:

$P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347$

3 0

3 years ago

What are materials both the moon and Earth have?

Doss [256]

The elements found in greatest abundance in the Earth include oxygen, silicon, aluminum, iron and calcium; these substances also make up the bulk of the moon. Although the moon is an airless world, it has large amounts of oxygen in the form of solid chemical compounds.

6 0

3 years ago

Find x and y Don’t argue in the comments I actually need help

igor_vitrenko [27]

X=132

To find y
180-132= 48
180-68-48=64
y=64

7 0

3 years ago

Read 2 more answers

The material used to make a storage box costs $1.25 per square foot. The boxes have the same volume, so how much does a company

riadik2000 [5.3K]

Answer: A company saves $134.38 by choosing to make 50 of Box 2 instead of Box 1

Step-by-step explanation:

Hi, to answer this question we have to calculate the surface area of both boxes.

Surface area (A) = 2wl + 2lh + 2hw,

Where w is width, l is length , and h is height.

Box 1 = A = 2(6x20) + 2( 20x4) + 2 (4 x 6) =2 (120)+ 2 (80)+ 2(24) =448 in2
Box 2 = A = 2 (4x15)+ 2(15x8)+ 2(8x4) = 2(60)+2(120)+2(32)=424 in2

Since 1 inch = 0.0833333 foot

Box 1 = 448 in2 x 0,0833333 =37.34 ft2
Box 2= 424 in2 x 0,0833333 =35.19 ft2

Since the material used to make a storage box costs $1.25 per square foot.

Box 1 =37.34 ft2 x1.25 = $ 46.675
Box 2= 35.19 ft2 x 1.25 =$43.98

Since 50 of each are made:

Box 1 = $ 46.675 x50 =2,333.750
Box 2= $43.98 x50 =2,199.37

Subtracting both costs:

2,333.750(1) - 2,199.37(2) = $134.38

6 0

3 years ago