[tex]\sqrt[3]{125 x^2 y^7}\qquad \begin{cases} 125=5\cdot 5\cdot 5\\ \qquad ~~ 5^3\\ y^7=y^{6+1}\\ \qquad y^6 y^1\\ \qquad (y^2)^3 y \end{cases}\implies \sqrt[3]{5^3 x^2 (y^2)^3 y}\implies 5y^2\sqrt[3]{x^2 y}[/tex]
Calculate the surface area to volume ratio of each prism
For shape A the area to volume ratio is 101: 66
For shape B the area to volume ratio is 197117.7 : 207034
For shape C the area to volume ratio is 202.71 : 529.2
What is area and volume?The area is the amount of space occupied by a two-dimensional flat object in a plane. Volume is defined as the space occupied by a three-dimensional object. The unit of area is in square units. The unit of volume is in cubic units.
For shape A, the area = 2(lh+lb+bh)
= 2( 2×12+12×5.5+5.5×2)
= 2 ( 24+ 66+ 11)
= 2 ( 101)
= 202m²
The volume of shape A = l×b×h = 2× 12× 5.5 = 132m³.
Therefore the ratio of area to volume of shape A = 202:132 = 101: 66
For shape B
The area of the cylinder = 2πr(r+h)
= 2×3.14× 28( 28+84.1)
= 197117.7m²
The volume of the cylinder =πr²h = 3.14×28²×84.1
= 207034
Therefore the ratio of area to volume = 197117.7 : 207034
in the third shape
The area = ½bh×2 + lb+lh+bh
=6.8×7.5+ 7.2×6.8+ 7.2×7.5+ 7.5×6.8
= 48.75+48.96+54+51 = 202.71
The volume of the shape= base area × height
= 7.2×6.8×7.5
= 529.2m⅗
Thereore the area to volume ratio is 202.71:529.2
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What does 3/4 + 1/2 =
What does 1/2 x 1/2 =
Determine the coordinates for the midpoint of a segment with the following endpoints: (12,-8) and (8,-4). Answer ___________
A. (-10,6)
B. (6,-10)
C. (-6,-10)
D. (10,-6)
The value of 3/4 + 1/2 is 5/4, 1/2 x 1/2 =1/4 and Midpoint of a segment with the endpoints (12,-8) and (8,-4) is (10, -6
What is Fraction?A fraction represents a part of a whole.
We have to find the value of 3/4 + 1/2
LC of 4 and 2 is 4
(3+2)/4
3/4 + 1/2 =5/4
1/2 x 1/2 =1/4
Midpoint of a segment with the endpoints: (12,-8) and (8,-4).
Midpoint=(12+8/2, -8-4/2)
=(10, -6)
Hence, the value of 3/4 + 1/2 is 5/4, 1/2 x 1/2 =1/4 and Midpoint of a segment with the endpoints (12,-8) and (8,-4) is (10, -6)
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Which point is located on the y-axis?
0,-3
-3,0
-3,3
3,-3
Answer:
(0, - 3 )
Step-by-step explanation:
Any point on the y- axis has an x- coordinate of zero
the only point with an x- coordinate of zero is (0, - 3 )
Peter is making an "x marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 centimeters. He will make the "x" by stretching red ribbon diagonally from corner to corner. How many centimeters of ribbon will peter need to make the "x"? round your answer to the nearest centimeter. Centimeters.
Peter will need approximately 169169 centimetres of red ribbon to make the "x" on his flag. Rounded to the nearest centimetre, this is 169200 centimetres.
To find the length of the red ribbon needed to make the "x" on the flag, we need to find the length of the diagonal of the square. The diagonal of a square is a line segment that connects two opposite corners of the square and passes through the centre of the square.
The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the two shorter sides of the right triangle are equal in length to the sides of the square, so the Pythagorean theorem can be written as:
[tex]a^2 + a^2 = c^2[/tex]
Where "a" is the length of a side of the square and "c" is the length of the diagonal.
To find the length of the diagonal of Peter's flag, we can substitute 121212 for "a" in the equation above:
[tex](121212)^2 + (121212)^2 = c^2[/tex]
Solving for "c" gives us:
c = 169169 centimetres
Therefore, Peter will need approximately 169169 centimetres of red ribbon to make the "x" on his flag. Rounded to the nearest centimetre, this is 169200 centimetres.
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Please help with all of these questions
1. solve 2 x 5/8 leave your answer as a improper fraction a. 7/16 b. 10/16 c. 7/8 d. 10/8
2. solve 9 x 2/3 leave your answer as a improper fraction a. 11/27 b. 18/27 c. 11/3 d. 18/3
3. solve 5 x 3/4 leave your answer as a improper fraction a. 15/20 b. 12/5 c. 15/4 d. 8/2
The solution for each operation, involving multiplication of fractions, is given as follows:
1. 2 x 5/8 = 10/8. (option d).
2. 9 x 2/3 = 18/3. (option d).
3. 5 x 3/4 = 15/4. (option c).
How to multiply fractions?A fraction has the notation given as follows:
Fraction = x/y.
In which the technical terms of each term are given as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.To multiply two fractions, we simply multiply the numerators among themselves, and the denominators among themselves, and then the product of the fractions is given by the multiplication of the numerators divided by the multiplication of the denominators.
For example:
2 x 5/8 = (2 x 5)/(1 x 8) = 10/8.
(as an integer term can be represented by a fraction with denominator one).
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What is the y-intercept of the line of best fit?
What is the slope of the line of best fit for this scatter plot?
What is the equation of the line of best fit?
NEED HELP ASAP
Answer:
slope: 1/2
Step-by-step explanation:
(2,7) and (4,6) are the points
the formula for finding slope when there are two points is
y2-y1/x2-x1
6-7/4-2=1/2
Combine as indicated by the signs.
(2x) / (y^(2)-x^(2))- (x)/(y-x)
The expression can be combined as [2x - xy - x²] / [y²-x²]
How to combine the expression as indicated by the signs?An expression is the collection of numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given: 2x/(y²-x²) - x/(y-x)
2x/(y²-x²) + x/(y-x) = 2x/(y-x)(y+x) - x/(y-x)
The LCM of (y-x)(y+x) and (y-x) is (y-x)(y+x)
= 2x/(y-x)(y+x) - x/(y-x)
= [2x - x(y+x)] / [(y-x)(y+x)]
= [2x - xy - x²] / [(y-x)(y+x)]
= [2x - xy - x²] / [y²-x²]
Note: y²- x² = (y-x)(y+x)
Thus, the expression can be combined as [2x - xy - x²] / [y²-x²]
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7 boys took 48 days to dig a garden. how long will it take 21 boys to dig a garden
Answer:
Step-by-step explanation:
144 días
a researcher recorded information about the possible speeds of a jackrabbit, a gray fox, and a squirrel. the gray fox’s speed is 35 mph
1. The jackrabbit runs at a constant rate, as the rate between the output and the input for each point on the table is constant.
2. The squirrel runs at a constant rate, as the graph is that of a linear function with a constant slope.
3. The rate of the jackrabbit is of 44 miles per hour.
4. The rate of the squirrel is of 11 miles per hour.
5. A.
The gray fox ran at a rate of 35 miles per hour.The squirrel ran slower than the gray fox.The jackrabbit ran faster than the gray fox.B. The jackrabbit ran the fastest.
6. In three hours, the fastest animal will have run 99 miles further than the slowest animal.
7. The point (0,0) means that all the animals, the jackrabbit, the gray fox and the squirrel start from the origin.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
The rates for the jackrabbit are given as follows:
k = 22/0.5 = 44/1 = 44 miles per hour.
This is also equals to k = 0/0, which can assume any value, and the point (0,0) means that all the animals, the jackrabbit, the gray fox and the squirrel start from the origin.
The rate for the squirrel is given as follows:
k = 11/1 = 11 miles per hour.
(as the graph passes through point (1, 11)).
The difference between the rates of the fastest and of the slowest animal is given as follows:
44 - 11 = 33 miles per hour.
Hence in three hours, the distance is given as follows:
3 x 33 = 99 miles.
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DOES ANYONE KNOW THE ANSWER or know if 2 to the square root of 3 divided by b is right?
Step-by-step explanation:
you did not say what needs to be done.
simplify ?
sqrt(12/b²)
12 = 4×3
4 is a square number (2² = 4).
3 is not.
b² is per definition a square "number".
in a multiplication or division we can apply the square root (or any root) individually to the different factors involved.
so,
sqrt(12/b²) = sqrt(12)/sqrt(b²) = sqrt(4×3)/b =
= 2×sqrt(3)/b
FYI - about your question : if somebody does not know (how to get) the answer, he/she will also not be able to doubtlessly determine, if a specific answer is right ...
A cube and sphere that has same volume
Answer: If a sphere and a cube have the same volume then the ratio of the surface of the sphere to that of the cube is 6: π
Which of these statements is true?
Answer
third choice
Step-by-step explanation:
Answer:
it would be the 3rd answer
A baby giraffe is about 612 feet tall at birth and grows about 12 foot per month for its first year. The function h=12m+612 represents the total height h of a baby giraffe for any number of months m within its first year. How much taller is the giraffe at the end of month 11 than at the end of month 2? write your answer as a whole number, fraction, or decimal.
4 and 1/2 ft taller is the giraffe at the end of month 11 than at the end of month 2.
The function h(m) = (1/2)*m + (6 + 1/2) represents the height (on feet) of the giraffe as a function of the number of months, m.
We want to find the difference in the height between month 11 and month 2, then we need to find:
difference = h(11) - h(2)
We can directly calculate this:
difference = [ (1/2)*11 + (6 + 1/2)] - [(1/2)*2 + (6 + 1/2)]
difference = (1/2)*11 - (1/2)*2 = (1/2)*(11 - 2) = (1/2)*(9) = 9/2
And we can write 9 = 9 + 1, then:
difference=9/2 = (8 + 1)/2 = 8/2 + 1/2
difference= 4 + 1/2
Therefore, the giraffe is (4 and 1/2) ft taller in month 11 than in month 2.
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Joseph has a loyalty card good for a 20% discount at his local pharmacy. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $42.05? Round to the nearest cent.
Answer:
$33.64
If this help please set brainliest.
Step-by-step explanation:
The total cost of all the items before the discount is $42.05. The discount Joseph receives is 20% of this amount, so the discount he receives is $42.05 * 20% = $8.41.
The total cost after the discount is applied is $42.05 - $8.41 = $33.64. This is the total cost in dollars and cents, before tax, rounded to the nearest cent.
Mariana and her children went into a movie theater and she bought $51.25 worth of
candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She
bought a total of 13 candies and pretzels altogether. Write a system of equations that
could be used to determine the number of candies and the number of pretzels that
Mariana Bought. Define the variables that you use to write the system.
On solving the provided question, we can say that - by the help of unitary method we have total cost is 4.74* 13 + 3.25 = $64.87
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
he bought = $51.25 worth of candies and pretzels
ach candy costs = $4.75 and each pretzel costs = $3.25.
total cost is 4.74* 13 + 3.25 = $64.87
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You check on manufactured parts in a factory. You need to take measurements to ensure quality. According to the drawing shown, what is the measurement of dimension A? O. 3/4" O. 1" O. 1 1/4" O 1 1/2" O. 1 3/4"
By understanding the property of circles, it can be concluded that the measurement of dimension A is 1 1/4".
Circle is a geometric shape in which all the constituent points are at a certain distance from the center point. A circle has a diameter that shows the maximum distance between any two points of the circle. Whilst the radius is half the diameter.
Now we take a look at the picture thoroughly.
The width of the manufactured part =
the diameter of the circle on the far left = 2 * the radius
= 2 * 1"
= 2"
This value is equal to the sum of A, the radius of the circle at the very bottom (1/2"), and the space between this circle and the edge (1/4"). We write it down mathematically:
2" = A + 1/2'' + 1/4''
2" = A + 3/4"
A = 2" - 3/4"
= 1 1/4"
Thus the measurement of dimension A is 1 1/4".
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The set $S$ is the union of the set of all points inside a regular nonagon with side length $2$ units and the set of all points less than $1$ unit away from an arbitrary point on the perimeter of the nonagon. What, in units, is the perimeter of $S$
The perimeter of nonagon in units is 24.28 units.
The perimeter is comprised of 9 segments of length 2 plus the circumference of a circle with a radius of 1 [each curved part of S is 1/9 of this circumference and there are 9 of them ]
The perimeter = 9*2 + 2pi (1) = 18 + 2pi ≈ 24.28 units
Calculate the perimeter of many forms by summing the lengths of their sides. Since there are two of each side length, the perimeter is calculated by simply adding the length and width and multiplying the result by two. The formula for perimeter is perimeter=(length+width)2.
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8 dm to 3.2 dm
as fraction
helpp pls
The value of 8dm to 3.2 dm as a fraction is 2 1/2.
How to illustrate the fraction?It is important to note that a fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
8dm to 3.2 dm as a fraction will be simply be gotten by dividing the values that are given in the question.
In this case, this will be Illustrated as:
= 8 / 3.2
= 80 / 32
= 5 / 2
= 2 1/2
Therefore, the fraction is 2 1/2.
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question1 pls answer
Answer:
f(3) = 10
Step-by-step explanation:
given f(x) = 12/x + 6,
we want to find f(3)
to do so we plug in x = 3
so,
==> f(3) = 12/3 + 6
==> f(3) = 4 + 6
==> f(3) = 10
HELP QUICK!!!
Find the distance between the two points. If necessary, round to the nearest tenth.
P(-3,-2) and Q(5,1)
Answer:
8.5440037453175 or 8.5 since the directions say to round, if necessary. Please let me know if you have any questions about this! Also, please mark brainliest! Thanks so much and have a blessed day!
Answer:
8.5
Step-by-step explanation:
Answer in the diagram
Timmy writes the equation f(x) = f(x) equals StartFraction one-fourth EndFraction x minus 1.x – 1. He then doubles both of the terms on the right side to create the equation g(x) = g(x) equals StartFraction one-half EndFraction x minus 2.x – 2. How does the graph of g(x) compare to the graph of f(x)?
The graph of the equation of g(x) is steeper than the graph of f(x) and has a lower y-intercept.
What is slope of a line?The ratio of how much y grows as x grows by a certain amount is called the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is.
Given that the equation of f(x) and g(x) are as follows:
[tex]f(x) = \frac{1}{4} x -1\\\\g(x) = \frac{1}{2} x -2[/tex]
Using the slope-intercept form [tex]y=mx+C[/tex], and comparing with the equations we have:
Here, m is the slope and C is the y-intercept.
Slope of f(x) = [tex]\frac{1}{4}[/tex]
Slope of g(x) = [tex]\frac{1}{2}[/tex]
y-intercept of f(x) = -1
y-intercept of g(x) = -2
The slope of g(x) is greater than the slope of f(x), also, the y-intercept of g(x) is less than the y-intercept of f(x).
Hence, the slope of g(x) is steeper than f(x) and has a lower y-intercept.
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Kala is putting money into a savings account. She starts with $750 in the savings account, and each week she adds $70. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Kala has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
Answer:
$1520
Step-by-step explanation:
The total amount of money in the savings account after W weeks is equal to the initial amount of money, $750, plus the amount of money added each week for W weeks. We can represent this relationship with the following equation:
S = 750 + 70W
To find the total amount of money in the savings account after 11 weeks, we can substitute 11 for W in the equation above:
S = 750 + 70(11)
= 750 + 770
= 1520
Therefore, the total amount of money in the savings account after 11 weeks is $1520.
Answer:
$1520
Step-by-step explanation:
S = $750 + $70W
S = $750 + $70(11) = $1520
A toy rocket launch can be represented by a parabolic function. Your most
recent launch for the science fair can be modeled by the function
y = -4(x - 5)² + 125 where y is the height of the rocket and x is the
number of seconds since launch. Graph this function and include all of the
points listed above, then discuss in context what the vertex and x-
intercepts mean in context.
The graph of the parabola is drawn below. And all the intersection points are shown in the diagram.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = -4(x - 5)² + 125
Where y is the height of the rocket and x is the number of seconds since launch.
The vertex of the parabola is at (5, 125).
The graph of the parabola is drawn below. And all the intersection points are shown in the diagram.
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Which of the following statements are true when considered direct student loans
(Stafford Loans)?
A direct subsidized loan requires you start paying interest immediately while you
are in school.
A direct unsubsidized loan will not cover interest while you are in school, and
you are responsible for paying the interest while you are in school.
A direct subsidized loan will cover the interest on the loan while you are in
school.
A direct unsubsidized loan will not require interest be paid until you graduate or
leave the school.
You are responsible for paying the interest while you are in school because a direct unsubsidized loan does not cover it.
What is meant by direct student loans?The Federal Direct Loan Program through William D. Ford offers "loans with low interest rates that parents and students can use to help cover the expense of a student's post-high school education. A bank or other financial institution is not the lender; rather, it is the U.S. Department of Education."
The U.S. Department of Education issues federal direct loans, which are loans for students. In most cases, if you obtained a federal student loan or consolidated your debt on or after July 1, 2010, you have a federal Direct Loan.
Federal and private loans are the two main categories of student loans. Federal government funding is used to support federal parent and student loans. Private student loans are made by lenders such as banks, credit unions, state agencies, or educational institutions and are not provided by the federal government.
Therefore, the correct answer is option a) A direct unsubsidized loan will not cover interest while you are in school, and you are responsible for paying the interest while you are in school.
The complete question is:
Which of the following statements are true when considered direct student loans (Stafford Loans)?
A direct subsidized loan requires you start paying interest immediately while you are in school.
A direct subsidized loan will cover the interest on the loan while you are in school.
A direct unsubsidized loan will not require interest be paid until you graduate or leave the school.
A direct unsubsidized loan will not cover interest while you are in school, and you are responsible for paying the interest while you are in school.
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Estimate how long it would take an investment of £100 to double with a compound interest rate of 3%. Then use your answer to see exactly what the answer would be after that many years. T = 72/3 = 24 So it would take approximately 24 years to double an investment at a 3% compound interest rate.
It would take 23.45 years to double the investment of £100 with a compound interest rate of 3% to £200.
How to find the number of years to double an investment?Using the formula A = P(1 + r)^t
Initial amount of investment, P = 100
Final amount(double the investment), A = (2 x 100) = 200
Interest rate, r = 3% = 0.03
Number of years, t = ?
A = P(1 + r)^t
200 = 100 (1 + 0.03)^t = 100(1.03)^t
Divide both sides by 100
200/100 = 100(1.03)^t/100
2 = (1.03)^t
In2 = t In(1.03)
t = In2/In(1.03)
t = 23.45 years
The amount of time it would take to make £200 from £100 is 23.45 years at a compound rate of 3% using the rule of 72 and the simple interest formula.
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a spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. how fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?
The rate of increase of the radius of the balloon at the instant when the radius is 30 cm is 0.0167 cm/min and when the radius is 60 cm, it is 0.0021 cm/min.
(a) At the instant when the radius of the balloon is 30 cm, the rate of increase of the radius of the balloon is
Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)
= (800 cm3/min) / (4/3 × π × (30 cm)^3)
= 0.0167 cm/min
(b) At the instant when the radius of the balloon is 60 cm, the rate of increase of the radius of the balloon is
Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)
= (800 cm3/min) / (4/3 × π × (60 cm)^3)
= 0.0021 cm/min
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The points shown on the graph represent the numbers
in a geometric sequence.
What is the initial value of the sequence?
1
2
3
8
Which of the following is a like radical to 3x√5?
O x(³√5)
O √5y
O 3 (³√5x)
O y √√5
3x√5 and 3(³√5x) are like radicals because they both have the same radicand (the number or expression inside the radical symbol) of 5 and the same index (the number that indicates the root being taken) of 3. The only difference is the coefficient (the number multiplying the radical) of 3 in front of the radical symbol, which is a factor that does not affect the radical itself.
x(³√5) and y √√5 are not like radicals to 3x√5 because they have different radicands.
√5y is not a like radical to 3x√5 because it has a different index.
Solve 5x + 3 = 10 in order
Answer:
5x+3y=10
subtract both sides by 5x
divide everything by 3
y= -5/3x +10/3
hopes this helps
What is the value of the logarithm log 750?
The logarithmic expression [tex]\log {750}[/tex] is the lograrithm with base 10 of 750 and it's value is approximately equal to 2.8751
Logarithms are expressed mathematically as [tex]\log_{x}b=y[/tex] where [tex]x[/tex] denotes the base of the logarithm, [tex]b[/tex] denotes a number and [tex]y[/tex] denotes the exponent. The above expression can also be written as [tex]x^{y}=b[/tex]
We will be using two logarithmic properties in this question:
The first one is, [tex]log(mn) = logm + logn[/tex]
And the second one is, [tex]log(m^{n}) = n*logm[/tex]
Whenever the base in the question is not shown then it is assumed to be 10 in mathematics.
∵ This is a base 10 logarithm, we must determine a value of [tex]y[/tex] for expression [tex]10^{y} = 750[/tex]
Since there is no other value of log given we have to use the calculator.
If the value of [tex]log_{}3[/tex] and [tex]log5[/tex] is given then we can solve the question:
[tex]log750 = log_{10} 750[/tex]
⇒[tex]log_{10}(3*5^{2} * 10)[/tex]
⇒[tex]log 3 + 2log 5 + log 10[/tex]
⇒[tex](0.47712) + 2(0.69897) + 1[/tex]
⇒[tex](0.47712) + (1.39794) + 1[/tex]
≈ [tex]2.8751[/tex]
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