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Nataly [62]
3 years ago
15

Ariel swims 2 1/6 miles in every 1/3 hour. Enter the number of miles Ariel swims in 1 minute.

Mathematics
1 answer:
weqwewe [10]3 years ago
4 0

In order to find the distance covered in 1 minute, we need to divide distance covered 2 1/6 miles by 20 minutes.We are given : Ariel swims 2 1/6 miles in every 1/3 hour.

Let us convert 1/3 hour into minutes.

There are 60 minutes in an hour.

Therefore, 1/3 hours = 60 × 1/3 = 20 minutes.

So, we could say, "Ariel swims 2 1/6 miles in every 20 minutes".


2 1/6÷ 20 = 13/6 ÷ 20.

Let us convert division sign into multiplication and flip 20 to 1/20.

We get

<h3>13/6 × 1/20 = 13/120 miles in 1 minute.</h3><h3>In decimal 0.11 mile in 1 minute.</h3>
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Lisle bought 38 pounds of red grapes and 512 pound of green grapes how many pounds of Grapes did he buy
Svet_ta [14]

Answer:

19/24

Step-by-step explanation:

From the question we are informed that Lisle bought 3/8 pounds of red grapes and 5/12 pound of green grapes

✓3/8 pounds of red grapes and 5//12

✓First thing to do is to add the fractions

But we need " the least common denominator" because their denominator are not the same, we need to make it the same...

✓ The two denominator ( 8 and 12) are both factor of 24, therefore their "least common denominator" is 24.

✓To make 3/8 pounds of red grapes has a denominator of 24, we multiply both the denominator & numerator with factor of 3.

3/8 = (3×3)/(8×3)=9/24

✓To make 5/12 pounds of green grapes has a denominator of 24, we multiply both the denominator & numerator with factor of 2.

5/12= (5×2)/(12×2)= 10/24

✓ we can see they both have the same denominator, then we can now "add both denominators"

(9+10)=19

✓ Then place the addition of the denominators on the least common denominator.

= 19/24.

Therefore, he bought 19/24 of grapes

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The sum of the least and greatest of three consecutive integers is 72. what are the three integers?
asambeis [7]
23+24+25  Add these integers to equal 72.
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4 years ago
Use mathematical induction to prove the statement is true for all positive integers n. 1^2 + 3^2 + 5^2 + ... + (2n-1)^2 = (n(2n-
Charra [1.4K]

Answer:

The statement is true is for any n\in \mathbb{N}.

Step-by-step explanation:

First, we check the identity for n = 1:

(2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}

1 = \frac{1\cdot 1\cdot 3}{3}

1 = 1

The statement is true for n = 1.

Then, we have to check that identity is true for n = k+1, under the assumption that n = k is true:

(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}

\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}

\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}

k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)

(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)

k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)

2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)

(k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)

Therefore, the statement is true for any n\in \mathbb{N}.

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3 years ago
The plattsville glee club is sending 8 of its members to a singing contest in cincinnati, ohio. the cost will be $588 per person
natulia [17]

Solution:

we are goiven that

The cost is  $588 per person.

we have been asked to find

How much will it cost for the entire group of 8 students to attend?

As we are give with the cost for one person, so for 8 person , we will multiply the given cost by 8.

Cost for the entire group of 8 students to attend=588\times8=4704 $

Hence the Cost for the entire group of 8 students to attend is 4704 $

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