A flagpole is 12 feet fall. Its shadow is
11 feet long. How far is it from the top of the flagpole to the end of its shadow?

Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.

To estimate the area under the curve of the function f(x) = x3 between the limits of integration a=0 and b=3, we must divide the interval [0, 3] into three subintervals of equal width.

Each subinterval's width, x, may be calculated as follows:

Δx = (b - a) / n = (3 - 0) / 3 = 1

So, the three subintervals are:

[0, 1], [1, 2], [2, 3]

To compute the right-hand total, we evaluate the function at each subinterval's right endpoint and multiply it by the breadth of the subinterval. Then we add these products together to calculate the area under the curve. The right-hand sum may be stated mathematically as follows:

RH = Δx * [f(1) + f(2) + f(3)]

where x represents the width of each subinterval, f(x) = x3 represents the function we are integrating, and f(i) represents the function's value at the right endpoint of the i-th subinterval.

RH = 1 * [f(1) + f(2) + f(3)]

= 1 * [(1³) + (2³) + (3³)]

= 1 * [1 + 8 + 27]

= 36

Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.

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The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.

The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.

In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.

The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.

The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.

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Answer:

Let's call the unknown number "x". According to the problem, we know that:

x * (x - 6) = 27

Expanding the left side of the equation, we get:

x^2 - 6x = 27

Subtracting 27 from both sides, we get:

x^2 - 6x - 27 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -6, and c = -27, so:

x = (-(-6) ± sqrt((-6)^2 - 4(1)(-27))) / 2(1)

x = (6 ± sqrt(180)) / 2

x = (6 ± 6sqrt(5)) / 2

x = 3 ± 3sqrt(5)

So the two possible solutions are:

x = 3 + 3sqrt(5) ≈ 8.746

x = 3 - 3sqrt(5) ≈ -2.746

Since the problem statement doesn't specify whether the number should be positive or not, both solutions are valid.

Answer: The answer could be 9 or -3.

Step-by-step explanation: The product(multiply) of a number(x) and 6 less than a number(x-6) is 27.

x(x-6)=27

x^2-6x-27=0

(x-9) (x+3)=0

x=9 or x=-3

The number is 9 or -3.

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1".

How to solve the question?

The line of reflection is the line that serves as the mirror for the original polygon such that each point on the original polygon is reflected to a corresponding point on the reflected polygon such that the distance between the line of reflection and each point is the same as the distance between the line of reflection and its reflection.

In this case, we are given two polygons, one original and one reflected. We need to determine the line of reflection that maps each point of the original polygon to its corresponding point on the reflected polygon.

Looking at the two polygons, we can see that the corresponding vertices are equidistant from a line of reflection that passes through the midpoint of the line segment joining V and V prime. Therefore, the line of reflection is the line that passes through the midpoint of the line segment joining V and V prime.

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1". The other options are incorrect because they do not pass through the midpoint of the line segment joining V and V prime and do not produce the corresponding points for the original and reflected polygons.

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A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.

A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.

By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.

Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"

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The rate of water flow is 6 gallons per unit of time.

What is slope?

Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.

a. To find the rate, we need to calculate the amount of water that flows per unit of time.

Method 1: Using the Graph

First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.

From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.

So, the slope of the line is:

slope = change in y-values / change in x-values

     = (60 - 30) / (10 - 5)

     = 6

Therefore, the rate of water flow is 6 gallons per unit of time.

Method 2: Using the Table

We can also find the rate by calculating the differences in y-values and x-values in the table.

x    y   Difference in y   Difference in x   Rate (y/x)

-------------------------------------------------------

5    30        -              -                 -

7    42        12             2                6

10   60       18             3                6

From the table, we can see that the rate of water flow is 6 gallons per unit of time.

b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.

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Answer: 2

Step-by-step explanation:

We can simplify the given logarithmic expression using the logarithmic property that states:

log a base b - log c base b = log (a/c) base b

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

log 16 base 2 - log 4 base 2 = log (16/4) base 2

Simplifying the numerator of the logarithm, we get:

log (16/4) base 2 = log 4 base 2

Now, we can evaluate the logarithm using the definition of logarithm, which states that:

log b base a = x if and only if a = b^x

In this case, we have:

log 4 base 2 = x if and only if 2^x = 4

We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.

Therefore, we have:

log 4 base 2 = 2

Hence, the value of the given logarithmic expression is 2.

Answer:

D. Line O

Step-by-step explanation:

We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.

Therefore, the answer is D.

Therefore, we estimate that there are 2250 Art majors in the total population.

In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.

Here,

We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.

The proportion of Art majors in the sample is:

75/250 = 0.3

We can assume that this proportion is representative of the proportion of Art majors in the population.

So, if x is the total number of Art majors in the population, then we can set up the following proportion:

0.3 = x/7500

To solve for x, we can cross-multiply and simplify:

0.3 * 7500 = x

x = 2250

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Answer:

630

Step-by-step explanation:

v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

The operation we are to carry out is:

Add -4(row 1) to row 3

This essentially means we should multiply the first row (row 1) by -4. Then, we will add each of the elements from the results to the corresponding elements on the third row

Multiplying by -4

-4 × [ 1     2    1   | -5

      -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

    4    -1     6  |  -8

+  -4   -8   -4  | 20

------------------------

    0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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The closest option among the given options is option B: 120 units².

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

The formula for the surface area of a right cylinder is:

SA = 2πr² + 2πrh

where r is the radius and h is the height.

Substituting the given values, we get:

SA = 2π(4)² + 2π(4)(11)

SA = 2π(16) + 2π(44)

SA = 32π + 88π

SA = 120π

Using the approximation π ≈ 3.14, we can calculate the surface area to be:

SA ≈ 120(3.14)

SA ≈ 376.8

Therefore, the closest option among the given options is option B: 120 units².

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The volume of the composite solid is  452. 160 ft³

First, it is important to note that the formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters of the formula are;

From the information given,

substitute the values

Volume = 3.14 × 6² × 12/3

Divide the values

Volume = 31.4 × 36 × 4

Multiply the values

Volume = 452. 160 ft³

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The volume of the gas at the height (i.e 6.5 Km) is 652 mL

The final volume of the gas can be obtained by using the Boyle's law equation as shown below:

[tex]P_1V_1 = P_2V_2[/tex]

[tex]1 \times 326 = 0.5 \times V_2[/tex]

[tex]326 = 0.5 \times V_2[/tex]

Divide both side by 0.5

[tex]V_2 = \dfrac{326}{0.5}[/tex]

[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]

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The answer of the given question based on the graph coordinate is , the rule for the values in the table is: Y = 7X - 0.

In mathematics, a coordinate is a set of values that specifies the position of a point in space. Coordinates are used to locate points, lines, and other geometric objects in a plane, a three-dimensional space, or even higher dimensions.

X    Y

5    35

1     7

4    28

2    14

One possible way to do this is to calculate the differences between successive pairs of X and Y values, and then see if there is a constant difference or ratio between them.

Taking the first two rows as an example, we have:

X Y

5 35

1 7

The difference between the X values is 5 - 1 = 4, and the difference between the Y values is 35 - 7 = 28. Dividing the difference in Y by the difference in X gives us:

(35 - 7) / (5 - 1) = 28 / 4 = 7

This means that for every increase of 1 in X, the corresponding increase in Y is 7. We can check this for the other pairs of values in the table and see that it holds true:

X Y

5 35

4 28 (decrease of 1 in X, decrease of 7 in Y)

2 14 (decrease of 2 in X, decrease of 14 in Y)

So the rule for the values in the table is:

Y = 7X - 0.

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Answer:

64π

Step-by-step explanation:

Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.

The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.

Mathematically, the area of a circle can be calculated by using this formula:

[tex]\text{Area} = \pi \text{r}^2[/tex]

Where:

[tex]\text{r}[/tex] represents the radius of a circle.

[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]

By substituting the radius into the formula for the area of a circle, we have the following;

[tex]\text{Area of circle} = \pi \times 8^2[/tex]

[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.

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On solving the provided question we can say that area of the polygon is 24 cm sq.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Area of this polygon is -

A = 1/2 * 6* 8

A = 24 cm sq.

Hence, area of the polygon is 24 cm sq.

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The value after solving mixed fraction is 32/10=3.2

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.

according to question,

=51/10 - 19/10

=32/10

=3.2

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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.

To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.

5 1/10 can be converted to an improper fraction as follows:

5 1/10 = (5 x 10 + 1)/10 = 51/10

1 9/10 can be converted to an improper fraction as follows:

1 9/10 = (1 x 10 + 9)/10 = 19/10

Now we can subtract the two fractions:

51/10 - 19/10 = (51 - 19)/10 = 32/10

32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.

So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

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The  polynomial with integer coefficients and a leading coefficient of 1  is (x-6) (x-3)²  which in turn will be: f(x) = x³ - 12x² + 45x - 54

Based on the question, If the zeros of a polynomial are said to be 6, 3, and 3, one can say that the polynomial can be written in factored form such as

f(x) = (x - 6)(x - 3)(x - 3)

The to solve this, we have to multiply it:

f(x) = (x - 6) (x² - 6x + 9)

f(x) = x³ - 6x² + 9x - 6x² + 36x - 54

f(x) = x³ - 12x² + 45x - 54

Therefore, the polynomial with integer coefficients and a leading coefficient of 1  will be f(x) = x³ - 12x² + 45x - 54

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Answer:

The distance between (3, 4.1) and (3, 1.2) is approximately 2.9 units.

Step-by-step explanation:

You're welcome.

The lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

Let's call the length of the median from vertex J to the opposite side LM, and the length of the median from vertex L to the opposite side JN. We can use the fact that the centroid divides each median into two parts, with the ratio of the longer part to the shorter part being 2:1.

First, we can find LM:

LM = 2 x QM = 2 x 10 = 20

Next, we can find JQ:

JQ = 2/3 x JN = 2/3 x 39 = 26

Finally, we can find KQ:

To find KQ, we need to use the fact that the three medians of a triangle divide each other into six smaller triangles with equal areas. Let's call the length of the third median KX. We know that the area of triangle JLK is:

1/2 x LM x JN = 1/2 x 20 x 39 = 390

Similarly, the areas of triangles JNQ, LMQ, JKP, LKP, and JLP are all equal to 390. Let's call this common area A. Then we have:

1/2 x KX x LM = A

1/2 x KX x JN = A

Dividing these two equations, we get:

LM / JN = KX / LM

Substituting the values we know, we get:

20 / 39 = KX / 20

Solving for KX, we get:

KX = 20 x (20 / 39) = 400 / 39

Now we can find KQ:

KQ = 2/3 x KX = 2/3 x (400 / 39) = 800 / 117

Therefore, the lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

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Answer:

53

Step-by-step explanation:

angle 2 and 3, angle 3 and 4 are both supplementary angle, which means a2+a3=180 degree, a3+a4=180 degree.

Since you know that the angle 2 and 4 are both 29 degree,

you can write

a3+29=180, and a3 is represented as 3x-8

so

(3x-8)+29=180 (<-- answer for b)

3x+21=180

3x+21-21=180-21

3x=159

x=53

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

Answer:

216 mi^3

Step-by-step explanation:

First of all you need to find the area of the base (or top, they are the same)

It is a right-angled triangle, you can simply calculate the area of the base by

A = 6*8/2 = 24 mi^2

The volume of prism is (base area)*height

volume = 24*9 = 216 mi^3

10 is redundant anyway

Answer: the volume of the prism is 62.35 mi cube

Step-by-step explanation:

so first we will find the area of triangular base of the prism, using heron formula.

and s(semi-perimeter)= a+b+c/2= 6+8+10/2= 24/2=12

Area of triangle= A = sqrt [s(s-a)(s-b)(s-c)] = sqrt {12*(12-6)(12-8)(12-10)} = sqrt {6*4*2} = sqrt (48)= 6.92 mi square

Volume = Area x Height

V= 6.92 x 9 = 62.35 mi cube.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]

the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

How to solve the question?

To determine the scale factor used in the dilation of triangle D to create triangle D', we need to compare the corresponding sides of both triangles. The corresponding sides of two similar triangles are proportional, meaning that they have the same ratio.

In this case, we can see that the length of every side of triangle D' is one-third the length of the corresponding side of triangle D. For example, the length of the shortest side of triangle D is 18, while the length of the shortest side of triangle D' is 6. Similarly, the length of the longest side of triangle D is 30, while the length of the longest side of triangle D' is 10.

We can use this information to find the scale factor by dividing the length of any side of triangle D' by the length of the corresponding side of triangle D. Let's choose the shortest side for this calculation:

scale factor = length of corresponding side in D' / length of corresponding side in D

scale factor = 6 / 18

scale factor = 1/3

Therefore, the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.

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The value of angle B and C are 63° and 61° respectively.

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore;

32/sin56 = 34/sinC

32sinC = 34sin56

32sinC = 28.187

divide both sides by 32

sinC = 28.187/32

sinC = 0.88

C = sin^-1(0.88)

C = 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore, B = 180-(61+56)

B = 180-(117)

B = 63°

therefore the value of angle B and C are 63° and 61°.

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Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.

Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.

Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.

Step-by-step explanation: