Alana deposited $20 in a savings account earning 5% interest, compounded annually.
To the nearest cent, how much will she have in 2 years?
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Answer:

Option A: [tex]\{0,\frac{\pi}{2},\frac{3\pi}{2}\}[/tex]

Step-by-step explanation:

[tex]sin^2(\theta)=2sin^2(\frac{\theta}{2}), [0,2\pi)[/tex]

[tex]sin^2(\theta)=2sin^2(\frac{\theta}{2})[/tex]

[tex]sin^2(\theta)=2sin(\frac{\theta}{2})sin(\frac{\theta}{2})[/tex]

[tex]sin^2(\theta)=2(\sqrt{\frac{1-cos(\theta)}{2}})(\sqrt{\frac{1-cos(\theta)}{2}})[/tex]

[tex]sin^2(\theta)=2(\frac{1-cos(\theta)}{2})[/tex]

[tex]sin^2(\theta)=\frac{2-2cos(\theta)}{2}[/tex]

[tex]sin^2(\theta)=1-cos(\theta)[/tex]

[tex]1-cos^2(\theta)=1-cos(\theta)[/tex]

[tex]-cos^2(\theta)=-cos(\theta)[/tex]

[tex]cos^2(\theta)=cos(\theta)[/tex]

[tex]cos^2(\theta)-cos(\theta)=0[/tex]

[tex]cos(\theta)[cos(\theta)-1]=0[/tex]

[tex]cos(\theta)=0[/tex]

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}[/tex]

[tex]cos(\theta)-1=0[/tex]

[tex]cos(\theta)=1[/tex]

[tex]\theta=0[/tex]

Therefore, the solutions contained within the interval are [tex]\{0,\frac{\pi}{2},\frac{3\pi}{2}\}[/tex]

Helpful Tips:

Half-Angle Formula: [tex]sin(\frac{\theta}{2})=\pm\sqrt{\frac{1-cos(\theta)}{2}}[/tex]

Pythagorean Identity: [tex]sin^2(\theta)+cos^2(\theta)=1,sin^2(\theta)=1-cos^2(\theta),cos^2(\theta)=1-sin^2(\theta)[/tex]

[tex]\sin^2 \theta = 2 \sin^2 \left(\dfrac{\theta}2 \right)\\\\\implies \sin^2 \theta = 1- \cos 2 \cdot \dfrac{\theta}2\\\\\implies \sin^2 \theta = 1- \cos \theta \\\\\implies 1-\cos^2 \theta = 1 - \cos \theta \\\\\implies -\cos^2 \theta - \cos \theta = 0\\\\\implies \cos^2 \theta - \cos \theta = 0\\\\\implies \cos \theta( \cos \theta -1) = 0\\\\\\\text{Now,}\\\\\cos \theta = 0\\\\\implies \theta = n\pi + \dfrac{\pi}2\\\\\text{For n = 0,1 and}~ [0.2\pi)\\\\[/tex]

[tex]\theta = \dfrac{\pi}2, \dfrac{3\pi}2[/tex]

[tex]\text{Again,} \\\\\cos \theta -1= 0\\\\\implies \cos \theta = 1\\\\\implies \theta = 2n\pi\\\\\text{For n= 0 and}~ [0,2\pi)\\\\\theta = 0\\\\\text{Combine solutions,}\\\\\theta = 0, \dfrac{\pi}2, \dfrac{3\pi}2[/tex]

Answer:

C

Step-by-step explanation:

Answer:

The answer is to the problem is 18.

Answer: 1 1/2 x 4 4/7

= 3/2 x 32/7

= 96/14

Step-by-step explanation:

1. Write the whole number as a fraction with a denominator of 1.

2. Multiply the numerators.

3. Multiply the denominators

4. Simplify. If needed, if your answer is greater than 1, you may want to write your answer as a mixed number.

1/27

Explanation:

You would multiply to get to the answer.                                                                                    

Answer:

1

Step-by-step explanation:

(3,3) has a positive x value and a positive y value which means it is in the first quadrant

Answer: 1 =.43, 2=.26, 3=.16 4=.33

Step-by-step explanation: So to find all these answers we have to know the total number of people in the chart 30. Then we have to find what info we need from the chart and divide it by the total number of people. I hope this helped I tried to make it simple.

Answer:

I believe it is f(2) = 12

Step-by-step explanation:

I don't know if the * symbol is supposed to be an x but if it is, it would be 12x instead of 12.

Answer:

66n-31m

Step-by-step explanation:

26n-7m+4(10n-6m)

26n-7m+40n-24m

66n-31m

The probability that she will obtain a scholarship given that she is accepted by the college is 0.54.

Given that the probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35, to determine, if the probability that she is accepted by the college is 0.65, the probability that she will obtain a scholarship given that she is accepted by the college, the following calculation must be performed:

Therefore, the probability that she will obtain a scholarship given that she is accepted by the college is 0.54.

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Answer:

Since the logarithmic function is define for ×>-3,thus,the graph has a vertical asymptote at ×=-3.

Answer:

S 25, L 41

Step-by-step explanation:

Small + Large = 66

Large = Small + 16

s + (s + 16) = 66

2s + 16 = 66

2s = 50

s = 25

25 + Large = 66

Large = 41

The value of x must be less than zero for the expression to make sense

The value of x must be less than zero for the expression to make sense

The value of x must be greater than zero for the expression to make sense

For each of the expressions to make sense, the values inside the square root must be greater than zero.

For the expression [tex]\sqrt{-2x^2}[/tex]

-2x^2 > 0

x^2 < 0/-2

x^2 < 0

x < 0

The value of x must be less than zero for the expression to make sense

For the expression [tex]\sqrt{(-2x)^3}[/tex]

(-2x)^3 > 0

-8x^3 > 0

x^3 < 0/-8

x^3 < 0

x < 0

The value of x must be less than zero for the expression to make sense

For the expression [tex]\sqrt{(-2x)^2}[/tex]

(-2x)^2 > 0

2x^2 > 0

x^2 > 0

x > 0

The value of x must be greater than zero for the expression to make sense

Learn more on inequality here: https://brainly.com/question/24372553

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

Cardiovascular system

Step-by-step explanation:

We have: [tex](-\frac{15}{18})[/tex] ÷ [tex](-\frac{20}{24})[/tex] = [tex]\frac{-15}{18} .\frac{-24}{20} = \frac{(-3)(5).(-4)(6)}{(3)(6).(4)(5)} = 1[/tex]

ANSWER: 1

ok done. Thank to me :>

Answer:

1

Step-by-step explanation:

[tex]( - \frac{15}{18} ) \div ( - \frac{20}{24} ) \\ now \: you \: have \: fraction \: divided \: by \: fraction \: then \: do \: reciprocal \: \\ ( - \frac{15}{18} ) \times ( - \frac{24}{20} ) \\ = 1[/tex]

Answer:

this is wrong answer

Step-by-step explanation:

Answer:

-4d

Step-by-step explanation:

L.c.m=15

15×2/5(d-10)-2/3×15(d+6)

3×2(d-10)-2×5(d+6)

6(d-10)-10(d+6)

6d-60-10d-60

6d-10d-60-60

-4d-0

-4d

Answer:

Step-by-step explanation:

slope of -2 means the slope is -2/1

from (3, - 8) you can find the y intercept by going backwords until x = 0

(2,-6)

(1,-4)

(0,-2)

so the y intercept is -2

y = -2x - 2

Answer:

Rate of change of length of shadow is [tex]\frac{15}{7} ft/s[/tex]

Step-by-step explanation:

Consider the figure

We have

[tex]\begin{aligned}&\frac{d x}{d t}=\text { rate of person walking } \\&\frac{d y}{d t}=\text { rate of change of shadow length } \\&\frac{d x}{d t}+\frac{d y}{d t}=\text { rate of change of tip of shadow }\end{aligned}[/tex]

[tex]\begin{aligned}&\frac{6}{20}=\frac{y}{x+y} \\&6(x+y)=20 y \\&6 x+6 y=20 y \\&6 x=14 y\end{aligned}[/tex]

[tex]6\left(\frac{d x}{d t}\right)=14\left(\frac{d y}{d t}\right)\\\\6(5)=14\left(\frac{d y}{d t}\right)\\\\\frac{30}{14}=\frac{d y}{d t}\\\\\frac{15}{7}=\frac{d y}{d t}\\\\[/tex]

Rate of change of length of shadow is [tex]\frac{15}{7} ft/s[/tex]

Answer:

b = 14

Step-by-step explanation:

Since both angles are diagonal each other, they are equal to each other.

5b = b + 56

-b      -b           (subtract b from both sides)

4b = 56

4       4            (divide both sides by 4 to solve for b)

 b = 14

Answer:

y= [tex]\frac{3}{2}[/tex]x -1

Step-by-step explanation:

To find slope I first found the two points on the graph which were (0, -1) and (2, 2). Then I used rise over run to find the slope the point went up 3 units and to the right two units.

then to find the y intercept I found a pint of the graph where the line had passed through the y-intercept line on the graph which just so happened to be -1.

__________________________________________________________

Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

Answer:

y = 3/2 - 1

Step-by-step explanation:

First let's take two coordinates in the line.

( 2 , 2 )     ( 0 , -1)

You can use y = m x + c to find the equation of the line.

Here,

m → slope

c  → y - intercept

( 2 , 2 )                ( 0 , -1)

 ↑  ↑                    ↑  ↑

( x1 , y1 )            ( x2 , y2 )

First let's find the slope of the line.

m = ( y1 - y2) / ( x1 - x2)

m = ( 2 - (-1) ) / (2 - 0 )

m = ( 2 + 1 ) / 2

m = 3 / 2

Now let's find the y - intercept of the line.

For that, let's use ( 0 , -1 ) coordinate

y = m x + c

y = 3/2 × 0 - 1

y = 0 - 1

y = ( - 1 )

Therefore, the equation of the line is,

y = 3/2x - 1

Hope this helps you :-)

Answer:

389

Step-by-step explanation:

MARK BRAINLIEST PLEASE

Answer:

Molly played 4 games

Answer:

x < 2/3 y + 2 1/3

Step-by-step explanation:

put it in a graphing calculator and they matched, I do not know

Answer:

2,572,800

Step-by-step explanation:

I hope this helps!

Answer: 40 x 40 x 402 x 2 x 2 =128,640

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

Given that a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year, to determine if this event is unusual, and specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year knowing that the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009, the following calculation must be performed:

Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.

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Answer:

1. The cost of the fencing material for each side of the playground.

2. The perimeter of the park

3. The labor fee

4. The cost of the fencing material for the whole park.

Step-by-step explanation:

Hope this helps! :)