Answers
The earthquake was a devastating one as its range is very high for the logarithm function.
We are given that:
M = log (A) - log (A₀) + c log (Δ)
where,
M = local magnitude of the earthquake
A = maximum amplitude in micrometers
A₀ = reference amplitude
c = calibration constant
Δ = distance in km between the seismograph and the epicenter
Now, we are given that:
M = 114370.61 ц m
A = ?
A₀ = 302 ц m
c = 2.76
Δ = 60 km
We have to find the maximum amplitude.
Substituting the values in the logarithm function, we get that:
9102 ц m = log (A) - log (302 ц m) + 2.76 log (60 km)
114370.61 ц m = log (A) - 2.48 + 2.76 (1.78)
114370.61 ц m = log (A) - 2.48 + 4.91
114370.61 ц m = log (A) + 2.43
log (A) = 114370.61 ц m - 2.43
log (A) = 114368.18 ц m
A = e¹¹⁴³⁶⁸°¹⁸ ц m
A = will come in the range 9 and over.
Therefore, the earthquake was a devastating one as its range is very high for the logarithm function.
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Related Questions
PLS HELP!!! NEED ASAP WILL MARK BRAINLIEST. WORTH 100 POINTS
Solve the inequality. Graph the solution, if possible.
1. |y-2|+11>0
2. 3|2a+8|-11≤-5
3. 1/3|2x+3|-1≤8
please show how you got your answer or if it’s no solution, thank u !
Answers
Answer:
1-13 and 2-13 and 4-13 because if you add them that is the answer
I was
following a recipe to make punch for a party. The rect cakks for 2 cups of juice for every 3 cups o
f seltzer. If I have 12 cups of seltzer, how many cups of juice do I need?
Answers
You need 8 cups of juice for 12 cups of seltzer.
Representing the first statement in ratio form. So, number of cups of juice: number of cups of seltzer = 2:3. Similarly, for second statement, let the number of cups of juice be x.
Forming the equation with ratio on both sides -
2:3 = x:12
Writing the mentioned equation as fraction to solve for the value of x
x = (2 × 12)/3
Performing multiplication in numerator to find the value of x
x = 24/3
Dividing the numerator and denominator by 3 to find the value of x
x = 8
Therefore, 8 cups of juice is needed for 12 cups of seltzer.
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How much money (in dollars) should be invested in an account that earns 5% interest, compounded quarterly, to yield $10,000 in 4 years? Round your answer to the nearest cent.
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P[/tex]
6 inches more than 2 times the height, 54 square inches what’s the base and height
Answers
6 inches more than 2 times the height, 54 square inches the base and height is
b=13.8 inches
h=3.9 inches
Let base and height be b and h respectively,
So ,
b=2h+6
Area = b*h= 54 square inches
So,
(2h+6)(h)=54
2h²+6h=54
h²+3h=27
h²+3h-27=0
h= [tex]\frac{-3 +\sqrt{3^{2}-4(-27)(1) } \\}{2}[/tex]
h=[tex]\frac{-3 +\sqrt{9+108} \\}{2}[/tex]
h=[tex]\frac{-3 +\sqrt{117} \\}{2}[/tex]
h=[tex]\frac{-3 +10.8\\}{2}[/tex]
h=3.9 inches
b=2h+6=13.8 inches
The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely cover a shape is its area. As a result, it is stated and measured in square units.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
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A produce packing company prepares crates of apples to ship to supermarkets. Suppose
that the weight of a randomly selected crate is known to be Normally distributed, with
a mean of 14 kg and a standard deviation of 1.4 kg.
(a) Find the weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05.
(b) Find the probability that a randomly selected crate will weigh more than 16kg.
(c) If 20 crates are randomly and independently selected, what is the probability that
at least 2 of them will weigh more than 16kg?
Answers
a. The weight of a particular crate such that the probability of randomly selecting a heavier crate is 0.05 is 16.30kg.
b. The probability that a randomly selected crate will weigh more than 16kg is 0.0764.
c. The probability that.at least 2 of them will weigh more than 16kg is 0.4584.
How to calculate the probability?a. From the information, there is a mean of 14 kg and a standard deviation of 1.4 kg. The weight will be:
Let the weight = x
X = (Z × mean × standard deviation)
= (1.645 × 1.4 ×14)
= 16.30kg
b. The probability that a randomly selected crate will weigh more than 16kg will be:
P(z > 16)
= P(Z > 16-14/1.40)
= P(Z > 1.43)
Looking under the normal distribution table, the value is 0.0764.
c. The probability that at least 2 of them will weigh more than 16kg when 20 crates are randomly and independently selected will be through binomial distribution where n = 20 and p = 0.0764.
This will give a value of:
= 1 - 0.5416
= 0.4584
Therefore, the probability that.at least 2 of them will weigh more than 16kg is 0.4584.
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Geoffrey buys 48 shares of Deegan Pharmaceuticals at $6.15.each, and his broker charges him a commission of $81. How
much did Geoffrey pay for his stock?
a. $376.20
b. $295.20
C. $450.30
d. $219.60
Answers
Answer:
A
Step-by-step explanation:
He paid $376.20
The equation C= 8h+25 represents the cost in dollars, C, to rent a canoe, where h is the number of hours the canoe is rented.
What is the cost to rent a canoe for 4 hours?
Answers
The cost to rent a canoe for 4 hours is $57.
How to calculate the cost?It should be noted that the equation given is illustrated as equation C= 8h+25 represents the cost in dollars, C, to rent a canoe.
C = 8h + 25.
where h = number of hours
C = 8h + 25
When h = 4..
C = 8h + 25
C = 8(4) + 25
C = 32 + 25
C = 57
Therefore, the cost to rent a canoe for 4 hours is $57.
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Given the following composite figure, d = 7.5 cm and w = 15.1 cm.
What is the area of the figure?
Answers
Answer:
157.41
Step-by-step explanation:
It can be identified that, given the figure, there is a rectangle and 2 semicircles.
Let's find the area of the rectangle first: A=L*w
Plugging in the given values => A=7.5*15.1 which equals 113.25.
Now the area for the semicircles: 1/2(3.14*r^2)
First, we need to find the radius. To find the radius, you just have to divide the diameter by 2. So, 7.5/2=3.75.
We can plug square the radius which is 3.75 and plug it into the formula: 1/2(3.14*3.75^2)=>22.078125.
22.078125 is the area of only one semicircle so we need to multiply it by 2 because we have two semicircles. So, we get 44.15625.
Finally, we can add them all up to find the total area of the figure: 113.25+44.15625=157.40625.
Rounding to the nearest hundredth=>157.41
Ashley received a $22 discount on a radio she bought for $96.00. What is the percent of discount she saved?
Answers
Answer:
18.64% discount
Step-by-step explanation:
If she had a $22 discount and bought the radio for $96, then the original cost was $118.
discount = (22 * 100) / 118
Given a regular pentagon with radius 5, and each side of length 6, find the area of the pentagon. A) 120 square units B) 60 square units C) 45 square units D) 30 square units
Answers
The area of the regular pentagon is 60 square units
How to determine the area of the pentagon?The given parameters are
Radius, r = 5 units
Side length, l = 6 units
The area of the pentagon is calculated as
A = 1/4√[25 + 10√5] * l^2
Substitute 6 for l in the above equation
So, we have
A = 1/4√[25 + 10√5] * 6^2
Evaluate the product
A = 60 (approximated)
Hence, the area of the regular pentagon is 60 square units
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what do r and y mean??
Answers
Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa
how many cups of milk is that
how many cups of cocoa is that
Answers
Han produced hot chocolate by combining 6 tablespoons of cocoa with 4 cups of milk. For every spoonful of cocoa, 0.67 glasses of milk are required.
The relationship between two values is described by a ratio. It displays how frequently one value appears in another. The answer to this question will depend on how many cups of milk there are to every tablespoon of chocolate.
Divide the provided cups of coffee by the cost of the tablespoon of coffee to get the required quantity of milk per tablespoon of chocolate.
Cups per tablespoon of coffee equal cups of milk divided by tablespoons of cocoa.
Given that,
Number of cups of milk = 4
Tablespoons of cocoa = 6
4/6=0.67 cups
Therefore, for every spoonful of cocoa, 0.67 glasses of milk are required.
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PLEASE HELP ASAP WILL GIVE BRAINLIST
Question 3(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation LC)
Find the product of (3 x 10^9) and (2 x 10^9). Write the final answer in scientific notation.
6 x 1081
6 x 10018
6 x 1018
6 x 109
Answers
Answer:
6 x 10^18
Step-by-step explanation:
u multiply numbers as normal and add exponents when they are being multiplied to each other
Answer:
C. 6 x 10^18
Step-by-step explanation:
Hope it helped :)
(Ik it was already answer but I just wanted to answer)
list 5 multiples of 9
Answers
Answer:
9, 18, 27, 36, 45
Step-by-step explanation:
multiples is like finding the factors. like 1*9=9 and 2*9=18, 9*3=27, 4*9=36, 9*5=45
0.39 x 10^9
Put in scientific notation and explain how it works.
Answers
Answer:
3.9 x [tex]10^{8}[/tex]
Step-by-step explanation:
0.39 is not in scientific notation. For a number to be in scientific notation the first factor has to be 1 or greater, but less then 10. 0.39 is less than one.
First we must write 0.39 in scientific notation. We need to move the decimal so that the number is greater than 1, but less than ten. If we move the decimal one place to the right, we get 3.9. The standard number is smaller than 3.9. How much smaller? [tex]10^{-1}[/tex] smaller.
0.39 in scientific notation would be 3.9 x [tex]10^{-1}[/tex]. We cannot forget the [tex]10^{9}[/tex], so our number looks like this now:
3.9 x [tex]10^{-1}[/tex] x [tex]10^{9}[/tex] The product of powers principle tells us that if we have powers with the same bases, we can add the exponents.
3.9 x [tex]10^{-1+9}[/tex]
or 3.9 x [tex]10^{8}[/tex]
last year 30 people went on a family trip to universal this is 5 times as many people that went the year before. how many people went the uear before?
Answers
Answer:
6 people
Step-by-step explanation:
To figure this out, let's set up an equation.
We know 30 people went last year to Universal, and that this is 5 times as many people as who went the year before
So to figure out how many went the year before, we divide 30 by 5
30/5 = 6
So 6 people went to Universal the year before.
I hope this helps :)
6 people went the year before
Explanation:
If 30 ppl went this year, you would have to find what times what equals 30. So jf it was 5 times more than before, the answer would be 6 because you would have to do 5 X 6 which would equal 30 so the answer is 6.
Hope this helped :)
graph the following. x= -1. y= 5
Answers
Answer:
NOT possible to draw
Step-by-step explanation:
Answer:
graph the following
x=-1 y =5
it look like a two line
Step-by-step explanation:
40 POINTS! Use the following figure to answer BOTH parts the question.
(a) Describe in words a sequence of transformations that maps ∆ABC to ∆A''B''C''.
(b) Write an ordered-pair rule for each transformation in the sequence.
Answers
Answer:
BC to ∆A''
Step-by-step explanation:
How far could you travel walking backwards in 15 minutes based on you speed for the 5 meter trial?
Answers
The correct answer answers will vary
Students should apply their findings to the calculation to determine a distance.
S=D÷T. The speed would be equal to the time and the speed from the 5-meter trial of walking backwards.
ought should be 15 minutes. To calculate the distance, students must multiply the speed by the time.
The distance that an item travels in relation to the amount of time it takes to do so may be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
The speed formula, which was developed by scientists, is used to determine different types of speed. The speed equation is:
Speed=Distance/Time
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If the measure of angle 2=a+15 and the measure of angle 3=a+35, find a if HL is perpendicular to HJ
Answers
The value of a if HL is perpendicular to HJ is 20
How to determine the value
From the information given, we have that;
HL = angle 2 = a + 15HJ = angle 3 = HJIt is important to note that perpendicular lines always intersect each other and the angle between perpendicular lines is equivalent to 90 degrees.
Then, we have that;
Angle 2 + angle 3 = 90 degrees
Substitute the values
a + 15 + a + 35 = 90
collect like terms
2a + 50 = 90
2a = 90 - 50
subtract like terms
2a = 40
Make 'a' the subject
Divide both sides by 2
2a/2 = 40/2
a = 20
Thus, the value of a if HL is perpendicular to HJ is 20
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Help!
Let y=0. Evaluate the expression.
4(6y+1)
4
0
244
5
Answers
Answer:
Given y = 0,
[tex]\sf 4(6y+1)\\4(6* 0+1)\\(6 * 0 + 1)\\(6 * 0)\\= 0\\= 0 + 1\\= 1\\= 1 * 4\\= 4[/tex]
Thus, the answer is 4.
what is the answer to this equation 21 x ___=7
Answers
Answer:
the answer is 3
Step-by-step explanation:
21 x 3 =7
hope it helps
Answer:
21/7
Step-by-step explanation:
Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3
4.)
Find the area of the polygon with the given vertices:
E(3, 1), F(3,-2), G(-2,-2)
Perimeter EFG =____
Answers
When a vehicle is in motion, it has _____.
Answers
Answer:
Kinetic energy
Step-by-step explanation:
because when something is in motion it gains kinetic energy
A house has decreased in value by 35% since it was purchased. If the current value is $104,000, what was the value when it was purchased?
Answers
The value when it was purchased is $160,000 in linear equation.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let the original price be = x
Decreased value = 0.35
Current value = 104000
x - 0.35x = 104000
0.65x = 104000
x = 104000/0.65
x = 160,000
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Beth is making a beanbag seat in the shape of a cube. Each side of the seat is 2 feet long. Beth needs to find the volume of the seat so that she can buy the correct amount of bean. Beans are sold in bags that hold 2 cubic feet of beans. How many bags should Beth buy?
Answers
With the help of the volume of cube it is concluded that Beth should buy 4 bags of beans.
What Is Volume of Cube?The volume of a cube is the total three-dimensional space that it occupy. A cube's volume is expressed as cubic units. The SI unit of volume is the cubic meter [tex](m^3)[/tex], which is the volume occupied by a cube with each side measuring 1 m.
The first thing to do in this case is to find the volume of the cube, which will be given by:
V = [tex]L ^ 3[/tex]
where, L = sides of the cube.
Substituting we have:
V = [tex](2) ^ 3[/tex]
V = [tex](8) ^ 3[/tex]
Since, beans are sold in bags that hold two cubic feet of beans.
Now, to find the number of bags, we calculate
n = 8/(2)
n = 4
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Aniela took 10 pages
of notes over the span of 4
classes. If Aniela worked at a
constant rate, how many notes
did she take in one class?
Answers
Answer: Aniela took 2.5 pages of notes per class
Step-by-step explanation: If you take the total amount of pages of notes taken and divide it by the number of classes you get the rate of pages of notes per class. So 10 pages/4 classes = 2.5 pages/class
Differentiate with respect to y
[tex]5y = {y} ln( {x}^{2} ) [/tex]
Answers
Answer:
[tex]{ \tt{5y = y ln( {x}^{2} ) }} \\ { \tt{impossible}}[/tex]
How do you simplify (2/3) with a sqrt of 2
Answers
What is 6 over 9 times 6 over 8 equal
Answers
Answer:
0.5
Step-by-step explanation:
Answer: the answer is 0.5 or 1/2
Step-by-step explanation: