i have been trying to solve this compound and double angle question please help me find the answer to these question guys​

Answer:

The volume of the solid is π/40 cubic units.

Step-by-step explanation:

Please refer to the graph below.

Recall that the area of a semi-circle is given by:

[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]

The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:

[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]

Substitute:

[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]

Simplify:

[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]

Integrate:

[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]

Evaluate:

[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]

The volume of the solid is π/40 cubic units.

Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]

For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.

We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.

The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1

Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.

If we take [tex]dx[/tex]x-axis, then the curve  [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]

Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:

[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).

Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]

Learn more about volume of three dimensional region here:

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Answer:

We accept H₀ with 95 % of Confidence Interval we have enough evidence to conclude that the majority of members agree with the new system

Step-by-step explanation:

Sample size      800

Sample   x₁   = 420   ( number of people in favor of a proposed scoring system), then

p₁ = 420/800   p₁  =  0,525    p₁  = 52,5 %  then

q₁  =  1  - p₁     q₁  =  1  - 0,525      q₁  =  0,475

Sample size enought to use the approximation of the binomial didtribution to normal distribution

If significance level is 0,05    α  = 0,05

and from z-table we look for z(c)  ( z critical value)

z (c)  = 1,64

Hypothesis Test:

Null Hypothesis                       H₀            p₁  = 0,5

Alternative Hypothesis           Hₐ            p₁  >  0,5

Alternative hypothesis tells us about a one tail-test to the right

To calculate

z(s) =  (  p₁  -  0,5) / √ (p₁*q₁) / n

z(s) =   0,025 / √ 0,525*0,475/800

z(s) =   0,025 / √0,000311

z(s) = 0,025/0,01765

z(s) = 1,416

Comparing z(c)  and z(s)

z(s) < z(c)       1,416 <  1,64

z(s) is in the acceptance region we accep H₀.

Answer:

0.525 = 52.5% probability that the two are from different families.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, the order in which the two participants are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

1 from the Harfield family(from a set of 7).

1 from the McCoy family(from a set of 9). So

[tex]D = C_{7,1}*C_{9,1} = \frac{7!}{1!6!}*\frac{9!}{1!8!} = 7*9 = 63[/tex]

Total outcomes:

2 from a set of 16. So

[tex]T = C_{16,2} = \frac{16!}{2!14!} = 120[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{63}{120} = 0.525[/tex]

0.525 = 52.5% probability that the two are from different families.

Answer:

-5

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Answer:

4 tokens.

Step-by-step explanation:

The expected value of a given event is calculated as:

EV = (x₁*p₁ + x₂*p2 + ... + xₙ*pₙ)

Where xₙ is the n-th outcome, and pₙ is its probability.

In this case, our experiment is:

You draw two times.

We have 30 cards with no prize

We have 10 cards with a prize.

A total of 40 cards.

As we draw two times (and the first time we draw a card we put it back in the deck) we can consider the events as independent, so we can find the expected value per draw.

Now we can define:

x₁ = drawing a blank card = 0 tokens

The probability will be equal to the quotient between the number of blank cards and the total number of cards

p₁ = 30/40 = 3/4

x₂ = drawing a prized card = 8 tokens.

The probability will be equal to the quotient between the number of prized cards and the total number of cards:

p₂ = 10/40 = 1/4

Then the expected value per draw is:

EV = ( (3/4)*0 tokens + (1/4)* 8 tokens) = 2 tokens.

And we have two draws, then the expected value of two draws is two times the expected value per draw, this means that the expected value in our case is:

expected value = 2*(2 tokens) = 4 tokens.

The correct option is the first one, counting from the top.

Answer:

t = 9.58 s

Step-by-step explanation:

Given that,

The height from where the cell phone is dropped, h = 450 feet

We need to find the time for the cell phone to reach the ground. Let the time be t. Using second equation of kinematics to find it.

[tex]h=ut+\dfrac{1}{2}at^2[/tex]

u is initial velocity, u = 0

a = g

So,

[tex]h=\dfrac{1}{2}at^2\\\\t=\sqrt{\dfrac{2h}{g}} \\\\t=\sqrt{\dfrac{2\times 450}{9.8}} \\\\t=9.58\ s[/tex]

So, it will take 9.58 seconds to reach the ground.

Answer:

56 feet.

Step-by-step explanation:

The formula for finding the length of a rectangle, given the diagonal and the width is [tex]\sqrt{d^2 -{w^{2}[/tex]. So, [tex]\sqrt{4900 - 1764[/tex]. If you put this thing in the calculator you get 56.

Answer:

10pi feet

Step-by-step explanation:

The formula for arc length (degrees) is: 2pi x radius x angle/360

2pi x 30 x 60/360

60pi x 1/6

10pi

Answer:

D

Step-by-step explanation:

All the x and y values have a proportion of 5:1

Answer:

D

Step-by-step explanation:

Proportional relationship means there is a common difference between X and Y. That is only present in D, where x/5 = y.

X       Y

5/5 = 1

10/5 = 2

15/5 = 3

20/5 = 4

25/5 = 5

Answer:

c=57.8

Step-by-step explanation:

6*7+4=46

5*7=35

c= 46^2+35^2=57.80138

Answer:

this should help you understand...

Step-by-step explanation:

Answer:

4x/7 - 143/56

Step-by-step explanation:

Answer:

[tex]2+2=4[/tex] obviously...

Answer:

well it depends

Step-by-step explanation:

if you wanna be hallarius then 22 but the real mathmatics is 4

PLS GIVE BRAINLIEST

Answer:

a) =2^(4+2)

=2^6

=64

b) =(-5)^(8-3)

=(-5)^5

= - 3125

c) =(81)(27)

=2187

Answer:

1.x²+x-2

=x²+2x-x-2

=x(x+2)-1(x+2)

=(x+2)(x-1)

2.

(x²+x-2)/(x-1)

={x²+2x-x-2}/(x-1)

={x(x+2)-1(x+2)}/(x-1)

={(x+2)(x-1)}/(x-1)

=(x+2) true

Answer:

Step-by-step explanation:

area of circle=π(5)²=25 π≈25×3.14≈78.5

Answer:

A≈78.54

Step-by-step explanation:

A=πr2=π·52≈78.53982

Also i left this out but the radius of the circle is 5.

Chill im only a 7th grade nerd studying in Real Estate and Finances

Also hopes this helps ;0

Answer:

27.30

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

because 5 is used for both numbers and that's why

Answer:

5x

Step-by-step explanation:

Both 10 and 15 have a HCF of 5

And both values have x in common

Answer:

55

Step-by-step explanation:

a triangle adds up to 180°

25+30+x= 180

55+x=180

x=180-55

x=125

x and y is a straight line so it adds up to 180°

x=125 y=?

x+y=180

125+y=180

y=180-125

y=55°

y= 55°

Answer:

First three terms: -2, 1, 6

Tenth term: 97

Step-by-step explanation:

Given

[tex]T_n =n^2 -3[/tex]

Required

The first three terms and the tenth

So, we have:

First term: n =1

[tex]T_1 = 1^2 - 3 = 1 - 3 = -2[/tex]

Second term: n = 2

[tex]T_2 = 2^2 - 3 = 4 - 3 = 1[/tex]

Third term: n = 3

[tex]T_3 = 3^2 - 3 = 9 - 3 = 6[/tex]

Tenth term: n = 10

[tex]T_{10} = 10^2 - 3 = 100 - 3 = 97[/tex]

Answer:

54 cm

Step-by-step explanation:

they are the same i think

Answer:

Volume

Step-by-step explanation:

The amount of water that fits in a fish tank represents the Volume of the fish tank.

When you pour water, it occupies the space and the weight of the tank increases. So, it represent the volume

Answer:

A 1.85

Step-by-step explanation:

cos 72 = 6/x

x cos 72 = 6

x = cos 72/6 = 1.84

Answer:

A

Step-by-step explanation:

1.84

Answer:

2[tex]\frac{1}{2}[/tex] cups

Step-by-step explanation:

Hi there,

When dealing with these types of problems, it is highly recommended to set the same denominators for the fractions you are dealing with. In this problem, we can see that 2[tex]\frac{1}{2}[/tex] is equivalent to [tex]\frac{5}{2}[/tex]; making this the correct answer choice.

Hope this explanation helps.

Cheers.

Answer:

139

Step-by-step explanation:

Inside angles of a triangle = 180 degrees

61 + 78 = 139

180 - 139 = 41

unknown interior angle = 41 degrees

So m<1 = 139

(Or just add the two interior angles together)

Answer:

5.4 is the length

Step-by-step explanation:

5.333 - (12√5)/5 - round to nearest hundreth (5.4)

length total 5.4

Thanks and Rate my Answer Please!

The length of the smaller leg is 3.8 unit.

Pythagoras theorem states that "the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)" i.e.

[tex]c^{2} = a^{2} + b^{2}[/tex]

Let the length of the leg be b and a.

According to the given question.

We have a rigth triangle which have congruent legs.

And hypotenuse, c = [tex]\frac{12\sqrt{5} }{5}[/tex]

Since, the legs are congruent.

Therefore,

a = b

Now, according to the Pythagoras theorem.

[tex]c^{2} = a^{2} + b^{2}[/tex]

[tex]\implies c^{2} = a^{2} + a^{2}[/tex]

[tex]\implies c^{2} = 2a^{2}[/tex]

[tex]\implies (\frac{12\sqrt{5} }{5} )^{2} = 2a^{2}[/tex]

[tex]\implies \frac{144\times 5}{25} = 2a^{2}[/tex]

[tex]\implies \frac{144}{5} = 2a^{2}[/tex]

[tex]\implies \frac{72}{5} = a^{2}[/tex]

[tex]\implies a = \sqrt{\frac{74}{5} }[/tex]

[tex]\implies a = \sqrt{14.8}[/tex]

[tex]\implies a = 3.84[/tex]

[tex]\implies a = 3.8[/tex] unit

Hence, the length of the smaller leg is 3.8 unit.

Find out more information about Pythagoras theorem here:

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