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3 years ago

10

The newly elected president needs to decide the remaining 7 spots available in the cabinet he/she is appointing. If there are 13

eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

1 answer:

Alexxx [7]3 years ago

8 0

Answer: 8648640 ways

Step-by-step explanation:

Number of positions = 7

Number of eligible candidates = 13

This can be done by solving the question using the combination Formula for selection in which we use the combination formula to choose 7 candidates amomg the possible 13.

The combination Formula is denoted as:

nCr = n! / (n-r)! * r!

Where n = total number of possible options.

r = number of options to be selected.

Hence, selecting 7 candidates from 13 becomes:

13C7 = 13! / (13-7)! * 7!

13C7 = 1716.

Considering the order they can come in, they can come in 7! Orders. We multiply this order by the earlier answer we calculated. This give: 1716 * 7! = 8648640

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Find the length x to the nearest whole number. A right triangle has a vertical leg of length x units, a base leg with a length o

wel

Complete Question

The diagram for this question is shown on the first uploaded image

Answer:

The value of x is $x = 274 \ unites$

Step-by-step explanation:

From the question we are told that

The length of the vertical length is $x$

The length of the base leg is L = 330 + d units

The length of the bisecting line segment is h

The base angle is $\theta = 28^o$

The angle between d and line segment is $\theta_1 = 56^o$

For the first angle

$Tan \theta_1 = \frac{x}{d}$

=> $d = \frac{x}{Tan \theta _1}$

For the whole big triangle

$Tan \theta = \frac{x}{330 + d}$

=> $d = \frac{x}{Tan \theta } -330$

So equating the both d

$\frac{x}{Tan \theta _1} = \frac{x}{Tan \theta } -330$

Substitute values

$\frac{x}{Tan (56)} = \frac{x}{Tan (28) } -330$

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Answer:

$13a.\ The \ probability\ of \ scoring\ a\ goal\ in\ a\ game\ is\ 0.36\\\\b. 3 \ games$

14.

$a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860$

15. This is not possible since p(yellow)=0.10 which is less than the stated 0.35

Step-by-step explanation:

13 a. -A goal-scoring statistic is the probability of a player scoring one goal in any given game played.

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b. To determine the number of games it takes to score a whole goal, we divide the probability by 1 goal:

$Games=\frac{1 \ game}{p(goal)}\\\\=\frac{1}{0.36}\\\\=2.778\approx 3$

Hence, it takes approximately 3 games to score a full goal.

14.-The cost of a GCSE retake is £600 and attracts a 15% deposit

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$C_g=0.15\times 600\\\\=\£90$

Hence, the 15% deposit amount equals £90

b.#The student pays the balance in a £20 per week scheme,the total number of weeks is calculated as:

$t=\frac{Balance}{Rate}\\\\=\frac{600-90}{20}\\\\=\frac{510}{20}\\\\=25.5\approx 26$

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$100\%=\frac{540}{0.1}\\\\=\£5400$

#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:

$=540\times 10\\\\=\£5400$

We subtract the discount amount for the per-discount price:

$Cost=Total -discount\\\\=5400-540\\\\=\£4860$

Hence, it will cost £4,860 without the discount.

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3 years ago

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Answer:

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Step-by-step explanation:

To determine whether the statemaent "If $a\Rightarrow b$ is true, then $\neg a\Rightarrow b$ is also true" holds, you can form the truth table:

$\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}$

When the result of the column $a\Rightarrow b$ takes value 1 (true), the result of the column $\neg a\Rightarrow b$ is not always 1, then the statement is false.

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