The outcomes in set A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)
The sum of the number cubes is odd if one die shows an even number and the other shows an odd number, or vice versa.
There are 3 even numbers and 3 odd numbers on a number cube, so there are 3 x 3 = 9 ways to get an odd sum.
The sum of the number cubes is divisible by 4 if both dice show either 2 or 4.
There are 2 ways to get a 2 on a number cube and 2 ways to get a 4, so there are 2 x 2 = 4 ways to get a sum of 4.
Therefore, the outcomes in A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)
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Find the Value of X.
The measure of the unknown sides is equivalent to 12.6
Circle geometry problemThe given figure is a circle geometry with the perpendicular lines intersecting both segments of the circle.
We need to determine the measure of x. Since the measure of the perpendicular lines are equal, hence the measure of the line of the segments will also be equal.
Hence:
x = 6.3 + 6.3
x = 12.6
Therefore the measure of x from the given diagram is equivalent to 12.6
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Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x+2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x-7.
Calculate the limit as 1.
The correct statement is:
"Divide out a common factor of x - 7." The limit of the given expression is 1/6.
Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):
This statement is not correct.
We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.
Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.
Divide out a common factor of x - 7:
This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Calculate the limit as 1/6:
This statement is not correct. We need to perform further simplification to determine the limit.
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.
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Find the slope and y intercept of the line 5x-9y=45
Answer:
slope = [tex]\frac{5}{9}[/tex] , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
5x - 9y = 45 ( subtract 5x from both sides )
- 9y = - 5x + 45 ( divide through by - 9 )
y = [tex]\frac{-5}{-9}[/tex] x + [tex]\frac{45}{-9}[/tex] , that is
y = [tex]\frac{5}{9}[/tex] x - 5 ← in slope- intercept form
with slope m = [tex]\frac{5}{9}[/tex] and y- intercept c = - 5
A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
The maximum distance of the fire engine from the school is D = 4.5 miles
Given data ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P = P ( -4 , -3 )
Let the second point be Q = Q ( -7 , -3 )
First distance D₁ = √ ( -4 + 7 )² + ( -3 + 3 )
D₁ = √9
D₁ = 3 units
Now , each unit on the grid represents 1/2 mile
And , the distance from P to school is S ( -4 , 3 )
D₂ = √ ( -4 + 4 )² + ( -3 - 3 )²
D₂ = √36
D₂ = 6 units
So , the total distance D = 3 + 6 = 9 units
And , the distance in miles = 9/2 = 4.5 miles
Hence , the distance is 4.5 miles
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The complete question is attached below :
A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
Determine the equation of the circle with center (0, -2) containing the point
(√12,-5).
Answer:
i think its
x^2 + (y + 2)^2 = 21.
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
To represent a circle with a diameter of 12 units and a center that lies on the y-axis, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
If the center of the circle lies on the y-axis, then the x-coordinate of the center is 0. Also, since the diameter is 12 units, the radius is 6 units.
Using these values, we can eliminate the equations that do not meet these conditions:
- x2 + (y – 3)2 = 36: This circle has a center at (0, 3), which is not on the y-axis.
- x2 + (y – 5)2 = 6: This circle has a center at (0, 5), which is not on the y-axis.
- (x – 4)² + y² = 36: This circle has a center at (4, 0), which is not on the y-axis.
- (x + 6)² + y² = 144: This circle has a center at (-6, 0), which is not on the y-axis.
- x2 + (y + 8)2 = 36: This circle has a center at (0, -8), which is on the y-axis.
Therefore, the two equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
- x2 + (y + 8)2 = 36
- x2 + (y - 8)2 = 36
Note that the second equation is also valid, since the center of the circle can also be located at (0, -8).
Suppose you want to buy a $160,000 home. You found a bank that offers a 30-year loan at 3.3% APR.
What will be your monthly payment? (Round to the nearest cent.)
$
How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.)
$
Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.)
$
How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.)
$
How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)
$
The required solution with the concern of mortgage has been shown below.
$695.67, $250,441.20, $783.93, $235179, and $15262.2.
Using the formula for the monthly payment of a mortgage:
[tex]P = L[c(1 + c)^n]/[(1 + c)^n - 1][/tex]
Here P is the monthly payment, L is the loan amount, c is the monthly interest rate, and n is the total number of payments (in this case, 30 years = 360 months).
Plugging in the values given:
L = 160000
c = 0.033/12 (monthly interest rate)
n = 360
P = 695.67
So the monthly payment is $695.67.
To find out how much will be paid in total over 30 years, we can multiply the monthly payment by the total number of payments:
Total payments = P * n = $695.67 * 360 = $250,441.20
So the total amount paid to the bank for the home over 30 years is $250,441.20.
To calculate the new monthly payment for a 25-year loan, we can use the same formula but with n = 25*12 = 300 months:
P = 160000[(0.033/12)(1 + (0.033/12))^300]/[(1 + (0.033/12))^300 - 1]
P = $783.93
So the new monthly payment for a 25-year loan is $783.93.
The total amount paid over 25 years would be:
Total payments = P * n = $783.93 * 300 = $235179
So the total amount paid to the bank for the home over 25 years is $235179.
The amount saved by reducing the time of the mortgage loan is the difference between the total amount paid for the 30-year loan and the total amount paid for the 25-year loan:
Savings = $250,441.20 - $235179 = $15262.2
So the amount saved by reducing the time of the mortgage loan is $15262.2.
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Given △HJK ~ △RST, what is cos T?
Answer:
cos T = 5/9-------------------
As per definition, the cosine function is:
cosine = adjacent / hypotenuseSince triangles are similar, the ratio of corresponding sides is same:
cos T = ST / RTcos T = cos K = JK / HK = 5/9Credit card A has an APR of 20.8% and an annual fee of $60, while credit card
B has an APR of 24.6% and no annual fee. All else being equal, which of these
equations can be used to solve for the principal, P, the amount at which the
cards offer the same deal over the course of a year? (Assume all interest is
compounded monthly.)
The amount at which the cards offer the same deal over the course of a year is a $2,333.33
Since credit card finance charge is the fee associated with using credit.
Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.
Data and Calculations:
Card A Credit B
APR 20.8% 24.6%
Annual fee $60 $0
To calculate the balance required, the required equation is
= 22%x + $40 = 24.6%x
Where x = required balance
Thus,
= 0.208x + $60 = 0.246x
= $60 = 0.03x (0.246x- 0.208x )
= 0.03x = $60
x = $60 /0.03
x = $2,333.33
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Determine whether the following individual event are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 5 red pieces of candy out of 49 pieces of candy total.
PLEASE HELP ASAP :) WILL GIVE BRAINLIEST
a metallurgist has one alloy containing 32% aluminum and another containing 44% aluminum. How many pounds of each alloy must he use to make 54 pounds of a third alloy containing 36% aluminum?
The number of pounds of each alloy he must use are: 49.33 of 32% aluminum and 4.67 of 44% Alloy
How to solve Algebra Word Problems?X = amount of alloy 1
Y = amount of alloy 2
Thus:
X + Y = 54
X = 54 - Y
0.32X + 0.44Y = 0.36 * 54
0.32X + 0.44Y = 19.44
Plugging in 54 - Y for X gives us:
0.32(59 - Y) + 0.44Y = 19.44
18.88 - 0.32Y + 0.44Y = 19.44
0.12Y = 19.44 - 18.88
Y = 0.56/0.12
Y = 4.67
X = 54 - 4.67
X = 49.33
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The equation and the table show two linear functions.
Function A:
x
-6
0
12
y
3
4
6
Function B: y = x +9
What is the rate of change of the function that has the greater rate of change?
h
Answer:
5/2
Step-by-step explanation:
In the figure, angle ESY is vertical to angle TSL. Find the value of x given that M angle ESF=125 degrees. Then find m Angle ESY, m Angle TSL, m Angle EST, m Angle YSF, and m Angle FSL.
Find the value of X
The measure of Angle YEA is 70 degrees in the given parallelogram
Given Parallelogram EASY with diagonal ES
∠AES = 40
∠Y = 110
∠ESY = 40 by Z theorem of a parallelogram
∠A = ∠Y by property of parallelogram
∠A = <110 as ∠Y=110
∠YES = 180 - ∠Y
∠YES = 180 - 110 - 40
∠YES = 30
∠YEA = ∠YES + ∠AES
∠YEA = 30 + 40
∠YEA = 70
Hence, the measure of Angle YEA is 70 degrees
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Megan has two boxes. There are x beads in box A. 7 of these beads are white. The rest of the beads are black. There are x beads in box B. 4 of these beads are white. The rest of the beads are black. She chooses at random a bead from box A. She notes the colour and then places this bead into box B. She then chooses at random a bead from box B. The probability of choosing a white bead from box A and a white bead from box B is 22 Work out the total number of beads in the two boxes:
The total number of beads in the two boxes: is: 20
How to solve Algebra Word problems?The parameters given are:
Number of white beads in box A = 7
Number of black beads in box A = x - 7
Number of white beads in box B = 4
Number of black beads in box B = x - 4
The probability of getting white from both boxes is:
P(W & W) = (7/x) * (4 + 1)/(x + 1)
P(W & W) = 35/(x(x + 1)
We are given that P(W & W) = 7/22
Thus:
35/(x(x + 1) = 7/22
Solving gives x = 10
Thus:
Box A has 10 beads and box B has 10 beads.
Total number of beads = 20 beads
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What is 5x6 + (5x5-5)
Answer:50
Step-by-step explanation:
An Intermediate Phase learner plays around with trapeziums and realises when you put them close to each other they tesselate and they have equal opposite angles. At which level of van Hiele’s levels of geometric thought is this learner?
According to van Hiele's levels of geometric thought, the Intermediate Phase corresponds to level 3, which is called the Informal Deduction stage.
What van Hiele’s level is the learner at ?The learner appears to be at level 3, known as the "Informal Deduction" stage. This is evident from their ability to use geometric properties in their reasoning.
At this phase, students start employing logical thinking to understand the connections and characteristics of geometry, using informal explanations and visual aids. Their ability to draw conclusions from particular instances is evident, though they may face difficulties when attempting to extrapolate their findings to broader contexts.
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if y varies inversely as the same of x, and =7/4 whenx = 1, find y when x=3
if y varies inversely as the same of x, and y=7/4 when x = 1 then value of y is 7/12 when x=3
If y varies inversely as the same of x, we can write the equation:
y = k / x
where k is the constant of proportionality.
Let us find the value of constant of proportionality k:
y = 7/4 when x = 1
7/4 = k / 1
Apply cross multiplication we get:
7/4 = k
k=7/4
Now plug in the value of k to find y when x = 3:
y = k /x
y = (7/4) / 3
When a fraction is divided by the whole number then fraction is multiplied with reciprocal of the whole number.
y=7/4×1/3
Multiply the numerators and denominators.
y=7×1/4×3
We know that 7×1 is 7 and 4×3 is 12.
y=7/12
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Question 5 of 25 The Wildcats and the Leopards are evenly matched football teams. When they play, there is a 0.5 probability that the Wildcats will win. If they play 9 times, what is the probability that the Wildcats will win 4 of the games? Round your answer to the nearest tenth of a percent. O A. 7.0% OB. 24.6% OC. 0.2% O D. 16.4% SUBMITTE
Answer:
24.6%
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
n = 9, r = 4, p = 0.5
P = ₉C₄ (0.5)⁴ (1−0.5)⁹⁻⁴
P = 126 (0.5)⁴ (0.5)⁵
P ≈ 0.246
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line (Each pair of variables has a significant comelation) Then use the regression equation to
predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below
130
360
(a)x= 180 calories
(c)x= 140 calories
Calories, x
Sodium, y
150
430
540
170
480
130
340
+
Find the regression equation
-0.0
(Round to three decimal places as needed)
Choose the correct graph below
540
(a) Predict the value of y for x 180. Choose the correct answer below
OA 396.195
OB. 526.275
OC 623.835
OD. not meaningful
(b) Predict the value of y for x 100. Choose the correct answer below
90
250
180
560
CITTD
ос
(b) x 100 calories
(d) x 210 calories
OD
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
Here, we have,
to find the equation of the regression line for a given data:
Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is
ŷ= 6.45x + 31.5.
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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complete question:
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
two buses leave the station at the same time.one travels at 50km/h on a bearing of 046, while the other travels at 90km/h on a bearing of 127.how far apart are they after two hours
The two buses are approximately 141.2 km apart after two hours.
We have,
We can use the Law of Cosines to solve this problem.
Let's call the distance between the two buses "d".
After 2 hours, the first bus will have traveled 100 km (50 km/h x 2 h) and the second bus will have traveled 180 km (90 km/h x 2 h).
Now we can use the Law of Cosines to find d:
d² = 100² + 180² - 2(100)(180)cos(127° - 46°)
d² = 10000 + 32400 - 36000cos(81°)
d² = 42400 - 36000cos(81°)
d ≈ 141.2 km
Therefore,
The two buses are approximately 141.2 km apart after two hours.
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MULTIPLE CHOICE QUESTION:
The table shows the amount of time different students studied for an exam and the scores they received. Draw a line that best represents the data, which equation in slope-intercept form best represents the line of best fit?
OPTION 1: y=1/3x +75
OPTION 2: y=3x + 67
OPTION 3: y=1/3x + 67
OPTION 4: y= 3x +75
Answer:
Option 3: y = 1/3x +67
Step-by-step explanation:
You want the equation of the best-fit line in slope-intercept form for the data given.
Best fitThe attached calculator display shows the best-fit line for the data, where x is in minutes, is approximately ...
y = 0.41x + 64
The closest answer choice is ...
Option 3: y = 1/3x +67
__
Additional comment
The second attachment shows a plot of the data (study minutes, test score) with the best-fit line in red, and the Option 3 line in blue.
<95141404393>
What are the exact values of a and b?
0 a =7/2,
The required exact values of a and b are 7 / 2 and 7√3/2 respectively. Option A is correct.
A triangle ABC is given with measures,
AB = 7, BC = a, and AC = b. Also, angle A is 30°.
To find out the missing measures, we need to apply the trigonometric ratio.
sinA = BC/AB
sin30 = a/7
1/2=a/7
a = 7 / 2
Similarly,
cosB = AC/AB
cos30 = b/7
√3/2 = b/7
b = 7√3/2
Thus, the required exact value of a and b are 7 / 2 and 7√3/2 respectively. Option A is correct.
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Twice the difference of a number and 9 is 3
Answer:
The number is 10.5-----------------
Let the number be n.
Twice the difference of a number and 9 is 3, set up an equation:
2(n - 9) = 32n - 18 = 32n = 21n = 10.5Hence the number is 10.5.
Stuck on this question pls help!!
a) The interval in which the height is increasing is given as follows: (0,2).
b) The interval in which the height is decreasing is given as follows: (4,10), .
c) The interval in which the height is constant is given as follows: (2,4), (10, ∞).
d) The height at 14 seconds is of zero, as when the balloon hits the ground, it does not fly anymore.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.The function is also said to be constant if the graph is a horizontal line.More can be learned about graphs and functions at https://brainly.com/question/12463448
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11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. How many rain jackets were sold
If 11 rain jackets were collected. At the end of the the drive, 10 times that number of rain jackets were collected. The number of rain jackets that were sold is 99.
What is the jackets sold?We must determine the total number of rain jackets gathered at the end of the campaign in order to determine how many were sold.
10 times the original quantity of raincoats gathered is:
= 10 * 11
= 110
So, 110 rain jackets were collected.
Number of raincoats sold:
= 110 - 11
= 99
Therefore 99 rain jackets were sold.
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A solid has as its base the region bounded by the curves y = –2x^2 + 2 and y =-x^2+ 1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the length of the lower base, and height equal to 2 times the length of the lower base.
simplify 2/3 (3x -2) – ¾ (2x -2)
Answer:
Sure, here are the steps on how to simplify 2/3 (3x -2) – ¾ (2x -2):
Multiply the factors in the numerator and denominator of each fraction.
2/3 (3x -2) = (2)(3x -2) / (3)(3) = 6x - 4 / 9
¾ (2x -2) = (3/4)(2x -2) / (3) = 3x - 6 / 12
Subtract the numerators of the two expressions.
6x - 4 / 9 - 3x - 6 / 12 = (6x - 4 - 3x - 6) / (9 * 12) = 3x - 10 / 108
Simplify the fraction by dividing the numerator and denominator by 3.
3x - 10 / 108 = (3x - 10) / (3 * 36) = x - 10 / 36
Therefore, the simplified expression is x - 10 / 36.
Step-by-step explanation:
Calculati :17,2+1,56-14,4
An earthquake in Gansu, China, on December 16, 1920, measured 8.6 on the Richter scale and killed 100 000 people. An earthquake that usually causes no damage measures 4 on the Richter scale. Compare the intensities of the two earthquakes. (THE ANSWER IS 40000).
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
Let's compare the intensities of the two earthquakes using the Richter scale.
Step 1: Understand that the Richter scale is logarithmic, which means each whole number increase represents a tenfold increase in intensity.
Step 2: Determine the difference between the magnitudes of the two earthquakes. The Gansu earthquake measured 8.6, and the earthquake causing no damage measured 4.
8.6 - 4 = 4.6
Step 3: Calculate the intensity ratio between the two earthquakes using the difference in magnitudes. Since each whole number increase represents a tenfold increase in intensity, we need to raise 10 to the power of the difference.
10^4.6 ≈ 39,810.71705535
Step 4: Round the result to a whole number.
39,810.71705535 ≈ 39,811
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
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