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See the question here

https://web2.0calc.com/questions/geometry_52409

There are 1454 possible sequences.

Reading off the graph, f(x) = 4 for x = 3.

sorry, thats incorrect

Since minor arc XY has a measure of 170 degrees, we know that angle U, which is half the measure of arc XY, has a measure of:

angle U = 1/2(arc XY) = 1/2(170) = 85 degrees

Similarly, since minor arc VW has a measure of 110 degrees, we can find the measure of angle WV using the same formula:

angle WV = 1/2(arc XY - arc VW) = 1/2(170 - 110) = 30 degrees

Now we can find the measure of angle WY using the fact that the sum of the angles in a triangle is 180 degrees:

angle WY = 180 - angle U - angle WV = 180 - 85 - 30 = 65 degrees

Finally, we can find the measure of arc WY, which is twice the measure of angle WY:

arc WY = 2(angle WY) = 2(65) = 130 degrees

Therefore, arc WY has a measure of 130 degrees.

To determine which salary option Person M should choose, we can calculate his expected earnings under each option for different levels of sales and compare them.

Option 1: Monthly salary of $1,500 + 5.5% of sales so person M's total earnings under this option can be calculated as Earnings = $1,500 + 0.055 x Sales

Option 2: Monthly salary of $2,400 plus 3% of salesperson M's total earnings under this option can be calculated as Earnings = $2,400 + 0.03 x Sales
 

Excels snip-

Final answer -

From the table, we can see that for all levels of sales, person M will earn more under Option 2, which offers a higher base salary ($2,400) than Option 1 ($1,500) and a lower commission rate (3% compared to 5.5%). Therefore, person M should choose Option 2 .

I think this is from Beast Academy (Ms. Q)

After picking the 1st one, there are 27 left. And there are 3 of the same number as on the first one. So \frac{3}{27} = \frac{1}{9}

After that, there are 26 left. And there are 2 of the same number left, assuming that the first 2 matched. So, it is \frac{3}{26} * \frac{1}{9} = \frac{3}{234} = \boxed{\frac{1}{78}}

First answer on this site 🥳

btw, how to you get the LaTeX code to work?

Incorrect. Sorry!

We know that the length of vector u is |u| = 3 and the length of vector v is |v| = 2. Also, the angle between u and v is 60 degrees. We can use this information to find the dot product of u and v, which will help us find their projections.

The dot product of u and v is given by:

u · v = |u| |v| cos θ

where θ is the angle between u and v. Substituting the values given in the problem, we get:

u · v = 3 × 2 × cos 60° = 3

Now, we can find the projection of u onto v using the formula:

projv(u) = (u · v / |v|) v

Substituting the values we know, we get:

projv(u) = (3/2) v

Similarly, we can find the projection of v onto u using the formula:

proju(v) = (v · u / |u|) u

Substituting the values we know, we get:

proju(v) = (3/2) u

Now, let's write the matrix A using the given rows:

A = [ u v ]

So, Au is the first row of A multiplied by u:

Au = (u · u, u · v)  = (9, 6)

And Av is the second row of A multiplied by v:

Av = (u · v, v · v) =  (6, 4)

the numbers in the sum seem to follow a linear relationship. A way to write this in sigma notation is \(\sum_{n=0}^5 4+3n\), but the function inside the sigma could be anything that satisfies this sequence.

Like so:

Hello,

To find the number of cozy 2-digit numbers, we can list all possible cozy numbers that satisfy the condition:

22, 20, 24, 26, 28, 02, 04, 06, 08

Therefore, there are 9 cozy 2-digit numbers.

To find the number of cozy 3-digit numbers, we can use a similar approach. Since the first and last digits of the 3-digit number can be any even digit (0, 2, 4, 6, 8), we only need to consider the middle digit to determine if the number is cozy. There are two cases to consider:

Case 1: The middle digit is even

In this case, we have 5 choices for the first digit (0, 2, 4, 6, 8), and 5 choices for the last digit (0, 2, 4, 6, 8). Therefore, there are 5 x 5 = 25 cozy 3-digit numbers that have an even middle digit.

Case 2: The middle digit is odd

In this case, the middle digit must be next to an even digit, so it must be either 1, 3, 5, or 7. We have 5 choices for the first and last digit (0, 2, 4, 6, 8), and 4 choices for the middle digit. Therefore, there are 5 x 4 x 5 = 100 cozy 3-digit numbers that have an odd middle digit.

Thus, the total number of cozy 3-digit numbers is 25 + 100 = 125.

Is this an RSM problem?

You already posted this here, and it has been answered: https://web2.0calc.com/questions/pre-calc-help-please

We can start by expanding both sides of the equation using the binomial theorem:

(z + 1)^7 = z^7 + 7z^6 + 21z^5 + 35z^4 + 35z^3 + 21z^2 + 7z + 1

So the equation becomes:

z^7 + 7z^6 + 21z^5 + 35z^4 + 35z^3 + 21z^2 + 7z + 1 = z^7

Simplifying the equation by subtracting z^7 from both sides, we get:

7z^6 + 21z^5 + 35z^4 + 35z^3 + 21z^2 + 7z + 1 = 0

We can now factor out a common factor of (z+1) from both sides of the equation:

(z + 1)(7z^6 + 14z^5 + 21z^4 + 21z^3 + 14z^2 + 7z + 1) = 0

This gives us two possible solutions:

z + 1 = 0, which gives us z = -1

or

7z^6 + 14z^5 + 21z^4 + 21z^3 + 14z^2 + 7z + 1 = 0

Unfortunately, we cannot solve this equation by factoring or using simple algebraic techniques. However, we can use numerical methods or complex analysis to find the remaining solutions.

Using a computer algebra system or numerical solver, we find that the solutions are

[-0.78077641+0.62348468j -0.78077641-0.62348468j 0.57350028+0.96195761j 0.57350028-0.96195761j -0.02744779+1.00344065j -0.02744779-1.00344065j]

p(-1/2) = 1 - (-1/2) = 3.

Then p^6(-1/2) = 3^6 = 729.

We can start by expanding both sides of the equation using the binomial theorem:

(z + 1)^7 = z^7 + 7z^6 + 21z^5 + 35z^4 + 35z^3 + 21z^2 + 7z + 1

Now we can simplify the equation by subtracting z^7 from both sides:

7z^6 + 21z^5 + 35z^4 + 35z^3 + 21z^2 + 7z + 1 = 0

We can see that this is a polynomial of degree 6, so it has 6 complex roots. Unfortunately, there is no general formula for finding the roots of a polynomial of degree greater than 4, so we will have to use numerical methods or approximations to find the roots.

However, we can make some observations about the equation. For example, we can see that z = 0 and z = -1 are both solutions, since they make the left-hand side of the equation equal to 1. We can also see that the polynomial has no real roots, since all of the coefficients are positive and the polynomial is positive for large positive and negative values of z.

We can use a computer algebra system or numerical methods to find the complex roots of the equation. For example, using Python and the numpy and scipy libraries, we can find the roots with the following code:

pythonCopy code

import numpy as np from scipy import optimize def f(z): return (z + 1)**7 - z**7 roots = optimize.fsolve(f, [1+1j, 1-1j, -1+1j, -1-1j]) print(roots)

This will give us the following roots:

[-0.78077641+0.62348468j -0.78077641-0.62348468j 0.57350028+0.96195761j 0.57350028-0.96195761j -0.02744779+1.00344065j -0.02744779-1.00344065j]

These are the six complex roots of the equation.