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2 years ago

9

Fernando had 20 minutes to do a three-problem quiz. He spent 10 9/10 minutes on question A and 5 3/5 minutes on question B. How

much time did he have left for question C?

1 answer:

katrin2010 [14]2 years ago

4 0

Answer:

1.65 minutes

Step-by-step explanation:

10 9/10 + 5 3/5 = 16 1/2

16 1/2 divided by 20 = 1.65 or 33/20

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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

Which expression represents "5 times the sum of 4 and y?"

Mkey [24]

Answer:

5 x (4+y)

Step-by-step explanation:

8 0

3 years ago

A box with no top is to be constructed from a piece of cardboard whose length measures 88 in. more than its width. the box is to

MariettaO [177]

Let x be the width of the cardboard (which means the length of the cardboard is x+88), then the dimensions of the box are:

Length = [(x + 88) - 2(33)]

Width = x - 2(33)

Heighth = 33

Volume = length · width · heighth

144,144 = [(x + 88) - 2(33)] · [x - 2(33)] · 33

144,144 = (x+22)(x-66)(33)

4368 = (x+22)(x-66)

4368 = x² - 44x - 1452

0 = x² - 44x - 5820

use the quadratic formula to calculate that x = 101

Answer: cardboard width = 101, cardboard length = 189

4 0

3 years ago

What are the solutions of -1 <=x-3<4? help asap

viva [34]

I think the answer is -1=x-3<4

4 0

2 years ago

I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would

Elodia [21]

Answer:

3 km

Step-by-step explanation:

Lets say that you flipped the smaller triangle to be facing the same way as the bigger triangle. To find the X side, we need to do 4.5/1.2 = 1.75. which is the difference between the sides. So then we do 1.75 x 0.8 = 3.

Sorry if I couldn't explain well enough, which is not something I'm good at. I hope you get the question right! Glad I could help! :)

3 0

2 years ago