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alexandr1967 [171]
3 years ago
14

Alexandra wants to design a game. In the game that Alexandra wants to create, it will involve two spinners and a game mat. The f

irst spinner will have the words, "left hand", "left foot", "right hand", and "right foot". The second spinner will have four colors, red, green, yellow, and blue. The game mat has 6 green dots, 6 yellow dots, 6 blue dots, and 6 red dots.
Mathematics
1 answer:
sattari [20]3 years ago
6 0
Ok, good for her.
What’s the question?
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If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n
natali 33 [55]

Answer:

f^{-1}=3ln_2(\frac{t}{100})

f^-1 represents the number of hours the bacteria developed

Step-by-step explanation:

f(t) = 100 \cdot  2^\frac{t}{3}

To find inverse of a function , replace f(t) with y

y= 100 \cdot  2^\frac{t}{3}

replace t with y and y with x

x= 100 \cdot  2^\frac{y}{3}

solve for y

divide both sides by 100

\frac{x}{100} =2^\frac{y}{3}

take ln on both sides

ln \frac{x}{100} =\frac{y}{3}ln 2

divide both sides by ln

ln_2(\frac{x}{100}) =\frac{y}{3}

multiply by 3 on both sides

y=3ln_2(\frac{x}{100})

Replace x with t  and y with f^-1

f^{-1}=3ln_2(\frac{t}{100})

f^-1 represents the number of hours the bacteria developed

7 0
3 years ago
Use DeMoivre's theorem to evaluate the expression
natima [27]

Answer:

B. \dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}

Step-by-step explanation:

DeMoivre's theorem:

If the complex number z=r(\cos \alpha+i\sin\alpha), then for natural number n

z^n=r^n(\cos n\alpha+i\sin n\alpha).

In your case,

z=\sqrt{3}\left(\cos\dfrac{5\pi}{12}+i\sin\dfrac{5\pi}{12}\right)

and you have to evaluate z^4.

By DeMoivre's theorem,

z^4=(\sqrt{3})^4\left(\cos 4\cdot \dfrac{5\pi}{12}+i\sin 4\cdot \dfrac{5\pi}{12}\right)=9\left(\cos \dfrac{5\pi}{3}+i\sin\dfrac{5\pi}{3}\right)=9\left(\dfrac{1}{2}-i\dfrac{\sqrt{3}}{2}\right)=\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}.

7 0
3 years ago
HURRY 20 POINTS!!!!! Given the geometric sequence an = 6(5)n − 1, which of the following values for n lies in the appropriate do
Lapatulllka [165]
<h2>Answer:</h2>

n = 1

<h2>Explanation:</h2>

Here we have the following Geometric Sequence:

a_{n} = 6(5)^{n-1}

Where:

a=6 \ \text{First term} \\ \\ r=5 \ \text{Common ratio} \\ \\ n: \ \text{Number of terms}

The first term occurs when n=1. Next the second term occurs when n=2, the third term when n=3 and so on. Therefore, the appropriate value of n that lies on the domain for n is n=1

7 0
3 years ago
Give another name for RS.
Zigmanuir [339]

Answer:

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Which of the following is a true statement?
Nikolay [14]

Answer:

The last choice: 68/5 - 22/5 = 9 1/5

Step-by-step explanation:

Solve each problem:

9 3/7 = 10 3/7

The fractions are the same so look at the whole numbers.

Does 9 equal 10? No, it doesn't so this is a false statement.

332/4 = 1/83

Simplify 332/4:

332/4 = 83/1

83 does not equal 1/83 so this is a false statement.

37/5 = 5 2/5

Convert the improper fraction into a mixed number:

7 2/5 = 5 2/5

These numbers do not equal each other so this is a false.

68/5 - 22/5 = 9 1/5

Subtract the numerators on the left side of the equation:

46/5 = 9 1/5

Convert the improper fraction into a mixed number:

9 1/5 = 9 1/5

These numbers equal each other so this is a true statement!

3 0
3 years ago
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