Are points G, K, and F collinear or noncollinear?

Two events are not independent if d) one event affects the likelihood of another event. This means that the occurrence of one event changes the probability of the other event happening.

For example, if flipping a coin, the probability of getting heads is 0.5, but if we know that the coin is weighted towards tails, the probability of getting heads will decrease, this means that the coin flip and the weight of the coin are not independent events because the weight of the coin affects the likelihood of getting heads.

In general, if the occurrence of one event changes the probability of another event, then the two events are not independent.

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Answer:

9) 15

10)22

11)25

Step-by-step explanation:

9)

\(area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\\)

substitute:

=2x+7

=2(7)+1

=15

10)

\(area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x\)

substitute:

=3x-2

=3(7)+1

=22

11)

\(area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25\)

Answer:

$49.12

Step-by-step explanation:

Answer: The slope of a position-time graph represents the velocity. The steeper the slope is, the faster the motion is changing. A negative slope means the velocity is negative i.e. the movement of the object is in a backward or opposite direction.

Step-by-step explanation:

Yeah- moving on ._.

Answer:

boring

Step-by-step explanation:

To prove the given identity, we'll start with the left side and simplify it step by step until we obtain the right side of the equation:

We have:

((sec y - tan y)(sec y + tan y)) / sec y

Using the difference of squares, we can rewrite the numerator:

((sec y)^2 - (tan y)^2) / sec y

Recall the trigonometric identity: (sec x)^2 - (tan x)^2 = 1

Substituting this identity into our expression:

(1) / sec y

Using the reciprocal identity: sec x = 1 / cos x

We can rewrite the expression as:

1 / (1 / cos y)

Simplifying further by multiplying by the reciprocal:

cos y / 1

Which simplifies to:

cos y

Therefore, we have shown that the left side of the identity ((sec y - tan y)(sec y + tan y)) / sec y simplifies to cos y, which is the same as the right side of the equation.

Interest = A - (50 * 456)

To determine how much you will have in the IRA when you retire at age 65, we can use the formula A = P[(1 + r)^t - 1] / r, where A is the future value, P is the monthly deposit, r is the monthly interest rate, and t is the number of months.

a. In this case, the monthly deposit is 50, the monthly interest rate is 5% or 0.05, and the number of months is (65 - 27) * 12 = 456 (from age 27 to 65).

Using the formula, we can calculate:
A = 50[(1 + 0.05)^456 - 1] / 0.05

b. To find the interest, we can subtract the total deposits from the future value:
Interest = A - (P * t)

In this case:
Interest = A - (50 * 456)

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The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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Answer:

g(x + 2) = 10x + 24

g(x) + g(2) = 10x + 28

Step-by-step explanation:

1) If g(x) = 10x + 4, then g(x+2) = 10(x+2) + 4

g(x) = 10x + 20 + 4

g(x + 2) = 10x + 24

2) If g(x) = 10x + 4, then g(x) + g(2) = 10x + 4 + 10(2) + 4

g(x) + g(2) = 10x + 4 + 20 + 4

g(x) + g(2) = 10x + 28

Answer:

36

Step-by-step explanation:

Mason's mom is 36

9 x 4 = 36

Answer:

53

Step-by-step explanation: all angles of a triangle add up to 180

Answer:

2 733.25 + 7270 = 10 003.25

Step-by-step explanation:

192 * 36 = 6 912 +358 = 7 270

45425 - 36000 ( allowed miles for 3 years )

9 425 * 0.29 = 2 733.25

Answer:

Now we need to find B' and C' by multiplying 0.125 with the x-coordinate and y-coordinate.

-----

x-coordinate of B is -2, y-coordinate of B is 8

x-coordinate of B'

y-coordinate of B'

So

-----

x-coordinate of C is 6 and y-coordinate of C is 4

x-coordinate of C'

y-coordinate of C'

So

Conclusion:

The below are the TRUE statements:

(i) The coordinates of C' are (0.75, 0.5)

(ii) The scale factor is 1/8

(iii) The coordinates of B' are (–0.25, 1).

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Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i got it correct

Answer:

The answer is $22.80

Step-by-step explanation:

Ahmad sells beaded neckless each large necklace sells for $6.10 and each small necklace sells for $4.50.

If Ahmad will sell 3 large necklaces and 1 small necklace then,

3 × $6.10 = $18.30

So, $18.30 + $4.50 = $22.8

Thus, If Ahmad will sell 3 large necklaces and 1 small necklace then he will earn $22.80.

-TheUnknownScientist 72

Answer: The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

The formulae that specify how much 8% solution in equation and how much 24% solution were utilized are x+ y=200 and x+3y=450.

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.

The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: x +y=200

Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:

\(0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\\)

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On solving the provided question, we can say that For the specified percentage, the 95% confidence interval is (0.864, 0.3580).

A confidence interval in statistics expresses the probability that a population parameter would fall between a set of values for a specific percentage of the time. Analysts commonly utilize 95% or 99% confidence intervals for their predictions.

If total samples = E = 36, then

8 results were obtained.

Chance = p = 8/36 = 0.2222

Z value at 95% confidence level = 1.96

p = \(0.2222 + 1.96 ( \sqrt{ 0.2222() 1 - 0.2222) / 36 } ) = 0.3580\)

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The error occurred in step 1

The justification for solving the equation -2(t + 3) + 4 = 12 + 6t is below;

2 |a + 1| = 5

Step 1:

2 |a + 1| = 5 or 2 |a + 1| = -5

2a + 2 = 5 or 2a + 2 = -5

combine like terms

2a = 5 - 2 or 2a = -5 - 2

2a = 3 or 2a = -7

divide both sides by 2

a = 3/2 or a = -7/2

2.

-2(t + 3) + 4 = 12 + 6t original equation

-2t - 6 + 4 = 12 + 6t Distributive property

-2t - 2 = 12 + 6t Addition property of equality

-2t - 2 - 6t = 12 + 6t - 6t Subtraction property of equality

-8t - 2 + 2 = 12 + 2 combine like terms

-8t / -8 = 14 / -8 Division property of equality

t = 14/-8 solution

t = 7/-4 simplified solution

Therefore, the equation -2(t + 3) + 4 = 12 + 6t has a simplified solution of t = 7/-4

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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Answer:

option 6b):) is correct

Answer: Devon, Tasha, Liza, Effon

Step-by-step explanation:

From the question, we are informed that four friends race their bikes down the street and that Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds.

The order that shows the friends' times from fastest to slowest is:

• Devon

• Tasha

• Liza

• Effon

Devon used 6.0999 seconds which is the fastest time, after then Tasha comes next with 6.168 seconds, then Liza with 6.188 seconds and lastly Effon with 6.2 seconds

Answer:

x=10

Step-by-step explanation:

-4 times x =-4x

-4 times 6 =-24

-4x-24=-64

add 24 to both sides

-4x=-40

divide -4 from both sides

x=10

Answer:

x = 10

Step-by-step explanation:

-4(x+6) = -64

-4x-24 = -64

-4x = -64+24

-4x = -40

x = 10

hope this helps!!! :)

The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The polar curve r = 5sin 2θ

When r = 0, θ = 0, π/2 which corresponds to one loop.

We need the limits to provide r=0 or cos(5x) =0 so:

Therefore the area of the region enclosed by this curve is

\(A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}\)

Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.

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The consequence of the institutionalized expectation of choice in family life is that individuals may experience increased pressure, anxiety, and uncertainty when making decisions about their family structure and relationships.

In modern society, there is a prevailing expectation that individuals should have the freedom and agency to make choices regarding their family life. This expectation stems from the recognition of personal autonomy and the desire to challenge traditional norms and structures. However, this institutionalized expectation of choice can have consequences on individuals.

One consequence is the heightened pressure and anxiety individuals may experience when making decisions about their family structure and relationships. With an abundance of options and possibilities, individuals may feel overwhelmed by the weight of their choices. They may worry about making the "right" decision, fearing potential regret or societal judgment if they make a choice that deviates from societal expectations or traditional norms. This pressure to make the "perfect" choice can lead to decision paralysis and increased stress.

Another consequence is the increased uncertainty that individuals may face. The expectation of choice implies that individuals are responsible for actively shaping their family lives, but it also means that the outcomes of those choices rest solely on their shoulders. This can create a sense of uncertainty and doubt about whether the chosen path will lead to desired outcomes or if alternative choices would have been better. Individuals may question their decisions, second-guessing themselves and experiencing a constant sense of uncertainty about the future.

Overall, the institutionalized expectation of choice in family life can result in increased pressure, anxiety, and uncertainty for individuals as they navigate decision-making processes related to their family structure and relationships.

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The sine of an angle in the second quadrant differs from the sine of its reference angle by a negative sign.

In the unit circle, the reference angle is the acute angle formed between the positive x-axis and the terminal side of an angle measured counterclockwise. The sine of an angle is defined as the y-coordinate of the point on the unit circle corresponding to that angle.

In the second quadrant of the unit circle, angles have values between 90 degrees and 180 degrees (π/2 and π radians). Since the reference angle is always the acute angle, the reference angle for an angle in the second quadrant is the angle formed between the terminal side and the negative x-axis.

When comparing the sine of an angle in the second quadrant to the sine of its reference angle, there is a sign difference. The sine function is positive in the first and second quadrants. However, in the second quadrant, the y-coordinate (sine value) is negative because it lies below the x-axis. This means that the sine of an angle in the second quadrant is the negative value of the sine of its reference angle.

Mathematically, if θ is an angle in the second quadrant, and α is its reference angle, then:

sin(θ) = -sin(α)

This relationship holds true because the y-coordinate (sine value) in the second quadrant is the negative value of the y-coordinate in the first quadrant. So, the sine of an angle in the second quadrant differs from the sine of its reference angle by a negative sign.

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer: a) Georgia, b) 120 words

Step-by-step explanation:

We can calculate how many words they each wrote by multiplying their time and the rate at which they write words.

Richard: 45*16 = 720 words total

Georgia: 70*12 = 840 words total.

Therefore, Georgia wrote 120 more words.

Based on the original trapezoid and the enlargement, the length of side A can be found to be 12 cm.

To find out the length of side A, you first need to find the enlargement scale used to enlarge the original trapezoid.

The enlargement scale can be found as:

= Base of enlarged shape / Base of original trapezoid

= 20 / 5

= 4

Using this scale, the length of side A is:

= Length on original shape x Enlargement factor

= 3 x 4

= 12 cm

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