Answers
Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
values of x, y, and z, we can use the system of equations
3x - 2y + z = 1
2x + y - z = 0
x + 2y + 3z = -1
We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:
3x - 2y + z = 1 (eq. 1)
2x + y - z = 0 (eq. 2)
x + 2y + 3z = -1 (eq. 3)
3x - 2y + z = 1 (eq. 1)
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
-0.3333y + 2.3333z = -1.3333 (eq. 3')
3.3333x - 0.3333z = 0.1667 (eq. 1')
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
2.1667z = -1.0833 (eq. 3')
z = -0.5
y = 0.1667
x = 0.5
Therefore, the solution to the system of equations is:
x = 0.5, y = 0.1667, z = -0.5
x = 0.500, y = 0.167, z = -0.500
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Related Questions
The sides of a triangle are 43,96 , and 89. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answers
Using Pythagorean theorem, the triangle is an acute triangle.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.
In equation form, this can be written as:
[tex]c^2 = a^2 + b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.
If the triangle is not a right triangle, then the inequality [tex]c^2 < a^2 + b^2[/tex]holds for an acute triangle and [tex]c^2 > a^2 + b^2[/tex] holds for an obtuse triangle.
Using this formula, we can check if the given triangle is right, acute, or obtuse:
a = 43, b = 96, and c = 89
[tex]c^2 = 89^2 = 7921[/tex]
[tex]a^2 + b^2 = 43^2 + 96^2 = 1849 + 9216 = 11065[/tex]
Since [tex]c^2 < a^2 + b^2[/tex], we can see that:
[tex]c^2 < a^2 + b^2[/tex]
So the triangle is an acute triangle.
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Which of the following is true of the location of an angle, Theta, whose tangent value is Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction?
Theta has a 30-degree reference angle and is located in Quadrant II or IV
Theta has a 30-degree reference angle and is located in Quadrant II or III
Theta has a 60-degree reference angle and is located in Quadrant II or IV
Theta has a 60-degree reference angle and is located in Quadrant II or III
Answers
Answer:
A
Step-by-step explanation:
we know that
tan x=sin x/cos x
if
then
x belongs to the II quadrant or IV quadrant
sin 30°=
cos 30°=
therefore
tan 30°=
the angle theta has a 30-degree reference angle and is located in Quadrant II or IV
Answer:
A
Step-by-step explanation:
Part A
SAVINGS A company has a bonus incentive for its employees. The company pays employees an initial signing bonus of $1000 and invests that amount for the employees. Suppose the investment earns 8% interest compounded quarterly.
a. If an employee receiving this incentive withdraws the balance of the account after 5 years, how much will be in the account? Round to the nearest cent.
Part B
b. If an employee receiving this incentive withdraws the balance of the account after 35 years, how much will be in the account? Round to the nearest cent.
Answers
After answering the given query, we can state that So, after 35 years, the amount account would have a value of $10,062.07.
What is amount ?aggregate attempting to determine the amount, total number, or duration needed. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how much you have, how much you need, or how much you get is its amount. He needs that much cash to get by.
a. We must first determine the quarterly interest rate in order to determine the account amount after five years:
r = 8% / 4 ≈ 2% every three months.
The amount after five years can then be determined using the compound interest formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where P = $1,000 as the original investment
2% is the quarterly interest rate (r).
N = 4 times per year that interest is added (quarterly)
If t = amount of years, then 5
[tex]A = \$1000(1 + 0.02/4)^{(4*5)} = $1,221.50[/tex]
So, after five years, the account would have a total of $1,221.50.
b. We employ the same method as before to determine the account balance after 35 years:
[tex]A = \$1000(1 + 0.02/4)^{(4*35)} = $10,062.07[/tex]
So, after 35 years, the account would have a value of $10,062.07.
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?
In a company's first year in operation, it made an annual profit of
$247, 500. The profit of the company increased at a constant 16% per
year each year. How much total profit would the company make over
the course of its first 10 years of operation, to the nearest whole
number?
Sum of Geometric series
Answers
Answer:
Total profit after 10 years = [tex]\$5,277,064[/tex]
Step-by-step explanation:
Let [tex]a_n[/tex] represent the profit in the nth year
Then [tex]a_{n+1}[/tex] represents the profit in year [tex]n+[/tex]1
[tex]\text{Common ratio } r = \dfrac{a_{n+1}}{a_n}[/tex]
The sum of a geometric sequence is given by
[tex]S_n = a_1 \cdot \dfrac{1 - r^n}{1-r}[/tex]
where
[tex]a_1 =[/tex] first term
[tex]r =[/tex] common ratio
[tex]n =[/tex] number of terms
Calculation of r
To calculate r we see that the profit increases by 16% every year
16% = 16/100 = 0.16
If profit increases by 0.16, then next year's profit
= this year's profit(1 + 0.16)
= this year's profit x 1.16
r = 1.16 the ratio of a term to the previous term
In this problem we are given the first term as
[tex]a_1 = 247,500[/tex] [tex]\text{ = profit in first year}[/tex]
[tex]n = 10 =[/tex] number of years
[tex]r = 1.16[/tex]
Plugging these values into equation [1] for the sum we get
[tex]\begin{aligned}S_n &= a_1 \cdot \dfrac{1 - r^n}{1-r}\\\\&= 247500 \cdot \dfrac{1-1.16^{10}}{1-1.16}\\\\& = 247500 \cdot \dfrac{-3.41143}{-0.16}\\& = 247500 \cdot 21.3215\\& = 5277064\end{aligned}[/tex]
Therefore the total profit after 10 years
= $5,277,064
What is the slope of the line that passes through the points (6, 10)(6,10) and (6, -2)(6,−2)?
Answers
The slope of the line that passes through the points (6,10) and (6,−2) is undefined.
The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In mathematical terms, the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Now, let's apply this formula to the given points (6, 10) and (6, -2). Here, x₁ = 6, y₁ = 10, x₂ = 6, and y₂ = -2. Substituting these values in the formula, we get:
slope = (-2 - 10) / (6 - 6)
Notice that the denominator is zero, which means that the line is a vertical line. In this case, the slope is undefined.
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A house painter charges a fee for supplies and an hourly fee for the time spent painting. A paint job
that takes 3 h costs $140. A paint job that takes 5 h costs $200.
Answers
Answer:
y=30x+50
Step-by-step explanation:
3x30+50=140
5x30+50=200
3. 8, 15, 100, 123.
4. line the numbers up to multiply them from the y side or x side
5. adding the word problem to find the solution
35 POINTS HELP
Answers
There are four numbers: 8, 15, 100 and 123.
What is number?Number is a mathematical object used to count, measure, and label. It is used in many different contexts, from everyday life to scientific research. Numbers can be represented in various forms, such as symbols, digits, and words. They are used to represent quantities, distances, time, and other concepts. Numbers can also be used to represent relationships, such as equations, which are statements that describe how two or more things are related.
To solve this problem, it is best to line the numbers up on the y axis or x axis. To multiply the numbers, start by multiplying the numbers on the y axis first. So, 8 x 15 = 120. Then, multiply the result by the number on the x axis which is 100. 120 x 100 = 12,000. Finally, multiply 12,000 by the last number on the x axis which is 123. 12,000 x 123 = 1,476,000. Therefore, the answer to the problem is 1,476,000.
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Simplify fully 9x + y - 6x + y
Answers
Answer:
Step-by-step explanation:
So first you would combine like terms which in this case are 9x, -6x, y, and y
So: 9x+y-6x+y
(9x-6x)+(y+y)
3x+2y is the final answer
hope this helped
Answer:
Step-by-step explanation:
5 Exam-style Samia invests £3000 in an account for one year.
At the end of the year interest is added to her account.
Samia pays tax on the interest at a rate of 20%.
She pays £7.80 tax.
Work out the percentage interest rate for the account.
Answers
The percentage interest rate added to the account at the end of the year is 1.3%
What percentage interest rate for the account?Tax is the compulsory levy paid by citizens to the government for buying goods and services.
Amount Samia invest = £3,000
Amount of interest = x
Rate of tax = 20%
Amount of tax = £7.80
So,
20% of x = £7.80
0.2x = £7.80
x = £7.80/0.2
x = £39
Percentage of interest rate:
x% of £3000 = £39
x% × 3000 = 39
x% = 39/3000
x% = 0.013
x% = 1.3%
Hence, 1.3% is the percentage of Samia investment added to the account.
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Angle Relationships & PT Quiz Review Are the angles are complementary, supplementary, or neither?
1. m<1=91°, m <2 = 89°
2: m< 3 = 17°, m<4 = 73°
3. m< 5 = 124° m <6 = 66°
4. m <7 = 33° m< 8 = 148°
5. m< 9 = 52° m <10 = 38°
pleasee help fast
Answers
answer the question picture is there
Answers
Answer:
Step-by-step explanation:
1. 500
2. 10
3. 25000
Sebastian is looking to buy a car and the he qualified for a 8-year loan from a bank offering a monthly interest rate of 0.25% Using the formula below, determine the maximum amount Sebastian can borrow, to the nearest dollar, if the highest monthly payment he can afford is $ 175 $175. � = � � 1 − ( 1 + � ) − � M= 1−(1+r) −n Pr
Answers
Answer:
блина я сама не
Step-by-step explanation:
What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3. 14. Cylinder with a segment from one point on the circular base to another point on the base through the center labeled 3. 2 feet and a height labeled 3. 8 feet
Answers
the volume of the cylinder is approximately 30.19 cubic feet.
To find the volume of a cylinder, we use the formula:
V = πr²h
where V is the volume, r is the radius of the circular base, h is the height, and π is a constant that approximates the ratio of the circumference of a circle to its diameter, which is approximately 3.14.
In this case, we're given that the cylinder has a height of 3.8 feet, and a segment from one point on the circular base to another point on the base through the center labeled 3.2 feet. This segment is the diameter of the circular base, which means that the radius of the base is half of that, or 3.2/2 = 1.6 feet.
Plugging these values into the formula, we get:
V = πr²h
V = 3.14 x (1.6 feet)² x (3.8 feet)
V = 3.14 x 2.56 square feet x 3.8 feet
V = 30.1864 cubic feet
Rounding to the nearest hundredth, we get:
V ≈ 30.19 cubic feet
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Find the interest on 20,000 at 6% interest for 3 years
Answers
The interest can be calculated using the simple interest formula:
I = Prt
Where:
I = Interest
P = Principal (the initial amount)
r = rate of interest per year
t = time period in years
Plugging in the given values:
P = 20,000
r = 6% = 0.06 (in decimal)
t = 3
I = 20,0000.063
I = 3,600
Therefore, the interest on 20,000 at 6% interest for 3 years is 3,600.
How to calculate a rate or unit rate?
Answers
To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.
What is rate ?
In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.
To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).
The formula for rate is:
rate = quantity / time
To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.
The formula for unit rate is:
unit rate = rate / 1
When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.
Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.
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Please please help me with this!
Answers
Answer:
288π in³
Step-by-step explanation:
V-sphere = 4/3πr³
D = 12in r = D/2 = 12/2 = 6 in
V = (4/3)(6)³π = (4/3)(216)π = 288π in³
The box-and-whisker plot below
represents some data set. What is the
range of the data?
50
Answer:
60
70
80
90
Answers
Answer: 32
Step-by-step explanation:
the min is 54 while the max is 86
86-54 is the range which is 32
Classify the triangle using its angles and sides. (Choose 2)
Answers
Based on the angles, a triangle can be classified as either acute, right, or obtuse and based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.
To classify a triangle, we need to consider both its angles and sides. Based on the angles, a triangle can be classified as either acute, right, or obtuse.
An acute triangle has all three angles measuring less than 90 degrees. A right triangle has one angle measuring exactly 90 degrees. An obtuse triangle has one angle measuring greater than 90 degrees.
Based on the sides, a triangle can be classified as either equilateral, isosceles, or scalene.
An equilateral triangle has all three sides equal in length. An isosceles triangle has two sides of equal length. A scalene triangle has all three sides of different lengths.
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Which inequality describes the graph?
Answers
Answer:
Step-by-step explanation:
I think y ≤ 3 - 3x
Dumisani earn 42 480 per month. He splits his earnings in the ratio 7:5. And then saves the lesser amount. How much does he save
Answers
If Dumisani earn $42480 per month and he splits his earnings in the ratio 7:5, then he saves $17,700 per month.
A ratio is a way of comparing two quantities or values. It expresses the relationship between two numbers or values in terms of their relative sizes or amounts.
To split Dumisani's earnings in the ratio 7:5, we need to divide his earnings into 7 + 5 = 12 equal parts.
Each part is therefore:
42480 ÷ 12 = 3,540
Dumisani saves the lesser amount, which is in the ratio of 5 parts to 7 parts.
So he saves:
5 × 3,540 = $ 17,700
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Work out the value of 5 cubed - 10 squared.
Give your answer as a power of 5
Answers
Answer:
5 cubed is 5 x 5 x 5 = 125.
10 squared is 10 x 10 = 100.
So, 5 cubed - 10 squared = 125 - 100 = 25.
We can also express 25 as a power of 5 by noting that 25 = 5 squared. Therefore:
5 cubed - 10 squared = 5 squared x 5 - 10 squared = 5^(2+1) - 10^(2) = 5^3 - 10^(2) = 125 - 100 = 25.
So, the answer is 5 squared or 5^2.
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
5 cubed - 10 squared
[tex]5^{3} - 10^{2} \\ = 125 - 100\\= 25[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
whats the missing side lengths!
Answers
5??????????????????????
Answer:
x = y = 4.24
Step-by-step explanation:
sin45 = x/6
x = 6(sin45) = 4.24
y = 6(cos45) = 4.24
Because this is a 45-45-90 isosceles triangle, x=y
The graph of y = x² - 2x + 3 is shown.
Use the graph to solve the equations
y = x + 3
y = x² - 2x + 3
or
x = 0
X =
3
y =
y =
-B
-1
18
16-
14
12
10
8
6-
2
O
3
4
6
( this is for simultaneous equations with a quadratic)
Answers
The system of equations y = x + 3 and y = x² - 2x + 3 when solved for x and y is x = 0 and y = 3 & x = 3 and y = 6
Solving the system of equationsFrom the question, we have the following parameters that can be used in our computation:
y = x² - 2x + 3
Using the graph to solve the equations
y = x + 3
y = x² - 2x + 3
We simply write out the point of intersection of y = x + 3 and y = x² - 2x + 3
When y = x + 3 is plotted, we have the intersection to be
(0, 3) and (3, 6)
Hence, the solutions are (0, 3) and (3, 6)
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(Please answer quickly!!!!) Given 7.05(−18.2), find the product.
−128.31
−12.83
77.55
578.10
Answers
Answer:
-128.31
First choice
Step-by-step explanation:
Using a calculator:
7.05(−18.2) = 7.05 x -18.2 = -128.31
A factory is making screws. The weight of the crews is normally distributed, and the variance is 0.64g^2.
In a sample the mean of the screws was 44g. Calculate a two sided(symmetrical) confidence interval with confidence level 95% for the expected value of the weight, if the sample size was
a)13
b)1300
Answers
a) Sample size 13:(43.614, 44.386)
b) Sample size 1300:(43.9663, 44.0337)
The weight of the screws is normally distributed and has a variance of 0.64g^2. In a sample, the mean of the screws was 44g. The following are the two-sided (symmetrical) confidence intervals with a 95 percent confidence level for the expected value of the weight:Option a) Sample size 13:For a sample size of 13, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(13) = 0.1772.The t-distribution should be used to calculate the confidence interval since the population's standard deviation is unknown.The t-value corresponding to the 95% confidence interval with 12 degrees of freedom (df = n – 1) is 2.179. Therefore, the confidence interval can be calculated as follows:44 ± 2.179(0.1772)= 44 ± 0.386= (43.614, 44.386)The expected weight of the screws in the population is estimated to be between 43.614 g and 44.386 g.Option b) Sample size 1300:For a sample size of 1300, the standard error of the mean is calculated as follows:SE = σ/√nwhere SE is the standard error, σ is the variance, and n is the sample size.In this case, SE = √(0.64)/√(1300) = 0.0172.The z-distribution should be used to calculate the confidence interval since the sample size is large enough to assume that the sample mean is approximately normally distributed.The z-value corresponding to the 95% confidence interval is 1.96. Therefore, the confidence interval can be calculated as follows:44 ± 1.96(0.0172)= 44 ± 0.0337= (43.9663, 44.0337)The expected weight of the screws in the population is estimated to be between 43.9663 g and 44.0337 g.
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The y-intercept of the graph of y=-7x+140y is located at (0, c) What is the value of c ?
Answers
The y-intercept of the graph is located at (0, 0). So, the value of c is 0.
What is graph?
A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.
To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.
Substituting x = 0, we get:
y = -7(0) + 140y
y = 140y
Simplifying the equation, we get:
139y = 0
Dividing both sides by 139, we get:
y = 0
Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.
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Which graph shows the solution to the inequality? x − (5 − 3x) ≤ 2x − 1 A. A number line with a closed dot at 2 shaded to the left. B. A number line with a closed dot at 2 shaded to the right. C. A number line with a closed dot at negative 1 shaded to the left. D. A number line with a closed dot at negative 1 shaded to the right.
Answers
Answer: To solve the inequality x − (5 − 3x) ≤ 2x − 1, we need to simplify it by first distributing the negative sign in front of the parentheses, and then combining like terms. This gives us:
x - 5 + 3x ≤ 2x - 1
4x - 5 ≤ 2x - 1
Next, we can isolate the variable on one side of the inequality by subtracting 2x from both sides:
4x - 2x - 5 ≤ -1
2x - 5 ≤ -1
Finally, we can isolate x by adding 5 to both sides and dividing by 2:
2x ≤ 4
x ≤ 2
So the solution to the inequality is x ≤ 2.
To graph this solution on a number line, we can put a closed dot at 2 and shade to the left of it, since all values less than or equal to 2 satisfy the inequality. Therefore, the correct graph is A, a number line with a closed dot at 2 shaded to the left.
Step-by-step explanation:
which division equation describes the situation
Answers
The division equation that describes the situation here is as follows:
4 ÷ 2/3 = 6.
Define division?Together with addition, subtraction, and multiplication, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same number of items is known as division.
This operation is used by mathematicians to organise and evenly distribute resources.
As we can see in the question, that there are 6 groups.
Now 6 groups of 2/3 parts.
Now the whole part has been given as = 4.
This can also be stated as:
The whole part (4) has been divided into 2/3 small parts to get 6 equal parts.
Therefore, the expression as per division can be:
4 ÷ 2/3 = 6.
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The map shows the distance in air miles from city A to both city B and city C.
City A to City B= 11
City A to city C= 29
City B to City C= X
What is X?
F. 39 miles
G. 40
H. 41
J. 42
Answers
The value of distance between city B to city C given by 'x' is found as: 41 miles.
How to solve linear equation?A line's equation can be expressed in a way that makes the slope evident and enables you to trace the path directly without performing any calculations. Students can compose linear equations using slope-intercept form if they feel confident solving a straightforward two-step linear equation. A linear equation has the slope-intercept form y = mx + b.Distance in air miles from city A to each city B and city C are-
City A to City B= 11
City A to city C= 29
City B to City C= X
Then,
Distance between city B to city C = distance between city A to city B + between city A to city C
x = 29 + 11
Solving the linear equation:
x = 41
Thus, the value of distance between city B to city C given by 'x' is found as: 41 miles.
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WHOEVER DOES MOST ASAP GETS AN EXTRA 50 POINTS
Answers
The figures converted from fraction to decimal to percent (Questions 9-14) are given as follows:
Percent Decimal Fraction
9) 316.2%. 3.162 3 4861/30000
10) 6.94%. 0.0694 347/5000.
11) 15.27%. 0.1527 1527/10000
12) 217 2761/3367% 2.178 1089/500
13) 723 12/21% 7.236 1809/250
14) 87% 0.87 87/100
9) Given the compound fraction: 3 4861/30000
To convert 3 4861/30000 to a decimal, we first need to convert the mixed number to an improper fraction:
3 4861/30000 = (30000*3 + 4861)/30000
= 94861/30000
To convert this fraction to a decimal, we divide the numerator by the denominator:
94861/30000 ≈ 3.162
To convert 3 4861/30000 to a percentage, we multiply the decimal by 100:
3.162 x 100 ≈ 316.2%
So, 3 4861/30000 as a percentage is approximately 316.2%
10) Given the decimal 0.0694
To convert 0.0694 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.0694 = 694/10000
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
694/10000 = (3472)/(50002) = 347/5000
So, 0.0694 as a fraction is 347/5000.
To convert 0.0694 to a percentage, we multiply the decimal by 100:
0.0694 x 100 = 6.94%
So, 0.0694 as a percentage is 6.94%.
11) Given the decimal - 0.1527
To convert 0.1527 to a percentage, we multiply the decimal by 100:
0.1527 x 100 = 15.27%
So, 0.1527 as a percentage is 15.27%.
To convert 0.1527 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.1527 = 1527/10000
12) Given the compound percentage - 217 2761/3367%
To convert 217 2761/3367% to a decimal, we first need to convert the mixed number to an improper fraction:
217 2761/3367% = (3367*217 + 2761)/3367% = 733400/3367%
743032/3367% = 217.82001782%
217.82001782% = 2.1782001782
220.680724681% [tex]\approx[/tex] 2.178
Thus, in fraction:
2.178 = 2.178/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000
= 2.178/1 x 1000/1000
= 2178/1000
= 1089/500
13) Given the compound fraction - 723 12/21%
To convert 723 12/21% to a decimal, we first need to convert the mixed number to an improper fraction:
723 12/21% = (21*723 + 12)/21% = (15195/21)%
(15315/21)% = 7.23571428571
15315/21% [tex]\approx[/tex] 7.236
Converting 7.236 to fraction:
7.236 = 7.236/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000
= 7.236/1 x 1000/1000
= 7236/1000: Divide numerator and denominator by 4
= (7236÷ 4)/(1000÷4)
= 1809/250
14) Given 0.87:
To convert 0.87 to a percentage, we multiply the decimal by 100:
0.87 x 100 = 87%
So, 0.87 as a percentage is 87%.
To convert 0.87 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.87 = 87/100
Learn more about Fractions:
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