The amount of eroded rock in cubic kilometres is 1 km3.
To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.
In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:
20 m / 1000 = 0.02 km
Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:
10 km * 5 km * 0.02 km = 1 km3
So the amount of eroded rock in cubic kilometres is 1 km3.
Complete Question:
The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?
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a number is at least 16
Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.
The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes
How to determine the time taken for 21,000 spectators to vacate the stadium?
A variation is a relation between a set of values of one variable and a set of values of other variables
Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively
We can write the variation as:
T α N/E
T = kN/E (where k is constant of proportionality)
when N = 25,000, E = 25, T = 20:
T = kN/E
k = TE/N
k = (20×25)/25000 = 0.02
when N = 21,000 and E = 15:
T = kN/E
T = (0.02×21,000)/15 = 28 minutes
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Can u please help......,,,....
The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17
The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17
By the SSS Congruence Theorem, ΔABC ≅ ΔDEF
How to prove triangle congruency postulate?We are given the coordinates of Triangles ABC and DEF as;
A(5, 3), B(7, 7), C(9, 4)
D(-8, 6), E(-12, 8), F(-9, 10)
The formula for distance between two coordinates is;
Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus;
AB = √[(7 - 3)² + (7 - 5)²]
AB = √20
AB = 2√5
Similarly;
BC = √[(4 - 7)² + (9 - 7)²]
BC = √13
AC = √[(4 - 3)² + (9 - 5)²]
AC = √17
Likewise;
DE = √[(8 - 6)² + (-12 + 8)²]
DE = √20
DE = 2√5
Similarly;
EF = √[(10 - 8)² + (-9 + 12)²]
EF = √13
DF = √[(10 - 6)² + (-9 + 8)²]
DF = √17
Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.
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The endpoints of a line segment AB are (1, -6) and (5, -6). The equation of a line BC is
y=x-11. Is triangle ABC a right triangle? Justify your answer.
No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.
A RIGHT TRIANGLEA right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.
In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.
Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.
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33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is [tex]m^2 = p^2 + z^2[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
since it it is right angled triangle
so the relation that be formed is
[tex]m^2 = p^2 + z^2[/tex]
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Is the inverse of every linear function also a function?
In most cases, the inverse of a linear function is also a linear function.
What is a linear function?The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.
Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).
These functions' graphs are mirror images of one another when viewed along the line y=x.
As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.
A linear function's inverse is typically also a linear function.
Therefore, in most cases, the inverse of a linear function is also a linear function.
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Wyatt says that 0.6 has the same value as 0.600 do you agree explain
Answer:
Yes, the zeros can be used as place holders. When using place holders, the value does not change.
SO MANY POINTS
Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.
Picking a prime number from the integers between 1 and 20
Picking a multiple of from the integers between 1 and 20
Picking a multiple of from the integers between 1 and 40
Answer:
Game 1
Equal chance
Game 2
Step-by-step explanation:
A BETTER CHANCE OF WINNING
Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.
Game I
a.Picking a prime number from the integers between 1 and 20
b.Picking a multiple of 5 from the integers between 1 and 20
c.Picking a multiple of 7 from the integers between 1 and 40
Hint:
Find the percent chance that each event will occur and compare the results.
a.Picking a prime number from the integers between 21 and 40
b.Picking a multiple of 5 from the integers between 1 and 40
c.Picking a multiple of 6 from the integers between 1 and 25
Answer:
Game 1
Equal chance
game 2
7x-2y=10 slope intercept form
Answer:
7/2
Step-by-step explanation:
7x – 2y = 10
using ( y = mx + b) as our guideline
where m is the slope
7x – 2y = 10
subtract 7x from both sides
7x – 7x – 2y = 10 – 7x
–2y = 10x – 7x
when arranged in slope form
–2y = –7x + 10
divide both sides by (–2) to get y
[tex] \frac{ \\ - 2y}{ - 2} = \frac{ - 7x}{ - 2} + \frac{10}{ - 2} [/tex]
[tex]y = \frac{ \\ 7y}{2} - 5[/tex]
[tex]the \: slope \: will \: be \: \frac{ \\ 7}{2} [/tex]
This is our answer.
i hope i
i need the correct answer only 2 try’s and due in 15 min
The sample space between A to C is A,B,C
What is the probability?The likelihood that a sample point will occur is quantified by its probability.
The likelihood of a sample point
According to tradition, statisticians have adopted the following guidelines.
Any sample point's probability can be between 0 and 1.
The probability of every sample point in a sample space added together is 1.
Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?
Solution: the total of all sample points' probability
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103M) solve on the interval 0 ≤ x < 2pi
sin ( 4x ) = √3 / 2
solving sin ( 4x ) = √3 / 2 , the value of x is 15°
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
For angle of 30° and 60°
sin 30° = 1/2
cos 60° = √3/2
tan60° = √3
for angle 60 °
sin60° = √3/2
cos 60° = 1/2
tan60° = 1/√3
since sin(4x) = √3/2
and sin 60° = √3/2
sin60° = sin(4x)
this means 60° = 4x
divide both sides 4
x = 60/4
x = 15°
therefore the value of x is 15°
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In 1800, the slave population in the United States of America was 893,602. By 1860, the slave population rose to about 1,953,760. How large of a percentage did the slave population increase by from 1800 to 1860?
To find the percentage increase of the slave population from 1800 to 1860, we can use the following formula:
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
percentage increase = (new value - original value) / original value x 100
We know that in 1800 the slave population was 893,602 and in 1860 the slave population was 1,953,760. So we can plug in these values into the formula:
percentage increase = (1,953,760 - 893,602) / 893,602 x 100
percentage increase = (1,060,158) / 893,602 x 100
percentage increase = 1.1885 x 100
percentage increase = 118.85
So, the slave population increased by 118.85% from 1800 to 1860.
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An art store manager buys easels for 10.20 each. He marks up the cost by 75% to get the selling price. What is the selling price of each easel
Answer:
17.85
Step-by-step explanation:
175% * 10.20 = 17.85
4x(3 +5) Please answer :(
Answer: 32x
Step-by-step explanation:
4x (3 + 5)
add 3 and
⇒ 4x (8)
⇒ 32x answer .
hope that helps...
Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?
The original amount placed in the account is $320.
What is simple interest ?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.
The interest earned is calculated as follows:
I = P*r*t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.
Substituting in the formula:
288 = P*0.075*12
Calculating:
288 = 0.9P
Dividing by 0.9:
P = $320
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What is the pattern?
Sydney says that if all of the side lengths of a cube are doubled, the volume of the cube will also double. Is she correct? Explain.
Answer:
no, it's not correct
Step-by-step explanation:
volume or the cube = L³
so if we doubled the side lengths
They would be 2L
then the volume= (2L)³ = 8L³
so that would make the volume 8 times the first value not double
solve for x and graph the solution on the number line below 7+x<16
Step-by-step explanation:
x<16-7x<11.....................
Jordan made this design from three pieces of square-shaped cloth. What is the total area of the design jordan made? 4cm 6cm 8cm Explain how you found your answer
The design has a total area of 116 cm² when measured using the area of a square.
What is the area?The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.
Create a square on paper by using a pencil.
Two dimensions make it up.
A shape's area on paper is the space it takes up.
Given that a square has equal sides, we can calculate its area as follows:
A = s²
The photograph below illustrates the three square-shaped pieces of fabric that Jordan used to create the design.
Find the area of each square-shaped piece of fabric and add them all up to get the total pattern area.
Inferring the area of a square, the total area would be as follows:
Total Area = 4² + 6² + 8²
Total Area = 116 cm²
Therefore, the design has a total area of 116 cm² when measured using the area of a square.
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I need to know how to solve e,d,f im so confused it’s about angles in a circle
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
what is circle ?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.
given
in 6th figure
61° + 52° + x = 180° ( sum of exterior angle )
113° + x = 180°
x = 67°
y = 67°
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
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What is negation example?
Let's say we have an expression P^A then the negation of P^A will be not( P^A ). This is an example of negation.
As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.
When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.
It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.
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what’s the perimeter of a rectangle that’s
6m
6m
9m
9m
Answer:
30
Step-by-step explanation:
perimeter is the outside of a shape so just add them all together honestly
What are the first 3 triangular numbers?
The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.
Explain the term triangular numbers?A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.
For instance, the fact that 6 may be expressed as 1+2+3, being sum of the initial three positive integers, indicates that it is a triangular number. If one takes the sum of the initial positive integer to be the first element, then sum of the earliest two positive integers to be the second element, then so on, triangular numbers comprise a sequence. In this scenario, n signifies the position of such a triangular number with in sequence if a number equals the sum of the initial n positive integers. Triangles can be formed from triangular numbers.Thus, the first three triangular numbers 1, 3, 6.
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What is the answer to 2/3x=-36
the answer to your question is 36
1. If triangle ABC has the following measurements, find the measure of angle A. a = 17 b = 21 C = 25 42.3° 137.7° 56.2° 81.5°
Answer: Triangle ABC is a right triangle, because it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
c^2 = a^2 + b^2
25^2 = 17^2 + 21^2
625 = 289 + 441
625 = 730
Since it is a right triangle, angle A is the angle opposite side a, which is the side that is the length of 17.
A right triangle also has one angle which is always 90 degree, that is the angle opposite the hypotenuse, so the remaining angle is A, which is 90- angle C, which is
90 - 42.3 = 47.7 degree.
Therefore the measure of angle A is 47.7°
So the correct answer is C. 42.3°
Step-by-step explanation:
The last digit of the heights of 36 statistics students were obtained as part of an experiment conducted for a class. Use the frequency distribution to the right to construct a histogram.
Digit Frequency
0 33 1 33 2 553 554 445 336 337 448 339 33 What can be concluded from the distribution of the digits? Specifically, do the heights appear to be reported or actually measured?
The plot for histogram is given below. Through digits distribution it can be seen that last digit of height of many students are same and the heights appear to be reported.
What is frequency distribution?
To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.
The table of data is given below.
According to the table the histogram is plotted.
The graphic representation of data points arranged into user-specified ranges is called a histogram. The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organising them into logical ranges or bins.
The digits distribution show that the maximum number of students have a height whose last digit is 3.
The heights appears to be reported by the students and not actually measured as maximum of them are having same last digit which corresponds to the possibility that the first digit might be different. This is a possible example of a survey.
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1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
x = 6 does not satisfy the given equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that an equation, 5(x – 3) = x + 13
Checking if x = 6 satisfy the equation or not,
5(x – 3) ? x + 13
5(6-3) ? 6+13
5×3 ? 19
15 ≠ 19
Hence, x = 6 does not satisfy the equation.
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1/5t + 2 - 2 = 17 - 2
Answer:
[tex]t=75[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5} t+2-2=17-2[/tex]
Lets solve for [tex]t[/tex].
Subtract 2 from 2.
[tex]\frac{1}{5} t=17-2[/tex]
Subtract 2 from 17.
[tex]\frac{1}{5} t=15[/tex]
Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].
[tex]\frac{t}{5} =15[/tex]
Multiply both sides of the equation by 5.
[tex]\frac{t}{5}*5 =15*5[/tex]
[tex]t=75[/tex]
Find the volume of the pyramid.
7 m
12 m
The volume is
16 m
cubic meters.
The value of volume of pyramids is 448 cubic meter.
How to calculate volume of pyramid?A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.
The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."
Given,
Length=12m
Width=7m
height=16m
volume =l * w * h / 3
= 12*7*16/3
= 448 cubic meter
Therefore volume of pyramid is 448 cubic meter .
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Find the surface area, volume, and radius and select all the correct measurements,
Answer:
surface area ---> i
volume ---> b
radius ---> d
Step-by-step explanation:
surface area= 4πr² =4x3.14x14²=2461.76cm²
volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³
radius = half the diameter = 14cm