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3 years ago

How many distinguishable a arrangements are there of the letters in "REPRESENTATION"?

Mathematics

1 answer:

Anika [276]3 years ago

5 0

Answer: There are 1,816,214,400 ways for arrangements.

Step-by-step explanation:

Since we have given that

"REPRESENTATION"

Here, number of letters = 14

There are 2 R's, 3 E's, 2 T's, 2 N's

So, number of permutations would be

$\dfrac{14!}{2!\times 3!\times 2!\times 2!}\\\\=1,816,214,400$

Hence, there are 1,816,214,400 ways for arrangements.

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The local public transport authority is conducting research into commuter behaviour. A previous census indicated that the mean c

kondor19780726 [428]

Answer:

$H_0:\mu = 45$ and $H_a:\mu < 45$

$T = 34.88$

The null hypothesis is not rejected

Step-by-step explanation:

Given

Random sample of 50 commuter times

Solving (a): The null and alternate hypothesis

From the question, a previous census shows that:

$\mu =45$ and $\sigma= 9.1$

This is the null hypothesis i.e.

$H_0:\mu = 45$

Reading further, a new test was to show whether the average has decreased.

This is the alternate hypothesis, and it is represented as:

$H_a:\mu < 45$

Solving (b) and (c): The test statistic (T).

This is calculated using:

$T = \frac{\mu}{\sigma/\sqrt n}$

In this case:

$n = 50$ $\mu =45$ and $\sigma= 9.1$

So:

$T = \frac{45}{9.1/\sqrt{50}}$

$T = \frac{45}{9.1/7.07}$

$T = \frac{45}{1.29}$

$T = 34.88$

Solving (c): Accept or reject null hypothesis

$\alpha = 0.05$

First calculate the degrees of freedom (df)

$df = n - 1 = 50 - 1$

$d f = 49$

From the t distribution table,

At: $d f = 49$ , $\alpha = 0.05$ and $T = 34.88$

the t score is:

$p = 1.676$

$p > 0.05$

So, the null hypothesis is not rejected

7 0

3 years ago

Which polynomial function gets larger and larger in the negative direction as x gets larger and larger in the

vekshin1

Answer:

The first one

Step-by-step explanation:

The first one because the largest exponent is odd and its coefficent is positive

5 0

2 years ago

WILL GIVE BRAINLIEST

Triss [41]

Answer:

(-10, 0) and (0,-5)

Step-by-step explanation:

For the function $f(x)=-\dfrac{1}{2}x-5,$ find x-intercept and y-intercept:

1. when y=0, then

$0=-\dfrac{1}{2}x-5,\\ \\\dfrac{1}{2}x=-5,\\ \\x=-10;$

2. when x=0, then

$y=-\dfrac{1}{2}\cdot 0-5,\\ \\y=-5.$

You get two points (-10, 0) and (0,-5). Plot them on the coordinate plane and connect, obtained line is the graph of the linear function $f(x)=-\dfrac{1}{2}x-5.$

5 0

3 years ago

Megan has a piece of fabric which is a right triangular shape. The length of leg 1 is 4 m. The length of the other leg is twice

Bess [88]

Answer:

8.94 m

Step-by-step explanation:

Use the Pythagorean Theorum - $a^2 + b^2 = c^2$ . Use leg 1 as a, leg 2 as b, and the third side as c.

We know leg 1 is 4, and that leg 2 is twice as long as leg 1...

$(4)^2 + (4*2)^2 = c^2$

Now, we use the Order of Operations to find $c^2$ ...

$4^2+8^2=c^2\\16+64=c^2\\80=c^2$

Now, we find the square root of $c^2$ to find c...

$\sqrt{80} =8.94$

So, the length of the third side is 8.94 m.

8 0

3 years ago

What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}? 2r ≤ 3r – 8 A. {8, 9, 10}

TiliK225 [7]

$2r\leq3r-8\\
r\geq8\\\Downarrow\\
\boxed{\{8,9,10\}}$

8 0

3 years ago