Using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².
What is Magnitude?The magnitude or size of a mathematical item defines whether it is larger or smaller than other objects of the same kind in mathematics.
Formally speaking, the size of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
The most frequent way to gauge an earthquake's size is through its magnitude.
It is a gauge for the magnitude of an earthquake's sole source.
As a result, it is the same regardless of how or where you view it, and the following computation can be made:
So, in the given situation we will be using the formula:
M = 2/3 log E/E₀
Where E is the power released in Joules and x, the minimal measure released by such an earthquake shall be allotted to.
Assuming 5.5, the same magnitude is given when the above equation is used:
M = 2/3 log E/E₀
5.5 = 2/3 log (E/10⁴°⁴)
8.5 = log (E/10⁴°⁴)
10⁸°⁵ = E/10⁴°⁴
E = 10⁴°⁴ * 10⁸°⁵
E = 4.5 * 10¹²
Therefore, using the magnitude formula we know the amount of energy released by an earthquake with a magnitude of 5.5 is 4.5 * 10¹².
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Correct question:
The magnitude, M, of an earthquake, is represented by the equation M=23logEE0 where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?
The diameter of a circle is 6 centimeters. What is the circle's area?
Use 3.14 for .
Answer: The area of circle is 28.26 cm^2
Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.
Area of circle = pi r^2
And the value of pi is to be taken 3.14
The area of the given circle is 28.26cm^2.
In need of assistance! If possible, I'd appreciate it!
Vector a: start at (1, 3) and end at (-4, -2) in blue.
Vector b: start at (-4, -2) and end at (1, 3) in red.
Vector a+b: start at (1, 3) and end at (2, 7) in green.
How do we calculate?To represent a+b using the parallelogram method,
we must draw vectors representing a and b.
The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).
Using the vector tool, we then draw the vectors a and b. We start at the initial point of each vector and select the terminal point.
Vector a: start at (1, 3) and end at (-4, -2)
Vector b: start at (-4, -2) and end at (1, 3)
We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.
We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.
Vector a: start at (1, 3) and end at (-4, -2) in blue.
Vector b: start at (-4, -2) and end at (1, 3) in red.
Vector a+b: start at (1, 3) and end at (2, 7) in green.
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Identify the coordinate of any local and absolute extreme points and inflection points. Graph the function.
Y=5x+5 sin x, 0
The inflection occurs at x = n*pi, while the absolute extreme points, while the critical points can be found with the expression 5 + 5cos(x) = 0.
What are the extreme and inflection points?To find local extreme points, absolute extreme points, and inflection points, we will first take the first and second derivatives of the function.
y = 5x + 5sin(x)
y' = 5 + 5cos(x)
y'' = -5sin(x)
To find critical points, we set the first derivative equal to zero.
5 + 5cos(x) = 0
cos(x) = -1
x = pi
This is the only critical point, so we only need to evaluate the function at x = pi to find any extreme points.
y(pi) = 5pi - 5
So the absolute minimum occurs at (pi, -5).
To find inflection points, we set the second derivative equal to zero.
-5sin(x) = 0
sin(x) = 0
x = k*pi, where k is an integer.
So the inflection points occur at x = n*pi, where n is an integer.
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NO LINKS!!! URGENT HELP PLEASE!!!
Find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1).
(x, y) = __________
Answer:
(-8.89, -26.69)
Step-by-step explanation:
To find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1), we can use the following steps:
Since the point is in the third quadrant, both the x-coordinate and the y-coordinate must be negative. Therefore, we can write (a, 3a) as (-|a|, -3|a|).We know that the distance between P(2,1) and (-|a|, -3|a|) is 5. We can use the distance formula to set up an equation and solve for |a|:[tex]\sqrt{(2 - (-|a|))^2 + (1 - (-3|a|))^2} = 5\\\sqrt{(2 + |a|)^2 + (1 + 3|a|)^2} = 5[/tex]
Squaring both sides of the equation and simplifying, we get:[tex]a^2 + 8a - 8 = 0[/tex]
Solving for a using the quadratic formula, we get:[tex]a = \frac{-8 ±\sqrt{8^2 - 4(1)(-8)}} {(2(1))}\\a = \frac{-8 ± \sqrt{96}}{ 2}\\a = -4 ± 2\sqrt{6}[/tex]
Since the point is in the third quadrant, we want the negative root, so:[tex]a = -4 - 2\sqrt(6)[/tex]
Substituting this value of a into (-|a|, -3|a|), we get:(x, y) =[tex](-|-4 - 2\sqrt(6)|, -3|-4 - 2\sqrt(6)|)[/tex]
(x, y) ≈ (-8.89, -26.69)
Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1) is approximately (-8.89, -26.69).
1. Radioactive decay results in the release of energy and matter from the nucleus of an atom. If the rate of radioactive decay for a particular substance is 3.75% per hour, how many grams of the substance will remain after 18 hours if the initial amount was 150 grams?
After answering the presented question, we may conclude that As a percentage result, around 74.43 grammes of the drug will remain after 18 hours.
What is percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also used on occasion. However, it is commonly indicated using the percent symbol "%." The % amount has no dimensions. Percentages are just fractions with a denominator of 100. Place a percent sign (%) next to a number to indicate that it is a percentage. For example, if you answer 75 out of 100 questions properly on a test (75/100), you score a 75%. Divide the money by the total and multiply the result by 100 to calculate percentages. The percentage is derived by multiplying (value/total) by 100%.
A substance's radioactive decay rate is expressed as a percentage per unit time. This indicates that the amount of material left after each unit of time will be lowered by the set percentage.
We may use the exponential decay formula to this problem:
[tex]N(t) = N_0 * e^{(-kt)}[/tex]
where:
N₀ = starting drug quantity
N(t) = the amount of material that remains after time. t k = decay constant (related to decay rate)
t = the amount of time that has passed
To calculate the amount of material left after 18 hours, we must first determine the value of k. Using the rate of decay stated in the issue, we may accomplish the following:
[tex]3.75% = k * 1 hour\\k = 0.0375/hour\\N(18) = 150 * e^{(-0.0375*18)}\\N(18) = 74.43 grams \\[/tex]
As a result, around 74.43 grammes of the drug will remain after 18 hours.
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The shaded area on the grid represents the part of kira's free throws that she made in the basketball practice today.
The percentage of Kira's free throws is 68%.
We have,
From the grid,
We can see that,
There are 25 boxes.
Now,
The number of shaded boxes = 17
Now,
The percentage of the shaded boxes.
= 17/25 x 100
= 17 x 4
= 68%
Thus,
The percentage of Kira's free throws is 68%.
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The complete question.
The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.
Find the percentage of Kira's free throws.
18 7/8 + __ = 20 1/5
what is the blank?
Answer:
x = [tex]\frac{53}{40}[/tex]
Step-by-step explanation:
18 7/8 + __ = 20 1/5
18 7/8 = 151/8
20 1/5 = 101/5
[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]
x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]
x = [tex]\frac{53}{40}[/tex]
So, the answer is [tex]\frac{53}{40}[/tex]
A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election. How many of these voters actually voted in that election? Construct a 95% confidence interval for the proportion of registered voters who voted in the most recent school board election
There are 25 persons who actually voted, the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07 that is (0.13, 0.27).
What is confidence interval?In statistics, a confidence interval, means the probability which a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. There are various types of confidence interval such as 90%, 95%, 99% etc.
A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election.
So in 125persons the persons who actually voted are
(125×20)/100
= 2500/100
= 25
For 95% confidence interval the z value is 1.96.
If we take p as probability of success that is the persons who actually voted then 1-p denotes the probability of failure.
p= 25/125= 1/5 = 0.2 n= 125
1-p= 1-(1/5)
= 1-0.2= 0.8
The formula for confidence interval is
p± z√{p(1-p)/n}
0.2 ±1.96√{(0.2×0.8)/125}
= 0.2 ± 1.96√(0.16/125)
= 0.2± 1.96 ×0.035777
= 0.2±0.07012
Hence , the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07
that is (0.13, 0.27).
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A right triangle has sides 14 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse.
Answer:
According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Substituting the given values, we get:
c^2 = 14^2 + 48^2
c^2 = 196 + 2304
c^2 = 2500
Taking the square root of both sides, we get:
c = 50
Therefore, the length of the hypotenuse is 50 units.
The equation -4x + y = 0 relates the
number of pages in a photo album y to
the number of pictures in the album x.
Tell whether the relationship is a direct
variation. Explain your answer.
Recall the general equation for a line in slope-intercept form:
[tex]y=mx+b[/tex]
where:
[tex]\text{y = y-coordinate}[/tex]
[tex]\text{m}=\bold{slope}[/tex]
[tex]\text{x = x-coordinate}[/tex]
[tex]\text{b = y-intercept}[/tex]
In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:
[tex]-4x+y=0[/tex]
[tex]-4x +4x+y=0+4x[/tex]
[tex]\implies y=4x+0[/tex]
Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.
If you were to graph the line, you would see the intersection at (0,0):
graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]
A diagram shows a garden bed. The area of the garden bed is 21ft to the power of 2. What is the Height of the garden bed. Need help ASAP
Answer: 1.75
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Since the garden bed looks like the shape of a trapezoid the equation to find the area of a trapezoid is A = 1/2h (base 1 + base 2)
The area is already given so you can just plug it in. Also you can plug in the bases.
21 = 1/2h (3 + 4)
21 = 1/2h (7) rewrite
21 = 1/2(7)h
21 = 3.5h Divide both sides by 3.5
6 = h
please helppppp this is past due will give brainliest
The mean of the data set is 25, the median is 25, the range is 20, the variance is 20, and the standard deviation is 4.47.
Solution to the Data AnalysisGiven the dataset:
x = 30, 20, 35, 25, 15
N = 5
Mean of the data set is the average of the dataset. To find the average, we add up all the numbers and divide by the total number of values:
Mean (Xbar) = (30 + 20 + 35 + 25 + 15) / 5 = 25
Median is the number that fall at the middle of the dataset. To find the median of the data set, we need to arrange the numbers in order from smallest to largest:
15, 20, 25, 30, 35
The median is the middle number, which is 25 in this case.
Range of the data set can be calculated by subtract the smallest value from the largest value:
Range = 35 - 15 = 20
Standard Deviation and Variance
First find the deviations of each value from the mean:
(x - Xbar) = d
30 - 25 = 5
20 - 25 = -5
35 - 25 = 10
25 - 25 = 0
15 - 25 = -10
To find the variance, we square each deviation, add them up, and divide by the number of values:
Variance = d²/N
= (5² + (-5)² + 10² + 0² + (-10)²) / 5
= 100/5 = 20
To find the standard deviation, we take the square root of the variance:
Standard Deviation = sqrt(variance)
= sqrt(20)
= 4.47 (rounded to two decimal places)
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What is Bd?
A. 7.5
B. 8.5
C. 9.4
D. 15
Thus, the length of chord BD of the given circle is found to be 8.5 units.
Explain about the chord of circle:A chord is indeed a straight line that connects two points on a circle's circumference. Because it connects to points on the circle's perimeter, the diameter is thought to be the chord with the longest length.
The lengthiest chord in a circle is called the diameter, and the chord's perpendicular distance to the circle's centre is zero.
Given that: From diagram.
CA = AD = 4.5 + 4 = 9.5 (radius of circle)AM = 4Now, in right triangle, MAD, using the Pythagorean theorem:
(AD)² = (AM)² + (MD)²
(9.5)² = (4)² + (MD)²
(MD)² = 9.5² - 4²
(MD)² = 90.25 - 16
(MD)² = 74.25
MD = 8.5
Thus, the length of chord BD of the given circle is found to be 8.5 units.
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Is 285mg more or less than 34.4 mg? My problem is not knowing for sure because of the decimal
Answer: 285 mg is more than 34.4 mg
Step-by-step explanation:
To compare the two quantities, we can simply look at the whole numbers before the decimal point.
285 is a larger whole number than 34, so we can say that 285 mg is more than 34.4 mg.
The decimals after the whole numbers are used to represent the fractions of the numbers.
The circle graph shows the results of a survey about favorite farm animals. If 400 people were surveyed, how many more people prefer pigs than chickens?
From the circle graph of the survey, 52 more people prefer pigs than chickens.
What is a circle graph?A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.
Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.
From the circle graph we see that the percentage of people who prefer chickens are 29%.
Thus, 29/100 (400) = 116 people
Also, 16% people prefer pig:
Thus, 16/100 (400) = 64 people
Thus, the difference is:
116 - 64 = 52
Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.
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The complete question is:
Find the circumference of the circle. Round to the nearest tenth.
A. 251.3 in.
B. 125.7 in.
C. 164.8 in.
D. 225.4 in.
Answer: A. 251.3 in.
Step-by-step explanation:
We can use this formula to solve for the circumference of a circle. r is equal to the radius, or half of the circle's width.
C = 2πr
C = 2πr
C = 2π(40)
C ≈ 251.3
A. 251.3 in.
What is the value of r in the equation 3r + 10 − 3r = 15?
Show all the steps by applying inverse operation, then check the answer to get full credit.
Answer:
no solution
Step-by-step explanation:
3r + 10 - 3r = 15 ← collect like terms on left side
10 = 15 ← false statement
this false statement indicates the equation has no solution
A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches. A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches. What is the difference in volume, cubic inches, between the two boxes. show your work
The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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help I need the answer quick
Answer: 228[tex]cm^2[/tex]
Step-by-step explanation:
The lateral area is 2lh + 2wh
= (2 * 14 * 6) + (2 * 5 * 6)
= 228[tex]cm^2[/tex]
Freshman
Sophomores
Total
Blology
0.15
0.2
0.35
Which statement is false?
Chemistry
0.1
0.25
0.35
Physical
science
0.2
0.1
0.3
OA. 15% of her students are in biology.
OB. 30% of her students are in physical science.
OC. 35% of her students are in chemistry.
OD. 45% of her students are freshmen.
Total
0.45
0.55
1.0
The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.
How is this statement false ?The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.
30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.
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Susan has a part-time job. The table below shows her earnings based on the number of hours worked.
Hours Worked, x
Earnings, E
Which equation best models this set of data?
An equation that best models this set of data is: D. y = 9.74x - 0.06
How to determine the line of best?In this scenario, the hours worked would be plotted on the x-axis (x-coordinate) of the scatter plot while the earnings would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the hours worked and earnings, an equation for the line of best fit is given by:
y = 9.74x - 0.06
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9x7x9x9x7x9 (I tried the answer 9^4 x 7^2 and it’s not correct
Answer:
321489
Step-by-step explanation:
according to the law of sines, which of the following is equal to sin(B)/b
Answer:
[tex]\frac{sin(A)}{a}[/tex]
a plumber has 6 1/3 feet of piping she needs 75 inches of piping does she have enough
Answer:
We need to convert both measurements to the same unit in order to compare them. Let's convert 6 1/3 feet to inches:
1 foot = 12 inches
6 feet = 6 x 12 = 72 inches
1/3 foot = (1/3) x 12 = 4 inches
6 1/3 feet = 72 + 4 + (1/3) x 12 = 76 inches
Therefore, the plumber has 76 inches of piping.
Since the plumber needs 75 inches of piping, we can see that she does have enough piping.
Step-by-step explanation:
A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the
volume of the silo if it has a height of 31 m and a radius of 5 m. Round your answer to
the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
I hope this helps you.
Help me please 14 points.
The best percentage bar graph that represents Camryn's data is:
C Winter | Spring | Summer | Fall
0% 20% 40% 60% 80% 100%
What is the use of a bar graph?A bar graph's purpose is to visually convey relational information quickly. The bars show the value for a specific type of data.
This is because the graph correctly shows the percentage of students who prefer each season, with the bar for each season extending to the appropriate percentage mark on the graph. It also clearly labels each season under the corresponding bar.
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Solve the following system of equations:
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
PLEASE HELP!! 25 POINTS!!
The solution to the system of equations is:
x = -19/5, y = 2, z = 1/10
How do we calculate?4x + 6y - 2z = 2 (multiply first equation by 2)
x + 2y - 3z = -5 (third equation)
Add the two equations, we get:
5x + 8y = -3 (eliminated z)
-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)
3x + y + 2z = 12 (second equation)
Add these two equations, we have:
-4x + 8y = -21 (eliminated z)
5x + 8y = -3
5x = -8y - 3
x = (-8y - 3)/5
Substituting this expression for x into the second equation, we get:
3((-8y - 3)/5) + y + 2z = 12
z = (39/10) - (19/10)y
Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:
2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1
Simplifying and solving for y, we get:
y = 2
x = (-8(2) - 3)/5 = -19/5
z = (39/10) - (19/10)(2) = 1/10
In conclusion, the solution to the system of equations is:
x = -19/5, y = 2, z = 1/10
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The solution to the given system of linear equations is
x = 3, y = -1 and z = 2
Solving System of Linear EquationsFrom the question, we are to solve the given system of linear equations.
The given system of linear equations is
2x + 3y − z = 1
3x + y + 2z = 12
x + 2y − 3z = −5
Multiply the third equation by 2
x + 2y − 3z = −5 ) ×2
2x + 4y - 6z = -10
Subtract the first equation from the resulting equation
2x + 4y - 6z = -10
- (2x + 3y − z = 1
----------------------------------------
y - 5z = -11 ---------- (1)
Now,
Multiply the third equation by 3
x + 2y − 3z = −5 ) ×3
3x + 6y -9z = -15
Subtract the second equation from the resulting equation
3x + 6y -9z = -15
- (3x + y + 2z = 12
-----------------------------------------
5y - 11z = -27 ----------- (2)
Solve equations (1) and (2) simultaneously
y - 5z = -11 ------------ (1)
5y - 11z = -27 ------------ (2)
Multiply equation (1) by 5
y - 5z = -11 ) ×5
5y - 25z = -55
Subtract the resulting equation from equation (2)
5y - 11z = -27
-( 5y - 25z = -55
-----------------------------
14z = 28
Divide both sides by 14
14z/14 = 28/14
z = 2
Substitute the value of z into equation (1)
y - 5z = -11
y - 5(2) = -11
y - 10 = -11
Add 10 to both sides of the equation
y - 10 + 10 = -11 + 10
y = -1
Substitute the value of y and z into the third equation
x + 2y − 3z = −5
x + 2(-1) − 3(2) = −5
x - 2 - 6 = -5
x - 8 = -5
Add 8 to both sides of the equation
x - 8 + 8 = -5 + 8
x = 3
Hence,
The solution is
x = 3, y = -1 and z = 2
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There are two yellow and three green balls in a tub. Ashraf picks a ball without looking. What is his probability that the ball is (i) yellow (ii) green (iii) red
Answer:
Since there are only yellow and green balls in the tub, there is no possibility of picking a red ball. Therefore, the probability of picking a red ball is zero.
(i) The probability of picking a yellow ball can be calculated by dividing the number of yellow balls by the total number of balls. In this case, there are two yellow balls and three green balls, so the total number of balls is 2 + 3 = 5. The probability of picking a yellow ball is 2/5 or 0.4, which is 40%.
(ii) Similarly, the probability of picking a green ball can be calculated by dividing the number of green balls by the total number of balls. In this case, there are three green balls and five total balls. Therefore, the probability of picking a green ball is 3/5 or 0.6, which is 60%.
(iii) As mentioned earlier, there are no red balls in the tub. Hence, the probability of picking a red ball is 0.
How are the lines below related
Answer:two lines are parallel if their slopes are equal and they have different y-intercepts
Step-by-step explanation:
Find m∠MQN. help me on this one.
Answer:
Vertically opposite angles are always same.
Straight angle=180°
Angle MQN=70°