Use the following triangles to determine the trig ratios below simplify all fractions rationalize and simplify all radicals and convert all decimals answers to fractions

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent iff we have:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Comparing it with chain rule will give

[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]

Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).

Two events are known to be independent even if the result of one event does not affect the result of the second event.

Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.

Thus, A is correct.

Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.

Thus, B is correct.

Hence, the correct options are A and B.

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Answer:

x = 20  ∠B = 92°  ∠C = 40°

Step-by-step explanation:

The sum of angles of a triangle is 180°.

48 +(6x -28) +2x = 180

8x +20 = 180

8x = 160

x = 20

∠B = (6x -28)° = (6*20 -28)° = 92°

∠C = 2x° = 40°

Answer

X= 20

m<B = 92°

m <C = 40°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So, 48 + 6x-28 +2x = 180

8x+20= 180

8x = 160

So x= 160/8 = 20

Substitute x in the equations:

m<B= 6×20-28= 92°

m<C = 2×20 = 40°

[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]

Answer:

- -=+ we should just add it to make the

Answer:

the answer is 49

Step-by-step explanation:

Step-by-step explanation:

there are 2 similar triangles : ABE and DCE

that means they have the same angles, and the scaling factor from one triangle to the other is the same for every side.

and that means that

DE/AE = EC/BE (= DC/AB)

we know that

AE = AD + DE

BE = BC + EC

a.

so, we have actually

DE/(AD+DE) = EC/(BC+EC)

DE/(10+DE) = 8/(2+8) = 8/10 = 4/5

DE = 4(10+DE)/5

5DE = 4(10+DE) = 40 + 4DE

DE = 40 cm

b.

AD/DE = 3/5

BC/EC must be 3/5 too.

15/EC = 3/5

15 = 3EC/5

75 = 3EC

EC = 25 cm

Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:

[tex]y = a(3)^x[/tex]

Hence, after 2 hours:

[tex]y = a(3)^2 = 9a[/tex]

Which means that the multiplier is of 9.

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Answer:

Random sampling

Step-by-step explanation:

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.

Step-by-step explanation:

you do know that the sum of all angles in a triangle is always 180° ?

so,

3u + 6u - 18 + u + 18 = 180

10u = 180

u = 18

The surface area of the triangular prism is 153 cm².

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The area of the triangular prism is the sum of the area of the rectangle and the area of the triangle, therefore, the area of the prism will be,

Area = A + B + C

        =(9 × 15) + (0.5×6×3) + (0.5×6×3)

        = 135 + 9 + 9

        = 153 cm²

Hence, the surface area of the triangular prism is 153 cm².

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Answer:

9*5 + 6*9 + 9*4 + 1/2*6*3 + 1/2*6*3

=1872+1/2*6*3+1/2*6*3

=1872+18

=1890cm²

Surface area= 1890cm²

Answer:

42

Step-by-step explanation:

6 times 7 is 42

Answer:

c.

Step-by-step explanation:

because on you have to add 4 to the number above. so 3+4 equals 7 so you move 4 spaces to the right on the number line to get you 7. so C is the correct answer

Step-by-step explanation:

please mark me as brainlest

Answer: x = 4/3

Step-by-step explanation: I just answered the answer

The height of the aquarium is h = 18 3/4 yd

The formula for calculating the volume of a rectangular box is expressed as

V = lwh

where

l is the length

w is the width

h is the height

Substitute

350 = 20/3 * 14/5 * h

350 = 280/15h

35 = 28/15h

28h = 35 * 15

28h = 525

h = 525/28

h = 18 3/4 yd

Hence the height of the aquarium is h = 18 3/4 yd

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Answer:

2 solutions

Step-by-step explanation:

y = - 2x + 3 → (1)

y = x² - 6x + 3 → (2)

substitute y = x² - 6x + 3 into (1)

x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )

x² - 4x = 0 ← factor out x from each term on the left side

x(x - 4) = 0

equate each factor to zero and solve for x

x = 0

x - 4 = 0 ⇒ x = 4

substitute these values into (1)

x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )

x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )

the 2 solutions are (0, 3 ) and (4, - 5 )

Answer:

40 L cranberry juice; 80 L apple juice

Step-by-step explanation:

Let x = number of liters of cranberry juice.

The total volume is 120 L, so the volume of apple juice is

120 - x.

The value of the cranberry juice is 0.5x.

The value of the apple juice is 0.35(120 - x).

The value of the mixture is 0.4(120) = 48

The value of the cranberry juice plus the value of the apple juice equals the value of the mixture.

0.5x + 0.35(120 - x) = 48

0.5x + 42 - 0.35x = 48

0.15x = 6

x = 6/0.15

x = 40

120 - x = 120 - 40 = 80

Answer: 40 L cranberry juice; 80 L apple juice

[tex]~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan \theta = \dfrac{LN}{LM}\\\\\\\implies \theta = \tan^{-1} \left( \dfrac{LN}{LM} \right)\\\\\\\implies \theta = \tan^{-1} \left(\dfrac{12.81}{7.72} \right)\\\\\\\implies \theta =58.92^{\circ}[/tex]

Answer:

Step-by-step explanation:

Combine like terms: Like terms have same variable with same power and to combine the like terms, add/subtract the co efficient of the variables.

      Perimeter = sum of all sides

a) Perimeter of ΔABC = AB + BC + CA

                                    = x + 14 + x + 14 + x + 14

                                    = x + x + x + 14 + 14 + 14    {Combine like terms}

                                   = 3x + 42

b) EF = DI - GH

        = 2x + 3 - x

       = 2x - x + 3

       = x + 3

c) FG = HI - ED

         = 12 + 2x - (x + 5)

         = 12 + 2x - x - 5 {To open the brackets, (-1) is distributed to x and 5}

         = 12 - 5 + 2x - x

         = 7 + x

d) Perimeter of DEFGHI = DE +  EF + FG + GH + HI + ID

                                       =  x + 5 + x + 3 + 7 +x  + x + 12 +2x + 2x + 3

                                       = x +x + x + x + 2x + 2x + 5 + 3 + 7 + 3 + 12  

                                       = 8x + 30

Answer:

8.97 × 10-3

Step-by-step explanation:

you move the decimal so its a number between 1 and less than 10 so we moved the decimal three spaces.

Answer:

its B

Step-by-step explanation:

Answer:

Second option is the correct answer

[tex]\bigodot (9a^2b^6-6ab^3c^6+4c^{12})[/tex]

Step-by-step explanation:

The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

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Answer:

C) 56

Step-by-step explanation:

. What is the length of BC¯¯?

2. What is the length of AC¯¯?

3. What is the length of AD

If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.

The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)

The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)

The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)

The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)

Therefore on application of these rules

For Case A

The point will be (-y , x)

For Case B

The point will be (x,y)

Therefore Option B is the answer.

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Answer:

50-20 or perimeter-2length

Step-by-step explanation:

15 inches is the width

The true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°

From the question, we are to determine the statement that is true about the angles in the given figure

In the given diagram, we can observe that

m∠3 + m∠8 + m∠9 + m∠10 = 180° (Sum of angles in a triangle)

Also,

m∠3 = m∠1 (Vertically opposite angles)

m∠9 + m∠10 = 90° (Vertically opposite angles)

∴ m∠1 + m∠8 + 90° = 180°

m∠1 + m∠8 = 90°

Hence, the true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°

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Answer:

Max or Min: min

Domain:  (−∞, ∞)

Range: (−2, ∞)

Increasing interval: (−4, ∞)

Decreasing interval: (−∞, -4)

Step-by-step explanation:

Max or Min: You determined that the curve opens upwards meaning that the vertex is at the min. If it opened down then it would be at the max.

In mathematical terms: if a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, the parabola opens downward, and the vertex is a maximum.

Domain: This is all possible x values, since the parabola is upwards its going to have any possible x values

Range: this is all possible y values. we know that the vertex point (min) doesn't go less than the value of -2 for y but anything above is possible hence -2 is the lowest possible y value and anything beyond above

Increasing interval: The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I.

Decreasing interval: The derivative, then set it equal to 0, and then find between which zero values the function is negative.

visual representation attached as well

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you got this !!

To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.

The area of a circle is pi*r^2. We are given the diameter, so divide that by 2 to get the radius.



Now that you have the area, divide by 6. That is the area of each slice. The problem asks for the area of 2 slices though, so multiply that by 2.