Meena is going to see a movie and is taking her 2 kids. each movie ticket costs $14 and there are an assortment of snacks available to purchase for $5 each. how much total money would meena have to pay for her family if she were to buy 3 snacks for everybody to share? how much would meena have to pay if she bought xx snacks for everybody to share?

The area bounded by y = in(x)/x, y = 0, and x = e¹⁹ is  361/2 square units.

To find the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹, we need to integrate the function ln(x)/x with respect to x over the interval [1, e¹⁹].

∫[1, e¹⁹] ln(x)/x dx

To solve this integral, we use integration by parts with u = ln(x) and dv/dx = 1/x dx.

∫ ln(x)/x dx = ∫u dv = uv - ∫v du

where v = ln(x) and du/dx = 1/x dx.

∫ ln(x)/x dx = ln(x)^2/2 |[1, e¹⁹] - ∫[1, e¹⁹] (1/x)(ln(x)/2) dx

Evaluating the definite integral at the limits gives:

ln(e¹⁹)²/2 - ln(1)²/2 = 361/2

So the area bounded by the curves y = ln(x)/x, y = 0, and x = e¹⁹ is 361/2 square units.

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Answer:

60 x 120

Step-by-step explanation:

2x(x) = 7200

2[tex]x^{2}[/tex] = 7200  divide both sides by 2

[tex]x^{2}[/tex] = 3600

[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{3600}[/tex]

x = 60

This is one of the dimensions.  The other dimension is twice 60 or 120.

a = lw

a = (60)(12)

a = 7200

Helping in the name of Jesus.

The duration of days after which the individual will run out of iced tea is 4 days, under the condition that  a pitcher can hold 13 cups of iced tea. The individual drinks 1. 75 cups of the tea every morning and 1. 5 cups of the tea each evening. 

So to solve this problem we have to relie on the basic principles of division
Total amount of tea consumed per day = 1.75 cups (morning) + 1.5 cups (evening)
= 3.25 cups
Total amount of tea in the pitcher = 13 cups
Number of days before running out of iced tea = 13 cups / 3.25 cups per day
= 4 days
Then, the duration of days until the iced tea runs out is 4 days.
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Answer:

Step-by-step explanation:

proportional means the graph passes through the origin, also known as (0,0). In this case, the only table with both 0’s in the x and y is the second one from the top.

Answer: yes, the game is fair.

Step-by-step explanation:

The game is fair because:

a. you are playing with multiple players, and they have equal odds

b. the odds of winning are higher, so there is balance since you earn less points.

Give brainliest please!

The location of the point P that is 2/5 of the way from A to B on the directed line segment AB is A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).

A line segment is generated from two distinct points set on a plane,  The location of the point P within the line segment can be found by means of the following vectoral formula below:

P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1     (1)

Where:

A(x, y) = Initial point

B(x, y) =  Final point

k =  Distance factor

We have that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:

P(x, y) = (- 8, -2)  + (2/5) · [(6, 19) - (- 8, -2)]

P(x, y) = (- 8, -2) + (2/5) · (14, 21)

P(x, y) = (- 12/5, 32/5)

In conclusion, the location of the point P that is 2/5 of the way from A to B on the directed line segment AB is A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).

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#complete question:

Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).

To find the derivative (f'(x)) of the function f(x) = 2x^4 In x, we will need to use the product rule and the chain rule of differentiation.

Using the product rule, we have:

f'(x) = [2(In x)](4x^3) + [2x^4](1/x)

Simplifying this expression, we get:

f'(x) = 8x^3 In x + 2x^3

Therefore, the derivative of f(x) is f'(x) = 8x^3 In x + 2x^3.
Hi! To find the derivative f'(x) of the function f(x) = 2x^4 * ln(x), we'll use the product rule. The product rule states that if you have a function h(x) = u(x)v(x), then h'(x) = u'(x)v(x) + u(x)v'(x). In this case, u(x) = 2x^4 and v(x) = ln(x).

First, find the derivatives of u(x) and v(x):
u'(x) = d(2x^4)/dx = 8x^3
v'(x) = d(ln(x))/dx = 1/x

Now, apply the product rule:
f'(x) = u'(x)v(x) + u(x)v'(x)
f'(x) = (8x^3)(ln(x)) + (2x^4)(1/x)

Simplify the expression:
f'(x) = 8x^3 * ln(x) + 2x^3

This is the derivative of the given function.

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The null hypothesis (H0) is that there is no significant difference in mean weight loss between men and women, or μm - μw = 0. The alternative hypothesis (Ha) is that there is a significant difference in mean weight loss between men and women, or μm - μw ≠ 0.

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The mean and the median of the data set is given as the median, 4, is greater than the mean, 3. The correct answer is option a.

To find the mean of the data set, we add up all of the numbers and divide by the total number of days. So, the mean is (1+4+5+5+1+5+5)/6 = 3.

To find the median, we first need to put the numbers in order from least to greatest: 1, 1, 4, 5, 5, 5. The median is the middle number, which in this case is 4.

Now we need to determine which value is greater. The options are:

A. The median, 4, is greater than the mean, 3.
B. The mean, 3, is greater than the median, 4.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.

We can eliminate options B and D because they don't make sense. The mean cannot be less than 0, and the median cannot be less than the mean.

Option A is correct. The median, 4, is greater than the mean, 3. This makes sense because there are two 1's in the data set, which bring down the mean. However, the median is not affected by outliers like this, so it remains higher.

Option C is incorrect because the mean is not 4, it is 3.

In summary, the mean of the data set is 3 and the median is 4. The median is greater than the mean, which is represented by option A.

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The base area of the pyramid is 5 units squared.

The pyramid has a volume of 20 cubic units and the height of the pyramid is 4 units.

Therefore, the area of the base can be calculated as follows:

Hence,

volume of the pyramid = base area × height of the prism

20 = base area × 4

Therefore,

base area of the pyramid = 20 / 4

base area of the pyramid = 5 units squared.

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The ratio of Kaido's age to Hiroshi's age to Saitama's age is 5:8:24.

Hiroshi is 6 years older than Kaido. Saitama is three times as old as Hiroshi. The sum of their three ages is 79.

Therefore, the ratio of Kaido's age to Hiroshi's age to Saitama's age can be calculated as follows:

Hence,

let

x = Kaido age

Hiroshi age = 6 + x

Saitama age = 3(6 + x) = 18 + 3x

Therefore,

x + 6 + x + 18 + 3x = 79

5x = 79 - 24

5x = 50

x = 50 / 5

x = 10

Therefore,

x = Kaido age = 10 years

Hiroshi age = 6 + x = 6 + 10 = 16 years

Saitama age = 3(6 + x) = 18 + 3x = 18 + 3(10) = 48 years

Hence, the ratio of there ages are as follows:

10:16:48

Let's divide through by 2

5:8:24

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Point B is the image of point A under a rotation about the origin.

Rotation is a transformation in which an object or a point is turned around a fixed point or a fixed axis. The fixed point or axis is called the center of rotation, and the angle of rotation specifies the amount and direction of the turn. When an object is rotated, its orientation changes but its shape and size remain the same.

For example, if you rotate a square by 90 degrees around its center, it will look the same as before, but it will be oriented differently. Similarly, if you rotate a point in a coordinate system around the origin, its position will change, but its distance from the origin will remain the same.

Rotations are commonly used in geometry, physics, and engineering to describe the motion of objects, such as the rotation of the Earth around its axis or the rotation of a wheel on an axle. They are also used in computer graphics to create animations and in robotics to control the movement of robotic arms and other devices.

When point A is rotated about the origin to form point B, the distance between the origin and each point remains the same. The direction from the origin to point A and the direction from the origin to point B are related by the angle of rotation. Specifically, point B is the image of point A under a rotation about the origin.

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The sequence 10, 9. 5, 9. 0, 8. 5,. has a common difference on -0.5

The sequence 200, 100, 50, 25, has a common ratio of 1/2

Let's start by discussing the sequence 10, 9.5, 9.0, 8.5. We can observe that each term is decreasing by 0.5. This means that the sequence has a common difference of -0.5.

In mathematical terms, the common difference is the constant value that is added or subtracted from each term in the sequence to obtain the next term. In this case, we can write the sequence as:

10, 10 - 0.5, 10 - 1.0, 10 - 1.5

where the common difference is -0.5.

Now, let's consider the sequence 200, 100, 50, 25. We can observe that each term is obtained by dividing the previous term by 2. This means that the sequence has a common ratio of 1/2.

In mathematical terms, the common ratio is the constant value that is multiplied by each term in the sequence to obtain the next term. In this case, we can write the sequence as:

200, 200/2, (200/2)/2, ((200/2)/2)/2

where the common ratio is 1/2.

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Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.

Point B is located at (2, -3), so it looks like

     |

     |

     |

     |

------B(2, -3)

     |

     |

     |

     |

To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).

Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.

So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

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Answer:

Step-by-step explanation:

The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.

Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.

To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,

so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.

Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.

Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.

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In the given Isosceles trapezoid ABCD, the following three statements are correct:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC

A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.

The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.

Thus, three correct statements in the given question are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

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The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.

- Vertical stretch by a scale factor of 2: Multiply the output by 2.

- Shift 3 units to the left: Replace x with x + 3.

- Shift 1 unit down: Subtract 1 from the output.

Thus, the function g(x) can be written as:

g(x) = 2 * f(x + 3) - 1

Substituting f(x) = 5^x, we get:

g(x) = 2 * 5^(x + 3) - 1

Simplifying:

g(x) = 2 * 125 * 5^x - 1

g(x) = 250 * 5^x - 1

The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.

The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.

Therefore, the function g(x) is g(x) = 250 * 5^x - 1.

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Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

a. Relevant parameter: the difference between actual and scheduled arrival time.

Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.

Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

b. Sample mean for Delta Air Lines: -2.31 minutes

Sample mean for United Air Lines: -4.01 minutes

Difference in sample means: -1.70 minutes

c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.

d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider

Delta over United.

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a. For the function, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).

CCUP: (0, π/4) and (5π/4, 2π)

CCDOWN: (π/4, 5π/4)

b. The coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).

a. To find the intervals for which f is concave up and concave down on [0,2π], we need to determine the second derivative of the function f(x):

f(x) = -5.5 sin x + 5.5 cos x

f'(x) = -5.5 cos x - 5.5 sin x

f''(x) = 5.5 sin x - 5.5 cos x

To find where f is concave up (CCUP), we need to find where f''(x) > 0. Thus, we solve the inequality:

5.5 sin x - 5.5 cos x > 0

sin x > cos x

This inequality holds for 0 < x < π/4 and 5π/4 < x < 2π. Therefore, the intervals for which f is concave up on [0,2π] are (0, π/4) and (5π/4, 2π).

To find where f is concave down (CCDOWN), we need to find where f''(x) < 0. Thus, we solve the inequality:

5.5 sin x - 5.5 cos x < 0

sin x < cos x

This inequality holds for π/4 < x < 5π/4. Therefore, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).

Thus, we have:

CCUP: (0, π/4) and (5π/4, 2π)

CCDOWN: (π/4, 5π/4)

b. To find the coordinates of any points of inflection for f on [0,2π], we need to find where the concavity changes, i.e., where f''(x) = 0 or is undefined. Thus, we solve the equation:

5.5 sin x - 5.5 cos x = 0

sin x = cos x

This equation holds for x = π/4 and x = 5π/4.

To determine the concavity at these points, we can examine the sign of f''(x) in the intervals surrounding these points:

For x in (0, π/4), f''(x) < 0, so f is concave down.

For x in (π/4, 5π/4), f''(x) > 0, so f is concave up.

For x in (5π/4, 2π), f''(x) < 0, so f is concave down.

Therefore, the points of inflection for f on [0,2π] are (π/4, f(π/4)) and (5π/4, f(5π/4)).

To find the coordinates of these points, we can substitute π/4 and 5π/4 into the original function:

f(π/4) = -5.5 sin(π/4) + 5.5 cos(π/4) = -2.75 + 5.5/√2 ≈ 2.45

f(5π/4) = -5.5 sin(5π/4) + 5.5 cos(5π/4) = -2.75 - 5.5/√2 ≈ -5.95

Therefore, the coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).

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The amount change in her bank account during that week after withdrawals and deposit is equal to $59.

Total number of withdrawals made by Sheila = 4

Amount made at the time withdrawals using ATM = $40

Amount withdraw using check card to purchase = $156

Amount deposited using paycheck = #375

Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,

4 withdrawals of $40 each

= 4 x $40

= $160

So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,

= $160 + $156

= $316

Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,

$375 - $316 = $59

Therefore, the amount in Sheila's account increased by $59 during that week.

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The above question is incomplete, the complete question is:

During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?

The measure of angle W in the kite WXYZ is 0 degrees.

To find the measure of angle W in the kite WXYZ, we can use the properties of kites. In a kite, the two opposite angles formed by the intersection of the diagonals are equal. Let's denote the measure of angle W as "x."

Step 1: Start with the given information that WXYZ is a kite.

Step 2: Recall that the diagonals of a kite intersect at right angles. Let's label the intersection point of the diagonals as point P.

Step 3: Draw the diagonals WX and YZ, which intersect at point P.

Step 4: Recognize that angles WXP and ZYP are congruent. Therefore, the measure of angle WXP is also x.

Step 5: Observe that the sum of the angles in a triangle is 180 degrees. Since triangle WXP is a triangle, we can write the equation: x + 90 + 90 = 180.

Step 6: Simplify the equation: x + 180 = 180.

Step 7: Subtract 180 from both sides: x = 0.

Step 8: Analyze the result. The measure of angle W, denoted by x, is equal to 0 degrees.

Therefore, the measure of angle W in the kite WXYZ is 0 degrees.

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In the equation , Felipe is correct.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is (372) (675) =18k7.

We know that the factor is a number that divides the another number and leaves no reminder .

If we divide 18k7 by 372 the we get remainder 675. So 372 is not factor of 18k7.

But 372 is divides the number 18k7.

Hence Felipe is correct.

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The sum of the heights of the two trees with given volumes and radius is equal to  9 cm (nearest whole number ).

Volumes of the cylindrical trunks of first tree = 904.78 cm³

and Volumes of the cylindrical trunks of first tree =113 cm³.

radius of the  first tree = 6cm

Radius of the second tree = 6cm

The formula for the volume of a cylinder is V = πr²h,

where r is the radius of the cylinder,

h is the height of the cylinder,

and π is the constant approximately value equal to 3.14.

For the first tree,

⇒904.78 = π(6)²h

⇒h = 904.78 / (π(6)²)

⇒h ≈ 8.004 cm

For the second tree, we have,

⇒113 = π(6)²h

⇒h = 113 / (π(6)²)

⇒h ≈ 0.9996 cm

This implies,

The sum of the heights of the two trees is equal to,

= 8.004 + 0.9996

= 9.003 cm

= 9 cm ( nearest whole number)

Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.

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The given question is incomplete, I answer the question in general according to my knowledge:

The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and  another one with radius 6cm and volume 113 cm³.

What is the sum of the heights of the two trees? Round your answer to the nearest whole number

The answer to the first question is: Burger Quick, because it has a larger median.

The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.

A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.

In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.

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Answer: x=55/6 or 55 over 6

Step-by-step explanation: Step 1: Distribute:

- 350= 12(x+20)

- 350= 12x + 240

Step 2: Subtract 240 from both sides:

- 350-240= 12x+240-240

Step 3: Simplify:

Subtract the numbers: 350-240= 12x+240-240= 110=12x+240-240

Subtract again: 110=12x+240-240= 110=12x

Step 4: Divide both sides by the same factor:

110=12x= 110/12= 12x/12

Step 5: Simplify:

- Divide the numbers: 110/12=12x/12= x=55/6=12x/12

- Cancel terms that are in both the numerator and denominator: 55/6=12x/12= 55/6=x

- Move the variables to the left: 55/6=x = x=55/6

Answer: x=55/6 or 55 over 6

Answer:

To solve this trigonometric identity, we need to use the definitions of the trigonometric functions and some algebraic manipulation. Here's how we can do it:

cos 14° - sin 14°/ cos 14° + sin 14°

= (cos 14°/cos 14°) - (sin 14°/cos 14°)/(cos 14°/cos 14°) + (sin 14°/cos 14°) (multiplying the numerator and denominator of the second term by cos 14°)

= 1 - tan 14°/1 + tan 14° (using the definitions of cosine and sine, and dividing both terms by cos 14°)

= (1 - tan²14°)/(1 + tan 14°) (using the identity 1 + tan²θ = sec²θ)

= 1/cot 14° - cot 14° (using the definition of cotangent and simplifying the numerator)

= cot 90° - cot 14° (using the identity cot(90° - θ) = tan θ)

= cot (90° + 14°) (using the identity cot(θ + 90°) = -tan θ)

= cot 104°

Since cot(104°) = cot(180° - 76°) = -cot 76°, we can also write the final answer as -cot 76°.

Therefore, the given identity is true, and we have shown that:

cos 14° - sin 14°/ cos 14° + sin 14° = cot 59​ = -cot 76°.

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According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

Hence, We get;

228 x 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 x 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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The probability is less than 0.489 is approximately 0.8980 or 89.80%  that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489

First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:

Mean = p = 0.48

Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071

Next, we need to standardize the sample proportion using the formula:

z = (sample proportion - population proportion) / standard deviation

z = (0.489 - 0.48) / 0.071 = 1.27

Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.

Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.

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The smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.

To determine the angle the smallest side will make with the ground, we can use the law of sines. The law of sines states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.

Let's label the sides of our triangle as follows:

The longest side (sitting on the ground) is side c

The second longest side is side b

The smallest side is side a

We know that side b is 2'3" long, which is equivalent to 27 inches. We also know that side a is 10 inches long. We can use the law of sines to solve for the angle opposite side a:

sin(A) = (a/c) * sin(C)

We can solve for sin(C) by using the fact that the sum of the angles in any triangle is 180 degrees:

C = 180 - A - B

We know that angle B is 18 degrees, so we can substitute that into our equation for C:

C = 180 - A - 18

C = 162 - A

Substituting this expression for C into our equation for sin(A), we get:

sin(A) = (a/c) * sin(162 - A)

We know that c is the longest side of the triangle and therefore opposite the largest angle. Since we are interested in the angle opposite side a, we can assume that angle A is the smallest angle in the triangle. We can use this assumption to simplify our equation for sin(A):

sin(A) = (a/c) * sin(162)

Plugging in the values for a, c, and sin(162), we get:

sin(A) = (10/27) * 0.951

sin(A) = 0.352

Taking the inverse sine of both sides, we get:

A = sin^-1(0.352)

A ≈ 20.6 degrees

Therefore, the smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.

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