Given that sin30˚=1/2. Find the exact value of sin120˚

The metric system is defined as the decimal system of units based on the meters, kilograms, and second as the units of length, mass, and time respectively. The imperial system is defined as the measurement system used in countries like the UK, Liberia, Myanmar, etc. that uses units like an inch, pound, ton etc.

The Metric and Imperial systems are both systems of measurement. That is, they are not just one unit of measure, but are correlated systems of many units of measure – measuring length and area, weight and mass, volume, force, temperature etc.

The imperial system of measurement is defined as a system that originated in Britain and came to formal use in the early 19th century with the Weights and Measures Act of 1824 and 1878. It uses some of the commonly used units there like an inch, ton, pound, gallon, pint, etc.

Most countries use the metric system which uses the measuring units such as meters and grams, and adds prefixes like kilo, milli, and centi to count orders of magnitude.

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The value of 5.9 feet after the conversion to centimeter is equivalent to   179.9 cm .

The "Feet" and "Centimeters" are both the units of measurement for length.

The unit "Feet" are primarily used in the United States and other countries that follow the Imperial system, while "centimeters" are part of the metric system used in most other parts of the world.

We know that 1 feet is approximately equal to 30.48 cm ;

So , the conversion factor is = 30.48cm ;

To convert the given number we multiply , by the conversion factor ,

We can write :

⇒ 5.9 feet = 5.9 × 30.48 cm ;

⇒ 5.9 feet = 179.832 cm ≈ 179.9 cm .

Therefore , the value of 5.9 feet is approximately equal to 179.9 cm  .

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If f(-x) = f(x) for all x in the domain of the function, then the function is said to be even function in mathematics. if a function meets the criterion that f(-x) = -f(x) for all x in the function's domain, then is said to be odd function .

An even function, then, is symmetric about the y-axis. The graph of an even function would look geometrically identical to its reflection across the y- axis if we were to plot it. The functions f(x) = x2, f(x) = cos(x), and f(x) = |x| are examples of even functions.

An odd function, then, is symmetric about the origin. If we were to draw the graph of an odd function geometrically, if we were to plot the graph of an odd function, it would appear to be identical to its reflection across the origin, after being rotated 180 degrees. Some examples of odd functions include f(x) = x³, f(x) = sin(x), and f(x) = 1/x.

It is also possible for a function to be neither even nor odd. In other words, a function does not need to exhibit either symmetry about the y-axis or the origin.

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Angle number 2, represents measures the ∠SXU.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

Given, Are three lines RS, TU, and VW and TU intersects RS and VW at

X and Y respectively.

We know when we write an ∠ABC we measure the angle of 'B'.

Given, An ∠SXU, in which we are measuring the angle of X with respect to S and U.

Therefore, 2 is the number that represents ∠SXU.

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Answer:a

Step-by-step explanation:

After getting the product, and simplifying it the correct statement should be: [tex](3^4) \times (2^3) = 648[/tex]

In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.

In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.

1. The error is in the simplification of the product of the two terms. The correct way to simplify it is to multiply the coefficients and add the exponents of x.

The correct solution is:

[tex](3x^2)(-2x^4) = (3 \times -2)x^{(2+4)} = -6x^6[/tex]

Therefore, the error is in the sign of the result, which should be negative instead of positive. The correct answer is[tex]-6x^6.[/tex]

2. The error is in the distribution of the exponent on the coefficient 4. The correct way to simplify the product is to add the exponents of a and then multiply by the coefficient 4.

The correct solution is:

[tex]4a^2 \times 3a^5 = (4 \times 3) a^{(2 + 5)} = 12a^7[/tex]

Therefore, the error is in the addition of the coefficients instead of multiplying them, and the incorrect distribution of the exponent on the coefficient 4. The correct answer is [tex]12a^7.[/tex]

3. There is no error in this simplification.

The product of[tex]x^6, x, and $ x^3 $[/tex] is equivalent to [tex]x^{(6+1+3)} = x^{10}[/tex]

However, the answer given in the question, x^9, is incorrect.

4. The given statement is incorrect.

The product of[tex](3^4) and (2^3)[/tex] can be simplified as follows:

[tex](3^4) \times (2^3) = 81 \times 8 = 648[/tex]

Therefore, the correct statement should be:

[tex](3^4) \times (2^3) = 648[/tex]

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Jerome can save an amount of R33377.27 per month which is the larger amount.

A ratio is a quantitative or qualitative connection between two things: "On the building site, the male-to-female ratio was 10 to one." This indicates there were 10 males and one lady present.

Here

He earns R52450 per month

He separated his earnings in a ratio 7: 4

If he saves a larger amount, then the required solution would be as:

⇒ 52450 × 7/(7+4)

⇒ 52450 × 7/11

Apply the multiplication operation, and we get the amount of savings:

⇒ 33377.27

Therefore, he can save an amount of R33377.27 per month.

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The system of equations has no solution. Option A is the correct optio.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations is

3x - 9y =0 .....(i)

-x + 3y = -3 .....(ii)

Multiply -3 with equation (ii)

3x - 9y = 9 .....(iii)

Subtract equation (i) from (iii):

3x - 9y = 9

3x - 9y =0

________

        0 = 9

Which is a false statement.

Thus the system of equations has no solution.

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Answer:

the answer is A. 0

The steps to convert Celsius to Fahrenheit has been explained

To convert Celsius to Fahrenheit, use the following formula:

F = (C x 1.8) + 32

Where C represents the temperature in Celsius and F represents the temperature in Fahrenheit.

To use this formula, simply multiply the temperature in Celsius by 1.8 and then add 32 to the result. The final result will be the temperature in Fahrenheit.

It's important to note that Celsius and Fahrenheit are two different temperature scales used in different parts of the world. Celsius is used in most countries, including Europe and Canada, while Fahrenheit is used primarily in the United States.

Therefore, the steps of conversion has been explained

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The given question is incomplete, the complete question is:

How to convert Celsius to Fahrenheit?

15 squares will there be when there are 24 triangles to maintain the ratio.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

We have 5 squares and 8 Triangles.

let the number of square be x when there is 24 triangles.

using Proportion

5/8 = x / 24

8x = 120

x = 15

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Answer:

individuals will test accurately?

b. what is the probability that none of the individuals test accurately?

c. what is the probability that at least two individuals test accurately?

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It should be noted that the value of the angles will be m<2= 101; m<1=79°.

It should be noted that if parallel lines are intersected by a transversal, the correspondng angles are congruent

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

In this case, m2 = 180 - 79

= 101°

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Answer:

here are signs for (A), (B) and (C) hope this helps :)

Step-by-step explanation:

(a) The signs of two rational numbers whose sum is positive can be either both positive or both negative. If the signs are different, the absolute value of one number is greater than the absolute value of the other.

Example:

1/2 + 3/4 = 1/4 (positive sum, both numbers are positive)

-2/3 + 4/5 = 2/15 (positive sum, both numbers are negative)

(b) The signs of two rational numbers whose product is positive can be either both positive or both negative.

Example:

1/3 * 4/5 = 4/15 (positive product, both numbers are positive)

-2/7 * -3/4 = 3/14 (positive product, both numbers are negative)

(c) The signs of two rational numbers whose quotient is positive can be either both positive or both negative.

Example:

2/3 ÷ 1/4 = 8/3 (positive quotient, both numbers are positive)

-5/6 ÷ -2/3 = 5/4 (positive quotient, both numbers are negative)

Answer:

First, you need to calculate your grade in percentages. The total answers count 230 - it's 100%, so we to get a 1% value, divide 230 by 100 to get 2.30. Next, calculate the percentage of 20: divide 20 by 1% value (2.30), and you get 8.70% - it's your percentage grade.

Step-by-step explanation:

i think sooooo

The price of an ice cream is 2.21666666667 in other words, 2.21$

The coordinates of point V are approximately (0.11, 0.16) to two decimal places.

What is the coordinate point?

The Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two dimensions) or a triplet of numbers (in three dimensions) that specified signed distances from the coordinate axis.

Let's call the coordinates of point V (x, y).

According to the problem, point V divides the segment RL in a 3:2 ratio. This means that the distance from R to V is three-fifths of the distance from R to L, and the distance from V to L is two-fifths of the distance from R to L.

We can use the distance formula to find the distance between R and L:

d(R, L) = √[(4 - (-2))² + (1 - 4)²] = √[(6)² + (-3)²] = √(36 + 9) = √45

To find the coordinates of V, we can use the fact that the distance from R to V is three-fifths of the distance from R to L:

d(R, V) = (3/5) * d(R, L) = (3/5) * √45

We can also use the midpoint formula to find the coordinates of the midpoint M of the segment RL:

M = ((-2 + 4)/2, (4 + 1)/2) = (1, 2.5)

Since V divides the segment RL in a 3:2 ratio, we can write:

d(R, V) / d(V, L) = 3/2

Substituting the expressions for the distances, we get:

[(3/5) * √45] / d(V, L) = 3/2

Solving for d(V, L), we get:

d(V, L) = [2 * (3/5) * √45] / 3 = (2/5) * √45

Now we can use the midpoint formula again to find the coordinates of V:

V = (1 + (2/5) * √45)(4, 1) + (1 - (2/5) * √45)(-2, 4)

Simplifying, we get:

V = (1 - (2/5) * √45, 2.5 - (3/5) * √45)

Therefore, the coordinates of point V are approximately (0.11, 0.16) to two decimal places.

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Answer: I think it’s A). linear

Step-by-step explanation: linear is the process of something increasing or decreasing at a constant rate, in this case it would be the heat going down at a constant rate of 50 degrees every 10 minutes

The inequality that represents the greatest distance that can be driven while staying within the daily budget is:

0.18x + 40 ≤ 67

Solving for x, we get:

0.18x ≤ 27

x ≤ 150

Therefore, the greatest distance that can be driven in a day while staying within the daily budget is 150 miles.

Two other two-step inequalities with the same solutions are:

0.18x ≤ 28

x ≤ 155

To find the weight of a baby at age 5 months, we can substitute x=5 in the given function:

f(5) = 1.5(5) + 7

f(5) = 7.5 + 7

f(5) = 14.5

Therefore, the weight of a baby at age 5 months is 14.5 pounds. Answer: D.

Answer:

there is a chance of 33.33% that she picks a song of 2min and 13sec

Answer:B.

Step-by-step explanation:

The actually answer is B. Equal to the likelihood of choosing a song that lasts 3 minutes 15 seconds

If functions h(x)= f(x)+g(x), the point (2, 2) is on h(x) and The point (–2, 0) is on h(x).

In mathematics, a function is a rule or a set of rules that assigns a unique output to each input of a given set of inputs. It is a type of mapping or transformation in which each member of one set (the inputs) is associated with a unique member of another set (the outputs). Functions are often represented by equations or graphs, and they can be used to describe relationships between different variables.

For example, the equation y = x2 describes the function that assigns to each number x its square y.

The point (2, 2) is on h(x) since h(x) = f(x) + g(x) = 2 + 0 = 2. The point (–2, 0) is on h(x) since h(x) = f(x) + g(x) = 0 + 0 = 0. The point (0, –3) is not on h(x) since h(x) = f(x) + g(x) = 0 + 2 = 2, which does not equal –3.

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The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.

P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.

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Answer:

y = (1/3)x - 4

Step-by-step explanation:

put y on one side

x -3y =12

y =12-x/-3

y=12/-3 -x/-3

y=-4 + 1/3x

chatgpt

Answer:

Step-by-step explanation:

If 1in is equal to 47 feet irl, then that means that the actual width is 47ft and the actual length is 94ft.

Multiply those two together and you get 4,418 sq ft as your answer.

Answer:

(1) a² +4a-2

Step-by-step explanation:

[tex]4a^2-3a\:+4\:-\:\left(3a^2-7a+6\right)\\\\= 4a^2-3a\:+4\:- 3a^2 + 7a -6[/tex]    

Grouping like terms
[tex](4a^2 -3a^2) +(-3a + 7a) +(4 - 6)\\\\= a^2 +4a - 2[/tex]

Answer:

After performing synthetic division, as the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.

Step-by-step explanation:

Given polynomial function:

[tex]2x^3+7x^2+3[/tex]

To determine is (x + 3) is a factor of the given polynomial by the method of synthetic division:

Note: As the x term is missing, place a zero in its place.

[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}\end{array}[/tex]

Bring the leading coefficient straight down:

[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&2&&&\end{array}[/tex]

Multiply the number you brought down with the number in the division box and put the result in the next column (under the 7):

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&&&\end{array}[/tex]

Add the two numbers together and put the result in the bottom row:

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&1&&\end{array}[/tex]

Repeat:

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&-3&9\\\cline{2-5}&2&1&-3&12\end{array}[/tex]

The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.  The last number in the bottom row is the remainder.

Therefore, if we divide the polynomial by (x + 3) we get:

[tex]2x^2+x-3+\dfrac{12}{x+3}[/tex]

As the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.

The exponential function that defines the number of teams remaining after n rounds is given as follows:

y = 64(0.5)^x, 0 ≤ x ≤ 6.

The standard definition of an exponential function is given as follows:

y = a(b)^x + c.

In which:

The initial number of teams is of 64, hence the parameter a is given as follows:

a = 64.

Each round, the number of teams is cut by half, as the losers of each game are eliminated, hence the parameter b is given as follows:

b = 0.5.

Hence the function is defined as follows:

y = 64(0.5)^x.

The domain is 0 ≤ x ≤ 6 as:

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The homogeneity of variance assumption in the independent measures t-test assumes that option (c) the variances of the two populations from which the samples are drawn are equal.

In mathematical terms, the t-test assumes that the two populations from which the samples are drawn have equal variances. The homogeneity of variance assumption is important because it affects the calculation of the t-statistic.

When the variances of the two populations are equal, the t-test uses a pooled estimate of the variance to calculate the standard error of the difference between the two sample means.

If the homogeneity of variance assumption is violated, meaning the variances of the two populations are not equal, the t-test may produce inaccurate results.

In this case, an alternative test such as Welch's t-test may be used. Welch's t-test does not assume equal variances and is therefore more robust when the homogeneity of variance assumption is violated.

Therefore, the right choice is option (c).

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The two lines that are parallel to y = 2x - 1 that pass through the given points are:

a) y = 2x + 1

b) y = 2x

A general linear equation is written in the slope-intercept form as:

y = a*x +b

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

Two lines are parallel if the slopes are equal but the y-intercepts are different.

So, here we want to find lines parallel to:

y = 2x - 1

These lines have the form:

y = 2x + b

a) If we want our line to pass thrugh A(0,1), we can replace the values of the point to get:

1 = 2*0 + b

1  = b

So the line is y = 2x + 1

b) if we want the line to pass through A(1,2) we can replace the values to get:

2 = 2*1 + b

2 = 2 + b

2 - 2 = b

0  =b

So this line is:

y = 2x

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