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The data shows mean concentrations (mg/l) of pollutants in rainwater leaving either green or conventional roofs. Correct Option is: (D)The Total Volume of Rainfall is needed to calculate the total amount of a pollutant leaving the roof during and following a rainstorm.

Volume:

Precipitation intensity is the water depth (mm) recorded during a shower divided by the duration of the shower (hours).

Expresses water depth per hour in millimeters (mm/hour).

[tex]rainfall intensity = total amount of rainwater(mm)/ duration of the rainfall (hours)[/tex]

A volume is a measure of three-dimensional space. Often quantified numerically using SI units (such as cubic meters and liters) or using various imperial or US customary units (such as gallons, quarts, and cubic inches). The definition of length (cube) relates to volume. Container volume is generally understood to mean the capacity of the container. That is, the amount of liquid (gas or liquid) that the container can hold, not the amount of space that the container itself moves.

In ancient times, volume was measured using similarly shaped natural vessels and later standardized vessels. The volume of some simple 3D shapes can be easily calculated using arithmetic formulas. The volume of more complex shapes can be calculated using integral calculations if there is an equation that constrains the shape. Zero, one, and two dimensional objects have no volume. In four dimensions and above, a concept analogous to ordinary volumes is a hypervolume.

Volume of Rainfall:

The Average Rainfall = Depth x Radius x Radius x 3.14. The area at the top of the bucket (this is the area where rain is collected). Dividing the precipitation by this area will give you the precipitation.

Complete Question:

The data in the table show mean concentrations (mg/L)(mg/L) of pollutants in rainwater leaving either green or conventional roofs. Which of the following data would be needed to calculate the total amount of a pollutant leaving the roof during and following a rainstorm?

A) Distance from street level to roof

B) Duration of the rain event

C) Total number of plants on the roof

D) Total volume of rainfall

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The probability you'll see one over half an hour is 0.26

The term probability in math is defined as  the possibility of the outcome of any random event

Here we have given that the probability you'll see a falling star in the sky over the course of one hour is 0.44.

Then in an hour can be taken as two half hours so we can write the probability to see a falling star as

Then it can be written as,

=> (1-P)*(1-P) = 1 - 0.44

When we simplify this one then we get

=> (1 - P)² = 0.56

Here we need to value of p then it can be written as,

=> 1 - P = √0.56

Then the value of P is calculated as,

=> -P = 0.74 - 1

=> P = 0.26

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The value x-coordinates which is required is found out to be as Q = -19.41 and +19.41.

The given values are,

radius , r = 35 feet

speed of ball = 11 ft./sec

location of the cup =  (0, 0)

starting location the ball = (-40. -50)

In order to find the possible x-coordinates of Q,

The coordinates of the rightmost edge of the golf course = (35, 0)

slope = m = ( y2 - y1)/ ( x2 - x1)

now , the equation for a circle is known as , (x - h)² + (y - k)² = r²

and the center of the course is given as ,  (h, k) = (0, 0)

Therefore the equation becomes (x - 0)² + (y - 0)² = x² + y² = 35²

equation of tangent , y = -3x/2

putting this value in the tangent = x² + ( -3x/2 )²  = 35²

13x² /4 = 35²

x = √ ( 35²  x 4 )/ 4 = 35²

x = 70/13√ 13 = 19.41

Therefore, the  coordinates of Q are found out to be as  -19.41 and +19.41

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The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Hence, The angle is 45 degrees between the trajectories the ball takes before and after hitting the rail.

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The volume of the composite solid, given the dimensions for the cylinder and cone, is D. 1, 099 cm ³

First, find the volume of the cone which can be found by the formula:

= π x radius ² x ( height / 3 )

Height = 3 inches

Radius = 3 inches

The volume is:

= π x radius ² x ( height / 3 )

= π x 3 ² x ( 2.5 / 3 )

= 28.27 inches ³

The volume of the cylinder is :
= π x radius ² x  height

= π x 3² x 2. 5

= 70. 69 inch ³

The volume of the composite solid is:

= 28. 27 + 70. 69

= 98.96 inch³

In cm³, this is:

= 98. 96 x 16.3871

= 1, 099 cm ³

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Answer: 84

Step-by-step explanation:

9^2+2*4-5

Let's solve according to PEMDAS and calculate the exponent first.

That leaves us with

81+2*4-5

Next, it's time to multiply.

81+8-5

From then on, we can just add and subtract to get the final answer:

84

Answer:

To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.

Food: 20% of $25,000 = $25,000 x 0.20 = $5000

Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250

Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750

So the family has $5000 for food, $6250 for shelter and $3750 for clothing.

The hikers will be 8 miles apart after 2 hours of hiking.

The formula used to calculate the distance apart is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two hikers, and the other two sides are the distances each hiker has traveled in the two directions: 3 miles to the west, and 4 miles to the north. The formula is written as a^2 + b^2 = c^2, where a and b represent the side lengths, and c represents the hypotenuse. Plugging in the values, 3^2 + 4^2 = c^2, or 9 + 16 = c^2. Solving for c, c^2 = 25, so c = 5. Therefore, the distance between the two hikers is 5 miles after two hours of hiking.

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Answer:

w

Step-by-step explanation:

Answer: 16 Teaspoons

Hope this helps! :)

Step-by-step explanation:

1 Tablespoon= 3 Teaspoons

6 Tablespoons= (6*3) 18 Teaspoons

18 - 2= 16 tsp

Answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15

These problems are really brute force, there is no real clever way. I only just listed all possible combinations

HOWEVER, notice in answer.

5 1 9

5 2 8

5 3 7

5 4 6

Since ALL the sets contain a 5, we just subtract 5 from 15.

So we need TWO terms in a set and they add up to 10, and also are unique.

This is quite easy.

1 9

2 8

3 7

4 6

5 5 (does not work because cannot repeat digit)

thus , answer is 4 of these sets contain a 5 in sets of three different numbers whose sum is 15

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A graph will be drawn where a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Types of Graphs and Charts

Statistical Graphs (bar graph, pie graph, line graph, etc.)

Exponential Graphs.

Logarithmic Graphs.

Trigonometric Graphs.

Frequency Distribution Graph.

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The maximum is N*(N-1)/2 and the minimum is N-1 if there are N vertices.

Proof:

Consider an adjacency matrix where each entry is either 1 (to denote the presence of an edge) or 0 (to indicate the absence of an edge) (to indicate the absence of an edge). Each row of the upper triangle must have at least one "1" in order for a graph to be connected.

By merely placing one 1 in each row of the upper triangle, the minimum is reached. Now, if the adjacency matrix is N by N, the first row will have N-1 elements in the upper triangle, the second row will have N-2 elements, the third row will have N, the fourth row will have N, and so on until the last row will have 0 items. Consequently, there are N total rows  "with an upper triangle", each with only one 1. Hence, the number of edges in N-1.

The maximum occurs if every element of the upper triangle has one. Now, the number of elements in the upper triangle of the whole matrix is

1 + 2 + ... + (N-2) + (N-1) = N*(N-1)/2.

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In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

Let

x -----> the number of minutes in a month

y ----> the charge  monthly

we know that

First Plan

y= 0.23 x ----> equation A

Second Plan

y= 0.12x+34.95 ----> equation B

Equate the equations A and B and solve for x

so x= 249.6

For x< 249.6  ----> is preferable the first plan

For  x> 249.6 ----> is preferable the second plan

therefore

In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

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Answer: 5

Step-by-step explanation:

We are looking for the number of years below the 25th percentile, which is given by the first quartile.

Since the first quartile is 5, we know that about 25% of Carlson High School teachers have fewer than 5 years of experience.

It is not possible to construct a triangle with 2cm, 3cm, and 7cm.

The sides measure 2 cm, 3 cm, and 7 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

2 + 3 > 7        Not true

2 + 7 > 3        True

3 + 7 > 2        True

As 2 + 3 > 7 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 2cm, 3cm, and 7cm in length.

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The value of x, considering the area of the rectangular regions, is given as follows:

x = 12.

The area of a rectangle is given by the multiplication of the two dimensions of the rectangle.

The area of the shaded region is obtained subtracting the area of the entire rectangle by the area of the inner white rectangle.

The area of the entire rectangle is given as follows:

(x + 8)(x + 5) = x² + 13x + 40.

The area of the white region is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the area of the shaded region is given as follows:

x² + 13x + 40 - (x² - x - 6)

x² + 13x + 40 - x² + x + 6

14x + 46.

As the area of the shaded region is of 214 units squared, the value of x is obtained as follows:

14x + 46 = 214

14x = 168

x = 168/14

x = 12.

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The correct statements are given below.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of two functions plotting distance vs time of two Alberto and Bianca

1) Early in the race Alberto runs faster.

2) Alberto maintains a contain speed of 20 km/hr

3) Meanwhile Bianca's Speed is 8.33 km/hr

4) The first person to cross the finish line is Bianca.

Hence, Bianca reached the finished line before Alberto.

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The given system of equation has no solution.

What is elimination method?

The elimination method is a way to get rid of one of the variables in a system of linear equations by using multiplication or division of the variable coefficients along with addition or subtraction of the variables and their coefficients.

Substitution, elimination, and augmented matrices are the three approaches that are most frequently used to solve equation systems.

Consider, the given system of equations

7x - 12y = -3       ..(1)

-7x + 12y = 2      ..(2)

Adding equation (1) and (2).

       7x - 12y = -3

 +   -7x + 12y = 2

___________________

                0 = -1

0 = -1 is false.

Hence, the given system of equation has no solution.

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The first piece is 7.2 feet long, and the second piece is 12- 7.2 = 4.8 feet long.

The ratio of the two pieces is 3 to 2. This means that the length of the first piece is 3/5 of the total length, and the length of the second piece is 2/5 of the total length.

If we let x be the length of the first piece, the length of the second piece is:

12 - x

Since the ratio of the two pieces is 3 to 2, we can set up the equation:

(3/5) * 12 = x

Solving for x:

x = 7.2

So, the first piece is 7.2 feet long, and the second piece is 12- 7.2 = 4.8 feet long

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The measure of the value of corresponding angle is found as : ∠BFG = 76.

For the given question:

Given values:

∠BCD = ∠BFG (Corresponding angles)

x + 26 = 2x - 24

2x - x = 26 + 24

x = 50

Then,

∠BFG = 2*50 - 24

∠BFG = 100 - 24

∠BFG = 76

Thus, the measure of the value of corresponding angle is found as : ∠BFG = 76.

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the complete question is-

Hint: Find the value of x first, then substitute the answer into 2x - 24.

The measure of angle BFG is ___.

∠BCD = x + 26

∠BFG = 2x - 24

The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

4, 5, 6, 7, ....

The first term is 4 and the common difference is given as,

d = 5 - 4

d = 1

Then the formula is given as,

aₙ = 4 + (n - 1) × 1

aₙ = 4 + n - 1

aₙ = n + 3

The formula describes the sequence will be aₙ = n + 3. Then the correct option is 3.

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The best equation that approximates the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex] .

Given:

Probability of children who live in households with incomes that are classified at a particular income level,p = 22/100 = 0.22

Number of children in a simple random sample,n = 300

Probability of children who do not live in households with incomes that are classified at a particular income level, q = 1-p = 0.78

The probability of children in the sample living in households that are classified at a particular income level,p₁ = 27/100 = 0.27

Now, we know

[tex]p(z > \frac{p_{1} -p}{\frac{\sqrt{p.q} }{n} } )[/tex]

So,

[tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex]

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The area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.

What is area and perimeter?

The area of a shape or figure is its area, whereas the perimeter of a shape is its outer boundary over a given distance. Area is measured in square units or unit2 while perimeter is measured in the same unit.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter.

Radius, r = 8 cm

Perimeter of a circle = 2πr

Perimeter of s quarter circle = 2πr/4 = 1/2πr

Perimeter of Shaded part = 1/2 * 2πr

                                          = 1/2 × 2 × π × 8

                                          = 8πcm.

Area of a circle = 2πr²

Area of quarter circle = 2πr²/4 = 1/2πr²

Area of a square = length ²

Area of Shaded part = Area of Quarter-circle - Area of Square

                                  = 0.5π(8)² - 8²

                                   = 0.5π(64) - 64

Area of Shaded part  = 36.53 cm^2

Hence, the area of the shaded region is 36.53 cm^2 and the perimeter of the shaded region is 8π cm.

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The difference between Georgina's total stock earnings and her real return is $119.70. he difference between Georgina's total stock earnings and her real return is $119.70.

What is the difference?

The term "difference" refers to the amount by which one quantity is greater or less than another.

The difference between Georgina's total stock earnings and her real return can be calculated as follows:

Difference = Total stock earnings - Real return

Difference = $395.50 - $275.80

Difference = $119.70

Hence, the difference between Georgina's total stock earnings and her real return is $119.70.

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The greatest possible weight of the large bag is 1.9n ounces.

Given:

Weight of 10 apples = n ounces

Weight of 1 apple = n/10 ounces

Weight of n apples = n²/10 ounces

It is given that a large bag of n of these apples weighs less than 40 ounces,

= n²/10 < 40

= n²< 400

= n < 20

So, the large bag contains at most 19 apples.

Hence, the weight of the large bag is at most 1.9n ounces, or (19/10)(n) ounces.

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Answer:

C. Use a compass and draw an arc across both the legs of the given angle.

Step-by-step explanation:

The interval that contains the median water bill is D: $200 - $225.

The data in tabular form is as follows: ata  :

Class interval ------- Frequency -------- Cummulative frequency

100 to 125, ----------- 1 --------------------1

125 to 150 -----------2--------------------3

150 to 175----------- 5 --------------------8

175 to 200----------- 10 ------------------18

200 to 225-----------13------------------ 31

225 to 250 ------------8 -----------------40

Median class = Cumulative frequency / 2

Cumulative frequency= 40

So

Median class = 40 / 2

Median class = 20

The class interval containing the 20th frequency is "200 - 225"

Therefore it is concluded that the interval which contains the median water bill is $200 - $225.

"

Complete question

A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.

Which interval contains the median water bill?

$150–$175

$175–$200

$200–$225

$225–$250

"

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The required converted number is 46.10 which is 46.1031 rounded to four significant figures.

Place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, using your place values, such as tens and hundreds.

To convert 46.1031 to four significant figures, we must first identify the four most significant digits. In this case, the four most significant digits are 46.10.

To express 46.1031 in four significant figures, we round it to 46.10.

Therefore, 46.1031 rounded to four significant figures is 46.10.

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