Ask question

Ask question

All categories

3 years ago

7

Below is the total benefit Michelle estimates she would get for eating handfuls of dried cranberries in one sitting. Number of H

andfuls Total Benefit (dollars) 1 $2.00 2 $3.50 3 $4.50 4 $5.00 5 $5.25 6 $5.00 7 $4.00 If a handful of dried cranberries costs $0.50, what is the optimal number of handfuls for Michelle to eat? 2 3 4 5 6
Help please don't have to just say how your day is

1 answer:

givi [52]3 years ago

3 0

Answer:

5

Step-by-step explanation:

You might be interested in

Olivia wants to walk 8000 steps today. She walked 45% of this total before lunch? How many steps did Olivia walk before lunch?

LiRa [457]

Answer:

3600 steps

Step-by-step explanation:

Step 1: Multiply 45 by 8000.

$45 * 8000$
$360000$

Step 2: Move the decimal point two places to the left.

$36000.0$
$3600.00$

Therefore, the answer is 3600 steps.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

4 0

3 years ago

You are building a scale model of a fishing boat. The boat is 62 ft long and 23 ft wide. The

Temka [501]

The wide of the model should be approximately 5.194 inches

Step-by-step explanation:

You are building a scale model of a fishing boat

The boat is 62 ft long
The boat is 23 ft wide
The model will be 14 in long

We need to find how wide should it be

∵ The boat is 62 feet long

∵ The model of the boat is 14 inches long

- That means 14 inches represents 62 feet

By using the ratio method

→ Actual (ft) : Model (in)

→ 62 : 14

→ 23 : x

By using cross multiplication

∵ 62 × x = 23 × 14

∴ 62 x = 322

- Divide both sides by 62 to find x

∴ x ≅ 5.194

∵ x represents the wide of the model

∴ The wide of the model is approximately 5.194 inches

The wide of the model should be approximately 5.194 inches

Learn more:

You can learn more about the scale drawing in brainly.com/question/570757

#LearnwithBrainly

5 0

3 years ago

We have 8 yards of wraping paper. if we use 2 feet for each present how many present can we wrap

kirill [66]

We can wrap 12 presents. multiply the number of yards by the feet.

3 0

4 years ago

Read 2 more answers

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

4 years ago

6.4x+2.8y=44.4, when x=3

ANEK [815]

6.4x + 2.8y = 44.4

6.4(3) + 2.8y = 44.4

19.2 + 2.8y = 44.4
-19.2 -19.2

2.8y = 25.2
------ ------
2.8 2.8

y = 9

7 0

4 years ago

Read 2 more answers