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3 years ago

What is 1 5/8 times 2 2/3

Mathematics

2 answers:

matrenka [14]3 years ago

8 0

Answer:

4 1/3

Step-by-step explanation:

1 5/8 × 2 2/3

First we turn it into an improper fraction:

1 5/8 × 2 2/3 = 13/8 × 8/3

Now we multiply them across:

13/8 × 8/3 = 104/24

Now we simplify:

104/24 = 13/3

because 3 × 8 = 24 and 13 × 8 = 104

Now we simplify again because we can't leave it as an improper fraction. So we turn it into a mixed fraction:

13/3 = 4 1/3

4 1/3 is answer

Pavel [41]3 years ago

6 0

Answer:

Step-by-step explanation:

Convert mixed fraction to improper fraction.

$1\frac{5}{8}*2\frac{2}{3}=\frac{13}{8}*\frac{8}{3}\\\\\\=\frac{13}{3}\\\\\\=4\frac{1}{3}$

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Solve the following proportion; -5/3=2-3a/7

Varvara68 [4.7K]

Answer:

a = <u>77</u>

This is the answer

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3 years ago

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

nolan works at a sandwich shop. he needs to make 7 turkey sandwiches. each sandwich has 1/3 of a pound of turkey. how many pound

FromTheMoon [43]

Turn 7 into a fraction so it can be multiplied. > 7/1

Multiply 7/1 by 1/3.

7/1 × 1/3 = 7/3

Simplify 7/3 into a mixed number.

7/3 = 2 1/3

Nolan will need 2 1/3 lbs of turkey.

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4 years ago

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Ray has a handful of dimes and nickels valuing $3.05. He has 5 more dimes than he does nickels. How many of each coin does he ha

Thepotemich [5.8K]

He he 3.05, 5 more dimes so subtract .50= 2.55, now dimes and nickels are even so divide 2.55/.15(one nickel and one dime), The answer is 17, now add the five extra dimes, 22 dimes and 17 nickels

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4 years ago

Find the range of the function f(x) = 4x - 7,

umka21 [38]

Answer:

range: {-27, -11, 5, 25}

Step-by-step explanation:

Evaluating the function for the given domain values gives the range values ...

{-27, -11, 5, 25}

For example, 4(-5)-7 = -20-7 = -27.

It's a matter of doing the arithmetic. A spreadsheet or calculator that works with lists can be helpful.

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3 years ago