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Nostrana [21]
3 years ago
6

A batch of cookies requires 1 1/2 of sugar. How many batches can Ty make with 7 and 1/2 cups of sugar

Mathematics
1 answer:
Leni [432]3 years ago
8 0
1 1/2 = 3/2. 7 1/2 = 15/2

15/2 divided by 3/2 = 5 batches of cookies
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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co
jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

5 0
3 years ago
-3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified cor
Jobisdone [24]

Answer:

the answer and explanation is in the picture

Step-by-step explanation:

hope this helps

please like and Mark as brainliest

7 0
3 years ago
Express 24.357 in words.<br> Write the expanded form using fractions or decimals.
Lelechka [254]

Answer:

Twenty-four and three hundred fifty-seven thousandths.

Step-by-step explanation:

The expanded form of 24.357 in decimals is 24.3757 because it is already in it's decimal form.

The expanded form of 24.357 in fractions is 24.357. It is a fraction in decimal form rather than in the form of a ratio. However, that does not stop it being a fraction:\frac{24357}{1000}.

4 0
3 years ago
A regular pentagon with a perimeter of 21 inches is dilated by a scale factor of
levacccp [35]
<h3>Answer: 35 inches</h3>

Each side of the pentagon is multiplied by 5/3 to get the length of each new side, so the perimeter is multiplied by 5/3 to get the new perimeter.

New perimeter = (scale factor)*(old perimeter)

New perimeter = (5/3)*(old perimeter)

New Perimeter = (5/3)*(21)

New Perimeter = (5/3)*(21/1)

New Perimeter = (5*21)/(3*1)

New Perimeter = 105/3

New Perimeter = 35 inches

5 0
3 years ago
Read 2 more answers
Evaluate the function f(x) = 2x + 8, when x = -2.
Tanzania [10]

4

search up math vvay  for more explantion also paste this in there

8 0
2 years ago
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