Answer:
0.7857
Step-by-step explanation:
Given :
Mean = 69 inches
Standard deviation, = 2.8 inches
The Zscore of a man who is 71.2 inches
The ZSCORE is obtained using the relation :
Zscore = (Score, x - mean) / standard deviation
Zscore = (71.2 - 69) / 2.8
Zscore = 2.2 / 2.8
Zscore = 0.7857
-09
2 1 point
The amount of a radioactive substance y that remains after t years is given by the equation y = a (e)^kt, where a is the initial
amount present and k is the decay constant for the radioactive substance. If a = 100, y = 50, and k = -0.035, find t.
Answer:
19.80
Step-by-step explanation:
Given the equation :
y = a (e)^kt
If a = 100, y = 50, and k = -0.035, find t.
50 = 100(e)^(-0.035t)
50/100 = e^(-0.035t)
0.5 = e^-0.035t
Take the In
In(0.5) = - 0.035t
-0.693147 = - 0.035t
-0.693147 / - 0.035 = t
19.8042 = t
Hence, t = 19.80
Could you help me and answer a couple questions for me?
Answer:
I think no. D is the answer
ES
What is the mZACB?
А.
10°
B
O 50°
(4x)
O 90°
O 180°
(7x-20)
С
Done
Intro
Answer:
B
O 50° is the mZACB out of the options
Need help please I don’t get it
the e-function stuff can be confusing sometimes, but notices that g(x) / the blue line, is just somewhat lower, rest is the same.
how much lower? look at the y-intercepts
f(0)= "about 5"
g(0)= "about -3"
with this y-intercept only option c can work
The sum of two numbers is 85. If four times the smaller number is subtracted from the larger number, the result is 5. Find the two numbers.
The larger number is
The smaller number is
Answer:
the larger number is 69
the smaller number is 16
Step-by-step explanation:
x is the smaller number
y is the larger number
x + y = 85
y - 4x = 5
y = 5 + 4x
x + 5 + 4x = 85
5x = 80
x = 16
y = 69
An angle with measure of 71° is bisect at what angle?
Answer:
A
Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.
Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
Know
Learn
Booste
V See
Answer:
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
Step-by-step explanation:
To solve these questions, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.
This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]
Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
This is 1 subtracted by the p-value of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997
1 - 0.8997 = 0.1003
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
[tex]\mu = 266, \sigma = 16[/tex]
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
This is the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 266}{16}[/tex]
[tex]Z = -0.375[/tex]
[tex]Z = -0.375[/tex] has a p-value of 0.3539.
0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 20[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]
[tex]Z = -1.68[/tex]
[tex]Z = -1.68[/tex] has a p-value of 0.0465.
0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 50[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]
[tex]Z = -2.65[/tex]
[tex]Z = -2.65[/tex] has a p-value of 0.0040.
0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?
Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.
X = 276
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = 2.42[/tex]
[tex]Z = 2.42[/tex] has a p-value of 0.9922.
X = 256
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
0.9922 - 0.0078 = 0.9844
0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC
Answer:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
Step-by-step explanation:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
What is the y-coordinate of the point that divides the
directed line segment from J to k into a ratio of 2:3?
13
12+
11+
10
9
8
7+
v = ( my mom n Ilv2 – va) + ve
O 6
0-5
6+
05
5
07
5
4+
3+
1 27
Mi
Answer:
5
Step-by-step explanation:
took the test
The coordinates of the point that divides the line segment from J to K into a ratio of 2:3 are P(-5,7), and the y-coordinate is 7, the correct option is D.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Ratio= 2:3
Now,
Let the point we are looking for be denoted as P(x,y), and let the ratio be 2:3, which means that the distance from J to P is 2/5 times the distance from J to K.
Using the distance formula, we can find the distance between J and K as:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
= sqrt((-8 - (-3))^2 + (11 - 1)^2)
= sqrt(25 + 100)
= sqrt(125)
The distance from J to P is 2/5 of the total distance, which is:
(2/5)d = (2/5)sqrt(125) = 2sqrt(5)
Using the ratio formula, we get:
x = (3* (-3) + 2 * (-8)) / (3+2) = -5
y = (31 + 211) / (3+2) = 7
Therefore, by the given ratio answer will be 7.
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Can someone help me with this question an my other work?
Which of the following is an acute triangle?
70
30*
24°
45
126
132
36°
90°
45
559 55°
Triangle A
Triangle B
Triangle C
Triangle D
A. Triangle B
B. Triangle A
O
C. Triangle C
O.
D. Triangle D
The correct answer will be option (B) Triangle A
Acute triangleAn acute-angled triangle is a type of in which all the three internal angles of the triangle are acute, that is, they measure less than 90°
How to solve this problem?
The steps are as follow:
In acute triangle the the internal angle should not or greater than 90 degreeIn triangle B one of internal angle is 126 degree which is greater than 90 degree so it is not acute triangleOne internal angle of triangle C is 90 degree so it is also not acute triangleFor triangle D one angle is 132 degree which is greater than 90 degree so it also not acute triangleIn triangle A all the internal angle is less than 90 degree so it is acute triangleSo the triangle A is acute triangle
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Carly is the principal at a middle school and wants to know the average IQ of all the female, seventh-grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Assume that all conditions are met, construct the 96% Confidence interval for the average IQ score of all seventh-grade girls in the school.
Answer:
The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 31 - 1 = 30
96% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.96}{2} = 0.98[/tex]. So we have T = 2.15
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.15\frac{15}{\sqrt{31}} = 5.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 105.8 - 5.8 = 105.
The upper end of the interval is the sample mean added to M. So it is 105.8 + 5.8 = 111.6
The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).
In 2019, 15.9% of Broadway actors were acting in their first role on Broadway. Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers. What are the mean and standard deviation for the sampling distribution of pÌ p^? 1. Mean: 0.159, Standard Deviation: 0.0592. Mean: 0.159, Standard Deviation: 0.36573. Mean: 0.184, Standard Deviation: 0.0634. Mean: 0.184, Standard Deviation: 0.0595. Mean: 0.159, Standard Deviation: 0.063In 2019 the CDC reported that 14.0% of US adults are smokers. Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.What is the mean and the standard deviation of the sampling distribution of pÌ p^ ?1. mean = 0.140, standard deviation = 0.0682. mean = 0.167, standard deviation = 0.0633. mean = 0.140, standard deviation = 0.0634. mean = 0.167, standard deviation = 0.068
Answer:
For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.
For the proportion of smokers, mean = 0.167, standard deviation = 0.068
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.
This means that [tex]p = 0.184, n = 38[/tex]
What are the mean and standard deviation for the sampling distribution of p^?
Mean:
[tex]\mu = p = 0.184[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]
Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.
This means that [tex]n = 30, p = 0.167[/tex]
What is the mean and the standard deviation of the sampling distribution of p^ ?
Mean:
[tex]\mu = p = 0.167[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]
Write the geometric sequence in function notation.
4,2,1,1/2,1/4,...
A) AX) = (2) - (1/4)x - 1
OB) Ax) = (2) - (1/2)x - 1
C) Ax) = (4) · (/4)x - 1
D AX) = (4) · (1/2)x - 1
Answer:
D
Step-by-step explanation:
Solve using the elimination method
x + 5y = 26
- X+ 7y = 22
Answer:
[tex]x=6\\y=4[/tex]
Step-by-step explanation:
Elimination method:
[tex]x+5y=26[/tex]
[tex]-x+7y=22[/tex]
Add these equations to eliminate x:
[tex]12y=48[/tex]
Then solve [tex]12y=48[/tex] for y:
[tex]12y=48[/tex]
[tex]y=48/12[/tex]
[tex]y=4[/tex]
Write down an original equation:
[tex]x+5y=26[/tex]
Substitute 4 for y in [tex]x+5y=26[/tex]:
[tex]x+5(4)=26[/tex]
[tex]x+20=26[/tex]
[tex]x=26-20[/tex]
[tex]x=6[/tex]
{ [tex]x=6[/tex] and [tex]y=4[/tex] } ⇒ [tex](6,4)[/tex]
hope this helps...
Answer:
x = 6, y = 4
Step-by-step explanation:
x + 5y = 26
- x + 7y = 22
_________
0 + 12y = 48
12y = 48
y = 48 / 12
y = 4
Substitute y = 4 in eq. x + 5y = 26,
x + 5 ( 4 ) = 26
x + 20 = 26
x = 26 - 20
x = 6
If 5x = 3x+12 then x = …..
↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]
[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Step-by-step explanation:
Explanation is in the attachmenthope it is h helpful to you
In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.
Point A′ is at
, and point D′ is at
.
Answer:
b
Step-by-step explanation:
There are 100 sheets of paper on table. It takes 10 seconds to count 10 sheets. How many seconds will you need to count 80 sheets?
Answer:
80 seconds
Step-by-step explanation:
10/10 = 1
now it takes 1 seconds to count 1 sheet
80 x 1 = 80 seconds to count 80 sheets
Step-by-step explanation:
10sheets=10seconds
1sheet=1sheet÷10sheets x 10seconds
=1second
80sheets=80sheets÷1sheet x 1second
80seconds
hope this is helpful
Ellen, Nick, and Ryan went shopping together. One of them bought a hat, another bought sunglasses, and another bought a belt. One paid $6, another paid $8, and another paid $10.
1) Nick bought the hat.
2) Ellen spent $8.
3) The belt did not cost $10.
4) Ryan spent the most. Which of the following is true?
(a) Nick bought the hat for $10.
(b) Ellen bought the belt for $8.
(c) Ryan bought the sunglasses for $8.
(d) Ryan bought the belt for $10
(e) Ryan bought the hat for 56.
Answer:
see down
Step-by-step explanation:
d is correct answer
√(9+ √32)
Please simplify
Answer:
3.82
Step-by-step explanation:
[tex]\sqrt{(9+\sqrt{32}) }[/tex] Do not confirm the answer unless your equation looks like that?
[tex]\sqrt{(9+\sqrt{32}) }[/tex] Start by the [tex]\sqrt{32}[/tex]
[tex]\sqrt{(9+5.65) }[/tex] Now add (9 + 5.65)
[tex]\sqrt{14.65}[/tex] Finally Simplify
[tex]3.82[/tex] Final answer
What is the inverse of function f? f(x)=3-x/7
Answer:
[tex] {f}^{ - 1} (x) = \frac{x}{3} + \frac{7}{3} [/tex]
hence option d is the correct option.
Answer:
Option C is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = (3-x) /7
Let f(x) be "y".
y = (3-x) /7
Interchanging "x" and "y".
x = (3-y)/7
7x = 3-y
y = 3-7x
Therefore, f'(x) = 3-7x.
Hope it helps!
if angle ACB = angle DCD, angle BAC = 3x-10, angle ECD= 45degrees, and angle EDC = 2x+10 wgat is x
Answer:
x = 20
Step-by-step explanation:
3x -10 = 2x +10
x = 20
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout($) 2 46 8 10
Probability 0.5 0.2 0.15 0.1 0.05
Expected Value = [?]
The expected payout is
2 × 0.5 + 4 × 0.2 + 6 × 0.15 + 8 × 0.1 + 10 × 0.05
= 1 + 0.8 + 0.9 + 0.8 + 0.5
= 4
The expected value of the winnings from this game is $3.90.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To find the expected value of the winnings, we multiply each possible payout by its probability and then sum these products.
So,
Expected Value = (2 x 0.5) + (4 x 0.2) + (6 x 0.15) + (8 x 0.1) + (10 x 0.05)
Expected Value = 1 + 0.8 + 0.9 + 0.8 + 0.5
Expected Value = 3.9
Therefore,
The expected value of the winnings from this game is $3.90.
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help I don't get it, help
Answer:
No, it is not possible.
Step-by-step explanation:
AB // CD and BC is transversal.
∠ABC = ∠BCD ---> Alternate interior angles are equal.
Here, it is different which is not possible.
Find the size of angle XZY give your answer
Answer:
yeah u forgot to add the picture ig
In 2006, there were 160 teachers in College A, and three fourth of them had their own vehicles. In 2007, 20 new teachers came to the school and 6 of them had own vehicles. Calculate the percentage increase in the numbers of teacher who had own vehicles.
Answer: 5%
Step-by-step explanation:
In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:
= 3/4 × 160
= 120
In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:
= 120 + 6
= 126
The percentage increase will be:
= Increase / Old vehicle owners × 100
= 6/120 × 100
= 1/20 × 100
= 5%
The Percentage increase is 5%.
Convert the following 11110011.001 to decimal
Answer:
243.125
Step-by-step explanation:
First do the integral part
11110011
1. From left to right, starting with a zero,
2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.
The successive results are
1
3
7
15
30
60
121
243
For the decimal part, we proceed similarly but
1. From the right-most digit proceed to the left, start with a zero.
2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.
Successive results are:
0.5
.25
.125
So the final result is 11110011.001 binary is 243.125 decimal
Simultaneous equations 5x-4y=19
X+2y=8
Answer:
x=5
y=3/2
Step-by-step explanation:
Take it or leave it, that's what the computer said.
SCALCET8 3.8.001.MI. A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population consists of two members. Find the population size after seven days. (Round your answer to the nearest whole number.) P(7)
Answer:
A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population · Q: For this discussion, you will work in groups to find the area and answer questions.
Step-by-step explanation:
Two systems of equations are given below. For each system, choose the best description of its solution.
x - 5y = 5
-x + 5y = -5
a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________
Answer:
Infinitely many solutions.
They must satisfy [tex]y = \frac{1}{5}(x - 5)[/tex]
Step-by-step explanation:
Given
[tex]x - 5y = 5[/tex]
[tex]-x + 5y = -5[/tex]
Required
The best description
Add both equations
[tex]x - x - 5y + 5y = 5 - 5[/tex]
[tex]0+0 =0[/tex]
[tex]0 = 0[/tex] ---- this means that the system has infinitely many solutions.
Make y the subject in: [tex]-x + 5y = -5[/tex]
Add x to both sides
[tex]5y = x - 5[/tex]
Divide through by 5
[tex]y = \frac{1}{5}(x - 5)[/tex]
Hence, they must satisfy: [tex]y = \frac{1}{5}(x - 5)[/tex]