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TEA [102]
3 years ago
14

Lula is buying meatballs for her beach theme party each package contains six beach balls generate the set of ordered pairs for t

he ratio relationship between the number of beach balls in the number of packages for a total of one, two, three, and four packages
Mathematics
1 answer:
andreev551 [17]3 years ago
8 0

Answer:

  {(1, 6), (2, 12), (3, 18), (4, 24)}

Step-by-step explanation:

We are given that ...

  (packages, balls) = (1, 6)

Multiplying by 2, 3, and 4, we find the set of ordered pairs to be ...

  {(1, 6), (2, 12), (3, 18), (4, 24)}

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This equation is an example of:
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Answer:

B. FOIL

Step-by-step explanation:

FOIL stands for Firsts, Outsides, Insides, and Lasts

This is a mnemonic to help you to remember how to multiply two binomials

From the image, we can see that the on the right side of the equals,

(x)(-5x^2) is the product of the <u>firsts</u> of the binomials

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You buy a total of 50 turkey burgers and veggie burgers for $90. You pay $2 per turkey burger and $1.50 per veggie burger. Write
Slav-nsk [51]

Answer:

T + V = 50

2T + (3/2) * V = 90

2T + 1.5V = 90

T = 50 * 1.5 - 90 * 1 / 1 * 1.5 - 2*1 = 30

V = 1 * 90 - 2 * 50 / 1 * 1.5 - 2 * 1 = 20

Step-by-step explanation:

T = 30

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2 years ago
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv
sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

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Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

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39.15 ^-^

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