Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 14,12,20,19,11,13,10,8,18,15

The calculated scale factor of the photograph is 3.5

From the question, we have the following parameters that can be used in our computation:

Photograph = 4" by 6"

Photograph copy = 14" by 21"

Using the above as a guide, we have the following:

Scale factor = Photograph copy/Photograph

substitute the known values in the above equation, so, we have the following representation

Scale factor = 14/4

Evaluate

Scale factor = 3.5

Hence, the scale factor of the photograph is 3.5

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The expressions that are equivalent to 36x² - 64 are (a) 4(3x - 4)(3x + 4) and (e) (6x - 8)(6x + 8)

From the question, we have the following parameters that can be used in our computation:

36x² - 64

For the expression, we can apply the difference of two squares

Using the above as a guide, we have the following:

36x² = (6x)²

64 = 8²

So, we have the following:

36x² - 64 = (6x)² - 8²

Apply the difference of two squares

36x² - 64 = (6x - 8)(6x + 8)

Factor out 4 from the expression

36x² - 64 = 4(3x - 4)(3x + 4)

Hence, the expressions that are equivalent to 36x² - 64 are 4(3x - 4)(3x + 4) and (6x - 8)(6x + 8)

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The value of the angle that has been marked as U is 77 degrees.

The cosine rule, also known as the law of cosines, is a trigonometric relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles.

If we know the lengths of the other two sides and the measurement of the included angle, we can use the cosine rule to determine the length of one side of a triangle.

We know that

[tex]v^2 = t^2 + u^2 - 2(ut) Cos 51\\v^2 = (22)^2 + (79)^2 - 2(22 * 79) Cos 51\\v^2 = 6725 - 2188[/tex]

v = 63

Using the sine rule;

v/Sin V = u /Sin U

U = Sin-1 (uSin V/v)

U = Sin1-1(79 * Sin 51/63)

U = 77 degrees

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To evaluate the limit of the function as x approaches 0, where f(x) = sin(x)/x, we can use L'Hôpital's rule.

According to L'Hôpital's rule, if we have an indeterminate form of the type 0/0 or ∞/∞, we can take the derivative of the numerator and denominator until we reach a determinate form.

Let's differentiate the numerator and denominator:

[tex]\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(\sin(x)) \\ &= \cos(x)\end{align}[/tex]

[tex]\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(x) \\ &= 1\end{align}[/tex]

Now we can evaluate the limit as x approaches 0 using the derivatives:

[tex]\begin{align}\lim_{x \to 0} f(x) &= \lim_{x \to 0} \frac{\sin(x)}{x} \\ &= \lim_{x \to 0} \frac{\cos(x)}{1} \quad \text{(using L'Hôpital's rule)} \\ &= \cos(0) \\ &= 1 \end{align}[/tex]

Therefore, the limit of f(x) as x approaches 0 is 1.

1. The amplitude is 3

2. The period is π

3. The phase shift is -90

4. The vertical shift is 2

5. The graph is attached

From the question, we have the following parameters that can be used in our computation:

y = 3sin[2(θ - 90)] + 2

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

So, we have

Amplitude = 3

Period = 2π/2

Phase shift = -90

Vertical shift = 2

Evaluate

Amplitude = 3

Period = π

Phase shift = -90

Vertical shift = 2

Hence, the amplitude is 3 and the period is π

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The one which shows the simplified function is:

1 − sin x

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have:

cos²x/(1 + sin x)

Recall that in trigonometry function:

cos²x = 1 - sin²x

            = 1² - sin²x  (difference of two squares)

            = (1 + sin x)(1 - sin x)

Thus, we can say:
cos²x/(1 + sin x) = [(1 + sin x)(1 - sin x)] / [(1 + sin x)]

                         = 1 - sin x

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The simplified expression as a single logarithm is:

log[tex][(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)[/tex]

Let's start by using the power rule of logarithms, which states that [tex]log(base b)(x^a) = a \times log(base b)(x).[/tex]

Using this rule, we can rewrite the expression as follows:

3log(x+4) + 2log(x-7) - 5log(x-2) + log([tex]x^2[/tex])

= log[tex](x+4)^3 + log(x-7)^2 - log(x-2)^5 + log(x^2)[/tex]

Next, let's apply the product rule of logarithms, which states that log(base b)(xy) = log(base b)(x) + log(base b)(y).

Using this rule, we can combine the logarithms:

= log[tex][(x+4)^3(x-7)^2] - log[(x-2)^5] + log(x^2)[/tex]

Finally, we can apply the quotient rule of logarithms, which states that log(base b)(x/y) = log(base b)(x) - log(base b)(y).

Applying the quotient rule, we can simplify further:

= log[tex][(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)[/tex]

Thus, the simplified expression as a single logarithm is:

log[tex][(x+4)^3(x-7)^2 / (x-2)^5] + log(x^2)[/tex]

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Answer:

D

Step-by-step explanation:

please say thank you and please verify this answer and name me brainliest

The maximum number of turns for the graph of f ( x )=- x ⁴ + 3 x ² can be found to be 2 turns.

The maximum number of turns for the function can be determined by looking at the number of changes in the sign of the derivative of the function.

If derived, the derivative of the function is f ' ( x ) = - 4x ³ + 6x.

The derivative is equal to 0 at x = 0 and x = 3/2.

As a result of the derivative being negative for x < 0 and x > 3 / 2, and positive for 0 < x < 3 / 2, the graph of the function has a maximum of 2 turns.

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The rate of increase for the function f(x) = 1/3(∛24)²ˣ is 2∛3

From the question, we have the following parameters that can be used in our computation:

f(x) = 1/3(∛24)²ˣ

When the exponent is evaluated, we have

f(x) = 1/3(2∛3)ˣ

An exponential function is represented as

f(x) = abˣ

Where

Using the above as a guide, we have the following:

b = 2∛3

Hence, the rate of increase for the function is 2∛3

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The function y=sin(x + sin(x+³)+5) has a phase shift of 1/3 units to the left. This is because the sine function is shifted 1/3 units to the left by the addition of sin(x+³). The function also has a vertical shift of 5 units up. This is because the constant 5 is added to the end of the equation.

The phase shift of a trigonometric function is the horizontal displacement of the graph of the function from the graph of the basic sine function. The phase shift is measured in units of x.

In order to find the phase shift of a trigonometric function, we can use the following formula:

Phase shift = -c/b

Phase shift = -0/1 = 0

This means that the graph of the function is not shifted horizontally.

The vertical shift of a trigonometric function is the vertical displacement of the graph of the function from the graph of the basic sine function. The vertical shift is measured in units of y.

Vertical shift = d

Vertical shift = 5

This means that the graph of the function is shifted 5 units up.

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Answer:

[tex]x=-5,-1,1,5[/tex]

Step-by-step explanation:

Use the Zero Product Property and set each factor equal to 0

[tex]h(x)=5(x-5)(x+5)^2(x^2-1)[/tex]

[tex]0=x-5\\x=5[/tex]

[tex]0=(x+5)^2\\0=x+5\\x=-5[/tex]<-- Multiplicity of 2

[tex]0=x^2-1\\0=(x-1)(x+1)\\x=-1,1[/tex]

Therefore, all real zeroes of the function are [tex]x=-5,-1,1,5[/tex]

Answer:

64

Step-by-step explanation:

we must multiply 2×4 which is 8 after that we multiply 2×4 which is 8 and then we multiply 8×8 which is 64

Answer:

x = 120 , y = 50

Step-by-step explanation:

1 and 140° are a linear pair and sum to 180° , that is

1 + 140 = 180 ( subtract 140 from both sides )

1 = 40

the sum of the 3 angles in Δ ABE = 180° , so

∠ BAE = 180° - ( 80 + 40)° = 180° - 120° = 60°

∠ BAE and ∠ CDE are same- side interior angles and sum to 180° , that is

x + 60 = 180 ( subtract 60 from both sides )

x = 120

the sum of the 3 angles in Δ CDE = 180° , that is

10 + x + 2 = 180

10 + 120 + 2 = 180

130 + 2 = 180 ( subtract 130 from both sides )

2 = 50

AED is a straight line , then

y + 80 + 2 = 180

y + 80 + 50 = 180

y + 130 = 180 ( subtract 130 from both sides )

y = 50

The volume of the prism is 48 cm³.

We are given that;

The dimensions 3cm by 4cm by 5cm

Now,

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

We can choose 3 cm and 4 cm as the base and height of the triangle.

Plugging in the values, we get:

Area of triangle=21​×3×4

Area of triangle=6

So, the area of the base is 6 cm sq,

To find the volume of the prism, we can multiply the area of the base by the height of the prism. This gives us:

Volume=6×8

Volume=48

Therefore, by the volume the answer will be 48 cm³.

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The simplified expression of the logarithmic expression is Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)

From the question, we have the following parameters that can be used in our computation:

Loga + 3Logaˣ - 2 Log a⁴ˣ

Express properly

So, we have

Log(a) + 3Log(aˣ) - 2 Log(a⁴ˣ)

So, we have

Log(a) + Log(a³ˣ) - Log(a¹⁶ˣ²)

The logarithmic expression can be simplified using the product and the quotient rule

This gives

Log(a * a³ˣ/a¹⁶ˣ²)

So, we have

Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)

Hence, the simplified expression is Log(a³ˣ ⁺ ¹ ⁻ ¹⁶ˣ²)

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Answer:

Step-by-step explanation:

Hey there,
Here's my reasoning regarding the problem:

Let's assume that the watch at the time it was lost was x years old.
When it was picked it was 3 times as old as it was when it was lost therefore it's currently 3x. The time between when it was lost and when it was found is 38 years. We can break this down into a simple algebraic formula:

3x - x = 38

2x = 38

x = 19

Answer:

4n + 8 = 48

Step-by-step explanation:

In the situation you described, there are 4 large tables with an equal number of guests seated at each table. Let’s represent the number of guests at each large table with the variable n. There are also 8 late-arriving guests seated at a smaller table. The total number of guests at the dinner is 48. So we can write an equation to represent this situation: 4n + 8 = 48, where 4n represents the total number of guests seated at the 4 large tables and 8 represents the number of late-arriving guests seated at the smaller table.

1) Note that  the grid needs to be 8 squares wide to accommodate the data.

2) a scale of 0.2 km per square on the vertical axis would provide a clear representation of the data while utilizing the available space effectively.

1) To find  the width of the grid, we need to find the total number of data points on the x- axis.

Here , the time since the start is given at intervals of 5 minutes. From 0 - 35 minutes, there are a total of 8 data points.

Thus, we are right to state that  the grid needs to be 8 squares wide to accommodate the data.

2)

We must decide the optimal scale for visualizing data on the vertical axis because the grid is 20 squares tall. Looking at  the distance from the starting point, we can see that the figures range from 0 to 1.9 kilometers.

To make the best  use of the grid area, we may select an appropriate scale that includes the  data range.

In this scenario, a vertical scale of 0.2 km per square would offer a clear depiction of the data while properly utilizing the available space.

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The slope of the line that passes through the points (3, 2) and (-1, -4) is 3/2.

The given coordinate point is (3, 2) and (-1, -4).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope(m) = (-4-2)/(-1-3)

= -6/(-4)

= 3/2

= 1.5

Therefore, the slope of the line that passes through the points (3, 2) and (-1, -4) is 3/2.

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]The cross-section could be of these shapes square and triangle.

We know that a cross-segment is a plane segment that is a segment of a three-dimensional item that is parallel to one among its planes of symmetry or perpendicular to considered one of its traces of symmetry.

An instance of a segment would be a circle.

However, cross-phase is seen whilst a 3-dimensional figure is reduced through a plane. within the case of the cone, a circular go-segment emerges while the cone is cut parallel to its base

The go-sectional region is the location of a 3-dim figure that is acquired whilst a three-dimensional object - inclusive of a cylinder - is sliced perpendicular to some designated axis at a point.

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The equation of the circle with the center (0, 4) and a point (-1, 8) on the circle is x² + (y - 4)² = 17.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

Given that the center is (0, 4) and a point (-1, 8) is on the circle, we can calculate the radius using the distance formula:

[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\r = \sqrt{(-1 - 0)^2+(8-4)^2} \\\\r = \sqrt{(-1 )^2+(4)^2} \\\\r = \sqrt{1+16} \\\\r = \sqrt{17}[/tex]

Now, let's plug the values of the center (0,4) and the radius √17 into the standard form of the equation of a circle:

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 4)² = (√17)²

Simplify

x² + (y - 4)² = 17

Therefore, the equation of the circle is x² + (y - 4)² = 17.

Option C) x² + (y - 4)² = 17 is the correct answer.

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Mowing lawns had more variation in earnings compared to shoveling snow.

To determine which job had more variation in earnings based on the given box plots, we need to compare the spread or interquartile range (IQR) of each job.

The interquartile range represents the range of the middle 50% of the data, which provides a measure of the variation in earnings.

Looking at the box plots, we can compare the lengths of the boxes or the distances between the first quartile (Q1) and the third quartile (Q3) for each job.

From the given information, it appears that the box plot for mowing has a larger spread than the box plot for shoveling. This can be observed by comparing the lengths of the boxes or the distances between Q1 and Q3.

Therefore, based on the given box plots, mowing lawns had more variation in earnings compared to shoveling snow.

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The present age of the father is 10 years.

Let

Age of the father = x

Age of each child = y

Number of children = 2

Current age:

x = 2y

After 5 years:

(x + 5) = 2(2y)

x + 5 = 4y

Substitute x = 2y into

x + 5 = 4y

2y + 5 = 4y

5 = 4y - 2y

5 = 2y

divide both sides by 2

y = 5/2

y = 2.5

So,

x = 2y

x = 2(2.5)

x = 5

Therefore, present age of the father;

x + 5

= 5 + 5

= 10

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Answer: It costs about 7.32 to buy enough lemons.

Answer:

       3 hundred blocks

       ----------------

       |      |       |

       | 100  |  100  |

       |______|_______|

       |      |       |

       | 100  |  100  |

       |______|_______|

       |      |       |

       | 100  |  100  |

       |______|_______|

       4 tens blocks

       -------------

       |     |     |

       | 10  |  10 |

       |_____|_____|

       |     |     |

       | 10  |  10 |

       |_____|_____|

       5 one's blocks

       -------------

       |   |   |

       | 1 | 1 |

       |___|___|

       |   |   |

       | 1 | 1 |

       |___|___|

       |   |   |

       | 1 | 1 |

       |___|___|

       |   |   |

       | 1 | 1 |

       |___|___|

       |   |   |

       | 1 | 1 |

       |___|___|

Answer:

Step-by-step explanation:

To find the difference between vectors a and b, we subtract the corresponding components of the vectors.

Given that a = ⟨ -7, 2 ⟩ and b = ⟨ 7, 2 ⟩, we can calculate the difference a - b as follows:

a - b = ⟨ -7, 2 ⟩ - ⟨ 7, 2 ⟩

Subtracting the corresponding components:

a - b = ⟨ -7 - 7, 2 - 2 ⟩

Simplifying:

a - b = ⟨ -14, 0 ⟩

Therefore, the difference a - b is ⟨ -14, 0 ⟩.

The solution after changing its unit is,

⇒ 32 hectare = 80 acre

We have to given that;

To convert the given square unit to the square unit indicated.

⇒ 32 ha to acres

Since, A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

We have to given that,

⇒ 1 acre = 0.4 hectare (ha)

Hence,

⇒ 1 hectare (ha) = 1 / 0.4 acre

So, WE get;

⇒ 32 hectare = 32 / 0.4 acre

⇒ 32 hectare = 320/4 acre

⇒ 32 hectare = 80 acre

Thus, The solution after changing its unit is,

⇒ 32 hectare = 80 acre

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The area of the compound shape is 84 cm squared.

A compound shape is a shape that has two or more shapes in it. Therefore, the sum of the individual area is the area of the compound shape.

Therefore,

area of the compound shape = area of the rectangle + area of the triangle

area of the rectangle = 3 × 8

area of the rectangle = 24 cm²

Let's find the base of the triangle using Pythagoras's theorem.

Hence,

17² - 8² = b²

b = √289 - 64

b = √225

b = 15 cm

Therefore,

area of the triangle = 1 / 2 × 15 × 8

area of the triangle  = 60 cm²

Finally,

area of the compound shape = 60 + 24

area of the compound shape = 84 cm²

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