a bag contains three red marbles five blue marbles and seven green marbles.what is the ratio of blue marbles to the total number of marbles​

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

The answer is

[tex] \frac{3}{x} = \frac{11}{10} - \frac{4}{5} \\ \frac{3}{x} = \frac{55 - 40}{50} \\ \frac{3}{x} = \frac{15}{50} \\ \frac{3}{x} = \frac{3}{10} \\ x = 10[/tex]

Answer:

20

Step-by-step explanation:

3 (b + a) = c

3 (4 + 5) = 7

12 + 15 = 7

27 = 7

27 - 7

20

[tex]\huge\boxed{ \sf{Answer}} [/tex]

Given,

[tex]a = 5 \\ b = 4 \\ c = 7[/tex]

And the equation we need to solve is,

[tex]3(b + a) = c[/tex]

To find the answer, you need to substitute the values of a, b & c in the equation.

[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]

↦ The answer is 20.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

Step-by-step explanation:

The total distance = 1/6 + 3/8 miles Change the denominators to 24

D = 1/6 + 3/8 = 4*1/6*4 + 3*3 / 8 * 3

D = 4/24 + 9/24

D = 13/24 of mile.

Answer:

2.5 years

Step-by-step explanation:

The given amount invested, which is the principal, P = $16,800

The simple interest rate, R = 5% per annum

The intended total value of the investment, A = $18,900

The simple interest on the principal, I = A - P

∴ I = $18,900 - $16,800 = $2,100

The formula for the simple interest, I, is given as follows;

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Therefore, we have;

[tex]T = \dfrac{I \times 100}{P \times R}[/tex]

Plugging in the values, gives;

[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]

The time it will take the investment to grow to $18,900 is T = 2.5 years

Answer:

x = 27.5.

Step-by-step explanation:

There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.

So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.

With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.

Therefore, x = 27.5.

Answer: Choice D

The graph will be discrete because there is no such thing as a partial person to sign up, and the booth is set up once each day for sign ups.

=========================================================

Explanation:

Let's start with the independent variable d. This acts as the variable x. It's the input. The value of d only takes on positive whole numbers (eg: d = 1, d = 2, d = 3, etc). We cannot have something like d = 2.718

So this bit of evidence shows that our function is discrete. Discrete input values (d) plug into the function to produce corresponding discrete output values (m).

Furthermore, we know that m is discrete because the number of people cannot be a fractional or decimal number. We can't have half a person for instance.

---------------

A quick way to see if a set is discrete or continuous is to ask the question: "is it possible to apply the midpoint formula for ANY two values, and have the output make sense?"

So a set like {1,2,3,4,5,...} is discrete because the midpoint of 2 and 3 is 2.5, but that value is not in the set mentioned.

In other words, discrete sets have "gaps" so to speak, while continuous ones do not.

---------------

Another useful property is that let's say that a < x < b, and x is drawn from the domain set. This reduced set will be finite if we're dealing with discrete data. Eg: The set {1,2,3,4,5,...} has the subset {2,3,4} which is finite and discrete.

In contrast, the subset of real numbers x such that [tex]2 \le x \le 4[/tex] is continuous and this subset is infinitely large (has infinitely many members) because we could have things like 2.718 or 3.14 etc

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

Answer:

Moving 4 to the right on the x axis

Answer:

(-1,-1)

Step-by-step explanation:

If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).

Step-by-step explanation:

=> (3x-12) =(x+6)

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

Answer:

8/15

Step-by-step explanation:

The ratio of perpendicular to base is tan B .

Here ,

=> tan B = 8 ft/ 15ft

=> tan B = 8/15

Answer:

x - 2y + 8 = 0

Step-by-step explanation:

that is the procedure above

Answer:

(1,-3) and (4,-6)

Step-by-step explanation:

The solutions are where the linear line intersects the graphed parabola.

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Answer:

160=130+x

x=160-130

x=30

answer:

to test whether agraph is linear

Answer:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

Answer:

3x-2

---------

x-1

Step-by-step explanation:

simplify 18x/6x = 3x/1x

simplify 108/54 = 2/1

Answer:

21/13

Step-by-step explanation:

3 1/2 = 7/2

2 1/6 = 13/6

7/2 divided by 13/6

7/2 X 6/13 = 42/26 = 21/13

Answer:

Step-by-step explanation:

3 1/2 = 7/2 and 2 1/6 = 13/6

7/2 divided by 13/6 = 7/2 x 6/13

42/26

21/13 is your final answer.

Answer:

B.

Step-by-step explanation:

Since the numbers in the root is all the same, lets say [tex]\sqrt{2}[/tex] is a variable.

7x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex]

Group with like terms:

7x[tex]\sqrt{2}[/tex] + x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

Combine like terms:

8x[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{2}[/tex]

There you have it! Since all the square roots are the same thing, we can treat them like variables.

the answer is B..................

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Answer:

2/60 = 1/30 = 3.3%

Step-by-step explanation:

Answer:

x² + 2² =(√15)²

x²+ 4. =15

x² =15-4

x² =11

x. =√11 mi

so the answer is 4th option

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Answer:

b. remains unchanged

Step-by-step explanation:

Formula for standard error of mean is;

SE = σ/√n

From the above, we can see that the standard error of mean is independent of the confidence coefficient as it doesn't affect the SE.

Now, we are given that;

random sample; n = 100

Standard deviation; σ = 1

Thus;

SE = 1/√100

SE = 1/10

Now, even if the confidence coefficient is reduced, we can see that it has no impact on the standard error of mean.

Thus, SE remains unchanged.