While factoring the given equation, the mistake occurred in Step 1 (option d.)
Upon reviewing the steps, we can see that the student made a mistake in Step 1. The factorization of the polynomial should be (x + 5)(x + 9), not (x + 5)(x - 9).
The correct factorization should be:
[tex]x^2 + 14x + 45 = (x + 5)(x + 9)[/tex]
The mistake occurred when the student incorrectly wrote (x - 9) instead of (x + 9) as one of the factors.
As a result, the subsequent steps are also affected. In Step 2, the student incorrectly set x - 9 = 0 instead of x + 9 = 0. This leads to an incorrect value in Step 3, where the student states that x = 9 instead of the correct value x = -9.
Therefore, the student made a mistake in Step 1, which caused subsequent errors in Step 2 and Step 3. The correct answer is d. The mistake occurred in Step 1.
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According to a study done by Pierce students, the height for Hawaiian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Hawaiian adult male is randomly chosen. Let X = height of the individual. What is the proper expression for this distribution? X-C. O X-N(66, 2.5) O X-U(2.5, 66) O X-N(2.5, 66) OX-E(66, 2.5)
The proper expression for the distribution of the height of a randomly chosen Hawaiian adult male is X ~ N(66, 2.5). This means that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches.
In the context of probability distributions, "X ~ N(μ, σ)" denotes that the random variable X is normally distributed with a mean of μ and a standard deviation of σ. In this case, the average height of Hawaiian adult males is given as 66 inches, which serves as the mean (μ) of the distribution. The standard deviation (σ) is specified as 2.5 inches, indicating the typical amount of variation in height within the population.
By using the notation X ~ N(66, 2.5), we explicitly state that X follows a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches, as determined by the study conducted by Pierce students. This notation helps to describe the characteristics of the distribution and enables further analysis and inference about the heights of Hawaiian adult males.
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Mean Median Minimum Maximum 75th percentile 25th percentile Interquartile Range Variance Standard Deviation 1 Convert the data into an Excel Table. 2 3 Create the same analysis completed in A3 to post the 4 summary statistics above each table column. But reference 5 6 the table columns with structured references (use the "Black Downward Arrow"pointing to the column header to reference the data table column) rather than highlighting the range of 3 8 cells within the table. 9 LO 11 SALE TYPE HOME TYPE ADDRESS 12 MLS Listing 13 MLS Listing 4 MLS Listing 5 MLS Listing 6 MLS Listing 17 MLS Listing 18 MLS Listing 19 MLS Listing 20 MLS Listing Mobile/Manufactured Home Single Family Residential Single Family Residential Single Family Residential Single Family Residential Single Family Residential Single Family Residential Single Family Residential Mobile/Manufactured Home 300 NW MAIN St 111 SE RONALD St 824 NW ORCHARD Dr 651 NE CHRISTIAN St 1787 UPPER CAMAS Rd 12661 LOOKINGGLASS Rd 100 KENYA Ct 1 MLS Listing 22 MLS Listing 23 MLS Listing 24 MLS Listing 25 MLS Listing 26 MLS Listing Single Family Residential Single Family Residential Mobile/Manufactured Home Mobile/Manufactured Home Mobile/Manufactured Home Mobile/Manufactured Home Single Family Residential 7 MLS Listing 1160 BROCKWAY Rd 401 SE GREGORY Dr 1068 RICE CREEK Rd 4546 MELODY Ln 2205 SE BOOTH Ave 4690 COOS BAY WAGON Rd 119 RUBY MAY Way 282 RIVER PLACE Dr Unit SP 62 1178 SE MYRTLE VIEW Dr 524 NE BROADWAY St 1740 RIVERSIDE Dr 170 SE WOODY Ct 330 NE BROADWAY St 867 NE HOLLY St 417 NE BROADWAY St 152 NE DEBBIE Way 600 NW T St 28 MLS Listing Single Family Residential 29 MLS Listing 30 MLS Listing 31 MLS Listing 12 MLS Listing 13 MLS Listing 4 MLS Listing Single Family Residential Single Family Residential Mobile/Manufactured Home Single Family Residential Single Family Residential Single Family Residential Single Family Residential Single Family Residential Multi-Family (2-4 Unit) Single Family Residential 5 MLS Listing 16 MLS Listing 17 MLS Listing 18 MLS Listing 237 HARMONY Dr 228 NW CIVIL BEND Ave 135 NE PLUM RIDGE Ct CITY Winston Winston Myrtle Creek Myrtle Creek Camas Valley Roseburg Winston Winston Winston Winston Roseburg Roseburg Roseburg Roseburg Roseburg Myrtle Creek Myrtle Creek Myrtle Creek Myrtle Creek Myrtle Creek Myrtle Creek Myrtle Creek Myrtle Creek Winston Roseburg Winston Winston i 1 Myrtle Creek 1.5 Camas Valley 3 1 Roseburg 5 3
By using structured references, the formulas will automatically refer to the data within the column of the Excel Table, even if the table expands or shrinks when you add or remove data.
To convert the data into an Excel Table and perform the analysis using structured references, you can follow these steps:
Select the entire data range, including the headers and the values.
In the Excel menu, go to the "Insert" tab and click on "Table." Choose a table style that you prefer.
Excel will automatically detect the range of your data. Make sure to check the box that says "My table has headers" if your data has headers.
Click "OK" to create the Excel Table.
Once you have created the Excel Table, you can perform the analysis and display the summary statistics using structured references. Here's how you can do it:
To calculate the Mean, use the formula =AVERAGE(Table1[LO]) and place it above the "LO" column header.
To calculate the Median, use the formula =MEDIAN(Table1[LO]) and place it above the "LO" column header.
To calculate the Minimum, use the formula =MIN(Table1[LO]) and place it above the "LO" column header.
To calculate the Maximum, use the formula =MAX(Table1[LO]) and place it above the "LO" column header.
To calculate the 75th percentile, use the formula =PERCENTILE.INC(Table1[LO],0.75) and place it above the "LO" column header.
To calculate the 25th percentile, use the formula =PERCENTILE.INC(Table1[LO],0.25) and place it above the "LO" column header.
To calculate the Interquartile Range, use the formula =QUARTILE.INC(Table1[LO],0.75) - QUARTILE.INC(Table1[LO],0.25) and place it above the "LO" column header.
To calculate the Variance, use the formula =VAR(Table1[LO]) and place it above the "LO" column header.
To calculate the Standard Deviation, use the formula =STDEV(Table1[LO]) and place it above the "LO" column header.
Make sure to adjust the table name (Table1) and column reference (LO) in the formulas based on your actual table and column names.
By using structured references, the formulas will automatically refer to the data within the column of the Excel Table, even if the table expands or shrinks when you add or remove data.
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Use these functions to answer this question.
P(x) = x2
– x – 6
Q(x) = x – 3
What is P(x) – Q(x)?
A. x2
– 3
B. x2
– 9
C. x2
– 2x – 3
D. x2
– 2x – 9
no linkss,,,,
Given:
The two functions are:
[tex]P(x)=x^2-x-6[/tex]
[tex]Q(x)=x-3[/tex]
To find:
The function [tex]P(x)-Q(x)[/tex].
Solution:
We need to find the function [tex]P(x)-Q(x)[/tex].
[tex]P(x)-Q(x)=(x^2-x-6)-(x-3)[/tex]
[tex]P(x)-Q(x)=x^2-x-6-x+3[/tex]
[tex]P(x)-Q(x)=x^2+(-x-x)+(-6+3)[/tex]
[tex]P(x)-Q(x)=x^2-2x-3[/tex]
Therefore, the correct option is C.
The two-way frequency table represents data from a survey asking a random sampling of people whether they can see the sunrise or sunset from the front of their home.
Which is the joint relative frequency for the people who can only see the sunset?
A) 5/38
B) 7/38
C) 12/38
D) 14/38
The joint relative frequency for people who can only see the sunset is 7/38.
To find the joint relative frequency for people who can only see the sunset, we need to look at the corresponding cell in the two-way frequency table. Let's assume the cell value is x. The total number of observations in the table is the sum of all the cell values, which is 38 in this case.
The joint relative frequency is the ratio of the cell value to the total number of observations. Therefore, the joint relative frequency for people who can only see the sunset is x/38.
Out of the given options, the value of x/38 that equals 7/38. Therefore, 7/38 represents the joint relative frequency for people who can only see the sunset based on the provided two-way frequency table.
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Evaluate x^4.x^2 when x=5
Answer:
i got u fam!!!!!!!!!!!!!!!
its 15625
Step-by-step explanation:
Kiara made a square baby blanket she decided to add one foot of material to one side then cut 4 inches of material off from the bed to sit outside of area of the rest salting blankets in 960 square inches find the area of the original blanket
Answer:
Step-by-step explanation:
960 which is the area u divide by the one foot which is 144 square units to get your answer,6.66666666667
Can someone help me with this. Will Mark brainliest.
Step-by-step explanation:
(-2,1), (-7,2)
[tex]y ^{2} - y ^{1} \\ x ^{2} - x ^{1} [/tex]
[tex]y ^{2} = - 7[/tex]
[tex]y ^{1} = 1[/tex]
[tex]x ^{2} = 2[/tex]
[tex]x^{1} = - 2[/tex]
[tex]m = \frac{ - 7 -( 1)}{2 - ( - 2)?} [/tex]
[tex]m = \frac{ - 8}{4?} [/tex]
[tex]m = - 2[/tex]
I only know how to find the slope.
Grandma’s Anzac cookie mixture has eight parts flour and six parts sugar. If Grandma needs to make 28 kilograms of the Anzac cookie mixture for a party, how many kilograms of flour will she need?
answer:
16
step by step explanation:
flour+sugar=8+6=14
[tex]14 = 28 \\ 8 = \\ \\ 8 \times 28 \div 4 = 16[/tex]
the object was turned 45 degrees around a fixed point that's called?
Answer:
A transformation that turns a figure around a fixed point, called the center of rotation. hope this helps
Step-by-step explanation:
what is the fraction for 0.875?
Answer:
7/8
Step-by-step explanation:
Answer:
7/8
Step-by-step explanation:
simplify 875/1000
Which scenarios below show ways governments or organizations work to solve large problems?
Answers
Red Cross volunteers travel to Haiti to help earthquake victims.
The United Nations passes a treaty to limit pollution into the Pacific Ocean.
A charity group from the United States travels to Africa to help victims of a virus.
Two ethnic groups begin fighting instead of negotiating.
A military dictator gives a threatening speech to other leaders.
A large company leaks pollutants into the Mississippi River
How does the volume of a cylinder with a radius of 12 units and a height of 15 units compare to the volume of a rectangular prism with dimensions 12 units x 12 units x 15 units?
The volume of the cylinder is smaller than the volume of the prism.
The volume of the cylinder is the same as the volume of the prism.
You cannot compare the volumes of different shapes.
The volume of the cylinder is greater than the the volume of the prism.
Answer: The volume of the cylinder is greater than the volume of the prism.
Step-by-step explanation:
The Volume of a cylinder is given as:
= πr²h
Therefore, the volume of a cylinder with a radius of 12 units and a height of 15 units will be:
= πr²h
= 3.14 × 12² × 15
= 6782.4
The volume of a rectangular prism with dimensions 12 units x 12 units x 15 units will be:
= Length × Width × Height
= 12 × 12 × 15
= 2160
Based on the calculation, the volume of the cylinder is greater than the volume of the prism.
Eliza's backpack weighs pounds with her math book in it. Without her math book, her backpack weighs pounds. How much does Eliza's math book weigh?
a. 2 pounds
b. 3 pounds
c. 4 pounds
d. 5 pounds
Eliza's math book weighs 3⁶⁵/₇₂ pounds, based on fractional subtractions.
What is fractional subtraction?Fractional subtraction involves the subtraction of a number with fractions from another.
Subtraction is one of the four basic mathematical operations, including addition, multiplication, and division.
Fractions are portions or parts of a whole value and may be classified as proper, improper, or complex.
The weight of the backpack with Eliza's math book = 18⁷/₉ pounds
The weight of the backpack without Eliza's math book = 14⁷/₈ pounds
The weight of the math book = 3⁶⁵/₇₂ (18⁷/₉ - 14⁷/₈) pounds
Thus, using fractional subtractions, we can conclude that Eliza's math book weights 3⁶⁵/₇₂ pounds.
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Question Completion
Eliza’s backpack weighs 18⁷/₉ pounds with her math book in it. Without her math book, her backpack weighs 14⁷/₈ pounds. How much does Eliza’s math book weigh?
In 2020 Phoenix, AZ was the fastest growing cities in the United States. In 2020 the population was approximately 1,730,000. The city population grew by 25,000 people that year. Write a model for the population of Phoenix x years after 2020 assuming it continues to grow by 25,000 people per year.
Answer : P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.
Explanation:
Given information: The population of Phoenix in 2020 was approximately 1,730,000 and the city's population grew by 25,000 people in 2020.
Model for the population of Phoenix x years after 2020 if it continues to grow by 25,000 people per year:
To find the population of Phoenix after x years since 2020, we need to add the number of people that moved into Phoenix since 2020, i.e., 25,000 people per year.
If x represents the number of years since 2020, then the model is given as follows:
P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.
We need to add 1,730,000 to 25,000x because 1,730,000 is the initial population in 2020.
Therefore the required model P(x) = 25,000x + 1,730,000P(x) represents the population of Phoenix after x years since 2020.
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Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
given:quadrillateral ABCD inscribed in a circle
prove angel A and angel C are supplementary angel B and D are supplementary
Answer:
Step-by-step explanation:
Given: quadrilateral ABCD inscribed in a circle
To Prove:
1. ∠A and ∠C are supplementary.
2. ∠B and ∠D are supplementary.
Construction : Join AC and BD.
Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,
∠1=∠2-----(1)
∠3=∠4-----(2)
∠5=∠6-------(3)
∠7=∠8------(4)
Also, sum of angles of quadrilateral is 360°.
⇒∠A+∠B+∠C+∠D=360°
→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4
→→→2∠1+2∠4+2∠6+2∠8=360°
→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,
→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)
As, ∠A+∠B+∠C+∠D=360°
∠A+∠C+180°=360°
∠A+∠C=360°-180°------Using A
∠A+∠C=180°
Hence proved.
credit: someone else
The length of a 1-inch paperclip is about 1.6 x 10−5 miles. It takes about 1.5 x 1010 paperclips linked together to reach the moon. What is the approximate distance to the moon?
Answer:
Distance from the moon is 2.4 × 10⁵ miles
Step-by-step explanation:
Length of 1-inch paperclip = [tex]1.6\times 10^{-5}[/tex] miles
Number of paperclips used to reach the moon = 1.5 × 10¹⁰
Total distance from the moon = Number of paper clips used × Length of one clip
= (1.5 × 10¹⁰) × (1.6 × 10⁻5)
= (1.5 × 1.6) (10¹⁰× 10⁻⁵)
= 2.4 × 10⁽¹⁰⁻⁵⁾ miles
= 2.4 × 10⁵ miles
Distance from the moon is 2.4 × 10⁵ miles.
(a) Calculate sinh (log(3) - log(2)) exactly, i.e. without using a calculator (b) Calculate sin(arccos(-)) exactly, i.e. without using a calculator. (c) Using the hyperbolic identity Coshºp – si
(a) The exact value of sinh (log(3) - log(2)) is 5/8.
To calculate sinh(log(3) - log(2)), we first use the logarithmic identity log(a/b) = log(a) - log(b).
Rewriting the expression:
sinh(log(3/2)).
Next, we use the definition of sinh in terms of exponential functions:
sinh(x) = ([tex]e^x - e^-x[/tex])/2.
Substituting
x = log(3/2),
We get the value:
sinh(log(3/2)) = ([tex]e^(log(3/2)[/tex]) - [tex]e^(-log(3/2))[/tex])/2
= (3/2 - 2/3)/2
= (9/4 - 4/4)/2
= 5/8
(b) The exact value of sin(arccos(x)) = sin(arcsin(acos(y))) = x.
Let's consider sin(arccos(x)). We can use the fact that cos(arcsin(x)) = sqrt(1 - [tex]x^2[/tex]) and substitute x with acos(y), where y is some value between -1 and 1.
Then we have:
cos(arcsin(x)) = cos(arcsin(acos(y)))
= cos(arccos(sqrt([tex]1-y^2[/tex])))
= sqrt([tex]1-y^[/tex])
Therefore, sin(arccos(x)) = sin(arcsin(acos(y))) = x.
(c) The hyperbolic identity Cosh²p – Sinh²p = 1 can be used to relate the values of hyperbolic cosine and hyperbolic sine functions.
By rearranging this identity, we get:
Cosh(p) = sqrt(Sinh²p + 1)
or
Sinh(p) = sqrt(Cosh²p - 1)
These identities can be useful in simplifying expressions involving hyperbolic functions.
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Jonathan has a bag that contains exactly one red marble (r), one yellow marble (y), and one green marble (g). He chooses a marble from the bag without looking. Without replacing that marble, he chooses a second marble from the bag without looking. Which outcomes would be included in the sample space for Jonathan’s experiment? Select three options.
yy
gr
gg
rg
yr
Answer: The answers B,D,E are correct
Step-by-step explanation:
Answer: gr, rg, yr
Step-by-step explanation:
PLZZZ HELP!
In 2002 Johan bought a collector car as an investment when its value was
$180,000. He sold the car in 2014. Over the time he owned it, its value
grew an average of 2.44% each year.
How much profit did Johan earn on
his investment?
bought for $180000 in 2002
sold it in 2014
180000*2.44\100
An investor has decided to commit no more than $80,000 to the purchase of the common stocks of the companies, Company A and Company & He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a() 12 profit from his investment in company and a(n) profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company in order to maximize his investment returns (XY) = What is the optimal profit? Need Help? Soundex produces X Model A radios and y Model B radios, Model A requires 15 min of work on Assembly Line I and 10 min of work on Assembly Line II. Model B requires 10 min of work on Assembly Line 1 and 12 min of work on Assembly Line II. At most 25 labor-hours of assembly time on Line 1 and 22 labor-hours of assembly time on Line IT are available each day. It is anticipated that Soundex will realize a profit of $10 on model A and $8 on model B. How many clock radios of each model should be produced each day in order to maximize Soundex's profit? (x, y) - What is the optimal profit?
The investor should invest $40,000 in Company A and $40,000 in Company B to maximize their investment returns.
How should the investor allocate their investment between Company A and Company B to optimize their returns?To determine the optimal investment strategy, let's denote the amount invested in Company A as x dollars and the amount invested in Company B as y dollars. The investor has set a maximum capital loss of $2,000 for each company. Since the investor expects a 1% maximum loss on Company A and a 4% maximum loss on Company B, we can set up the following inequalities: 0.01x ≤ $2,000 and 0.04y ≤ $2,000. Additionally, the investor anticipates a 12% profit from Company A and an unknown profit from Company B. Let's denote the profit from Company B as p. Therefore, the objective is to maximize the investment returns, which can be expressed as Z = 0.12x + p. The total investment constraint is x + y = $80,000. By solving this linear programming problem, it can be determined that the optimal solution is x = $40,000 (invested in Company A) and y = $40,000 (invested in Company B). Consequently, the optimal profit will be 0.12($40,000) + p.
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A machine shop needs a machine continuously. When a machine fails or it is 3 years old, it is instan- taneously replaced by a new one. Successive machines lifetimes are i.i.d. random variables uniformly distributed over 12,5) years. Compute the long-run rate of replacement.
The long-run rate of replacement is 0.444 machines per year.
Given that a machine shop needs a machine continuously. Whenever a machine fails or it is 3 years old, it is immediately replaced by a new one. We can assume that the machines' lifetimes are i.i.d. random variables uniformly distributed over (1, 2.5) years.
The question requires us to compute the long-run rate of replacement. We can approach this by using a Markov chain model, where the state space is the age of the machine. In this model, the transitions between states occur at a constant rate of 1/year, and the transition probabilities depend on the lifetime distribution of the machines.
Let xi denote the expected lifetime of the machine when it is i years old.
Then, we have: x1 = (1/2.5)∫(1,2.5)tdt = 1.25 years x2 = (1/2.5)∫(2,2.5)tdt + (1/2.5)∫(0,1.5)(t+1)dt = 1.75 years x3 = (1/2.5)∫(3,2.5)(t+1)dt + (1/2.5)∫(0,2)(t+2)dt = 2.25 years
The expected time to replacement from state i is xi.
Therefore, the long-run rate of replacement is given by: 1/x3 = 1/2.25 = 0.444.
Hence, the long-run rate of replacement is 0.444 machines per year.
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What is the best definition for parabola?
Answer: curve shape of something
Step-by-step explanation:
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.......
A parabola is a curve where any point is at an equal distance from: a fixed point (the focus), and. a fixed straight line (the directrix)
Hope it helps!
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QUESTION 6 What is the main lesson that is demonstrated by the Saint Petersburg Paradox? Choose one 1 point
a. Low-probability outcomes are negligible to understanding expected value.
b. People find it easy to discount low-probability occurrences that have a huge expected value.
c. Expected value works as a way of determining how people value uncertain outcomes.
d. People overestimate easy to remember situations.
According to the question the correct option is c. Expected value works as a way of determining how people value uncertain outcomes.
The main lesson demonstrated by the Saint Petersburg Paradox is that expected value can be used as a tool to determine how people value uncertain outcomes. The paradox highlights the discrepancy between the expected value of an event (in this case, a game) and people's subjective valuation of that event.
Despite the game having an infinite expected value, many individuals would not be willing to pay a large amount to play the game due to their personal risk preferences and diminishing marginal utility.
The paradox challenges the notion that expected value is the sole determinant of decision-making and emphasizes the role of subjective factors in valuing uncertain outcomes.
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Why do banks offer higher interest on savings accounts than on checking accounts?
The benefit: Savings accounts typically have higher interest rates than checking, making it easy for you to grow your money faster. ... Going over that limit can result in a fee or, if you do it multiple times, your bank might convert the account to checking.
consider the partially completed anova table shown. supposing all groups are of the same size, how many values are in each group of the data set this is based on?
The number of values in each group of the data set would be equal to the degrees of freedom for each group plus one.
In order to determine the number of values in each group of the data set based on the partially completed ANOVA table, we need to consider the total number of observations and the number of groups.
The ANOVA table consists of three main components: "Source of Variation," "Sum of Squares (SS)," and "Degrees of Freedom (df)." The "Source of Variation" represents the different factors or groups in the data set, while the "Sum of Squares" measures the variability within each group. The "Degrees of Freedom" represents the number of independent pieces of information available for estimating the population parameters.
In this case, since all groups are of the same size, we can determine the number of values in each group by examining the "Degrees of Freedom" column. The degrees of freedom for each group is the group size minus one (df = group size - 1). By adding one to the degrees of freedom for each group, we obtain the number of values in each group.
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On May 1, you sign a $1000 note with simple interest of 8.5% and a maturity date of December 19. You make partial
payments of $475 on June 2 and $200 on November 4. How much will you owe on the date of maturity?
A) $355.79
B) $354.39
C) $359.53
D) $358.96
Answer:
The amount to be repaid is $379.26.
Step-by-step explanation:
Period of note from May 1 to December 19 = 233 days
Amount of note or principal = $1,000
Simple interest rate = 8.5%
Maturity date = December 19
Repayments:
June 2 = $475
Nov. 4 = $200
Total paid $675
Simple interest = $54.26 ($1,000 * 8.5% * 233/365)
Total amount to be repaid = $1,054.26
Total amount repaid = 675.00
Balance to be paid on maturity $379.26
using the fplot command in matlab graph the function f(x)=xsin(x) between x=0 and x=2.5
To graph the function f(x) = (x)sin(x) in MATLAB using the fplot command, you can follow the steps below:
matlab
Define the function
f = (x) (x.)sin(x);
Set the range of x values
x = linspace(0, 2.5, 100);
Plot the function
fplot(f, [0, 2.5])
Add labels and title
xlabel(x)
ylabel(f(x))
title(Graph of f(x) = (x)sin(x))
Display the grid
grid on
In this code, we first define the function f(x) = (x)sin(x) using an anonymous function (x). Next, we create a range of x values using linspace from 0 to 2.5 with 100 points. Then, we use the fplot command to plot the function f over the specified range. Finally, we add labels, title, and grid to the graph.
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Let (V, f) an inner product space and let U be a subspace of V. Let w € V. Write w=u_w + v_w with u_w € U and v_w €U. Let u € U.
(a) Show that f(w-u, w-u) = ||u_w - u ||² + ||v||².
We have proved the given equation f(w - u, w - u) = ||u_w - u||² + ||v_w||².
The given inner product space is (V, f) and U is a subspace of V. It is given that w € V and it can be written as w = u_w + v_w with u_w € U and v_w €U.
Also, u € U. To show that f(w-u, w-u) = ||u_w - u ||² + ||v||², we have to prove it.
Let's consider the left-hand side of the equation. We can expand it as follows:
f(w - u, w - u) = f(w, w) - 2f(w, u) + f(u, u)
By the definition of w and the fact that u is in U, we know that w = u_w + v_w and u = u. So we can substitute these values:
f(w - u, w - u) = f(u_w + v_w - u, u_w + v_w - u) - 2f(u_w + v_w, u) + f(u, u)
Now, using the properties of an inner product, we can rewrite this as:
f(w - u, w - u) = f(u_w - u, u_w - u) + f(v_w, v_w) + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)
The term f(v_w, v_w) is non-negative since f is an inner product. Similarly, the term f(u, u) is non-negative since u is in U. Hence we can write the above equation as:
f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u)
We can write f(u_w, v_w) as f(u_w - u + u, v_w) and then use the properties of an inner product to split it up:
f(u_w - u + u, v_w) = f(u_w - u, v_w) + f(u, v_w)
By definition, u is in U so f(u, v_w) = 0. Hence we can simplify:
f(u_w - u + u, v_w) = f(u_w - u, v_w) = f(u_w, v_w) - f(u, v_w)
Now we can substitute this back into the previous equation:
f(w - u, w - u) = ||u_w - u||² + ||v_w||² + 2f(u_w, v_w) - 2f(u_w, u) + f(u, u) = ||u_w - u||² + ||v_w||² + 2f(u_w - u, v_w) + f(u, u)
Since U is a subspace, u_w - u is also in U. Hence, f(u_w - u, v_w) = 0.
Therefore,
f(w - u, w - u) = ||u_w - u||² + ||v_w||².
Therefore, we have proved the given equation.
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please help me i don't understand this. the teacher said that she does not care and its due in 20 mins please help me :(
A galaxy is likely to be a collection of which of the following?
A :Universe and interstellar matter
B : Stars and interstellar matter
C: Clusters and constellations
D :Stars and clusters
Answer:
C
Step-by-step explanation: