For the following exercises,
(a) find the angle between 0 and 2π in radians that is coterminal with the given angle.
(b) find the reference angle of each one.

a)32π/13 b)-17π/6

The angle of the turn at Deer Trail is of 105 degrees.

Notice that both of the lines that go up to the left are parallel, thus, the angles formed betwen the intersections are all equal (for the respective lines).

Now, also know that two adjacent angles in an intersection should add up to 180°.

We can see that the angle to the right of deer trail has a measure of 75°, then the angle to the left (which is adjacent) must have a measure M such that:

M + 75° = 180°

M = 180° - 75°

M = 105°

That is the angle of the turn.

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Note that in the proof stated above, there is no incorrect statement.

The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.

The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.

The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.

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Answer:

so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand

Step-by-step explanation:

hope this helps !

If function "h" is one-to-one function which is having values h(-9) = 5, and h(3) = -4, then the inverse statement is (d) h⁻¹(-4) = 3.

We know that the function "h" is a one-to-one function, so, it has an inverse function (h⁻¹). To find the inverse function, we need to exchange  roles of "x" and "y" and solve for y. This gives:

x = h(y)

y = h⁻¹(x)

The given values of function "h" are h(-9) = 5 and h(3) = -4, we find the values of h⁻¹(5) and h⁻¹(-4):

h(-9) = 5

So, h⁻¹(5) = -9 (by exchanging roles of x and y)

and h(3) = -4

So, h⁻¹(-4) = 3 (exchanging the roles of x and y)

The function "h⁻¹(-4) = 3" is represented in option (d).

Therefore, the correct option is (d).

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there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.

what is critical points ?

In calculus, critical points are points on a function where its derivative is either zero or undefined. These points are important because they can indicate the location of maximum or minimum values of the function or points of inflection where the concavity of the function changes.

In the given question,

To find the critical points of the function f(x) = x - 1/x² + 3, we need to find the values of x where the derivative of the function is equal to zero or undefined.

First, we need to find the derivative of the function:

f'(x) = 1 + 2/x³

Next, we set the derivative equal to zero and solve for x:

1 + 2/x³ = 0

2/x³ = -1

x³ = -2

Since there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.

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we know that

discriminant of quadratic is [tex]b^{2}[/tex]-4ac

putting values we get

81-32

= 49

hence the discriminant is 49

Answer:

0.1

Step-by-step explanation:

P(red shirt, black pants | 1 shirt, 1 pants)

= P(red shirt | 1 shirt) * P(black pants | 1 pants)

= (1)/(2+2+1) * (1)/(2)

= 1/10

=0.1

The 90% confidence interval based on the data provided will be (0.6152, 0.7848)

It should be noted that standard error = ✓[(p * q) / n]

p = population proportion

q = 1 - p

n = sample size

sample proportion = x / n = 105 / 150 = 0.7

standard error = ✓(p * q) / n] = sqrt[(0.7 * 0.3) / 150] = 0.0516

margin of error = 1.645 * 0.0516 = 0.0848

Confidence interval = sample proportion ± margin of error

                 = 0.7 ± 0.0848

                 = (0.6152, 0.7848)

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The measures of center for this data set are the mean and median. The mean is 5.1 and median is 6.

The measure of variability is the range. The range is 10.

The measures of center describe the typical or central value of the data. For this data set, we can use the mean or the median as measures of center. The mean is the average of all the quiz scores, while the median is the middle value when the scores are arranged in order.

Mean = (0x1 + 1x0 + 2x0 + 3x0 + 4x0 + 5x2 + 6x4 + 7x2 + 8x2 + 9x1 + 10x0) / (1+0+0+0+0+2+4+2+2+1+0) = 5.1

Median = 6 (the middle score)

The measures of variability describe the spread or dispersion of the data. For this data set, we can use the range. The range will be:

= Highest score - Lowest score

= 10 - 0

= 10

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The line plot shows a student's quiz scores.

Quiz Scores

0 = 1

1,2,3,4 = 0

5 = 2

6 = 4

7 = 2

8 = 2

9 = 1

10 = 0

Which measures of center and variability should be used to describe the data?

Step-by-step explanation:

Please it would be very helpful and useful if you try to use a calculator. Good luck.

Step-by-step explanation:

|6| - | -6|-(-6) =

 6  -   6   +6  = 6

Answer:

r=4

center: (-2,4)

Step-by-step explanation:

The equation of a circle is:

(x-h)²+(y-k)²=r²

(h,k) would be the center of the circle and r would be length of the radius

To find r, we simply take the square root of 16, which would be 4

And the center is given in the equation

Answer:

5.6 mi

Step-by-step explanation:

1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that

The amount of water in the basement is V = 22,500 gallons

Given data ,

To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.

First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:

50 feet x 40 feet x 1.5 feet = 3,000 cubic feet

There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:

3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons

Hence , there are 22,500 gallons of water in the basement

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Let's assume that the number of Android phones sold is x and the number of iOS phones sold is y. Then we can write two equations based on the given information:

x + y = 110    (equation 1)

400x + 650y = 54000   (equation 2)

To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method:

From equation 1, we can solve for x in terms of y: x = 110 - y

Substitute x = 110 - y into equation 2 and solve for y:

400(110 - y) + 650y = 54000

44000 - 400y + 650y = 54000

250y = 10000

y = 40

Substitute y = 40 into equation 1 and solve for x:

x + 40 = 110

x = 70

Therefore, the phone store sold 70 Android phones and 40 iOS phones.

The exponent property of nth roots states that for any real number a and any positive integer n, the nth root of a raised to the nth power equals a.

The property of nth roots, concerning exponents states that if 'a' is a real number and 'n' is a positive integer, then the nth root of 'a' when raised to the nth power will always be equal to 'a':

√ ( a ⁿ ) = a

This can greatly simplify expressions involving nth roots by multiplying the exponent by 'n', taking the nth root of the base:

( √ a ) ⁿ = √ ( a ⁿ )

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The length of the rectangle with the above information is calculated as: 7 feet.

Let the length of the rectangle be l and the width be w. Then, we know that:

Perimeter = 2(l + w) = 18 feet

Area = lw = 14 square feet

We can use the first equation to solve for one of the variables in terms of the other:

l + w = 9

l = 9 - w

Substituting l = 9 - w into the equation for the area, we get:

(9 - w)w = 14

w² - 9w + 14 = 0

Factorize

(w - 2)(w - 7) = 0

Therefore, w = 2 or w = 7. Since the length of the rectangle must be larger than its width, we choose w = 2 and l = 9 - w = 7.

Thus, the length of the rectangle is 7 feet.

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The resulting matrix after row 1 is multiplied by 2 is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The first row is given as follows:

7, -4 and 8.

Multiplying the first row by two, we have that:

(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

(the second row was kept constant, while the first row was multiplied by 2).

The matrix is:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

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If we substitute x = 21 into the equation Y = 25 - 2x, we get:

Y = 25 - 2(21)

Y = 25 - 42

Y = -17

Therefore, if x = 21, then Y = -17.

If we substitute x = 19 into the equation Y = 25 - 2x, we get:

Y = 25 - 2(19)

Y = 25 - 38

Y = -13

Therefore, if x = 19, then Y = -13.

when T = 0, L = 150 (the original number of pages  to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).

A chart can be defined as a pictorial representation or  diagram that presents data or values ​​in an organized manner. Points on a graph often represent a relationship between two or more things.

We can use a linear equation of the form to describe a function that relates the number of pages read to the time elapsed since the start of reading:

L = mT + b

where L is the number of pages remaining, T is the elapsed time  in hours, m is the page read rate  in pages per hour, and b is the original number of pages remaining when T = 0.  

In this case, we know that Ray is reading at a constant rate of 25 pages per hour, so m = -25 (since we are counting  the remaining pages). We also know that when T = 0 (start of  reading),  150 pages remain unread, so b = 150. Combining everything we get:

L = -25T + 150

This formula describes a function that combines the number of pages being read with the time elapsed since the start of  reading. Note that when T = 0, L = 150 (the original number of pages  to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).

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The result of engaging in the row multiplication operation in a matrix would be [ 1 /2   0 | 3 / 4 ]

[ -1   5 | 4 ].

First, you should multiply the first row by the value given of 1 / 4 to be:

( 1 / 4 ) x 2 = 1 / 2

( 1 / 4 ) x 0 = 0

( 1 / 4 ) x 3 = 3 / 4

Then you can replace the values found by the values in the matrix to be :

[ 1 / 2   0 | 3 / 4 ]

[   - 1     5 | 4      ]

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For A∩B , shade the middle common part in the Venn diagram.

What is Venn diagram?

Using circles to represent relationships between objects or limited groupings of objects, a Venn diagram is one example. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.

Here the given Venn diagram contains two sets A and B.

The A intersection B or A∩B means , common elements in both A and B.

So we have shade the middle part of Venn Diagram.

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Gabriela walks 1 mile distance on her way home from school as she is running part of the way.

The distance between two things is measured in distance units like miles, kilometres, or metres. Given that it only possesses magnitude and not direction, distance is a scalar number.

We must ascertain Gabriela's total trip distance before we can respond to this query.

We can get the overall distance by adding the distance she runs to the distance she walks because she runs a portion of the route and walks the other.  

Gabriela commutes two miles to school, so

She needs to travel a total of 2 miles.

We need to figure out how far she runs because she is running a portion of the way.

Since running is typically faster than walking, we can infer that she covers the distance in one mile by running half of it.

She will therefore need to walk the additional mile.  

Gabriela walks a mile on her way home from school, which is the answer to the question.

This is because she walks the remaining mile and runs the first mile.

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Using the given vectors v and w, we found v•w =  66 and v•v = 73.

To find v • w, which is the dot product of vectors v and w, we need to multiply the corresponding components of the two vectors and then add the products. In other words,

v • w = (-8i)(-9i) + (-3j)(-7j)

= 72 + 21

= 93

So, v • w = 93.

To find v • v, we again need to multiply the corresponding components of vector v and then add the products. In other words,

v • v = (-8i)(-8i) + (-3j)(-3j)

= 64 + 9

= 73

So, v • v = 73.

Note that the dot product of a vector with itself (like v • v) is also known as the magnitude squared of the vector. In this case, ||v||² = v • v = 73.

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The correct angle of elevation for the lighthouse's top is roughly 1.91°.

Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.

The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".

a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.

[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]

putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.

[tex]tan3 = \frac{20}{d}[/tex]

[tex]d = \frac{20}{tan3}[/tex]

d = 354.14 (rounded to 2 decimal points

The life raft is therefore roughly 354.14 meters away from the lighthouse.

b)

Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.

[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]

solving for [tex]\alpha[/tex] we get,

[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]

Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.

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The complete question in the form of the image below:

The statement that could be true for the domain of g is g(-4) = -11.

option A.

The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.

The given statements that could be true for g is calculated as follows;

Option A: g(-4) = -11

Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.

Therefore, this could be true.

Option B: g(-13) = 20

Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.

Option C: g(0) = 2

We are given that g(0) = -2, so option C is not true.

Option D: g(7) = -1

Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.

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The solution to the system of equations shown above include the following: A. x = 5, y = -2

In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;

y + x = 3            ......equation 1.

y - 2x = -12       ......equation 2.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair [5, -2].

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