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3 years ago

Find two positive numbers if their ratio is 8:5 and the difference is 150.

1 answer:

7 0

Let's call the two numbers x and y. We can write a system of equations to describe the situation:

5x = 8y

x - y = 150

Let's solve the first equation for x:

x = 8y/5

Now we can use substitution to solve the system by plugging 8y/5 in for x in the second equation:

(8y/5) - y = 150

Simplify:

3y/5 = 150

3y = 750

y = 250

If y = 250, then x is:

x = 8(250)/5 = 400

The answer is 250 and 400.

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25 is 36% of what number

ch4aika [34]

Answer:

x = 69.44

Step-by-step explanation:

We have, 36% × x = 25

or, 36/100 × x = 25

Multiplying both sides by 100 and dividing both sides by 36,

we have x = 25 × 100/36

x = 69.44

If you are using a calculator, simply enter 25×100÷36, which will give you the answer.

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1 year ago

What was the median number of posts made?

Svetradugi [14.3K]

Answer: The median number of posts made is 8.5

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2 years ago

Thetime(inhours)requiredtorepairamachineis an exponentially distributed random variable with parameter λ = 1 . What is 2 (a) the

mihalych1998 [28]

Answer:

a) 0.1353

b) 0.3679

Step-by-step explanation:

Let's start by defining the random variable T.

T : ''The time (in hours) required to repair a machine''

T ~ exp (λ)

T ~ exp (1)

The probability density function for the exponential distribution is

(In the equation I replaced λ = L)

$f(x)=Le^{-Lx}$

With L > 0 and x ≥ 0

In this exercise λ = 1 ⇒

$f(x)=e^{-x}$

For a)

$P(T>2)$

$P(T>2)=1-P(T\leq 2)$

$P(T>2)=1-\int\limits^2_0 {e^{-x} } \, dx$

$P(T>2)=1-(-e^{-2}+1)$

$P(T>2)=e^{-2}=0.1353$

For b)

$P(T\geq 10/T>9)$

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur

$P(T\geq 10/T>9)=P(T\geq 1)$

$P(T\geq 1)=1-P(T$

$P(T\geq 1)=1-(-e^{-1}+1)=e^{-1}=0.3679$

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3 years ago

What are the coefficients for the binomial expansion of (p+q)^6

seropon [69]

Answer:

1 6 15 20 15 6 1

Step-by-step explanation:

To figure this out, we need to look at Pascal's Triangle, which is a tricky little way to find the coefficients for any binomial expression like this! Check the attached photo.

Because this is to the sixth, we need the 6th row, which is <u>1 6 15 20 15 6 1.</u> From this, we know that those numbers are the coefficients!

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3 years ago

Read 2 more answers

Write a real-world problem that could be represented by the following inequality. 70 + 5x < 30 + 15x

kondaur [170]

Justin wants to paint his room. So he put together some quotations from two different painters. The first painter's total charge was based on the number of hours (denoted as x) worked was modeled as f( x ) = 70 + 5 x, while that of the second painter was g( x ) = 30 + 15 x. Justin knows that it will take more than 4 hours to decorate the house so he was certain to go with the first painter whose cost is low-priced when the number of hours is above 4 hours.

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3 years ago