2.5/6 = h/9 h=? What does this mean

two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral

\(\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}~ ~~ units^2\)

Answer:

C.

Step-by-step explanation:

It is an equilateral triangle.

DB = 6, AB = 12, DC = height

\(DC=\sqrt{(CB)^{2}- (DB)^{2} } =\sqrt{144-36} =\sqrt{108}=\sqrt{(36)(3)} =6\sqrt{3}\)

\(A=\frac{(DC)(AC)}{2} =\frac{(6\sqrt{3})(12) }{2} =\frac{72\sqrt{3} }{2} =36\sqrt{3}\)

Hope this helps

Answer:

At the very end, the amounts of money are:

A -- 24

B -- 24

C -- 24

If A and B received as much as they had just prior to the last transaction, they must each have received 12 and they must have received it from C, so at the end of the previous step, the situation must have been:

A -- 12 (24 minus 12)

B -- 12 (24 minus 12)

C -- 48 (24 plus 12 plus 12)

Before that, A and C got half of what they had above from B, so:

A -- 6 (12 minus 6)

B -- 42 (12 plus 6 plus 24)

C -- 24 (48 minus 24)

And initially, B and C got half of what they had above from A, so:

A -- 39 (6 plus 21 plus 12)

B -- 21 (42 minus 21)

C -- 12 (24 minus 12)

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

B=54

C=54

Step-by-step explanation:

180-72=108

108/2=54

54*2=108

108+72=180

Answer:

50

Step-by-step explanation:

probability to get on 4 = 1/6

1/6 x 300 = 50

Answer:

50 times

Step-by-step explanation: you divide 300 divide by 6=50, you got a 1/6/ 300

The value of the derivatives of f df(x, y, z)/dx + df(x, y, z)/dy is 20, when x = 1, y = 1, and z = 1.

To determine df/dt using the chain rule, we need to compute the partial derivatives of f with respect to x, y, and z, as the derivatives of x(t), y(t), and z(t) with respect to t.

We are given that the function as f (x, y, z)= 3x² + xyz + 4y³ z²

To Find df(x, y, z)/dx + df(x, y, z)/dy when x = 1, y = 1, and z = 1.

f (x, y, z)= 3x² + xyz + 4y³ z²

Therefore,

df(x, y, z)/dx = 6x + yz

df(x, y, z)/dy = xz + 12y² z²

Now we have;

df(x, y, z)/dx + df(x, y, z)/dy

6x + yz + xz + 12y² z²

When x = 1, y = 1, and z = 1 then we get;

6 + 1 + 1 + 12

= 20

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Answer:

radius = 12.3 cm

Step-by-step explanation:

The formula to find the circumference of a circle:

Circumference = 2 × π × r

77 = 2 × π × r

r = \(\frac{77}{2*\pi } \)

r = 12.3 cm (in 3 significant figures)

Let x be the number

40% of x = 8

Multiply both-side of the equation by 100

Divide both-side of the equation by 40

Therefore, 8 is 40% of 20

Answer:

Step-by-step explanation:

12

Answer:

c(0) = 24*0 = 0  

c(8) = 24*8 = 192  

Your range is [0,192]

Step-by-step explanation:

Answer:

You have 8 cups of flour it takes 1 cup of flour to make 24 cookies the function c(f)=24f

c represents the number of cookies

f represents the cups of flour

You have 8 cups of  flour, we can use only 0 to 8 cups of flour.

so domain f is 0 to 8 cups [0,8]

Now we find the range

1 cup of flour to make 24 cookies

So 8 cups of flour = 24* 8 = 192 cookies

using 8 cups you can make 192 cookies

So number of cookies is from 0 to 192

Range is [0,192

Step-by-step explanation:

Answer:

Cylinder

Step-by-step explanation:

V cylinder= πr²h= 3.14*2.1²*6= 83.0844 cm²

V prism= bh= 1/2*4*3.5*10= 70 cm²

Cylinder holds more as it has greater volume

In Costello et al. (2003), the independent variable that was not manipulated by the research team was the gender of the participants.

The study examined the effects of different levels of alcohol consumption on cognitive performance and mood states in young adults. Participants were assigned to different alcohol consumption groups based on their self-reported drinking habits. However, the gender of the participants was not manipulated, and the study included both male and female participants. This means that any differences in the results based on gender cannot be attributed to the research team's manipulation of the independent variable, but rather to other factors that may have affected the results.

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Answer:

300 is greater than 3x + 75

The equation you would use to solve would be

300=75+3x

x= the amount of movies he watches

meaning x= 75

300=75+3x

225=3x

x=75

he can rent up to 75 movies

The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:

$1,830.

The total cost is obtained applying the proportions in the context of the problem.

The number of kilowatt hours is given as follows:

Hence:

200 x 61 x 3 = 36,600 kwh.

The cost is of $0.05 per kwh, hence the total cost is given as follows:

0.05 x 36600 = $1,830.

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Answer:

the future value would be 473.72 if p is referring to future value

if p is referring to present value it is 121.59

if p is referring to payment it is 58.37

Step-by-step explanation:

you can use spreadsheets to solve this equation using =pmt/=fv/=pv

Step-by-step explanation:

\(s .i = \frac{prt}{100} \)

\(240 = p \times \frac{12}{100} \times 6\)

\(240 = \frac{18}{25} p\)

\(240 \div \frac{18}{25} = p\)

\(p = 333.3333\)

Hope the above helps you......

Answer:

-2x + 6 \(\leq\) 8x or 5x + 3 < 9

Step-by-step explanation:

-2x + 6 \(\leq\) 8x   -> x\(\geq\) 3/5

5x + 3 < 9       -> x < 6/5

Answer:

Step-by-step explanation:

y=x^2-8x+14

To write in vertex form, group the two x-terms to make a complete square, adjust the constant term accordingly

y = x^2-8x+16  -2

factor the first three terms on the right hand side

y = (x-4)^2 -2

This means that the vertex is at x-4 = 0, or x=4, and y=2.

There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

So, we know that:

27 black socks.

18 grey socks.

9 navy socks.

Probability formula: P(E) = Favouravle events/Total events

Now, insert values in the formula as follows:

P(E) = Favouravle events/Total events

P(E) = 27+18/27+18+9

P(E) = 45/54

P(E) = 15/18

P(E) = 5/6

Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?

Answer:

m∠2 = 57°

Step-by-step explanation:

From the triangle given in the picture,

By applying triangle sum theorem in ΔABC,

m∠BAC + m∠ABC + m∠BCA = 180°

90° + m∠2 + 33° = 180°

m∠2 + 123° = 180°

m∠2 = 180° - 123°

m∠2 = 57°

Answer:

A) \(-\dfrac{1}{8}x\right + \dfrac{3}{16}\)

Step-by-step explanation:

We can simplify the expression using the Distributive Property, which states that:

\(A(B+C) = AB + AC\)

Applying this to the problem at hand...

\(-\dfrac{1}{2}\left(\dfrac{1}4x - \dfrac{3}{8}\right)\)

\(= \left(-\dfrac{1}{2}\cdot\dfrac{1}4x\right) - \left(-\dfrac{1}2\cdot\dfrac{3}{8}\right)\)

\(= -\dfrac{1}{8}x\right + \dfrac{3}{16}\)

So, option A is correct.

Answer:

Step-by-step explanation:

a)

The best estimate for height of the lamp post will be 6m.

Given options for height of lamp post include heights in cm's but for a lamp post heights can not be this low because if height is very low such as 6cm and 60cm the light will not incident on proper place.

So for the lamp post height will be in the range of (5-15)m which is the ideal range for the height of lamp post. Thus option 4 is also neglected.

Hence 6m will be appropriate height for a lamp post.

b)

The best estimate for mass of a pear will be 10g.

Given estimates for a mass of pear can not be of the range kilograms.

As pear possess very less matter in it , the ideal weight of a pear will be in the range of grams.

Hence 10g will be appropriate for the estimation.


c)

Filled kettle will have 2 litres of water in it.

Given quantity of water in the kettle will be of the range in litres as a kettle that contains water will have (1-5)litres of capacity.

Hence for filled kettle the amount of water will be 2litres.

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Answer:

This answer is A.Hope you like answer

Answer:

y = 7x - 4

Step-by-step explanation:

To solve the equation of this line ( in point - slope form ) we would have to first identify the slope. If we are given the points ( 0, - 4 ) and ( 1, 3 ) then through the change in y / change in x, we can calculate the value of this slope. Take a look at the steps below;

\(( 0, - 4 ), ( 1, 3 )\\\\Slope = y2 - y1 / x2 - x1,\\\\Slope = - 4 - 3 / 0 - 1,\\Slope = - 7 / - 1\\Slope = 7 / 1\\\\Slope = 7\)

Now that we have the slope of this line, we have assume part of the equation of this line ( that passes through the points ( 0, - 4 ) and ( 1, 3 ) );

\(y = mx + b -\\m = slope, b = y - intercept\)

Plug in the value of slope for " m " in y = mx + b, and determine the y - intercept by plugging in x as 0 and y as - 4, given the point ( 0, - 4 );

\(- 4 = 7 * ( 0 ) + b,\\- 4 = 0 + b,\\b = - 4\)

From this information, we can say that the equation of this line is y = 7x - 4;

Solution, y = 7x - 4

The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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Answer:

5 times as many should be your answer.

Answer:

10/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100}\)

\(\frac{13}{25} = \frac{13 \times 4}{25 \times 4} = \frac{52}{100}\)

Fractions whose values are between 9/20 and 13/25 :

\(\frac{46}{100}, \ \frac{47}{100}, \frac{48}{100}\), . . .

Answer:

d=7

Step-by-step explanation: