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4 years ago

Proport

Mathematics

2 answers:

larisa [96]4 years ago

6 0

Answer:

5.25, 5/14, or 21/4 hours

Step-by-step explanation:

400 700

------ = ------

3 x

Gwar [14]4 years ago

4 0

It takes 5 minutes per square foot (400/180=5) and so 5 minutes per square for 720 squares: 720x5=3,600. 3,600 minutes is equivalent to 60 hours so it takes him 60 hours.

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Suppose we want to choose 5 colors, without replacement, from 8 distinct colors.1. If the order is relevant, how many can be don

Charra [1.4K]

(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.

The formula is given as;

$nP_r=\frac{n!}{(n-r)!}$

This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.

Therefore, we would have;

$\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}$

Therefore, if the order is relevant, this selection can be done in 6,720 ways.

(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

$_nC_r=\frac{n!}{(n-r)!r!}$

The formula can now be applied as follows;

$\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}$

If the order is not relevant, then the selection can be done in 56 ways.

3 0

1 year ago

an arts academy requires there to be 3 teachers for every 75 students and 6 tutors for every 72 students. How many students does

Zinaida [17]

Each teacher has 25 students. 75/3 would be 25. I hope this helped!

5 0

3 years ago

Help help help please

Veronika [31]

Answer:

{9,14,20}

Step-by-step explanation:

hope it helps

8 0

2 years ago

Read 2 more answers

If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

What product have the same sign as ( -2 3/7 ) (-6/11) ?

motikmotik

Answer:

1. -7/8

2.-9/14

3. 9/14

4. 7/8

2. what is the product of -2/7 and -3/7?

1. -7/8

2.-6/49

3. 6/49

4. 7/8

How do the expressions 72÷ 9 and -72÷ (-9) compare when they are evaluated?

1. They have different values and are different signs.

2. They have different values but are the same sign.

3. They have the same value but are different signs.

4. They have the same value and the same sign.

Step-by-step explanation:

Multiplying fractions: multiply numerators and multiply denominators

1. 3/4 X -6/7 = -18/28 = -9/14

2. -2/7 X -3/7 = 6/49

3. 4 because 72/9 is 8. -72/-9 is 8. Two negatives makes a positive when multiplying and dividing.

7 0

3 years ago