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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:

≈ 11.78 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{\frac{\pi }{4} }{2\pi }[/tex] ( cancel 2π on numerator/ denominator )

     = 15 × [tex]\frac{\pi }{4}[/tex]

     = [tex]\frac{15\pi }{4}[/tex]

     ≈ 11.78 in ( to 2 dec. places )

Answer:

946 square Inches

Step-by-step explanation:

First, you should split up the shape into parts.

1st part 28x7

2nd part 30x25

We are multplying simply because

Area = Length x Width

Now that we have split up the parts lets multply them and add them togeher.

28 x 7 =  196

30 x 25 = 750

196 +750 = 946

So the area of this figure is 946 square inches.

Answer:

i dont understand

Step-by-step explanation:

i took test

subtract 2 from both sides

3a - 3y =  15 - 2x

factor out the common term 3

3 (a-y) = 15 - 2x

divide both sides by 3

a - y = 15 - 2x/3

add y to both sides

a = 15-2x/3 + y

then solve put the value for a =

15-2x/3 + y + 7 ÷10​

simplify using the common denominator

10(15-2x)+7*3/30

simplify 7 * 3 to 21

10(15-2x)+21/30

expand

150-20x+21/30

simplify 150-20x+21 to -20x + 171

-20x+171/30

Answer: -20x+171/30

[tex]\huge\bf Question:– [/tex]

[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]

[tex] \bf \huge \: To \: Find:–[/tex]

[tex] \boxed{\bf \: Value\: of \: A}[/tex]

[tex]\huge\bf Solution:–[/tex]

[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]

[tex]\boxed{ \bf \: Add -2x \: to \: both \: sides}[/tex]

[tex]\sf \longmapsto \: 3a+2x−3y+−2x=15+−2x[/tex]

[tex]\sf \longmapsto \: 3a−3y=−2x+15[/tex]

[tex]\boxed{ \bf \: Add \: 3y \: to \: both \: sides}[/tex]

[tex]\sf \longmapsto \: 3a−3y+3y=−2x+15+3y[/tex]

[tex]\sf \longmapsto \: 3a=−2x+3y+15[/tex]

[tex] \boxed{\bf \: \: Divide \: both \: sides \: by \: 3}[/tex]

[tex]\sf \longmapsto \: \dfrac{3a}{3} = \dfrac{−2x+3y+15}{3} [/tex]

[tex] \boxed{\bf \: Cross \: Multiply}[/tex]

[tex]\boxed{\sf \longmapsto \: a = \dfrac{ - 2}{3} x + y + 5}[/tex]

______________________________________

[tex]\bf \: Put\:The\: Value[/tex]

[tex] \sf \longmapsto \: \dfrac{−2x+3y+15}{3} +7÷10[/tex]

[tex] \boxed{\bf \: Distribute}[/tex]

[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x+y+5+ \dfrac{7}{10} [/tex]

[tex] \boxed{\bf \: Combine \: Like \: terms}[/tex]

[tex]\sf \longmapsto \: \bigg( \dfrac{ - 2}{3} x\bigg) + y +\bigg( 5 + \dfrac{7}{10} \bigg)[/tex]

[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x + y + \dfrac{57}{10} [/tex]

______________________________________

[tex]\boxed{\bf The Answer\: is:–}[/tex]

[tex]\boxed{{\underline{\bf\dfrac{ - 2}{3} x + y + \dfrac{57}{10}} }}[/tex]

Answer: you would multiply and the other one is 1536

Step-by-step explanation:

Have nice night

Answer:

[tex]y=\frac{4}{5}x+4[/tex]

Step-by-step explanation:

You'll need to get this equation in slope-intercept form by solving for y. I do a little extra here to get it in the correct form, but I think it's pretty clear. Let me know if I need to clarify.

[tex]\\\\\frac{8x}{5}-2y=-8\\\\-2y=-\frac{8x}{5}-8\\\\2y=\frac{8x}{5}+8\\\\y=\frac{4}{5}x+4[/tex]

Once it's in slope-intercept form, both the slope and the y-intercept are readily available so you can easily graph it. I graphed both of them in the attached image so you can see that they are the same line.

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

Answer:

225 children tickets, 450 adult tickets and 500 student tickets were sold

The population 5 years from now would be 60482

The population growth rate is given as:

[tex]r(t) = 400(1 + \frac{2t}{24 + t^2})[/tex]

The value of t, 5 years from now is represented as:

t = 5

Substitute 5 for t in the function r(t).

So, we have:

[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 5^2})[/tex]

Evaluate the exponent

[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 25})[/tex]

Evaluate the products

[tex]r(5) = 400(1 + \frac{10}{24 + 25})[/tex]

So, we have:

[tex]r(5) = 400(1 + \frac{10}{49})[/tex]

Divide 10 by 49

[tex]r(5) = 400(1 + 0.204)[/tex]

This gives

[tex]r(5) = 400(1.204)[/tex]

Expand

[tex]r(5) = 481.6[/tex]

The current population is given as 60000.

So, the population (P) 5 years from now would be

[tex]P = 60000 + 481.6[/tex]

[tex]P = 60481.6[/tex]

Approximate

[tex]P = 60482[/tex]

Hence, the population (P) 5 years from now would be 60482

Read more about population functions at:

https://brainly.com/question/20115298

Answer:

.2

Step-by-step explanation:

3:15 to 4:30 is 75 minutes

she had to assemble 15 since there were already 67 made

divide 15/75

.2 per minute

Answer:

Ayo

Step-by-step explanation:

Thanks bro

Answer:

$4.35

Step-by-step explanation:

The expected value of a random variable X, often denoted as E(X), indicates the probability-weighted average of all possible values/events. The general formula of expected value is

[tex]\mathrm{E(\textit X \mathrm)} = \displaystyle\sum_{\mathclap{i=1}}^{k} \ X \times P(X) \\ \\ \\ = X_{1} \times P(X_{1}) \ + \ X_{2} \times P(X_{2}) \ + \ X_{3} \times P(X_{3}) + \ \cdots \ + X_{k} \times P(X_{k})[/tex].

Therefore, the expected value of the winnings from a game is

[tex]\mathrm{E(\textit X \mathrm)} \ = \ 1 \times 0.35 \ + \ 2 \times 0.2 \ + \ 5 \times 0.1 + \ 8 \times 0.2 \ + 10 \times 0.15 \\ \\ = \ 4.35 \ \ (\mathrm{nearest \ hundredth})[/tex].

Answer: Obtuse Isosceles.

Explanation: Two angles are congruent, which means the triangle is isosceles. One angle is over 90°, which means the triangle is obtuse.

Step-by-step explanation:

-0.5 cause decimals and fraction are not included

Answer:

y = -30

Step-by-step explanation:

3 (y + 8) = 2y - 6

3y + 24 = 2y -6                Distribute the 3

y + 24 = -6                       Subtract 2y on both sides

y = -30                              Subtract 24 on both sides

Answer:

23, so 1. i know because i added 14+9 and got 23. im sorry if you meant like a definition term, please comment if thats what you meant. because i'll help you then.

Step-by-step explanation:

Answer: (-7,-5)

Step-by-step explanation:

Because when you mark point M and A if you mirror point M and A on the x Axis then you will get (-7,-5)

Answer:

yes

Step-by-step explanation:

x increases by 2, and y increases by 3 consistently

Answer:

No

Step-by-step explanation:

please mark me brainliest

Answer:

C and B

Step-by-step explanation:

20%=1/5 so D+1/5D

1.2 = 120%

Answer:

Step-by-step explanation:

3x3 then 4 x v ?

Answer:An outlier is any data point that falls above the 3rd quartile and below the first quartile. The inter-quartile range is and . The lower bound would be and the upper bound would be . The only possible answer outside of this range is .

Step-by-step explanation:

Answer: Select the correct answer.

Which point represents the outlier?

(3, 13)

Step-by-step explanation:

A. (2, 3)

B. (4, 5)

C. (3, 13)

D. (8, 9)

Answer:

5

Step-by-step explanation:

If Wendy has $27 to buy seeds, and each seed bag costs $5, then:

5 · 5 = 25

5 · 6 = 30

27<30

27>25

So, Wendy is able to buy 5 bags and remain with 2 dollars.

Answer:

85m

Step-by-step explanation:

Perimeter of a rectangle = 2(l+b)

b=72m, l=?

perimeter =314m

314=2(l+72)

314/2= l+72

157=l+72

l=157-72

l=85m

Answer:

possible arrangements

CCNNN

CNCNN

CNNCN

CNNNC

NCCNN

NCNCN

NCNNC

NNCCN

NNCNC

NNNCC

Ten ways to arrange the window

for any one of these there are

NHL

7 ways to fill the first position

6 ways to fill the second

5 ways to fill the third

7•6•5 = 210 ways to select the NHL jerseys

CFL

8 ways to fill the first position

7 ways to fill the second

8•7 = 56 ways to select the CFL jerseys

210•56 = 11760 ways to select a set of 5 jerseys

11760•10 = 117 600 possible ways to arrange the window

Answer:

x=65

Step-by-step explanation:

y= 23213

Answer:

Step-by-step explanation:

The answer is 65. You just add the number of computer towers that fall into that category. So your sum would look like this:

Divisor: 5+ 12 + 21 + 15 + 12 = 65

The question does not ask you to do any more than figure out what you will be dividing by. Thank goodness it does not ask what you will be dividing into which is a whole lot more complicated problem.