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BlackZzzverrR [31]

2 years ago

6

Bino has answered 15 % of the questions on her ELA homework If she has 25 questions for her homework , how many has she answered

?

1 answer:

MAXImum [283]2 years ago

6 0

She has answered 3.75/25

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Convert 510° from degrees to radians

vitfil [10]

Answer:

$\frac{17\pi }{6}$

Step-by-step explanation:

To convert from degrees to radians

radian = degree measure $\frac{\pi }{180}$

= 510 × $\frac{\pi }{180}$

= $\frac{51\pi }{18}$

= $\frac{17\pi }{6}$ radians

6 0

2 years ago

Read 2 more answers

<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

If x is the least common multiple of the set {6, 8, 12} and y is the greatest common factor

Anarel [89]

Answer:

12

Step-by-step explanation:

The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12

8 0

2 years ago

Leo ordered 79.25 pounds of cookies for a party. When that order came,he received 76.875 pounds of cookies. How many pounds of c

lara31 [8.8K]

2.375 pounds. Just take 79.25 and subtract 76.875 and you get your results.

7 0

2 years ago

Write three numbers that round to 70 when rounded to the nearest ten

Trava [24]

The digit 7 is in the tens place so 74 will become either 70 or 80 after rounding off to the nearest ten. Draw a number line with 3 numbers on it: 70, 75 and 80. (Both possible rounded off numbers and the number in the middle.

3 0

3 years ago