To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted

the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

O

Relative Frequency

Relative Frequency

7

9

2

11

9

7

X+S

9

0. 40

0. 35

0. 30

0. 25

0. 20

0. 15

0. 10

0. 05

0. 40

0. 35

0. 30

0. 25

0. 20

0. 15

0. 10

0. 05

8

x + 2s

9

x + 3s

H

Need Help?

7 4 8 10

1

6

5

10

8

748

10 8

USE SALT

5. 526

8

4

9

8

7

(a) Construct a relative frequency histogram to describe the data.

Frequency of lumber

5

Interval

Read It

3. 382 to 11. 961

6

06 9

11 10 11 8 8 10 8 8 12

1. 237 to 14. 106

7

7

11

8 8 10

9

9560

Frequency of lumber

L

77

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

amount of lumber

7 8

to 9. 816

7 7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

amount of lumber

7 7

10 10 7 4 8 7

(c) Calculates for the data. (Round your answer to three decimal places. )

S = 2. 145

✔timber trees

(b) Calculate the sample mean x as an estimate of μ, the mean number of trees for all 50-by-50-foot squares in the tract.

(Round your answer to three decimal places. )

X = 7. 671

timber trees

Construct the intervals x ±s, x ± 2s, and X + 3s. Calculate the percentage of squares falling into each of the three intervals,

and compare with the corresponding percentages given by the Empirical Rule and Tchebysheff's Theorem. (Round your

interval values to three decimal places. Round actual percentages to two decimal places. )

Actual Percentage

Relative Frequency

X %

Relative Frequency

X %

0. 40

0. 35

0. 30

0. 25

0. 20

0. 15

0. 10

0. 05

X %

0. 40

0. 35

0. 30

0. 25

0. 20

0. 15

0. 10

0. 05

Frequency of lumber

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

amount of lumber

Frequency of lumber

at least 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

amount of lumber

Tchebysheff

at least 75%

at least 89%

%

95

Empirical

≈ 68%

≈ 99. 7%

%

The missing values are 81/4 and 9/2, the complete square is x² - 9x + 81/4 = ( x - 9/2 )².

Given square in the question;

x² - 9x + [ ] = ( x - [ ] )²

To complete the square, we use the form ax² + bx + c.

Compare the form to the square;

Now, consider the vertex form of a parabola.

a( x + d )² + e

We find d, using the formula

d = b/2a

Plug in the values

d = -9/(2×1 )

d = -9/2

Next, find the value of e, using the formula

e = c - b²/4a

Plud in the values

e = 0 - (-9)²/(4×1)

e = -81/4

Hence, the complete square will be;

x² - 9x + 81/4 = ( x - 9/2 )²

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Based on the concept of measurement, the decimal equivalent is 0.75.

To start, it is important to understand that time is a form of measurement that can be expressed in a variety of ways, including hours, minutes, seconds, and even fractions of seconds. Decimals are also a common way to express time, especially in situations where precision and accuracy are important.

To convert 45 minutes into a decimal, you need to first understand the relationship between minutes and hours.

There are 60 minutes in one hour, which means that 45 minutes is equivalent to 0.75 hours

=> (45/60 = 0.75).

Once you have this decimal equivalent, you can express it in a variety of ways, depending on the context.

If you were measuring time in terms of a workday (i.e. 8 hours), 0.75 hours would be equal to 45 minutes. On the other hand, if you were measuring time in terms of a percentage of an hour (i.e. 100%), 0.75 hours would be equal to 75%.

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The conversion of 80°C to Fahrenheit is equivalent to 176 degrees Fahrenheit.

Whereas most other nations and for scientific reasons across the world use the Celsius or centigrade scale, the United States uses the Fahrenheit system.

The formula to convert a temperature from the Celsius (°C) scale to its Fahrenheit (°F) equivalent is:

°F = (9/5 × °C) + 32.

To convert 80 degrees Celsius to Fahrenheit, we can use the following formula:

°F = (°C x 1.8) + 32

Plugging in the value for 80°C, we get:

°F = (80 x 1.8) + 32

°F = 144 + 32

°F = 176

Therefore, 80 degrees Celsius is equivalent to 176 degrees Fahrenheit.

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It is important to consider scholarships and grants before loans to pay for higher education because Scholarships and grants are free money that do not need to be paid back. That is option A.

Scholarship and grants are defined as payments that are being granted to an individual upon an academic achievement which usually involves a stipulated amount of money.

Scholarship and grants are important due to the following reasons:

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The conversion of 71 inches is equal to 5.9166666667 feet.

The US customary measuring unit is the foot,

It is denoted by the letter "ft."

To convert 5 meters (m) to feet,

The imperial and American customary systems of measuring both use the symbol "in" to represent 1 inch as a unit of length.

It was decided that one inch was exactly equal to 25.4 millimetres.

12 inches make up a foot, and 36 inches make up a yard.

We know that,

1 in = 0.0833333333 ft

1 ft = 12 in

1 in = 2.54 cm and 1 cm equals 0.3937007874 in

To convert inches to feet,

We need to divide the number of inches by 12,

Since there are 12 inches in a foot.

Therefore,

71 inches divided by 12 gives us:

71 inches ÷ 12 = 5.9166666667 feet

(rounded to ten decimal places)

So 71 inches is equal to approximately 5.9166666667 feet.

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Answer:

Approximately 9.23 cm

Step-by-step explanation:

We can start by finding the height of each domino in the chain, starting with domino 0, which is 5.00 cm tall.

Let h be the height of domino 5. Then we can express the height of each domino in terms of h as follows:

Domino 0: 5.00 cm

Domino 1: 1.13 * 5.00 = 5.65 cm

Domino 2: 1.13 * 5.65 = 6.38 cm

Domino 3: 1.13 * 6.38 = 7.21 cm

Domino 4: 1.13 * 7.21 = 8.16 cm

Domino 5: 1.13 * 8.16 = h cm

Since we know that domino 5 is the tallest domino and is number 5 in the sequence, we can set the height of domino 5 equal to h and solve for h:

h = 1.13 * 8.16

h ≈ 9.23 cm

Therefore, the height of domino 5 is approximately 9.23 cm.

The product of -1 and -3/4 is 3/4, and the quotient of -3/4 divided by 1/-3 is 9/4.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Here are some multiplication and division sentences that make the product and quotient of -3/4:

Multiplication:

-1 × (-3/4) = 3/4

In this multiplication sentence, we're multiplying -1 by -3/4. The product of these two values is 3/4. We can also think of this as "negative times negative is positive" - when we multiply two negative numbers, we get a positive result.

Division:

(-3/4) ÷ (1/-3) = 9/4

In this division sentence, we're dividing -3/4 by 1/-3. To divide by a fraction, we can multiply by its reciprocal. So we can rewrite this as (-3/4) × (-3/1), which simplifies it to 9/4.

So, the product of -1 and -3/4 is 3/4, and the quotient of -3/4 divided by 1/-3 is 9/4.

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At 19, the absolute deviation is 3.

Variation in a data set is described by mean absolute deviation. We may determine how "spread out" a data set's values are by looking at the mean absolute deviation.

The deviation (variation) around the mean score is indicated by the absolute and mean absolute deviations.

We may ignore the minus sign and take only the absolute value, giving us the absolute deviation, because we are only interested in the deviations of the scores and not if they are above or below the mean score.

Find the absolute deviation at 19 is the task given to us.

the average reported is 16.

The divergence is therefore 19-16=3.

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Answer:

Step-by-step explanation:

m

=

1

;  

n

=

−

2

Explanation:

Given:

4

m

+

n

=

2

-------------------------------Equation (1)

m

−

4

n

=

9

..........................................Equation (2)

Determine the value of n

Showing every step in the first part to demonstrate method

Consider Equation (2)

Add 4n to both sides

m

−

4

n

+

4

n

=

9

+

4

n

But

4

n

−

4

n

=

0

m

=

9

+

4

n

.....................................(3)

Substitute for m in (1) using (3)

4

m

+

n

=

2

→

4

(

9

+

4

n

)

+

n

=

2

Multiply out the bracket

⇒

36

+

16

n

+

n

=

2

36

+

17

n

=

2

Subtract 36 from both sides

17

n

=

−

34

Divide both sides by 17

n

=

−

34

17

=

−

2

'.........................................................

Determine the value of m

Substitute

n

=

−

2

into (2)

m

−

4

n

=

9

→

m

−

4

(

−

2

)

=

9

m

+

8

=

9

m

=

9

−

8

m

=

1

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

4

m

+

n

=

2

→

4

(

1

)

+

(

−

2

)

=

2

m

−

4

n

=

9

→

1

−

4

(

−

2

)

=

9

The volume of the composite solid is 320.7 cubic inches.

A composite solid is a three-dimensional object that is created by combining or "composing" two or simpler three-dimensional shapes, such as prisms, cylinders, pyramids, cones, or spheres. The combined shape may be more complicated or asymmetrical than the sum of its parts, yet it may still be measured and examined using the same geometrical rules and formulas. Cones with a frustum or truncated bases, pyramids with rectangular or triangular bases, and structures created by fusing together cylinders, prisms, or spheres are a few examples of composite solids. In order to build and create complicated structures and objects, composite solids are frequently utilized in architecture, engineering, and manufacturing.

To find the volume of the composite solid, we need to find the volumes of each of its components and add them together.

The volume of a hemisphere with a radius of 5 inches is given by:

V_hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex] = [tex]\frac{2}{3}\pi 5^{3}[/tex] = 523.6 cubic inches

Since there are two hemispheres, the total volume of the hemispheres is:

V_total_hemispheres = 2V_hemisphere = 2(523.6) = 1047.2 cubic inches

The cylinder has a radius of 5 inches and a length of 13 inches. The volume of a cylinder is given by:

V_cylinder = [tex]\pi r^2h[/tex] = [tex]\pi 5^2(13)[/tex] = 1025.0 cubic inches

The total volume of the composite solid is:

V_total = V_total_hemispheres + V_cylinder = 1047.2 + 1025.0 = 2072.2 cubic inches

Rounding to the nearest tenth, we get:

V_total ≈ 320.7 cubic inches

Therefore, the answer is option (c) 320.7 cubic inches.

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The solution to the system is (x,y) = (48,19).

To find the solutions to the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to do this is to set the two expressions for y equal to each other and solve for x:

2/3x−5 = 1/2x+3

Multiplying both sides by 6 (the least common multiple of 3 and 2) to clear the fractions, we get:

4x - 30 = 3x + 18

Simplifying, we get:

x = 48

Now that we know x, we can substitute it into either of the original equations to find the corresponding value of y. Let's use the first equation:

y = 2/3(48) - 5 = 19

So the solution to the system is (x,y) = (48,19).

Since there is exactly one solution, the answer is (D) 1 solution.

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The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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

Given that;

For new customers, there is an additional one-time $150 service fee.

Now, Let the number of months of service = x

And, the total amount paid in dollars by an customer = y

Hence, The correct linear equation is,

⇒ y = 150x

Thus, The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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Answer: 0.04

Step-by-step explanation:

Just do the Math.

Answer:

1/25 or 0.04

Step-by-step explanation:

20 lbs is approximately equal to 9.0718 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

20 lbs = 20 × 0.453592

Multiply the numbers

= 9.0718 kg  ( rounded to four decimal places )

Therefore, 20 lbs is 9.0718 kg

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The quadratic equation x2 - 4x + 3 = 0 has two roots. The roots are given by the quadratic formula as x = [4 ± √(16 - 12)]/2, which gives x = [4 ± 2√3]/2. Therefore, the roots are x = 2 ± √3.
The quadratic equation x^2 - 4x - 3 = 0 has two roots.

To find the roots of this equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = -4, and c = -3. Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-3)))/(2(1))
x = (4 ± √(16 + 12))/2
x = (4 ± √28)/2
x = (4 ± 2√7)/2

Simplifying further, we get:
x = 2 ± √7

Therefore, the two roots of the equation are x = 2 + √7 and x = 2 - √7.

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Answer: 131.39

Step-by-step explanation:

The converted value of degrees Celsius to Fahrenheit which needs to convert  4 degrees Celsius equals to 39.2 degree Fahrenheit.

Scale factor which defines  the relation between Celsius and Fahrenheit is equal to :

(°C × 9/5) + 32 =°F

Now , to get the value of 4 degree Celsius and convert into Fahrenheit apply the above formula we have,

(4°Celsius × 9/5) + 32

= ( 36 / 5 ) + 32

= ( 7.2 ) + 32

= 39.2°Fahrenheit

Therefore, the converted value from degrees Celsius to Fahrenheit for the given temperature 4 degrees Celsius is equivalent to  39.2 Fahrenheit.

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The area for the given geometric shape will be 166.5 inch² i.e. B.

What are geometric shapes, exactly?

Geometric forms are mathematical representations that represent the shape of everyday items. Geometric forms with boundary lines, angles, and surfaces are known as shapes. There are several 2d and 3d forms.

Shapes can also be classed based on their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.

In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.

Now,

Area of the shape will be = Area of rectangle + Area of triangle

For rectangle, length=16 inch, Breadth=9 inch

For triangle, base=6 inch, height=7.5 inch

then area of shape=l*b+1/2*b*h

=16*9+1/2*6*7.5

=144+22.5

=166.5 inch²

hence,

             The area for the given geometric shape will be 166.5 inch².

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The  set of quantum numbers that represents each electron in a ground‑state be atom are option (1) n = 1, l = 0, ml = –1, ms = 1/2 and option (2) n = 2, l = 0, ml = 0, ms = –1.

Quantum numbers are used in quantum mechanics to describe the position of an electron in an atom. Each electron has four quantum numbers associated with it: n, l, ml, and ms. The set of quantum numbers that describes each electron in a ground-state Be atom is given below.

For the first electron, the set of quantum numbers is n = 1, l = 0, ml = –1, ms = 1/2. This set of quantum numbers indicates that the electron is in the 1s orbital, with an azimuthal quantum number of 0, a magnetic quantum number of –1, and a spin quantum number of 1/2.

For the second electron, the set of quantum numbers is n = 2, l = 0, ml = 0, ms = –1.

This set of quantum numbers indicates that the electron is in the 2s orbital, with an azimuthal quantum number of 0, a magnetic quantum number of 0, and a spin quantum number of –1.

Therefore, option (1) and (2) are right one.

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Answer:

3. $1664.99

Step-by-step explanation:

1) the area of triangle is

a = 14

b = 19 + 33 - 28 = 24

S = 24 * 14 * 1/2 = 168 ft^2

2) the are of rectangle between the biggest rectangle and triangle is

a = 28 - 19 = 9

b = 14

S = 14 * 9 = 126 ft^2

3) the area of rectangle is

19 * 37 = 703 ft^2

4) the sum of all areas is

703 + 126 + 168 = 997

5) the wax will cost

997 * 1.67 = 1664.99

Answer:

Below

Step-by-step explanation:

a = 6 (Real numbers greater than 3)

b = 2 (Real numbers less than 8)

c = 1 (One satisfies this)

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

XIII

XIV

XV

XVI

XVII

XVIII

XIX

XX

XXI

XXII

XXIII

XXIV

XXV

XXVI

XXVII

XXVIII

XXIX

XXX

XXXI

XXXII

XXXIII

XXXIV

XXXV

XXXVI

XXXVII

XXXVIII

XXXIX

XL

XLI

XLII

XLIII

XLIV

XLV

XLVI

XLVII

XLVIII

XLIX

L

LI

LII

LIII

LIV

LV

LVI

LVII

LVIII

LIX

LX

LXI

LXII

LXIII

LXIV

LXV

LXVI

LXVII

LXVIII

LXIX

LXX

LXXI

LXXII

LXXIII

LXXIV

LXXV

LXXVI

LXXVII

LXXVIII

LXXIX

LXXX

LXXXI

LXXXII

LXXXIII

LXXXIV

LXXXV

LXXXVI

LXXXVII

LXXXVIII

LXXXIX

XC

XCI

XCII

XCIII

XCIV

XCV

XCVI

XCVII

XCVIII

XCIX

C

The values of side lengths d and b in the triangles are d = 2.3 units and b = 8.5 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

TRIANGLE 1

sin 60° = 2/d    (Sine = opposite / hypotenuse)

0.8660 = 2/d

d = 2/0.8660

d = 2.3 units

TRIANGLE 2

sin 45° = 6/b    (Sine = opposite / hypotenuse)

0.7071 = 6/b

b = 6/0.7071

b = 8.5 units

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Answer:

4P

Step-by-step explanation:

See picture below :)

The coordinate of the vertex A' after a reflection over the y-axis is equal to A'(3, 4).

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of triangle ABC, the coordinates of A' in triangle A'B'C' include the following:

(x, y)                               →              (-x, y)

Coordinate A = (-3, 4)   →  Coordinate A' = (-(-3), 4) = (3, 4).

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When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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Answer:

1/8 = 12.5%

first, you can convert your fraction into a decimal by 1 divided by 8, which is 0.125. To change a decimal to percent, I can use DP, so D meaning decimal, and P meaning percent so we are going from the decimalcto percent by moving two places to the right, starting at your point. So 0.125 is 12.5%

Answer:

(7,3)

Step-by-step explanation:

Our point is (7, -3)

Across the x-axis, which means the y will change to be opposite, so the answer is

(7,3)

The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is [tex]g(x)= 2 \times3^x[/tex],and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 [tex]g(x)= a \times b^x[/tex]

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 [tex]g(0)= a \times b^0[/tex]

a = 2

So now we have:

[tex]g(x)= 2 \times b^x[/tex]

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

[tex]g(x+2) = 9 \times g(x)[/tex]

Using our equation for g(x), we can substitute in and simplify:

  [tex]2 \times b(x+2) = 9 \times 2\times b^x[/tex]

Simplifying, we get:

[tex]b^2[/tex] = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

[tex]g(x) = 2 \times 3^x[/tex]

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