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3 years ago

How many different ways can the first twelve letters of the alphabet be arranged?

Mathematics

2 answers:

Reika [66]3 years ago

8 0

There are 3628800 ways to arrange those letters.

Marta_Voda [28]3 years ago

8 0

12!
12!=12*11*10*9*8*7*6*5*4*3*2*1
=479001600

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A rectangle is 20 meters long and 20 meters wide. If the length is increased by 10% and the width is decreased by 10%, what is t

Solnce55 [7]

Consider that the initial length and width of the rectangle are given as,

$\begin{gathered} l=20 \\ b=20 \end{gathered}$

After the length is increased by 10%, the new length (L) of the rectangle is calculated as,

$\begin{gathered} L=(1+\frac{10}{100})\cdot l \\ L=(\frac{110}{100})\cdot20 \\ L=22 \end{gathered}$

After the width is decreased by 10%, the new width (B) of the rectangle is calculated as,

$\begin{gathered} B=(1-\frac{10}{100})\cdot b \\ B=(\frac{90}{100})\cdot20 \\ B=18 \end{gathered}$

Then the area (A) of the new rectangle is calculated as,

$\begin{gathered} A=L\times B \\ A=22\times18 \\ A=396 \end{gathered}$

Thus, the new area of the rectangle is 396 square meters.

7 0

1 year ago

Solve: 2 + = 2. Give solutions in interval [0, 2)

Dovator [93]

$\because\cos 2x+\sin x=\sin 2x$ $\because\sin 2x=2\sin xcosx$ $\because\cos 2x=\cos ^2x-\sin ^2x$

→ Substitute cos 2x and sin 2x by their expressions

$\therefore\cos ^2x-\sin ^2+\sin x=2\sin x\cos x$

→ Subtract both sides by sin x

$\cos ^2x-\sin ^2x=2\sin xcosx-\sin x$

→ Take sin x as a common factor in the right side

$\therefore\cos ^2x-\sin ^2x=\sin x(2\cos x-1)$

From the graph, the equation has 4 solutions, the intersection points between the 2 graphs

7 0

1 year ago

A professional organization sells term life insurance and major medical insurance. Of those who have just life insurance, 60% wi

kherson [118]

Answer:

The answer is "0.765 and 0.2353".

Step-by-step explanation:

Please find the complete question in the attached file.

In point a:

P(a substantive term only) $=0.75-0.2 =0.55$

P(major health insurance only) $= 0.45-0.20=0.25$

P(both) $= 0.20$

P(renewal) =P(insurance and renewal term only)+P (substantial and renewable health insurance only)+P (both and renew)

$=0.55\times 0.7+0.25 \times 0.8+0.2 \times 0.9 \\\\ =0.765$

In point b:

In reality, the probability of having both life and major medical insurance provided the policyholder would renew next year

$= \frac{\text{P(both and renew)}}{\text{P(renew)}}$

$=\frac{0.2\times 0.9}{0.765}\\\\=0.2353$

4 0

3 years ago

One canned juice drink is 25% orange juice another is 10% orangw juice. How many liters of each should be mixed together in orde

Vsevolod [243]

Answer:

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

Step-by-step explanation:

Let the amount of the 25% orange juice be "x", while the amount of the 10% one be "y". The sum of these must be equal to 15 l, therefore:

$x + y = 15$

The sum of the concentration of juice on each can must be equal to the final product, therefore:

$25\%*x + 10\%*y = 15*20\%\\0.25*x + 0.1*y = 3$

We can now solve the system of equations as shown below:

$\left \{ ({{x + y=15})*(-0.1) \atop {0.25*x + 0.1*y=3}} \right. \\\left \{ {{-0.1*x - 0.1*y=-1.5} \atop {0.25*x + 0.1*y=3}} \right. \\-0.1*x + 0.25*x = 3 - 1.5\\0.15*x = 1.5\\x = \frac{1.5}{0.15} = 10\\y = 15 - x = 15 - 10 = 5$

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

4 0

3 years ago

I'll Give brainliest too! I need help with these.

Ann [662]

This is not seeing me clearly so that's why I can't able to help u.

3 0

3 years ago

Read 2 more answers