The area of a triangle is half the product of the base and the height.
Since multiplication is commutative, the following expressions are equivalent:
[tex]A=(bh)\cdot \dfrac{1}{2} = \dfrac{b}{2}\cdot h = \dfrac{h}{2}\cdot b[/tex]
So, option D is correct
Option (D) Multiply 1/2 base by altitude should be used to find the area of a triangle.
Area of the triangleA triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Area of a Triangle = A = ½ (b × h) square units
where b and h are the base and height of the triangle, respectively.
Now, let's see how to calculate the area of a triangle using the given formula.
The area of a triangle is half the product of the base and the height. Since multiplication is commutative, the following expressions are equivalent:
[tex]$$A=(b h) \cdot \frac{1}{2}=\frac{b}{2} \cdot h=\frac{h}{2} \cdot b$$[/tex]
So, option D is correct Multiply 1/2 base by altitude.
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What is the following product? Assume x ≥ 0
\sqrt[3]{x^{2} } . \sqrt[4]{x^{3} }
A. x\sqrt{x}
B. \sqrt[12]{x^{5} }
C. x(\sqrt[12]{x^{5} } )
D. x6
For this case we must multiply the following expression:
[tex]\sqrt [3] {x ^ 2} * \sqrt [4] {x ^ 3}[/tex]
By definition of properties of otencias and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
We rewrite the terms of the expression:
[tex]\sqrt [3] {x ^ 2} = (x ^ 2) ^ {\frac {1} {3}} = (x ^ 2) ^ {\frac {4} {12}}\\\sqrt [4] {x ^ 3} = (x ^ 3) ^ {\frac {1} {4}} = (x ^ 3) ^ {\frac {3} {12}}[/tex]
So, we have:
[tex](x ^ 2) ^ {\frac {4} {12}} * (x ^ 3) ^ {\frac {3} {12}} =[/tex]
Applying the above definition we have:
[tex]\sqrt [12] {(x ^ 2) ^ 4} * \sqrt [12] {(x ^ 3) ^ 3} =[/tex]
We multiply the exponents:
[tex]\sqrt [12] {x ^ 8} * \sqrt [12] {x ^ 9} =[/tex]
We combine using the product rule for radicals.
[tex]\sqrt [12] {x ^ 8 * x ^ 9} =[/tex]
By definition of multiplication properties of powers of the same base, we put the same base and add the exponents:
[tex]\sqrt [12] {x ^ {8 + 9}} =\\\sqrt [12] {x ^ {17}} =\\\sqrt [12] {x ^ {12} * x ^ 5} =\\x \sqrt [12] {x ^ 5}[/tex]
Answer:
Option C
Answer:
its c
Step-by-step explanation:
Is 3[g(x)] = x a linear function?
Answer: no
Step-by-step explanation:
Linear functions are straight lines and are also written in the form y=mx+b
The linearity of 3[g(x)] = x depends on the form of g(x). If g(x) is linear, such as g(x) = ax, then the equation is linear. Otherwise, if g(x) involves non-linear operations, the overall equation will not represent a linear function.
Whether or not the equation 3[g(x)] = x represents a linear function depends on the form of g(x). If g(x) is a linear function, then the equation represents a linear transformation. If g(x) is nonlinear, then the overall function is not linear.
For example, if g(x) = exp(3x), the relationship is non-linear due to the exponential function. However, if the g(x) function is a simple linear function like g(x) = a₁x, with a constant coefficient, the equation maintains its linearity. In this scenario, the function could even represent a constant multiple of the identity function, where g(x) = x/3.
It is important to note that in the context of mathematics, understanding whether a function is linear involves recognizing if it can be written in the form of g(x) = mx + b, where m and b are constants, and the function results in a straight line on a graph.
The mass of a small virus is 10^-20 kg. The mass of an average human cell is 10^-12 kg. Which of the two has lesser mass? how many less is it?
For this case we have:
[tex]10 ^ {- 20}[/tex], we must run the decimal point 20 spaces to the left.
[tex]0.00000000000000000010 \ kg[/tex]
[tex]10 ^ {- 12}[/tex], we must run the decimal point 12 spaces to the left.
[tex]0.000000000010 \ kg[/tex]
Thus, it is observed that the mass of a small virus is smaller!
We subtract and obtain:
[tex]10 ^ {-11}[/tex]
ANswer:
The mass of a small virus is less!
Answer: -10kg
Step-by-step explanation:
10-20 =-10
10-22 =-12
-10 is lesser
Which of the following shows the polynomial below written in descending order
When it asks for descending order of the polynomial it wants you to put the exponents in order from largest to smallest like so...
C. [tex]x^{12} +3x^{7} + 4x^{3} -9x[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Option C
Step-by-step explanation:
In this question the given polynomial is 4x³ + 3x⁷ - 9x + x¹²
If we rewrite it in the descending order of the powers then the polynomial will be
x¹² + 3x⁷ +4x³ + 9x
This polynomial matches with option C.
Option C is the answer.
Factor completely. 81x^4 − 1
The expression 81x⁴ - 1 can be factored completely by identifying it as a difference of squares. First, factor it into (9x² + 1)(9x² - 1) and then further factor (9x² - 1) into (3x + 1)(3x - 1). The final factored form is (9x² + 1)(3x + 1)(3x - 1).
We are given the expression 81x⁴ - 1 and need to factor it completely. This is a difference of squares, which can be written as:
81x⁴ - 1 = (9x²)² - 1²The difference of squares formula is a²- b² = (a + b)(a - b). Applying this formula, we get:
(9x²)² - 1² = (9x² + 1)(9x² - 1)Next, notice that 9x²- 1 is also a difference of squares:
9x² - 1 = (3x)²- 12Again using the difference of squares formula, we get:
(3x)² - 1 = (3x + 1)(3x - 1)Putting everything together, the complete factorization of 81x⁴ - 1 is:
81x⁴ - 1 = (9x² + 1)(3x + 1)(3x - 1)2-digit numbers less than 91 which are 1 less than a multiple of 10
Answer:
{19, 29, ... , 79, 89}
Step-by-step explanation:
Multiples of 10 are {10, 20, 30, 40, ... , 90}
Numbers which are each 1 less than these multiples of 10 would be:
{9, 19, 29, ... , 79, 89}.
Note that the last number, 89, is less than 91.
We must omit 9 from this set, since 9 is not a 2-digit number. Then our final list is {19, 29, ... , 79, 89}.
Answer:
The numbers are 19,29,39,49,59,69,79,89
Step-by-step explanation:
2 digit numbers starts from 10 and ends on 99.
2 digit numbers less than 91 starts from 10 and ends at 90.
2 digit numbers less than 91 and multiple of 10 are 10,20,30,40,50,60,70,80,90.
2 digit numbers less than 91 and which are 1 less than a multiple of 10 are 19,29,39,49,59,69,79,89.
The numbers are 19,29,39,49,59,69,79,89
what is x and y when the right angle side is 7 and the angles are 90,45 and 45?
Answer:
x=7
Step-by-step explanation:
The other angle is equivalent to 45 degrees. According to the 45-45-90 triangle theorem, the hypotenuse is a times the square root of 2 and the legs are equivalent to a. In this scenario a is equivalent to 7. X is another leg and therefore is also 7.
What is the greatest common factor of 8 and 36
Answer:
4
Step-by-step explanation:
When multiplying, the greatest common factor of each is four.
8= 4 x 2
36= 4 x 9
The greatest common factor (GCF) of 8 and 36 is 4. The correct option is B.
GCF stands for "Greatest Common Factor." It refers to the largest positive integer that divides evenly into two or more given numbers. In other words, the GCF is the largest number that is a factor of all the given numbers.
Finding the GCF is useful in various mathematical operations, such as simplifying fractions, finding equivalent fractions, or solving equations. It helps in identifying common factors and simplifying calculations.
To find the GCF, you can identify the common factors of both numbers and determine the largest one they share.
The factors of 8 are 1, 2, 4, and 8.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The largest factor that both 8 and 36 share is 4.
Therefore, the greatest common factor of 8 and 36 is 4.
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Use the net to find the surface area of the cylinder
give your answer in terms of pi
A 25pi yd2
B 70pi yd2
C 50pi yd2
D 120pi yd2
Answer:
D) 120pi yd2
Step-by-step explanation:
The given line passes through the points (-4,-3) and (4,1) what is the equation in point-slop
e form, of the line that is perpendicular to the given line and passes through the point (-4,3)?
let's bear in mind that perpendicular lines have negative reciprocal slopes...... hmmmm what's the slope of the given line anyway?
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{4-(-4)}\implies \cfrac{1+3}{4+4}\implies \cfrac{4}{8}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so, we're really looking for a line whose slope is -2 and runs through (-4 , 3)
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-2[x-(-4)] \implies y+3=-2(x+4) \\\\\\ y+3=-2x-8\implies y=-2x-11[/tex]
The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
s > 0
s 4
s 8
s 16
Answer:
[tex]s\geq 4\ cm[/tex]
Step-by-step explanation:
we know that
[tex]s(V)=\sqrt[3]{V}[/tex]
where
s is the side length, in units, of a cube
V is the volume of a cube in cubic units
For a [tex]V=64\ cm^{3}[/tex]
substitute in the formula
[tex]s=\sqrt[3]{64}[/tex]
[tex]s=4\ cms[/tex]
If Jason wants to build a cube with a minimum of 64 cubic centimeters
therefore
the minimum length side of the cube is 4 cm
[tex]s\geq 4\ cm[/tex]
Which expresión is equivalente to (4g3 h2 k4)3
Answer: [tex]\bold{64g^9h^6k^{12}}[/tex]
Step-by-step explanation:
[tex]\text{Apply the product rule:} (a^b)^c=a^{b*c}\\\\(4g^3h^2k^4)^3\\\\=4^{(1*3)}g^{(3*3)}h^{(2*3)}k^{(4*3)}\\\\=4^3g^9h^6k^{12}\\\\=64g^9h^6k^{12}[/tex]
Yuto solved the equation below.
What is the solution to Yuto’s equation?
For this case we have the following equation:
[tex]-2 (x + 5) = - 2 (x-2) +5[/tex]
We apply distributive property to the terms within parentheses:
[tex]-2x-10 = -2x + 4 + 5[/tex]
We add similar terms to the right side of the equation:
[tex]-2x-10 = -2x + 9[/tex]
We add 2x to both sides of the equation:
[tex]-10 = 9[/tex]
Equality is not fulfilled, so the equation has no solution.
Answer:
It has no solution
Answer: Yuto's equation has no solution.
Step-by-step explanation:
To find the solution to Yuto’s equation, you need to solve for the variable "x":
Apply Distributive property:
[tex]-2(x+5)=-2(x-2)+5\\\\-2x-10=-2x+4+5\\\\-2x-10=-2x+9[/tex]
Add [tex]2x[/tex] to both sides of the equation:
[tex]-2x-10+2x=-2x+9+2x\\\\0x-10=9\\\\-10=9\ (False)[/tex]
Therefore, the equation has no solution.
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of
a pound. Which equation represents this situation?
Of(x) = 8+2[x-1, where x > 0
Of(x) = 6+2Lx-1), where x > 0
O (x) = 6+2[x+1), where x > 0
Of(x) = 6+2x+1), where x > 0
Answer:
6 + 2[x - 1) , where x > 0. I think.
Answer:
f(x) = 6+2Lx-1), where x > 0
Step-by-step explanation:
To answer this you need to understand two things, variables and constants, the constant price of the shipping is $6 so that is a constant, now the company would charge you with $2 for every fraction or pound extra over the one pound that you are charged for the $6, so your variable is the weight of the package, and this will be expressed by X
So the function would look like this:
[tex]f(x)= 6+ 2(x-1) when x > 0[/tex]
If the weight of your package is less than oneyou´d just pay the 6 bucks, since when the weight is bigger than 1 pound you would pay 2 extra bucks, you just need yo know how many extra buck you´ll pay that´s why it´s expressed with the Lx-1)
Stefania pours 2 liters of orange juice and 1.5 liters of pineapple juice into a punch bowl. How many liters are in the punch bowl?
Answer:
3.5 liters
Step-by-step explanation:
2 liters + 1.5 liters = 3.5 liters
Zed is making a centerpiece for his dining room table by putting sand in a cube-shaped vase. The vase is 0.25 meters in length, width, and height. He bought 25 kg of sand. Assume the density of dry sand is 1,602 kgm3. What is the volume of the sand that Zed purchased?
The volume of the sand is approximately __________ m3.
Enter your answer as the number that correctly fills in the blank in the previous sentence. If necessary, round your answer to six decimal places, like so: 42.536475
The answer is:
The volume of the sand is approximately 0.015605 m3
Why?To solve the problem, and find the volume of the sand that Zed purchased, we need to use the formula to calculate the density and isolate the volume from it.
So, solving we have:
[tex]density=\frac{mass}{volume}[/tex]
From the statement we know that:
The mass of the sand is 25 kg
The density of the dry sand is 1,602 kg/m3
So, substituting and solving we have:
[tex]density=\frac{mass}{volume}\\\\volume=\frac{mass}{density}\\\\volume=\frac{25kg}{1,602\frac{kg}{m^{3}}}=0.015605m^{3}[/tex]
Hence, the volume of the sand is approximately 0.015605 m3
Have a nice day!
Maria has three red dresses, 2 white dresses, and one blue dress . What is the probability she will wear a blue dress at her party?
Answer:
1/6
Step-by-step explanation:
there are 6 dresses altogether and 1 blue dress.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We have been given that Maria has three red dresses, 2 white dresses, and one blue dress. We are asked to find the probability that Maria will wear a blue dress at her party.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
We know that number of blue dresses is 1, so number of favorable outcomes is 1.
Total dresses = 3 Red dresses + 2 White dresses + 1 Blue dress = 6 dresses.
[tex]\text{Probability that Maria will wear a blue dress at her party}=\frac{1}{6}[/tex]
Therefore, our required probability is [tex]\frac{1}{6}[/tex].
gerard’s baby brother spends 7/8 of his day sleeping. How many hours does his baby brother sleep? i
[tex] \frac{7}{8} \times 24 = 21 \\ [/tex]
You multiply 7/8 to the number of hours in a day which 24
Gerard's baby brother sleeps for 7/8 of the day, which equals 21 hours when calculated (7/8 * 24 hours).
Explanation:Gerard's baby brother spends 7/8 of his day sleeping.
To calculate how many hours this is, we need to know how many hours there are in a full day.
A full day has 24 hours. So, we multiply 7/8 by 24 to find out the total hours spent sleeping.
Here's the step-by-step calculation:
Multiply the fraction of the day spent sleeping (7/8) by the total number of hours in a day (24).7/8 * 24 = 21 hours.Therefore, Gerard's baby brother sleeps for 21 hours a day.
Order these values given in scientific notation from least to greatest.
1.49 x 10^5
1.05 x 10^-6
3.81 x 10^8
2.44 x 10^-9
3.75 X 10^4
Answer:
2.44x10^-9
1.05x10^-6
3.75x10^4
1.49x10^5
3.81x10^8
Final answer:
Values in scientific notation are ordered by their exponent values. First, compare the sign and size of the exponents, and then compare the coefficients if necessary. The ordered values from least to greatest are: 2.44 x 10^-9, 1.05 x 10^-6, 3.75 x 10^4, 1.49 x 10^5, 3.81 x 10^8.
Explanation:
To order the given values in scientific notation from least to greatest, we look at the exponent to determine their relative sizes. The values with negative exponents will be smaller than those with positive exponents, and among those with the same sign exponents, the one with the smaller absolute value of exponent is smaller. Then we compare the coefficients if necessary, that is if the exponents are the same.
[tex]2.44 x 10^-9[/tex]
[tex]1.05 x 10^-6[/tex]
[tex]3.75 x 10^4[/tex]
[tex]1.49 x 10^5[/tex]
[tex]3.81 x 10^8[/tex]
71, 92, 94, 93, 98, 85, 66, 70, 68, 93, 87, 71, 85, 52, 61, 62, 85, 69, 95, 79
Calculate the mean for the data list above.
ОА. 82
ОВ. 78.8
Ос. 93
Op. 87
To find the mean you must add all the numbers together then divide the sum by the total amount of numbers in the data set
71 + 92 + 94 + 93 + 98 + 85 + 66 + 70 + 68 + 93 + 87 + 71 + 85 + 52 + 61 + 62 + 85 + 69 + 95 + 79 = 1576
There are at total of 20 numbers in this data set so you must divide 1576 by 20
1576 / 20 = 78.8
Hope this helped!
~Just a girl in love with Shawn Mendes
Use the properties of exponents to rewrite the expression
(-3yz)(-3yz)(-3yz)(-3yz)
[tex]\bf (-3yz)(-3yz)(-3yz)(-3yz)\implies (-3yz)^1(-3yz)^1(-3yz)^1(-3yz)^1 \\\\\\ (-3yz)^{1+1+1+1}\implies (-3yz)^4\implies (-3)^4 y^4 z^4\implies 81y^4 z^4[/tex]
The expression (-3yz) (-3yz) (-3yz) (-3yz) is (-3yz) ⁴
What is a number multiplicative?A multiplicative indicates how many copies of a number are multiplied together.negative multiplicative is the reciprocal of a number with a positive multiplicative which can be mathematically represented as. X ⁻¹ = 1/X⇒(-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹=(-3yz)¹⁺¹⁺¹⁺¹
⇒ (-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹ = (-3yz)⁴
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For the straight line y=-
-4, what are the slope and y-intercept?
slope = 5, y-intercept = 4
slope = -
y-intercept = 4
slope =
y-intercept = -4
slope =
y-intercept = 4
Answer:
y-intercept is [0, -4]
Step-by-step explanation:
Straight lines NEVER have rate of changes [slopes].
Solve the following equation for x: 2x + 5y = 8.
Answer:
x = -5/2 y +4
Step-by-step explanation:
2x+5y = 8
Subtract 5y from each side
2x+5y -5y = -5y+8
2x = -5y+8
Divide each side by 2
2x/2 = -5y/2 +8/2
x = -5/2 y +4
PLEASE HELP PLEASE
Tricia has the same number of nickels and dimes in her pocket. The coins total $3.60. How many of each coin does she have?
A) 12 nickels and 12 dimes
B) 24 nickels and 24 dimes
C) 36 nickels and 36 dimes
D) 48 nickels and 48 dimes
Answer:
B
Step-by-step explanation:
Find out the total value of each option and see which one gives a total of $3.60
For A, 12 nickels + 12 dimes = 12 x $0.05 + 12 x $0.10 = $1.80 ≠ $3.60
For B, 24 nickels + 24 dimes = 24 x $0.05 + 24 x $0.10 = $3.60 (correct)
For C, 36 nickels + 36 dimes = 36 x $0.05 + 36 x $0.10 = $5.40 ≠ $3.60
For D, 48 nickels + 48 dimes = 48 x $0.05 + 48 x $0.10 = $7.20 ≠ $3.60
Answer:
For my opinion, the best option it B.
Dimetri says that a function that is made of terms
where the variable is raised only to an odd power
will be an odd function. Do you agree with
Dimetri?
Answer:
Dimetri says that a function that is made of terms
where the variable is raised only to an odd power
will be an odd function. Do you agree with
Dimetri?
Step-by-step explanation:
If g is an odd function and f is an odd function then g ◦ f is odd.
g ◦ f (x) = g (f (x)) = g (−f (−x)) = −g (- (- f (−x))) = −g (f (−x)) = - g ◦ f (−x)
The answer is: No, I am not agree with Dimetri, statement is false because there are so many counterexamples.
Answer:
Sample Response: He is correct only if there is no constant term. −x to an odd power is −x, so the signs will change on the terms with the variable but not on the constant term.
Step-by-step explanation:
What is the solution to the equation
Answer:
x = 12
Step-by-step explanation:
5(x - 6) = 2(x + 3)
Distribute
5x - 30 = 2x + 6
Put like terms on each side by subtracting both sides by -2x and adding 30 on each side
3x = 36
Simplify
3x/3 = 36/3
x = 36/3
x = 12
Plug is back in to check
5(12) - 30 = 2(12) + 6
60 - 30 = 24 + 6
30 = 30
Answer:
x=12
Step-by-step explanation:
5(x-6) = 2(x+3)
Distribute
5x-30 = 2x+6
Subtract 2x from each side
5x-2x -30 = 2x-2x+6
3x-30 =6
Add 30 to each side
3x-30+30 = 6+30
3x=36
Divide each side by 3
3x/3 = 36/3
x =12
Identify an equation in point slope form for the Line perpendicular to y=-4x-1 that passes through (-2,7)
Answer:
[tex]y - 7 = \frac{1}{4}(x + 2)[/tex]
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are. Plus, perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES] so −4 becomes ¼.
I am joyous to assist you anytime.
Determine the range of the function graphed above.
A. [4,∞)
B. [-4,0]
C. [0,4]
D. (-∞,4]
Answer:
D. (-∞,4]
Step-by-step explanation:
The range is the y values
The lowest y values is negative infinity
The highest y values is 4
( - inf, 4]
We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4
Choose the required figure.
A right triangle circumscribed about a circle:
Answer:I think that in this problem you need a right angle with a circle in it
What is the definition of a base number
Answer:
main number
Step-by-step explanation:
Final answer:
A base number in mathematics is the number raised to a power, where in scientific notation it is always 10, whereas in economic terms, a base year is a reference year for economic measurements.
Explanation:
The definition of a base number in mathematics generally refers to the number that is being raised to a certain power. In the context of scientific notation, the base number is always 10. This is used to succinctly represent very large or very small numbers in the form N x 10^n, where N is a number greater than or equal to 1 and less than 10, and n is a positive or negative integer; for example, 10^0 = 1. However, the concept of a base extends beyond just the number 10; any number can act as a base in different mathematical contexts.
When discussing numbers in a positional numeral system, the base determines the value of each digit in the number and how those digits are combined to represent the overall number. For instance, in the base-10 system, the digits 0 through 9 are used, and the position of each digit indicates how many multiples of powers of 10 it represents. Finally, in the context of economic indexes, a base year is a reference year against which economic growth or inflation is measured.