8) If x and are odd, then J a perfect square-Prove this! 9) Prove that if (a,b)=c; then (a}6²)_c² 10) Prove that if a b², then alb 11) Explain whether or not if a² | c² a/c # dit her
Answers
While the first statement is true, the second statement is not universally true.
To prove that if x and y are odd, then xy is a perfect square, we can express x and y as x = 2k + 1 and y = 2m + 1, where k and m are integers.
Now, let's calculate the product xy:
xy = (2k + 1)(2m + 1)
= 4km + 2k + 2m + 1
= 2(2km + k + m) + 1.
We can see that xy is an odd number since it can be written as 2 times an integer plus 1. Any odd number can be expressed as (2n + 1)^2 for some integer n, which is a perfect square.
Therefore, if x and y are odd, their product xy is a perfect square.
To prove that if (a, b) = c, then (a/c)^2 = (a/b) * (b/c), we can use the properties of the greatest common divisor (gcd).
Let's assume that (a, b) = c, which means that c is the greatest common divisor of a and b. We can write a = cx and b = cy, where x and y are integers.
Now, let's substitute these values in the equation we want to prove:
(a/c)^2 = (cx/c)^2 = x^2.
(a/b) * (b/c) = (cx/cy) * (cy/c) = x^2.
We can see that (a/c)^2 = (a/b) * (b/c), both sides simplify to x^2, which means they are equal.
Therefore, if (a, b) = c, then (a/c)^2 = (a/b) * (b/c).
To prove that if a < b^2, then a < lb, we can use the fact that if a and b are positive real numbers, then a < b implies a < lb.
Since a < b^2, we can take the square root of both sides to get sqrt(a) < b. Now, let's multiply both sides by sqrt(a):
sqrt(a) * sqrt(a) < b * sqrt(a).
This simplifies to a < b * sqrt(a).
Since sqrt(a) is a positive number, we can let sqrt(a) = c, where c = sqrt(a) > 0. Then, the inequality becomes a < lb.
Therefore, if a < b^2, then a < lb.
The statement "if a^2 divides c^2, then a divides c" is true. If a^2 divides c^2, it means that there exists an integer k such that c^2 = (a^2)k. Taking the square root of both sides, we have c = a * sqrt(k). Since k is an integer, sqrt(k) can be rational or irrational. Regardless, c is equal to a multiplied by some number, which implies that a divides c.
However, the statement "a/c does not divide c" is not necessarily true. For example, let's consider a = 2, c = 6. In this case, a^2 = 4 divides c^2 = 36, and a divides c since 2 is a factor of 6. But a/c = 2/6 = 1/3 does not divide c.
Therefore, while the first statement is true, the second statement is not universally true.
learn more about perfect square here
https://brainly.com/question/13521012
#SPJ11
Related Questions
Triangle EFG has vertices E(0, 7), F(−5, −1), and G(3, 0). Find the coordinates of the image of points E', F', and G' after a reflection across the x-axis.
Answers
Answer:
see explanation
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
E (0, 7 ) → E' (0, - 7 )
F (- 5, - 1 ) → F' (- 5, - (- 1) ) → F' (- 5, 1 )
G (3, 0 ) → G' (3, 0 ) ← unchanged as G is on the x- axis
which function has a range of {y|y ≤ 5}?
a. f(x) = (x – 4)2 5
b. f(x) = –(x – 4)2 5
c. f(x) = (x – 5)2 4
d. f(x) = –(x – 5)2 4
Answers
The correct option is \(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\).\) The function that has a range of \(\(\{y | y \leq 5\}\)\) is option \(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\).\)
To determine this, let's analyze the options:
\(\(a.\) \(f(x) = \frac{{(x - 4)^2}}{5}\)\): This function will have a range of \(\(y\)\)-values greater
than or equal to 0, so it does not have a range of \(\(\{y | y \leq 5\}\).\)
\(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\)\) : This function is a downward-opening parabola, and when we substitute various values of \(\(x\)\) , we get \(\(y\)\)-values less than or equal to 5. Therefore, this function has a range of \(\(\{y | y \leq 5\}\).\)
\(\(c.\) \(f(x) = \frac{{(x - 5)^2}}{4}\)\): This function is an upward-opening parabola, and its
range will be \(\(y\)\)-values greater than or equal to 0, so it does not have a
range of \(\(\{y | y \leq 5\}\).\)
\(\(d.\) \(f(x) = -\frac{{(x - 5)^2}}{4}\)\): This function is a downward-opening parabola, and its range will be \(\(y\)\)-values less than or equal to 0, so it
does not have a range of \(\(\{y | y \leq 5\}\).\)
Therefore, the correct option is \(\(b. f(x) = -\frac{{(x - 4)^2}}{5}\).\)
To know more about parabola visit-
brainly.com/question/31047093
#SPJ11
if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents. how much would you expect to gain after 20 tosses?
Answers
We could expect $30.00 to gain after 20 tosses.
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
The probability of all the events occurring need to be 1.
if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents.
We need to find out How much would you expect to gain after 20 tosses (in $ dollars).
Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.
Therefore, We could expect $30.00 to gain after 20 tosses.
Learn more about probability here;
brainly.com/question/11234923
#SPJ1
help needed i have 14 questions anybody wanna help help me with ALL
Answers
Greetings from Brasil...
Here we have supplementary angles, that is, the sum of both results in 180. Therefore,
A + B = 180 ⇔ ∠1 + ∠2 = 180
∠1 + ∠2 = 180 by defining supplementary angles
143 + ∠2 = 180
∠2 = 180 - 143
∠2 = 37°
Comparing two algorithms.
Say we have two different algorithms with respective runtimes of f(n) and g(n). Given the following cases, prove whether or not f(n) = ϴ(g(n)) is true in each case. Show your work but with the crucial steps only. P.S. sqrt(n) means the square-root of n, aka n^(½).
Case
f(n)
g(n)
A
log(n^200)
log(n^2)
B
sqrt(n)
log(n)
C
3^n
5^n
D
sin(n)+3
cos(n)+1
Answers
f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).
A) \(log(n^200) log(n^2)\)
Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:
f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100
This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.
B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:
f(n) / g(n) = [sqrt(n) / log(n)]
As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.
C) 3^n 5^n
Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:
f(n) / g(n) = \([3^n / 5^n]\)
As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.
D) sin(n) + 3 cos(n) + 1
Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:
f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]
As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.
Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.
To know more about log refer here:
https://brainly.com/question/32621120
#SPJ11
CD players are going out of fashion in the modern era. If 400,000 CD players were sold this year and sales are declining at a rate of 17% per year, how many will be sold 3 years from now?
68,000
6,800,000
240,199
240,198
Answers
You have a balance of 17,426 on your credit card. Your minimum monthly payment is 461 . If your interest rate is 15.5%, how many years will it take to pay off your card assuming you don't add any debt? Enter your response to two decimal places (ex: 1.23)
Answers
With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.
To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.
To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).
We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.
In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).
Learn more about multiplying here:
https://brainly.com/question/30875464
#SPJ11
Suppose that Susan enjoys sugar in her coffee. She has very particular preterences. and she must have exactly four spoonts of sugar for each cup of cottee, et be the number of cups of coflee. and S be the number of spoonfuls of sugar. Also. let P. be the price of a cup of collee and P. be
the nricc of a spoont of stoar. SunDosc Susan has to snend on Coitcc and Stigar V 8 9 2. A so.
the price of a spoonful of Sugar is P. = $.25.
Straph Susan S Price Constmption curve for prices. re = Sl. rc = 32. and rc = So. Picase put the number ot cups of coffee (C) on the honzontal axis, and the number of spoontils of Sugar (S) on the vertical axis Be sure to graph each budget constraint associated with each price ot ottee, Identity Susan's optimal
Duncle on each Daager constranne. and make sure your scape is labeled caretary and accurately.
Answers
1. Price constraint: Pc = $8
2. when Pc = $8, C ≈ 10.22, and S ≈ 40.88.
Price constraint: Pc = $9
3. when Pc = $9, C = 9.2, and S = 36.8.
Price constraint: Pc = $2
4. When Pc = $2, C ≈ 30.67, and S ≈ 122.68.
To graph Susan's consumption curve and budget constraints, we'll use the given information:
The price of a cup of coffee is denoted as Pc = $8.
The price of a spoonful of sugar is denoted as Ps = $0.25.
Susan's budget for coffee and sugar combined is $92.
Let's start by plotting the consumption curve for prices re = Sl, rc = 32, and rc = So. We'll calculate the number of cups of coffee (C) and the number of spoonfuls of sugar (S) corresponding to each price point.
Price constraint: Pc = $8
Since Susan spends exactly four spoonfuls of sugar (S) for each cup of coffee (C), we can express S in terms of C: S = 4C.
Using the budget constraint equation, we have: 8C + 0.25S = 92.
Substituting S = 4C into the equation: 8C + 0.25(4C) = 92.
Simplifying the equation: 8C + C = 92.
Combining like terms: 9C = 92.
Solving for C: C = 92 / 9, approximately 10.22.
Therefore, when Pc = $8, C ≈ 10.22, and S ≈ 40.88.
Price constraint: Pc = $9
Using the same approach, we substitute the new price into the equation.
9C + 0.25(4C) = 92.
Simplifying the equation: 9C + C = 92.
Combining like terms: 10C = 92.
Solving for C: C = 92 / 10, which is exactly 9.2.
Therefore, when Pc = $9, C = 9.2, and S = 36.8.
Price constraint: Pc = $2
Applying the same method:
2C + 0.25(4C) = 92.
Simplifying the equation: 2C + C = 92.
Combining like terms: 3C = 92.
Solving for C: C = 92 / 3, approximately 30.67.
Therefore, when Pc = $2, C ≈ 30.67, and S ≈ 122.68.
Now, we can plot these points on a graph with the number of cups of coffee (C) on the horizontal axis and the number of spoonfuls of sugar (S) on the vertical axis:
Consumption curve: Connect the three plotted points (10.22, 40.88), (9.2, 36.8), and (30.67, 122.68).
Budget constraint for Pc = $8: Plot the point (10.22, 40.88) and draw a straight line from the origin to that point.
Budget constraint for Pc = $9: Plot the point (9.2, 36.8) and draw a line from the origin to that point.
Budget constraint for Pc = $2: Plot the point (30.67, 122.68) and draw a line from the origin to that point.
Make sure to label the axes and the curves accurately.
Learn more about price from
https://brainly.com/question/29023044
#SPJ11
A. Find the equation of the L line that intersects graph C at point A (2, -5). B. Find the line equation with the coefficient of direction equal to -10 and touch and graph C
Answers
Graph C has a function
\(f(x)=2x^3-16x+11\)Since the line L intersects the graph at the point, A (2, -5)
To find the slope of the line we will differentiate the f(x) and substitute x by 2
\(\begin{gathered} f^{\prime}(x)=2(3)x^{3-1}-16x^{1-1}+0 \\ f^{\prime}(x)=6x^2-16 \\ m=6(2)^2-16 \\ m=24-16 \\ m=8 \end{gathered}\)The slope of the line is 8, substitute it in the form of the linear equation
\(\begin{gathered} y=mx+b \\ y=8x+b \end{gathered}\)To find b substitute x by 2 and y by -5
\(\begin{gathered} -5=8(2)+b \\ -5=16+b \end{gathered}\)Subtract 16 from both sides to find b
\(\begin{gathered} -5-16=16-16+b \\ -21=b \end{gathered}\)Then the equation of the line is
\(\begin{gathered} y=8x+(-21) \\ y=8x-21 \end{gathered}\)Suppose you borrowed $2,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?
Select the correct answer.
a. $614.04
b. $620.64
c. $610.74
d. $623.94
e. $617.34
Answers
An annual payment is found approximately $617.34. The correct option is e.. $617.34.
To find the size of your payments, you can use the formula for calculating the equal installments on a loan.
First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.
Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.
Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.
Know more about the annual payment
https://brainly.com/question/23168751
#SPJ11
While leaving an amusement park, a simple random sample of 25 families of four is taken. The mean amount of money spent is found to be m = $193.32 with a standard deviation of sx = $26.73. 14. While leaving an amusement park, a simple random sample of 25 families of four is taken. The mean amount of money spent is found to be ] = $193.32 with a standard deviation of sx = $26.73.
Answers
The mean amount of money spent by a random sample of 25 families of four while leaving the amusement park is $193.32, with a standard deviation of $26.73.
What is the average amount spent by families of four while leaving the amusement park?When studying the amount of money spent by families of four while leaving an amusement park, a simple random sample of 25 families was taken. The sample mean, which represents the average amount spent, was found to be $193.32, with a standard deviation of $26.73. This indicates that, on average, each family spent approximately $193.32.
The standard deviation of $26.73 shows the variability in the amount spent among the sampled families.To gain a deeper understanding of the data and draw more comprehensive conclusions, further analysis could be conducted. For instance, calculating the confidence interval would provide a range within which we can be confident that the true population mean lies.
Additionally, conducting hypothesis testing could help determine if the observed mean is significantly different from a predetermined value or if there are any statistically significant differences between subgroups within the sample.
Learn more about money spent
brainly.com/question/17020837
#SPJ11
simplify 15(p+4+2) using distributive property pleasee, literally help meeee ill give brainliest
Answers
Answer:
15p+90
Step-by-step explanation:
15(p+4+2)
Add 4+2 since not doing it would make it WAY more confusing than it needs to be. Also, it's just common sense to add it first..! :D
15(p+6)
Now you just distribute <3
15p+90
Graph the image of point A and B after a reflection over the x-axis
Answers
B x=2 y =3
An airplane travels at 300 mph in the direction s 45° e. what is the component form of the velocity vector?
Answers
The component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.
The component form of the velocity vector of an airplane traveling at 300 mph in the direction of S 45° E can be represented as ⟨300cos(45°), -300sin(45°)⟩. This breaks down the velocity vector into its horizontal (x) and vertical (y) components.
To determine the component form of the velocity vector, we need to consider the given direction and magnitude. The direction S 45° E can be broken down into two components: south (negative y-axis direction) and east (positive x-axis direction).
The magnitude of the velocity is given as 300 mph. The horizontal component of the velocity can be found by multiplying the magnitude by the cosine of the angle (45°) since cosine represents the adjacent side divided by the hypotenuse. Thus, the horizontal component is 300 * cos(45°) = 300 * √2 / 2 = 150√2.
Similarly, the vertical component of the velocity can be found by multiplying the magnitude by the sine of the angle (45°) since sine represents the opposite side divided by the hypotenuse. Therefore, the vertical component is 300 * sin(45°) = 300 * √2 / 2 = 150√2.
Combining these components, the component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.
Learn more about Velocity Vector here:
brainly.com/question/33520497
#SPJ11
WILL NAME BRANLIST OR WHATEVER Find the value of x. Write your answer in simplest radical form, if necessary.
Answers
Answer:
x= sqrt141
Step-by-step explanation:
x^2 + 22^2 = 25^2 by the pythagorean theorem
x^2 + 484 = 625
x^2 = 141
x= sqrt141
What condition has no solution?
Answers
A condition that is impossible to satisfy has no solution.
Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.
In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.
An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.
This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.
To learn more about solution, click here:
https://brainly.com/question/25785824
#SPJ4
Which is NOT a condition / assumption of the chi-square test for two-way tables? a.Large enough expected counts b.Normal data or large enough sample size c.None of these options: all three conditions / assumptions are necessary d.Random sample(s) of individuals that fall into just once cell of the table
Answers
The option that is NOT a condition/assumption of the chi-square test for two-way tables is: d. Random sample(s) of individuals that fall into just one cell of the table.
In the chi-square test for two-way tables, it is not required that the sample consists of individuals who fall into just one cell of the table. The chi-square test analyzes the association between two categorical variables in a contingency table. The conditions/assumptions for the chi-square test are:
a. Large enough expected counts: The expected frequency for each cell in the table should be at least 5 or higher. This ensures that the chi-square test statistic follows the chi-square distribution.
b. Normal data or large enough sample size: The chi-square test is based on an asymptotic distribution and works well for large sample sizes. However, it is not dependent on the assumption of normality.
c. None of these options: all three conditions/assumptions are necessary: This is an incorrect option because the assumption of normality is not necessary for the chi-square test. The other two conditions (large enough expected counts and random sample) are indeed necessary for the validity of the test.
To know more about chi-square test, visit:
https://brainly.com/question/32120940
#SPJ11
If you compare the medians of each data set, who spends more time online? alternative text
a. seventh graders
b. eighth graders
c. both grades spend an equal amount of time online.
d. impossible to determine from the data sets.
Answers
From the data set attached the median of time 7th graders spend online is 90 minutes and 8th graders spend online is 120 minutes. That is 8th graders spend more time online.
Therefore the answer is (b) eighth graders.
From the given data set, the amount of time twenty 7th graders spend online in the ascending order is
30, 30, 60, 60, 60, 60, 90, 90, 90, 90, 90, 90, 90, 120, 120, 120, 120, 150, 150, 180
The middle two values are 90 and 90, therefore median is the average which is 90 minutes.
Similarly in the case of 8th graders the data values are
30, 60, 60, 90, 90, 90, 120, 120, 120, 120, 120, 120, 120, 120, 150, 150, 150, 150, 180, 180
There are two values in the middle and they are 120 and 120, therefore the median is the average of the two values which is 120 minutes.
Thus comparing the median, eighth graders spend more time online.
--The question is incomplete, answering to the data set attached--
To know more on median
https://brainly.com/question/28060453
#SPJ4
(a) write the joint density f(x, y). (b) find e(ax by c). (c) find e[x2 ]. (hint: use the variance identity.) (d) find var(ax by c).
Answers
i) Joint density distribution function is given as
f(x,y) = 1/2Πσ1σ2 exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]
ii) E(aX + bY + c) = aµx + bµy + c iii) E(X^2) = σx^2 + µx^2
We have been given that, X ~ N(µx , σx^2) and Y~ N(µy , σy^2)
and X and Y are independent that is
ρ = 0
Note that the joint density function of two normal distribution is known as bivariate normal distribution which is given as
(X , Y) ~ BVN(µ1 , µ2 , σ1^2 , σ2^2 , ρ)
And whose joint density function is
f(x,y) = 1/(2Πσ1σ2√(1-ρ^2)) exp[(-1)/(2(1-ρ^2)) {((x-µ1)^2)/(σ1^2)-2ρ (x-µ1)(y-µ2)/σ1σ2+ ((y-µ2))/(σ2^2)}]
Where ρ = correlation coefficient of (x,y)
i) Joint density function of given X and Y which follows
(X , Y) ~ BVN(µx , µy , σx^2 , σy^2 , 0) is given as
f(x,y) = 1/2Πσ1σ2 exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]
ii) E(aX + bY + c) = aE(X) + bE(Y) + c
= aµx + bµy + c
iii) E(X^2) = V(X) + [E(X)]^2 {V(X) = E(X^2) - [E(X)]^2}
= σx^2 + µx^2
Learn more about distribution here :
brainly.com/question/4079902
#SPJ4
how many times does 70 go into 2,800
Answers
Answer:
40
Step-by-step explanation:
Answer:
40
here is the awnser buddy I hope it's right
11 more than twice x is less than 44. What is a way to write this sentence as an algebraic inequality?.
Answers
We can identify key terms in word problems that can tell use what math symbols or operations to use:
Less than = <Greater than = >Equal to =There are other key terms that can help us, including:
more than = addtwice = multiply by 2Solving the Question
We're given:
11 more than twice x is less than 4411 is more than twice x:
11 + 2xLess than 44:
< 44Combine all of these to get the inequality:
11 + 2x < 44Answer11 + 2x < 44
an2-25art 2 10) Which fraction represents 72-7-20 eXP expressed in simplest form? 2) X-5 X-4 3) x+5 4+4 4) 25 X + 20
Answers
The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)
A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.
Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)
x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)
Factoring x^2 – x – 20,
x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)
Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:
(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)
Note: The question is incomplete. The complete question probably is: What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)
Learn more about Simplest form:
https://brainly.com/question/17227519
#SPJ4
What is the parameter estimate on assets? Is assets
statistically significant - explain?
Answers
The parameter estimate on assets refers to the coefficient assigned to the variable "assets" in a statistical model. To determine whether this parameter estimate is statistically significant, you would need to analyze the p-value associated with the estimate.
If the p-value is below a predetermined significance level (commonly set at 0.05), it suggests that the parameter estimate is statistically significant. However, if the p-value is above the significance level, the estimate is not considered statistically significant.
In statistical analysis, a parameter estimate represents the relationship between a dependent variable and one or more independent variables. When analyzing the significance of a parameter estimate, statisticians often use hypothesis testing. The null hypothesis assumes that there is no relationship between the independent variable (assets) and the dependent variable.
To test this hypothesis, statisticians estimate the parameter associated with the independent variable (assets) in a statistical model and calculate its standard error. The standard error measures the variability of the parameter estimate.
The next step is to calculate the test statistic, which is obtained by dividing the parameter estimate by its standard error. This test statistic follows a t-distribution. By comparing the test statistic to the critical value from the t-distribution at a specific significance level (commonly 0.05), statisticians calculate the p-value.
The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. If the p-value is less than the significance level, typically 0.05, it suggests strong evidence against the null hypothesis. In this case, the parameter estimate is considered statistically significant, indicating that there is a relationship between the independent variable (assets) and the dependent variable.
However, if the p-value is greater than the significance level, we fail to reject the null hypothesis. This implies that the parameter estimate is not statistically significant, indicating that there is insufficient evidence to suggest a relationship between assets and the dependent variable.
In conclusion, the parameter estimate on assets is statistically significant if its associated p-value is below the predetermined significance level (usually 0.05).
To know more about Hypothesis Testing here
https://brainly.com/question/33445215
#SPJ4
The endpoints of $\overline{YZ}$ are $Y(1,\ -6)$ and $Z(-2,\ 8)$ . Find the coordinates of the midpoint $M$ .
Answers
The coordinates of the midpoint of the line segment YZ is; (-1/2, 1).
What is the midpoint of the line segment, YZ as given in the task content?The midpoint, M of the line segment YZ as required in the task content can be determined as follows;
x-axis;
= (-2+1)/2 = -1/2.
y-axis;
= (8+(-6))/2 = 1.
Therefore, the coordinates of the midpoint is;
M = (-1/2, 1).
Read more on coordinates of midpoint;
https://brainly.com/question/18315903
#SPJ1
Consider the points below. P(θ),−4,0),Q(5,1,−2),R(6,4,1) (a) Find a nonzero vector orthogonal to the plane through the points P,Q, and R. (b) Find the area of the triangle PQR.
Answers
(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.
(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:
PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)
PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)
Taking the cross product of PQ and PR, we have:
n = PQ x PR = (9, 1, -2) x (10, 4, 1)
Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.
(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:
|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)
Evaluating the magnitude gives |n| = \(\sqrt\)(811).
The area of triangle PQR is then:
Area = |n| / 2 = \(\sqrt\)(811) / 2.
To know more about nonzero vector refer here:
https://brainly.com/question/32673773#
#SPJ11
answer the question picture is there
Answers
Answer:
Step-by-step explanation:
1. 500
2. 10
3. 25000
On the graph shown, what is f(-1)?
Answers
Answer:
where is the graph?
Step-by-step explanation:
Use the Distributive Property to expand the algebraic expression. -5 (-3b - 2c)
Answers
Answer:
-5(-3b) - (-5(2c)
Step-by-step explanation:
a sample of 90 adult randolph county residents showed that 59 own a home. what is the risk of owning a home?
Answers
The risk of owning a home in Randolph County based on the given sample can be calculated as:
Risk of owning a home = Number of residents who own a home / Total number of residents in the sample
Risk of owning a home = 59 / 90
Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.
CDEF is inscribed in circle G. Solve for
and y.
F
110°
(x+38)
(6y-44)
E
Answers
Answer:
x=65, y=19
Step-by-step explanation:
When a quadrilateral is inside a circle, the angles that lie opposite each other have a sum of 180 degrees.
∠E+∠C=180°
(6y-44)°+110°=180°
(6y-44)°=70°
6y-44=70
6y=114
y=19
∠F+∠D=180°
(x+38)°+77°=180°
(x+38)°=103°
x+38=103
x=65