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miv72 [106K]
3 years ago
5

Kelly makes fruit juice each morning. She uses 2 1/3 pints of strawberries and 1 2/5 pints of grapes in her juice. How many more

pints of strawberries then pints of grapes does she use?
Mathematics
1 answer:
Monica [59]3 years ago
6 0
2 1/3 -1 2/5 =1 1/10
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<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B
riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

It follows that

\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0
2 years ago
$4750 invested at 10% p.a compounded semiannually for 10 years, calculate the interest
alexgriva [62]
<h3>Answer:  $7,853.16</h3>

Work Shown:

A = P*(1+r/n)^(n*t)

A = 4750*(1+0.10/2)^(2*10)

A = 12,603.164099436

A = 12,603.16

That represents the account balance after 10 years. To find the interest only, subtract off the deposit amount.

interest = A-P = 12,603.16 - 4,750 = 7,853.16

6 0
2 years ago
What is the solution to the equation log2 (5x - 2) = 3?
Advocard [28]

From log BNE to BEN

X=2

if you want explaination then ask me

4 0
3 years ago
1+1=?..............................................................
KengaRu [80]
The answer is 2 
1 + 1 = 2
8 0
2 years ago
Read 2 more answers
The M&amp;M’s website says that 24% of milk chocolate M&amp;M’s are blue. Suppose that we buy 5 small packets of milk chocolate
SVEN [57.7K]

Answer:

The correct option is A: 24%, 24%, 24%, 24%, 24%

Step-by-step explanation:

Since the overall probability of M&M's produced is stated as 24% and the packets are filled with different colored candies at random, the probability of blue colored candies in each packet cannot be ascertained individually.

Hope that answers the question, have a great day!

7 0
3 years ago
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