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lana66690 [7]
3 years ago
8

The variable z is directly proportional to x, and inversely proportional to y. When x is 20 and y is 6, z has the value 66.66666

6666667. What is the value of z when x= 25, and y= 12
Mathematics
1 answer:
sergejj [24]3 years ago
6 0

Answer:

41.667 to the nearest thousandth.

Step-by-step explanation:

z = kx/y where k is the constant of proportionality.

Inserting the given values:

66.666666666667 = k*20/6

20k = 6*66.666666666667

k = 6*66.666666666667 / 20

=  20

So the equation of variation is z = 20x /y

When x = 25 and y = 12:

z = 20*25/12

= 41.666666666667.

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Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of
miss Akunina [59]

Answer:

The function that represents the mass of the sample after t days is A(t) = 390(0.41)^t.

The percentage rate of change per hour is of -2.46%.

Step-by-step explanation:

Exponential amount of decay:

The exponential amount of decay for an amount of a substance after t days 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.

Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.

This means, respectively, that r = 0.59, A(0) = 390

So

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

A(t) = 390(1-0.59)^t

A(t) = 390(0.41)^t

The function that represents the mass of the sample after t days is A(t) = 390(0.41)^t.

Hourly rate of change:

Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So

-59%/24 = -2.46%

The percentage rate of change per hour is of -2.46%.

5 0
3 years ago
if there is 27 marbles in a bag and the amount of red marbles is 5 less than 3 times the amount of blue marbles how many marbles
alexira [117]

Answer:

54

Step-by-step explanation:

5-3=2

so you multiply 2 times 27.

2 times 27 is 54

8 0
3 years ago
4/5 + r=-3<br><br> What is the answer to this equation?
Zolol [24]

Answer:

r= -19/5

Step-by-step explanation:

6 0
3 years ago
Which of these is equivalent to 1 over x to the power of 5 ? 1 fifth x negative x to the power of 5 x to the power of 5 x to the
Kisachek [45]

Answer:

x^-5 = x to the power of negative 5

Step-by-step explanation:

Which of these is equivalent to 1 over x to the power of 5 ?

Mathematically this is expressed as

(1/x)⁵

We have a rule when it comes to expressing power

(1/a)^b = a^-b

Hence, applying this rule to our question

(1/x)⁵ = (1/x)^5

= x^-5

This is written in words as:

x to the power of negative 5

5 0
3 years ago
What is the length of an arc defined by a 60 degree central angle in a circle with a radius of 5 in.?
Natali [406]

Answer:

5.24 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference × fraction of circle

     = 2πr × \frac{60}{360}

     = 2π × 5 × \frac{1}{6}

     = \frac{10\pi }{6} ≈ 5.24 in (2 dec. places )

3 0
3 years ago
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