B and E are true.The regression output can be used to determine whether there is a relationship between Red Sox away games and daily revenue.
The output can also be used to calculate the average daily revenue for each scenario.
For the scenario where the Red Sox do not play away, the output will give the average daily revenue, which is $1,768.32. So, statement A is true.
For the scenario where the Red Sox play away, the output will give the average daily revenue, which is $2,264.57. So, statement B is true.
For the scenario where the Red Sox do not play away, the output will also give the average daily revenue, which is $1,272.07. So, statement D is false.
Finally, the output can be used to calculate the difference between the average daily revenue when the Red Sox play away and when they do not, which is $496.25. So, statement E is true.
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What amounts of 35% pure silver and 40% pure silver should be mixed to obtain 14 grams of 37% pure silver? (either give EXACT answers, which are fractions, or give 5 decimal places) number of grams of 35% silver is number of grams of 40% silver is
5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37% amount of pure silver.
Let x be the number of grams of 35% silver and y be the number of grams of 40% silver.
We know that the total amount of silver is 14 grams, which is the sum of x and y. Therefore,
x + y = 14
We also know that the total amount of pure silver is 37%, which is the sum of 35% pure silver and 40% pure silver. Therefore,
0.35x + 0.40y = 0.37(x+y)
Substituting the first equation in the second equation,
0.35x + 0.40y = 0.37(14)
Solving for x and y,
x = 5.12 and y = 8.88
5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37% pure silver.
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Part B Find the minimum initial height hmin at which the car can be released that still allows the car to stay in contact with the track at the top of the loop: Express your answer numerically; in meters_
The minimum equation initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.
hmin = 8.90 m
We can use the equation for centripetal force to solve for the minimum initial height hmin at which the car can be released and still stay in contact with the track at the top of the loop.
Fc = mv2/r
where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the loop.
We know that the mass of the car is 250 kg, the speed of the car is 14 m/s, and the radius of the loop is 20 m.
We can rearrange the equation to solve for hmin:
Fc * r = m * v2
hmin = (m * v2) / Fc
hmin = (250 kg * (14 m/s)2) / (25000 N)
hmin = 8.90 m
The minimum initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.
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Carmen bought a wrench for $7.19. The cashier gave Carmen $2.25 in change. How much money did Carmen give the cashier?
Answer:
9.44
Step-by-step explanation:
7.19+2.25 =9.44
711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
List all of the factors for each number 28
the factors for 28 are 1,2,4,7,14 and 28
How long will it take 5300 to become 7500 if it’s invested at 9% and us compounded quarterly?
It would take approx 4 years for 5300 to become 7500 if it’s invested at 9% and us compounded quarterly.
What is compound interest?The interest earned on a deposit is known as compound interest because it is computed using both the initial principal and the interest accrued over the course of previous periods. Compound interest is simply interest that is earned on interest, to put it another way. Interest can be compounded daily, monthly, or yearly, among other frequency schedules.
Compound interest increases with a higher number of compounding periods. A snowball-like image comes to mind. Your snowball will grow faster if you start saving early and contribute more money to it.
The compound interest formula is given by:
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here,
A = 7500
P = 5300
r = 9%
n = 4 (quarterly)
t = year to find
Putting the values in the formula
[tex]$7500 = 5300 (1 + \frac{0.09}{4})^{4t}[/tex]
t = 3.90
Thus, It would take approx 4 years for 5300 to become 7500 if it’s invested at 9% and us compounded quarterly.
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declare a 2-dimensional array, , of empty arrays. all arrays are zero indexed. declare an integer, , and initialize it to . there are types of queries, given as an array of strings for you to parse: query: 1 x y let . append the integer to . query: 2 x y let . assign the value to . store the new value of to an answers array.
A dynamic array is an array with a big improvement: automatic resizing.
How does dynamic array works?A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.Explanation :
Initial Values:
n = 2
arr[0] = [ ]
arr[1] = [ ]
Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5]
arr[1] = [ ]
Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]
arr[0] = [5]
arr[1] = [7 ]
Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5, 3]
arr[1] = [7 ]
Query 3: Assign the value at index 0 to arr [( 1 ⊕ 0 ) % 2 )] = arr[1] to
Last Answer, print Last Answer.
last answer = 7
arr[0] = [5, 3]
arr[1] = [7 ]
Query 4: Assign the value at index 1 to arr [( 1 ⊕ 7 ) % 2 )] = arr[0] to
Last Answer, print Last Answer.
last answer = 3
arr[0] = [5, 3]
arr[1] = [7 ]
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the following segmented bar chart shows the number of flights that were either on time or delayed at three different airports on one day.
The correct answer is C. Airport S has 100 on-time flights, and Airport T has 200 on-time flights. Since 100 is one-half of 200, Airport S has one-half the number of on-time flights that Airport T has.
Given that,
The number of flights that were either on time or delayed at three separate airports on a given day is depicted in the segmented bar chart below.
Which of the following statements is the bar chart evidence for?
The options are : In comparison to the other two airports, A Airport T has the highest proportion of on-time flights.
In comparison to the other two airports, B Airport R has the lowest percentage of on-time flights.
C The proportion of on-time flights at Airport S is less than half that at Airport T.
D The proportion of on-time flights at Airport R is lower than that at Airport S.
E There are exactly as many flights at Airport T as there are at Airports R and S put together.
As the number of flights that were either on time or delayed at three different airports on one day can be exactly represented by
The correct answer is less than half as many flights arrive on time at Airport S than at Airport T.
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The Complete Question is :
Which of the following statements is the bar chart evidence for the number of flights that were either on time or delayed at three different airports on one day.?
In your own words, describe how you can use col-lections of objects (such as toothpicks or Popsicle sticks) to show the values of some base-ten units. Discuss also how the values of adjacent places in base-ten representations of numbers are related
You can use collections of objects such as blocks to model a number. Each type of block can be used to show the value of each digit in the number
The values of adjacent places in base-ten representations of numbers are related as each place is always 10 times the value represented by the place to its imme- diate right
What are base 10?Unit blocks, rods, flats, and cubes are the names of base ten block types. The digit in the ones place is represented by the unit blocks. To demonstrate how many tens are in a number, rods are each worth one ten, i.e., ten rods equal one flat, which is worth one hundred each.
Students use base ten blocks, also referred to as multibase arithmetic blocks or Dienes blocks, as a type of math manipulative to learn the basics of addition, subtraction, number sense, place value, and counting.
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A farmer wishes to study the effect of three different fertilizers on crop yields. He takes a rectangular field and divides it into four plots of equal area. Then he randomly assigns the three different fertilizers to one of the four plots. One plot receives no fertilizer. The plots are harvested after a growing period and the yields are measured and compared. Which of the following statements best describes the design of the study?
I.This design has matched pairs.
II.This design has blocks.
III.This is a completely randomized design.
answer choices
I only
I and III only
I and II only
II only
III only
Option E is the correct option
In this experiment, a farmer completed 4 stages of therapy using the Randomized Design idea.
Complete randomization of the design
In terms of comfort and ease of data processing, a totally random design is essentially the simplest experimental design. Subjects are randomly assigned to treatments in this design.
In fact, randomization is what this fully randomized design depends on to account for the impacts of unimportant factors. In reality, the investigator anticipates that uncontrollable variables will generally impact treatment conditions in an equal manner, so any meaningful variations across conditions may be accurately assigned to the independent variable.
Design for double blinds:
In an experiment, the placebo effect will be diminished or abolished if participants in the control group are aware that they are getting a placebo, and the placebo will no longer function as a control.
Blinding fundamentally involves withholding information about whether or not a person is getting a placebo. Thus, the placebo effect is equally felt by participants in the control and treatment groups. It's common practice to hide the fact that certain groups get placebos from analysts who review the trial. Double blinding is the term for this procedure. It ensures that their appraisal is not affected by knowledge of real treatment circumstances and stops the analysts from "spilling the beans" to the participants through subtle indications.
Designing Matched Pairs .
A randomized block design is a specific example of the matched pairs design. It can be employed when there are essentially just two treatment conditions in an experiment, and participants can be paired off based on some sort of blocking variable. The individuals are then randomly randomized to various treatments within each pair.
Block design using randomization:
In a randomized block design, participants are really split up into smaller groups called blocks so that the variance within blocks is less than the variance between blocks. After that, patients within each block are allocated to treatment scenarios at random.
So, in this experiment, the farmer applied 4 doses of therapy.
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The sum of the ages of the mother and her daughter is 68 years. the mother is 22 years older than her daughter. how old is her mother
Answer:
her mother is 45 years old
Step-by-step explanation:
daughter = n
mother = n + 22
n + n + 22 = 68
2n = 46
x = 23
n + 22 = 23 + 22 = 45
Answer: mothers age = 45 years old
Step-by-step explanation:
mothers age = 22 + x
daughters age= x
create the equation:
22 + x + x = 68
2x = 68 - 22
2x = 46
x = 23 (daughters age)
in order to get the mother's age you should add 22 to daughter's age (23) as they say the mother is 22 years older than the daughter
therefore: 22 + 23 = 45 years old
A television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off. If he paid 8% sales tax on the sale price, how much did he pay in total?
$281.88 is the total amount sam paid for television.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off.
Let us find the 50% of 522
50/100×522
0.5×522
$261
8% sales tax on the sale price
8/100×261
0.08×261
$20.88
The total he paid is $261+$20.88 is $281.88.
Hence, $281.88 is the total amount sam paid for television.
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ohanna Lucy makes wooden boxes in which to ship motorcycles. Lucy and her three employees invest a total of 30
hours per day making the 200
boxes.
Part 2
a) Their productivity
boxes/hour. (Round your response to two decimal places.)
Part 3
Lucy and her employees have discussed redesigning the process to improve efficiency. Suppose they can increase the rate to 300
boxes per day.
b) Their new productivity equals
boxes/hour. (Round your response to two decimal places.)
Part 5
c) The unit increase in productivity is enter your response here
boxes/hour. (Round your response to two decimal places.)
Part 6
d) The percentage increase in productivity is enter your response here
%.
(Enter your response as a percentage rounded to two decimal places.)
Riverside Metal Works produces cast bronze valves on a 12
-person
assembly line. On a recent day, 200
valves were produced during
6
-hour
shift.
Part 2
a) Labour productivity
of the line
valves/labour hour. (Round your response to two decimal places.)
Part 3
b) The manager at Riverside changed the layout and was able to increase production
to 220
units per 6
-hour
shift. The new labour productivity equals
valves/labour hour. (Round your response to two decimal places.)
Part 4
c) The percentage of productivity increase equals
enter your response here%.
(Round your response to one decimal place.)
Answer: Question one:
a) 6.67 boxes/ hour
b) 10 boxes/ hour
c) 3.33 boxes/ hour
d) 49.93% increase
Step-by-step explanation:
Question two:
a) 33.33 valves/ hour
b) 36.67 valves/ hour
c) 10.02% increase
Please help me figure this out.
To make b the subject of the equation, we have: b = 2a + c
What is subject of formula?Subject of formula is the process expressing a required alphabet in the terms of others in a given expression. It involves the applications of arithmetic operations so as to arrive at the required answer.
Thus, rearranging the equation and make b the subject in the question, we have;
a = 1/2 (b - c)
a = (b - c)/ 2
multiply through by 2
2a = b - c
express b in terms of a and c to have;
b = 2a + c
Therefore, after rearranging the equation, b as a subject is:
b = 2a + c
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problem 10: the various lines represent paths taken by different people walking in a city. all blocks are square and 140 m on a side. randomized variables l
The lines represent different routes taken by people walking in a city, where each block is 140m by 140m in size. The routes are determined by randomized variables, such as starting point, destination, and available pathways.
For a route that is 140m by 140m:
1. Calculate the diagonal length of the route: √2 x 140 = 196.4 m
2. Calculate the perimeter of the route: 4 x 140 = 560 m
3. Calculate the area of the route: 140 x 140 = 19600 m2
When calculating a route that is 140m by 140m, the first step is to calculate the diagonal length of the route. This is done by using the Pythagorean Theorem, which is written as √2 x 140. The result of this calculation is 196.4m. The second step is to calculate the perimeter of the route. This is done by multiplying the length of each side of the route by 4, which gives a total of 560m. The final step is to calculate the area of the route. This is done by multiplying the length and width of the route (140m x 140m), which gives a total of 19600m2. By using these calculations, one can easily measure the length, width, and area of a route that is 140m by 140m.
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What is the scale factor?
The scale factor is ________ the original figure
The scale factor applied to the triangle is k = 1/2.
How to get the scale factor?When we have a length L and we apply to it a scale factor K, the new length will be:
L' = k*L
Then the scale factor is:
L'/L = k
And if a scale factor is applied to a polygon, like a triangle, all the sides get affected by the scale factor in the same way.
Then if the original length of the given side is:
L = 5ft
And the new length is:
L' = 2.5ft
The scale factor is:
k = 2.5ft/5ft = 1/2
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The length of a rectangle is represented by the expression 10.5g - 3.4k, and the width is represented by the expression
5.7k+2.4g.
Which expression represents the perimeter of the rectangle?
Remember, the perimeter of a rectangle is the sum of all four sides of the rectangle.
A. 16.2g + (-k)
B.12.9g + 2.3k
C.25.8g + 4.6k
D. 32.4g + (-2k)
The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L. The same wire can be reused to make a square, considering that all the sides are equal in length. Look at the image below showing the perimeter of a rectangular park.
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The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.The perimeter of a shape is defined as the total distance around the shape.
It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L. The same wire can be reused to make a square, considering that all the sides are equal in length. Look at the image below showing the perimeter of a rectangular park.
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It takes a hose 5 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 12 inches tall. How long will it take the same hose to fill an aquarium measuring 22 inches by 27 inches by 29 inches?
minutes
To find out how long it will take the hose to fill the larger aquarium, we need to compare the volume of water in each aquarium. The volume of the first aquarium is 8 x 9 x 12 = 864 cubic inches, and the volume of the second aquarium is 22 x 27 x 29 = 14,938 cubic inches. The second aquarium is 14,938 / 864 = 17.2 times larger than the first aquarium.
The time it takes to fill the first aquarium is 5 minutes, so it will take 5 x 17.2 = 86 minutes to fill the second aquarium with the same hose.
It will take 86 minutes to fill the second aquarium.
4.) A grade six class went on a field trip. of this group of pupils, only 98% or 49 joined the activity. what is the total techan triangle
The total number of candidates in the group will be 50.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the grade six class went on a field trip. of this group of pupils, only 98% or 49 joined the activity.
The total number will be calculated as,
Total number = [ 49 x 100 ] / 98
Total number = 50
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need help with my math I want to make sure is correct
The value of 3.8 in mixed number and improper fraction are 3 8 / 10 and 38 / 10.
How to convert decimals to fractions?Fractions are numbers that are written in 2 parts: a numerator and a denominator. The numerator is the top value while the denominator is the bottom value.
A mixed fraction is a combination of fractions and whole number.
Let's write the decimal 3.8 as a mixed fraction and improper fraction.
Hence, as a improper fraction,
3.8 = 38 / 10
In mixed fraction,
3.8 = 38 / 10 = 3 8 / 10
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What number when multipled by 1 1/4 has a product of 1?
Answer:
if we multiply 11/4 to 4/11 it gives product as 1
a scale drawing for a backyard is shown below. In the drawing, 4cm represents 5m. Assuming the patio is rectangular, find the area of the real patio.
:
The the area of the real patio is = 50 m²
How to find the area?Recall that area deals with the floor space occupied by the rectangular field
The area of the lawn is represented by
Area = L*W
2 cm for length = 5 m.
4 cm for width = 10 m.
Area = width • length. 10•5=50cm²
Having computed the area, we now conclude that the the area of the real patio 50cm²
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this question involves the implementation of the point class which is used to represetn a single (x, y0 point
The Python program above defines the class Cse20, which is used to generate a subject.
What is meant by python program?The class Cse20, which is used to generate a subject, is defined in the preceding Python program ( instance of the Cse20 object). The getter methods, such as get length, get title, and get length in days, return a topic's length, title, and length in days, respectively, but the __str__ and __add__ methods override the topic's string object and addition of length, respectively.
class Cse20_topic:
def __init__(self, title, length):
self.title = title
self.length = length
def get_length(self):
return self.length
def get_title(self):
return self.title
def get_length_in_days(self):
return self.length*7
def __str__(self):
return f'Title: {self.title}, length: {self.length}'
def __add__(self, other):
return self.length+other.length
The complete question is:
Write the implementation of a class Cse20 Topic that represents a topic in the cse20 class. The class should implement the init function, getters, and override the str and add functions.
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Ms. Morales bought the kiddie pool shown below for her children. A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
A) 5,832π in.^3
B) 6,561π in.^3
C) 7,776π in.^3
D) 8,748π in.3
The quantity of water that Ms. Morales put in the pool in terms of π would be = =6561π in³
What is the volume of the pool?The volume of the pool can be calculated by using the formula of the volume of a cylinder which is = πr²h
Where,
r = 54/2 = 27in
volume = π × 27²× 12
= π × 8748
= 8748π in³
Therefore the quantity of the pool that's as filled with water = 3/4 of 8748π
= 3× 8748/4
= 26244/4
=6561π in³
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During a quality control check, a factory found that 5% of the parts it produces are defective. The factory recently completed an order for 144,000 parts. Approximately how many of the parts from the order may be defective?
The approximate number of defective parts the factory produced is 7200.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, During a quality control check, a factory found that 5% of the parts it produces are defective.
Let, 'x' be the number of defective parts.
Therefore, 'x' is 5% of 144000 which can be numerically expressed as,
(5/100)×144000.
= 5×1440.
= 7200.
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if a cube from this box is chosen without looking, what is the probability it will be blue?
A) certain
B) impossible
C) possible
D) probability
Answer:
C) Possible.
Step-by-step explanation:
Hope it helps! =D
Verify that the following equation is an identity.
(5sinx+5cosx)^2=25sin2x+25
An identity is an equation that is always true for any value of the variable. To verify that an equation is an identity, we can substitute different values for the variable and see if the equation still holds true.
The given equation is (5sinx+5cosx)^2=25sin2x+25
We can start by expanding the left side of the equation:
(5sinx+5cosx)^2 = (5sinx)^2 + 2(5sinx)(5cosx) + (5cosx)^2
= 25sin^2x + 50sinxcosx + 25cos^2x
= 25(sin^2x + cos^2x) + 50sinxcosx
= 25 + 50sinxcosx
Now we can use the trigonometric identity sin^2x + cos^2x = 1 to simplify the equation further:
25 + 50sinxcosx = 25 + 50(sinxcosx) = 25 + 25sin2x
Now we can see that the left side of the original equation is equal to the right side of the equation, 25sin2x+25.
Therefore, the equation (5sinx+5cosx)^2 = 25sin2x+25 is an identity for all values of x.
The function f shown in the graph is an even
function. The graph has been hidden for x ≥ 0.
Complete the following sentences.
over the interval 0 < x < 2.
fis
DONE
f(2)=
DONE
fis
DONE
over the interval 2 < x < 5.
#
6
4
2
y
x
The given function f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
What is a function?
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
An example of a simple function is f(x) = x^2. In this function, the function f(x) takes the value of “x” and then squares it. For instance, if x = 3, then f(3) = 9. A few more examples of functions are: f(x) = sin x, f(x) = x^2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.
Now,
As the given function f is increasing till x<2 and increasing after x>2
Hence,
f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
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Prove that the union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other
The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other.
Let [tex]$V_1, V_2$[/tex] be two subspaces of V.
Suppose is a subspace of V.
Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and [tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]x_1+x_2 \in V_1 \cup V_2$.[/tex]
But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex].
Only the elements that are already present in the two subspaces are combined.
A subspace is formed by the union of two subspaces of a vector space, and each subspace contains the other.
Either way, by the existence of additive inverses and closure properties for subspaces we have:
[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]
Or
[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]
By associative/commutative properties we have:
[tex]x_2 \in V_1[/tex] or [tex]x_2 \in V_1[/tex]
Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex].
If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex].
If [tex]$x_2 \in V_1$[/tex] for all [tex]x_2 \in V_2[/tex] then [tex]$V_2 \subseteq V_1$[/tex].
In either case, we see one subspace is a subset of the other.
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find four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term g
Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are [tex]7 , -28 , 112,-448[/tex].
Geometric sequence is type of sequence in which ratio of two consecutive term is equal.
Let the geometric sequence be [tex]G_{1} , G_{2} , G_{3} , G_{4}[/tex] and common ratio be [tex]r[/tex]
According to the question,
[tex]G_{1} = G_{2} + 35[/tex] (eq 1)
⇒ [tex]G_{1} = rG_{1} +35[/tex] ∵ [tex]G_{2}= rG_{1}[/tex]
⇒ [tex]G_{1} (1-r) = 35[/tex]
⇒ [tex]1-r = \frac{35}{G_{1} }[/tex]
⇒ [tex]r = 1 -\frac{35}{G_{1} }[/tex] (eq 2)
Also according to the question,
[tex]G_{3} = G_{4} + 560[/tex]
⇒ [tex]G_{3} = rG_{3} + 560[/tex]
⇒ [tex]G_{3} (1-r) = 560[/tex]
⇒ [tex]r^{2} G_{1} (\frac{35}{G_{1} } ) = 560[/tex]
⇒ [tex]35r^{2} = 560[/tex]
⇒ [tex]r^{2} = 16[/tex]
⇒ [tex]r=[/tex] ±[tex]4[/tex]
∴ [tex]r = -4[/tex] as we can see that value is decreasing at even term and at even term the power of common ration is odd.
Now putting [tex]r= -4[/tex] in eq 2 we get :
[tex]G_{1} =7[/tex]
Hence , Geometric sequence will be [tex]7 , -28 , 112,-448[/tex].
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