The Magnitude of earthquake that hit Texas is 5.8; The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex].
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]
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A sorter at a recycling center separates pieces of glass
into large bins. The table shows the number of pieces
of each color of glass. If each bin can hold 150 pieces of
glass, how many bins will the pieces completely fill? table:
The number of large bins that the pieces will completely fill is 3.
How many bins will the pieces completely fill?Each large bin can contain only one type of colour. In order to determine the number of large bins that would be used for each color, divide the color for each piece.
Number of large bins that would be used for Brown color = 283 / 150 = 1.89.
1 large bins would be completely filled with brown glass color
Number of large bins that would be used for Green color = 116 /1 50 = 0.7
No large bin would be completely filled with the green glass color
Number of large bins that would be used for Clear color = 315 / 150 = 2.1
2 large bins would be completely filled with the clear glass color
The total number of large bins that would be completely filled = 1 + 2 = 3
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Find the mode for the distribution of scores in the following frequency distribution table.
The mode for the distribution of scores in the following frequency distribution table is 3, which is the second option.
What is mode?This is a term used in statistics to refer to the number of highest occurrence. Mode refers to the value that highest the number of frequency. In finding the mode, it is better to orderly arrange the given data to help see the value that occurs more frequently as this is the mode.
For the values given in the distribution of scores in the frequency distribution table the mode is three ( 3 ) and it is the second option
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Four more than the quotient of a number and three is at least nine.
Answer:
umber is greater than or equal to 15.
Step-by-step explanation:
Let number be x
Quotient of number and 3 =
4 more than = 4+
4+ is at least 9
4+≥9
Simplifying it ,we get
≥9-4
≥5
x ≥ 5(3)
x≥15
Number needs to be greater than or equal to 15
Equation
(x ÷ 3) + 4 ≥ 9
___________
Solution
x ≥ 15
Step-by-step explanation:
Solve the inequality
[tex]\left(x\div3\right)+4\ge \:9\\x\div 3+4-4\ge \:9-4\\x\div 3\ge \:5\\3x\div 3\ge \:5\cdot \:3\\x\ge \:15[/tex]
Thus, the inequality solution is x ≥ 15
PLEASE HELP!!! I NEED HELP ASAP IF YOU CAN HELP IT WILL BE VERY NICE!!!!!!!!! (PLEASE HELP ME WITH THE QUESTIONS BELOW)
The solution to question 8, in scientific notation is 9.563 x 10¹¹.
The solution to question 9, in scientific notation is 9.83 x 10⁸.
The solution to question 10, in scientific notation is 1.35759 x 10⁹.
The solution to question 11, in scientific notation is 8.70366 x 10⁴.
What is scientific notation?
Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.
Solution to question 8, in scientific notation(9.5 x 10¹¹) + (6.3 x 10⁹)
= (950 x 10⁹) + (6.3 x 10⁹)
= (950 + 6.3) x 10⁹
= 956.3 x 10⁹
= 9.563 x 10¹¹
Solution to question 9, in scientific notation(1.03 x 10⁹) - (4.7 x 10⁷)
= (103 - 4.7) x 10⁷
= 98.3 x 10⁷
= 9.83 x 10⁸
Solution to question 10, in scientific notation(1.357 x 10⁹) + 590,000
= (1.357 x 10⁹) + (5.9 x 10⁵)
= (13570 x 10⁵) + (5.9 x 10⁵)
= (13570 + 5.9) x 10⁵
= 13,575.9 x 10⁵
= 1.35759 x 10⁹
Solution to question 11, in scientific notation87,100 - (6.34 x 10¹)
= 87,100 - 63.4
= 87,036.6
= 8.70366 x 10⁴
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Write each expression as a single natural logarithm. ln 18-ln 10
Expression as a single natural logarithm of equation ln 18-ln 10 is = 0.5877866649.
What is natural logarithm?ln 18-ln 10
= [tex]ln (18/10)[/tex]
= ln 1.8
= 0.5877866649
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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Solve each equation. Check your answers.
ln (2 m+3)=8
After solving the equation In (2m + 3) = 8, the value of m is equal to 5/2.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
We have been asked to find m in (2 m+3) = 8
⇒ (2 m+3) = 8
⇒ 2m + 3 = 8
⇒ 2m = 8 - 3
⇒ 2m = 5
⇒ m = 5/2
So, m is equal to 5/2 in (2 m+3) = 8
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PLSS HELP :((
will mark brianlist if its the correct answer ty
The step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle that is :
∠o + ∠p = 180°
What are alternate interior angle ?
An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.
Alternate angles between a transverse and parallel lines are equal .
Here, the step 1 is correct :
as the sum of angles of a triangle is 180 degree therefore,
∠m +∠n + ∠o = 180°.............(1)
the step 2 is incorrect :
as angle o and angle p form supplementary angles not alternate interior angle therefore it will be :
∠o + ∠p = 180°........(2)
after that step 3 and 4 is correct to get the final result as :
step 3 : ∠m +∠n + ∠o = ∠o + ∠p
step 4 : ∠m +∠n = ∠p
Therefore, the step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle.
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1. Elena wants to put together some of her favorite songs on her computer. She wants to store 60 minutes
worth of music. Elena wonders how many songs she will be able to include. She looks online and finds a
source that says the average song length is 3 minutes. If this is true, about how many songs will Elena be
able to store? Show your work
Answer:
20 Songs
Step-by-step explanation:
60 minutes / 3minutes per song =20 songs
The endpoints of YZ are Y(1, -6) and Z(-2, 8). Find the coordinates of the midpoint M.
Midpoint M
Find YZ. Round your answer to the nearest tenth if necessary.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad Z(\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +1}{2}~~~ ,~~~ \cfrac{ 8 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies \stackrel{\textit{\LARGE M}}{(-0.5~~,~~1)}[/tex]
The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.
We have,
To find the coordinates of the midpoint M of the line segment YZ, we can use the midpoint formula:
Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints Y and Z, respectively.
Given:
Y(1, -6) and Z(-2, 8)
Now, apply the midpoint formula:
Midpoint M = ((1 + (-2)) / 2, (-6 + 8) / 2)
Midpoint M = (-1 / 2, 2 / 2)
Simplify:
Midpoint M = (-1/2, 1)
To find the length of YZ, we can use the distance formula:
Length of YZ = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given:
Y(1, -6) and Z(-2, 8)
Now, apply the distance formula:
Length of YZ = √[(-2 - 1)² + (8 - (-6))²]
Length of YZ = √[(-3)² + (8 + 6)²]
Length of YZ = √[9 + 196]
Length of YZ = √205
Length of YZ ≈ 14.32 (rounded to the nearest tenth)
Thus,
The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.
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y=8 and x= -1 are equations parallel, perpendicular or neither
Answer:
Parallel
Step-by-step explanation:
After three quarters of the season has past, the Tigers basketball tean has won 48 out of 72 games. How many of the remaining games must they win in order to win more than 70% of all their games this season?
Answer: at least 3 more games
Step-by-step explanation:
70% of 72 is 50.4
50.4 - 48 = 2.4
Because one can't win only a fourth of a game, you need to round up. Bringing us to at least 3 more games to win
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
we can state that Option D may be accurate and true.
Assuming that the function, g, it has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8
Then the following properties must hold
1. The value(s) of x must be between -1 and 4
2. The values of g(x) must be between 0 and 18.
3. g(-1)=2
4. g(2)=9
We consider the options and state why they are true or otherwise.
A: g(5)=12
The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.
B: g(1) = -2
The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.
C: g(2) = 4
The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.
D: g(3) = 18
Given that its domain is between -1 and 4 and its range is between 0 and 18, this claim is reasonable.
Therefore, we can say that Option D can be true.
This question is incomplete
The provided options are:
Options
(A) g(5) = 12
(B) g(1) = -2
(C) g(2) = 4
(D) g(3) = 18
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Do the top question don’t understand it pls help me
Answer:
6/11
Step-by-step explanation:
3/11 + 3/11
to add both of the fractions just add the numerators (the numbers on the top) and u dont needa add the denominators which is the numbers on the bottom
that makes the answer 6/11 and u cant rlly simplify it so try that.
If its wrong mb
Answer:
A) [tex] \sf \frac{3}{11} + \frac{3}{11} = \frac{6}{11} [/tex]
B) [tex] \sf \frac{9}{10} + \frac{3}{5} = 1 \frac{1}{2}[/tex]
Complete the solution of the equation. Find the value of y when x equals -13. -3x+9y=57
Answer:
y = 2
Step-by-step explanation:
- 3x + 9y = 57 ← substitute x = - 13 into the equation
- 3(- 13) + 9y = 57
39 + 9y = 57 ( subtract 39 from both sides )
9y = 18 ( divide both sides by 9 )
y = 2
Answer: y is 2
solved it with a calculator.
Write each expression in simplest form. (x⁻⁴/₇)⁷
The given expression can be simplified by using rules of exponents.
There will be two rules applied, one for negative exponent and other for multiplication of exponents.
The expression can be solved by using either of the rules first. In this case, we will solve for the negative exponent first.
The base term x has a negative exponent of -4/7. The negative exponent rules states that the term with the negative exponent can be expressed in a reciprocal or reverse form without the negative sign.
In the general form, x^-a=1/x^a.
Applying the rule here,
(x^⁻⁴/₇)^7=(1/x^4/7)^7
Now multiplying the powers and simplifying,
(1/x^4/7)^7=1^7/x^(4/7)*7=1/x^4
The simplest form of the expression (x^⁻⁴/₇)^7 is 1/x^4
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simplify the following
Answer:B
Step-by-step explanation:
In the figure below, AD and AB are tangent to the circle centered at O. The segment DB passes through the center of the circle. Given that AD=10.6 and DB=5.6, find DC.
The length of DC found using Pythagorean theorem given AD = 10.6 and DB = 5.6 and AD and AB are tangent of circle O, is DC = 1.6
How can Pythagorean theorem be used to find DC?The given parameters are;
The tangents of circle O = AD and AB
The segment passing through O = DB
AD = 10.6
DB = 5.6
Required; The length of DC
Solution;
According to Pythagorean theorem, we have;
AB = √(10.6² - 5.6²) = 9
AB = AC = 9
AD = DC + AC
Which gives;
10.6 = DC + 9
DC = 10.6 - 9 = 1.6
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I really dont know how to do this please help!
Angles ECD and ACB are congruent, since they form a pair of vertical angles. Let their measure by [tex]y[/tex].
The sum of the interior angles of any triangle is 180°. This means
• in ∆CDE, we have
[tex]x + 100^\circ + y = 180^\circ[/tex]
• in ∆ABC, we have
[tex]4x + 49^\circ + y = 180^\circ[/tex]
Solve for [tex]x[/tex] by eliminating [tex]y[/tex].
[tex](x + 100^\circ + y) - (4x + 49^\circ + y) = 180^\circ - 180^\circ[/tex]
[tex]-3x + 51^\circ = 0[/tex]
[tex]3x = 51^\circ[/tex]
[tex]\boxed{x = 17^\circ}[/tex]
Write an expression to represent:
2 times the sum of 5 and x.
5x + 8
2(5x+8)
2(5x+8) is the express of twice the sum of 5 times a number and 8
answer: 2 (5x+8) = 12
What is the number of real roots of the equation
2 x²+3 x=-4 ?
There will be 2 roots of the equation 2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 .
2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 is a quadratic equation . This is because it has degree 2 . Degree is the power of variable which is maximum in function .
Since , x is the variable in this equation , therefore it's degree is 2 .
The no . of roots a polynomial will have is equal to the degree of polynomial .
Hence , the eq . will have 2 real roots .
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MATHEMATICS: The 5 and 11 terms of an Arithmes Progression (AP) are 13 and 31 respectively. Find the sum of its first term and common difference!
Answer:
[tex]a_1 = 1\\d = 3[/tex]
Step-by-step explanation:
The nth term of an arithmetic progression is [tex]a_n = a_1 + (n - 1)d[/tex].
You are given that [tex]a_5 = 13[/tex] and [tex]a_{11} = 31[/tex].
Therefore, we can solve the following system of equations to get the first term, as well as the difference.
[tex]-\begin{cases}a_1 + 4d = 13\\a_1 + 10d = 31\end{cases}\\\\\to 6d = 18\\\to d = 3\\\\\text{Substitute d = 3 into one of the equations to find }a_1\text{:}\\a_1 + 4 \times 3 = 13\\a_1 + 12 = 13\\\to a_1 = 1[/tex]
The number line shows the distance in meters of two birds, A and B, from a worm located at point X:
A. Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.
B. Using additive inverses, the distance = 2.5 + 2.5 = 5 meters
How to Find the Distance on a Number Line?The distance between any two points on a number line is the absolute difference of the coordinates of the two points.
What is an Additive Inverse of a Number?The additive inverse of a number is the number that is added to the number to make it zero. For example, the additive inverse of a is -a.
Part A:
Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.
Part B:
The additive inverse of -2.5 is 2.5.
Using additive inverses, the distance = 2.5 + 2.5
Using additive inverses, the distance = 5 meters
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Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hour
Answer:
9, 11, and 19
Step-by-step explanation:
9, 11, and 19 are the only plausible answers because there were only 2 periods where the phone was at 100% (other than when the graph started) and these are the only hours that fell within those periods..
3cm
/8cm
please find the area of the circle on the outside . and write the formula please thank you !!
The difference of two numbers is 29. The largest number is 3 more than twice the smallest number. What are the two numbers?
Answer:
x + y = 29 equation 1
Five more than means add 5+5 three times the smaller number:
3x equals the larger number: = y 3x + 5 = y equation 2
From equation 1x + y = 29subtract x from both sidesy = 29 - x
We now have two things that are both equal tothe larger number y.
They must be equal to each other.
3x + 5 = 29 - x
Add x to both sides 3x + x + 5 = 29 - x + x4x + 5 = 29
subtract 5 from both sides 4x + 5 - 5 = 29 - 54x = 24
divide both sides by 44x/4 = 24/4x = 6
We now know x = 6
We also know y=29-x y = 29 - 6y = 23
Your numbers are 6 and 23
Step-by-step explanation:
Solve the following radical equations.
∛x-1=√x-1
The solution of the radical equation of x is 1.
A linear equation in one variable is an equation which can be represented in the form of ax+b where x is the variable and 'a' is the coefficient and 'b' is the two constants.
A radical equation is defined as an equation where the variable is under a radical or root.
We know that n-th root of a variable x can be written as x to the power of (1/n). Mathematically : [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]
In the given equation:
∛x-1=√x-1
adding 1 to both sides we get:
or, ∛x=√x
Cross multiplying we get:
or, ∛x/√x =1
We know that (aˣ/aⁿ)=a⁽ˣ⁻ⁿ⁾
therefore :
or, [tex]x^{\frac{1}{3}-\frac{1}{2} }=1[/tex]
or, [tex]x^{-\frac{1}{6} }=1[/tex]
or, x=1
Hence the value of x in the radical equation is 1
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the answer and work showing
[tex]\stackrel{mixed}{-6\frac{2}{7}}\div -\cfrac{8}{21}\implies -\cfrac{6\cdot 7+2}{7}\div -\cfrac{8}{21}\implies \stackrel{improper}{-\cfrac{44}{7}}\div -\cfrac{8}{21} \\\\\\ -\cfrac{44}{7}\cdot -\cfrac{21}{8}\implies \cfrac{(-44)(-21)}{(7)(8)}\implies \cfrac{924}{56}\implies \cfrac{33}{2}\implies {\LARGE \begin{array}{llll} 16\frac{1}{2} \end{array}}[/tex]
How do you solve this?? It says solve for X.
Answer:
x = 7
Step-by-step explanation:
Ok, so these angle are equal, because they are opposite angle
So we could write as x+16 = 4x - 5
Now we solve the equation:
x+16 = 4x - 5
16+5 = 4x -x
21 = 3x
7 = x
Identify the terms, coefficients, and constants in the expression.
5c2+7d
Answer:
the coefficient is 5 and 7 the constant is 2
Which angle is the included angle for sides ABand BC?
A
C
O Angle B
Angle C
O Angle A
B
For the given sides AB and BC the angle included would always be Angle B
When we form a triangle we name the vertex as A, B and C. So, the sides AB and BC will always have an Angle B regardless of the naming convention we use.
A triangle is a polygon with three vertices and three edges that has three sides. It is a basic geometric shape. The term "abc" refers to a triangle containing the vertices a, b, and c. Any three non-collinear points in Euclidean geometry combine to create a singular triangle and a singular plane.
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