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meriva
3 years ago
15

Please help me with this. Thxxx

Mathematics
1 answer:
grandymaker [24]3 years ago
4 0
You need to higher the points because this may be a site to get help but to have others do your work and to put your thanks means you think people are losers. Try and do it yourself ya selfish a! why does this look like you literally are in class and quickly snap a picture so you don't have to do it. You have to have SOME work done if you REALLY need help. Thanks
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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.

7 0
1 year ago
ΔHAT is similar to ΔCAN.<br><br><br><br> What is the value of y?
arlik [135]
6/y=9/5(due to similarity)
y=6*5/9=30/9=10/3=3.333..
8 0
3 years ago
Use the box method to distribute and simplify (-5x-2)(-2x^2+6x).
Mkey [24]

Answer:

10x^{3} - 26x^{2} - 12x

Step-by-step explanation:

1)  Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd.

10x^{3} - 30x^{2} + 4x^{2} -12x

2)  Collect like terms.

10x^{3} + (-30x^{2} +4x^{2} )-12x

3) Simplify.

10x^{3} - 26x^{2} -12x

Therefor, the answer is, 10x^3 - 26x^2 - 12x.

3 0
2 years ago
(<br> x<br> −<br> 3<br> )<br> (<br> x<br> −<br> 1<br> )<br> (x−3)(x−1)
galina1969 [7]

Answer:

x² - 4x + 3

Step-by-step explanation:

When multiplying binomials (two terms in an expression), use FOIL. It stands for the first, outside, inside, and last terms in each bracket.

(x−3)(x−1)           Expand with FOIL

= x² - x - 3x + 3      Collect like terms

= x² - 4x + 3

7 0
3 years ago
3. A kite is aloft at the end of a 1500 foot string. The string make an angle of 43° with the
sineoko [7]

Answer:

h= 1500\,*\,sin(43^o)

Step-by-step explanation:

Notice that there is a right angle triangle formed with sides as follows:

hypotenuse is the actual 1500 ft string. The acute angle 43 degrees is opposite to the segment that represents the height of the kite from the ground. Therefore, the trigonometric ratio that we can use to find that opposite side to the given angle, is the sine function as shown below:

sin(43^o) = \frac{opposite}{hypotenuse} \\sin(43^o) = \frac{opposite}{1500}\\opposite = 1500\,*\,sin(43^o)\\h= 1500\,*\,sin(43^o)

8 0
3 years ago
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