All categories

3 years ago

In how many different, distinguishable orders can the letters of the word mathematics be arranged?

Mathematics

1 answer:

Natalka [10]3 years ago

7 0

Answer:

B)4,989,600

Step-by-step explanation:

The letters of 'MATHEMATICS' contains 11 letters.

The following letters repeats twice, TT,MM,AA.

When we talk of distinguishable wasy, we are referring to arrangement without repetition.

Therefore the letters of "MATHEMATICS" can be arranged in $\frac{11!}{2!2!2!}=4,989,600$ distinguishable ways.

The correct answer is B.

You might be interested in

Mary has some trading cards. Julie has 3 times as many trading cards as Mary. They have 36 trading cards in all. Which of these

riadik2000 [5.3K]

Answer:

C. X+3x=36

Step-by-step explanation:

1. If you add the x's to get: 4x=36

2. Do division to get 9.

3. if you plug in 9 in the original,and multiply: 9+27=36

4. There's your answer..... and i ran out of steps.

3 0

3 years ago

If a > b > c > d, then which is larger, a+c or b+d ? Can we tell from a > b > c > d which of a+d and b+c is la

victus00 [196]

Answer:

1. a+c is larger than b+d

2. No way to tell whether a+d or b+c is larger.

Step-by-step explanation:

1. Which is larger, a+c or b+d?

Let a, b, c, and d be any numbers such that $a > b > c > d$ .

Specifically, note that $a > b$ , and subtracting b from both sides of the inequality, observe that $a-b > 0$ .

Similarly, $c > d$ , and subtracting d from both sides of the inequality, observe that $c-d > 0$ .

From this, add "a-b" (a positive number, as proven above) to both sides of the inequality.

$(a-b)+(c-d) > (a-b)+0$

Addition by zero (the additive identity) doesn't change anything, so the right side remains "a-b"...

$(a-b)+(c-d) > a-b$

... and "a-b" is positive...

$(a-b)+(c-d) > a-b > 0$

... so, by the transitive property of inequality...

$(a-b)+(c-d) > 0$

Recall that subtraction is addition by a negative number...
$a+(-b)+c+(-d) > 0$

...and that addition is associative and commutative, so things can be added in any order, so the middle two terms on the left side can be rearranged...

$a+c+(-b)+(-d) > 0$

Adding b + d to both sides of the inequality

$(a+c+(-b)+(-d))+(b+d) > 0+(b+d)$

... and simplifying

$a+c > b+d$

So, a+c is larger than b+d.

2. Which is larger, a+d or b+c?

Consider the following two examples:

Example 1

Suppose a=10; b=3; c=2; d=1.

Note that $a > b > c > d$ ( $10 > 3 > 2 > 1$ ) and, also observe that $a+d=(10)+(1)=11$ , and $b+c=(3)+(2)=5$ , so a+d is larger than b+c.

Example 2

However, suppose a=10; b=9; c=8; d=1.

Note that $a > b > c > d$ ( $10 > 9 > 8 > 1$ ) but that $a+d=(10)+(1)=11$ , and $b+c=(9)+(8)=17$ , so a+d is smaller than b+c.

So, in one example, a+d is bigger, and in the other, a+d is smaller. Therefore, there is no way to tell which of a+d or b+c is larger from only the given information.

5 0

2 years ago

What is the total cost or sale price to the nearest cent? $50 tool set; 10% markup.

Komok [63]

$55

50 x 0.10=5 + 50= 55

3 0

3 years ago

+ PRINCIPLES OF MATHEMATICS

GREYUIT [131]

Answer:

$9,840

Step-by-step explanation:

Let the money earned from college be 'x'.

Given:

Total money earned from the two jobs = $50,450

Money earned at the store = 1250 + 4(Money earned at college)

∴ Money earned at the store = $1250 +4x$

Now, total money earned by Erica is the sum of money earned at store and college. Therefore,

Total money = Money at store + Money at college

$50450=1250+4x+x\\5x+1250=50450\\5x=50450-1250\\5x=49200\\x=\frac{49200}{5}=\$9840$

Therefore, the money earned by Erica from her job at the college is $9,840.

3 0

3 years ago

Explain and find the instantaneous velocity for s(t) = -3 - 7t when t = 5 seconds using the limit of the difference quotient.

Taya2010 [7]

Answer:

-7 m/s

Step-by-step explanation:

The limit of the difference quotient is used to find the slope passing through two point. It is gotten by taking the limit as h approaches zero. It is given by:

$\frac{f(x+h)-f(x)}{h}$

Given that:

The function s(t) = -3 - 7t

$s(t+h)=-3-7(t+h)=-2-7t-7h$ .

Using the limit of the difference quotient formula:

$Limit\ of\ difference= \lim_{h \to 0} \frac{s(t+h)-s(t)}{h}=\lim_{h \to 0}\frac{-3-7t-7h-(-3-7t)}{h}= \lim_{h \to 0}\frac{-3-7t-7h+3+7t)}{h}$

$Limit\ of\ difference= \lim_{h \to 0}\frac{-7h}{h}= -7.\\Therefore\ instantaneous\ velocity=-7\\at\ t=5\\instantaneous\ velocity=-7\ m/s$

3 0

3 years ago