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disa [49]
3 years ago
10

Show all work please

5E%7B2%7D%20%7D%7B3%7D%20" id="TexFormula1" title=" \frac{7r}{2} \div \frac{ {14r}^{2} }{3} " alt=" \frac{7r}{2} \div \frac{ {14r}^{2} }{3} " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

3 / 4r

Step-by-step explanation:

Simplify : 7r/ 2 ÷ 14r²/3

7r/ 2 ÷ 14r²/3

Changing the ÷ sign to multiplication :

Multiply 7r/2 by the reciprocal of the denominator :

7r/ 2 * 3/14r²

((7 * r) / 2) * (3) / 14 * r * r

= 3 / 4r

For clarity, kindly check attached picture for detailed simplification.

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Alex_Xolod [135]
Prime: 2/8
Even: 6/8
Number 5: 1/8
4 0
3 years ago
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Tony took a math quiz last week. There were 80 problems on the quiz and Tony answered 70% of them correctly. How many problems d
Nutka1998 [239]

Answer:

56 problems

Step-by-step explanation:

So we already know that the answer is: 56. However, a good help is knowing how to obtain this answer from the data provided.

Tony's quiz had 80 questions

Tony correctly answered 70% of them.

We can always write a percentage amount as a ratio by dividing the amount by 100.

70\% = \frac{70}{100} = 0.7.

This means that for every 100 questions, tony will respond correctly 70.

So, if Toni did a questionnaire of n questions, the amount that will answer correctly is calculated by the following expression:

C = n*\frac{70}{100}

If n = 80 then:

C = 80 * \frac{70}{100}\\\\C = 56

7 0
3 years ago
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(1 point) Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose
Kamila [148]
Here L = W, but H can be different.
 
The sum L+H+W  must be less than or equal to 192 cm.  

We can solve L + H + W = 192 for H:  H = 192 - W - L.  Remembering that W = L,   the formula for H becomes 192 - 2W.

The formula for volume would be V = L*W*H.

This becomes V = W*W*H, or  V = W^2*(192-2W)

Multiplying this out:  V = w^2*192 - 2W^3

Two ways of determining W:

1) graph V = 192W^2 - 2W^3 and determine the value of W at which V is at a max with the constraint W + L + H is equal to or smaller than 192.

2) Differentiate V with respect to W and set the result equal to zero:

384W - 6W^2 = 0.  Solving for W:  W(384 - 6W) = 0.

W = 0 is trivial, so just solve 384 - 6W = 0 for W:  6W = 384, and W = 64.

The width is 64 cm, the length is 64 cm also, and the height is (192-2W) cm, or 64 cm.

These dimensions produce the max volume.
4 0
3 years ago
(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected
Lera25 [3.4K]

Answer:

a.   0.71

b.   0.9863

Step-by-step explanation:

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

-To estimate the probability that a randomly selected house  has a value less than $500,000:

P(X

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume normal distribution.

-The probability can therefore be calculated as:

P(\bar X)=P(z

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

3 0
3 years ago
Edward received a paycheck in the amount of $788. He is an appliance salesman and has a base salary of $200 a week. If he sells
vova2212 [387]

Answer: The total is  $13,133.33

Step-by-step explanation:

We know that Edward's paycheck was $788

He has a base salary of $200, so the commission is:

$788 - $200 = $588

Now, we know that if he sells  $10,000, his commission is a 4%.

So let's suppose that he sold exactly $10,000

Then his commission is the 4% of $10,000, this is:

Commission = (4%/100%)*$10,000 = $400

This is not enough, so he sold more than $10,000 in this week.

There is:

$588 - $400 = $188 left.

We know that if sells more than $10,000, he gets a commission of the 6% for the extra sales.

Then let's suppose that the extra is N.

The extra $188 must be equal to the 6% of N, then we get:

$188 = (6%/100%)*N

$188 = 0.06*N

$188/0.06 = N

$3,133.33

This means that he sold $3,133.33 more than $10,000

Then, in total, he sold $10,000 +  $3,133.33 =  $13,133.33

3 0
3 years ago
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