The sum of two numbers is 56 . one number is 3 times as large as the other. what are the numbers?

Element X is a radioactive isotope such that its mass decreases by 26% every day. If an experiment starts out with 810 grams of

ioda

Answer:

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

The function to represent the mass of the sample after t days is $A(t) = 810(0.74)^t$

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the amount of a substance is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Hourly rate of change:

Decreases 26% by day. A day has 24 hours. This means that $A(24) = (1-0.26)A(0) = 0.74A(0)$ ; We use this to find r.

$A(t) = A(0)(1-r)^t$

$0.74A(0) = A(0)(1-r)^{24}$

$(1-r)^{24} = 0.74$

$\sqrt[24]{(1-r)^{24}} = \sqrt[24]{0.74}$

$1 - r = (0.74)^{\frac{1}{24}}$

$1 - r = 0.9875$

$r = 1 - 0.9875 = 0.0125$

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

Starts out with 810 grams of Element X

This means that $A(0) = 810$

Element X is a radioactive isotope such that its mass decreases by 26% every day.

This means that we use, for this equation, r = 0.26.

The equation is:

$A(t) = A(0)(1-r)^t$

$A(t) = 810(1 - 0.26)^t$

$A(t) = 810(0.74)^t$

The function to represent the mass of the sample after t days is $A(t) = 810(0.74)^t$

5 0

2 years ago

Substitute this equation y=-2x-12 if y=-8

lozanna [386]

Answer:

x=-2

Step-by-step explanation:

6 0

3 years ago

The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m

photoshop1234 [79]

Answer: 0.1353

Step-by-step explanation:

Given : The mean of failures = 0.025 per hour.

Then for 8 hours , the mean of failures = $\lambda=8\times0.25=2$ per eight hours.

Let X be the number of failures.

The formula to calculate the Poisson distribution is given by :_

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

Now, the probability that the instrument does not fail in an 8-hour shift :-

$P(X=0)=\dfrac{e^{-2}2^0}{0!}=0.1353352\approx0.1353$

Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353

7 0

3 years ago

An airplane is flying from New York City to Los Angeles the distance it travels in Miles D is related to the time in seconds T b

tatiyna

Answer:

It takes 85 seconds to go 12.75 miles

Step-by-step explanation:

We are given

An airplane is flying from New York City to Los Angeles

the distance it travels in Miles D is related to the time in seconds T by the equation

$d=0.15T$

we are given to find time when distance is 12.75 miles

so, we can set d=12.75

and then we can solve for T

$12.75=0.15T$

We can divide both sides by 0.15

$T=\frac{12.75}{0.15}$

$T=85$

So,

It takes 85 seconds to go 12.75 miles

6 0

3 years ago

How would you write 4n + 3 as a verbal expression

Tatiana [17]

<h3>4 times a number increased by 3.</h3>

When we have a number that appears

right before a variable, it means multiplication.

So 4n means the same thing as 4 times a number.

Remember, n is a variable which is just a

letter that represents any number.

Since we are adding 3 to 4n, we can say

4 times a number increased by 3.

So 4n + 3 can be written as 4 times a number increased by 3.

5 0

3 years ago

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