Answer: 227
Step-by-step explanation: (5 + 4 ) = 9
= 3 x 9^2 - 4^2
9^2 = 81
= 3 x 81 - 4^2
4^2 = 16
= 3 x 81 - 16
3 x 81 = 243
= 243 - 16
243 - 16 = 227
= 227.
write an explicit formula for an, the nth term of the sequence 25,33,41
Answer:
[tex]a_{n}[/tex] = 8n + 17
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
33 - 25 = 41 - 33 = 8
this indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 25 and d = 8 , then explicit formula is
[tex]a_{n}[/tex] = 25 + 8(n - 1) = 25 + 8n - 8 = 8n + 17
In a traditional IRA account, a
$1000.00 investment is taxed at 12%.
In a Roth IRA account, the $1000.00
investment is taxed at 10%. Which
plan reduces the overall tax burden?
A. The Traditional will reduce the tax burden because it's applied at a
higher percentage.
B. Both tax burdens will come out the same since both tax
calculations start with a $1000.00 account.
C. The Roth IRA reduces the tax burden because its taxes are
calculated in a lower bracket.
D. The Traditional IRA reduces the tax burden because its taxes are
calculated in a lower bracket.
C. The Roth IRA reduces the tax burden because its taxes are calculated in a lower bracket.
In a traditional IRA, contributions may be tax-deductible in the year they are made, but withdrawals in retirement are taxed as ordinary income. This means that the $1000.00 investment in a traditional IRA would be taxed at the investor's ordinary income tax rate when it is withdrawn in retirement. If the investor's ordinary income tax rate is 12%, then the tax burden on the $1000.00 investment in a traditional IRA would be $120.00.
In a Roth IRA, contributions are not tax-deductible, but withdrawals in retirement are tax-free. This means that the $1000.00 investment in a Roth IRA would be taxed at the investor's ordinary income tax rate when it is made, but it would not be taxed when it is withdrawn in retirement. If the investor's ordinary income tax rate is 10%, then the tax burden on the $1000.00 investment in a Roth IRA would be $100.00.
Overall, the tax burden on the $1000.00 investment in a Roth IRA is lower than the tax burden on the same investment in a traditional IRA because the taxes on the Roth IRA are calculated in a lower bracket (10% vs 12%).
a popular online video game can be played on multiple platforms: video game consoles, personal computers, and mobile devices. the game offers 333 gameplay modes: solo, duo, and squad. lee and avery regularly play matches as teammates in duo mode on a video game console. they are curious how their average scores per match compare to other players. they use the game's website to take a large random sample of duo mode players on any platform. the sample has a mean of 585585585 points per match.
Choose 1 answer: a. Only the players in the sample b. Only duo mode players who also play on a video game console c. Players of any mode who play on a video game console d. only Only duo mode players who play on any platform e. Players of any mode on any platform
Only duo mode players who play on any platform .
The correct answer will be Option D.
Given, Popular online video game .
As they have taken the random sample from the population of duo mode players from any of the three platform, in this regard, 558 points will be the legitimate estimate of the mean from that population only as this sample is a part of that population.
In general, we can say 558 points is the point estimate of the mean of the population that play duo mode in any platform.
Hence option D is correct .
Know more about average,
https://brainly.com/question/2426692
#SPJ12
nora has $640 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $418.55. she buys 2 bicycle reflectors for $19.39 each and a pair of bike gloves for $27.23. she plans to spend some or all of the money she has left to buy new biking outfits for $38.86 each. use the drop-down menu below to write an inequality representing oo, the number of outfits she can buy while staying within her budget.
Layla should by not more than 4 outfits in order not to exceed her budget
The inequality expression is n ≤ 4
price of a new bicycles = $418.55
2 bicycle reflectors = $19.39
a pair of bike gloves = $27.23
new biking outfits = $38.86 each
Nora's total money to spend at a bicycle store = $38.86
How to write the required inequalityLayla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items
We write the expression as;
$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86
where n represents the number of the new biking outfits
$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86
( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) / $38.86≥ n
( $640 - $484.56 ) / $38.86 ≥ n
( $155.44) / $38.86 ≥ n
4 ≥ n
Layla should by not more than 4 outfits in order not to exceed her budget
Read more on inequalities here: brainly.com/question/11613554
#SPJ4
a rectangle has its base on x-axis and its upper two vertices on the parabola y= 12 - x2. What is the largest area of rectangle?
A rectangle's greatest area is 32 square units.
Given:
A parabola's equation is y = 12 - x2, which is an even function
As a result, its rectangular shape is also even at the origin.
We are aware that the area of a rectangle is equal to its length times its width.
Here,
width = y, length = 2x
A = 2x, where (12 - [tex]x^{2}[/tex])
⇒ A = 24x - 2[tex]x^{3}[/tex]
Consider the A derivative with regard to x.
⇒ A' = 24 - 6 [tex]x^{2}[/tex]
When A' = 0, the area is the largest.
⇒ 24 - 6x2 = 0
⇒ [tex]x^{2}[/tex] = 4
⇒ x = 2
Replace x with its value in y = 12 - [tex]x^{2}[/tex].
⇒ y = 12 - 4
⇒ y = 8
Area = 2(2)(8) = 32
Hence, a rectangle's greatest area is 32 square units.
To learn more about function:
https://brainly.com/question/21145944
#SPJ4
Which are ways of showing probability select 4?; Can 5 by 4 Be the probability of an event justify your answer?; Can 3 by 5 be the probability of an event?
5/4 cannot be the probability of an event as its value is greater than 1 and probability always lies between 0 and 1. Yes, 3 by 5 can be the probability of an event.
We know that the probability of an event is the chance of occurring of an event. The ways of showing probability could be in ratio or it could be in percentage and the percent may be between 0%-100%
The value of 5/4 = 1.25 which is greater than 1, so it cannot be the probaility of any event.
The value of 3/4 = 0.75, its value is less than 1, so it can be the probability of an event.
The probability of an event always lie between 0 and 1. It is equal to zero if the event will never occur and is equal to 1 if the event is certain to occur.
Therefore, the probability of an event cannot be 5/4 but 3 by 5 can be the probability of an event. as its value of 5/4 is greater than 1 whereas the value of 3/5 is less than 1 and probalilty always lies between 0 and 1.
To learn more about probability refer here
https://brainly.com/question/25870256
#SPJ4
The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50.
Part 1: The point of maxima is 21.212
Part 2: x = 21.212 is approximately equal to the year 2022
Part 3: The percentage at that time is 16.37%
Part 4: The rate of change of the percentage at that time is 0.294
Part 1:
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
where x is the number of years since 2000, data from 0<=x<=50
Differentiating the function with respect to x and equating it to 0
p'(x) = -0.00066x^2 + 0.028x - 0.0033
We will find the critical points of p'(x)
p''(x) = dp'(x)/dx = -0.00132x + 0.028
Critical points of p'(x) lies at x where p''(x) = 0
Thus, -0.00132x + 0.028 = 0
x = 0.028/0.00132 = 21.212
Now, p'''(x) = -0.00132<0
x = 21.212 is a point of maxima of p'(x)
Therefore, the maximum possible values of x could lie at x = 21.212 as well as the extreme points of the domain p'(x), i.e. at x = 0 and 50
p'(0) = -0.00066(0)^2 + 0.028(0) - 0.0033 = -0.0033
p'(21.212) = -0.00066(21.212)^2 + 0.028(21.212) - 0.0033 = 0.2936
p'(50) = -0.00066(50)^2 + 0.028(50) - 0.0033 = -0.2533
Hence p'(x) attains maxima at x = 21.212
Therefore, p(x) increases most rapidly at x = 21.212
Part 2:
From the given condition in the question, x = 0 corresponds to the year 2000
Thus x = 21.212 is approximately equal to year 2022
Part 3:
The percentage at that time:
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
p(21.212) = -0.00022(21.212)^3 + 0.014(21.212)^2 - 0.0033(21.212) + 12.236
= 16.365
= 16.37%
Part 4:
Rate of change of the percentage at that time
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
p'(21.212) = -0.00066(21.212)^3 + 0.028(21.212) - 0.0033
= 0.2936
=0.294
Learn more about differentiation;
https://brainly.com/question/24898810
#SPJ4
I need help with this 1 question. I dont understand how to get it.
Answer:
82 degrees
Step-by-step explanation:
due to the resemblance of 90 degrees
Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.a. In every case.b. Only if n1≥30n1≥30 and n2≥30n2≥30.c. Only if n1p⎯⎯1≥5,n1(1−p⎯⎯1)≥5,n1p¯1≥5,n1(1−p¯1)≥5,n2p⎯⎯2≥5n2p¯2≥5 , and n2(1−p⎯⎯2)≥5.n2(1−p¯2)≥5.d. Only if n1p⎯⎯1≥30,n1(1−p⎯⎯1)≥30,n1p¯1≥30,n1(1−p¯1)≥30,n2p2≥30n2p2≥30 and n2(1−p⎯⎯2)≥30.n2(1−p¯2)≥30.
To conduct a hypothesis test for the difference between two population proportions under independent sampling is,
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5.
What is population proportion?
In statistics, a population proportion is a parameter that describes a percentage value connected to a population. It is typically denoted by P or the Greek letter π.
As per central limit theorem sample size needs to be greater than 30.
So required conditions are Only if n1 ≥ 30 and n2 ≥ 30.
Also for normal approximation we need the condition
[tex]np \geq 5 and[/tex] n(1 - p) ≥ 5
So one more condition is Only if
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
Hence, to conduct a hypothesis test for the difference between two population proportions under independent sampling is
n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5
To know more about population proportion, click on the link
https://brainly.com/question/18514274
#SPJ4
How many ways are there to choose six tiles that spell the word WATERS?
Answer:
0
Step-by-step explanation:
5•5/5(5-4)
help me please!!
Answer:
5
Step-by-step explanation:
First, work out parenthesis 5*5/5(1)
Then, Multiply/divide from left to right 25/5(1) -> 5(1) = 5
evaluate the expression 2x−yz , where x=34 , y=−0.2 , and z = 6. responses 0.3 0.3 1.95 1.95 2.7 2.7 i don't know.
the evaluation of the expression 2x−yz is 69.2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all arithmetic operations that are possible, however division by variables is not one of them. The polynomial x2+x-12 is an illustration of one with one variable. Three terms—x2, x, and -12—are included in this case.
the expression 2x−yz , where x=34 , y=−0.2 , and z = 6.
So putting the value of x,y and z.
2(34)- (-0.2*6) = 68+1.2
=69.2
Hence the evaluation of the expression is 69.2.
Learn more about polynomials space here:
https://brainly.com/question/11383
#SPJ1
Which of the following pricing strategies could be ethical in many situations? A.Predatory pricing
B.Price baiting
C.Price gouging
D.Price discrimination
The following pricing strategies could be ethical in many situations is price discrimination.
Predatory pricing is a strategy in which a company establishes a price that is too low to get new customers.
Price baiting is a strategy in which businesses make customers believe that they will have to pay less than the actual price of the product.
Price gouging is when a company puts a price that is too high for a product in a level that is not reasonable and this is considered to be unethical.
Price discrimination is a strategy in which businesses charge different prices to different customers based on what they believe that a group of customers would be willing to pay.
For example, when an airline sees that a specific route has a high demand, it increases the price of the ticket.
learn more about the price here:
https://brainly.com/question/19091385
#SPJ4
Answer:
D. Price discrimination
What is the absolute value of |- 32 |?; What is the value of 27 |?; What is the absolute value of |- 12 |?; What is the absolute value of -| 14 |?
The absolute value of |-32| is 32; absolute value of |27| is 27; absolute value of |-12| is 12; absolute value of -|14| is -14.
The Absolute value |x| of a real number x is the non-negative value of x without regard to its sign.
|x| = x ; |-x| = x
Therefore absolute value of
|-32| = 32
|27| = 27
|-12| = 12
- |14| = - 14
Absolute value describes the distance from zero that a number is on the number line , without considering direction. The absolute value of a number is never negative. Sometimes a sign is attributed to a numeric value to signify the direction, in addition to the value.
The absolute value of a number is defined as its magnitude irrespective of the sign of the number.
To know more about absolute value here
https://brainly.com/question/24534147
#SPJ4
The Mean Corporation manufactures a line of unassembled furniture. Based on historical evidence, the customer service manager knows that the proportion of customers that have not had any problems with assembling the furniture at home is 0.63.
Improvements have been made to the instructions provided with the furniture, and the customer service manager believes that this will increase the proportion of customers that can assemble the furniture without problems (TT) to above 0.63. A hypothesis test is conducted in order to find out.
The null and alternative hypotheses are:
H0: Pi symbol = 0.63
HA: Pi symbol > 0.63
To run the test, the manager randomly selects a sample of 102 people and asks them to assemble a piece of furniture produced by the Mean Corporation. The proportion of people in this sample that succeed is 0.67. You may find this standard normal table useful throughout this question.
a)Calculate the test statistic (z). Give your answer to 2 decimal places.
z =
b)Calculate the P-value. Give your answer as a decimal to 4 decimal places.
P =
The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
Given that,
There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.
The null and alternative hypotheses are:
H₀: π = 0.63
H₁: π > 0.63
We have to find
(a) Calculate the test statistic (z).
(b) Calculate the P-value.
We know that,
a) z = p - π / √(π(1-π)/n)
= 0.67 - 0.63 / √(0.63×0.37/102)
= 0.04 / 0.0478
= 0.84
b) p value(one tailed) is 0.2005.
Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.
To learn more about statistic visit: https://brainly.com/question/11969248
#SPJ4
Rewrite the equation `6y=2x+12`into slope intercept form.
Answer:
y=1/3x+2
Step-by-step explanation:
................
Answer:
y=1/3x+2
Step-by-step explanation:
slope intercept form: y=xm+b
6y=2x+12
/6 /6
y=2/6x+2
y=1/3x+2
have a great day!
(3) construct a quadratic equation
For -1/3 and -2/3
Answer:
y = 9x² +9x +2
Step-by-step explanation:
You want a quadratic equation with roots -1/3 and -2/3.
FactorsWhen p is a root of a polynomial, x-p is a factor. That means your quadratic will have factors (x -(-1/3)) and (x -(-2/3)). If we want integer coefficients, we can multiply each of these by 3:
y = (3x+1)(3x+2)
y = 9x² +9x +2 . . . . . . the result of multiplying it out
Independent random samples, each containing 80 observations, were selected from two populations. The samples from populations 1 and 2 produced 33 and 28 successes, respectively.
Test H0:(p1−p2) = 0 against Ha:(p1−p2) ≠ 0. Use α = 0.05
The test statistic should be: _______
The P-value is _______
From two populations, independent random samples were drawn, each having 80 observations. The test statistic should be z = 2.18 because samples from populations 1 and 2 yielded 33 and 28 successes, respectively.
P-value is set at 0.030.
State the null and alternate hypotheses in step one.
H0: (p1-p2) = 0
Ha: (p1-p2) ≠ 0
Step 2: Calculate the test statistic
We can calculate the test statistic using the formula:
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
where,
p = (successes in sample 1 + successes in sample 2)/(n1+n2)
= (33 + 28)/(80 + 80)
= 61/160
= 0.30
n1 = sample size of population 1
= 80
n2 = sample size of population 2
= 80
Therefore,
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
= (33/80 - 28/80)/√(0.38125(1−0.38125)(1/80+1/80))
=2.18
Learn more about test statistic here
https://brainly.com/question/14128303
#SPJ4
The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, 11.77.
Referring to Table 1 a confidence interval for this sample would be based on the t distribution with __________ degrees of freedom.
Referring to Table 1, the critical value for a 99% confidence interval for this sample is __________.
Referring to Table 1, a 99% confidence interval for the mean voltage of the power packs is from __________ to __________.
For this sample, a confidence interval based on the t distribution with 95% degrees of freedom would be appropriate.
Confidence interval: What is it?In most research, the 95% confidence interval (95 CI) is reported. If the confidence interval (e.g., 95%CI 0.9-1.1) crosses 1, it is assumed that there is no difference between the research arms.
In the two-tailed t table, determine the critical value of t. Add s/n to the crucial value of t. Calculate the top limit of the confidence interval by adding this value to the mean, and the lower limit by deducting this value from the mean.
With a significance level of 0.05 (i.e., a confidence level of 95%), the confidence interval is calculated using the T function.
The critical value for a 99% confidence interval for this sample, according to Table 1, is 2.576.
The t distribution is a symmetric distribution with a peak in the middle that gets closer to the horizontal axis as it moves away from the centre.
To learn more about The t Distribution refer to:
https://brainly.com/question/29734811
#SPJ4
Simplify the expression (9-4i)(-7-4i)-(12-3i)
Which one is not a polynomial? (a) 4x² + 2x-1 (b) x²-1
(c) y² + 5y + 1
So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.
In mathematics, what does a polynomial mean?An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.
What makes a polynomial unique?It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.
Which regulations apply to polynomials?Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.
To know more about polynomials visit:
https://brainly.com/question/29182596
#SPJ4
What are the coordinates of the point on the directed line segment from (−6,6) to (2,−10) that partitions the segment into a ratio of 1 to 3?
Answer:
I think its (-4,2)
Step-by-step explanation:
Assume a company has two divisions, Division B and Division C. Division B has provided the following information regarding the one product that it manufactures and sells on the outside market: Selling price per unit (on the outside market) $ 60 Variable cost per unit $ 44 Fixed costs per unit (based on capacity) $ 8 Capacity in units 20,000 Division C could use Division B’s product as a component part in the manufacture of 4,000 units of its own newly-designed product. Division C has received a quote of $58 from an outside supplier for a component part that is comparable to the one that Division B makes. If the company’s divisional managers are evaluated based on their division’s profits and Division B is currently selling 15,000 units on the outside market, what is Division C’s highest acceptable transfer price if it were to buy 4,000 units from Division B?
Division C’s highest acceptable transfer price if it were to buy 4,000 units from Division B should be $58.
What is the transfer price?The transfer price is the price that Division B should charge Division C for the internal supply of goods or services.
Ordinarily, the transfer price equals the outlay cost (production cost) plus the opportunity cost (profit from selling outside).
The highest acceptable transfer price that Division C should reflect the market price at which Division C could acquire the parts from outside.
Division B:
Outside market selling price per unit = $60
Variable cost per unit = $44
Fixed cost per unit = $8
Capacity in units = 20,000 units
Units sold outside by Division B = 15,000 units
Excess units = 5,000 units (20,000 - 15,000)
Units required by Division C = 4,000 units
Outside supplier's price per unit = $58
Thus, the highest acceptable transfer price should be $58 and not $60.
Learn more about transfer pricing at https://brainly.com/question/15698480
#SPJ1
What is the solution of the system of equations? y= x + 2, y = 3x
Answer:
[tex]x = 1 , y = 3[/tex]
Step-by-step explanation:
Note that each equation is equal to y. Set the equations equal to each other:
[tex]y = x + 2\\y = 3x\\\\x + 2 = y = 3x\\x + 2 = 3x[/tex]
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract x from both sides of the equation:
[tex]x + 2 = 3x\\x (-x) + 2 = 3x (-x)\\2 = 3x - x\\2 = 2x[/tex]
Next, divide 2 from both sides of the equation:
[tex]2x = 2\\\frac{2x}{2} = \frac{2}{2} \\x = \frac{2}{2} = 1\\x = 1[/tex]
Next, plug in 1 for x in one of the given equations:
[tex]y = x + 2\\\\x = 1 \\[/tex](given).
[tex]y = (1) + 2\\y = 3[/tex]
[tex]x = 1 , y = 3[/tex] is your answer.
~
Learn more about solving for system of equation, here:
https://brainly.com/question/13997560
3 5/2 in radical form
The simplest form of the exponent number of 3^(5/2) is √243.
What is exponential form of a number?
To express numbers that are either too large or too tiny, use exponential notation, which raises the number to the power of the appropriate exponent. The exponent's power might either take the positive or negative form.
For instance, we may express the exponential form of 5 × 5 × 5 × 5 as 5⁴, where 5 is the base and 4 is the power. The power here indicates how many times we are multiplying the base by itself.
Given number is 3^(5/2)
The base of the given number is 3 and exponent 5/2.
Apply the formula a^(m/2) = √a^m in the given number:
3^(5/2) = √3⁵
Putting 3⁵ = 243
3^(5/2) = √243.
To learn more about radical form, click on below link:
https://brainly.com/question/16339629
#SPJ1
Find the equation of the line through (−2,−5) which is perpendicular to the line y=x3+7.
The equation of the line perpendicular to the line y = 3x+7 is 3y = -x-17
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Given that, a line is perpendicular to line y = 3x+7 and passing through points (-2,-5)
The slope of perpendicular lines is negative reciprocal of each other.
Therefore, the slope of the asked line is -1/3
Finding c,
-5 = -1/3x(-2)+c
c = -17/3
Therefore, the equation of the line is y = -1/3x-17/3 or 3y = -x-17
Hence, The equation of the line perpendicular to the line y = 3x+7 is
3y = -x-17
For more references on slope, click;
https://brainly.com/question/3605446
#SPJ1
For each of the following expression, explain whether the expression
is a sentence or not. If the expression is a sentence, please show at least three models of
the sentence.
1. 3x+2 ≥ {}
2. x-y=1
3. 2x+y > 0
4. x4y+=
For given expressions:
1. 3x+2 ≥ {}
This is not a sentence.
2. x-y=1
This is an open sentence.
3. 2x+y > 0
This is an open sentence.
4. x4y+=
This is not a sentence.
In this question, we have been given some expressions.
We need to check which expression is a sentence.
We know that a mathematical sentence makes a statement about two expressions. The two expressions wither use variables, numbers or combination of both.
1. 3x+2 ≥ {}
this is not a sentence. Because when we use comparision than we must have two value to compare.
2. x-y=1
We know that an open sentence containing the sign ‘=‘
So, above expression is a sentence.
For x = 3 and y = 2,
x - y = 3 - 2
= 1
For x = 9 and y = 8,
x - y = 9 - 8
= 1
3. 2x+y > 0
This is an open sentence, as it is not known whether or not the sentence is true or false
4. x4y+=
This is not a sentence.
Therefore, for given expressions:
1. 3x+2 ≥ {}
This is not a sentence.
2. x-y=1
This is a sentence.
3. 2x+y > 0
This is a sentence.
4. x4y+=
This is not a sentence.
Learn more about an expression here:
https://brainly.com/question/1859113
#SPJ4
brainly explain why we need to define the vector space p n as the set of all polynomials with degree up to and including n instead of the more obvious set of all polynomials of degree exactly n .
Any n-dimensional vector should be able to be represented in space.
The highest degree of terms is written first when writing a polynomial in its standard form, then the next highest degree, and so on.
If there are multiple variables in a single term, add the exponents of each term together and choose the largest sum or highest power of the variable to determine the polynomial's degree.
It should be possible to represent any n-dimensional vector in space. It can only express polynomials of degree n if it only has terms of degree n.
To learn more about the standard form of a polynomial, visit the link below:
brainly.com/question/26552651
#SPJ4
4. Find the average value of the given function on the given interval. Then find all points c whose existence is guaranteed by the Mean Value Theorem for Integrals. (a) f(x) = x2 – 8x + 10 on (2, 5] (b) f(x) = Vx on [1, 16]
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
What is Average?
The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
(a) f(x) = x2 – 8x + 10
f = 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]
f = 1/5-2 [tex]\int\limits^5_2 {x^{2} -8x+10} \, dx[/tex]
Here, a=2
b=5
f(x) =x2 – 8x + 10
f = 1/3 (x³/3 - 8x²/2+10x)5/2
f = -25/9 -20/9
f = -45/9
= -5
Mean Value Theorem
If f(x) = continous on (a, b)
If f(x) = differentiable on (a, b)
Then f(c) = f(b) -f(a)/b-a
were c∈ (a,b)
Here, f(c) = f(-5)-f(2)/5-2
f(c) = -5+2/3
f(c) = -1 ......................(1)
Here, f(x) = x²-8x+10
f(c) = c²-8c+10
f(x) = 2c-8...................(2)
equating 1&2
2c -8 = -1
2c = -1 +8
c = 7/2
c∈ (2,5)
(b) f(x) = Vx on [1, 16]
f = [tex]\sqrt{x}[/tex] on (1 ,16)
f= 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]
f = 1/16-1 [tex]\int\limits^6_1 {\sqrt{x} } \, dx[/tex]
f = ( 2x (3/2)/45)₁¹⁶
f = 128/45-2/45
f = 126/45
= 14/5
Mean Value Theorem
f(x) = [tex]\sqrt{x}[/tex]
f(c) =[tex]\sqrt{c}[/tex]
f(c) = 1/2[tex]\sqrt{c}[/tex]....................(1)
we know that
f(c) = f(b)-f(a)/b-a
f(c) = f(16)-f(1)/16-1
f(c) = [tex]\sqrt{16}[/tex] -[tex]\sqrt{1}[/tex]/15
f(c) = 4-1/15
= 3/15.....................(2)
Equating (1) and (2)
1/2[tex]\sqrt{c}[/tex] = 3/15
2[tex]\sqrt{c}[/tex] = 15/3
2[tex]\sqrt{c}[/tex] = 5
[tex]\sqrt{c}[/tex] = 5/2
c = (5/2)²
=25/4
c≅ 6.25
6.25 = (1 ,16)
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
To learn more about Average visit
brainly.com/question/27193544
#SPJ4
9. Six people arrive at a party (A, B, C, D, E, F). They arrive at different times. In how
many ways can they arrive? Find the probability that A arrives first and F arrives last.
Answer: the answer is your mom
Step-by-step explanation:
Answer:
Step-by-step explanation: 720 ways overall , First and Last set = 24 ways, Probability of First and Last happening =130
