The sine function is an odd function

Given expression:[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5[/tex]

[tex]\left(4g^3h^2k^4\right)^3:\quad 2^6g^9h^6k^{12}[/tex]

[tex]8:\quad 2^3[/tex]

[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}=\frac{2^6g^9h^6k^{12}}{2^3g^3h^2}[/tex]

[tex]=2^3g^6h^4k^{12}[/tex]

[tex]\left(h^5k^3\right)^5=h^{25}k^{15}[/tex]

[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5=2^3g^6h^4k^{12}-h^{25}k^{15}[/tex]

[tex]=8g^6h^4k^{12}-h^{25}k^{15}[/tex]

Therefore, correct option is 4th option [tex]8g^6h^4k^{12}-h^{25}k^{15}[/tex].

Answer:

ANSWER IS D
Step-by-step explanation:

Final answer:

Explanation of units for trigonometric functions and how to apply the Law of Sines in triangle problems.

Explanation:

The units for sine, cosine, and tangent must be dimensionless. These trigonometric functions relate angles to side lengths in a triangle.

The Law of Sines can be used to solve triangles when you have a known angle and the opposite side length. It states that the ratio of the length of a side to the sine of its opposite angle is constant.

When given measurements may or may not form a triangle, you can apply the Law of Sines to determine if a triangle can be solved. If not, it means no triangle can be formed.

[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]

Step-by-step explanation:

Given :

[tex]\rm sin^-^1(\dfrac{2}{5})=\theta[/tex]

Calculation :

[tex]\rm sin\theta = \dfrac{perpendicular}{hypotenuse}[/tex]

According to Pythagorean theorem,

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

here a = 2, c = 5. Then,

[tex]2^2+b^2=5^2[/tex]

[tex]b^2=25-4=21[/tex]

[tex]b=\pm\sqrt{21}[/tex]

Nothing is given in the question so we take positive

[tex]b = \sqrt{21}[/tex]

Therefore,

[tex]\rm tan\theta=\dfrac{perpendicular}{base}[/tex]

[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]

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The answer is (SAS) Theorem. Because  we know triangle ERT is congruent to  triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).

Hope its correct.

Answer:

64:27

Step-by-step explanation:

Answer with explanation:

⇒A game will be fair , if there is equal chance of winning and losing.

→The game would be fair , if

Landing on Blue sector gives 3.5 points.

Then the, Expected value will be

   [tex]E(x_{i})=x_{i} \times P(x_{i})\\\\E(x)=x_{1} \times P(x_{1})+x_{2} \times P(x_{2})+x_{3} \times P(x_{3})+x_{4} \times P(x_{4})\\\\E(x)=-1 *\frac{2}{7}+(0) *\frac{2}{7}+(1) *\frac{2}{7}+(3.5) *\frac{1}{7}\\\\E(x)=(3.5) *\frac{1}{7}\\\\E(x)=0.50[/tex]

→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.

A game is considered fair if the expected value for all players is zero, balancing the potential wins and losses over the long run. By adjusting winnings and losses so that the sum of the expected values of all outcomes is zero, and recalculating these expected values, we can prove the fairness of the game.

To make a game fair using expected values, one must ensure that the expected value for all players is zero, meaning that there's no advantage or disadvantage to playing the game in the long run. The expected value is calculated by multiplying the value of each possible outcome by its probability and summing these products.

Let's consider the card and coin flipping game and determine its fairness. The expected value (EV) for this game can be expressed as:

To avoir long-term loss, the sum of the expected values for all outcomes should be zero. If the current values do not result in a fair game, we can adjust the winnings and losses such that the expected value is balanced. By recalculating these probabilities with new values, we can verify if the game is fair or not.

Answer:

Sample Response:  Shifts in supply and demand occur when the amount of goods available increases or decreases, or when the demand for a particular good increases or decreases. Shifts in supply can happen when consumers change their spending habits, when competitors produce similar goods, or when the availability of labor or resources changes. Shifts in demand occur when the price changes or when the number of people trying to buy the good changes. It can also happen when people's tastes change.

Final answer:

To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.

Explanation:

The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"

To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.

Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:

the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).

By solving these equations:

leg A = cos(50°) × 7 inches

leg B = sin(50°) × 7 inches

After calculating, we find:

leg A ≈ 4.5 inches (to the nearest tenth)

leg B ≈ 5.4 inches (to the nearest tenth)

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore

so, distance they travel before they ran out of gas = 15 miles

distance they floated back down river = 9 miles

So, they are at

[tex]15-9\\\\=6\ miles[/tex]

Hence, They are 6 miles far.

Therefore, Option 'C' is correct.

since A is a horizontal line it is constant

 so A would be linear constant

By defining a constant line, we will see that the correct option is interval A.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

We say that a line is a constant line if the slope is equal to zero, so we get:

y = b

This would be graphed as a horizontal line.

So we only need to see which interval on the graph has a horizontal line. We will see that the interval is the A interval.

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y = kx

15 = k5

k = 15/5

k = 3

Answer:

776 revolutions per mile

Step-by-step explanation:

First we need to find the Circumference of the wheel.

Formula for circumference = πD

Where D = Diameter of the car wheel = 26 inches

Circumference of the car wheel = π × 26

= 81.68 inches

We have to find, how many inches make 1 mile.

1 mile = 63360 inches.

To determine the number of revolutions a car wheel of diameter 26 inches will travel,

= 63360 inches ÷ circumference of the car wheel

= 63360 inches ÷ 81.68inches

= 775.71 revolutions per mile

To the nearest whole number = 776 revolutions per mile.

AC = sqrt(56^2 + 33^2) = 65cm

EC = sqrt(65^2 - 16^2) = 63 cm

to find AD 33-25 = 8

8^2 + 56^2 = AD^2

64 + 3136=3200^2

square root (3200) = 56.5685 round off to 56.6cm

To solve this problem, we must remember that the sum of interior angle of a polygon is:

Sum of interior angles = (n – 2) * 180˚

So, we can say that:

Sum of interior angles = angle A + angle B + angle C + angle D = (4 – 2) * 180˚

Where,

angle C + angle D = 110 + 70 = 180˚

Therefore substituting this value:

angle A + angle B + 180˚ = 2 * 108˚

angle A + angle B = 360˚ - 180˚

angle A + angle B = 180˚            (answer)

Hence we can also conclude that,

angle A + angle B = angle C + angle D

The answer is 180 degrees because...

angle A + angle B + 180˚ = 2 * 108˚

angle A + angle B = 3

angle A + angle B = 180˚  60˚ - 180˚

Hope this helps, have a BLESSED and wonderful day! As well as as a safe one! :-)

-Cutiepatutie ☺❀❤

diagonal = sqrt(a^2 +b^2)

20 = sqrt(12^2 +b^2)

20= sqrt(144+b^2)

20^2 = 144 + b^2

400 = 144 + b^2

256 = b^2

b = sqrt(256) = 16

 it is 16 inches wide

Answer:

Area of the circle will be  (4.20 [tex]\pi[/tex])

Step-by-step explanation:

We have to find the area of the circle with diameter given is 4.10 m.

Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]

Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m

Formula of the area of a circle is A  = [tex]\pi r^{2}[/tex]

So area of the circle with radius 2.05 m will be

A = [tex]\pi (2.5)^{2}[/tex]

  = 4.20 [tex]\pi[/tex]

Area of the circle will be  (4.20 [tex]\pi[/tex])

The absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane is |v - 84.5| ≤ 10.5, where v is the wind speed.

To write an absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane, you will center it around the average of the two, which is (74 + 95) / 2 = 84.5 mph. The difference between the maximum speed and the average speed is 95 - 84.5 = 10.5 mph. Thus, the absolute value equation to represent the wind speeds of this hurricane category is |v - 84.5| ≤ 10.5, where v represents the wind speed.

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An absolute value equation representing the minimum and maximum sustained wind speeds of a Category 1 hurricane can be written as |v - 84.5| = 10.5, where v is the wind speed in miles per hour. This equation indicates that the wind speed can deviate by 10.5 mph above or below 84.5 mph, encompassing the range of 74 to 95 mph.

To represent the minimum and maximum sustained wind speeds of a Category 1 hurricane using an absolute value equation, we can use the variable v to stand for the wind speed. The absolute value of a number represents its distance from zero regardless of direction, which in the context of wind speed means how much the speed differs from a certain value.

For instance, if the center value is the average of the minimum and maximum speeds, that would be (74 + 95) / 2 = 84.5 miles per hour. Therefore, the absolute value equation that represents the wind speeds that form the boundaries of Category 1 could be written as |v - 84.5| = 10.5. This equation means that the Category 1 wind speed, v, can be 10.5 miles per hour above or below 84.5 miles per hour, which corresponds to the range between 74 and 95 miles per hour.

However, there usually isn't just one single absolute value equation to represent this range. Another approach could involve setting two absolute value inequalities that represent the minimum and maximum separately, such as |v - 74| ≥ 0 for the minimum speed and |v - 95| ≤ 0 for the maximum speed.

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The measure of arc UV is  24°  .

An “arc” is a smooth curve joining two endpoints. In general, an arc is one of the portions of a circle. It is basically a part of the circumference of a circle. Arc is a part of a curve.

According to the question

The Triangle formed inside the triangle

with angles 90° , 36° , ∠W

As sum of angle of triangle

99° + 36° + ∠W  = 180°

∠W  = 180° - 99° - 36°

∠W  = 45°

Now,

According to the relation

∠W  = [tex]\frac{1}{2}[/tex](arc SP - arc UV)

As

Arc SP = 94° + 20°

           = 114°

so ,

45°  = [tex]\frac{1}{2}[/tex]( 114° - arc UV)

90° = 114° - arc UV

arc UV = 114° - 90°

           = 24°

Hence, the measure of arc UV is  24°  .

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