how many hours of physical activity are you required to complete to receive credit for the physical education course

Answer:

B

Step-by-step explanation:

Answer:

x=-14 and x=-1

Step-by-step explanation:

x+6=-7                 x-6=-7

x=-14                      x=-1

Using trigonometry, the angle of elevation of the top of the building from A is 36.87 degrees

The angle of elevation of the building from A, we can apply the concept of trigonometry;

tan(θ) = opposite/adjacent

tan(θ) = height/180m

Since we're given that the angle of the top of the building is 45 degrees when the man is 180m away from point A, we can set up the equation:

tan(45°) = height/180m

The tangent of 45 degrees is 1, so the equation becomes:

1 = height/180m

Solving for the height:

height = 180m

Using the tangent of the angle;

tan(θ) = height/distance

tan(θ) = 180m/240m

Simplifying:

tan(θ) = 0.75

θ = tan⁻¹(0.75)

θ = 36.87 degrees

Therefore, the angle of elevation of the top of the building from point A is approximately 36.87 degrees.

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Answer:

7%

173

Step-by-step explanation:

Given that :

Daily sales last week = 200

Daily sales this week = 186

% decrease in newspaper circulation :

(Decrease / initial amount) * 100%

((200 - 186) / 200) * 100%

(14 / 200) * 100%

0.07 * 100%

= 7%

Part B: If circulation decreases by the same percent next week, what will the daily circulation be?

7% decrease the following week :

(100% - 7%) of 186

93% * 186

0.93 * 186

= 172.98

= 173

Answer:

The correct option is (a).

Step-by-step explanation:

We need to find the expression that is equivalent to 1.5(6x+3y)+2x-0.05y.

Firstly opening brackets as follows :

\(1.5(6x+3y)+2x-0.05y=1.5\times 6x+1.5\times 3y+2x-0.05y\\\\=9x+4.5y+2x-0.05y\)

Now taking x terms and y terms together

\(9x+4.5y+2x-0.05y=(9x+2x)+(4.5y-0.05y)\\\\=11x+4.45y\)

So, 1.5(6x+3y)+2x-0.05y is equal to 11x+4.45y.

The upper control limit (UCL) at a 99% confidence interval with a z value of 3 is 0.165.(option c)

In statistical process control, the UCL is a key parameter used to determine the upper boundary for acceptable variation in a process. To calculate the UCL for a defect rate, we use the formula UCL = p' + z * sqrt(p'(1-p')/n), where p' is the proportion of defects in the sample, z is the z value corresponding to the desired confidence level, and n is the sample size.

In this case, we have collected 20 samples of 100 items each, and the total number of defective items is 75. Therefore, the proportion of defects in the sample is 75/2000 = 0.0375. Using the formula mentioned earlier, with a z value of 3 and n value of 100, we can calculate the UCL as follows: UCL = 0.0375 + 3 * sqrt(0.0375 * (1-0.0375)/100) ≈ 0.165.

Therefore, the correct answer is C. 0.165.

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Answer:

\( \displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }\)

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

\( \displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5, \)

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

the steps for solving a linear homogeneous recurrence relation are as follows:

Step-1:Create the characteristic equation

\( {x}^{2} - 7x+ 12= 0\)

Step-2:Solve the polynomial by factoring

factor the quadratic:

\(( {x}^{} - 4)(x - 3) = 0\)

solve for x:

\(x = \rm 4 \:and \: 3\)

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

\( \displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n } \)

so substitute the roots we got:

\( \displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n } \)

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

\( \begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}\)

solve the system of equation which yields:

\( \displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3} \)

finally substitute:

\( \displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }\)

\( \displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}\)

and we're done!

Consider the generating function of the sequence \(a_n\), defined by

\(A(z) = \displaystyle \sum_{n=0}^\infty a_nz^n = a_0 + a_1z + a_2z^2 + \cdots\)

(this is also known as the Z-transform of \(a_n\))

While the given sequence isn't exactly defined for n = 0, we can use the recurrence to extend it to cover this case. For n = 0, we get

\(a_2 - 7a_1 + 12a_0 = 0 \implies a_0 = -\dfrac16\)

Since for all n ∈ {0, 1, 2, …} we have that

\(a_{n+2}-7a_{n+1}+12a_n=0\)

Multiplying both sides by \(z^n\) and summing over all n gives the relation

\(\displaystyle \sum_{n=0}^\infty a_{n+2}z^n - 7 \sum_{n=0}^\infty a_{n+1}z^n + 12 \sum_{n=0}^\infty a_nz^n = 0\)

Manipulate the first two series to get them in terms of A(z) :

\(\displaystyle \sum_{n=0}^\infty a_{n+2}z^n = \frac1{z^2}\sum_{n=0}^\infty a_{n+2}z^{n+2} \\\\ \sum_{n=0}^\infty a_{n+2}z^n = \frac1{z^2} \sum_{n=2}^\infty a_nz^n \\\\ \sum_{n=0}^\infty a_{n+2}z^n = \frac1{z^2}\left(\sum_{n=0}^\infty a_nz^n - a_0 - a_1z\right) \\\\ \sum_{n=0}^\infty a_{n+2}z^n = \frac{A(z)-\frac16-z}{z^2}\)

and

\(\displaystyle \sum_{n=0}^\infty a_{n+1}z^n = \frac1z \sum_{n=0}^\infty a_{n+1}z^{n+1} \\\\ \sum_{n=0}^\infty a_{n+1}z^n = \frac1z\sum_{n=1}^\infty a_nz^n \\\\ \sum_{n=0}^\infty a_{n+1}z^n = \frac1z\left(\sum_{n=0}^\infty a_nz^n - a_0\right) \\\\ \sum_{n=0}^\infty a_{n+1}z^n = \frac{A(z)-\frac16}{z}\)

The third series is simply A(z).

Solve this new recurrence for A(z) :

\(\displaystyle \frac{A(z)-\frac16-z}{z^2} - \frac{7A(z)-\frac76}{z} + 12 A(z) = 0 \\\\ \frac{A(z)}{z^2}-\frac{7A(z)}{z} + 12A(z) = \frac1{6z^2}+\frac1z-\frac7{6z} \\\\ \frac{A(z)-7zA(z)+12z^2A(z)}{z^2} = \frac{1-z}{6z^2} \\\\ \frac{1-7z+12z^2}{z^2}A(z) = \frac{1-z}{6z^2} \\\\ A(z) = \frac{1-z}{6(1-7z+12z^2)}\)

The next step is to find the power series expansion for A(z) to recover \(a_n\). Factorize the denominator, then decompose A(z) into partial fractions:

\(1-7z+12z^2 = (1-3z)(1-4z)\)

\(\displaystyle \frac{1-z}{(1-3z)(1-4z)} = \frac a{1-3z} + \frac b{1-4z} \\\\ 1-z = a(1-4z) + b(1-3z) \\\\ 1-z = a+b + (-4a-3b)z \\\\ \implies a=-2, b=3\)

\(\implies \displaystyle A(z) = \frac16\left(\frac3{1-4z} - \frac2{1-3z}\right)\)

Recall that for |z| < 1, we have

\(\displaystyle \sum_{n=0}^\infty z^n = \frac1{1-z}\)

Then if |4z| < 1, we can write A(z) as the sum of two convergent geometric series,

\(\displaystyle A(z) = \frac12 \sum_{n=0}^\infty (4z)^n - \frac13 \sum_{n=0}^\infty (3z)^n\)

and some rewriting to put this in the canonical G.F. form lets us easily pick out \(a_n\).

\(\displaystyle A(z) = \sum_{n=0}^\infty \left(\frac{(4z)^n}2 - \frac{(3z)^n}3 \right) \\\\ A(z) = \sum_{n=0}^\infty \left(\frac{2^{2n}}2 - \frac{3^n}3\right)z^n \\\\ A(z) = \sum_{n=0}^\infty \left(2^{2n-1} - 3^{n-1}\right)z^n\)

\(\implies \boxed{a_n = 2^{2n-1} - 3^{n-1}}\)

Clare needs to have her air conditioner repaired, and the total cost for parts is $61.60, with a labor rate of $30.00 per hour. The total cost to fix the air conditioner, including parts and labor, is $136.60. The number of hours the job will take is 2.5 hours.

To find the number of hours the job will take, write an equation using the given information:

Total Cost = Cost of Parts + (Labor Rate × Hours of Labor)

Plug in the known values:

$136.60 = $61.60 + ($30.00 × Hours of Labor)

Now, isolate the variable (Hours of Labor) by subtracting the cost of parts from the total cost:

$75.00 = $30.00 × Hours of Labor

Next, divide both sides of the equation by the labor rate ($30.00):

Hours of Labor = $75.00 / $30.00

Hours of Labor = 2.5

So, it will take 2.5 hours of labor to complete the job.

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If I offered to bet you a tasty beverage that I could toss a coin ten times and produce a sequence of heads and tails that has less than a 1 in 1000 chance of occurring, your chances of winning the bet is 0.99902.

If the coin is fair, the likelihood of getting a head or a tail in a coin toss is equal.

P(H) = P(T)

P(H) = 0.5

The coin has now been tossed ten times.

The probability of receiving 10 heads or 10 tails is binomial and equal.

P(X=10) = \(^{10}\textrm{C}_{10}\) · (0.5)¹⁰ · (1-0.5)⁰

P(X=10) = \(\frac{10!}{10!(10-10)!}\) · 0.00098 · (0.5)⁰

P(X=10) = \(\frac{10!}{10!0!}\) · 0.00098 · 1

P(X=10) = 0.00098

P(X=10) = 0.00098

You win the bet if the dealer does not now deliver a string of 10 heads.

As a result, your chances of winning the wager are 1 - 0.00098 = 0.99902. This is quite high, thus you ought to accept the wager.

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Ok, evaluate the function of f(5) is just to replace x=5 in the function, so let's do it:

This mean that f(5)=19.

The angle of elevation from Phillip to the space shuttle is 1.64°, calculated using the Pythagorean theorem and the square root of both sides.

Given that Phillip is watching a space shuttle launch from an observation spot 66 miles away and the space shuttle is at a height of 1.9 miles. The angle of elevation from Phillip to the space shuttle can be found using the following formula: tan θ = opposite/adjacent Where θ is the angle of elevation, opposite is the height of the shuttle, and adjacent is the distance between the shuttle and the observation spot. Using the Pythagorean theorem, we can find the hypotenuse as follows:hypotenuse² = opposite² + adjacent²Substituting the given values, we get:hypotenuse² = 1.9² + 66²= 3.61 + 4,356= 4,359.61Taking the square root of both sides, we get: hypotenuse ≈ 66.083 miles Substituting the given values in the first formula to find the angle of elevation, we get: tan θ = 1.9/66.083θ

tan⁻¹(1.9/66.083)θ ≈ 1.64°Therefore, the angle of elevation from Phillip to the space shuttle is approximately 1.64°.

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An even number of data values will always have two middle numbers, and an odd number of data values will always have one middle value. Therefore, the true statements are:

An even number of data values will always have two middle numbers.

An odd number of data values will always have one middle value.

What is even number?

An even number is an integer that is divisible by 2, i.e., when divided by 2, the remainder is 0. Examples of even numbers are 2, 4, 6, 8, 10, 12, etc.

The statement "an even number of data values will always have two middle numbers" is true. When there is an even number of data values, there is no single middle number because there are two values in the center.

For example, in the set {1, 2, 3, 4}, the middle numbers are 2 and 3. In general, if there are an even number of data values, the middle two values are found by taking the average of the two values in the center of the set. This is different from the case when there is an odd number of data values, where there is a single middle value.

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Answer:

955$

Step-by-step explanation:

there is your answer

Answer:

B multiply -6 and 3

After the solution of the expression 3x/2-|x| ≤ 1 the interval notation is:

\(\left(-2, \frac{1}{2}\right] \cup(2, \infty)\)

So, get x, by simplification of both sides of the inequality before isolating the variable.

Form of Inequality:

Interval notation:

(Refer to the graph diagram given below)

Therefore, after the solution of the expression 3x/2-|x| ≤ 1 the interval notation is:

\(\left(-2, \frac{1}{2}\right] \cup(2, \infty)\)

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The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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Answer:2 3/ 8

Step-by-step explanation: 5 1/8 - 2 3/4

                                            = 41/ 8  - 11/4

                                          = 41/8 - 22/8

                                           =19/8

                                        =2 3/ 8

Change to improper fraction .Then make the denominator the same ,make both denominator to 8 . Now you have 41/8 and 22/8 ,you can subtract it and it gives you 19/8.Lastly you make the improper fraction to mixed  numbers which is 2 3/ 8 .

a.The probability that X > 37, P(X > 37) = 0.9641

b. P(X < 41) = 0.1587

c. X = 39

d. X = 42 and X = 50 (symmetrically distributed around the mean)

a. To find the probability that X > 37, we need to calculate the area under the normal distribution curve to the right of 37. Using the z-score formula:

z = (X - μ) / σ

where X is the given value, μ is the mean, and σ is the standard deviation, we can calculate the z-score:

z = (37 - 46) / 5 = -1.8

Using the cumulative standardized normal distribution table, we can find the corresponding probability. The table indicates that P(Z < -1.8) = 0.0359.

Since we are interested in P(X > 37), which is the complement of P(X ≤ 37), we subtract the obtained value from 1:

P(X > 37) = 1 - 0.0359 = 0.9641 (rounded to four decimal places)

b. To find the probability that X < 41, we calculate the z-score:

z = (41 - 46) / 5 = -1

From the cumulative standardized normal distribution table, we find that P(Z < -1) = 0.1587.

Therefore, P(X < 41) = 0.1587 (rounded to four decimal places).

c. To find the X-value for which 10% of the values are less, we need to find the corresponding z-score. From the cumulative standardized normal distribution table, we find that the z-score for a cumulative probability of 0.10 is approximately -1.28.

Using the formula for the z-score:

z = (X - μ) / σ

we rearrange it to solve for X:

X = μ + (z * σ)

X = 46 + (-1.28 * 5) ≈ 39 (rounded to the nearest integer)

Therefore, 10% of the values are less than X = 39.

d. To find the X-values between which 60% of the values are located, we need to determine the z-scores corresponding to the cumulative probabilities that bracket the 60% range.

Using the cumulative standardized normal distribution table, we find that a cumulative probability of 0.20 corresponds to a z-score of approximately -0.84, and a cumulative probability of 0.80 corresponds to a z-score of approximately 0.84.

Using the z-score formula:

X = μ + (z * σ)

X1 = 46 + (-0.84 * 5) ≈ 42 (rounded to the nearest integer)

X2 = 46 + (0.84 * 5) ≈ 50 (rounded to the nearest integer)

Therefore, 60% of the values are between X = 42 and X = 50.

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The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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Step-by-step explanation:

hope it helps if there's any questions feel free to ask me but I'm sure that's how that question is hanled

Answer:

\(sln \\ (1 \times 10000) + (9 \times 1000) + (5 \times 100) + (2 \times 10) \\ 10000 + 9000 + 500 + 20 \\ 19520\)

♡ The Question/Task ♡    

(1 × 10,000) + (9 × 1,000) + (5 × 100) + (2 × 10)  

The expanded notation of a number is shown. What is the number written in standard form?  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*    

♡ The Answer ♡    

19,520 / 19520  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*    

♡ The Explanation/Step-By-Step ♡    

Solve individually!

1 x 10,000 = 10,000

9 x 1,000 = 9,000

5 x 100 = 500

2 x 10 = 20

Add together!

10,000 + 9,000 + 500 + 20 = 19,520  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*    

♡ Tips ♡    

Copy and Paste your equation, for example, (1 × 10,000) + (9 × 1,000) + (5 × 100) + (2 × 10), into a browser! It'll automatically solve with a calculator, and the answer will appear in an answer bar.

The odds in favor of the event happening are 5 to 4.

We have,

To find the odds in favor of an event happening, we use the formula:

Odds in favor = Probability of the event happening / Probability of the event not happening

In this case,

The probability of the event happening is 5/9.

The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:

Odds in favor

= 5/9 / 4/9

= 5/4

Therefore,

The odds in favor of the event happening are 5 to 4.

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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The calculation; (9.04-8.23+21.954+81.0) * 3.1416 should have three significant figures.

To determine the number of significant figures in a calculation, we follow these rules:

1. When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

2. When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Let's calculate the expression:

(9.04 - 8.23 + 21.954 + 81.0) * 3.1416

First, perform the addition and subtraction:

(0.81 + 21.954 + 81.0) * 3.1416

= 103.764 * 3.1416

Next, perform the multiplication:

325.8512544

To determine the number of significant figures, we look at the original numbers involved in the calculation.

9.04 has three significant figures.

8.23 has three significant figures.

21.954 has five significant figures.

81.0 has three significant figures.

3.1416 has five significant figures.

Among these numbers, the number with the fewest significant figures is 81.0 with three significant figures.

Therefore, the result of the calculation, 325.8512544, should have three significant figures to match the least precise value.

In scientific notation, the result would be expressed as 3.26 x 10^2.

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The given calculation would yield a result with five significant figures because we base our significant digits off of the least precise term within the parentheses, which is 81.0. The result is then rounded according to this rule.

In the case of the calculation (9.04-8.23+21.954+81.0) * 3.1416, it's important to first consider the rule for significant figures in calculations - the result should be reported with the smallest number of decimal places in the numbers used in the calculation. The number 81.0 has two numbers after the decimal point, therefore, our final answer should have two numbers after the decimal point. When you calculate the inside of the parentheses, the result is 103.764. Multiplying that by 3.1416 would approximately yield 325.854. Rounding this to the least precise measurement (which is to two decimal places due to 81.0) would give us 325.85 which has five significant figures, effectively limiting our calculated value to five significant figures.

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The true statements are,

A.) The pre-image is in quadrant III.

B.) The orientation of the vertices changed.

D.) The line of reflection is the x-axis.

It is determined by the order in which a figure's vertices are labeled. It refers to the sequence of points after a transformation has been applied to a geometric figure. The order may be clockwise or counterclockwise.

Here, we have,

from the given figure ,we get,

the true statements are,

A.) The pre-image is in quadrant III.

B.) The orientation of the vertices changed.

D.) The line of reflection is the x-axis.

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Answer:its b

first off its a straight line ill give it that but its not going through the origin is think its b

hoped this helped lmk if it did

Answer:

linear monomial

Step-by-step explanation:

We can see here that the different orders that she can wear the shorts is 25.

In mathematics, an order refers to the degree or highest exponent of a term in a polynomial equation. For example, the equation y = 3x^2 + 2x + 1 is a polynomial of order 2, because the highest exponent of x is 2.

In computer science, an order is a set of instructions for a computer to perform a specific task. For example, an order can be used to sort a list of numbers in ascending or descending order.

We see here that if the 5 pairs of basketball will go round on every day of the five days. Thus, it is: 5 x 5 = 25.

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Answer:

Correct option is option A

It is because:

The given eqn is y=2x+8 and since the required line is parallel thus its eqn must be y=2x+K.....thus either opion A or B is correct ..To ensure we take the given point (-4,1) which satisfies option A thus it is correct ans