this homework is due now!!!!!

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 is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

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.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

Significant digits, also known as significant figures, refer to the digits in a quantity that are considered to be reliable and meaningful based on the precision of the measurement.

The significant digits in a given quantity include all the digits that are known with certainty, as well as one uncertain digit that is estimated based on the measurement's precision.

For example, if the length of a table is 1.23 metres, the digits "1," "2," and "3" are all significant, whereas the digit "0" is not significant because it is just a placeholder.

The number of significant digits in a number is determined by the measurement instrument or method used.

For example, if you use a centimeter-marked ruler to measure the length of a table, you can estimate the length to the nearest millimetre, implying that the last digit is uncertain and estimated. Because you have three certain digits and one estimated digit, the number of significant digits in this case is three.

When performing mathematical operations on numbers with varying numbers of significant digits, the result should be rounded to the same number of significant digits as the least precise measurement. This is necessary to maintain the calculation's accuracy and precision.

Understanding significant digits is essential for precise scientific measurements and calculations. It can aid in the prevention of errors and the production of reliable and meaningful results.

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Answer:

Step-by-step explanation:

You want the measures of angles d° and e° in the given figure.

Usually, geometry problems tell you not to assume anything that isn't marked or stated regarding the figure. In order to answer this question, we need to assume ...

The base angles in an isosceles triangle are congruent. That means each of them is the complement of half the vertex angle.

  ∠D = 90° -1/2∠A = 90° -8°/2 = 86°

The segments CD and BE are parallel, so angle E is the supplement of angle D:

  ∠E = 180° -86° = 94°

The angle measures are d° = 86° and e° = 94°.

__

Additional comment

This is not a "word problem." All of the relations necessary for answering the question are shown in the diagram, not stated in words. (The question is necessarily written in words—for any problem.)

If b is a base angle and v is the vertex angle of an isosceles triangle, then the sum of angles is ...

  b + b + v = 180°

  2b = 180° -v . . . . . . subtract v

  b = 90° -v/2 . . . . . . divide by 2

Effectively, the altitude of an isosceles triangle bisects the vertex angle and creates two congruent right triangles. The acute angles in that triangle are the original base angle and half the vertex angle. They are complementary.

To convert any number of meters to miles, you simply need to multiply the number of meters by this conversion factor 0.000621371192

The conversion factor from meter to miles is  0.000621371192

1 meter = 0.000621371192 miles

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

So, to convert meter to miles you can multiply the number of kilometers by 0.000621371192

The distance in miles = conversion factor × The distance in meters

Therefore, the steps to convert meter to miles has been explained

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The average rate of change over the interval [9,10] is greater by 6490.

The average rate of change of a polynomial is the slope of the function.

The average rate of change over the interval [7, 9] is the slope between  ( 7, f(7) )  and  ( 9, f(9) )

where f(7) and f(9) is the value of the function at 7 and 9.

So, the slope between  ( 7, 1852 )  and  ( 9, 3878 )

= (3878-1852)/(9-7)

= 2026/2

= 1013

Similarly,

The average rate of change over the interval [4, 6]

i.e. slope between  ( 4, f(4) )  and  ( 6, f(6) )

So, the slope between  ( 4, 358 )  and  ( 6, 1178 )

= (1178-358)/(6-4)

= 820/2

= 410

and

1013-410 = 603

So, the polynomial is 603 greater than the average rate of change over the interval [7, 9] than the interval ​ [4, 6]

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The maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.

What is sphere ?

A sphere is a three-dimensional shape that is perfectly round, with all points on the surface at an equal distance from the center.

The formula for the volume of a sphere is given by V = (4/3)πr³, where r is the radius of the sphere.

The maximum error in the measurement of the radius is given as 0.03 cm. Therefore, the actual radius of the sphere can be anywhere between 20.97 cm (21 - 0.03) and 21.03 cm (21 + 0.03).

To find the maximum error in using this value of the radius to compute the volume of the sphere, we need to find the maximum possible difference in the volumes calculated using these two values.

So, we can calculate the volume of the sphere using the maximum and minimum values of the radius as follows:

V_max = (4/3)π(21.03)³

V_min = (4/3)π(20.97)³

Now, we can find the difference between these two values to get the maximum possible error:

Max error = V_max - V_min

Max error = (4/3)π(21.03)³ - (4/3)π(20.97)³

Max error ≈ 554.86 cubic centimeters

Therefore, the maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.

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Answer:

0.0651

Step-by-step explanation:

To find 21% of 0.31, we can use the following formula:

21% × 0.31

We can convert the percentage to a decimal by dividing by 100:

0.21 × 0.31

Multiplying these two numbers, we get:

0.0651

Therefore, 21% of 0.31 is 0.0651.

Due to the exponential growth of bacteria it only took 10 minutes to fill 3 additional empty bottles.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes.

Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

The answer needed is -

The full bottle doubled after 5 minutes.

The 2 full bottles doubled after 5 minutes.

Exponential growth is a multiplicative rate of change.

Therefore, due to exponential growth bacteria filled the bottle fast.

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Answer:

The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

The correct answer is:

greater than zero for all values of x.

Probability is a way of evaluating how likely something is to happen. Several 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, with 0 denoting an impossibility and 1 denoting a certainty.  One is the probability of every event in a sample space.

Now in the given question ,

A probability density function (PDF) of a continuous random variable x is a function that describes the relative likelihood of x taking on different values in a continuous range. The PDF is defined such that the area under the curve between any two values a and b represents the probability of x being in that range, i.e., P(a ≤ x ≤ b).

Since probabilities are non-negative, the PDF of a continuous random variable must also be non-negative. That is, f(x) > 0 for all values of x. This condition ensures that the area under the curve is non-negative, which is necessary for it to represent a valid probability distribution.

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Answer:

Step-by-step explanation:

(1)To write this in standard form, we want the x and y terms on the same side of the equation and the constant on the other side. To do this, we can subtract 3x from both sides:

-3x + y = 1

So the standard form of the equation is:

-3x + y = 1

(2)y = -9/5x + 3

To write this in standard form, we want to eliminate the fraction by multiplying both sides by the denominator (5):

5y = -9x + 15

Next, we can move the x term to the left side by adding 9x to both sides:

9x + 5y = 15

So the standard form of the equation is:

9x + 5y = 15

The standard error of mean is a technique for calculating the sampling distribution's standard deviation.

A technique for assessing the standard deviation of a sampling distribution is standard error of the mean. The acronym SEM stands for standard error of the mean, which is another name for it. For instance, in a sample space, the sample mean is often the projected population mean value. But, if we choose another sample from the same population, the result can be different.

As a result, a population of the sampled means with unique variance and means will emerge. The standard deviation of such a sample mean, which includes all feasible samples taken from the same specified population, could be referred to as the standard error of mean. SEM is an approximation of standard deviation that was determined from the sample.

The standard error of the mean (SEM) demonstrates how the mean changes when the same quantity is evaluated in various tests. Consequently, the SEM will be higher if the outcome of random fluctuations is crucial. Yet if repeated attempts fail to reveal any change in the data points, the standard error of the mean will be equal to zero.

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The angle of elevation from the stake up to the tent pole is, 54.55°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.

Also, The state is 11 feet away and it is the adjacent length.

We know, cos = adjacent/hypotenuse.

cos = 11/19.

Ф = cos⁻¹(0.58).

Ф = 54.55°.

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Answer:

1) What are your options?

2) 847,200

3) 6.7 × 10^5

Step-by-step explanation: You always move the decimal until you get to the first digit after zeroes and then x 10 and the power is how many times it took to place the decimal in front of the number.

The +equation represents exponential growth

What is the exponential functions?

An exponential function is a mathematical function that has the form f(x) = a*b^x, where a and b are constants, and x is the independent variable.

The equation y = 80(1.3)^x represents exponential growth.

In this equation, "y" represents the value of the function at a given time or input, "x" represents the time or input, and "1.3" is the growth factor, which is greater than 1.

As "x" increases, the value of the function "y" grows at an increasing rate. This is because the growth factor is greater than 1, which means that each input value results in a larger output value than the previous one.

Hence, this equation represents exponential growth.

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Answer:

The rate of change between (-2/3, -4) and (-3, 4) is:

(change in y) / (change in x) = (4 - (-4)) / (-3 - (-2/3))

= 8 / (-2/3)

= -12

Therefore, the rate of change is -12.

Step-by-step explanation:

=]

False, every component of the matrix is multiplied by the same amount when you multiply a matrix by a number. A new matrix is created by this operation; it is known as a scalar multiple.

A rectangular matrix is a grouping of numbers in rows and columns. A matrix element/entry is the term used to describe each number in the matrix. The combination of a real number and a matrix is referred to as scalar multiplication.

Each entry/element of the matrix is multiplied by the specified scalar in scalar multiplication. Comparatively, matrix multiplication describes the result of two matrices. This operation is totally different. We can't just multiply the corresponding entries in two matrices to multiply them.

The first matrix must have exactly as many columns as the second matrix has rows in order to perform matrix multiplication. The resulting matrix has the same number of columns and rows as the second matrix, and its number of columns matches the number of rows in the first matrix.

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The 95 % conversion in decimal is 0.95.

To convert a percentage to a decimal, you divide the percentage by 100.

Therefore, to convert 95% to a decimal, you divide 95 by 100:

95 ÷ 100 = 0.95

So, 95% as a decimal is 0.95.

A percentage is a fraction expressed as a fraction of 100 in mathematics. It is frequently used to express percentages, rates, or frequencies in terms of 100. For example, if 95 out of 100 people agree on something, we can express this as a 95% probability.

To convert a percentage to a decimal, simply divide it by 100. The outcome is a number between 0 and 1, with 1 representing the entire (or 100%). In the case of 95%, dividing by 100 yields 0.95 as the decimal equivalent.

Simply multiply a decimal by 100 to convert it to a percentage. To convert 0.95 to a percentage, multiply it by 100 to get:

0.95 x 100 = 95%

As a result, percentages and decimals are two different ways of representing the same value. While percentages are frequently used to express proportions or rates, decimals are frequently used in mathematical computations or scientific notation.

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The sum of the first 10 terms of the sequence -5, 15, 45, 135 is 295240.

We can use the following formula to determine the sum of a geometric sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

where an is the first term, r is the common ratio, and n is the total number of terms, S is the sum of the sequence.

We can see that the first term in the series -5, 15, 45, 135 is -5, and the common ratio is 3. (since each term is obtained by multiplying the previous term by 3). The series contains 4 terms, hence n is equal to 4. Adding these values to the formula yields the following results:

S = -5(1 - 3^4) / (1 - 3) (1 - 3)

S = -5(1 - 81) / (-2) (-2)

S = 5(80) (80)

S = 400

The total of the numbers 5, 15, 45, and 135 equals 400.

We may once more use the following formula to determine the sum of the first 10 entries in the same sequence:

S = a(1 - r^n) / (1 - r) (1 - r)

Instead, we will use a = -5, r = 3, and n = 10 this time. By replacing these values, we obtain:

S = -5(1 - 3^10) / (1 - 3) (1 - 3)

S = -5(1 - 59049) / (-2) (-2)

S = 5(59048) (59048)

S = 295240

The result is 295240 for the first 10 terms in the series, which are -5, 15, 45, and 135.

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Answer:

h = 12 feet

Step-by-step explanation:

using the right triangle shown in the diagram.

the base of the triangle is half the measure of the base of the square side.

then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 16² = 20²

h² + 256 = 400 ( subtract 256 from both sides )

h² = 144 ( take square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12

the height h of the pyramid is 12 feet

Linear transformation of a matrix is discussed below.

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Given is to discuss the linear transformation of a matrix.

Therefore, linear transformation of a matrix is discussed above.

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The equation of the line perpendicular to y = -4x + 4 that contains the point (5, -1) is y = 1/4x - 9/4.

The given equation is y = -4x + 4, which is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the given line, we can compare it to the slope-intercept form and see that the slope is -4.

Since we want to find the equation of a line that is perpendicular to the given line, we know that its slope will be the negative reciprocal of -4.

The negative reciprocal of -4 is 1/4, so the slope of the perpendicular line is 1/4.

Now we have the slope of the line and a point that it passes through, so we can use the point-slope form of a line to write the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope we just found.

Plugging in the values, we get:

y - (-1) = 1/4(x - 5)

Simplifying this equation, we get:

y + 1 = 1/4x - 5/4

Subtracting 1 from both sides, we get the final equation:

y = 1/4x - 9/4

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Answer:

35.112

Step-by-step explanation:

15.4% = 0.154. 228*0.154=35.112.

Answer:

The area is one side times the other side

Make the other side x.

12x=42

x=42/12=3.5

The perimeter is 2x+2y where x and y are sides of the rectangle.

P= 2(3.5)+2(12)=7+24=31 inches

Hope this helps.

Answer: 3.5

Step-by-step explanation:

42/12 = 3.5

Answer:

It would be zero

Step-by-step explanation:

Step-by-step explanation:

all pairs of corresponding sides have the same scale factor.

so, we only need to find one to know it for all.

a)

we know 2 corresponding sides : 6 and 12.

that means

12 × s = 6

s = 6/12 = 1/2

b)

x = 5 × s = 5 × 1/2 = 2.5 = 2 1/2

y = 13 × s = 13 × 1/2 = 6.5 = 6 1/2

c)

to be right-angled triangles they need to fulfill the Pythagoras criteria :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle).

a and b are the legs.

so, for the larger triangle we have

13² = 12² + 5²

169 = 144 + 25 = 169

correct. it is right-angled.

for the smaller triangle :

6.5² = 6² + 2.5²

42.25 = 36 + 6.25 = 42.25

as expected : also correct. so, yes, they are both right-angled.

Answer:

the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.

Step-by-step explanation:

Let x be the measure of the angle we are trying to find.

By definition of supplementary angles, we know that the angle's supplementary angle measures 180° - x.

We are also given that the angle measures 120.2° less than its supplementary angle. This can be written as:

x = (180° - x) - 120.2°

Simplifying the equation, we get:

x = 59.9°

Therefore, the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.

Step-by-step explanation:

yes, they are, because both triangles have the same 3 angles :

the right angle = 90°

65°

25°

now, the side lengths can be different, but because of the same angles, the ratio between the corresponding side lengths will be the same for all sides (e.g. if one pair of sides has the scaling factor of 3 from the smaller to the larger triangle, then the other pairs will also have the same scaling factor 3).

that is the difference between equivalent and similar : for "equivalent" also the side lengths must be the same.

for "similar" only the angles need to be the same.

The value of x is given as follows:

x = 9.

Similar triangles are triangles that share these two features presented as follows:

Similar triangles have congruent angle measures, and the angles of 3x + 15º and 42º are congruent, hence the value of x is obtained as follows:

3x + 15 = 42

3x = 27

x = 9.

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The conversion of 720 minutes to hours is equal to 12 hours.

The units involved in this conversion are minutes and hours.The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. An hour (symbol: h; also abbreviated hr.) is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions.The conversion factor from minutes to hours is 0.0166667, which means that 1 minutes is equal to 0.0166667 hours:1 min = 0.0166667 hr, There are 60 minutes in one hour. To convert 720 minutes to hours, you can divide 720 by 60:

720 minutes ÷ 60 minutes/hour = 12 hours

So, 720 minutes is equal to 12 hours.

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Answer:

y - 12 = -5(x + 2)

Step-by-step explanation: