Inverse Trig Ratios FINDING MISSING ANGLES IP youknow the Sin; cosne; 0r tangent ratio of anangle you canuse the inverse Aunction (sin! cos tan ) to fnd the measure of the agle Examples: Find the value of x Round to the nearest tenth.'

Let the vector pace P2 have the inner product the following for p=2x, q=5x2 for ∫4−4p(x)q(x)dx are

1) For ⟨p,q⟩=∫4−4p(x)q(x)dx we can put the value of the  p=2x, q=5x² so  

⟨p, q⟩= ∫4− 4(2x)(5x²) dx

= ∫4−40x³ dx

2) For d(p,q)=  4−40x³dx  ............( after derivating)

= 0 - 120 x²

= -120x²

3) ∥p∥ = ||2x||  = 2||x||   ( ||x|| > 0)

given that p is not any number which will be not affected by any sign of the x and will remain positive.

4) ∥q∥ = ||5x²|| = 5||x²||   (||x² > 0)

given that q is not any number which will be not affected by any sign of the x² and will remain positive.

In mathematics, objects called vectors have both magnitude and direction. The vector's magnitude determines its length. It is shown as a line with an arrow, with the length of the line indicating the vector's magnitude and the direction of the arrow indicating its direction. Other names for it include Euclidean vector, Geometric vector, Spatial vector, and simply "vector."

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The amount of light that passes through a camera lens is determined by the aperture, which is the size of the opening in the lens that lets light in. changing from f/1.4 to f/8 reduces the amount of light that can pass through the lens by a factor of 32.49,

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The new price of the car after the 4% reduction is $18,240

Percentage is simply number or ratio expressed as a fraction of 100.

Given that,

To determine the new price of the car after reduction;

New price = Initial price × ( 100% - 4% )

New price = Initial price × ( 96% )

Note that 96% is the same as 96/100

New price = $19,000 × 96/100

New price = $19,000 × 0.96

Multiply  $19,000 and 0.96

New price = $18,240

Therefore, the new price is $18,240.

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The solution of inequality would be, C = -4, C = 2

What is solution to the inequality?

An inequality is a relationship characterized by a non-equal comparison of two numbers or mathematical expressions.

A number is a solution to an inequality in x if it can be used to replace x with a true statement. Thus, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the inequality solution set.

The solution to the inequality -C + 2 > 1 is C < 1.

So, the answer is:

C = -4

C = 2

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The statement that describes a key feature of function g if [tex]g(x)=e^x-7[/tex]  is Horizontal asymptote of y= -7.

A horizontal line that is not a part of a function's graph but is essential because it directs the graph's x values is known as a horizontal asymptote.

A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.

A line that is asymptotically sloped, vertical, or both has the equation x = a, y = a, or y = ax + b

In this instance, the declaration that enumerates the primary property of the function g if g(x) = [tex]e^x[/tex] - 7 is that the horizontal asymptote of y = -7.

This can be seen from the equation given.

Therefore option (d) is correct

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x>-7/3 is the solution of the inequality −3x+8<15.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is −3x+8<15

Minus three times of x plus eight less than fifteen.

Subtract 8 from both the sides

-3x<7

Divide both sides by 3

-x<7/3

x>-7/3

Hence, x>-7/3 is the solution of the inequality −3x+8<15.

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Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

The expression to find how many points Colleen had after her ten turns is 260 - 170 = 90. This expression can be written mathematically as P = 260 - 170, where P is the total points after ten turns. To solve this equation, we first subtract 170 from 260. This yields a total of 90 points, which is the number of points Colleen had after her ten turns. The calculation can be summarized as follows:

P = 260 – 170

P = 90

Therefore, after ten turns,Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

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The 36.5 °C when converted to Fahrenheit it is equal to 97.7 °F.

                                  = 97.7

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No the confidence interval does not provide convincing evidence that the two population proportions are equal.

No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.

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No the confidence interval does not provide convincing evidence that the two population proportions are equal.

No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.

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No, it is not required to be accurate. The growth rates of the two functions can vary.

It's not necessary for log f(n) to equal log g(n). Depending on the equation's constants and the inputs to the two functions, the growth rates of the two functions may differ. For instance, log f(n) = 2 log n and log

g(n) = 3 log n,

which are not equal, if

f(n) = n2 and g(n) = n3.

In this instance, log f(n) is equal to (log n) and log g(n) to (log n3), indicating that the two functions grow at various rates. Likely not equal are log f(n) and log g(n) if

f(n) = n and g(n) = n2,

respectively. Log f(n) is defined as (log n) and log Therefore, the statement "log f(n) = (log g(n)" is not necessarily true.

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The height of the water tank of the air cooler brought by Anu is 40 cm.

Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.

given,

Length = 50 cm

Width = 20 cm

Maximum tank volume = 40 liters = 40,000 cm3

Tank height?

Steps,

Tank volume = length x width x height

40,000 = 50 x 20 x height

40,000 = 1000 x height

Tank height = 40,000 : 1000

Tank height = 40 cm

So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.

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The expression modeled by the number line: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 is the sum of the first ten negative integers. The expression can be written as $-1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10$

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The solution for the given expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex] will be [tex]\frac{xy}{x^{3} + y^{3} }[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

We will solve this equation using the simplification methods,

Since,

a³ + b³ = (a +b)(a² +b² - ab)

From this formula;

=> [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

=> [tex]\frac{x^{2} + y^{2} }{(x + y)(x^{2} + y^{2} - xy) } - \frac{1}{x + y}[/tex]

taking 1/(x +y) common,

=> 1/(x +y) { (x² + y²)/(x² +y² - xy) - 1}

=>  1/(x +y) { xy/(x² +y² - xy)}

=> xy/(x³ +y³)

Therefore, [tex]\frac{xy}{x^{3} + y^{3} }[/tex] will be the simplified form of the given Equation.

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The given equation does not represent y as a function of x.

A relation is a function if for every unique x value, there exists only one unique y value. The equation 5x³y = 15 does not define a unique value for y for a given value of x, and therefore does not represent y as a function of x.

The equation 5x³y = 15 does not represent y as a function of x. A function must have exactly one output value for each input value, but this equation doesn't have the unique output restriction.

The equation 5x³y = 15 represents a 3-dimensional surface in the x-y-z plane, where z = 5x³y. It does not define y as a function of x, because for a given x there can be multiple values of y that satisfy the equation. To define y as a function of x, additional information, such as an equation that relates y and x in a one-to-one manner, is needed.

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The solution of the initial value problem is [tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.

In this case, the differential equation is given by:

dy/dt = t² + 1, t ≥ 0

with the initial value y = 6 when t = 0.

To solve this initial value problem, we can use the method of integrating factor.

We can find the integrating factor for this differential equation by using the formula:

[tex]= > e^{\intP(t)dt,[/tex]

where P(t) = t² + 1

So,

[tex]= > e^{\int P(t)dt} = e^{t^3/3 + t}[/tex]

By the product rule, we have:

[tex]= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})[/tex]

We can evaluate the integral on the right side using standard integration techniques, and we get:

[tex]= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)[/tex]

Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):

[tex]= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

To find the value of C, we can use the initial value y = 6 when t = 0:

6 = Ce⁰

So, C = 6.

Therefore, the solution to the initial value problem is:

[tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

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The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.

Given r = sinθ and the range of θ is 0 < θ < π

If 0 < θ < π the range of sinθ is:

                                      0 ≤ sinθ ≤ 1

So, in  0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.

Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.

Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.

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1. B has the greater rate of change.

2. A has the greater rate of change.

3. B has the greater rate of change.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the rate of change, we must look at the slope of each function.

From the graph or from a table, the slope is given dividing the change in y by the change in x.

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Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.

To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:

1. We must make a rule of three to find the exact amounts of each ingredient as shown below:

According to the above, the following ingredients are needed for this recipe:

Note: This question is incomplete because there is some information missing. Here is the complete information:

120g strawberry jelly

8 sponge fingers

420ml custard

180 g tinned fruit

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The closest point on the line 3x - y = 4 to the point A(-2, 3) is (4, 3).

The point on the line closest to point A can be found by finding the line that is perpendicular to the line 3x - y = 4 and passes through A, then finding the point of intersection between the two lines.

To find the perpendicular line, we can use the slope-point form of a line, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. The slope of a line perpendicular to the line 3x - y = 4 is the negative reciprocal of the slope of the line, which is undefined since the line 3x - y = 4 is a vertical line. Hence, the perpendicular line is a horizontal line with slope 0, and it passes through the point A(-2, 3). So, the equation of the line is y = 3.

The point of intersection of the two lines is the point closest to A. Solving the equations 3x - y = 4 and y = 3, we get the intersection point (x, y) = (4, 3).

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Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

Avery can interpret 302 = 3 by understanding that 30 is the total amount of soup to be divided, and 2 represents the number of equal parts she wants to divide the soup into. This means that Avery can divide the 30 cups of soup into 3 equal containers, each containing 10 cups of soup.

Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

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A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.

A mean = 10

Standard Deviation = 25

We have to determine the z score for the value of 35. So X = 35.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.

The formula is:

Z = (X - mean)/Standard Deviation

Now putting the values

Z = (35 - 10)/25

Z = 25/25

Z = 1

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The required straight-line distance between the school and the movie theater is 10 miles, as of the given condition.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

The straight-line distance between the school and the movie theater can be found using the Pythagorean theorem. If the skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park, then the distance between the school and the movie theater is given as,
= √8² + 6² =
= √64 + 36
= √100.
= 10 miles

Thus, the straight-line distance between the school and the movie theater is 10 miles.

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The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)

What is center of dilation?

A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.

The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.

A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)

B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)

C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)

So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).

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The correct statement regarding the transformation and the difference of functions f(x) and g(x) is given as follows:

A.

The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.

The parent function for this problem is given as follows:

f(x) = 7^x.

The transformed function for this problem is given as follows:

g(x) = f(x)/3 = (1/3) x 7^x.

The only transformation is a multiplication by the constant 1/3. As the constant has an absolute value less than 1, the graph of g(x) is a vertical compression of the graph of f(x) by a factor of 3.

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A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ [tex]= \frac{360}{n}[/tex]

θ  [tex]=\frac{360}{5} = 72[/tex]

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

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The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

The experimental probability of landing on a number greater than 5 is 2/15.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1.

Given A number cube is tossed 60 times,

Outcome       Frequency

1                         12

2                        13

3                         11

4                         6

5                         10

6                          8

The number of times greater than 5 comes up = 8 (frequency of 6 is 8)

Probability of getting a number greater than 5

=  (frequency of getting6) / (total number of trials)

⇒ probability of getting a number greater than 5  = 8 / 60 = 2/15

Hence probability is 2/15.

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Utilize the following formula to convert metres to miles: m/1,609.344=mi (meters divided by 1,609.344 equals miles).

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Answer:

60 miles

Step-by-step explanation:

We know

3/5 = 0.6

one-quarter of an hour = 15 minutes

So, we know

0.6 mile in 15 minutes

2 1/2 hours = 150 minutes

0.6 times 10 = 60 miles

So, the bird flies 60 miles in 2 1/2 hours.

The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Now, We can simplify as;

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 10 both side,

⇒ 23p - 101 = 65p - 40 - 0.1p

And, ⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 100 both side,

⇒ 230p - 1010 = 650p - 400 - p

Thus, The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

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The complete question is this;

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

The true equation is m∠A + m∠B = 180°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Here, we have

Given:  the dot indicates the center of the circle.

we have to find which equation is true.

"The angle formed by a diameter at the circumference is always a right angle (that is 90 degrees).

We concluded that the true equation is m∠A + m∠B = 180°

Hence, the true equation is m∠A + m∠B = 180°

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