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Viefleur [7K]
3 years ago
15

Luna bought a package of 5 oatmeal cookies. The total weight of the cookies was 1 ounce. How much did each cookie weigh?

Mathematics
1 answer:
Anarel [89]3 years ago
6 0
Each cookie weighed 1/5 ounce
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What is z x y+b if b x g= 533773
umka2103 [35]

Step-by-step explanation:

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7 0
3 years ago
A seafood restaurant owner orders perch and salmon. Perch is four dollars per pound and salmon is three dollars per pound. He wa
Svetach [21]

Answer:

He can buy at least 34 pounds of fish.

Step-by-step explanation:

4x + 3x \leq 240

7x \leq 240

(240 divided by 7 gives you a decimal, so you would round it to the nearest whole number)

x \leq 34

0 0
3 years ago
Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find
inna [77]

Best guess for the function is

\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}

By the ratio test, the series converges for

\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1

When x=1, f(x) is a convergent p-series.

When x=-1, f(x) is a convergent alternating series.

So, the interval of convergence for f(x) is the <em>closed</em> interval \boxed{-1 \le x \le 1}.

The derivative of f is the series

\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n

which also converges for |x| by the ratio test:

\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1

When x=1, f'(x) becomes the divergent harmonic series.

When x=-1, f'(x) is a convergent alternating series.

The interval of convergence for f'(x) is then the <em>closed-open</em> interval \boxed{-1 \le x < 1}.

Differentiating f once more gives the series

\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)

The first series is geometric and converges for |x|, endpoints not included.

The second series is f'(x), which we know converges for -1\le x.

Putting these intervals together, we see that f''(x) converges only on the <em>open</em> interval \boxed{-1 < x < 1}.

6 0
2 years ago
Lin's family has completed 90% of a trip. They have traveled 45 miles. How far is the trip?
Lina20 [59]

Answer:

50 miles

Step-by-step explanation:

90% completed (in percentage)

45 mi completed (in miles)

Thus, we can say:

45 is 90% of what number??

This "what number" is the total (what we are trying to find). Now, we let this "what number" part be equal to "x". Also, we know "IS" means "=" and "OF" means "*". Thus we can write:

45 is 90% of what number??

45 = 90% * x

90% converted to decimal is:

90/100 = 0.9

Thus, the equation becomes:

45=0.9x

Solving for x:

45=0.9x\\x=\frac{45}{0.9}\\x=50

The trip is 50 miles

3 0
3 years ago
Read 2 more answers
What the slope of this please help :)
enyata [817]

Answer:

-0.1

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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