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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Need help with this ASAP
a) The solution to the equation is given as follows: x = -12.
b) The solution to the inequality is given as follows: -12 ≤ x < 7.
How to solve?The equation for this problem is given as follows:
f(x) = g(x).
The point of intersection of the functions f(x) and g(x) is given as follows:
(-12, -7).
Hence the solution is given as follows:
x = -12.
For the inequality, we have that:
f(x) = g(x) at x = -12.f(x) = h(x) at x = 7.Hence the solution to the inequality is given as follows:
-12 ≤ x < 7.
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Which translation moves a triangle 6 units to the right and 3 units down?
Answer:
A translation of (x+6, y-3)
Step-by-step explanation:
X goes left or right, while Y goes up or down. So, to move the triangle 6 units to the right, we take our current x coordinate, and add 6 to it.
48+24x3-x+10x4-5x2 in standard form
The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.
The given expression is:
48 + 24x3 - x + 10x4 - 5x2
First, we arrange the terms in descending order of degree:
10x4 + 24x3 - 5x2 - x + 48
Next, we combine the like terms:
10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48
Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
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9) The graph shows the amount of money Lucy makes for babysitting. a) Using the graph, give an equation in the form of d=rh , where d is dollars,r is rate, and h is hours, that accurately describes this situation.
The linear equation that gives the graph expression is: d = 2h
How to solve Linear equation Graphs?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
We are given the equation as: d = rh
where:
d is dollars
r is rate
h is hours,
From the graph, we can find the rate by finding the slope of the graph.
(1, 4) and (2, 8)
Thus:
Slope = (8 - 4)/(2 - 1)
Slope = 2
Thus, r = 2
Then d = 2h
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Simplify the following fraction:
x² + x -6 / x²-9
pls help asap
Answer:
The answer is located inside the file sent below
Find the value of x
if:
a square’s perimeter is (x+7) cm
and its side length is 12 cm
.
Answer:
41
Step-by-step explanation:
Given
Perimeter of a square ( P ) = (x + 7) cm
Side length ( L ) = 12 cm
To find : The value of x
Formula :
Perimeter of a square = 4L
4 * 12 = x + 7
48 = x + 7
x + 7 = 48
x = 48 - 7
x = 41
tly cloudy
The value of a certain investment over time is given in the table below. Answer the
questions below to determine what kind of function would best fit the data, linear or
exponential.
Number of
Years Since
Investment
Made, x
Value of
Investment
(s), f(x)
1
27,171.30
22,507.26 18,718.31
3
values change
function is approximately
function would best fit the data because as x increases, the y
The
of this
Q Search
15,412.40
GM
An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.
How to identify an exponential function?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.
The rate of change for this problem is approximated as follows:
22507.26/27171.30 = 0.828.18712.31/22507.26 = 0.831.15412.4/18712.31 = 0.824.Hence the rate can be rounded to 0.8275.
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PLEASE HELP!!!
Find the x and y intercepts for8x - 16y= 64.
A. x=4; y = 8
B. x=8;y = 4
C. x=8; y = -4
D. x=1/4; y = 8
Answer:
C. x =8; y = -4
Step-by-step explanation:
To find the x and y intercepts, substitute with zero.
8x - 16y = 64
Finding the x-intercept:
8x - 16(0) = 64
8x = 64
Divide both sides by 8.
x = 8
Finding y-intercept:
8(0) - 16y = 64
-16y = 64
Divide both sides by -16.
y = -4
Which of the following functions M best represents the area of the figure shown ?
The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)
The total area of the composite figure is the sum of the areas of the individual shapes
So, we have
Area = Rectangle + Triangle
Using the area formula, we have
M(x) = (x + 2)(x - 2) × 1/2 × x × (x + 2)
Factorize the expression to get the function
M(x) = (x + 2)(x - 2 + x/2)
So, we have
M(x) = (x + 2)(3/2x - 2)
Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)
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A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 13 millimeters long, and the height of the equilateral triangle is 11.3 millimeters. The pyramid's slant height is 17 millimeters. What is its surface area?
The surface area of the Triangular pyramid is approximately 331.3 square millimeters.
The surface area of a triangular pyramid, we need to calculate the area of its base and the area of each triangular face, then add them together. The formula for the surface area of a triangular pyramid is:
SA = (1/2)P*l + B
where SA is the surface area, P is the perimeter of the base, l is the slant height of each triangular face, and B is the area of the base.
In this case, the base of the triangular pyramid is an equilateral triangle with legs of 13 millimeters and a height of 11.3 millimeters. To find the area of the base, we can use the formula for the area of an equilateral triangle:
B = (sqrt(3)/4)*a^2
where a is the length of a side of the equilateral triangle.
Substituting a = 13 into the formula, we get:
B = (sqrt(3)/4)*13^2
B = (sqrt(3)/4)*169
B = 43.7 square millimeters (rounded to one decimal place)
Next, we can find the perimeter of the base:
P = 3a
P = 3*13
P = 39 millimeters
Now we can use the formula for the surface area of a triangular pyramid:
SA = (1/2)P*l + B
Substituting P = 39, l = 17, and B = 43.7, we get:
SA = (1/2)*39*17 + 43.7
SA = 331.3 square millimeters (rounded to one decimal place)
Therefore, the surface area of the triangular pyramid is approximately 331.3 square millimeters.
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The figure shows the dimensions for a package to be shipped.
A trapezoidal prism. The front and back are trapezoids.The distance from the trapezoidal front to the trapezoidal back is 15 inches.
The slant is on the right side. The Height on the left is 6 inches, On the top, the width from the left to the top of the slanted side is 4 inches. The distance of the slant from top to bottom is 10 inches. The entire width of the base from the left to right (that is, from the left side of 6 inches to the bottom of the slant) is 12 inches.
What is the minimum amount of wrapping paper, in square inches, needed to cover the package?
The minimum amount of wrapping paper that is needed to cover the package is 576 square inches.
How to calculate the total surface area of a trapezoidal prism?In Mathematics and Geometry, the total surface area of a trapezoidal prism can be calculated and determined by using this mathematical equation or formula:
Total surface area of a trapezoidal prism, TSA = (a + b)h + (a + b + c + d)l
Where:
TSA represent the total surface area of a trapezoidal prism.l represent the length of a trapezoidal prism.a, b, c, d represent the base edges of a trapezoidal prism.h represent the height of a trapezoidal prism.By substituting the given parameters into the total surface area of a trapezoidal prism, we have:
TSA = [(12 + 4) × 6/2] × 2 + [(12 × 15) + (10 × 15) + (4 × 15) + (9 × 15)]
TSA = 96 + 180 + 150 + 60 + 90
TSA = 576 square inches.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
10. A plane is flying from Winnipeg to Calgary against a strong headwind of 50 km/hr. The plane
1/2 takes hour longer for this flight than it would take in calm air. If the distance from Winnipeg to
Calgary is 1200 km, what is the speed of the plane in calm air, to the nearest kilometer per hour?
The speed of the plane in calm air is 372 km/h
Given that a plane is travelling from Winnipeg to Calgary against a 50 km/hr headwind.
This flight takes half an hour longer than it would in calm air.
The distance between Winnipeg and Calgary is 1200 km.
Since we know that,
Speed may be defined as the distance travelled by an item in relation to the time it takes to travel that distance.
In other words, it measures how rapidly an item travels but does not provide direction. The term "velocity" refers to the combination of direction and speed.
The speed is defined by the rate of distance.
We must determine the plane's speed in calm air.
xy=1200
(x-50)(y+1/2) =1200
x² - 50 x-12000=0
By using quadratic formula.
x=372 as x>0
Hence, 372 km/h is the speed of the plane in calm air
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In a recent election, there were six candidates and 3200 total votes. The table below summarizes the votes by candidate. This information is also presented as a
circle graph.
Find the central angle measure, xº, for the Bowerman slice in the circle graph. Do not round.
Candidate
Mendez
Watkins
Choi
Nguyen
DeWitt
Bowerman
Number
of Votes
864
384
736
704
288
224
Choi
Watkins
Nguyen
Mendez
Bowerman
DeWitt
Español
111
K
The measure of x is 25.2 degree
Given that,
Total number of votes = 3200
Bowerman's share = 224
Now the percentage of Bowerman's share = (224/3200)x100
= 7%
Now we know that.
The complete angle of circle is 360 degree.
Therefore the value of x shown in the figure is,
x = 7% 360
= (7 x 360)/100
= 25.2 degree
Therefore,
⇒ x = 25.2 degree
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A retirement account has a balance of $300,000. You want to receive monthly payments(withdrawals) from the account for a total of 25 years. The retirement account earns 4% interest. How much will you be able to receive each month?
The monthly payments you can withdraw from the retirement account is $1,583.4.
What is the amount received each month?The monthly payments you can withdraw from the retirement account, is calculated as;
PV = Px [(1 - (1 + r)⁻ⁿ) / r]
where;
PV is the present value of the annuity P is the monthly payment you want to receiver is the interest rate per period n is the total number of periodsThe total number of periods = 25 years x 12 months/year = 300 months
PV = P x [(1 - (1 + r)⁻ⁿ) / r]
$300,000 = P x [(1 - (1 + 0.04/12)⁻³⁰⁰) / (0.04/12)]
$300,000 = P x 189.47
P = $300,000 / 189.47
P= $1,583.4
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Reflection over the x-axis of the point ( − 3 , − 7 ) (−3,−7)
The image of the point (-3, -7) after a reflection over the x-axis is (-3, 7)
Calculating the image of the point after a reflection over the x-axis?From the question, we have the following parameters that can be used in our computation:
Point = (-3, -7)
Transformation rule
A reflection over the x-axis
The rule of a reflection over the x-axis is
(x, y) = (x, -y)
Using the above as a guide, we have the following:
Image = (-3, 7)
Hence the image of the point after a reflection over the x-axis is (-3, 7)
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The length of a rectangle is 50 meters and the width is 24 meters. Find the perimeter and the area.
Answer:
[tex]Area = 1200m^2[/tex]
[tex]Perimeter = 148m[/tex]
Step-by-step explanation:
To find the area, just multiply the length by the width. In fact, we have a simple formula for this:
[tex]A(area) = lw[/tex]
[tex]l(length) = 50[/tex]
[tex]w(width)= 24[/tex]
Now, we need to plug in our values:
[tex]A(area)= 50*24[/tex]
Simplify:
[tex]A(area) = 1200[/tex]
Therfore, the area of the rectangle is:
[tex]1200m^2[/tex]
Now, lets move on to the perimeter(again, we have a simple formula!):
[tex]P(perimeter) = 2(l+w)[/tex]
Plug in our values from before:
[tex]P(perimeter)= 2(50 + 24)[/tex]
Simplify:
[tex]P(perimeter)= 2(74)[/tex]
Multiply it out:
[tex]P(perimeter) = 148[/tex]
Therfore, the perimeter of your rectangle is 148 m
Always remember to include the proper units and format your work well to minimize mistakes and leave less room for error.
I hope this helped!
~~~Harsha~~~
tions using any method: word problems WHE
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Clarksville City Cafe recently introduced a new flavor of coffee. They served 60 grande cups
and 59 jumbo cups of the new coffee today, which equaled a total of 61,644 grams. The day
before, 60 grande cups and 74 jumbo cups were served, which used a total of 71,184 grams.
How much coffee is required to make each size?
There are 968
grams in a grande cup of coffee and
Submit
grams in a jumbo one.
For this reason, 968 grams of coffee are needed to make a grande cup, and 998 grams are needed to make a jumbo cup.
Let's call the amount of coffee required to make a grande cup "g" and the amount of coffee required to make a jumbo cup "j". We want to find the values of g and j.
From the first piece of information, we know that:
60g + 59j = 61,644
From the second piece of information, we know that:
60g + 74j = 71,184
We can solve this system of equations by using the method of elimination. To eliminate g, we can subtract the first equation from the second equation:
(60g + 74j) - (60g + 59j) = 71,184 - 61,644
Simplifying, we get: 15j = 9540
Dividing by 15, we get: j = 636
Now that we know j, we can substitute it into either equation to find g. Let's use the first equation:
60g + 59(636) = 61,644
Simplifying, we get: 60g = 59,880
Dividing by 60, we get: g = 998
Therefore, the amount of coffee required to make a grande cup is 968 grams, and the amount of coffee required to make a jumbo cup is 998 grams.
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2
S17
3
Check
5
7
(about 89%) of the
(a) According to Chebyshev's theorem, at least
lifetimes lie between] hours and hours. (Round your answer to the
nearest whole number.)
(b) According to Chebyshev's theorem, at least (Choose one) of the
lifetimes lie between 746 hours and 1110 hours.
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries. To investigate its new line of Ultra batteries, BIG
randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 928 hours, with a standard deviation of 91 hours. Suppose that this mean and
standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.
Search
X
10
3
11
12
13
Save For Later
Submit As
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a) According to Chebyshev's Theorem, at least 89% of the lifetimes are between 655 hours and 1201 hours.
b) According to Chebyshev's theorem, at least 75% of the lifetimes lie between 746 hours and 1110 hours.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].The lifetimes within 2 standard deviations of the mean are given as follows:
928 - 2 x 91 = 746 hours.928 + 2 x 91 = 1110 hours.The lifetimes within 3 standard deviations of the mean are given as follows:
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WILL MARK BRAINLIEST
An account invested in a money market fund grew from $73,310.56 to $73,608.40 in a month. What was the interest
rate to the nearest tenth?
What was the interest rate?
%
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answer:
1 - ($73,310.56/$73,608.40)^12 = .047
= 4.7%
Use the functions s(x) and c(x) to determine each value.
s(5)
The Trigonometric functions sine (s) and cosine (c) c(5) ≈ -0.2837.
The trigonometric functions sine (s) and cosine (c). To determine s(5), we need to know the value of sine of 5 radians.
We can use a scientific calculator or a trigonometric table to find this value.
Using a calculator, we can simply enter "sin(5)" and get the answer. On most calculators, the answer will be displayed as a decimal.
Using a trigonometric table, we can look up the value of sine for 5 radians. The table will list the sine of angles in degrees, so we need to convert 5 radians to degrees first. One radian is equal to 180/π degrees, so
5 radians = (5 × 180)/π degrees ≈ 286.48 degrees
Looking up the sine of 286.48 degrees in the table, we get:
sin(286.48°) ≈ -0.9589
Therefore, s(5) ≈ -0.9589.
To determine c(5), we need to know the value of cosine of 5 radians.
We can again use a calculator or a trigonometric table to find this value.
Using a calculator, we can enter "cos(5)" to get the answer.
Using a trigonometric table, we can look up the cosine of 5 radians. Since we have already converted 5 radians to degrees, we can simply look up the cosine of 286.48 degrees in the table. We get:
cos(286.48°) ≈ -0.2837
Therefore, c(5) ≈ -0.2837.
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Write a exponential function
Answer:
2f2y3ui2ke9i22881o228j11 GJ
Answer:
[tex]y = 0.0625(2) {}^{x} [/tex]
Step by step
[tex]y = a(b^{x} )[/tex]
X = 1 y = 0.125
[tex]0.125 = ab^{1} \\ a = \frac{0.125}{b} [/tex]
X = 4 y = 1
[tex]1 = a( {b}^{4} ) \\ ab^{4} = 1 \\ replace \: a = \frac{0.125}{b} \: in \: ab^{4} = 1 \\ \frac{0.125}{b} \times b^{4} = 1 \\ {b}^{3} = \frac{1}{0.125} \\ b = \sqrt[3]{ \frac{1}{0.125} } \\ b = 2[/tex]
[tex]replace \: b = 2 \: in \: a = \frac{0.125}{b} \\ a = \frac{0.125}{2} \\ a = 0.0625[/tex]
[tex]therefore \: \\ y = 0.0625( {2})^{x} [/tex]
Can anyone help me on this one
Hello !
Answer :
[tex]{x}^{ - \frac{8}{3} }[/tex][tex]\sqrt[3]{ {x}^{ - 8} }[/tex][tex]\sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }[/tex]Explanation :
[tex] \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } [/tex]
[tex] \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } [/tex]
[tex] ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}[/tex]
Have a nice day ;)
If a rectangular container is 25cm by 37cm by 21cm how much does it overflow
If a rectangular container is 25cm by 37cm by 21cm, then it will overflow after reaching the volume of 19425 cm³.
To know the volume after which the container will overflow, first we have to calculate the volume it can contain.
As, Volume of cuboid= length × breadth × height
So, Volume of rectangular container = 25 × 37 × 21 cm³
Volume = 19425 cm³
So, volume of rectangular container whose dimensions are 25cm by 37cm by 21cm is 19425 cm³ and it will overflow after reaching this volume.
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Find dx/dt when x = e^6t
A bag contains red and yellow cubes in the ratio of 3:4. What is the probability that a red cube is picked at random from the bag?
Answer:
Step-by-step explanation:
ok Let me explain :
Your argument of saying that the prob is 1/2 because there are 2 colors.
Had there been red, blue and green cubes you would have ended up calculating the prob as 1/3.
But this concept is wrong.
Prob is the chance occurrence of an event given many such events.
here since we have 4 cubes , the chance to pick any one is equal and that is 1/4
chance of picking a blue cube (1/4)*1 ....since we have one blue cube
chance of picking a red cube (1/4)*3 ....since we have one red cubes
You can think in a simple manner also, when something is greater in number (3>1) , the chances to pick that would obviously be more , so the probability cannot be half.
Find the x intercepts of the parabola with vertex (-1,2) and y intercept (0,3).
The x intercepts of the parabola are -1 + i√(2) and -1 - i√(2)
How to find the x intercepts of the parabolaUsing the equation:
y = a(x - h)²+ k
where (h, k) is the vertex of the parabola
y = a(x + 1)²+ 2
solving for a at the y intercept
y = a(x + 1)²+ 2
3 = a(0 + 1)²+ 2
a = 1
To find the x intercepts we need to set y = 0 and solve for x:
0 = (x + 1)²+ 2
x + 1 = ±√(-2)
x + 1 = ±i√(2)
x = -1 ± i√(2)
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Richard is selling bundles of wood. The total weight of the wood he is selling is 3,941 pounds, and there are 70 bundles. If each bundle weighs the same, how much does one bundle of wood weigh?
Answer:
Each bundle of wood weighs approximately 56.3 pounds.
Explanation:
To determine the weight of one bundle, we divide the total weight of all the bundles by the number of bundles. Thus, the weight of one bundle is equal to 3,941 pounds divided by 70 bundles, which is approximately 56.3 pounds. Therefore, each bundle of wood weighs approximately 56.3 pounds.
Henry has 50 apples. He gives 4 apples to f friends. What is the different in the expression 50 - 4f? What does the different represent?
Answer:
I don't understand you
Write an expression to represent:
5 times the sum of x and 3
Answer:
5(x + 3)
Step-by-step explanation:
the sum of x and 3 is x + 3, then multiply by 5 to obtain
5(x + 3)
2x + 8 > -4. 2.find the solution set of x and express the solutions set in number form
The solution set of this inequality is {x| x > -6.1}
How to find the solution set?Here we have the inequality:
2x + 8 > -4.2
To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:
2x + 8 > -4.2
2x > -4.2 - 8
2x > -12.2
x > -12.2/2
x > -6.1
So the set of all numbers larger than -6.1, this in number form is:
{x| x > -6.1}
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