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3 years ago

Spilled $40 into the ratio of 3:7

Mathematics

2 answers:

ohaa [14]3 years ago

8 0

Answer:

$12/$28

Step-by-step explanation:

Let x and y represent the two amounts of money adding up to $40.

Assume that x is the smaller amount. Then:

x 3

----- = ----- Remembering that x + y = $40, we get x = $40 - y

y 7

amd sp we have

$40 - y 3

-------------- = ------ which, after cross-multiplication, is $280 - $7y = 3y

y 7

Simplifying this, we get $280 = 10 y, so that y must be $28. If y = $28, x must be $40 - $28, or $12.

$12

Then $40, split in the ratio 3/7, is the ratio ----------------

$28

Check: Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.

galina1969 [7]3 years ago

5 0

Answer: 12:28

Step-by-step explanation:

40/10=4

4x3=12

4x7=28

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What is the area of the blue shaded region???????

Anna [14]

Answer:

Step-by-step explanation:

22/7x7^2=154

22/7x3^2=28(approx)

154-28=126

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3 years ago

Dave loves underwater diving. His house boat is 250 feet above sea level. He jumped from that level. He went 600 feet below sea

nikklg [1K]

Answer:

Step-by-step explanation:

<u>I would just like to explain how this works with a visual (please enjoy my drawing <3 haha)</u>

With my drawing we know that the bird is 150 feet above sea level, and the fish is 100 feet below sea level.

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<h3>This is equal to 250 feet, </h3>

so we know from the bird (150 feet above sea level) to the fish(100 feet below sea level).

<h2>Knowing this information we can easily answer this question</h2><h3>Dave is 250 feet above sea level, and he went 600 feet nelow sea level, meaning<u> he only went 600 feet under the water.</u></h3>

Download pdf

7 0

2 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

Bianca deposits $3,000 in a savings acct earning 4.25% simple interest per year.

murzikaleks [220]

Answer:

$637.50

Step-by-step explanation:

P = $3000

t= 5years

r = 4.25% per annum

Interest = (p×r×t)/100

= (3000×4.25×5)/100

= $637.50

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3 years ago

Without using the formula, work out the gradient of the graph shown.

Harman [31]

Answer:

1/3

Step-by-step explanation:

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2 years ago