There are 30 people in student council that are running for the offices of president and vice president. In how many different ways can those offices be assigned?900
870
59

Answers

Answer 1

Answer: The answer is 870 because each person can have 1-29 people for their vice president so you multiply 29×30=870

Answer 2

Answer: I believe it would be 870

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For what values of r does the function y = erx satisfy the differential equation y'' + 5y' + 6y = 0?
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Without graphing, classify each system of equations as independent, dependent, or inconsistent. Solve independent systems by graphing.1) 5 - y = 2x 6x - 15 = -3y2) 6y + 2x = 812y + 4x = 4
Prove that (1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A

Trig help (Problems already solved)?The calculation for the problems are already done but I have to list a reason or what is being done in each step. "Each = and newline made" means a place I have to write what is being done in the calculation.

1. (secx + sinx)cotx = cscx + cosx
=(secx + sinx)cotx = cscx + cosx
=(1 / sinx) + cosx
=cscx + cosx

2. cosx + tanx sinx = secx
=cosx + tanx sinx = cosx + (sinx / cosx)sinx
=cosx + (sin^2x / cosx) = (1 / cosx)(cos^2x + sin^2x)
=1 / cosx
=secx

3. cscx - cosx cotx = sinx
=cscx - cosx cotx = (1 / sinx) - cosx(cosx / sinx)
=(1 / sinx) - (cos^2x / sinx)
=(1 - cos^2x) / sinx
=sin^2x / sinx = sinx

4. (cosx / (1 + cosx)) + (cosx / (1 - cosx)) = 2cotx cscx
=(cosx / (1 + cosx)) + (cosx / (1 - cosx)) = ((cosx (1 - cosx) + cosx (1 + cosx))) / (1 + cosx)(1 - cosx)
=(cosx - cos^2x + cosx + cos^2x) / (1 - cos^2x)
=2cosx / sin^2x
=2(cosx / sinx)(1 / sinx) = 2cotx cscx

Thank you to whoever decides to help me with explaining what is happening on each line.

Answers

The first identity uses the definition of the reciprocal functions $\sec x,\csc x,\cot x$ and the distributive property of multiplication.

$(\sec x+\sin x)\cot x=\left(\frac1{\cos x}+\sin x\right)(\cos x)/(\sin x)$
$=(\cos x)/(\cos x\sin x)+(\cos x\sin x)/(\sin x)$
$=\frac1{\sin x}+\cos x$
$=\csc x+\cos x$

The second uses the definition of $\tan x$ and the distributive property. Then a factor of $\frac1{\cos x}$ is pulled out, which allows you to use the identity $\sin^2x+\cos^2x=1$ .

$\cos x+\tan x\sin x=\cos x+(\sin x)/(\cos x)\sin x$
$=\cos x+(\sin^2x)/(\cos x)$
$=(\cos^2x)/(\cos x)+(\sin^2x)/(\cos x)$
$=\frac1{\cos x}\left(\cos^2x+\sin^2x\right)$
$=\frac1{\cos x}*1$
$=\frac1{\cos x}$
$=1$

The third uses the same ideas as the second: rewrite the reciprocal functions, then invoke the Pythagorean identity $\sin^2x+\cos^2x=1$ , which is equivalent to $\sin^2x=1-\cos^2x$ .

$\csc x-\cos x\cot x=\frac1{\sin x}-\cos x(\cos x)/(\sin x)$
$=\frac1{\sin x}-(\cos^2x)/(\sin x)$
$=\frac1{\sin x}\left(1-\cos^2x\right)$
$=\frac1{\sin x}\sin^2x$
$=(\sin^2x)/(\sin x)$
$=\sin x$

In the last one, you combine the fractions by enforcing common denominators. This lets you add the numerators together, and the denominator can be simplified. Once you do that, you rewrite the factors of cos and sin in the numerator and denominator to make up the cot and csc functions, and you're done.

$(\cos x)/(1+\cos x)+(\cos x)/(1-\cos x)=(\cos x(1-\cos x))/((1+\cos x)(1-\cos x))+(\cos x(1+\cos x))/((1-\cos x)(1+\cos x))$
$=(\cos x(1-\cos x)+\cos x(1+\cos x))/((1-\cos x)(1+\cos x))$
$=(\cos x(1-\cos x+1+\cos x))/(1-\cos^2x)$
$=(2\cos x)/(\sin^2x)$
$=2(\cos x)/(\sin x)\frac1{\sin x}$
$=2\cot x\csc x$

Calculate an estimate for the mean temperature

Answers

The temperature was in the range of 10-13 on 7 of the days.
Give it the weight of the middle of the range = 11.5 for 7 times = 80.5

The temperature was in the range of 14-17 on 9 of the days.
Give it the weight of the middle of the range = 15.5 for 9 times = 139.5

The temperature was in the range of 18-21 on 16 of the days.
Give it the weight of the middle of the range = 19.5 for 16 times = 312

The temperature was in the range of 22-25 on 22 of the days.
Give it the weight of the middle of the range = 23.5 for 22 times = 517

The temperature was in the range of 26-29 on 6 of the days.
Give it the weight of the middle of the range = 27.5 for 6 times = 165

Total weight for all ranges = (80.5 + 139.5 + 312 + 517 + 165) = 1,214

Total number of days = 60

Estimated mean temperature = (1,214) / (60) = 20.23°C

Can you tell me what 6+3.9 is

Answers

Answer:

9.9

Step-by-step explanation:

6 + 3.9 = 9.9

you add the two whole numbers together and get 9

then you need to add whatever is behind the decimal point which is 9

add them together and you get 9.9

What is 15 - 7 x 2+ 2 to the 3rd power

Answers

15 - 7 x 2 + 2^3
15 - 7 x 2 + 8
15 - 14 + 8
= 9

What is the value of the expression?
25 – 4 + (40 ÷ 20)5

Answers

25 - 4 + (40 ÷ 20)5 = 31

Which graph represents the function on the interval [-3,3]
F(x)=[x]-2

Answers

Answer:

Shown below

Step-by-step explanation:

The most famous of the step functions is the greatest integer function, which is denoted by the parent function $[x]$ .

So, this function is defined as:

$f(x)=[x] \ the \ greatest \ integer \ less \ than \ or \ equal \ to \ x$ .

These are the characteristics of this function:

The domain of the function is the set of all real numbers.
The range of the function is the set of all integers.
The graph has a $y-intercept$ at $(0,0)$ and $x-intercept$ in the interval $[0,1)$
The graph is constant between each pair of consecutive integers.
The graph jumps vertically one unit at each integer value.

The function $F(x)=[x]-2$ represents the parent function shifted 2 units downward. Therefore, the correct option has been chosen in the attached figure.