Answer:
x=3
Step-by-step explanation:
[tex]3x^{2}[/tex]-7x-6=0
9x-7x-6=0
=9x-7x=0+6=6
2x=6
x=6/2=3
List four monthly cost that a homeowner needs to pay?
Answer:
A homeowner has to pay phone bill, home insurance, cable bill, internet bill
Step-by-step explanation:
If the homeowner doesn't pay these then they won't get to continue using it until they pay for it again.
Answer:
The answer should contain any four of the following:
utility fees
association fees
private mortgage insurance (PMI)
title insurance
homeowners insurance
property taxes
Step-by-step explanation: This is the PLATO answer.
Find the equation of the straight line passing through the point (0, 1)
which is perpendicular to the line
y = -2x + 2
:)
Answer:
[tex]y = \frac{1}{2} x+1[/tex]
Step-by-step explanation:
Perpendicular => So, it will have a slope of a negative reciprocal to this slope
Slope = m = 1/2
Now,
Point = (x,y) = (0,1)
So, x = 0 and y = 1
Putting this in slope-intercept equation to get b
=> [tex]y = mx+b[/tex]
=> 1 = (1/2)(0) + b
=> b = 1
Now putting m and b in the slope intercept equation to get the required equation
=> [tex]y = \frac{1}{2} x+1[/tex]
Answer:
y = \frac{1}{2} x+1
Step-by-step explanation:
My fourth number is 39 my fifth number is 43 what is my first number ?
Answer:
27
Step-by-step explanation:
39+4=43
27, 31, 35, 39, 43
Answer:
27
Step-by-step explanation:
When you add u subtract 39 from 43 u will get 4
Therefore u will subtract 4 from 39 to get the third number which is 35 then subtract 4 from it to get the second number which is 31 then subtract another 4 to get the first number that's 27
In studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively as being single and ambitious and having good job prospects. For one group of participants, the description also said that he had a great sense of humor. For another group, it said that he has no sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive). A score of 4 indicates a neutral rating. The females who read the "great sense of humor" description gave the potential partner an average attractiveness score of M = 4.53 with a standard deviation of s = 1.04. If the sample consisted of n = 16 participants, is the average rating significantly higher than neutral (μ = 4)? Use a one-tailed test with α = .05
Answer:
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
Step-by-step explanation:
Step(i):-
The Population of the mean 'μ' =4
sample size 'n' = 16
sample mean 'x⁻' = 4.53
given sample standard deviation 's' = 1.04
level of significance α = 0.05
Step(ii):-
Null hypothesis:H₀ : There is no significance difference between two means
Alternative hypothesis : H₁: There is significance difference between two means
Test statistic
[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{4.53-4}{\frac{1.04}{\sqrt{16} } }[/tex]
t = 2.038
Degrees of freedom ν = n-1 = 16-1 =15
t₀.₀₂₅ = 2.145
Conclusion:-
The calculated value t = 2.038< 2.145 at 0.05 level of significance
Null hypothesis is accepted
There is the average rate is less than μ ≤ 4
write the equation of the line that passes through the points(7, —4) and (—1, 3) first point-slope form, and then im slope-intersept form.
Answer:
The slope of the line is -7/8
When the point (7, –4) is used, the point-slope form of the line is
y+4=(-7/8)(x-7)
The slope-intercept form of the line is y=(-7/8)x+(17/8)
Step-by-step explanation:
In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Answer:0.92
Step-by-step explanation:
Given
[tex]57\%[/tex] of Population is vaccinated
So, Probability of a person being vaccinated is [tex]P=0.57[/tex]
and simultaneously , probability of not vaccinated is [tex]1-P[/tex]
[tex]=1-0.57=0.43[/tex]
Now, Probability that atleast one of them has been vaccinated is given by
[tex]=1-P(\text{None of them is vaccinated})[/tex]
[tex]=1-0.43\times 0.43\times 0.43[/tex]
[tex]=1-0.0795[/tex]
[tex]=0.92[/tex]
Answer:
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
Step-by-step explanation:
Step(i):-
Given 57 % of the people have been vaccinated
p = 57% =0.57
q = 1-p =1-0.57 = 0.43
n = 3
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
Step(ii):-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = P( x =1) + P(x =2)+P(x=3) [tex]P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}[/tex]
[tex]P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}[/tex]
= 0.316179 + 0.419121 +0.185193
= 0.920493
Final answer:-
The probability that AT LEAST ONE of them has been vaccinated
P( X ≥1) = 0.920493
Complete the table to investigate dilations of
exponential functions.
2
2*
3-2
23.x
-2
1
4
3
4
64
1
8
-1
2
2 3 4
0
a
c
d
e
1
2
4.
12
64
Answer: itz 780
Step-by-step explanation:
Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?
Answer:
87.49% probability that the sample average was less than 375 days
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]
What is the probability that the sample average was less than 375 days?
This is the pvalue of Z when X = 375. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{375 - 359}{13.95}[/tex]
[tex]Z = 1.15[/tex]
[tex]Z = 1.15[/tex] has a pvalue of 0.8749.
87.49% probability that the sample average was less than 375 days
The graph of a line passes through the points (0,5) and (-10, 0). What is the
equation of the line?
Answer:
The equation is y=1/2x+5
Step-by-step explanation:
Answer:
y=1/2x+5
Step-by-step explanation:
I learned this last year. I know this is the answer
The point A(5, -2) has been transformed to A'(-5, 2). The transformation is described as ______.
Answer:The transformation is described as a rotation of 180 degrees clockwise around the origin.
Step-by-step explanation:
2(v-1) + 8 = 6(2v -4)
Choose statement that solves the solution
Answer:
V=3
Step-by-step explanation:
2(v-1)+8=6(2v-4)
2V-2+8=12v-24(calculate)
2v+6=12v-24(move terms)
2v-12v=-24-6(collect like terms)
-10v=-30(devide both sides by-10)
V=3
hi I hope this helps.
express 1)32.12353535... 2)2.3333...+4.15151515... as a fraction in simplest form
(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .
Subtracting these gives
10000x - 100x = 321235.353535... - 3212.353535...
9900x = 321235 - 3212
9900x = 318023
x = 318023/9900
(2) By the same process as above, we start with
x = 2.333...
y = 4.151515...
Then
10x = 23.333...
==> 10x - x = 23.333... - 2.333...
==> 9x = 23 - 2
==> x = 21/9
and
100y = 415.151515...
==> 100y - y = 415.151515... - 4.151515
==> 99y = 415 - 4
==> y = 411/99
After this, we get
x + y = 2.333... + 4.151515...
==> x + y = 21/9 + 411/99
==> x + y = 231/99 + 411/99
==> x + y = 642/99 = 214/33
What’s the correct answer for this question?
Answer: choice A
Step-by-step explanation:
The shaded area represents the complement of B.
Bc or B’ is the complement of B and B’=1-B or B’=S-B
The probability that Events A and B occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B), which in this example would be equal to B.
The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B), which in this example is equal to S.
6th grade math help me ! :D...
Answer: D) 180 Minutes
Step-by-step explanation:
If every hour is equal to 60 minutes and the movie (Lord of the Rings) was 3 hours longs...then we just have to multiply....
60 x 3 = 180
I hope this helps!
If the first term in an arithmetic sequence is -3 and the tenth term is 15, what is the common difference?
A. d = 2
B. d = 3
C. d = 6
D. d = 12
Answer:
2
Step-by-step explanation:
a10=a1+(n-1)d
15=-3+(10-1)d
15+3=9d
d=2
you have 4 reindeer, Bloopin, Balthazar, gloopin abd prance, and you want to have 3 fly your sleigh. you always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer?
Answer:
24
Step-by-step explanation:
There are 4 options for the first reindeer.
After the first reindeer is selected, there are 3 options left for the second reindeer.
After the second reindeer is selected, there are 2 options left for the final reindeer.
The number of possible permutations is:
₄P₃ = 4×3×2 = 24
Convert 78% to a decimal
78% means 78/100=0.78
What’s the value of x?
Answer:
Step-by-step explanation:
here ,
6x +238 = 3x+178 ( vertically opposite angles are equal)
so 6x - 3x = 178 -238
3x =-60
x =-60/3
x=-20
hope it helps / please mark me as the brainliest..
Answer:
x= -20
Step-by-step explanation:
The 2 angles are opposite each other. Therefore, they are vertical angles and congruent. We can set them equal to each other and solve.
6x+238=3x+178
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
First, subtract 3x from both sides
6x-3x+238=3x-3x+178
6x-3x+238=178
3x+238=178
Next, subtract 238 from both sides
3x+238-238=178-238
3x=178-238
3x=-60
Finally, divide both sides by 3.
3x/3= -60/3
x=-60/3
x= -20
Researchers at a lake have determined that the percentage of fish in the lake that are intolerant to pollution can be estimated by the function
P(W,R,A)= 49-1.61W-1.41R-1.38A
where W is the percentage of wetland, R is the percentage of residential area, and A is the percentage of agricultural area surrounding the lake. Answer the questions below.
1.Use this function to estimate the percentage of fish that will be intolerant to pollution if 3 percent of the land is classified as wetland, 15 percent is classified as residential, and 0 percent is classified as agricultural.
(Note: The land can also be classified as forest land.)
2. What is the maximum percentage of fish that will be intolerant to pollution?
3. Which variable has the greatest influence on P W, R, or A
Answer:
a. 23.02 %
b. 49%
c. W
Step-by-step explanation:
Solution:-
- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:
[tex]P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A[/tex]
Where,
W: percentage of wetland
R: percentage of residential area
A: percentage of agriculture
- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:
[tex]P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\[/tex]
- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.
[tex]P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49[/tex]
- Hence, the maximum value of the function is 49%.
- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.
- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .
One of the great mysteries of the world is my hotdogs and hotdog buns come in packages of different sizes hotdogs come in packs of eight and burns came in packs of 12 at your local store what is the least number of each you can buy in order to have a equal number of hot dogs and buns
Answer:
3 pack of hot dogs and 2 pack of buns 24
Step-by-step explanation:
hot dogs come in packs of 8
burns came in packs of 12
what is the least number of each you can buy in order to have a equal number of hot dogs and buns
so to get equal number
we have to look for the LCM of 8 and 12 = 24
therefore the packs will be equal to product
hot dogs come in packs of 8 = 8*3 = 24
burns came in packs of 12 = 12 *2 = 24
therefore, 3 pack of hot dogs and 2 pack of buns 24
In 1925, Zbigniew Morón published a rectangle that could be dissected into nine different sized squares as shown in the diagram.
The lengths of the sides of these squares are
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
1
,
4
,
7
,
8
,
9
,
10
,
14
,
15
and
18.
What is the area of Morón’s rectangle?
Answer:
Area of the rectangle = 1056 square units
Step-by-step explanation:
Rectangle published could be dissected into nine different squares with different sizes.
Area of the squares with different measure of sides will be,
For side length = 1 unit
Area of the square = (Side)²
= 1²
= 1 square units
For side length = 4 units
Area of the square = 4² = 16 units²
For side length = 7 units
Area of the square = 7² = 49 units²
For side length = 8 units
Area of the square = 8² = 64 units²
For side length = 9 units
Area of the square = 9² = 81 square units
For side length = 10 units
Area of the square = 10² = 100 square units
For side length = 14 units
Area of the square = 14² = 196 square units
For side length = 15 units
Area of the square = 15² = 225 square units
For side length = 18 units
Area of the square = 18² = 324 square units
Total area of the rectangle by adding these 9 squares
= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324
= 1056 square units
Gale wants to buy tickets to the aquarium or the wave pool and invite some friends. He sets up a table to track the total cost for the tickets at each place to determine the best value. Use the drop-down menus to select appropriate column labels.
Column 1 label:
Column 2 label:
Column 3 label:
here are the label options
Gale
tickets
total cost for aquarium
total cost for wave pool
Answer:
This is the answer EDGE 2020
6(a–1.4)=3.5a+1.6
Please answer fast!
In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 119 out of 415 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05 level of significance.What is the hypothesized population proportion for this test?
Answer:
We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
Step-by-step explanation:
We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children
However, in the special program for talented and gifted children, 119 out of 415 students are only children.
Let p = proportion of only children in the special program.
So, Null Hypothesis, [tex]H_0[/tex] : p = 24% {means that the proportion of only children in the special program is equal to the proportion for the school district}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 24% {means that the proportion of only children in the special program is significantly different from the proportion for the school district}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of only children in the special program = [tex]\frac{119}{415}[/tex] = 0.29
n = sample of students = 415
The hypothesized population proportion for this test is 0.24.
So, the test statistics = [tex]\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }[/tex]
= 2.385
The value of z test statistic is 2.385.
Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 49 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?
a. More than 59 pounds
b. More than 56 pounds
c. Between 56 and 57 pounds
d. Less than 53 pounds
e. Less than 49 pounds
Answer:
a) 10.38% probability that the sample mean will be more than 59 pounds.
b) 67.72% probability that the sample mean will be more than 56 pounds.
c) 22.10% probability that the sample mean will be between 56 and 57 pounds.
d) 1.46% probability that the sample mean will be less than 53 pounds.
e) 0% probability that the sample mean will be less than 49 pounds.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 56.8, \sigma = 12.2, n = 49, s = \frac{12.2}{\sqrt{49}} = 1.74285[/tex]
a. More than 59 pounds
This is 1 subtracted by the pvalue of Z when X = 59. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 56.8}{1.74285}[/tex]
[tex]Z = 1.26[/tex]
[tex]Z = 1.26[/tex] has a pvalue of 0.8962.
1 - 0.8962 = 0.1038
10.38% probability that the sample mean will be more than 59 pounds.
b. More than 56 pounds
This is 1 subtracted by the pvalue of Z when X = 56. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228.
1 - 0.3228 = 0.6772
67.72% probability that the sample mean will be more than 56 pounds.
c. Between 56 and 57 pounds
This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56. So
X = 57
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{57 - 56.8}{1.74285}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a pvalue of 0.5438
X = 56
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228.
0.5438 - 0.3228 = 0.2210
22.10% probability that the sample mean will be between 56 and 57 pounds.
d. Less than 53 pounds
This is the pvalue of Z when X = 53.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{53 - 56.8}{1.74285}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
1.46% probability that the sample mean will be less than 53 pounds.
e. Less than 49 pounds
This is the pvalue of Z when X = 49.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49 - 56.8}{1.74285}[/tex]
[tex]Z = -4.48[/tex]
[tex]Z = -4.48[/tex] has a pvalue of 0.
0% probability that the sample mean will be less than 49 pounds.
Marie bought 5 1/2 gallons of paint. She uses 1/3 of the paint for a bedroom. How many gallons of paint did Marie use?
Answer:
1 5/6 gallons
Step-by-step explanation:
1. 5 1/2 = 11/2 gallons
2. She uses: 1/3 x 11/2 = 11/6 gallons
3. so: 11/6 = 1 5/6 gallons
I'M MARIE!!!
The best player on a basketball team makes 70% of all free throws. The second-best player makes 65% of all free throws. The third-best player makes 55% of all free throws. Based on their experimental probabilities, estimate the number of free throws each player will make in his or her next 60 attempts. Explain.
For the best player, one equation that gives the estimated number of free throws is
▼
The best player will make about
nothing free throws.
Answer:
Best: 42/60 free throws
Second Best: 39/60 free throws
Third Best: 33/60 free throws
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of the model of moon = 4/3(πr³)
= 4/3(π)(1)³
= 4.2 feet³
Volume of cylinder = πr²h
= (3.14)(0.5)²(0.5)
= 0.39 feet³
Cylindrical clay boxes to be used = 4.2/0.39
=10.7 ≈ 11
What does the graph of f(x)=(x-3)^2+12 look like
Answer:
see attached for a graph
Step-by-step explanation:
When g(x) is transformed to
f(x) = f(x -h) +k
The graph of g(x) is translated h units right and k units up.
__
Here, the function g(x) = x^2 is transformed to ...
f(x) = g(x -3) +12 = (x -3)^2 +12
Then the graph of f(x) is the graph of g(x)=x^2 translated 3 units right and 12 units up.
Find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution. (Enter your answer using interval notation.) (x − 5)y'' + 3y = x, y(0) = 0, y'(0) = 1
Answer:
The largest interval is [tex]-\infty < 0 < 5[/tex]
Step-by-step explanation:
From the question the equation given is
[tex](x-5)y'' + 3y = x \ \ \ y(0) = 0 \ , y'(0) = 1[/tex]
Now dividing the both sides of this equation by (x-5)
[tex]y'' + \frac{3y}{(x-5)} = \frac{x}{x-5}[/tex]
Comparing this equation with the standard form of 2nd degree differential which is
[tex]y'' + P(x)y' + Q(x) y = R(x)[/tex]
We see that
[tex]Q(x) = \frac{3y}{(x-5)}[/tex]
[tex]R(x) = \frac{x}{(x-5)}[/tex]
So at x = 5 [tex]Q(x) \ and \ R(x)[/tex] are defined for this equation because from the equation of [tex]Q(x) \ and \ R(x)[/tex] x = 5 give infinity
This implies that the largest interval which includes x = 0 , P(x) , Q(x) , R(x ) is
[tex]-\infty < 0 < 5[/tex]
This because x = 5 is not defined in y domain
