Rachna has nickels, dimes, and quarters in her piggy bank. She has $4.65 altogether. She has three more quarters than dimes and twice as many nickels as quarters. How many quarters does Rachna have?

A. 8
B. 11
C. 22
D. 41

Answers

Answer 1

Answer:
we can translate the given statements into algebraic expressions. In this case,

0.05x + 0.10y + 0.25z = 4.65z = 3 + yx = 2 z
solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11

Answer 2

Answer:

For this case we have the following variables:

x: number of nickels

y: number of dimes

z: number of quarters

We now write the system of equations that models the problem:

$0.05x + 0.1y + 0.25z = 4.65 z = y + 3 x = 2z$

Rewriting the equations as a function of z we have:

$0.05 (2z) + 0.1 (z-3) + 0.25z = 4.65$

From here, we clear the value of z:

$0.1z + 0.1z - 0.3 + 0.25z = 4.65 0.1z + 0.1z + 0.25z = 4.65 + 0.3 0.1z + 0.1z + 0.25z = 4.65 + 0.3 0.45z = 4.95$

$z = (4.95)/(0.45) z = 11$

Answer:

The number of quarters that Rachna has is:

B. 11

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Answers

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An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

Answers

The volume of a sphere:
$V=(4)/(3) \pi r^3$
r - the radius

3392.92 cubic inches are poured into 30 spheres.
$3392.92=30 * (4)/(3) \pi r^3 \n \n3392.92=40\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ |/ 40 \n \n84.823=\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ \pi \n \nr^3=(84.823)/(\pi) \n \nr=\sqrt[3]{(84.823)/(\pi)} \n \nr \approx \sqrt[3]{27} \n \nr \approx 3$

The diameter is twice the radius.
The diameter of each sphere should be approximately 6 inches.

Answer:

6 inches

Step-by-step explanation:

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Answers

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Nathan has 80 stamps in his collection. He adds 1 stamp to it today. Each day he plans to add twice the number of stamps as the previous day. If he keeps adding stamps at this rate for n days, which recursive function represents the number of stamps he has on any day in the future?

Answers

The recursive function which represents the number of stamps he has on any day in the future is F(n) = 80 + 2ⁿ.

Given that:

Number of stamps that Nathan has in the beginning = 80

He adds 1 stamp to it today.

Each day he plans to add twice the number of stamps as the previous day.

So, the number of stamps will be in the order:

80 + 1, 80 + 2(1), 80 + 2(2(1)), 80 + 2(2(2(1))), ...

That is each day, the added stamps become twice.

On the first day, he added 1, on the second day, he added 2, on the third day, he added 4, ...

So, the recursive function can be written as:

F(n) = 80 + 2ⁿ, where n starts from 0.

Learn more about Recursive Functions here :

brainly.com/question/26993614

#SPJ2

111
We start with 80 and we add 1 on the first day, 2 on the 2nd, 4 on the 3rd, etc.. Looking at the numbers being added 1 = 202 = 214 = 228 = 2316 = 24...We start with 80 and we add 2n to it where n represents the number of days into the iterationwith n starting at 0 The function that shows how many stamps we have on any given day is DS = 80 + ∑ 2n Where D is the number of days we are into the iteration n=0NOTE: This starts at day 0 which would be S = 80 + 20 = 80 + 1 = 81 stamps Example: To find how many stamps we have on D = 4 we would haveS = 80+20+21+22+23+24 = 80+1+2+4+ 8+16 = 111 stamps

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