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NNADVOKAT [17]
3 years ago
13

emily has a bowl of M&M's for every 25 M&M's there are blue 5 M&M's. what percent of her M&M's are blue

Mathematics
1 answer:
KonstantinChe [14]3 years ago
8 0

Answer:

twenty percent.

Step-by-step explanation:

25/5=5

100/5=20

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What is the slope of the line that passes through the points (4, -9)(4,−9) and (8, -3) ?(8,−3)? Write your answer in simplest fo
faltersainse [42]

Answer:

\frac{3}{2}

Step-by-step explanation:

I am assuming that you mean (4,−9) and (8, -3).

m=\frac{rise}{run}=\frac{-3+9}{8-4}=\frac{6}{4}=\boxed{\frac{3}{2}}

Hope this helps.

6 0
2 years ago
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I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).
Aleksandr-060686 [28]

Answer:

\frac{7\pi}{24} and \frac{31\pi}{24}

Step-by-step explanation:

\sqrt{3} \tan(x-\frac{\pi}{8})-1=0

Let's first isolate the trig function.

Add 1 one on both sides:

\sqrt{3} \tan(x-\frac{\pi}{8})=1

Divide both sides by \sqrt{3}:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}

Now recall \tan(u)=\frac{\sin(u)}{\cos(u)}.

\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}

or

\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}

The first ratio I have can be found using \frac{\pi}{6} in the first rotation of the unit circle.

The second ratio I have can be found using \frac{7\pi}{6} you can see this is on the same line as the \frac{\pi}{6} so you could write \frac{7\pi}{6} as \frac{\pi}{6}+\pi.

So this means the following:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}

is true when x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi

where n is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi

Add \frac{\pi}{8} on both sides:

x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi

Find common denominator between the first two terms on the right.

That is 24.

x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi

x=\frac{7\pi}{24}+n \pi (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval [0,2\pi).

So if \sqrt{3} \tan(x-\frac{\pi}{8})-1=0 and we let u=x-\frac{\pi}{8}, then solving for x gives us:

u+\frac{\pi}{8}=x ( I just added \frac{\pi}{8} on both sides.)

So recall 0\le x.

Then 0 \le u+\frac{\pi}{8}.

Subtract \frac{\pi}{8} on both sides:

-\frac{\pi}{8}\le u

Simplify:

-\frac{\pi}{8}\le u

-\frac{\pi}{8}\le u

So we want to find solutions to:

\tan(u)=\frac{1}{\sqrt{3}} with the condition:

-\frac{\pi}{8}\le u

That's just at \frac{\pi}{6} and \frac{7\pi}{6}

So now adding \frac{\pi}{8} to both gives us the solutions to:

\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}} in the interval:

0\le x.

The solutions we are looking for are:

\frac{\pi}{6}+\frac{\pi}{8} and \frac{7\pi}{6}+\frac{\pi}{8}

Let's simplifying:

(\frac{1}{6}+\frac{1}{8})\pi and (\frac{7}{6}+\frac{1}{8})\pi

\frac{7}{24}\pi and \frac{31}{24}\pi

\frac{7\pi}{24} and \frac{31\pi}{24}

5 0
3 years ago
Simplify two to the fifth power over three to the second power
Savatey [412]
[/tex]\frac{32}{9}
This changes to a mix fraction
3 [tex] \frac{5}{9}
8 0
3 years ago
Which statement is best represented by the inequality d>11?
ankoles [38]

For this case we have the following inequality:d> 11

Assuming that "d" is the variable that represents the number of hours worked by Mo during this week, we have that the hours were greater than 11, according to the inequality sign.

So, the correct option is:

Mo worked more than 11 hours this week.

Answer:

Option A

5 0
3 years ago
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Compute the values of dy and Δy for the function y=e^(2x)+6x given x=0 and Δx=dx=0.03.
Maksim231197 [3]

Answer:

  • dy = 8·dx
  • Δy = 0.24

Step-by-step explanation:

The derivative of your function is ...

  y' = dy/dx = 2e^(2x) +6

At x=0, the value is ...

  y'(0) = 2e^0 +6 = 8

  dy = 8·dx

__

  Δy = y'(0)·Δx

  Δy = 8(.03)

  Δy = 0.24

6 0
2 years ago
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