From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
What is Descending order?
Descending order can be defined in such a way that the order is from largest to smallest.
Given numbers are ,
0.51 , 7.6 , 10^2 , 5.6 , 105 , 4.9 , 10^-3
10^2 = 10*10 = 100 .
so a^m = a multiplied by m times .
a^-m = 1/ a^m.
10^-3 = 1/1000 = 0.001
So,
We have to write from largest to smallest
we get,
105,100,7.6,5.6,4.9,0.51,0.001
Hence, From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
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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 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 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.
all of the following are precautions to prevent static electricity damage when replacing a control module except
To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.
Static electricity discharge can damage disc drives, media drives, electronic boards, and adapters. To avoid this harm, these gadgets are enclosed in antistatic bags. Take the following safety measures to guard against static electricity discharge harming this equipment.
To stop electrostatic discharge from harming your hardware, fasten a wrist strap to a painted metal surface.
Be sure to observe all electrical safety precautions while utilizing a wrist strap. For static control, a wrist strap is used. When you use or work on electrical equipment, your risk of getting shocked by electricity is not increased or decreased.
If you do not have a wrist strap, you must touch an unpainted metal surface of the system for at least 5 seconds before removing it from the ESD packing and installing or replacing components.
When you're ready to install the device in the system, take it out of the antistatic bag.
Touch the gadget to the system's metal frame while it is still in its antistatic bag.
Grasp the edges of the cards and boards. On the adaptor, stay away from the parts and gold connectors.
The complete question is :-
All of the following are precautions to prevent static electricity damage when replacing a control module EXCEPT:
Touch a known good ground before opening the package.
Wipe the terminals clean before installing the component.
Ground the package to a known good ground before opening.
See Electronic Service Precautions
Open the package only when ready to install the component.
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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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You use beads to make design. Of the beads, 1/3 are red and 1/6 are blue. The rest are white. What fraction of the beads are red red or blue?
Answer:
1/2
Step-by-step explanation:
First, let's find the GCF of 3 and 6. In this case, it's 6.
Then, lets convert every fraction so that the denominator is 6. 1/6 already has this property, so let's convert 1/3. And to do that, we multiply the fraction by 2/2.
[tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]
Finally, we add the fraction of beads that are red and blue together, then simplify.
[tex]\frac{2}{6} + \frac{1}{6}=\frac{3}{6} =\frac{1}{2}[/tex]
Therefore, the answer is 1/2.
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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what is the answer!??
Answer:
8.75 miles
Step-by-step explanation:
using the equation for the line of best fit
y = 0.8x + 0.75
substitute x = 10 into the equation
y = 0.8(10) + 0.75 = 8 + 0.75 = 8.75
the equation predicts she will run 8.75 miles in week 10
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 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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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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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 _
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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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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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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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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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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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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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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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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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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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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if a pizza feeds 3 kids, but you need to feed 6, what would the scale factor be for calculating how many pizzas you need?
Answer:
2
Step-by-step explanation:
If a pizza feeds 3 kids and you need to feed 6 kids, the scale factor for calculating how many pizzas you need would be 2.
A scale factor is used to determine the relationship between the size of an object and a similar or corresponding object. In this case, you have a pizza that can feed 3 kids and you need to feed 6 kids, so the relationship between the number of kids that can be fed by one pizza and the number of kids you need to feed is 6/3 = 2
So, you need to double the quantity of pizza to feed 6 kids, therefore the scale factor would be 2.
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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Can a slope have two negative signs
If the slope of the line has two negative signs, then it is positive.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the linear function.
If we have two points on the linear function, then the slope is obtained by the division of the change in the output by the change in the input.
If both changes are negative, then we are dividing two negative numbers, meaning that the slope is positive, as the quotient of two negative numbers is positive.
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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 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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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]
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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