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3 years ago

The value of y varies directly with x. If x= 3, then y= 21. What is the talue of x when y = 105?

Mathematics

1 answer:

Anna007 [38]3 years ago

6 0

Answer:

Step-by-step explanation:

y=21 x 5 = 105

x=3 x 5 = 15

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Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

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1 year ago

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Answer:

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Step-by-step explanation:

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3 years ago

Which table identifies the one-sided and two-sided limits of function at x = 2?

Yuliya22 [10]

Answer:

Table 3

Step-by-step explanation:

Check table three;

$lim\:_{x\to \:2^-}\:f\left(x\right)=\:4$

$lim\:_{x\to \:2^+}\:f\left(x\right)=\:1$

Since the left hand limit $(lim\:_{x\to \:2^-}\:f\left(x\right))$ is not equal to the right hand limit $(lim\:_{x\to \:2^+}\:f\left(x\right))$ , the limit as x approaches to 2 does not exist.

Therefore "nonexistent" is true, and table 3 is the correct model of the limits of the function at x = 2

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3 years ago

The table below provides the values of the functions Flx) and gbx) for several values of z.

Artist 52 [7]

Answer:

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Step-by-step explanation:

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3 years ago

Which property can be used to expand the expression -2(3/4*+7)?

nika2105 [10]

Answer:

C. The distributive property

Step-by-step explanation:

The distributive property of binary activities is generalized in mathematics by the distributive law of Boolean algebra and elementary algebra. Distribution applies, in propositional logic, to two clear substitution laws. The rules allow one to reformulate, within logical facts, conjunctions and disjunctions.

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3 years ago

The value of y varies directly with x. If x= 3, then y= 21. What is the talue of x when y = 105?​

The value of y varies directly with x. If x= 3, then y= 21. What is the talue of x when y = 105?