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3 years ago

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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?

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&M’s website says that 24% of milk chocolate M&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