What is the mean of this data set? 3, 5, 10, 11, 15

Answer:

[tex]x=\dfrac{1}{2} \pi, \dfrac{3}{2} \pi \quad \textsf{in the interval}\:[0,2 \pi)[/tex]

Step-by-step explanation:

Rewrite the given equation so that it equals zero, using the trig identity:

[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]

[tex]\begin{aligned}\sin(2x) & =2\cos(x)\\\sin(2x)-2\cos(x) & =0\\2\sin(x)\cos(x)-2\cos(x) & =0\\2\cos(x)[sin(x)-1] & =0\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Therefore}:\quad 2\cos(x) & =0\\\cos(x) & =0\\x & =\dfrac{1}{2} \pi \pm 2 \pi n, \dfrac{3}{2} \pi \pm 2 \pi n\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Therefore}:\quad \sin(x)-1 & =0\\\sin(x) & =1\\x & =\dfrac{1}{2} \pi \pm 2 \pi n\end{aligned}[/tex]

[tex]\implies x=\dfrac{1}{2} \pi, \dfrac{3}{2} \pi \quad \textsf{in the interval}\:[0,2 \pi)[/tex]

An equation is formed of two equal expressions. The value of x for which the sin(2x) = 2cos(x) will have solution in the interval [0, 2π) is (π/2) and (3π/2).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation can be rewritten as,

sin(2x) = 2 cos(x)

2 sin(x) cos(x) = 2 cos(x)

2 sin(x) cos(x) - 2 cos(x) = 0

Taking 2cos(x) as common,

2 cos(x) [sin(x) - 1] = 0

Now, the two factors can be written as,

cos(x) = 0

x = (π/2)±2πn, (3π/2)±2πn

sin(x) - 1 = 0

sin(x) = 1

x = (π/2)±2πn

Hence, the value of x for which the sin(2x) = 2cos(x) will have solution in the interval [0, 2π) is (π/2) and (3π/2).

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A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².

A triangle is a polygon with 3 sides and 3 vertices.

Since the area of a single triangle is a cm², and the shape is formed of 12 triangles, therefore, the area of the 12 triangles will be equal to,

[tex]\text{Area of the complete figure} = 12 \times a = 12a\rm \ cm^2[/tex]

Given that the area of the complete dark portion is b cm², therefore, the area of the 6 triangles with a cm² of area each, and the black portion can be written as,

[tex]\text{Area of the complete figure} = (6 \times a)+b = (6a+b)\rm \ cm^2[/tex]

As the dark portion also consists of 6 triangles with an area of a cm² each and the total sum of this dark area is b cm². Also, the light portion consists of 6 triangles with an area of a cm². Therefore, the total area can be written as,

[tex]\text{Total area} = 6a+6a = b+b = 2b\rm\ cm^2[/tex]

Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².

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Answer:

32%

Step-by-step explanation:

In order to find the percent of the cost of the cell phone has Jackie saved,

See below how it's done:

[tex] \dfrac{56}{175} \times 100[/tex]

dividing yields:

[tex] 0.32 \times 100[/tex]

multiplying yields:

[tex]32\%[/tex]

Alternative:

Instead of dividing,we can consider reducing the fraction and multiply that with 100 to get the answer.

[tex] \dfrac{56}{175} \times 100 \\ \implies \frac{8}{25} \times 100 \\ \implies 8 \times 4 \\ \implies \boxed{32\%}[/tex]

In conclusion:

Jackie has saved 32% of the cost of the cell phone

Answer:

1

Step-by-step explanation:

Median is the middle number when the numbers are arranged least to greatest.

So:

1, 1, 1, 2, 2

1, 1, 1, 2, 2

1 is the middle number in this data set.

Hope this helps! :D

Answer:

x=1000

Step-by-step explanation:

10⁵x= 10⁸

x= 1000

Answer:

B

Step-by-step explanation:

4,000 is a constant so i cannot be a rate. That instantly eliminates 'D' as an option. If x = 0 at the very start that means the 4,000 must be how many gallons of water there is initially.

Answer:

its dont make since bro what is the fraction?

Step-by-step explanation

divide

Answer:

0,(037)

Step-by-step explanation:

At this question, if I understood correctly, the answer for that is 0,037037037037...

You can write it as 0,(037)

I hope that I helped :)

Answer:

After 12 days both bamboo plants were 9ft tall

Answer:

C

Step-by-step explanation:

If you factorise 6x-24 you will get 6(x-4) as 6 times x equals 6x and 6 times -4 equals -24.

Answer:

D (x-3)(x+3)

It's the difference of two squares

Answer:

25pi or 78.54

Step-by-step explanation:

The formula for the area of a circle is pi*r^2

We know that r=5ft

A=pi*(5ft)^2

A=25pi ft2

You can write it as 25pi ft2 but you can also write as 25*pi ft2 which is about 78.54 ft2

Hope that I helped :)

Answer:

1/3 x 1/7

Step-by-step explanation:

when dividing fraction you take the reciprocal of the divisor and multiply.

Answer:

1/3 x 1/7

Step-by-step explanation:

1/3 x 1/7

Multiplying the reciprocal.

Answer: 1/30

Step-by-step explanation:

3/10 of 90 = 27

1/9 of 27 = 3

3/90 = 1/30

Answer:

3       1/30

Step-by-step explanation:

90 * 3/10   got A

 of these 1/9 = perfect

  90 * 3/10 * 1/ 9 = 3

3 out of 90 = 3/90 = 1/30

Answer:

3.65 ≤ x < 3.75

Step-by-step explanation:

We are finding the lower and upper bounds:

The lowest possible number that can be rounded to 3.7 is 3.65 as the 5 makes the 6 go next.

The maximum possible number to 2 d.p that will be 3.74 as the 4 keeps it at 3.7.

But someone can say 3.749 is a bigger number that 3.74 that will get rounded to 3.7

Someone else can argue with 3.7499.

So to solve this argumnet we put 3.75 but we don't include it.

Therefore our final answer is :

3.65 ≤ x < 3.75

Hope this helped and branliest please.

Step-by-step explanation:

The given shape is a cube.

SURFACE AREA

= 6(a²)

= 6(5²)

= 6(25)

= 150cm²

Answer:

150 cm²

Step-by-step explanation:

Given figure is of a cube, probably like an ICE cube.

Surface area = ?

We know that,

Here a denotes edge.

Given that edge is 5 .

Substituting,

SA of cube = 150 cm²

Answer:

the way you form it or the material you use should be perfect

Answer:

B.  3.53*4.37^x

Step-by-step explanation:

See attached graph.

The exponential regression equations that best fits the data is y = 3.53(4.37)ˣ

The equation of an exponential regression model takes the following form: y = abˣ where: y: The response variable x: The predictor variable a, b: The regression coefficients that describe the relationship between x and y.

Given is a table, we need to determine the exponential regression equation, for the same,

So,

The general exponential regression equations is, y = abˣ

where, a is initial value and b is growth factor.

Using graph calculator, we get,

a = 3.53

b = 4.37

Put the value of a and b in general equation, to find the exponential regression equation.

y = 3.53(4.37)ˣ

Hence the option B is correct.

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Answer:

The probability that a student taking only math will get picked is approximately 29%

Step-by-step explanation: This is because out of the total number of students taking math (95), 52 of such students are also taking science. In order to get the number of students only taking math you have to do 95-52=43 and to put that against the amount of total students the ratio would be 43:147 or 42/147 and if you plug 42/147 into a calculator you will recieve a long decimal that you can then round to 29%.

Answer:

A)

Step-by-step explanation:

The slope predicts a temperature increase of about  [tex]\frac{1}{4}[/tex]º for every increase of 1 chirp per minute. The y-intercepct shows that when the crickets are not chirping (x = 0), the temperature is 50º

The statistical test that would be most appropriate determine the answer the researcher is interest in knowing is a chi-square test.

A chi-square test is a statistical test used to test the relationship between categorical variables. It is used to determine the difference between the expected data and the observed data is due to chance.

Chi squared = [tex]\frac{(O_{i} - E_{i} )^{2} }{E_{i} }[/tex]

Where:

The researcher is interested in knowing if the response to lowering the legal age for drinking alochol (observed value)) varies by gender (expected value). Thus, a chi-square test would be used.

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The vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j).

Let be a vector in rectangular form, that is, a vector of the form (x, y). A vector in polar (trigonometric) form is defined by the following expression: (r, θ)

And the magnitude (r) and direction of the vector (θ), in degrees, are, respectively:

[tex]r = \sqrt{x^{2}+y^{2}}[/tex]     (1)

[tex]\theta = \tan^{-1}\frac{y}{x}[/tex]

And the vector in rectangular form is described below:

(x,y) = (-7, 9) - (-5, 2)

(x,y) = (-2, 7)

And its polar form is determined below:

[tex]r = \sqrt{(-2)^{2}+7^{2}}[/tex]

[tex]r = \sqrt{53}[/tex]

r ≈ 7.280

θ = tan⁻¹ (-7/2)

θ ≈ 105.945°

And the vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j). [tex]\blacksquare[/tex]

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The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

We can use the fact that:

[tex]\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)[/tex]

to convert the sine to cosine.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

[tex]y= 3\cos(2(x + \pi/2)) - 2[/tex]

The options are:

Checking all the options one by one:

[tex]y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2[/tex]

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

This option if would be true, then from option 1 and this option, we'd get:
[tex]-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0[/tex]

which isn't true for all values of x.

Thus, this option is not same as the given function.

The given function is [tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]

This option's function simplifies as:

[tex]y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2[/tex]

Thus, this option isn't true since [tex]\sin(2x) \neq \cos(2x)[/tex] always (they are equal for some values of x but not for all).

The given function simplifies to:[tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]

The given option simplifies to:

[tex]y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2[/tex]

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

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Answer:

a

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

And The opposite of the 54 is 1200s. That 1200 go on top and then below the hypothesis D. So Since it's opposite of hypotenuse opposite over hypotenuse, we signed 54 is 1200 over d. Here's what he says, Another way to look at this is like this 1200 Indians. This dash line drew is also 1200 And when it comes to this 54° angle, it's the same thing opposite. 1200 divided by the hypothesis of D.

Answer:

x° = 45°

y° = 90°

z° = 45°

Step-by-step explanation:

Angles on a straight line add up to 180°

⇒ z° + 135° = 180°

⇒ z° = 180° - 135°

⇒ z° = 45°

The dashes on the side lengths mean that the sides are of equal length.  Therefore this is an isosceles triangle.  The base angles of an isosceles triangle are equal.

⇒ x° = z°

⇒ x° = 45°

The sum of the interior angles of a triangle is 180°

⇒ x° + y° + z° = 180°

⇒ 45° + y° + 45° = 180°

⇒ y° = 180° - 45° - 45°

⇒ y° = 90°

Answer:

B 13.8 oz

Step-by-step explanation:

20 %  is  .20 in decimal

.20 * 11.5 oz = 2.3 oz   more than 11.5

2.3 + 11.5 =13.8 oz

Answer:

G is the correct answer

.

.

Answer:

less then 1..2

Step-by-step explanation:

hese are equivalent because 42+35=77 and 7(6+5)=77.

Answer: Yes this is a right triangle

We can determine this by using the converse of the pythagorean theorem.

a = 5, b = 12, c = 13

[tex]a^2 + b^2 = c^2\\\\5^2 + 12^2 = 13^2\\\\25 + 144 = 169\\\\169 = 169 \ \ \checkmark\\\\[/tex]

Since those a,b,c values work in the pythagorean theorem, this proves we have a right triangle.