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3 years ago

I really need help with this math problem.

Mathematics

1 answer:

Art [367]3 years ago

3 0

Answer D.

$(36\dfrac{3}{4} +36\dfrac{3}{8} +37\dfrac{1}{2} +z):4=36\dfrac{5}{8}\\\\\\36\dfrac{6}{8} +36\dfrac{3}{8} +37\dfrac{4}{8} +z=4\cdot36\dfrac{5}{8}\\\\\\36\dfrac{6}{8} +36\dfrac{3}{8} +37\dfrac{4}{8} +z=4\cdot36\dfrac{5}{8}\\\\\\109\dfrac{13}{8}+z=4\cdot36+4\cdot\dfrac{5}{8}\\\\\\110\dfrac{5}{8}+z=144+\dfrac{20}{8} \\\\\\z=144+\dfrac{20}{8} -110-\dfrac{5}{8}\\\\\\z=34+\dfrac{15}{8}\\\\\\z=34+1\dfrac{7}{8}\\\\\\z=35\dfrac{7}{8}$

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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

The radius of a circle is 19 miles. What is the circle's circumference?<br> Use 3.14 for .

insens350 [35]

Answer:

119.38

Step-by-step explanation:

the circumference is πd so it is 19 X 2, which is 38, times π, which is 38π. this equals 119.38

7 0

2 years ago

Read 2 more answers

You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery

riadik2000 [5.3K]

Answer:

Loss of $1.20

Step-by-step explanation:

The possible outcomes for this lottery and their probabilities are:

- a 1 in 100 chance of winning $450

- a 2 in 100 chance of winning $120

- a 4 in 100 chance of winning $30

- a 93 in 100 chance of losing $10

Therefore, the expected value of this lottery when buying one ticket is:

$E(X) = \frac{1}{100}*\$450+ \frac{2}{100}*\$120+ \frac{4}{100}*\$30-\frac{93}{100}*\$10 \\E(X) = -\$1.2$

Therefore, you are expected to lose $1.2 per ticket.

3 0

3 years ago

One and three seven divided by two

Vladimir [108]

Answer:

0.7 or 5/7

Step-by-step explanation:

(1 3/7) ÷ 2 =

8 0

3 years ago

There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same sta

Morgarella [4.7K]

Answer:

a) rCn = 1176

b) 2352

Step-by-step explanation:

a)Each committee should be formed with 3 members ( no two members could be of the same state) then

Let´s fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then

rCn = n! / (n - r )! *r!

rCn = 49!/ (49 - 2)!*2!

rCn = 49*48*47! / 47!*2!

rCn = 49*48 /2

rCn = 1176

So we can choose in 1176 different ways a senator for a given state

b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.

1176*2 = 2352

6 0

3 years ago