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Let's divide this problem up into cases:

Case 1 (2 1's, 2 2's, 3 4's) - There are \({7! \over 2! 2! 3!} = 210\) cases.

Case 2 (1 1's, 3 2's, 3 4's) - There are \({7! \over 3! 3!} = 140\) cases.

Case 3 (1 1's, 2 2's, 4 4's) - There are \({7! \over 2! 4!} = 105\) cases.

Case 3 (1 1's, 2 2's, 3 4's, 1 3, 5, or 6) - There are \({7! \over 2! 3!} \times 3 = 1260\) cases.

So, there are \(210 + 140 + 105 + 1260 = \color{brown}\boxed{1,715}\) sequences. 

First of all, write your question properly ! Do you see anything missing ?

Altitude ==[2  x  area] / side length

1. (x,y) = (-4,3).

2. (x,y) = (8, 13/2).

This is in Finnish:

Milja deposited €64,145 for 31.3. – 28.8. and received a net interest of €292.4 on his deposit, when the withholding tax was 30%. What was the nominal annual interest rate of the deposit (= interest rate that includes both the depositor's and the taxpayer's share)?

March 31 to August 28 ==150 days

292.40 ==net interest before 30% tax.

292.40 / [100% - 30%] ==292.40 / 0.70 ==417.71 - gross amount of interest before 30% tax.

64,145 x [150 / 365] x R ==417.71

26,360.96 x R ==417.71

R==417.71 / 26,360.96 ==1.584578 % - gross annual simple interest rate.

R==292.40 / 26,360.96==1.109216% - net annual interest rate after 30% tax.

The answer is \(126\sqrt{3}\)

\(\left(2x+10\right)^4\left(x+5\right)^4=\left(\left(2x+10\right)\left(x+5\right)\right)^4\)

\(\left(\left(2x+10\right)\left(x+5\right)\right)^4=\left(2x+10\right)^4\left(x+5\right)^4\)

\(\left(2x+10\right)^4\left(x+5\right)^4\) is your answer

Go to the bottom of the page and scroll down to the next page and should see the answer on the top of that 2nd page.

X = 0, since 0 multiplied by any number always equals 0.

as a equation pls

Write your question in PLAINTEXT and clearly!

The fourth roots are

1.4021 - 0.1846i

-1.4021 + 0.1846i

0.1846 + 1.4021i

-0.1846 - 1.4021i

The probability is 1/12.

This simplifes to 1.

3. The axis of symmetry is x = 0.

2. The axis of symmetry is x = 3.

You have 3 sides of an isosceles triangle.

Find the area by using "Heron's Formula"

Once you get the area, then:

[2 x area] / 15 = 1st height

[2 x area] / 20=2nd height

[2 x area] / 20=3rd height.

Take it from here.

The formula for the volume of a cylinder is in your Math Textbook, lazy ! Just Look it up:

V = Pi x Radius^2 x Height

V =3.14  x  17^2  x  17

Take it from here.

Where is "as shown below", lazy ?!

Sqrt[2 * 6 * 110 * 120* 450 * 520]

37065600000 = sqrt[2^10 * 3^4 * 5^5 * 11 * 13]

Sqrt[2^(10/2) * 3^(4/2) * 5^(5/2)]

2^5 * 3^2 * 5^2 sqrt(5 * 11 * 13)

7200 sqrt(715)

Thank you!

You get the maximum when (x,y) = (10,60).

1. The equation is y = x^2 - 8x - 20.

If two angles are complementary, then they add up to 90 degrees. Since the measures of angles A and B are in the ratio of 7 to 23, we can write A=7x and B=23x for some value of x. Substituting these values into the equation A+B=90, we get 7x+23x=90, which gives us x=2. Therefore, A=14 and B=46. The complements of angles A and B are 90−A=76 and 90−B=44, respectively. The ratio of the measures of the complements of angles A and B is 76/44​=19/11​​.

Hello,

I would like to suggest you here

Let's first define what y-[y] means. This is the fractional part of y, which is the difference between y and the greatest integer less than or equal to y. For example, if y = 3.5, then [y] = 3 and y-[y] = 0.5. If y = 4.2, then [y] = 4 and y-[y] = 0.2.

Now, we want to find the probability that y-[y]=1/3, where 0 <100. Since y is chosen at random, we can assume that y is uniformly distributed on the interval (0,100). We can then break up this interval into subintervals of length 1/3, since we are interested in the case where y-[y]=1/3.

Let's consider the first subinterval, (0,1/3). For y to satisfy y-[y]=1/3 in this interval, we need y to be between 1/3 and 2/3. The probability of this happening is 1/3, since y is uniformly distributed on the interval (0,1).

Next, let's consider the subinterval (1/3,2/3). For y to satisfy y-[y]=1/3 in this interval, we need y to be between 2/3 and 1. The probability of this happening is also 1/3.

We can continue this process for the remaining subintervals, up to the interval (98 2/3, 99). For this interval, we need y to be between 98 2/3 and 99. The probability of this happening is again 1/3.

Therefore, the total probability that y-[y]=1/3 is the sum of the probabilities for each subinterval, which is:

1/3 + 1/3 + ... + 1/3 (98 times)

= 98/3

= 32.67%

Hmm!