We have expression ln a-2 ln b+1/3 ln c as a single natural logarithm
㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
What is a natural logarithm?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.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to express ln a-2 ln b+1/3 ln c as a single natural logarithm.
⇒ ln a-2 ln b+1/3
⇒ ㏑ (a) - ㏑ (b²) + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ln a-2 ln b
⇒ ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
⇒ ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
Finally, we have expressed ln a-2 ln b+1/3 ln c as a single natural logarithm ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
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Solve the equation 42 = v + 35 for v.
Answer:
v = 7
Step-by-step explanation:
Reverse sides
[tex]v+35=42[/tex]
Subtract 35
[tex]v+35-35=42-35[/tex]
Simplify
[tex]v=7[/tex]
Answer:
v = 7
Step-by-step explanation:
Subtract 35 from both sides
Your friend says that the magnitude of vector (8 , 3) is 4 times that of vector (2 , 3) since 8 is 4 times 2 . Explain why your friend's statement is incorrect.
With the help of the Magnitude formula, we can say that Magnitude of 1st vector is more than the 2nd vector.
A vector is an object that has both magnitude and direction. To find the size of a vector, we need to calculate the length of the vector. Variables such as velocity, distance, force, and momentum are vector variables. But velocity, mass, distance, volume, temperature, etc. is a scalar quantity. A vector has both magnitude and direction, while a scalar has only one magnitude.
The Magnitude of a vector is the length of the vector. The Magnitude value of vector a is represented by ∥a∥.
For a two-dimensional vector a= (a1, a2), the formula for its Magnitude is written below.
By using the Magnitude formula, we can say that Magnitude of 1st vector is more than the 2nd vector.
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is y= -x³+2x linear or nonlinear?
Answer:
nonlinear
Step-by-step explanation:
In a linear equation, there are no multiplications of variables by variables.
x³ means x × x × x, so there is a multiplication of variables in the equation, and the equation is not linear.
Answer:
Non-linear
Step-by-step explanation:
Since one of the terms has an exponent of 3, this is a cubic equation, a third degree equation. It is a curve and therefore, NOT a linear equation.
11,408 DIVIDED BY 9,617
PLEASE USE LONG DIVISION
THE PERSON WHO USES LONG DIVISION GET BRAINLIEST AND 10 POINTS
Answer:
0.834 is the correct answer
Simplify the expression. Write your answers using integers or improper fractions.
− 3/2(− 3/2 q+ 5/3)+8q
Answer:
[tex] \sf \: \frac{41}{4} q + \frac{ - 5}{2} [/tex]
Step-by-step explanation:
Let's simplify step-by-step.
−3/2(−3/2q+5/3)+8q
Distribute:
=(−3/2)(−3/2q)+(−3/2)(5/3)+8q
=9/4q+−5/2+8q
Combine Like Terms:
=9/4q+−5/2+8q
=(9/4q+8q)+(−5/2)
=41/4q+−5/2
slope of 4 and passes through the point (1, 9) What is its equation in slope-intercept form?
Answer:
y = 4x + 5
Step-by-step explanation:
hope this helps !!
the equation is " y = (slope)x + (y-intercept) "
A scientist grows a species of bacteria in a petri dish. Explain why there is a linear correlation coefficient of 0.1 in the plot of Number of Bacteria versus Time.
A. The bacteria have grown at a steady rate and a line fits the data very well.
B. The bacteria have grown at an exponential rate and a line poorly fits the data.
C. The bacteria have grown at an exponential rate and the line fits the data very well.
D. There is a strong negative correlation between number of bacteria and time.
Based on the fact that the correlation coefficient was 0.1 in the plot of Bacteria versus Time, the reason is B. The bacteria have grown at an exponential rate and a line poorly fits the data.
What is the correlation coefficient?The correlation coefficient shows the relationship between two variables. It is between -1 and 1 and figures closer to 0 denote a weak correlation.
In this instance, Bacteria is known to increase exponentially which means that a linear regression model would make a line that poorly fits the data. This would lead to a low correlation coefficient when it should instead be high.
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indicate whether the following variables are categorical (qualitative) or quantitative. a. model of automobile b. flavor of ice cream c. religious denomination d. testscoreoutof100 e. miles per gallon of gasoline f. top three television networks g. lengthofbirthcontractioninseconds
The variable a. model of automobile is Qualitative b. flavor of ice cream is Qualitative c. religious denomination is Qualitative d. test score out of 100 is Quantitative e. miles per gallon of gasoline is Quantitative f. top three television networks is Qualitative g. length of birth contraction in seconds is Quantitative.
The Quantitative variable is defined as the variable which takes numerical value. for eg. 2mph, 90 , 34m.
The Qualitative variable is defined as the variable which takes values such as name/label etc. for eg, john , smith , Toyota ,vanilla.
According to the question
VARIABLE CATEGORY CLASSIFIED
a. model of automobile Qualitative on the basis of name
b. flavor of ice cream Qualitative on the basis of name
c. religious denomination Qualitative on the basis of name
d. test score out of 100 Quantitative on the basis of number
e. miles per gallon of gasoline Quantitative on the basis of number
f. top three television networks Qualitative on the basis of name.
g. length of birth contraction Quantitative on the basis of number.
(in seconds)
Therefore , The variable a. model of automobile is Qualitative
b. flavor of ice cream is Qualitative
c. religious denomination is Qualitative
d. test score out of 100 is Quantitative
e. miles per gallon of gasoline is Quantitative
f. top three television networks is Qualitative
g. length of birth contraction in seconds is Quantitative
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which anwer choice correctly represents the quoinet of 28, 134, devided by 71
The answer choice that correctly represents the quotient of 28134 divided by 71 is 28134/71
How to determine the answer choice that correctly represents the quotient of 28134 divided by 71The quotient statement is given as
28134 divided by 71
In mathematics, quotient is represented by division using the symbol /
i.e. the quotient of a and b is a/b
Using the above as a guide, we have the following quotient expression
28134/71
Hence. the answer choice that correctly represents the quotient of 28134 divided by 71 is 28134/71
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The warehouse can purchase 10 pairs of sandals for 126.50 dollars and will get one free pair. What is the cost rate
Answer:
12.65:1
Step-by-step explanation:
The cost per one pair of sandal is 12.65 dollars.
Hopefully this helped have a great day :D
Solve. √2 x+3 -7=0
The solution is 22.5
To solve the given equation, rewriting the equation -
√(2x + 3) - 7 = 0
Shifting 7 to the Right Hand Side of the equation
√(2x + 3) = 7
Taking square on both sides of the equation
(√(2x + 3))² = 7²
Solving the square
2x + 3 = 49
Shifting 3 to the Right Hand Side of the equation
2x = 49 - 3
Performing subtraction on Right Hand Side of the equation
2x = 45
Shifting 2 to the Right Hand Side of the equation
x = 45 ÷ 2
Performing division on the Right Hand Side of the equation
x = 22.5
Hence, the solution is 22.5
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what is the length of the segment ĀB
The length of line segment AB shown in the line graph is is 2 units
With the given line graph it is very obvious that the line segment AB has two point A and B with -4 and -2 as their value
To measure the length we need to subtract the x coordinate of one end point from the another end point
here we will deduct the x coordinate of b point from the x coordinate of A point which is shown below
- 4 - (-2)
and using the simple integer properties we can solve this problem of line graph
- 4 + 2
which comes out to be 2
hence, the length of line segment AB shown in the line graph is is 2 units
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Addison's Pizzeria made 12 thin-crust pizzas and 2 thick-crust pizzas. What is the ratio of the number of thin-crust pizzas to the number of thick-crust pizzas?
What goes in with the 2? __ : 2
Answer:
12 is the fill in
Step-by-step explanation:
what is 30 -12 · 2 in order of operations
Answer:
6
Step-by-step explanation:
PLEASE HELP ME. The table gives the number of beads needed to make bracelets of certain lengths. Suppose you graph the ordered pairs (bracelet length, number of beads) on the coordinate plane. Would the point (10.5, 42) make sense in this context? Explain.
Using a proportional relationship, it is found that point (10.5, 42) makes sense in this context, as when x = 10.5, y = 42 is the output of the relation.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, defined by k, in the case of a direct relationship, according to the following rule:
y = kx
For the case of an inverse relationship, we have that:
y = k/x.
From the table in this problem, the constant is given as follows:
k = 28/7 = 32/8 = 36/9 = 40/10 = 4.
Hence the relation is modeled as follows:
y = 4x.
In which:
x is the bracelet length in inches.y is the number of beads.When x = 10.5, we have that:
y = 4(10.5) = 42.
Hence point (10.5, 42) makes sense in this context.
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PLEASE HELP WILL GIVE 100 POINTS
Answer:
Step-by-step explanation:
The answer for this one would be Angles ABC and CDA are congruent according to the property parallelograms (opposite angles congruent). The shape is a parallelogram and that's why that answer would make sense and the opposite angles is another way to prove it's congruent!
Hope this helped!
:D
Answer:
ABC and CDA are congruent according to the system/property of parallelograms(Opposite angles congruent(A.K.A option B)).
Step-by-step explanation:
CDA and ABC are opposite angles that are equal in measure, and equal in length, which directly follows this property. Thus, they are congruent.
A woman sold an article for $200,000 and made a profit of 25%. Find the cost price of the article.
Answer:
The original cost is 160,000
Step-by-step explanation:
X x 25/100 + X = 200,000
25X/100 + X =200,000
X= 200,000-25X/100
X= (20,000,000-25X) / 100
100X = 20,000,000-25X
125X = 20,000,000
X = 160000
9 less than the quotient of a number x and 4 is 65
Answer: x=296
Step-by-step explanation:
Write each expression as a single logarithm.
log₆5+log₆x
The expression log₆5+log₆x as a single logarithm is log₆5x.
The logarithm is exponent's inverse function in mathematics. This indicates that the exponent to which a fixed number(say a) at base b, must be raised in order to create a number x, is represented by the logarithm of that number.
For example if 8=2³ can be written in the logarithmic form as
log₂8=3.
The general properties of logarithm for a fixed base are:
logₐa=1logₐx+logₐy=logₐxylogₐx-logₐy=logₐ(x/y)logₐxⁿ=n logₐxlogₓy=(logₐy)/(logₐx)Here the given logarithmic expression is (log₆5+log₆x)
So according to the properties of logarithms we can use the above property "logₐx+logₐy=logₐxy" to simplify the given expression.
Therefore:
log₆5+log₆x
=log₆(5×x)
=log₆5x
Hence written as a single logarithm the expression is log₆5x.
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Evaluate each expression to four decimal places.
e⁻⁴
The value of the expression e⁻⁴ is 0.0183 to four decimal places.
We are given the expression:
e⁻⁴
We need to evaluate the expression to four decimal places.
Now, we know that the value of e is:
e = 2.71828182846
Now, e⁻⁴ can also be written as:
e⁻⁴ = 1 / e⁴
Substituting the value of e, we get that:
1 / e⁴ = 1 / (2.71828182846)⁴
= 1 / 54.5981500331
= 0.0183156389
Now rounding off to 4 decimal places, we get that:
= 0.0183
Therefore, the value of the expression e⁻⁴ is 0.0183.
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find the measure of the segment
8.547 to the nearest whole number
Answer: 9
Step-by-step explanation:
What is 4,550 divided by 64 as a decimal?
Based on the given task content, the division of 4,550 by 64 is approximately 71.09 to two decimal places.
The division of whole numbers to give decimal4,550 divided by 64
The divisor which is a number or expression that another number divides is 4,550
The dividend which is the number or the expression which is used to divide another is 64
The quotient here simply refers to the result which is obtained by dividing one number by another.
4,550 divided by 64
= 4,550 / 64
= 71.09375
This result above can be correctly approximated to two decimal places, that is, two values after the decimal point.
Approximately,
71.09375
= 71.09
What are decimal numbers?This is a number expressed in the decimal system (base 10), particularly fractional numbers.
For instance, in the illustration below:
13¼ = 13.25 as a decimal number.
So therefore, the division of 4,550 by 64 is approximately 71.09 to two decimal places.
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14. -9√24 + 2√600 what is this in simplest form?
Answer:
2√6(Decimal: 4.898979)
Step-by-step explanation:
−9√24+2√600
=2√6(Decimal: 4.898979)
I need to find the mean of 6, -12, 24, -48
Answer:
-7.5
Step-by-step explanation:
[tex]\frac{6 + (-12) + 24 + (-48)}{4} =\frac{-30}{4} =-7.5[/tex]
Which angles are adjacent to each other?
Answer:
angles 1 and 5
Step-by-step explanation:
The two angles are said to be adjacent angles when they share the common vertex and side.
so angles 1 and 5 are adjacent angles
what is the graph of y=-2x + 11
Answer:
the equation is " y = (slope)x + (y-intercept) "
Step-by-step explanation:
here ya go ! hope this helps
Answer: Hope this helps. This graph is at a highschool level so if you are actually in highschool this should help you. If you are in middle school I can adjust it to a more simple graph.
Step-by-step explanation:
I need help with this
Answer: Answer is C
Step-by-step explanation:
What is the answer to this problem?
Answer:
a = 6,c = 15, b = 12, P = 33
Step-by-step explanation:
Answer:
a = 6,c = 15, b = 12, P = 33 is the answer :)
Step-by-step explanation:
help these 3 questions (calculating positive and negative numbers)
Answer:
1st question: $-4.5
2nd question: 32
3rd question: -27
Step-by-step explanation:
1st question:
Alan's octopus is $-7 dollars right now. After reloading $50 dollars in, it just means that he put $50 dollars in. We can work it out like this:
-7+50=43 (you can switch the equation around but the sign has to go with it: 50-7)
Now Alan's octopus has $43 in it. It then says that Alan spends $48.5 for a really expensive pencil case. You can calculate it like this:
43-48.5=-4.5 (43-48.5 is the same as 43.0-48.5 and you can work it out on a number line).
This leaves Alan's octopus to only have $-4.5 which means he is in debt again.
2nd question:
I can make it out that it says: Tony adds -18 to +50. Find the results (I hope I saw it right). The equation of it would look like:
-18+50 or you can flip it around but the sign has to go with them like in question one which will look like this: 50-18=32. So the result of Tony's problem is 32.
3rd question:
Patty subtracts +11 from -16. Find the results.
First of all don't do this 11-16 because that would be 16 subtracted from 11 which is wrong because 1, the sign completely disappears unless you make it -16 plus 11 and 2, it's order would be incorrect. The correct equation should look like this:
-16-11=-27 ( -16-(+11) positive combined with negative is negative).
You can think of it like this: If it's the same sign that's addition or subtraction eg. -4-2 or +6+8, you just add it up together and put the sign in front which you would not have to do for the addition one unless you are asked to.
I hope you find this helpful!