Given the expression

Choose all the equivalent expressions as your answer.

Answer:

u = 4 , v = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the tangent and sine ratios in the right triangle and the exact values

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{u}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

u = 2 × 2 = 4

and

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{v}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

v = 2[tex]\sqrt{3}[/tex]

Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants.

Assuming that each descendant has an average of 2.5 children, we can use the formula:

where n is the number of generations.

In this case, n = 15 (fifteenth-generation), so we can plug in the values and get:

number of descendants = [tex](2.5)^{15}[/tex]= 1,220,703.125

Therefore, Wei-Ling's fifteenth-generation ancestor is estimated to have around 1,220,703 descendants. However, it is important to note that this is just an estimation and may not be entirely accurate due to various factors such as reproductive rates and other variables.

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Answer:

never true

Step-by-step explanation:

If angles A and B are complementary, their measures add to 90º.

This means that if:

m∠B = 55º,

then:

m∠A = (90 - 55)º = 45º

Using this information, we can make the assertion that because:

55º ≠ 45º,

m∠A ≠ m∠B,

and thus:

sin(A) ≠ sin(B)

because 55º and 45º are NOT coterminal angles.

Therefore, the statement

sin(A) = sin(B)

is never true.

According to given conditions, the biggest number is 46.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Let the two numbers in the first ratio be 3x and 5x, where x is some constant of proportionality.

According to the problem, if we subtract 9 from each number, the new ratio is 12:23. So, we have:

(3x - 9) : (5x - 9) = 12 : 23

We can cross-multiply to get:

23(3x - 9) = 12(5x - 9)

Simplifying this equation, we get:

69x - 207 = 60x - 108

9x = 99

x = 11

So, the two numbers in the first ratio are 3x = 33 and 5x = 55.

To find the biggest number, we need to determine which of these numbers is larger after subtracting 9.

33 - 9 = 24

55 - 9 = 46

Therefore, according to given conditions, the biggest number is 46.

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To streamline your betting odds and increase your chances of making a profit from your initial 100 scrap, you can use a combination of different betting strategies.

Here are a few possible strategies:

1) Spread your bets: Instead of betting all of your scrap on one number, you can spread your bets across multiple numbers to increase your chances of winning.

For example, you could bet 25 scrap on 1 (yellow), 25 scrap on 3 (green), 25 scrap on 5 (blue), and 25 scrap on 10 (pink). This way, you have a 48% chance of winning on 1 (yellow), a 24% chance of winning on 3 (green), a 16% chance of winning on 5 (blue), and an 8% chance of winning on 10 (pink).

2) Bet on the most likely outcomes: Another strategy is to bet on the numbers with the highest probabilities of winning. For example, you could bet 50 scrap on 1 (yellow) and 50 scrap on 3 (green), which have the highest probabilities of winning at 48% and 24%, respectively.

3) Use a combination of the above strategies: You could also combine the above strategies to increase your chances of winning. For example, you could bet 25 scrap on 1 (yellow), 25 scrap on 3 (green), 25 scrap on 5 (blue), and 25 scrap on 10 (pink), and then also bet an additional 50 scrap on 1 (yellow) and 50 scrap on 3 (green).

Overall, the key to streamlining your betting odds is to spread your bets across multiple numbers and focus on the numbers with the highest probabilities of winning. By using a combination of different betting strategies, you can increase your chances of making a profit from your initial 100 scrap.

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The first term of the sequence is 30 (36 divided by 5 and then subtract 2).

A term by term rule is used for a sequence in which the next term is obtained from the previous term. Example: Arithmetic sequence. In an arithmetic sequence, each term (other than the first term) is obtained by adding or subtracting a constant value from the preceding term.

To work out the term to term rule, give the starting number of the sequence and then describe the pattern of the numbers. The first number is 3. The term to term rule is 'add 4'. Once the first term and term to term rule are known, all the terms in the sequence can be found.

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Using logarithmic identities and quadratic equation, the value of lg a * lg c is 4/3

Using logarithmic identities, we can rewrite the given equations as:

logₐa + log_b c = 4

log_b b + logₐ c = 3

Simplify the first equation using the fact that logₐa = 1/log_aₐ = 1, and simplify the second equation using the fact that log_b b = 1:

1 + log_b c = 4

1 + logₐ c = 3

Solve for log_b c and logₐ c:

log_b c = 3

logₐ c = 2

Now we can use the fact that logₐ c = logₐ (a · c)/a = logₐ a + logₐ c/a to write:

logₐ a + logₐ c/a = 2

Substitute logₐ c = 2 into this equation to get:

logₐ a + 2/a = 2

Multiply both sides by a to get:

logₐ a · a + 2 = 2a

Rearrange this equation as a quadratic equation:

logₐ a · a - 2a + 2 = 0

This quadratic has a maximum value when the coefficient of logₐ a is zero, i.e., when:

a = 2^(2/3)

Substituting this value of a into the equation logₐ c = 2, we get:

log₂ c = log₂ a^2 = 2/3 · log₂ 2^2 = 4/3

Therefore, logₐ c = log₂ c/log₂ a = (4/3) / (2/3) = 2

Finally, we can find the maximum value of logₐ a · logₐ c by multiplying logₐ a and logₐ c:

logₐ a · logₐ c = log₂ a/log₂ a · log₂ c/log₂ a = log₂ c = 4/3

Therefore, the maximum value of logₐ a · logₐ c is 4/3.

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The value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively

A polygon is called regular if it has equal sides and angles. Thus, a regular triangle is an equilateral triangle, and a regular quadrilateral is a square.

An hexagon is a six sided polygon. This means that;

The sum of angle in an hexagon = (6-2)180 = 180× 4 = 720

Therefore each angle in the hexagon = 720/6 = 120°

The angles are equally bisected

therefore, angle 3 = 120/2 = 60°

angle 1 = 180-(60+60)

= 180-120 = 60°

angle 2 = 180-(90+60)

= 180-150

= 30°

therefore the value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively

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Answer:

125.6637061

Step-by-step explanation:

Answer:

40π inches, or approximately 125.66 inches

Step-by-step explanation:

The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

In this case, the radius of the tire is 20 inches. So, the circumference of the tire is:

C = 2πr

C = 2π(20)

C = 40π

Therefore, the circumference of the tire is 40π inches, or approximately 125.66 inches if you round to two decimal places.

Answer:

Step-by-step explanation:

The two 'slashes' on the 2 edges indicate that it's an isosceles triangle ( the base angles are equal)

Total angles in a triangle = 180.

Thus,

3x + 4x+2+4x+2= 180.

11x+4=180

11x=176

Therefore, x= 16°

Thus,

3x = 3(16) = 48°

The (4x+2)'s =

4(16)+2

=66° each.

Hope this helps! :)

The length of PR is 6 units. To find the length of PR, we need to use the fact that the triangles are similar.

Since the triangles are similar, their corresponding sides are proportional. That is,

AB/DE = BC/EF = AC/DF

We know that AB = 8, BC = 6, AC = 10, DE = 6, EF = 4, and DF = 8. Therefore,

AB/DE = 8/6 = 4/3

BC/EF = 6/4 = 3/2

AC/DF = 10/8 = 5/4

Since we are looking for the length of PR, which corresponds to BC in the smaller triangle, we can use the ratio of BC/EF from above. We have:

BC/EF = 3/2 = PR/4

Solving for PR, we get:

PR = (3/2) * 4 = 6

Therefore, the length of PR is 6 units.

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The triangles are similar. PR = ___ units

Answer:

sin(2x) = 2sin(x)cos(x)

= 2(-3/5)(-2/5)

= 12/25

cos^2(x) = (2/√13)^2 = 4/13

sin^2(x) = (-3/√13)^2 = 9/13

cos(2x) = cos^2(x) - sin^2(x) = (4/13) - (9/13) = -5/13

= cos(2x) = -5/13

tan(2x) = 3/4

Explanation:

Given tan(x) = -3/2 and x terminates in quadrant II.

We know that tan(x) = sin(x) / cos(x)

Using this, we can find sin(x) and cos(x):

tan(x) = sin(x) / cos(x) = -3/2

cos(x) = -2/√13

sin(x) = 3/√13

Using double angle formulas, we can find sin(2x), cos(2x), and tan(2x):

sin(2x) = 2sin(x)cos(x) = 2(3/√13)(-2/√13) = -12/13

cos(2x) = cos²(x) - sin²(x) = (-2/√13)² - (3/√13)² = 4/13 - 9/13 = -5/13

tan(2x) = (2tan(x)) / (1 - tan²(x)) = (2(-3/2)) / (1 - (-3/2)²) = 3/4

We know that tan(x) = -3/2 and x is in quadrant II. Therefore, we can use the Pythagorean theorem to find the opposite side (y) and the hypotenuse (r) of a right triangle with an angle of x in quadrant II.

Let r = 2, so y = -3 and x = arctan(-3/2) ≈ -56.31°.

Using the double angle formulas:

sin(2x) = 2sin(x)cos(x) = 2(-3/2)(√5/2) = -3√5/2

cos(2x) = cos²(x) - sin²(x) = (√5/2)² - (-3/2)² = (5-9)/4 = -1/2

tan(2x) = 2tan(x)/(1-tan²(x)) = 2(-3/2)/(1-(-3/2)²) = 3/4

So, the answers are: sin(2x) = -3√5/2, cos(2x) = -1/2, and tan(2x) = 3/4.

Hope this helps you! Sorry if it's wrong. If you need more help, ask me! :]

if lucky got 20 questions correct then lucky had missed 4 tests.

If Lucy got 4 out of 5 questions correct, then the proportion of questions she got correct is:

4/5 = 0.8

We can use this proportion to find the number of questions she got correct in the larger set of 20 questions:

0.8 x 20 = 16

So, Lucy got 16 questions correct out of 20. To find the number of questions she missed, we can subtract the number she got correct from the total number of questions:

20 - 16 = 4

Therefore, Lucy missed 4 questions on the test.

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Answer:

To solve the equation 3(x+2)=17, we start by simplifying the expression on the left side by distributing the 3:

3(x+2) = 17

3x + 6 = 17

Next, we isolate the variable term by subtracting 6 from both sides:

3x + 6 - 6 = 17 - 6

3x = 11

Finally, we solve for x by dividing both sides by 3:

3x/3 = 11/3

x = 11/3

Therefore, the solution to the equation 3(x+2)=17 is x = 11/3.

To solve the equation 4x+3=2x+15, we start by simplifying the expression by combining like terms:

4x + 3 = 2x + 15

2x + 3 = 15

Next, we isolate the variable term by subtracting 3 from both sides:

2x + 3 - 3 = 15 - 3

2x = 12

Finally, we solve for x by dividing both sides by 2:

2x/2 = 12/2

x = 6

Therefore, the solution to the equation 4x+3=2x+15 is x = 6.

Step-by-step explanation:

A snail moves at a speed of 1. 2 feet per minute. the snail will move 12 yards in half an hour

There are 60 minutes in an hour, so half an hour is 30 minutes.

The snail moves at a speed of 1.2 feet per minute. Therefore, in 30 minutes, it will travel:

1.2 feet/minute * 30 minutes = 36 feet.

To convert feet to yards, we need to divide by 3 since there are 3 feet in a yard:

36 feet / 3 = 12 yards.

Therefore, .

the snail's speed may seem slow to us, it's important to remember that different animals have different speeds that are adapted to their particular ecological niche.

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The function represents the height of the plant in centimetres after n days, so n cannot be negative.

Part A:

To find a reasonable domain to plot the growth function, we need to consider the practical limitations of the growth of the plant. Also, since the function represents the growth of a particular species of plant, there may be an upper limit to how many days the plant can grow.

Assuming that the plant is not a perennial plant and has a limited lifespan, we can choose a reasonable domain for the function as [0, t], where t is the expected lifespan of the plant in days.

Since we do not have information about the expected lifespan of the plant, we can choose a reasonable value such as [tex]t = 365[/tex]  (assuming it is an annual plant). So the domain for the function can be  [tex][0, 365][/tex]  .

Part B:

The y-intercept of the graph of the function f(n) represents the height of the plant when it was planted or started growing, that is, at n = 0. To find the y-intercept, we can substitute n = 0 in the equation:

[tex]f(0) = 15(1.02)^0 = 15[/tex]

Therefore, the y-intercept of the graph of the function f(n) is [tex]15[/tex] cm.

Part C:

The average rate of change of the function f(n) from n = 1 to n = 4 can be calculated using the formula:

average rate of change [tex]= [f(4) - f(1)] / (4 - 1)[/tex]

Substituting the values in the equation, we get:

average rate of change [tex]= [15(1.02)^4 - 15(1.02)^1] / 3[/tex]

average rate of change [tex]≈ 1.42 cm/day[/tex]

Therefore, The average rate of change of the function f(n) from n = 1 to n = 4 represents the average daily growth rate of the plant during this period.

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The correct answer is x = 9.

Making use of the logarithm table, Compute the characteristic that the provided integer's whole number component dictates. Using the significant digits of the given number, find the mantissa. Add a decimal point after combining the characteristic and mantissa.

The student's solution has a division by zero error. The wrong step is when ln(x2) = ln(3x) - 0. It would have been better to first simplify the addition of ln(9) - 2ln(3) as follows:

The formula is ln(9) - 2ln(3) = ln(9) - ln(32) = ln(9/32) = ln(1/3).

When we substitute this number into the first equation, we get:

ln(1/3) - ln(3x) = 2ln(x)

ln(3x/1/3) = 2ln(x)

2ln(x) = ln (9x)

If we multiply both sides by their exponential, we get:

E = 2ln(x) + eln (9x)

x^2 = 9x

x^2 - 9x = 0

x(x - 9) = 0

As a result, the solutions are x = 0 and x = 9, but since ln(0) is undefined, we must determine whether x = 0 is a valid solution. So x = 9 is a workable answer.

Hence, the right response is x = 9.

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Answer:

34$

Step-by-step explanation:

Answer:$8,890.83

Step-by-step explanation:

If there were 56 people who were all 48 years old, then the total number of years that the people had lived would be: 56 people x 48 years/person = 2,688 years

This calculation multiplies the number of individuals (56 people) by their age (48 years per person) to determine the total number of years of life experience represented by the group. In essence, it is calculating the cumulative age of everyone in the group. The result, 2,688 years, reflects the sum total of all the years that the 56 people have lived in total. Therefore, the total number of years that the people had lived is 2,688.

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Answer:

(i) xy² +xy +y +1 can be factorized by grouping:

xy² + xy + y + 1

= xy(x + y) + 1(x + y)

= (xy + 1)(x + y)

Therefore, xy² +xy +y +1 = (xy + 1)(x + y).

(ii) x² -7x +12 can be factorized by finding two numbers that multiply to 12 and add up to -7. These numbers are -4 and -3, so we can write:

x² - 7x + 12 = (x - 4)(x - 3)

Therefore, x² -7x +12 = (x - 4)(x - 3).

(iii) x² - 144 is a difference of squares, and can be factorized as:

x² - 144 = (x + 12)(x - 12)

Therefore, x² - 144 = (x + 12)(x - 12).

Answer:

x²-7x+12

X²+(4+3)x+12

x²-4x+3x+12

x (x+4) +3 (x+4)

(x+3) (x+4)

The possible lengths of the stage (in feet) can be described by the inequality:

L ≥ A/10

where A is the minimum required area of the stage and L is the length of the stage.

Let's denote the length of the rectangular stage as 'L' in feet.

The area of a rectangle is given by the formula A = L × W, where A is the area, L is the length, and W is the width.

We are given that the width of the stage is 'W' feet and the area of the stage must be at least 'A' square feet. So we can write the inequality:

A ≤ L × W

Substituting the given values, we get:

A ≤ L × 10

Dividing both sides by 10, we get:

A/10 ≤ L

Therefore, the possible lengths of the stage (in feet) can be described by the inequality:

L ≥ A/10

where A is the minimum required area of the stage and L is the length of the stage.

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If David paid $1. 25 per drink and purchased 6 drinks, then the total price of drink is option (C) c =$7.50

To solve this problem, we need to first understand what we are looking for - the total price that David paid for all the drinks he purchased. We know that David purchased 6 drinks and paid $1.25 for each drink.

To find the total price, we can multiply the price per drink by the number of drinks. This gives us:

c = 1.25 x 6

Multiply and Simplifying this equation, we get:

c = $7.50

Therefore, the correct option is (C) c =  $7.50

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Answer: monkey jungle conclusion of 10-4=21

Step-by-step explanation:

The United States Declaration of Independence, officially The unanimous Declaration of the thirteen united States of America, is the pronouncement and founding document adopted by the Second Continental Congress meeting at Pennsylvania State House, which was later renamed Independence Hall, in Philadelphia, Pennsylvania, on July 4, 1776. Enacted during the American Revolution, the Declaration explains why the Thirteen Colonies at war with the Kingdom of Great Britain regarded themselves as thirteen independent sovereign states and no longer subject to British colonial rule. With the Declaration, the 13 states took a collective first step in forming the United States and, de facto, formalized the American Revolutionary War, which had been ongoing since April 1775.

The Declaration of Independence was signed by 56 of America's Founding Fathers who Second Continental Congress delegates from New Hampshire, Massachusetts Bay, Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Maryland, Delaware, Virginia, North Carolina, South Carolina, and Georgia. The Declaration became one of the most circulated and widely reprinted documents in early American history.

The Committee of Five drafted the Declaration to be ready when Congress voted on independence. John Adams, a leading proponent of independence, persuaded the Committee of Five to charge Thomas Jefferson with authoring the document's original draft, which the Second Continental Congress then edited. The Declaration was a formal explanation of why the Continental Congress had voted to declare its independence from Great Britain, a year after the American Revolutionary War broke out. The Lee Resolution for independence was passed unanimously by the Congress on July 2.

After ratifying the text on July 4, Congress issued the Declaration of Independence in several forms. It was initially published as the printed Dunlap broadside that was widely distributed and read to the public. Jefferson's original draft is currently preserved at the Library of Congress in Washington, D.C., complete with changes made by Adams and Benjamin Franklin, and Jefferson's notes of changes made by Congress. The best-known version of the Declaration is the signed copy now displayed at the National Archives in Washington, D.C., which is popularly regarded as the official document. This engrossed copy was ordered by Congress on July 19 and signed primarily on August 2, 1776.[2][3]

The sources and interpretation of the Declaration have been the subject of much scholarly inquiry. The Declaration justified the independence of the United States by listing 27 colonial grievances against King George III and by asserting certain natural a

Answer:

The solution is (2,10). None of the above answers are correct.

Step-by-step explanation:

[tex]6y = 12x + 36\\15y = 45x + 60\\\\[/tex]

Now, reduce the equations.

[tex]y = 2x + 6\\y = 3x + 4[/tex]

Solve for x by subtracting the equations

[tex]y = 2x + 6\\- (y = 3x+4)\\-x + 2 = 0\\x=2[/tex]

Now plug in x into either of the original equations.

[tex]6y = 12(2)+36\\6y=24+36\\6y=60\\y=10[/tex]

Solution: (2,10)

Mean value of the function = E(X) = ∞/πOption (b) ∞/π is the correct option.

Given a density function of a random variable X as f(x)={ 2 π ​ , 0, ​ 0. The question is to find the mean value of the function.As we know,The mean value of the function = E(X) = ∫xf(x)dx, where x is the random variable and f(x) is the density function,∫ denotes integral from negative infinity to infinityOn substituting the given values,∫xf(x)dx= ∫x (2/π)dx= (2/π) ∫xdx= (2/π)(x^2/2)+C ……(1)Where C is the constant of integration.But given the density function is zero for all negative x values and f(0) = 2/π, so the integral should be calculated from 0 to infinity instead of negative infinity to infinity.On substituting the values,∫0∞ x (2/π)dx= (2/π) ∫0∞xdx= (2/π) (x^2/2) [0,∞]= ∞/πTherefore, mean value of the function = E(X) = ∞/πOption (b) ∞/π is the correct option.

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Answer:

x = -22/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ (3x/2) + 12 = 1

Then the value of x will be,

→ (3x/2) + 12 = 1

→ (3x/2) + (24/2) = 1

→ (3x + 24)/2 = 1

→ 3x + 24 = 1 × 2

→ 3x + 24 = 2

→ 3x = 2 - 24

→ 3x = -22

→ [ x = -22/3 ]

Hence, value of x is -22/3.

The value of h of the parallelogram is = 4.2

A parallelogram is a special kind of quadrilateral made up of parallel lines. A parallelogram can have any angle between its adjacent sides, but for it to be a parallelogram, its opposite sides must also be parallel.

If the opposing sides of a quadrilateral are parallel and congruent, the shape will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is said to be a parallelogram.

A parallelogram's area is determined as follows:

Area = base × height

In the given parallelogram, we can note that the base is 8.4 inches, and the corresponding height is 5 inches.

This means that:

Area of parallelogram = 8.4 × 5 = 42 in²

This same area can be calculated using the other base (6 in) and its corresponding height (h)

This means that:

Area of parallelogram = 10 × h

42 = 10 × h

h = 42/10

h = 4.2 inches.

Hence, value of h in the parallelogram is equals to 4.2.

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Answer: C 27

Step-by-step explanation:

there would be 24 sheep, which means there is 36 horses.

if ratio from horses to goats is 4-3

then there is only 27 goats.