By applying the exponential properties, it can be concluded that the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
Exponential is a repeated multiplication method with the same number, which is notated in the form aⁿ, where a is called the base and n is the exponent or power.
Some properties of exponent:
[tex]a^{x}[/tex] x [tex]a^{y}[/tex] = [tex]a^{x+y}[/tex]
[tex]a^{x}[/tex] : [tex]a^{y}[/tex] = [tex]a^{x-y}[/tex]
[tex](a^{x}) ^{y}[/tex] = [tex]a^{xy}[/tex]
[tex](\frac{a}{b} )^{x}[/tex] = [tex]\frac{a^{x} }{b^{x} }[/tex]
a⁰ = 1
a⁻ˣ = 1 / aˣ
In mathematics, a radical is described as [tex]\sqrt[n]{x}[/tex], where n is a positive integer ≥ 1 and x is a real number. Then n is called the index of the radical, x is the radicand, and the symbol √ is the radical.
The radical can be written as a rational exponent as follows:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex] or [tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
From the problem, we can denote the expression as follows:
square root of x = √x
the fourth root of x = ⁴√x
The product of the two expressions will be:
(√x) x (⁴√x) = [tex]x^{\frac{1}{2}}[/tex] x [tex]x^{\frac{1}{4} }[/tex]
= [tex]x^{\frac{3}{4} }[/tex]
Thus the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for 5 hours is 0.2 or 20%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
A table is given where the first column represents the number of hours a student studied Math and the second column represents the number of students.
The sum of the second column is 35 so it is the total number of students
And only 7 of them studied mathematics for 5 hours.
Therefore, The probability that a student studied for 5 hours is,
= 7/35
= 0.2 or 20%.
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you drop a rock into a deep well. you can't see the rock's impact at the bottom, but you hear it after 6 seconds. the depth of the well is 285.9 feet. ignore air resistance. the time that passes after you drop the rock has two components: the time it takes the rock to reach the bottom of the well, and the time that it takes the sound of the impact to travel back to you. assume the speed of sound is 1100 feet per second. note: after seconds the rock has reached a depth of feet where
There is a distance of 656.088 feet to the bottom of the well.
What is Speed?
Speed is the ratio between the distance an object travels and the time it takes to cover that distance.
Since speed just has magnitude and no direction, it is a scalar quantity.
Because the amount of time that passes after you drop the rock is made up of both the amount of time it takes for it to fall to the bottom of the hole and the amount of time it takes for the sound of the impact to reach you,
Let t be the moment when a rock was attained at depth d, which is the well's bottom.
And this is the moment when you hear the sound of impact.
t + t' = 7 seconds
⇒ t' = 7 - t
Speed = Distance / Time
1100 feet per second = d / t'
d = 1100 t
Also d = 16t²
1100 t' = 16t²
1100 (7 - t) = 16t²
7700 - 1100t = 16t²
16t² + 1100t - 7700 = 0
4t² + 275t - 1925 = 0
This is a quadratic equation.
Discriminant = √(b² - 4ac) = √[275² - (4 × 4 × -1925)] = 326.228
t = (-275 ± 326.228) / (2 × 4)
t = 6.404 or t = -75.15
t = -75.15 is not possible because it is negative and t + t' = 7 seconds.
So t = 6.404 seconds
t' = 7 - 6.404 = 0.596 seconds
d = 16 × (6.404)² = 656.088 feet
Hence the distance from the well to the bottom is 656.088 feet.
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the charge of sphere 2 is twice that of sphere 1. which vector below shows the force of 2 on 1 if the distance
The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$[/tex] because the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm.
Step 1: Calculate the charge of sphere 2. Since it is twice that of sphere 1, the charge of sphere 2 is 2 x the charge of sphere 1.
Step 2: Calculate the distance between the two spheres. This is given as 5 cm.
Step 3: Calculate the force. The force is equal to the product of the charges of the two spheres divided by the square of the distance between them.
Step 4: Construct the vector. The vector representing the force of sphere 2 on sphere 1 is[tex]$\frac{2}{5} \vec{i}$.[/tex]
The vector representing the force of sphere 2 on sphere 1 is [tex]$\frac{2}{5} \vec{i}$[/tex], as the charge of sphere 2 is twice that of sphere 1 and they are separated by a distance of 5 cm. This is calculated by multiplying the charges of the two spheres and dividing by the square of the distance between them.
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Two distinguishable fair dice are rolled: Define the following events: (sum of the numbers rolled is divisible by 4] (sum of the numbers rolled is less than 4} (a) What is the total number of possible outcomes in this experiment? (b) List the outcomes in A (c) List the outcomes in B (d) Find the probability P(A) (e) Find the probability P(B) (f) Find the probability P(AU B) (g) Find the probability P(AnB) (h) Are events A and B independent?
Event A is the event that the sum of the numbers rolled on the two dice is divisible by 4. Event B is the event that the sum of the numbers rolled on the two dice is less than 4.
(a) The total number of possible outcomes in this experiment is 36 (6 possible outcomes for each die).
(b) Outcomes in A are (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), and (12, 6).
(c) Outcomes in B are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), and (2, 6).
(d) P(A) is 5/36. (e) P(B) is 6/36. (f) P(A U B) is 11/36. (g) P(A n B) is 0 (there are no outcomes that belong to both A and B). (h) Events A and B are not independent because P(A U B) does not equal P(A) + P(B).
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A farmer has enough food to feed 20 animals in his cattle for 6 days. How long
would the food last if there were 10 more animals in his cattle?
Answer:
Food supply would only last 4 days
Step-by-step explanation:
(20 cattle)(6 days) = 120 cattle·days (this is the current feed supply on hand)
20 cattle + 10 = 30 cattle total
(120 cattle·days) / (30 cattle) = 4 days
THAT IS NEXT IN PATTERN 3,5,12,55,648
Note that the next number in the progression or sequence or pattern is 35,585.
What is progression?Note that a number pattern is a series of numbers that adheres to a set of criteria. The rule might be mathematical, such as adding a constant value to each item in the series, or it can be based on some other logical relationship.
The next term in the sequence or pattern is derived as follows:
3x5 -3 = 12
5x12 -5 = 55
12x55 -12 = 648
55x648 -12 = 35,585
Therefore, it is correct to state that 35,585 is the next term in the sequence
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In a certain year, a movie and its sequel grossed a combined total of $1518 million. If the sequel grossed $116 million more than the movie, then how much did each movie gross?
The movie gross is $701
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total amount earned from the movie and the sequel = $1518
Amount earned from the movie = x
Amount earned from the sequel = x + $116
Now,
x + (x + 116) = 1518
2x + 116 = 1518
2x = 1518 - 116
2x = 1402
x = 1402/2
x = 701
Now,
x = $701
x + 116 = 701 + 116 = $817
Thus,
The movie gross is $701
The sequel gross is $817
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Find all the complex roots. Leave your answer in polar form with the argument in degrees. The complex fifth roots of 3. Zo= ___ (cos ___º + i sin ___º)z₁=___(cos___º + i sin ___º)z2=___(cos___º + i sin___º) z3=___ (cos___º + i sin___º) z4=___(cos___º + i sin___º)
The complex fifth roots of 3 are Z₀ = ∛3 (cos 0° + i sin 0°), Z₁ = ∛3 (cos 72° + i sin 72°), Z₂ = ∛3 (cos 144° + i sin 144°), Z₃ = ∛3 (cos 216° + i sin 216°) and Z₄ = ∛3 (cos 288° + i sin 288°)
The complex fifth roots of 3 can be found by finding the roots of the equation z^5 = 3. To find the roots in polar form, we first convert 3 to polar form:
3 = |3| (cos 0 + i sin 0) = 3 (cos 0 + i sin 0)
Next, we find the argument of the fifth roots, which is equal to 360°/5 = 72°. The polar form of the first root is then:
z₁ = ∛3 (cos 0° + i sin 0°) = ∛3 (cos 0° + i sin 0°)
The polar form of the other roots can be found by rotating the argument by 72°, 144°, 216°, and 288° respectively. The result is:
z₂ = ∛3 (cos 72° + i sin 72°)
z₃ = ∛3 (cos 144° + i sin 144°)
z₄ = ∛3 (cos 216° + i sin 216°)
z₅ = ∛3 (cos 288° + i sin 288°)
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Aaliyah and Yohance are having a competition to see who can read
more pages over the coming weekend. Aaliyah has bet Ms. Solomon that
she'll read 50 more pages than Yohance. Both scholars read at an
average rate of 40 pages per hour. Yohance says that he's going to read
for 7.5 hours this weekend. How many hours will Aaliyah need to read in
order to fulfill her promise of reading 50 more pages than Yohance?
According to the information, Aaliyah is going to need 8.75 hours to read 50 more pages than Yohance.
How to calculate how many hour will Aaliyah need to read?To calculate how many hours Aaliyah will beed to read, we have to perform the following mathematical procedure
First, we have to calculate how many pages Yohance is going to read this week, so if she is going to read during 7.5 hours we have to multiply the number of pages she read per hour by time (7.5 hours).
40 * 7.5 = 300So, Yohance is going to read 300 pages. Now if we want to know how many hours needs Aaliyah to read 50 more pages we have to perform the following operation:
300 + 50 = 350350 / 40 = 8.75According to the above, Aaliyah needs to read for 8.75 hours to complete 50 more pages than Yohance.
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In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded. A regression line was generated and shown to be an appropriate description of the relationship. The results of the regression analysis are below. Depend Variable: Top Speed Variable Constant Weight Coefficient 107.58 0.8710 s.e. of Coeff 11.12 0.4146 t-ratio 9.67 2.10 prob 0.000 0.062 R squared = 30.6% R squared (adjusted) = 23.7% s = 10.42 with 12 - 2 = 10 degrees of freedom Part A: What is the LSRL based on the analysis provided? Make sure to identify what the variables represent in the context of the problem. (4 points) Part B: What is the predicted value for the top speed of a boat if its weight is 4 tons? Show your work.
Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.
What do you mean by linear regression?Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.
Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.
Solution(a)
Given in the question
Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)
from the coefficient table of Enova summary we can write least square regression line as follows
Top speed = 107.58 +0.8710* Weight of boat
Here intercept of regression line = 107.58
Slope of regression line = 0.8710
Solution(b)
if X = 4 tons
than predictive value of the top speed of a boat can be calculated as
Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.
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Complete question:
Solution set
2x + 4 / 2 - 3x / x - 2 = X
On solving the given equation, the value of x = -4.
Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function.
Simply swap out all instances of x with the value of x to do this. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
Given,
[tex]\frac{2x + 4}{2} - \frac{3x}{x-2} = x\\ \\[/tex]
Taking LHS
⇒ [tex]\frac{2x^2 - 4x + 4x - 8 - 6x}{2(x-2)} \\[/tex]
⇒ [tex]\frac{x^2-4-3x}{(x-2)}[/tex]
Equating both sides,
⇒ [tex]\frac{x^2-4-3x}{(x-2)} = x\\x^2-4-3x = x^2 - 2x\\x = -4[/tex]
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lan collects stamps. He put 34% of his stamp collection in an album. If there are
204 stamps in the album, how many stamps does he have in his collection?
well, there are a total of "x" stamps in his collection, which oddly enough is 100%.
now, we know that 34% of "x" is 204, what the heck is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 204& 34 \end{array} \implies \cfrac{x}{204}~~=~~\cfrac{100}{34} \\\\\\ \cfrac{ x }{ 204 } ~~=~~ \cfrac{ 50 }{ 17 }\implies 17x=10200\implies x=\cfrac{10200}{17}\implies x=600[/tex]
What is the perimeter of a rectengular park that measure 20 1/4 yards by 32 5/8
The perimeter of the rectangular park is 423/4 units.
What precisely is a perimeter?The lengths of a shape's edges and sides are added to find its perimeter.
The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. That shape's perimeter is equal to the side lengths added together algebraically.
The perimeter of a shape is equal to the length of its boundary or whole circumference. The perimeter of a closed 2D form is the product of its sides.
Given : Length = 20 1/4
= 81/4
Width = 32 5/8
= 261/8
So, Perimeter = 2 ( L + B)
= 2 ( 81/4 + 261/8)
= 2 ( 423/8)
= 423/4 units.
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consider the expresson 1/2x to the second power +x+7. complete 2 descriptions of the part of the expression
The entire expression is a sum with 0 factors
The coefficients are 1/2, 1 and 7
How to describe the expressionFrom the question, we have the following parameters that can be used in our computation:
1/2x² + x + 7
The above expression is a quadratic expression and it has three terms
Quadratic expressions with real roots have 2 factors, otherwise it would have 0 factor
The expression 1/2x² + x + 7 does not have a real root because
b² < 2ac
Also in the expression, the coefficients are 1/2, 1 and 7
i.e. a = 1/2, b = 1 and c = 7
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Complete question
consider the expresson 1/2x² + x + 7.
complete 2 descriptions of the part of the expression
The entire expression is a sum with __ factors
The coefficients are _
A rectangle has length x and width y. Select all the statements that must be true.
The area of a rectangle with length x and width y is xy unit square.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Area is the amount of space occupied by a figure. Area is usually calculated for a two dimensional shape while volume is calculated for a three dimensional shape.
A rectangle have equal opposite sides which are parallel to each other and all angles are at 90 degrees.
Area of rectangle = length * width
Area = x * y = xy
The area is xy unit square.
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I need the answers for this whole side work must be shown or you get reported please don’t make me waste my points
a. The percentage of the original price that the consumers are going to pay will be 8.57%.
b. The markup percentage of the gallons will be
c. The percentage that decided not to sell the juice is 41.7%.
d. The price of each bottle will be:
How to calculate the percentage?a. The percentage of the original price that the consumers are going to pay will be:
= (3.50 - 3.20) / 3.50 × 100
= 0.30 / 3.50 × 100
= 8.57%
b. The markup percentage of the gallons will be:
= (3.20 - 2.70) / 2.70 × 100
= 0.50 / 2.70 × 100
= 18.5%
c. The percentage that decided not to sell the juice is:
= 125 / 300 × 100
= 41.7%
d. The price of each bottle will be:
= (1 - 15%) × $2.25
= $1.91
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a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections.
The type of sampling design is used: simple random sample
The correct answer is an option (a)
We know that in data analysis, the sampling is nothing but the selecting the group or subset of the population to make statistical inferences.
The types of probability sampling are:
Simple random sampling, Systematic sampling, Stratified sampling and Cluster sampling.
In simple random sampling, the researcher randomly selects a subset of data from the population.
In Stratified random sampling, the population is divided into smaller subgroups called as strata.
In case of clustered random sampling, the population is divided into clusters, and then we randomly select some of these clusters as sample.
As we know multistage sampling is a type of cluster sampling.
Here, it has been decided to randomly select 4 of the 10 lab sections.
This means, simple random sampling design is used in given scenario.
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The complete question is:
a. suppose there are 10 lab sections of a statistics class that each have the same number of students enrolled. a class evaluation is about to be administered to some of the students. it has been decided to randomly select 4 of the 10 lab sections and give the evaluation to all the students in those sections. What type of sampleing design is used?
a) Simple random sample
b) Stratified random sample
c) Clustered random sample
d) Multistage sample
Zach had been walking for
distance.
when both boys had walked exactly the same
Place the correct value to complete the sentence.
Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier
than Carlos
Two boys, Zach and Carlos, go for a walk. Zach begins walking 20 seconds earlier than Carlos and they both walked the same distance.
How to calculate the distance?
To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.
Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.
The sentence is describing a scenario in which two boys, Zach and Carlos, go for a walk. It is stated that Zach begins walking 20 seconds earlier than Carlos. This means that Zach starts his walk 20 seconds before Carlos does. It is also stated that both boys had walked exactly the same distance. This means that despite Zach starting his walk 20 seconds earlier than Carlos, they both covered the same distance during their walk.
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please help me i’ll give you brainlist!
X intercept: 10/5
Y intercept: 0
How to find intercept of a linear equation?To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.
For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.
X Intercept:
To find the X intercept, set Y equal to 0 and solve for X.
5x - 2(0) = 10
5x = 10
x = 10/5
X intercept = 10/5
Y Intercept:
To find the Y intercept, set X equal to 0 and solve for Y.
5(0) - 2y = 10
-2y = 10
y = -10/2
Y intercept = 0
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You deposit $120 in an investment account that earns 6.4% annual interest compounded quarterly write a function that represents the balance y (in dollars) of the investment account after t years
Answer:
$ balance = 120*(1+6.4%/4) ^4t
Step-by-step explanation:
principal =120
r =6.4% annual = 1.6% per quarter compounding every quarter
so 4 times a year, for t years
$ balance = 120*(1+6.4%/4) ^4t
The function that represents the balance of the investment account after t years is [tex]y = 120 (1.016)^{4t[/tex].
How to calculate the compound interest?The formula for calculating the balance of an investment account that earns compound interest is:
[tex]A = P (1 + \dfrac{r}{n})^{nt}[/tex]
where:
A = the balance after t years
P = the principal (initial amount deposited)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, we have:
P = $120
r = 6.4% = 0.064 (as a decimal)
n = 4 (compounded quarterly)
Therefore, the function that represents the balance y (in dollars) of the investment account after t years is:
[tex]y = 120 *(1 + \dfrac{0.064}{4})^{4t}[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]y = 120 (1.016)^{4t[/tex]
This is the function that represents the balance of the investment account after t years.
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Which of the following are not linear equations in one variable?
A.x²-5x+6=0
B. x³ = x
C. 3x-4=0
D. 7x-6x = 3 + 9x
The linear equations which are not in one variable are x²-5x+6=0 and x³ = x
What is linear equation ?
Linear equation can be defined as the equation in which highest degree is one.
Given Equations are
x^2 - 5x + 6 = 0
Here the highest degree is greater than one so it is not a linear equation
And x
x^3 = x
x^3 - x = 0
Here also the highest degree is greater than one so it is not a linear equation
3x-4=0
Here the highest degree is equals to one so it is a linear equation
7x-6x = 3 + 9x
x = 3+9x
8x+3 = 0
Here the highest degree is equals to one so it is a linear equation
Therefore , The linear equations which are not in one variable are x²-5x+6=0 and x³ = x
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Find a number that
has exactly 7 different prime factors.
Explain how you found it.
Answer:
957,697,598
Step-by-step explanation:
You want a number that has 7 different prime factors.
PrimesIf we choose 7 primes at random from the first 20, we might have the list ...
{2, 11, 13, 23, 41, 53, 67}
The product of these primes will have 7 different prime factors.
2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598
The number 957,697,598 has exactly 7 different prime factors.
__
Additional comment
Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.
The second attachment shows the first 20 prime numbers.
Help please
Determine whether the statement is true or false. If the statement is false, make the necessary changes) to produce a true statement.
Image attached
The complex number statement (3+8i)/(2+8i)=3/2 is false. The correct complex number statement is (3+8i)/(2+8i) = (24i + 6)/(-64i² + 16).
What is a complex number?
Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and i is a imaginary number called a "iota."
The given complex number equation is (3+8i)/(2+8i)=3/2
Simplify both sides of the equation.
On the left side, there is -
= (3+8i)/(2+8i)
= (3+8i)/(2+8i) × (2-8i)/(2-8i)
= (6+24i-24i-64i²)/(2² + 2×8i-8i²)
= (-64i² + 24i + 6)/(-64i² + 16)
= (24i + 6)/(-64i² + 16)
On the right side, there is -
3/2 = 3/2
It can be seen that the simplified forms of both sides are not equal, so the original statement is false.
To make the statement true, change the right side of the equation to the left side simplified form.
(3+8i)/(2+8i) = (24i + 6)/(-64i² + 16)
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Which two of the following are not characteristics of surveys?
A. One or more treatment groups and a control group a
the study.
B. Two or more treatments are compared in the study.
C. The result of the study are analyzed statistically.
D. Data are gathering during the course of the study.
The following are not characteristics of surveys :
A. The study involves on or more treatment groups and a control group
B. The study compared two or more treatments
What is a surveyA survey is a research technique used to gather data from a predetermined sample of respondents in order to learn more and acquire insights into a range of interesting topics.
There are Characteristics of an Effective Survey :
measurable survey objectivessound research design.effective survey question designsound sampling strategy, when needed effective survey response strategy. meaningful data summary. effective data display and reporting.Learn more about survey at:https://brainly.com/question/27396612
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W तल दिइएका तथ्याङ्कको मध्यिका पत्ता लगाउनुहोस् । Find the median of the following data: 16, 15, 14, 18, 17, 20, 25 .00 16
Answer:
arrange in ascending order
14,15,16,17,18,20,25
there are odd number of terms so
median = (n+1/2) th observation
here n = 7 which is odd
therefore, 7+1/2 th observation
which is 4th observation
ans) 17
Given f(x)=9/5 x + 32, find the folwing.
The inverse of the function as it has been written is f(x) = (x - 32) 5/9.
What is the inverse of the function?We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.
Let y = f(x)
Hence;
y=9/5 x + 32
y - 32 + 5/9 = x
We would then have the inverse of the function as;
f(x) = (x - 32) 5/9
This is the procedure that would help us to obtain the inverse of the function that have been given here.
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Missing parts;
Given f(x)=9/5 x + 32, find the following;
Inverse of the function
Find the derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial. Write your answer as a summation with lower limit of summation equal to 0.
The derivative of the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].
From the given data,
The derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial is [tex]$y=\sum_{n=0}^{\infty} \frac{(-1)^n x^{2 n+1}}{3^{2 n} \cdot(n !)^2}$[/tex]
The process of finding the derivative is called differentiation. The inverse process is called anti-differentiation. Let’s find the derivative of a function y = f(x). It is the measure of the rate at which the value of y changes with respect to the change of the variable x. It is known as the derivative of the function “f”, with respect to the variable x.Derivatives can be classified into different types based on their order such as first and second order derivatives.
Derivative⇒ [tex]$y^{\prime}=\sum_{n=0}^{\infty} \frac{(-1)^n \cdot(2 n+1)(x)^{2 n}}{3^{2 n} \cdot(n !)^2}$[/tex]
⇒ [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex].
Therefore, the summation with lower limit that equal to 0 is [tex]$$y^{\prime}=\sum_{n=0}^{\infty}(-1)^n \cdot \frac{(2 n+1)}{(n !)^2} \cdot\left(\frac{x}{3}\right)^{2 n}$$[/tex]
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Find median for average life of a particular brand of a T.V sets from the following data
life in years : 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of sets : 2 16 26 39 43 21 8 4
The median for average life of a particular brand of a T.V sets from the following data is given as follows:
17.5.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The total number of observations in this problem is given as follows:
2 + 16 + 26 + 39 + 43 + 21 + 8 + 4 = 159.
This is an odd cardinality, hence the median is found in the class when the counter hits:
(159 + 1)/2 = 80.
Which is the class 15-20, as 2 + 16 + 26 < 80 and 2 + 16 + 26 + 39 > 80, and the median value is given as follows:
(15 + 20)/2 = 17.5.
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use left rectangles and delta (x) = 0.5 to approximate the area under f(x) = (2x)^2 +6 from x = 2 to x=4 . give one decimal place in your answer.
The estimated area under the curve is 112.
We can use the left rectangle method to approximate the area under the curve f(x) = (2x)^2 + 6 from x = 2 to x = 4.
First, we need to choose a value of Δx = 0.5, which will determine the width of the rectangles. Then, we can find the height of each rectangle by evaluating the function at the left endpoints of the intervals.
For x = 2, the height of the first rectangle is f(2) = (2 * 2)^2 + 6 = 20.
For x = 2.5, the height of the second rectangle is f(2.5) = (2 * 2.5)^2 + 6 = 28.25.
For x = 3, the height of the third rectangle is f(3) = (2 * 3)^2 + 6 = 42.
For x = 3.5, the height of the fourth rectangle is f(3.5) = (2 * 3.5)^2 + 6 = 57.75.
For x = 4, the height of the fifth rectangle is f(4) = (2 * 4)^2 + 6 = 76.
Finally, we can multiply the height of each rectangle by its width (0.5) to find the area of each rectangle:
Area of first rectangle = 20 * 0.5 = 10
Area of second rectangle = 28.25 * 0.5 = 14.125
Area of third rectangle = 42 * 0.5 = 21
Area of fourth rectangle = 57.75 * 0.5 = 28.875
Area of fifth rectangle = 76 * 0.5 = 38
The total area under the curve can be estimated by adding up the areas of the rectangles:
Estimated area = 10 + 14.125 + 21 + 28.875 + 38 = 112
So the estimated area under the curve using the left rectangle method and Δx = 0.5 is 112.
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Build it #1
Drag the points to create a graph that satisfies the following requirements:
A graph that satisfies the given requirements 1 ≤ x ≤ 3 and 2 ≤ y ≤ 7 is shown in the image attached below.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
For the domain of this graph, the x-value would be placed at point 1 and then dragged to point 3 on the x-coordinate. Similarly, the y-value for the range of this graph would be placed at point 2 and then dragged to point 7 on the y-coordinate as shown in the image attached below.
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