The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.
Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.
Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.
Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.
For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.
Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.
To know more about chemical properties click on below link:
https://brainly.com/question/1728902#
#SPJ11
Please help
What is the value of x?
Enter your answer in the box.
X =
F
E
L
24
25
1
2 3 4 5
x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.
Give a brief account on Pythagoras theorem.The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².
It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.
Given,
DF = 24
DE = 25
Using Pythagoras theorem:
Hypotenuse² = Base² + Perpendicular²
25² = x² + 24²
x² = 25² - 24²
x² = 625 - 576
x² = 49
x = √49
x = 7
To know more about Pythagoras theorem, visit:
https://brainly.com/question/343682
#SPJ1
IXL
An equilateral triangle with center C is shown below.
(HELP!!)
The area of the equilateral triangle is 36√3 square units
What is area of the equilateral triangle?
Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.
In an equilateral triangle, the center, the centroid, and the circumcenter coincide.
The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.
The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.
So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.
The area of an equilateral triangle with side length s is given by:
A = (s² * √3) / 4
Substituting s = 12, we get:
A = (12² * √3) / 4
= 36√3
Therefore, the area of the equilateral triangle is 36√3 square units.
To know more about area of the equilateral triangle visit,
https://brainly.com/question/10681095
#SPJ1
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped box has an edge length of 45 meter.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
The volume of the container is 91125 cubic meters.
What is volume?
A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.
Given the edge of a cube is 45 meters.
The formula of volume is V = s³.
The volume of the container is
45³
= 91125 cubic meter.
To learn more about the volume of cuboids, click on the below link:
https://brainly.com/question/12279134
#SPJ9
Which statements about this system of equations are true? Check all that apply
2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1.
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4 y = negative 12.
x = 17
y = negative 3
There are infinitely many solutions to the system of equations.
As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.
What sort of equation would that be?The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The statements that are true about this system of equations are:
The x-variable will be eliminated when adding the system of equations.
There are infinitely many solutions to the system of equations.
To eliminate the x-variable, we can add the two equations as follows:
(2x - 7y) + (-2x + 11y) = -13 + 1
Simplifying the left-hand side and the right-hand side gives:
4y = -12
Dividing both sides by 4 yields:
y = -3
Substituting y = -3 into either of the original equations gives:
2x - 7(-3) = -13
Simplifying this equation yields:
2x + 21 = -13
Subtracting 21 from both sides yields:
2x = -34
Dividing both sides by 2 yields:
x = -17
Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.
The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.
The statement "x = 17" is false since the correct solution is x = -17.
The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.
To know more about Equation visit:
https://brainly.com/question/22688504
#SPJ1
the concentration of a drug in a patient's bloodstream is monitored over 10-minute intervals for two hours. t (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 c (mg) 0 2 17 37 55 72 89 103 111 113 113 103 68 a.) how fast is the concentration of the drug changing at 50 minutes? 1.7 mg/min b.) how fast is the concentration of the drug changing at 85 minutes? 1 mg/min c.) is the drug's concentration increasing or decreasing at 115 minutes? decreasing
a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.
b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.
c) The drug's concentration is decreasing at 115 minutes.
a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.
f'(x) = (f(x+h) - f(x-h))/2 × h ....(1)
As per the question, we have h = 10 and x = 50
Substitute the values of h = 10 and x = 50 in (1),
f'(40) = (f(50+10) - f(50-10))/2 × 10
f'(40) = (89-55)/20
f'(40) = 1.7 mg/min
b) For the rate of change of concentration at 85 minutes:
Here, f(80) = 111 mg and f(90) = 113.
The concentration at 90 minutes is 113 mg.
Rate of change = (f(90) - f(80)) / h
= (113 - 111) /10
= 2 / 10
= 0.2 mg/min
c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.
Therefore, the drug's concentration is decreasing at 115 minutes.
Learn more about the concentration here:
https://brainly.com/question/30884067
#SPJ12
HELP ME ASAPPPPP!!!!
Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).
What is simple interest?Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.
by the question.
The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:
A(n) is the value of the investment after n periods.
P is the principal or initial investment
i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)
n is the number of periods
To derive the explicit formula for A(n), we can use the formula for simple interest:
I = P * i * n
where I am the total interest earned over n periods. We can then express A(n) as:
A(n) = P + I
Substituting the expression for I, we get:
A(n) = P + P * i * (n-1)
Simplifying, we can factor out P to get:
A(n) = P * (1 + i * (n-1))
To learn more about amount:
https://brainly.com/question/13024617
#SPJ1
how many acres are in a government rectangular survey that consists of the sw 1/4, ne 1/4, and nw 1/4 of section 13, blendon township?
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
We have,
In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.
Each section is divided into quarters.
If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:
SW 1/4:
This represents one-fourth of the section.
The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.
NE 1/4:
The NE 1/4 of Section 13 is also 160 acres.
NW 1/4:
The NW 1/4 of Section 13 is 160 acres.
To find the total acreage, add up the individual acreages:
160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)
= 480 acres
Therefore,
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
Learn more about government rectangular surveys here:
https://brainly.com/question/14390891
#SPJ12
in a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 5. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 42 and 52?
Using empirical rule, the approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.
Mean = 47
SD = 5
Using Empirical Formula ,approximate percentage of daily phone calls numbering between 42 and 52
Normal Distribution has bell shape curve
The Empirical Rule states that in a normal distribution
68% of the data falls with in one standard deviation ( -1 to 1)
95% of data falls with in two standard deviations, and (-2 to 2)
99.7% of data falls with in three standard deviations from the mean. (-3 to 3)
z score = ( Value - mean)/SD
Calculate z score for 60
Z = (42 - 47)/5
Z = -1
Calculate z score for 66
Z = (52 - 47)/5
Z = 1
As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
Learn more about Empirical rule:
https://brainly.com/question/28873888
#SPJ4
Please help with #10 and #13!!
The angle of rotation in standard form is 251.5651 degrees.
The length of arc S is approximately 20.94 feet.
How do we solve this?If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:
(-1)² + (-3)² = 10
1 + 9 = 10
So, the point (-1, -3) satisfies the equation of the circle.
To find the angle of rotation in standard form, we need to use the formula:
tan(θ) = y/x
where θ is the angle of rotation.
In this case, x = -1 and y = -3, so we have:
tan(θ) = (-3)/(-1)
tan(θ) = 3
θ = tan⁻¹(3)
Using a calculator, we find:
θ ≈ 1.2490 radians or 71.5651 degrees
To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:
θ ≈ 71.5651 + 180 ≈ 251.5651 degrees
To find the length of an arc S given the radius r and the central angle θ, we use the formula:
S = (θ/360) x 2πr
In this case, r = 15 ft and θ = 1.396 radians
Substituting the values:
S = (1.396/2π) x 2π(15 ft)
S ≈ 1.396 x 15 ft
S ≈ 20.94 ft
Learn more about the length of an arc at: https://brainly.com/question/8020286
#SPJ1
Complete question:
Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form
Find the length of the arc S when r = 15 ft and θ = 13.96°
The figure below is composed of a regular hexagon and three congruent triangles. What is the area of the figure rounded to the nearest square meter?
The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.
Describe regular pentagon?With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.
Regular pentagons have a number of distinctive features, including:
A regular pentagon has 108 degree internal angles that are all equal.
A standard pentagon's outside angles are all 72 degrees in angle.
A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.
Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.
First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:
s = r * √(3)
where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:
s = 5 * √(3)
simplifying, we get:
s ≈ 8.7 meters
Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:
A = (1/2) * b * h
where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:
h = (1/2) * s * √(3)
Plugging in the value for s, we get:
h ≈ 7.5 meters
Now we can calculate the area of one of the triangles:
A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters
Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:
A = 6 * (s²) * √(3)/4 + 3 * A
Plugging in the values we calculated, we get:
A ≈ 96.9 square meters
Rounding to the nearest square meter, we get:
A ≈ 97 square meters
Therefore, the answer is A. 97 m².
To know more about triangles visit:
https://brainly.com/question/27184247
#SPJ1
A walkway forms one diagonal of a square playground. The walkway is 22m long. How long is a side of the playground?
Answer:
15.556
Step-by-step explanation:
The length of the diagonal of a square is equal to the length of one side of the square multiplied by the square root of 2
22=x√2
you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
Learn more about time here
https://brainly.com/question/28050940
#SPJ4
how many ways can you select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer?
There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.
In this case, n = 15 and r = 3.
Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To know more about combination formula refer here:
https://brainly.com/question/22436873#
#SPJ11
suppose that at your favorite restaurant to-go orders arrive at the rate of 10 per hour. assume that the numbers of to-go orders on different hours are independent. the distribution of the average number of to-go orders per hour over 700 random hours is
By using Central Limit Theorem, the distribution of to-go orders per hour over 700 random hours at a restaurant with a rate of 10 per hour can be approximated by a normal distribution with a mean of 10 and a standard deviation of 0.119.
The distribution of the average number of to-go orders per hour over 700 random hours can be approximated by the Central Limit Theorem (CLT). In this case, the population mean (μ) is 10 to-go orders per hour, and the population standard deviation (σ) can be calculated using the Poisson distribution formula:
σ = sqrt(μ) = sqrt(10) ≈ 3.162
The sample size (n) is 700, which is larger than 30, so we can use the CLT to approximate the distribution of the sample means. The mean of the sample means is equal to the population mean, which is 10 to-go orders per hour. The standard deviation of the sample means (also called the standard error) is equal to:
SE = σ / sqrt(n) = 3.162 / sqrt(700) ≈ 0.119
Therefore, the distribution of the average number of to-go orders per hour over 700 random hours is approximately normal with a mean of 10 and a standard deviation of 0.119
To know more about Central Limit Theorem:
https://brainly.com/question/898534
#SPJ4
Find the circumference of each circle.Use your calculators value of pi.Round your answer to the nearest tenth.
Answer:
5) 59.7 in
6) 39.0 mi
7)
8) 50.3 mi
Step-by-step explanation:
5) C = [tex]\pi (19)[/tex]
C = 59.7 in
6) C = [tex]2\pi (6.2)[/tex]
C = 39.0 mi
7) RADIUS IS CUT OFF
use C = [tex]2\pi r[/tex]
8) C = [tex]2\pi (8)[/tex]
C = 50.3 mi
the empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when i find the z-scores that mark off the middle 95% of the standard normal distribution i calculate -1.96 and 1.96. is this a contradiction? why or why not? in other words why are the normal distribution calculators not agreeing with the empirical rule?
The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?
The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.
On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.
To know more about empirical rule click here
brainly.com/question/30404590
#SPJ11
if elisa gets an allowance of $30 per week and spends $10 of it on food and drink, $5 on entertainment and $5 on miscellaneous things, how much does she have available to put aside for savings each week?
Answer: She has 10$ to save
Step-by-step explanation:
Elsia has 30$ to start her week. She spent 10 on food and drink, (30-10=20) 5 on entertainment, (20-5=15), and 5 on Misc. things. (15-5=10). This means that the answer is 10.
Steps:
30-10=20
20-5=15
15-5=10
I hope it helped! :D
what is the center of dilation
The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:
Step-by-step explanation:
GUYS PLEASE HELP
* I’LL GIVE YOU BRAINLIEST
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
what is polynomial ?When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.
given
A = πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):
A₁ = π(4a-6)²
If we condense this phrase, we get:
A₁ = π(16a² - 48a + 36)
A₂ = π(4a-6)²
A₂ = π(16a² - 48a + 36)
A₃ = π(4a-6)²
A₃ = π(16a² - 48a + 36)
A₄ = π(4a-6)²
A₄ = π(16a² - 48a + 36)
We can add up the areas of each of the four circles to determine their combined area:
A1 + A2 + A3 + A4 Equals A total
A total is equal to π (16a2 - 48a + 36) + π(16a2 - 48a + 36) + π(16a2 - 48a + 36).
π(64a2 - 192a + 144) = A total
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
To know more about polynomials visit:
https://brainly.com/question/11536910
#SPJ1
The difference between numbers tell you how far apart they are on the number line 8 and -16 our units apart because 8 -6 = 14
The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.
What is the use of number line?A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:
Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.
Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.
Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.
Actually, the difference between 8 and -16 is not 14, it is 24.
To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:
8 - (-16) = 8 + 16 = 24
Therefore, 8 and -16 are 24 units apart on the number line.
To know more about Real number system visit:
https://brainly.com/question/30093910
#SPJ1
a particular triangle has sides of length 14 cm, 8 cm and 9 cm. in centimeters, what is the perimeter of the triangle?
Answer:
31cm
Step-by-step explanation:
14 + 8 + 9 = 31
Make sure to add the cm on the end!
The perimeter of the triangle is 31cm.
The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.
In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.
In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.
For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.
In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.
To know more about perimeter refer here:
https://brainly.com/question/6465134
#SPJ11
Find the volume of the triangular prism below
We can claim that after answering the above question, the As a result, the triangular prism has a volume of 240 cubic centimetres.
what is prism?A prism is a polyhedron with an n-sided polygonal basis, a second base that is a shifted copy of the first base, and n extra faces (necessarily all parallelograms), with two connecting the corresponding sides of the base. All cross sections that are parallel to the base are translations of it. A prism is a two-sided, solid, three-dimensional object with two faces. It has the same cross-sections, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with no bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by two planes that are obliquely oriented to one another. A typical prism has two triangular faces and three parallel rectangular faces. They are made of either glass or metal.
To calculate the volume of a triangular prism, multiply the area of the triangular base by the prism's height.
Triangle area = 1/2 * base * height
Triangle area = 1/2 * 8 cm * 6 cm
Triangle area = 24 cm2
We must now determine the prism's height. The diagram shows that the prism has a height of 10 cm.
Finally, the volume of the triangular prism can be calculated by multiplying the area of the triangle base by the prism's height:
Prism volume = base area * The prism's height
Prism volume = 24 cm2 * 10 cm
Prism volume = 240 cm3
As a result, the triangular prism has a volume of 240 cubic centimeters.
To know more about prism visit:
https://brainly.com/question/27914026
#SPJ1
Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Answer:
-45
Step-by-step explanation:
Darius wrote two integers on the chalkboard. The integers she wrote were 256 and -17. How much larger is 256 than -17?
Answer: 239
Step-by-step explanation:
Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger
Hope this helps
Answer: They are exactly 273 places away.
Step-by-step explanation:
If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.
Hope this helps!
Have a blessed day!
5 Ahmid used the total number of people who bought a
hot dog and the total number of people who did not
buy a hot dog to make the relative frequency table
below. Does it provide evidence that there is an
association between buying a hot dog and buying a
drink at a baseball game? Explain why or why not.
Drink
No Drink
Total
Hot Dog
70.2%
29.8%
100%
No Hot Dog
38.5%
61.5%
100%
The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.
What does the table show?The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.
This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.
Learn more about a frequency table here:
https://brainly.com/question/16148316
#SPJ1
suppose the first and the last page of the document must be printed in color, and only two printers are able to print in color. the two color printers can also print black-and-white. how many ways are there for the 100 pages to be assigned to the four printers?
If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.
The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2
Number of colors printed by printers = 2
We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²
= 4
Number of remaining pages of document = 98
Number of avaliabile printers = 4
Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.
Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸
= 4 × 4⁹⁸ = 4⁹⁹
Hence, required number of ways are 4⁹⁹.
For more information about fundamental counting principle, refer:
https://brainly.com/question/30869387
#SPJ4
there is a three term arithmetic sequence with the first term 9. if you add 2 to the second term and 20 to the third term it forms a geometric sequence. what is the smallest number the third term in the geometric sequence could be?
The geometric sequence is 9 + 2 + 20 = 29.
The smallest number the third term in the geometric sequence can be is 29.
This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,
the third term of the geometric sequence is 9 + 2 + 20 = 29.
Learn more about geometric sequence
brainly.com/question/30491267
#SPJ11
which events are independent? check all that apply.each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number.
The events that are independent are,
1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye
The events that are independent are:1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye.
The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically
1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.
2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.
3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.
Learn more about independent event here
brainly.com/question/30905572
#SPJ4
The given question is incomplete, the complete question is:
Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.
an 8-person committee is to be formed from a group of 15 women and 12 men. in how many ways can the committee be formed if the committee must contain four men and four women? if there must be at least two men? if there must be more women than men?
The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of Permutation and Combination.
If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.
To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.
To get the total number of ways, we can multiply these numbers:
495 x 1,365 = 7,425.
To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.
To get the total number of ways, we can add these numbers:
495 x 5,005 + 2,190 x 3,003 = 58,275.
To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.
To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.
Adding these numbers gives us the total number of committees with more women than men:
15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700
To learn more about Permutation and Combination here:
https://brainly.com/question/28720645#
#SPJ11
The plane traveled 6 mores miles after passing the George Washington Bridge, descending at a 2° angle before landing in the Hudson River.
5a) At what altitude (in feet) did the airplane cross over the G.W. Bridge (e)?
The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
What is altitude?Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.
In the given question,
To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.
Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:
tan(2°) = (h - e) / 6
To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:
6 tan(2°) = h - e
Adding e to both sides, we get:
h = 6 tan(2°) + e
We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:
h = 6(0.03492) + e
h = 0.2095 + e
Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
To know more about trigonometry, visit:
https://brainly.com/question/29002217
#SPJ1