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3 years ago

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]

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

8 0

2 years ago