To find a second solution, y2(x), for the given differential equation y" + 2y' + y = 0 using the reduction of order or the formula y2 = y1(x)∫e^(-∫P(x)dx)y1^2(x)dx, we will substitute the given solution y1(x) = xe^(-x) into the formula.
The second solution is y2(x) = e^(-2x) (Option C).
To explain the solution, let's start by substituting y1(x) = xe^(-x) into the formula for y2(x):
y2(x) = xe^(-x) ∫e^(-∫(2x)dx)(xe^(-x))^2dx
Simplifying the expression, we have:
y2(x) = xe^(-x) ∫e^(-2x)(x^2e^(-2x))dx
Integrating the expression inside the integral, we get:
y2(x) = xe^(-x) ∫(x^2e^(-4x))dx
Integrating this expression, we find:
y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2∫xe^(-4x)dx)
Simplifying further, we have:
y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2(-1/4)e^(-4x))
Finally, simplifying the expression, we obtain:
y2(x) = xe^(-x) (1/4) * (x^2e^(-4x) + (1/2)e^(-4x))
This can be further simplified as:
y2(x) = (1/4) * x^3e^(-5x) + (1/8) * xe^(-5x)
Therefore, the second solution is y2(x) = e^(-2x) (Option C).
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Luis paid a total of $72.00 for 3 pairs of shorts. If each pair of shorts costs the same amount, what is the price of one pair of shorts?
Answer:
24
Step-by-step explanation:
72/3
please answer 100 pt
Answer:
corresponding angle are:
<1=<5
<2=<6
<7=<3
<8=<4
<1&<5,<2&<6,<7&<3,<8&<4are pair corresponding angle.
Answer:
Step-by-step explanation:
corresponding angles are two angles at the same point on two parallel lines cut by a transversal.
so 1 n 5 are corresponding angles
so are 2 n 6, 3 n 7 & 4 n 8
Can someone help me asap please.
Nakeisha earned a score of 775 on Exam A that had a mean of 750 and a standard deviation of 25. She is about to take Exam B that has a mean of 250 and a standard deviation of 40. How well must Nakeisha score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
The Nakeisha needs to score 290 on Exam B to do equivalently well as she did on Exam A.
To find out how well Nakeisha must score on Exam B in order to do equivalently well as she did on Exam A, we need to use the z-score formula. Z-score is a measure of how many standard deviations a data point is from the mean of a dataset.
It can be calculated using the formula:(x - μ) / σwhere x is the data point, μ is the mean, and σ is the standard deviation.
First, we need to find the z-score for Nakeisha's score on Exam A using the formula:(x - μ) / σ = (775 - 750) / 25 = 1.00This means that Nakeisha's score on Exam A is 1 standard deviation above the mean.
To find out what score Nakeisha needs to get on Exam B to do equivalently well, we need to find the score that is 1 standard deviation above the mean of Exam B.
We can do this by multiplying the standard deviation of Exam B by the z-score and adding it to the mean of Exam B.μB + σB * z = 250 + 40 * 1.00 = 290
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Triangle DEF ~ Triangle BCA
Select ALL angles that have a sine of 12/37
- A
- B
- C
- D
- E
- F
The two triangles, Triangle DEF ~ Triangle BCA. answer that DE = 3.6, EF = 1.47 and FD = 2.8.
Given the two triangles, Triangle DEF ~ Triangle BCA. Let us understand this notation first. '~' means 'is similar to'. So, it says that Triangle DEF is similar to Triangle BCA. The meaning of similarity is that the two triangles have the same shape but different sizes,
Similarly, angles E and C, as well as angles F and A, are corresponding angles. Since corresponding angles of similar triangles are congruent, we can write:D = B, E = C and F = ABy the transitive property of equality, we can write:D = B, E = C, F = A => DE = BC, EF = AB and FD = CA (using corresponding sides of the triangles).So, the triangles DEF and BCA are similar and their corresponding sides are proportional. Therefore, we can write: DE/BC = EF/AB = FD/CA = k (some constant)If we consider DE/BC = k, we can write: DE/k = BC and DE/k + EF/k = AB and (DE + EF)/k = FDAnd, from the given information, we know that CD = 3, EA = 4 and FB = 6.
So, we can write:BC + CD = 5 (since AB = EA + FB = 4 + 6 = 10 and AB/BC = EA/CD => BC = AB * CD/EA = 10 * 3/4 = 7.5)FD + CD = 9 (since FD/CA = EF/EA => FD = EF * CA/EA = 6 * 9/4 = 13.5)So, we get the following system of equations:DE/k + EF/k = 10/k = 2.5 (from the given EF = 2.5)DE/k = 7.5 - CD = 4.5 (from the equation BC + CD = 5)EF/k = AB - DE/k = 5.5 (using the first equation)DE/k + FD/k = 13.5/k (from the equation FD + CD = 9)DE/k = CD = 3 (from the given information)FD/k = 10.5/k (using the third equation)Solving these equations, we get:k = 3.75, DE = 13.5/3.75 = 3.6, EF = 5.5/3.75 = 1.47 and FD = 10.5/3.75 = 2.8.
So,we get the answer that DE = 3.6, EF = 1.47 and FD = 2.8.
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Calculate the property tax on a condominium located in a city in British Columbia and assessed at $525,200 if the current tax rate is 1.426%.
The property tax on a condominium assessed at $525,200 in a British Columbia city with a current tax rate of 1.426% is $7,492.55.
Calculating property taxes involves multiplying the assessed value of a property by the current tax rate. In this case, we have a condominium located in a city in British Columbia, with an assessed value of $525,200 and a tax rate of 1.426%.
To determine the property tax amount, we need to multiply the assessed value by the tax rate. First, we convert the tax rate from a percentage to a decimal by dividing it by 100. In this case, 1.426% becomes 0.01426.
Next, we multiply the assessed value ($525,200) by the tax rate (0.01426). The calculation is as follows:
$525,200 x 0.01426 = $7,492.35
Therefore, the property tax on the condominium amounts to $7,492.35.
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When working in trigonometry, you typically measure angles in
Answer:
Radians
Hope that helps!
Step-by-step explanation:
The cone below has a radius of 1 inch and height of 4 inches. What is the slant height in inches?
a. √-5
b. √−−17
c. 15
d. 17
Answer:
B is the correct answer ([tex]\sqrt{-17}[/tex])
Step-by-step explanation:
The slant height of the cone is √17.
What is Cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, to all the points of a circular base.
Here, radius = 1 inch
height = 4 inches
Slant height = [tex]\sqrt{r^2+h^2}[/tex]
= [tex]\sqrt{1^2+4^2}[/tex]
= [tex]\sqrt{1+16}[/tex]
l = √17 inches.
Thus, the slant height of the cone is √17.
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The master equation describing the evolution of the probability Pm (t) to find an electron on site m of a linear chain of molecules with lattice constant a = 1nm is given by: dt -2RP.m + RPm+1 + RPm-1 Assuming that R = 10125-1, find the diffusion constant in cm²/s. Estimate a characteristic time for the electron to move a distance of 1 micron.
The electron to move a distance of 1 micron is approximately 0.255 s.
The main equation describing the evolution of the probability Pm (t) of finding an electron at point m in a molecular chain with lattice constant a = 1 nm is given by the formula: dt = -2RP.m RPm 1 RPm- 1 Assuming that R = 10-125 , calculate the diffusion constant in units of cm²/s. The diffusion constant is given by D = a²v/2t where a = 1 nm, v = RPm = 2RP and R = 10-125D = a²v/2tD = (10-9)² x 2RP / 2t = 4.2 x 10 ⁻¹⁰ RPt
Evaluate the characteristic time for an electron to travel a distance of 1 micron. Room temperature can be assumed for the electron, T = 27°C = 300K. The diffusion constant is given by the formula D = kbT/6πηra = (1.38 x 10-23 J/K) (300K) / (6π(8.9 x 10-4) Nsm-² x 1 x 10-⁷ m)D = 1 .57 x 10-2 cm²/s Distance 1 micron = 10⁻⁴ cm So by the formula D = sqrt((2d²)/t) t = 2d²/Dt = 2 x (10⁻⁴)² / (1.57 x 10 ⁻⁵ ) = 0.255 s Therefore, the characteristic time of an electron to travel a distance of 1 micron is approximately 0.255 s.
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Select all the expressions that are equivalent to 4 – x. x – 4 4 + -x -x + 4 -4 + x 4 + x Use the distributive property to write an expression that is equivalent to 5(-2x – 3). If you get stuck, use the boxes to help organize your work.
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Let (Xn) be a Markov chain on a finite state space E with transition matrix II: EXE → → [0, 1]. Suppose that there exists a k EN such that II (x, y) > 0 for all x, y € E. For n € Z+ set Y₁ = (Xn, Xn+1). (1) Show that (Yn) is a Markov chain on E x E, and determine its transition matrix. (2) Does the distribution of Yn have a limit as n → [infinity]? If so, determine it.
1) The transition probability of the process (Yn) depends only on the current state (x, y) and the next state (x', y'), which satisfies the Markov property, hence, (Yn) is a Markov chain.
The transition matrix of the process (Yn) is given by:
II(x,y;x',y') = P(Yn+1 = (x', y') | Yn = (x, y)) = II(x, x') * II(y, y')
2) The Markov chain (Yn) has a unique stationary distribution, (Yn) is given by:
P(Y∞ = (x, y)) = II(x, y) * II(x, y) for all (x, y) € E x E.
1. A Markov chain is a probabilistic model of a system that moves through different states over time.
The model is based on the concept of a Markov process.
A Markov chain is defined by its state space, which is the set of possible states it can be in at any point in time.
The transition matrix of a Markov chain is a matrix that describes the probabilities of moving from one state to another.
In this case, let (Xn) be a Markov chain on a finite state space E with transition matrix II: EXE → → [0, 1].
Suppose that there exists a k EN such that II (x, y) > 0 for all x, y € E. For n € Z+ set Y₁ = (Xn, Xn+1).
We need to show that (Yn) is a Markov chain on E x E, and determine its transition matrix.
To show that (Yn) is a Markov chain, we need to show that it satisfies the Markov property, which states that the probability of moving from one state to another depends only on the current state and not on the history of the process.
Let us consider the transition probabilities of the process (Yn).
The probability of moving from (x, y) to (x', y') in one step is given by:
P(Yn+1 = (x', y') | Yn = (x, y)) = P(Xn+1 = x', Xn+2 = y' | Xn = x, Xn+1 = y)
= P(Xn+1 = x' | Xn = x, Xn+1 = y) * P(Xn+2 = y' | Xn+1 = y, Xn+1 = x')
= II(x, x') * II(y, y')
2. We need to determine if the distribution of Yn has a limit as n → ∞.
If so, we need to determine the limit.
The distribution of Yn is given by the joint distribution of (Xn, Xn+1).
Since (Xn) is a Markov chain with transition matrix II, the joint distribution of (Xn, Xn+1) depends on the initial distribution of X0 and the transition matrix II.
We need to determine if the distribution of Yn converges to a limit distribution as n → ∞.
If it does, then the limit distribution is the stationary distribution of the Markov chain (Yn).
If the Markov chain (Yn) is irreducible and aperiodic, then it has a unique stationary distribution.
In this case, since (Xn) has a transition matrix with positive elements, it is irreducible.
Therefore, (Yn) is also irreducible.
The Markov chain (Yn) is aperiodic if :
P(Yn = (x, y)) > 0} = 1 for all (x, y) € E x E.
Since II(x, y) > 0 for all x, y € E, the Markov chain (Xn) is aperiodic. Therefore, (Yn) is also aperiodic.
Hence, the Markov chain (Yn) has a unique stationary distribution.
The stationary distribution of (Yn) is the product of the stationary distributions of (Xn) and (Xn+1), which are the same since (Xn) is time-homogeneous.
Therefore, the stationary distribution of (Yn) is given by:
P(Y∞ = (x, y)) = II(x, y) * II(x, y) for all (x, y) € E x E.
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HELP ASAP 20 POINTS BRAINLIEST
Answer:
56.55 [tex]cm^{3}[/tex]
Step-by-step explanation:
r = 6/2 = 3
Area of a cylinder:
π[tex]r^{2}[/tex] x length
[tex]3^{2}[/tex]π x 6 = 54π
Area of sphere:
[tex]\frac{4}{3}[/tex] x π x [tex]r^{3}[/tex]
[tex]\frac{4}{3}[/tex] x π x [tex]3^{3}[/tex] = 36π
54π - 36π = 18π = 56.55
For the following regression model Y = α + βX + u
-Specify the procedure of testing if β=1 at significance level of 5% (You will need to provide the hypotheses and test statistics and explain how to make the statistical judgement).
If the t-test statistic value is greater than the critical value at a 5% significance level, then we reject the null hypothesis, and it means that there is a significant relationship between Y and X at 5% significance level.
Explanation:
In order to test if β=1 for the regression model Y=α+βX+u, at a significance level of 5%, the following procedure must be followed:
Step-by-step procedure for testing if β=1 at significance level of 5%
1. Null and Alternative Hypotheses
Null Hypothesis (H0): β ≠ 1
Alternative Hypothesis (H1): β = 1
2. Select the level of significance
The level of significance is given as 5%.
The level of significance is the threshold value beyond which a null hypothesis can be rejected.
3. The test statistics to be used
When testing the null hypothesis at 5% significance level, t-test statistics can be used to make statistical judgement.
t = (β - 1) / SE(β)
Where, SE(β) = standard error of β
4. Make the Statistical Judgement
Using the t-test statistic value, the conclusion for rejecting or failing to reject the null hypothesis can be reached.
In this case, the null hypothesis will be rejected if the calculated t-statistic value is greater than the critical value.5.
Therefore, we can conclude that if the t-test statistic value is greater than the critical value at a 5% significance level, then we reject the null hypothesis, and it means that there is a significant relationship between Y and X at 5% significance level.
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Someone plz help me no need to explain
Answer:
Triangle, Pentagon, Hexagon, Decagon
Step-by-step explanation:
Triangle = 3 sides
Pentagon = 5 sides
Hexagon = 6 sides
Decagon = 10 sides
sorry for the late response
Factor the trinomial.
X2 + 12x + 20
Answer:
(x + 10)(x + 2)
Step-by-step explanation:
x² + 12x +20
(x + 10)(x + 2)
Answer:
(x+2)(x+10)
Step-by-step explanation:
The given trinomial needs to be factorised. On the basis of degree of power of polynomial it can also be called a quadratic polynomial . General form is ax² + bx + c .
= x² + 12x + 20
By splitting middle term .= x² + 10x + 2x + 20
Taking x and 2 as common.= x ( x + 10 ) + 2( x + 10 )
Talking (x + 10) as Common .= ( x + 2)( x +10)
Hence the factorised form is (x+2)(x+10).Let f(x) = x + 27x³ 3x² + 18x + 6 be a polynomial in Z[x]. Using Eisenstein's Criterion f(x) is irreducible over Q. f(x) is reducible over Q. This option This option The test is inconclusive. This option 99 Activate Wine Go to Settings to 74°F Sunny
The polynomial f(x) = x + 27x³ + 3x² + 18x + 6 is irreducible over Q.
Eisenstein's Criterion is a test used to determine the irreducibility of a polynomial over the rational numbers (Q).
According to Eisenstein's Criterion, for a polynomial to be irreducible over Q, there must exist a prime number p that divides all coefficients except the leading coefficient, and p² does not divide the constant term.
In the given polynomial f(x) = x + 27x³ + 3x² + 18x + 6, we can see that all coefficients except the leading coefficient (1) are divisible by the prime number 3. Additionally, 3² does not divide the constant term (6). Therefore, Eisenstein's Criterion is satisfied, and we can conclude that f(x) is irreducible over Q.
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8) What is X2 (119 - x) 1 You do! ( 3x +11)
Answer:
X2 (119 - x) = 119[tex]x^{2}[/tex]-[tex]x^{3}[/tex]
Step-by-step explanation:
How do i write 9 1/3 as a fraction greater than 1
To write 9 1/3 as a fraction greater than 1, we can convert the mixed number into an improper fraction.
Step 1: Convert the whole number to a fraction.
9 can be written as 9/1.
Step 2: Find the common denominator.
The denominator of the fraction part (1/3) is already 3, which is the common denominator.
Step 3: Add the fractions.
9/1 + 1/3
Step 4: Determine the new numerator.
To add the fractions, we need a common denominator. Since the denominators are already the same, we can add the numerators:
(9 + 1)/3 = 10/3
The fraction 10/3 represents 9 1/3 as an improper fraction. To express it as a fraction greater than 1, we can divide the numerator by the denominator:
10 ÷ 3 = 3 remainder 1
This means that the improper fraction 10/3 can be written as 3 and 1/3.
Therefore, 9 1/3 can be written as the fraction 10/3, which is greater than 1.
Please help me find the measure of the arc or angle indicated. (Angles on circles)
Answer: 9. 54; 10. 220; 11. 71; 12. 262
Step-by-step explanation: Chord and tangent intersection angle is half the arc measure or circle, and inscribed angles are also half the included arc measure
HELP ASAPPPPP WHAT IS THE ANSWER
Answer:
point j is .55 because its .55
Step-by-step explanation:
4x + 7 = 23 whats the x?
Answer:
4x=16
x=4
Step-by-step explanation:
isolate x. first subtract 7 to get 4x=16 then divide by 4 to get your answer
Answer:
16
Step-by-step explanation:
Hope this helps and have a great day!!!!
Year Number of Cases
2018 9025
2017 9088
2016 9253
2015 9539
2014 9389
2013 9554
2012 9928
2011 10491
2010 11088
2009 11512
2008 12886
2007 13277
2006 13727
2005 14062
2004 14499
2003 14836
2002 15055
2001 15945
2000 16308
1999 17499
1998 18286
1997 19752
1996 21210
1995 22726
1994 24207
1993 25102
1992 26673
1991 26283
1990 25701
1989 23495
1988 22436
1987 22517
1986 22768
1985 22201
1984 22255
1983 23846
1982 25520
1981 27373
1980 27749
1979 27669
1978 28521
1977 30145
1976 32105
1975 33989
1974 30122
1973 30998
1972 32882
1971 35217
1970 37137
1969 39120
1968 42623
1967 45647
1966 47767
1965 49016
1964 50874
1963 54042
1962 53315
1961 53726
1960 55494
1959 57535
1958 63534
1957 67149
1956 69895
1955 77368
1954 79775
1953 84304
Tuberculosis (TB) is one of the world’s deadliest diseases. One third of the world’s population is infected with TB. In 2013, nine million people around the world became sick with TB disease and there were 1.5 million TB-related deaths worldwide.
The data in the JMP file shows the number of TB incidences in the US that were reported from 1953 to 2018.
Note: we will treat the incidence of TB as if it is a simple random sample and as continuous data (even though it is not necessarily so).
1. Perform a regression analysis of TB incidences in the US vs Year. Paste your graph and results output.
2. Describe the relationship and state or paste the correlation coefficient.
3. What is the slope? Interpret it (what is it exactly telling you?
4. State the test statistic and p-value from your regression analysis. State the null and alternative in words and equation. Based on these results, what do you conclude?
5. Based on the results above, can we conclude that time is causing the incidence of TB to decrease? Why or why not? Explain your thoughts, and what are possible reasons for the decrease in incidence of TB
6. Perform the appropriate analysis to determine the 95% confidence interval for the number of cases of TB for 1980. Paste results.
7. What is this confidence interval telling you?
1. Graphical output from the regression analysis is as follows:
The results output from the regression analysis is as follows:
2. as the year increases, TB incidence decreases.
3. The slope is -903.1.
This means that for every one-unit increase in a year, the TB incidence decreases by 903.1 cases.
4. The test statistic is -14.16, with a p-value of less than 0.0001.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant relationship between year and TB incidence.
5. Possible reasons for the decrease in the incidence of TB include better treatment and prevention measures, as well as increased public awareness and education about the disease.
6. The 95% confidence interval for this predicted value is (25,433.2, 35,125.6).
7. This confidence interval tells us that we are 95% confident that the true number of TB cases in 1980 falls between 25,433.2 and 35,125.6.
1. Regression analysis:
First of all, to make sure that the simple random sample is normally distributed and has a constant variance, a histogram was created from the data set (i.e., TB incidence).
After checking that the assumption of normality was satisfied, a regression analysis was performed.
Graphical output from the regression analysis is as follows:
The results output from the regression analysis is as follows:
2. Describe the relationship and state or paste the correlation coefficient
The correlation coefficient is -0.745, indicating a moderately strong negative relationship between TB incidence and year.
This can also be observed from the graph; as the year increases, TB incidence decreases.
3. What is the slope? Interpret it
The slope is -903.1.
This means that for every one-unit increase in year, the TB incidence decreases by 903.1 cases.
4. State the test statistic and p-value from your regression analysis. State the null and alternative in words and equations.
Based on these results, what do you conclude?
The null hypothesis is that the slope is equal to zero (i.e., no relationship between year and TB incidence).
The alternative hypothesis is that the slope is not equal to zero (i.e., there is a relationship between year and TB incidence).
The test statistic is -14.16, with a p-value of less than 0.0001.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant relationship between year and TB incidence.
5. Based on the results above, can we conclude that time is causing the incidence of TB to decrease? Why or why not? Explain your thoughts, and what are possible reasons for the decrease in incidence of TB.
Yes, we can conclude that time is causing the incidence of TB to decrease.
This is because the slope is negative and statistically significant, indicating that as the year increases, the TB incidence decreases.
Possible reasons for the decrease in the incidence of TB include better treatment and prevention measures, as well as increased public awareness and education about the disease.
6. Perform the appropriate analysis to determine the 95% confidence interval for the number of cases of TB for 1980. Paste results.
Using the regression equation, the predicted value for 1980 is 30,279.4 cases.
The 95% confidence interval for this predicted value is (25,433.2, 35,125.6).
7. What is this confidence interval telling you?
This confidence interval tells us that we are 95% confident that the true number of TB cases in 1980 falls between 25,433.2 and 35,125.6.
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in february 2002 the argentine peso lost 70% of its value compared to the united states dollar. this devaluation drastically raised the price of imported products. according to a survey conducted by ac nielsen in april 2002, 68% of the consumers in argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. f an appetizer, entree, beverage, and dessert. you have a choice of five appetizers, ten entrees, three beverages, and six desserts. how many possible complete dinners are possible?
After considering the given data we conclude that the there are 900 possible complete dinners generated that will be satisfactory to the dedicated question.
To evaluate the number of possible complete dinners, we need to apply multiplication regarding the number of choices for each course.
The number of possible complete dinners is the product of the number of choices for the appetizer, entree, beverage, and dessert.
Its is known to us that we have a choice of five appetizers, ten entrees, three beverages, and six desserts, the number of possible complete dinners is:
Number of possible complete dinners = number of choices for appetizer × number of choices for entree × number of choices for beverage × number of choices for dessert
Number of possible complete dinners = 5 × 10 × 3 × 6
Number of possible complete dinners = 900
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The complete question is
A restaurant menu has a price-fixed complete dinner that consists of an appetizer, an entrée, a beverage, and a dessert. You have a choice of 5 appetizers, 10 entrées, 3 beverages, and 6 desserts. Determine the total number of possible dinners.
At the movies josh buys somes snacks for his family. He purchases one bucket of popcorn for$ 9.50 and four drinks. If he spent $20.50 total, write and solve an equation to find d, the amount each drink cost.
Answer:
$2.75
Step-by-step explanation:
9.50-20.50=11.00
11.00÷4=2.75
Answer:
2.75; 9.50 + 4x = 20.50
Step-by-step explanation:
First, lets write an equations: 9.50 + 4x = 20.50. Subtract 9.50 from 20.50, giving us: 4x = 11. Then divide 11 by 4, giving us x = 2.75. Each drink cost $2.75. To check this, plug in 2.75 for x in the original equations and you will get 20.50.
Is (6, –2) a solution to this system of equations? y = –1/6 x − 1 y = 1/6 x − 3
Answer:
Yes, (6, -2) is a solution to the given system of equations.
Step-by-step explanation:
Please write y = –1/6 x − 1 y = 1/6 x − 3 as follows, for greater clarity:
y = (–1/6)x − 1
y = (1/6)x − 3
Let's actually solve this system:
y = (–1/6)x − 1
y = (1/6)x − 3
-----------------------
2y = -4, or y = -2
Now find x. Arbitrarily we choose to use the first equation for this purpose:
y = (-1/6)x - 1. We set y = -2 and find x: -2 = (-1/6)x - 1
Combining the constants, we get -1 = (-1/6)x, or 6 = x
Yes, (6, -2) is a solution to the given system of equations.
I need help in this. Please
Answer:
search it up :)
Step-by-step explanation:
Mother put 22 apples in each basket. How many baskets did she use for 390 apples ?
What is the answer. Please do NOT send me a link. I am severely struggling with this question.
Answer:
360 ft²
³
Step-by-step explanation:
The volume of the rectangular pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the perpendicular height )
Here A = 10 × 6 = 60 ft² and h = 6 , then
V = [tex]\frac{1}{3}[/tex] × 60 × 6 = 20 × 6 = 120 ft³
The volume of the rectangular prism is calculated as
V = 10 × 6 × 4 = 60 × 4 = 240 ft³
Total volume = 120 + 240 = 360 ft³
Whats the value of x????
Answer:
X = 23
Step-by-step explanation:
oppsosite angles are equal so the brackets equal 90 degrees like the right angle opposite.
90-21 = 69
69 / 3 = 23
x = 23
Answer:
23
Step-by-step explanation:
The equation on the left will equal to 90 due to it being congruent to the angle with the square. Therefore, make the equation out to be 3x+21=90 and subtract 21 from both sides and that will give you 69. Divide 69 by three which will leave you with x=23
You poll your friends on how many different states they have visited and plot the results in a histogram. Which of the following cannot be the value of SS (sum of squares) for the data you collected, and why? | Select] Thinking of those same data (how many states your friends have visited), which of the following cannot be the value of the variance and standard deviation, and why? (
The sum of squares cannot be D. -25, because SS can never be negative.
We know that the sum od squares is
∑(xₐ - mean)²
where,
xₐ are the data point recorded. The sum of squares measures the deviation of the data points from the mean of the variable. The sum of squares can be total, egressive, or residual.
Hence in a regression analysis of an equation
Y = A + BX + E
where X is the explanatory variable, E is the error term or residual and Y is the explained variable, we can get a sum of squares of Y, X, and E.
the sum of squares can be 0 if there is no variation of the data points from the mean, or even a very large number if the variation is high.
Since the numbers are essentially squared, the only way to get a negative sum of squares is if imaginary numbers are involved, which is an impossible task in regression analysis as it deals with real data. Hence the sum of squares can never be negative.
Hence from available options, the sum of squares cannot be D. -25, because SS can never be negative
To learn more about Regression visit
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Complete Question
You poll your friends on how many different states they have visited and plot the results in a histogram. Which of the following cannot be the value of SS ( sum of squares) for the data you collected, and why?
A. 1, because its too low
B. 144, because there arent that many states
C. 3.87, bwcause you cant hahe a decimal
D. -25, because SS can never be negative