The required bearing angle of town B from Thomas is 65°.
Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.
Given that Thomas is facing towards town A, which is at a bearing of 300°.
Implies that town A is 300° from north.
If Thomas turns 125° clockwise, then he faces towards town B,
The bearing angle will be 300+125 = 425°
Since, one complete round makes angle 360°, therefore
The required bearing angle = 425 - 360 = 65
The bearing angle of town B from Thomas is 65°.
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A certain state uses the following progressive tax rate for calculating individual income tax: Progressive Income Range ($) Tax Rate 0 - 10,000 10,001 - 50,000 50,001 - 100,000 3% 5% 5.5% Calculate the state income tax owed on a $90,000 per year salary. tax = $[ ? ] Round your answer to the nearest whole dollar amount.
The required state income tax owed on a $90,000 per year salary is $4950.
Given that,
A table shows the income tax owed by the state on the particularar salary,
Income Range ($) Tax Rate
0 - 10,000 3%
10,001 - 50,000 5%
50,001 - 100,000 5.5%
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
on $90,000
Tax owed = 5.5% of 90000, because this salary lies in the segment 50,001 - 100,000.
Tax owed = 0.055[90000] = $4950
Thus, the required state income tax owed on a $90,000 per year salary is $4950.
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i need help with this
Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
What is a Pythagoras theorem?
The theorem 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 other two sides. This relationship is often expressed in the form of the equation:
a² + b² = c²
To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem 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 other two sides.
In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:
KL² = KM² + KN²
Substituting the given values, we get:
24² = 10² + KN²
Solving for KN, we get:
KN² = 24² - 10²
= 576 - 100
= 476
KN = √476
= 21.84
Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
What is a Pythagoras theorem?
The theorem 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 other two sides. This relationship is often expressed in the form of the equation:
a² + b² = c²
To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem 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 other two sides.
In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:
KL² = KM² + KN²
Substituting the given values, we get:
24² = 10² + KN²
Solving for KN, we get:
KN² = 24² - 10²
= 576 - 100
= 476
KN = √476
= 21.84
Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
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A university will spend Atmos 6000 by monitors and keyboards for computer lab each monitor will cost $200 and each keyboard will cost $25 which inequality represents all possible combinations of x the number of monitors and y the number of keyboards the university can buy for the computer lab?
Answer:
Answer: 200x + 25y <= 6000
Step-by-step explanation:
Hi can someone solve this with steps?
Answer:
42
Step-by-step explanation:
Given function:
[tex]f(x)=4x^4-2x^3-3x^2+3x[/tex]
Use the method of synthetic substitution to find the value of the function when x = 2.
Place the value of x in the left box and write the coefficients of the function in descending order, remembering to write a zero for the coefficient of any missing term.
(As there is no constant term in this function, the last coefficient should be written as zero).
[tex]4x^4-2x^3-3x^2+3x[/tex]
[tex]\begin{array}{c|ccccc}2&4&\:\:-2&\;\;-3&\;\:\:\:\:3&\;\;0\\\cline{1-1} \end{array}[/tex]
Bring the leading coefficient down:
[tex]\begin{array}{c|ccccc}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &&&\\\cline{2-6}&4\end{array}[/tex]
Multiply the number you brought down with the number in the box and put the result in the next column (under the -2):
[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&&\\\cline{2-6}&4\end{array}[/tex]
Add the two numbers in the second column together and put the result under them in the bottom row:
[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&&\\\cline{2-6}&4&6\end{array}[/tex]
Repeat:
[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&\\\cline{2-6}&4&6&9\end{array}[/tex]
[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&18\\\cline{2-6}&4&6&9&21\end{array}[/tex]
[tex]\begin{array}{c|rrrrr}2 &4&-2&-3&3&0\\\cline{1-1}&\downarrow &8&12&18&42\\\cline{2-6}&4&6&9&21&42\end{array}[/tex]
The last value, 42, is the value of the function when x is 2.
Therefore,
[tex]f(2)=4x^4-2x^3-3x^2+3x=42[/tex]
Bennett has 107 photographs to place in the school yearbook. He will put the same number of photos on each of the 13 pages. If he can put 4 pictures in a row, how many photographs will not be placed in the yearbook?
Answer:
2 rows on each page equals 104, which means that there would be 3 non-used photos
Step-by-step explanation:
A lione ha 4 cub that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day. How much food will be needed to feed all the cub for one year?
The food will be needed to feed all the cub for one year is 1825 kg.
Given :
A lion ha 4 cubs that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day.
one cub eats food = 1.25 kg
4 cubs eats food = 1.25 kg * 4
= 125 / 100 * 4 kg
= 500 / 100 kg
= 5 kg
5 kg for one day.
cub eats food for one year = 365 * 5 kg
= 1825 kg.
Therefore the food will be needed to feed all the cub for one year is 1825 kg.
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161% of 200 = what ?
Answer:332
Step-by-step explanation:Solution for 161 is what percent of 200:
161:200*100 =
(161*100):200 =
16100:200 = 80.5
Now we have: 161 is what percent of 200 = 80.5
Question: 161 is what percent of 200?
Percentage solution with steps:
Step 1: We make the assumption that 200 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=200$.
Step 4: In the same vein, $x\%=161$.
Step 5: This gives us a pair of simple equations:
$100\%=200(1)$.
$x\%=161(2)$.
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{200}{161}$
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{161}{200}$
$\Rightarrow x=80.5\%$
Therefore, $161$ is $80.5\%$ of $200$.
Like ha blue and red ball. Every day he win 2 blue ball and loe 3 red. After 5 day he won the ame amount of blue ball a red. After 9 day he had twice a many blue ball a red. How many red ball he have at the beginning
He started out with 47 balls after winning 2 blue balls and losing 3 red balls.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party.
Here,
Let the number of blue balls be x and the number of red balls be y,
after 5 days ,
x + 10 = y - 15
after 9 days ,
x + 18 = 2 * ( y - 27 )
subtracting both,
8 = y - 39
y = 47
The number of red balls in beginning is 47.
He had 47 balls in the beginning as he win 2 blue ball and lose 3 red balls.
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s is inversely proportional to t.
When s = 0.9, t = 2
Work out s when t = 0.6
Answer:
s = 3
Step-by-step explanation:
We model the proportion with the equation:
[tex]s =\frac{k}{t}[/tex]
We have s and t, but we need to find the k (i.e., the constant of proportionality) by plugging in the s and t we already have:
[tex]0.9=\frac{k}{2}\\ 1.8=k\\s=\frac{1.8}{t}[/tex]
To find s when t = 0.6, we simply plug in 0.6 for t in last equation we found with k:
[tex]s=\frac{1.8}{0.6}\\ s=3[/tex]
Please name these last two shapes
Answer:
Step-by-step explanation:
Square, Irregular shape
Dee chose A as the correct answer. What was her error? Answer in a complete sentence.
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, square feet = 40.5 square feet
Rate at which he paints the wall =40.5/10
= 4.05 square feet per minute
As we know 1 hour =60 minutes
Now, number of square feet
= 4.05×60
= 243 square feet
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
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A laptop computer originally priced at $2100 now ell for $2,200. What i the percent of increae?
The percent of increase is 4.761 %
Given :
A laptop computer originally priced at $2100 now and sell for $2,200.
Percentage :
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Difference = sell price - original price
= 2200 - 2100
= 100
Percent of increase = 100 * 100 / 2100
= 100 * 1 / 21
= 100 / 21
= 4.761 %
Therefore 4.761 % increase in percent.
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Circle a ha a diameter of 9cm. Cirlce b ha a radiu of 5 cm. 1. Which circle ha a larger circumference? 2. About how many centimeter larger i it
Circle B will have larger circumference by 3.14 centimeter
What is Circumference of Circle ?The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.
The circumference of the circle is = 2пr where r is radius
According to the information
Circle A has diameter = 9 cm
Radius of circle A = [tex]\frac{9}{2}[/tex] cm
Circumference of Circle A = 2пr
= 2 × 22/7 × 9/2
= 28.28 centimeter
Circle B has radius = 5 cm
Circumference of circle B = 2 × 22/7 × 5
= 31.42 centimeter
Circle B will have larger circumference by 3.14 centimeter
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Milan runs7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes
Answer:
2.8 Miles in 24 minutes
Step-by-step explanation:
60 / 24 = 2.5
2.5 / 7 = 2.8
Answer:
17.5mi
Step-by-step explanation:
7mi = 17.5mi
60min = 24min
60/24=2.5
2.5*7=17.5
I don’t feel like typing
Answer:
A
Step-by-step explanation:
mass / volume
m/v
Answer: d = m/V
Step-by-step explanation: density is the mass divided by volume or d= m/V
the sum of 5 and a number x
show work
Answer:
x+5 or 5+x
Step-by-step explanation:
It seems we are looking for a math expression that is the same as English expression you wrote.The sum is what we get when we add numbers. Therefore, we could restate the English expression as what do we get when we add 5 to the number x? While we do not know what specific number x represents, we do know that if we add 5 to the number x we get 5 plus x. Now the question can be restated as, "How do we write 5 plus the number x?" Do you know the answer now? Does 5 + x sound right? How about x + 5? Both of these expressions are correct as they both represent the sum of 5 and the number x.
1 and (-1,-4) y-intercept
The graph's intersection with the x-axis is known as the x-intercept. The graph's intersection with the y-axis is known as the y-intercept.The y-intercept is (0,-4).
what is X-intercept and Y intercept?To find Y intercept substitute x=0;
here X interept is (1,-1)
Y intercept (0,-4)
The x- and y-intercept visual concept is quite straightforward. Where the graph crosses the x-axis is known as the x-intercept, and the y-intercept is where the graph crosses the y-axis. A line's X-intercept provides information about the point where the x-axis is crossed.In a similar manner, the line's y-intercept represents the location at which the y-axis is crossed. In a given equation, only one intercept can be determined at once.The point at which a line crosses the x axis is known as the line's x-intercept. (i.e., in the case where y = 0) X interept=(x,0)The point at which a line crosses the y axis is known as the line's y-intercept. (i.e. in the case where x = 0) Y interept =(0,y)To learn more about X-intercept and Y intercept refer to:
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question is in the screenshot
The base length of the isosceles triangle is 23. Therefore, the correct option is C.
How to find the side of an isosceles triangle?An isosceles triangle is a triangle with (at least) two equal sides. It also has two angles equal to each other.
The base angle of an isosceles triangle is equal in length.
The legs of an isosceles triangle are equal. Therefore,
3x - 1 = - 3x + 41
3x + 3x = 41 + 1
6x = 42
divide both sides by 6
x = 42 /6
x = 7
Let's find the length of the base side.
Therefore,
4x - 5
where
x = 7
4(7) - 5 = 28 - 5 = 23
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Ahley' chocolate bar i 72% cocoa. If the weight of the chocolate bar i 51 gram, how many gram of cocoa doe it contain?
Answer: 36.72 G
Step-by-step explanation:
I sell
Jon bought 6 gallons of gas for $24
A( Find the cost of 1 gallon
B( Find the cost of 12 gallons
Answer:
A/ $4 for 1 gallon
B/ $48
Step-by-step explanation:
Take 24 divided by 6 = $4 per gallon
Then take 4 times 12 = $48 for 12 gallons
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1. please Prove that the angle that an are of a circle subtends at the centre is twice that which it substends at any point on the remaining part of the circumfrence.
A middle chool took all 6th grade tudent on a field trip to ee a ballet. The tudent filled 702 eat leaving 35% vacant how manny eat were in the theater
There were 1080 seats in the theater.
In this question, we have been given that the 6th grade students went on a field trip to see a ballet.
The students filled 702 seats leaving 35% vacant.
We need to find the total seats in the theater.
Let there were n seats in the theater.
Given that 35 percent of total seats were vacant.
So, we get an equation,
702 + (35% of n) = n
702 + 0.35n = n
(1 - 0.35)n = 702
0.65n = 702
n = 1080
Therefore, the total seats in the theater = 1080
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Find the difference between the actual quotient and the etimated quotient of 78,070÷37. (Dividend i rounded off to nearet thouand and divior to nearet ten)
The actual quotient and the estimated quotient of 78,070÷37 is 2110 , so the difference between them is 0.
On dividing 78,070 by 37 ,
we get
78,070 /37
=2110
Since , the number gets divided completely
therefore the estimated quotient and the actual quotient will be 2110.
We first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient. When the divisor in a division sum has two or more digits, it is helpful to first estimate the quotient before attempting to discover the exact number.
The outcome of dividing two numbers is known as the quotient. Divided divisor = quotient + remainder is the formula for expressing the terms of division.
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(1). 7/10 - 2/5
(2). 3/4 + 5/6
(3). 17/9 - 11/12
(4). 2/3 + 1/4 - 7/12
Answer:
1. 3/10
2. 19/12
3. 35/36
4. 1/3
Step-by-step explanation:
A bread is cut into 10 equal parts. How many children can share all parts of the bread if each child takes 0.2 parts
5 children can share all parts of the bread if each child takes 0.2 parts.
What are Fractions?Fraction are numbers of the form [tex]\frac{a}{b}[/tex] where a and b are real numbers. It is represented as a portion or part of a whole.
The number on the top is called numerator and the number on the bottom is called denominator.
There are 10 equal parts of bread and each child takes 0.2 part.
Total parts of the bread = 10
Part each child takes = 0.2 = [tex]\frac{2}{10}[/tex]
2 parts out of 10 are taken by each child.
Remaining are [tex]\frac{8}{10}[/tex] parts.
[tex]\frac{2}{10}[/tex] × 4 = [tex]\frac{8}{10}[/tex]
Remaining parts can be shared by 4 children.
Hence number of children who can share the bread if each takes 0.2 parts = 5
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Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.
180 ft2 be the area of the rectangular sheep pen .
What is rectangle?
A quadrilateral is a shape with two opposed sides that are equal and parallel.
There are four 90-degree angles on its four sides, making it a four-sided polygon. The shape of a rectangle is two dimensional.
Length of the sheep pen =60ft
150 ft of fencing bought
One side of rectangular sheep pen is covered with barn which is equaling the width
perimeter of rectangular sheep pen = 2(length +width)
length need to covered is 2 Length+ width
150 =2 length+width
150 = 2 x60 +width
150-120= width
30= width
Area of rectangle = 60 x 30
= 180 ft2
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multiplications of matrices
The product of A x B of matrix is
a) [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
b) [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
c) [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
d) [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \left[\begin{array}{ccc}4\\5\\\end{array}\right][/tex]
The value of matrix B is
[tex]B = \left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]
Now , the dimensions of matrix A is 2 x 1 and of matrix B is 1 x 2
So , matrix multiplication is possible
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}4\\5\\\end{array}\right] *\left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]
So , the value of matrix C is calculated as
[tex]C = \left[\begin{array}{ccc}( 4 * 2 ) &( 4 * 3 )\\( 5 * 2 ) &(5 * 3 )\\\end{array}\right][/tex]
On simplifying the matrix , we get
[tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]
b)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}3\\4\\\end{array}\right][/tex]
The value of matrix B is
[tex]B = \left[\begin{array}{ccc}1&2\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}( 3 * 1 ) &( 3 * 2 )\\( 4 * 1 ) &(4 * 2 )\\\end{array}\right][/tex]
On simplifying the matrix , we get
[tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]
c)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}-1\\6\\\end{array}\right]\\[/tex]
The value of matrix B
[tex]B = \left[\begin{array}{ccc}7&2\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]
d)
C be the result of A x B
The value of matrix A
[tex]A = \left[\begin{array}{ccc}8\\5\\\end{array}\right]\\[/tex]
The value of matrix B
[tex]B = \left[\begin{array}{ccc}3&-12\\\end{array}\right][/tex]
Now , let C be the result of A x B
And ,
[tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]
Hence , the matrix multiplication is done and the results are given
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1.03 of 0.054 is what number?
Answer:
1.03% of 0.054=0.0005562
please help its due tomorrow and im failing the class
Answer:
the slope is -1/9
Step-by-step explanation:
The first thing to do is use the slope formula y^1 - y^2 over x^1 - x^2. You substitute each value into these variables and solve, which will then give you a negative slope of -1/9.
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Drag each label to the correct location in the equation. not all tiles will be used.
the density of mercury is 13.6 grams per cubic centimeter. complete the steps for converting 13.6 g/cm3 to kg/m3. (1 kg = 1,000 g, 1 m3 = 106 cm3)
13,600 10^6 1,360 1 g 1 kg 1 m3
13.6g/cm^3 x ( )/1000g x ( ) cm^3/( ) = ( ) kg/m^3
As per the given equation, the resulting conversion is written as,
13.6g/cm³ x 1kg/1000 x 10⁶cm³/m³ = 13600kg/m³
Equation:
An equation consist the value of the variable, numbers and the constants.
Given,
Here we have the density of mercury is 13.6 grams per cubic centimeter.
Now, we have to convert this one into kg/m3.
Here the process of conversion of 13.6 g/cm3 to kg/m3
We know that, 1 Kg of weight is equal to 1000 grams of weight
Then it can be written as
=> 1 g = 1 kg/1000
Then the first blank (numerator) will be filled with 1 Kg
Similarly, 1 meter is equal to 100 centimeter
So, for cubic unit it can be written as,
=> 1 cm³ = 1m³/100³
It can be simplified as,
=> 1 cm³ = 1m³/10⁶
Now, the second blank (numerator) will be filled with 10⁶
Finally, the third blank (denominator) will be filled with 1m³
Therefore, the last blank will be 13600
Hence, we have find the all the values on the blanks.
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