Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is aⁿ = a(3)ⁿ and Second sequence nth formula is aⁿ = a + (n-1)5.
Define arithmetic mean.A list's values are added together to get the average values, also known as the group's mean, which is then multiplied by the maximum population of list items. Similar progression trends can be seen in math. The average of the actual numbers 5, 8, and Nine is 3, while a mean of the actual numbers 5, 7, & 9 is 4, and indeed the number 21 times three (there now multiple 3 numbers) equals seven. This is demonstrated by the following equation.
Here,
Given :
First sequence :
=> 7,21,63 ....
We can see it is a type of geometric progression:
As,
=> 21/7 = 3
=> 63/21 = 3
So, it's nth formula is : aⁿ = a(3)ⁿ
And
Second sequence :
=> 3, 8, 13,....
it is a type of arithmetic progression:
As,
=> 8 -3 =5
=> 13 -8 = 5
So, it's nth formula is : aⁿ = a + (n-1)5
Therefore , the solution of the given problem of arithmetic comes out to be First sequence nth formula is aⁿ = a(3)ⁿ and Second sequence nth formula is aⁿ = a + (n-1)5.
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Miss Chen puts the same number of art supplies at each of 12 work stations. Each work station receives several containers of paints and 3 paint brushes. Miss Chen uses 132 items in all.
Which equation can be used to determine the number of containers of paint, p, at each work station?
Answer:
11 containers of paint and 3 paint brushes
Step-by-step explanation:
The equation that can be used to determine the number of containers of paint, p, at each work station is p = 132 / (12 * 3) = 11. Therefore, each work station receives 11 containers of paint and 3 paint brushes
A house was valued at $384,000. Over several years, the value increased by 18%, giving the house a new value.
The new value of the house will be $453120.
How can we express : "a% of b" ?We can write : a% of b as -
a% of b = a/100 x b
a% of b = ab/100
Given is that a house was valued at $384,000. Over several years, the value increased by 18%.
We can write the new value as -
{x} = 384000 + 18% of 384000
{x} = 384000 + 18/100 x 384000
{x} = 384000 + 18 x 3840
{x} = 384000 + 69120
{x} = 453120
Therefore, the new value of the house will be $453120.
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Calculate the standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849
The standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849 is 21.
What is Standard deviation?The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
We have Σx=272 and Σx² = 11849.
n= 17
So, the Variance of the Data
= Σx²/n - (Σx/ n)²
= 11849 / 17 - (272/17)²
= 697 - 256
= 441
Then, the Standard deviation is
= √Variance
= √441
= 21
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What are the coordinates of point P?
On a coordinate plane, Point P is 2 units to the left and 4.5 units down.
(Negative 4.5, negative 2)
(Negative 2, negative 4.5)
(2, negative 4.5)
(4.5, negative 2)
Answer:
they’re both negative to -4.5 is the answer
Step-by-step explanation:
Answer: They’re both negative to -4.5 is the answer
Step-by-step explanation:
how to read a ruler in inches
One inch is equal to 2.54 centimeters on the ruler, so, to read on the ruler, every 2.54 cm will be equal to one inch.
Normally a ruler scale if of length 15cm. we have certain marks on the ruler to read the rules of the scale/ruler.
Now, from the standard unit conversion methods, we know, one inch is equal to about 2.54 centimeters.
Now, what we to is, to read the ruler, we mark every 2.54cm on the ruler and that becomes equal to one inch. On a scale of 15cm there will be 6 inches on the ruler.
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Question 3(Multiple Choice Worth 2 points)
(Effects of Changes in Data MC)
The shoe sizes of a group of middle school girls are shown.
5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
If a shoe size of 7 is added to the data, how does the IQR change?
The IQR becomes a 2.5.
The IQR becomes a 1.5.
The IQR remains a 3.
The IQR remains a 2.
If a shoe size of 7 is added to the data the IQR remains the same 2. Option D is the correct answer.
What is IQR?The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.
By using linear interpolation, the data set is separated into quartiles, or four rank-ordered even sections, to determine the IQR.
The shoe size in increasing order are written as:
5,5.5,6,6.5,6.5,7,7.5,8,8.5
The median of the data is:
Median = 5th value
Median = 6.5
The IQR of the data is given as:
IQR = Q2 - Q1
IQR = (7.5 + 8)/ 2 - (5.5 + 6) / 2
IQR = 2
When 7 is added to the data, the new order is:
5,5.5,6,6.5,6.5,7,7,7.5,8,8.5
The median of the new data is:
Median = 5th + 6th value/ 2
Median = (6.5 + 7)/2 = 6.75
The IQR of the data is given as:
IQR = Q2 - Q1
IQR = (7.5 + 8)/ 2 - (5.5 + 6) / 2
IQR = 2
Hence, if a shoe size of 7 is added to the data the IQR remains the same 2. Option D is the correct answer.
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You are told that you will have to wait for 5 hours in a line with a group of other people. Determine whether:
1. You know the number of minutes you have to wait.
2. You know how many people have to wait.
For each statement, if you answer yes draw an input-output diagram and write a statement that describes the way one quantity depends on another.
If you answer no give an example of 2 outputs that are possible for the same input.
The number of hours you have to wait is 300 minutes.
What is the unit rate?
A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Given that,
You are told to you will have to wait 5 hours in a line with a group of other people.
Based on the above information, the calculation is as follows:
We know that
1 hour = 60 minutes
5*60
= 300 minutes
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What is factors of 37 ?
The factors of 37 are 1 and 37. This is because 1 is a factor of every number, and 37 is a prime number that is only divisible by 1 and itself.
The factors of 37 are the numbers that can be multiplied together to get 37 as a product. In other words, the factors of 37 are the divisors of 37 that divide it evenly without a remainder.
Therefore, 1 and 37 are the only numbers that can be multiplied together to get 37 as a product.
It is important to note that the factors of a number are always positive integers since negative numbers cannot be multiplied together to give a positive result.
Additionally, every number has at least two factors, 1 and itself, and some numbers may have many more factors depending on their prime factorization.
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What is the conversion of 72cm to inches?
Answer:
28.346
Step-by-step explanation:
divide the length value by 2.54
how to solve an inequality
While solving an inequality, you can do the following: add the same amount to each side, deduct the same amount from each side, and multiply or divide each side by the same positive amount. When each side is multiplied or divided by a negative number, the inequality sign must be flipped.
Inequalities may be solved in the same way as any other mathematical problem, but they require some extra steps to guarantee you get the correct solution.
Identify the terms in the inequality first. After that, simplify the equation such that it just has one variable.
Then, attempt to isolate the variable in the equation. To do this, carry out any necessary procedures on both sides of the equation to cancel out the terms that are unrelated to the equation.
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Find the magnitude of ax , the acceleration of the car after the brakes are applied. Express your answer in terms of some or all of the variables d , treact , and v0
The magnitude of the car's acceleration after the brakes are applied is:
a = 2 × (d - vo × treact) / treact^2
Initially, the car is traveling at a constant velocity of magnitude vo, so its acceleration is zero. When the driver notices the garbage can, the car has a distance d from the can.
After the driver applies the brakes, the car slows down at a constant rate until it comes to a stop just before the garbage can. Let a be the magnitude of the car's acceleration during this period.
The distance traveled by the car during this time can be expressed as the sum of two distances: the distance traveled while decelerating from vo to zero velocity, and the distance traveled while the car is at rest.
The distance traveled while decelerating can be calculated using the equation:
d = (vo × treact) + (1/2 × a × treact^2)
The distance traveled while the car is at rest is zero, since the car is not moving.
Setting d equal to the initial distance between the car and the garbage can (d = d), and solving for a, we get:
a = 2 × (d - vo × treact) / treact^2
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The given question is incomplete, the complete question is:
A car is traveling at a constant velocity of magnitude vo when the driver notices a garbage can on the road in front of him. At that moment, the distance between the garbage can and the front of the car is d. A time treact after noticing the garbage can, the driver applies the brakes and slows down at a constant rate before coming to a halt just before the garbage can. What is the magnitude of the car's acceleration after the brakes are applied?
What is 7.1093 round to the nearest hundredth?
The number round to the nearest hundredth according to the rules is 7.11.
The steps to round the digits to nearest hundredth are as follows -
Step 1 - Firstly read the number and analyse the number at the position hundredth. We see that 0 is present at the hundredth position.
Step 2 - Now check the number on the right hand side of the number. We see that it is 9.
Step 3 - If the number is greater than 5, then add one to the prior digit (the one at hundredth position).
Step 4 - Write the final number using above points. The number will be 7.11. The number 3 will be dropped as we are directed to shorten the number.
The rounded number is 7.11.
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Given f(2) = 12, which of the following could be an equation of the function?
A.
f(x) = 8x – 2
B.
f(x) = 4x + 4
C.
f(x) = 6x – 4
D.
f(x) = –4x – 4
We can use the given value of f(2) = 12 to determine the correct equation for the function.
A. f(x) = 8x - 2
If we plug in x = 2, we get f(2) = 8(2) - 2 = 14, which does not match the given value of 12.
B. f(x) = 4x + 4
If we plug in x = 2, we get f(2) = 4(2) + 4 = 12, which matches the given value of 12.
C. f(x) = 6x - 4
If we plug in x = 2, we get f(2) = 6(2) - 4 = 8, which does not match the given value of 12.
D. f(x) = -4x - 4
If we plug in x = 2, we get f(2) = -4(2) - 4 = -12, which does not match the given value of 12.
Therefore, the correct equation for the function could be f(x) = 4x + 4, or choice B.
what is the FOIL method and how does it connect with polynomials?
Answer:
The FOIL method is a technique used to multiply two binomials. The word "FOIL" is an acronym that stands for "First, Outer, Inner, Last." I will dive in it briefly for u!
Step-by-step explanation:
To use the FOIL method, you multiply the first term of the first binomial with the first term of the second binomial. Then, you multiply the outer terms (first term of the first binomial and the second term of the second binomial), followed by the inner terms (second term of the first binomial and the first term of the second binomial), and finally the last terms (second term of both binomials). You then combine the like terms to simplify the result.
The FOIL method is especially useful when multiplying polynomials, which are expressions with one or more terms involving variables with various powers. For example, to multiply the binomials (x + 3) and (x - 2), you would use the FOIL method as follows:
First: x × x = x²
Outer: x × (-2) = -2x
Inner: 3 × x = 3x
Last: 3 × (-2) = -6
Combine the like terms: x² - 2x + 3x - 6 = x² + x - 6
Thus, the product of (x + 3) and (x - 2) is x² + x - 6.
Answer:
The FOIL method is a mnemonic device used to multiply two binomials. It stands for "First, Outer, Inner, Last" and it is a step-by-step process that helps to remember the order of operations for multiplying binomials. When multiplying two binomials, the FOIL method involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms, and then adding the resulting terms together to simplify the expression.
The FOIL method is used in polynomial algebra because it is an efficient way to multiply two polynomials of degree one, also known as binomials. When multiplying two binomials, we can use the FOIL method to distribute each term in the first binomial to each term in the second binomial, resulting in a new polynomial expression. This method allows us to simplify polynomial expressions and solve equations by factoring, which is a crucial skill in algebra and calculus.
In summary, the FOIL method is a mnemonic device used to multiply two binomials by remembering the order of operations for each term. This method is commonly used in polynomial algebra because it is an efficient way to simplify polynomial expressions and solve equations by factoring.
what will happend to the curve, When two variables move in oppositeA) downward sloping, and we say the variables are negatively relatedB) upward sloping, and we say the variables are positively related..
A negative relationship exists when two connected variables move in opposite directions. As a result, Option A is right which has a downward slope and variables that are negatively correlated.
An inverse correlation, sometimes referred to as negative correlation, is a relationship between two variables in which, when one variable's value is high, the other variable's value is likely low.
For instance, with the variables A and B, when A is high, B is low, and when A is low, B is high. In statistical nomenclature, an inverse correlation is frequently expressed by the correlation coefficient "r," which has a value between -1 and 0, with r = -1 signifying complete inverse correlation.
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5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14
The algebraic expression of the statement is 5 + 3y ≤ z + 14
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14
When represented as expression, we have
5 + 3y is less than or equal to z + 14
As an inequality, we have
5 + 3y ≤ z + 14
hence, the expresion si 5 + 3y ≤ z + 14
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Brody and his children went into a movie theater and he bought $44.50 worth of
drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He bought a
total of 12 drinks and pretzels altogether. Determine the number of drinks and the
number of pretzels that Brody bought.
Answer:
10 pretzels and 2 drinks
Step-by-step explanation:
2 drinks are 12
10 pretzels are 32.50
Answer:
2 drinks, 10 pretzels
Step-by-step explanation:
d = # of drinks
p = # of pretzels
1) d + p = 12
2) $6d + $3.25p = $44.50
solve equation 1 for d: d = 12 - p substitute this into equation 2 and solve for p
6(12 - p) + 3.25p = 44.50
72 - 6p + 3.25p = 44.50
-2.75p = 44.50 - 72
-2.75p = -27.50
p = -27.50/-2.75 = 10 plug this into equation 1 and solve for d
d = 12 - 10 = 2
double check the answers: 6(2) + 3.25(10) = 44.50 correct!
16. To the nearest hundredth of a mile per hour, a luge rider's top speed was 81.73
mph. What are some possible speeds to the thousandth of a mile per hour?
Some possible speeds to the thousandth of a mile per hour are 81.729 mph, 81.730 mph, 81.731 mph
How to find possible speeds to the thousandth of a mile per hourTo find some possible speeds to the thousandth of a mile per hour, we can look at the two nearest thousandths above and below the given speed of 81.73 mph.
The nearest thousandth below 81.73 is 81.729, and the nearest thousandth above is 81.731. Therefore, some possible speeds to the thousandth of a mile per hour are:
81.729 mph
81.730 mph
81.731 mph
All these speeds are all within 0.001 mph of the given speed of 81.73 mph.
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Here is another picture of two squares and a circle. Use the picture to explain why the area of this circle is more than 18 square units and less than 36 square units.
The area of the circle is more than 18 square units of the smaller square inside it and less than 36 square units of the bigger square which the circle is enclosed in. The circumference of the circle is question 2 is equal to 47 to the nearest whole number.
What is the circumference of a circleThe circumference of a circle is the distance around its edge or perimeter. It can be calculated using the formula:
Circumference = 2 x π x radius
where π (pi) is a mathematical constant approximately equal to 3.14.
Alternatively, the formula can be expressed using the diameter of the circle, which is the distance across the circle passing through its center:
Circumference = π x diameter
The second question have its diameter as 15cm hence its circumference is evaluated as:
Circumference = 3.14 × 15cm
Circumference = 47.1cm.
The first question have the area of the bigger square equal to 36 square units and that of the smaller square equal to 18 square units, since the smaller square is enclosed by the circle and the circle is enclosed by the bigger square, then the area of the circle is more than 18 square units and less than 36 square units.
In conclusion, the area of the circle is more than 18 square units and less than 36 square units for the first question. And the circumference of the circle for the second question is equal to 47 to the nearest whole number.
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What is one solution to the trigonometric equation sinx − cos^2 x - 1 = 0 in the interval [0, 2π]?
The solution to the trigonometric equation given in the task content is; π / 2.
What is a solution to the given trigonometric equation?Given; sin x − cos² x - 1 = 0 in the interval [0, 2π].
Recall; cos² x = 1 - sin² x
Therefore; sin x − 1 + sin² x - 1 = 0
sin² x + sin x - 2 = 0
Let, y = sin x;
y² + y - 2 = 0
y = -2 or y = 1
Therefore, the valid value of y is; y = 1.
Therefore; 1 = sin x
x = sin-¹ (1)
x = 90° = π/2.
Consequently, the one solution which represents the solution as required is; π / 2.
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Question
HELP NEEDED FAST!!
Write the equation of the line in slope-intercept form that passes through the coordinates (6, -5) and (8, -6).
Responses
y−6=−12(x+5)
y minus 6 is equal to negative 1 half times open paren x plus 5 close paren
y=−12x−2
y is equal to negative 1 half x minus 2
y=12x−8
y is equal to 1 half x minus 8
y=−12x+8
An equation of the line in slope-intercept form that passes through the coordinates (6, -5) and (8, -6) is: B. y = -1/2(x) - 2; y is equal to negative 1 half x minus 2
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (6, -5), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-5) = (-6 - (-5))/(8 - 6)(x - 6)
y + 5 = (-6 + 5)/(8 - 6)(x - 6)
y + 5 = -1/2(x - 6)
y = -1/2(x) + 3 - 5
y = -1/2(x) - 2
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what is grain to gram ?
Although both grains and grams are weight-measuring units, they are not interchangeable.
The weight of gunshots, arrows, and gunpowder is often measured in the United States using a unit of mass called a grain. A grain weighs around 0.06479891 grams.
In contrast, a gram is a mass unit in the International System of Units (SI) that is often employed in scientific and practical contexts. There are 15.4323584 grains in one gram.
You may multiply the total number of grains by 0.06479891 to convert grains to grams. If you have 500 grains, for instance, you would convert them to grams as follows: 500 grains x 0.06479891 grams per grain = 32.399455 grams.
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Which function is not graphed correctly? Help needed ASAP!!
Answer:
Step-by-step explanation:
A is not graphed correctly. The graph is turned upside down from what it should be.
How to calculate corporate governance
Answer:
Focus on strategic measures.
Develop performance measurement skills.
Get board and CEO buy-in.
Track progress over time.
Measure often.
Step-by-step explanation:
The Tabletop Games club, a student-led campus group, hosted a virtual concert last week to raise awareness about their club and bring community members together. They sold full-price tickets for$7. 00, tickets for senior citizens were $5. 25and student tickets cost $5. 50. After the concert, they counted up the totals. There were a total of 215 tickets sold, and ticket sales brought in $1,214. 0. It was noted that there were 3 times as many senior citizen tickets sold as there were full-price tickets. Write and solve a linear system to determine how many of each type of ticket were sold. There were _____full-price tickets. There were ____senior citizen tickets. There were ____student tickets
There were 42 full-price tickets sold, 126 senior citizen tickets sold, and 47 student tickets sold.
Let's define the variables:
Let's call the number of full-price tickets sold "f".
Let's call the number of senior citizen tickets sold "s".
Let's call the number of student tickets sold "t".
From the problem statement, we know:
The total number of tickets sold is 215: f + s + t = 215
The total revenue from ticket sales is $1,214.00: 7f + 5.25s + 5.50t = 1214
The number of senior citizen tickets sold is 3 times the number of full-price tickets sold: s = 3f
We can use the third equation to substitute "3f" for "s" in the first two equations, and simplify:
f + 3f + t = 215 -> 4f + t = 215
7f + 15.75f + 5.50t = 1214 -> 22.75f + 5.50t = 1214
Now we have two equations with two variables, which we can solve using any method of our choice. For simplicity, we will use the substitution method:
From the first equation, we can isolate "t":
t = 215 - 4f
We can substitute this expression for "t" in the second equation, and solve for "f":
22.75f + 5.50(215 - 4f) = 1214
22.75f + 1182.5 - 22f = 1214
0.75f = 31.5
f = 42
So, there were 42 full-price tickets sold. We can use the third equation to find the number of senior citizen tickets sold:
s = 3f = 3(42) = 126
Finally, we can use the first equation to find the number of student tickets sold:
f + s + t = 215 -> 42 + 126 + t = 215 -> t = 215 - 42 - 126 = 47
Therefore, there were 42 full-price tickets sold, 126 senior citizen tickets sold, and 47 student tickets sold.
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A marble has a radius of 9 cm. Find the volume of the marble.
We can calculate this using this equation:
[tex]V =\dfrac{4}{3}\pi r^3[/tex]
Solving the Question[tex]V =\dfrac{4}{3}\pi r^3[/tex]
We're given that the radius is 9 cm:
[tex]V =\dfrac{4}{3}\pi (9)^3\\\\V=3053.63[/tex]
AnswerV = 3053.63 cm³
You can compare two marginal distributions to see if the corresponding two variables are related.T or F
You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .
The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.
The given question is related to probability and statistics.
Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.
The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.
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If the length of an aqueduct is to be 3000 meters, what will be drop at the end destination if the slope is 0.5%?
The drop at the end destination of the aqueduct would be 15 meters.
To see why, we can use the formula:
drop = slope * length
where the slope is given as 0.5% (or 0.005 as a decimal) and the length is given as 3000 meters.
So,
drop = 0.005 * 3000 = 15
Therefore, the drop at the end destination of the aqueduct would be 15 meters.
The solution to the equation
log2x + log2(x – 6) = 4 is x =
still If we plug in x = -2 into the original equation.
What is the logarithm?A logarithm is a mathematical function that helps to determine how many times a particular number must be multiplied by itself to obtain a specific value. In other words, the logarithm of a number is the exponent to which another fixed value, called the base, must be raised to produce that number.
Given by the question.
Using logarithm rules, we can simplify the left-hand side of the equation:
log2x + log2(x – 6) = log2(x (x – 6))
So, the equation becomes:
log2(x (x – 6)) = 4
Using the description of logarithms, we can rewrite this as:
[tex]2^{4}[/tex] = x (x – 6)
Simplifying the left-hand side, we get:
16 = [tex]x^{2}[/tex] – 6x
Moving all the terms to one side, we get a quadratic equation:
[tex]x^{2}[/tex] – 6x – 16 = 0
We can break this using the quadratic formula:
x = [6 ± sqrt ([tex]6^{2}[/tex]+ 4(1)(16))] / 2
x = [6 ± sqrt (100)] / 2
x = [6 ± 10] / 2
x = 8 or x = -2
still, we need results are valid, because we cannot take the logarithm of a negative number or of zero.
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how to convert 0.06 as a fraction?
The value 0.06 as a fraction is 3/50 .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
0.06 *100/100 =3/50
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