if the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____.

Answers

Answer 1

If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.

In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.

To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.

In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.

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Related Questions

Can someone help me out with these two problems and show work please !!

Answers

Answer :

( 6 y^4 + 3 y^2 -7) - (12 y^4 - y^2 + 5)

Step-by-step explanation:

(6 y^4+ 3 y^2-7) - (12 y^4 - y^2 + 5 )

=6 y^4 +3 y ^2 - 7 - 12 y^4 + y^2 - 5

=6 y ^4 - 12 y ^4 +3 y ^2 + y ^2 - 7 -5

= -6 y ^4 + 4 y ^2- 12

Hope this helps!

Can someone help me please?
A. 0.43, because 13 of the 30 days were cloudy.
B.0.35, because 13 of the 37 days were cloudy.
C.0.22, because 13 of the 60 days were cloudy.
D.0.80, because 24 of the 30 days were cloudy.

Answers

Using the probability concept, the correct option of the probability of a day in May being cloudy in Sacramento is:

A. 0.43, because 13 of the 30 days were cloudy.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For Sacramento, 30 days were considering, of which 13 days were cloudy, hence the probability of a day in May being cloudy in Sacramento is given as follows:

p = 13/30 = 0.43.

Hence the correct option is:

A. 0.43, because 13 of the 30 days were cloudy.

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A British pound cost $2.00 in U.S. dollars in 2008, but $1.27 in U.S. dollars in 2017. a)Was the pound weaker or stronger against the dollar

Answers

The pound was stronger in 2008 against the dollar than in 2017.

The Pound to greenback rate reached a high of $2.649 on the sixth Mar 1972. That remains the most powerful the Pound has been towards USD because it freely floated in 1971.

One might count on that the strongest economies might have the most powerful international currencies; but, that is not always the case. It turns out that lengthy-term movements in forex costs are extra essential than alternate quotes, that's why the British pound is worth extra than the U.S. dollar.

What topics is how the price of that forex adjustments over the years relative to different currencies. Historically, for over 20 years one U.S. dollar has been really worth less than one British pound. As of July 31, 2020, the greenback is sitting around 1.32 to at least one pound. 2  this is down from 1.68 in may additionally 2014 and 1. forty in March 2018.

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A group of friends is on a rafting trip. They plan to travel 5 miles downstream and then 5 miles back upstream. They need to finish their rafting trip in 6 hours to allow enough time to get back to their hotel. The group knows that the river is moving at a rate of 2 miles per hour.

Answers

Answer:

I don't understand what the question is what do you need to find?

?? math-domain and range

Answers

Answer:

Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]

Step-by-step explanation:

For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.

Sonny substituted 5 for x in the proportion startfraction 16 over x endfraction = startfraction 48 over 15 endfraction and cross multiplied to get 240 = 240. why is this?

Answers

The cross products of the proportion are equal.

According to the question, Sonny's equation can be written as follows.

16/x = 48/15

Now, the variable x is replaced by the constant 5. So the equation can now be written as follows.

16/5 = 48/15

When two fractions are equal to one another as shown above, the constants are cross multiplied with one another in order to form an equation.

16*15= 48*5

The values of both the products are equal which is 240.

Therefore, because the cross products of the proportion are equal.

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Expand (x – 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.

Answers

The expansion of  (x – 3)^5 is     [tex]x^5-15x^4+90x^3-270x^2+405x-243[/tex]

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power. A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc. Binomial Expression: A binomial expression is an algebraic expression that contains two dissimilar terms.

Pascal's Triangle is a never-ending equilateral triangle in which the arrays of numbers arranged in a triangular manner. The triangle starts at 1 and continues placing the number below it in a triangular pattern

Using Binomial theorem,

=[tex]\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}\left(-3\right)^i[/tex]

=[tex]x^5-15x^4+90x^3-270x^2+405x-243[/tex]

Using Pascal Triangle  for (x-1)

                                               1

                                       1    1              

           1    2    1            

        1    3    3    1        

     1    4    6    4    1      

  1    5    10    10    5    1  

1    6    15    20    15    6    1

Accordingly replacing 1 with 3 we get

= [tex]x^5-15x^4+90x^3-270x^2+405x-243[/tex]

Thus the expansion of  (x – 3)^5 is      [tex]x^5-15x^4+90x^3-270x^2+405x-243[/tex]

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what the picture says

Answers

By applying the law of cosine, the length of side BM is equal to 7.05 cm..

What is a polygon?

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

TriangleQuadrilateralPentagonHexagonNonagonOctagon

Note: The number of sides (n) of a pentagon is 5.

In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:

Interior angle = 180 × (n - 2)/n

Interior angle = 180 × (5 - 2)/5

Interior angle = 180 × 3/2

Interior angle = 108°.

For the central angle, we have:

Central angle, O = 360/5

Central angle, O = 72°.

By applying the theorem of intersecting secants, angle OCB will be given by this formula:

<OCB = ½ × (180 - 72)

<OCB = ½ × 108

<OCB = 54°.

In order to determine the length of side BM, we would apply the law of cosine:

cos(θ) = Adj/Hyp

cos54 = BM/12

BM = 12 × cos54

BM = 12 × 0.5878

Side BM = 7.05 cm.

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Plis help! Will give brainliest! 5th grade math!

Answers

Answer:

(32÷(10-8)÷2)-3

Step-by-step explanation:

(32÷(10-8)÷2)-3

(32÷2÷2)-3

(16÷2)-3

8-3 = 5

Zara is preparing a juice blend.In her recipe, the amount of water is twice the amount of strawberry juice, and amount of lemon juice is 1/5 the amount of strawberry juice. What is the ratio of the lemon water?

Answers

The ratio of the lemon water is 10:1

How to determine the ratio

From the information, we have that;

The ratio of water to strawberry juice  is 2 : 1

That of strawberry juice to lemon juice is 5: 1

The, we have that of water to lemon juice to be 10: 1 when compared

Hence,  the ratio of the lemon water is 10: 1

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SOMEONE HELP PLEASEiiiii

Answers

Answer: (2, -1)

Step-by-step explanation:

[tex]y=-3x^2 +12x-13\\\\y=-3(x^2 - 4x)-13\\\\y=-3\left(\left(x-2 \right)^{2}-4 \right)-13\\\\y=-3(x-2)^{2}+12-13\\\\y=-3(x-2)^2 - 1[/tex]

So, the vertex is (2, -1).

Erin tried to evaluate an expression step by step.
8 x 2 x 5

Step 1
=8×2×5

Step 2
=8×(2×5)

Step 3
=16×10

Answer
=160

Find Erin's mistake.

Need Answer Soon As Possible Please!

Answers

Erin multiplied (8x2) times (2x5) instead of 8 times (2x5)

Answer:

step 2

Step-by-step explanation:

Erin's mistake is in step 2 it should be 8*2 first and 16* 5 which equals to 86

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.7 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answers

The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.

What is the decision rule for the p-value approach to hypothesis testing?

The decision rule based on p-value states,

If p > α (significance level), then the null hypothesis is not rejectedIf p < α (significance level), then the null hypothesis is rejected in favor of the alternative hypothesis.

Calculation:

Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si

So, Defining the hypothesis:

Null hypothesis H0: μ = 5.4

Alternative hypothesis Ha: μ ≠ 5.4

It is given that,

The valve was tested on 24 engines. I.e., Sample size n = 24

The sample mean X = 5.7

Standard deviation σ = 1.0 and

The significance level = 0.05

Since the population distribution is approximately normal,

the test statistic is calculated as follows:

z = (X - μ)/(σ/[tex]\sqrt{n}[/tex])

On substituting the value,

z = (5.7 - 5.4)/(1.0/[tex]\sqrt{24}[/tex])

  = (0.3)/0.204

  = 1.471

Fron this z-score, the p-value is calculated as 0.142.

Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.

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Rewrite the expression in the form x^n

Answers

Answer:

x ^ (1/3)

Step-by-step explanation:

solution:

the answer is in the picture I have sent.

I hope this will help you

2. Is x² + 4√x a polynomial ? Justify your answer. ​

Answers

Answer:

No it isn't

As the variable "x" has root in it which means it isn't a whole number and for a expression to be a polynomial the variable must be whole no.

Hope it helps you!

Answer:

yes

Step-by-step explanation:

A polynomial is an algebraic expression of two or more terms

[tex]x^{2} +4\sqrt{x}[/tex]  It is an algebraic expression of two terms, It is more common to label it binomial, but it is also a polynomial.

Hope this helps

What is the slope of the line that contains the points (4, 3) and (2, 7)?
OA-1
B. -5
C. -2
OD. -

Answers

Answer:

B. -2

Step-by-step explanation:

To find a slope of a line, you have to identify x and y variables:

(4, 3) => (x1, y1) (2, 7) => (x2, y2).

We use the formula;

m = ∆y/∆x

= (y2 - y1)/(x2 - x1)

m is slope

Substitute the values into the formula above.

m = (7 - 3)/(2-4)

= 4/-2

= -2

Therefore, the slope of the line is passing through points (4,3) and (2,

7) is -2.

What is the direction of a line with the slope 3/-2
a, vertical
c. upward, left to right
b, horizontal
d. downward, left to right

Answers

Answer: b

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The weight of a baby during the birth is 3 kilograms and it increased to 6 kilograms after 8 months. find the average rate of change in weight.

Answers

The average rate of change in weight is 3/8.

According to the statement

Weight of baby during birth = 3 kg

Weight of baby after 8 months = 6 kg

Average rate of change of in weight is calculated by

Average rate = Increased weight - Real weight / Time period

Average rate = 6-3 / 8

Average rate = 3/8

So, the average rate of change in weight is 3/8.

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the bus bound for northtown departs every 15 minutes and the bus for eastown departs every 18 minutes from the central station. Both buses start at 9:30 AM each morning. When is the next time both buses will depart from the central station at the same time?

Answers

Considering the least common factor of 15 and 18, it is found that they will depart from the central station at the same time at 11 AM.

How to find the time it takes for periodic events to repeat at the same time?

To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.

In this problem, the periods are of 15 and 18, hence their lcm is found as follows:

15 - 18|2

15 - 9|3

5 - 3|3

5 - 1|5

1 - 1

Hence:

lcm(15,18) = 2 x 3 x 3 x 5 = 90 minutes.

They will depart from the central station at the same time in 90 minutes from 9:30 AM, hence at 11 AM.

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What kind of sequence is this? 206, 190, 174, 158

Answers

Answer:

Arithmetic

Step-by-step explanation:

Arithmetic Sequence is a sequence that has common difference - a common difference is same difference in a sequence. If we take next term to subtract the previous term and you keep getting same difference or value then that's a common difference. It can be mathematically expressed as an equation of:

[tex]\displaystyle{d=a_{n+1}-a_n}[/tex]

Now, I'll show why the sequence is arithmetic - take the sequence to subtract for common difference:

190 - 206 = -16174 - 190 = -16158 - 174 = -16

Notice how we keep getting -16 after subtracting previous term with next term. Hence this sequence is arithmetic sequence for sure!

Geometric Sequence is a sequence with common ratio - a common ratio is similar to common difference except ratio is all about division. Since common difference is expressed as subtraction of next term and previous term then common ratio is division of next term and previous term which can be mathematically expressed as:

[tex]\displaystyle{r = \dfrac{a_{n+1}}{a_n}}[/tex]

However this sequence is not geometric sequence because if you divide next term with previous term then you'll keep getting difference result and common ratio means having same ratio or constant ratio for entire sequence.

Now see why this sequence cannot be geometric sequence:

190/206 = 0.922174/190 = 0.915158/174 = 0.908

Notice that none of values are equal and thus, this sequence doesn't have common ratio which leads to not being geometric sequence.

Lightfoot Inc., a software development firm, has stock outstanding as follows: 30,000 shares of cumulative preferred 2% stock, $25 par, and 38,000 shares of $75 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $5,700; second year, $9,600; third year, $59,720; fourth year, $117,220.

Answers

The calculation of the dividends per share on each class of stock for each of the four years for Lightfoot Inc. are:

                                 1st Year       2nd Year       3rd Year      4th Year

Preferred stock          $0.19            $0.32            $0.99          $0.50

Common stock           $0                 $0                $0.79          $2.69

How is dividend per share calculated?

The dividend per share for each class of stock can be computed by dividing the total dividend distributed by the number of shares outstanding.

For cumulative preferred stock, the unpaid dividends in a year are carried forward for distribution when profits are made.  Note also that preferred stock dividends enjoy preferential payment before common stock dividends.

Data and Calculations:

Cumulative preferred stock = 30,000 shares

Par value of preferred stock = $25

Dividend rate = 2%

The total value of preferred stock = $750,000 ($25 x 30,000)

Expected annual dividend for preferred stockholders = $15,000 ($750,000 x 2%)

Common stock = 38,000 shares

Par value of common stock = $75

The total value of ordinary stock = $2,850,000 ($75 x 38,000)

Dividends distribution:

                                        1st Year       2nd Year       3rd Year      4th Year

Dividends distributed    $5,700           $9,600       $59,720       $117,220

Preferred stock             $5,700            $9,600      $29,700        $15,000

Preferred stock per share $0.19           $0.32        $0.99             $0.50 ($15,000/30,000)

Common stock                  $0                   $0         $30,020      $102,220

Common stock per share $0                  $0            $0.79           $2.69 ($102,220/38,000)

Thus, the dividends distribution of Lightfoot Inc. shows that the common stockholders started earning dividends after the second year.

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Question Completion:

Calculate the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "O."

Help me please help me fast

Answers

The value of [tex]f^{-1}(49)[/tex] is 4

Inverse of a function

The given function is:

[tex]f(x)=(x+3)^2[/tex]

Let f(x) be represented by y

[tex]y=(x+3)^2[/tex]

Make x the subject of the formula

[tex]\sqrt{y} =x+3[/tex]

Subtract 3 from both sides

[tex]x=\sqrt{y} -3[/tex]

Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x

[tex]f^{-1}(x)=\sqrt{x} -3[/tex]

Substitute x = 49 into the inverse function

[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]

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PLS HELP PLS
Determine the length of side QR in the following triangle

Answers

Answer:

12.22 cm

Step-by-step explanation:

We'll be using cosine laws to solve for QR side:

[tex]\displaystyle{QR^2 = QP^2+RP^2-2QP\cdot RP \cdot \cos P}[/tex]

We know that QP = 13 cm, RP = 4 cm and cosP = 70°. Hence:
[tex]\displaystyle{QR^2=13^2+4^2-2(13)(4)\cos 70^{\circ}}[/tex]

Then evaluate the expression:

[tex]\displaystyle{QR^2=169+16-104 \cos 70^{\circ}}\\\\\displaystyle{QR^2=185-104\cos 70^{\circ}}\\\\\displaystyle{QR^2=185-35.57}[/tex]

Square root both sides, since length can only be positive. The negative side will be cancelled:

[tex]\displaystyle{\sqrt{QR^2}=\sqrt{185-35.57}}\\\\\displaystyle{QR=\sqrt{185-35.57}}\\\\\displaystyle{QR=12.22}[/tex]

Therefore, the length of QR will be around 12.22 cm or 12 cm when rounded to nearest integer.

Pick the correct answer
Help me please thank you :)

Answers

Answer: D
Steps: In partially legible pic below. Sorry not the best explanation

Find the remainder when:
(75*56)^28+(58*34)^31 is divided by 19

Answers

Answer:

Exact form: 19 multiply 4200^28 + 1972^31 / 19

Decimal form: 3.55481422 multiply 10^101

Solve the following system of equations.
can you please show all the steps to complete this problem
7x + 4y = -8 -8x - 5y = 13

Answers

7x + 4y = -8 (1)
-8x - 5y = 13 (2)

(2) + (1)
(-8x-5y)+(7x+4y) = (13)+(-8)
-8x-5y+7x+4y = 5
-x-y = 5 (3)

(3)x4
-4x-4y = 20 (4)

(4) + (1)
(-4x-4y)+(7x+4y) = (20)+(-8)
-4x-4y+7x+4y = 12
3x = 12
x = 4

Sub x=4 into (4)
-4x-4y = 20
-4(4)-4y = 20
-4y = 36
y = -9

Therefore x=4, y=-9.

Answer:

x=4 and y=−9

Step-by-step explanation:

Problem:

Solve 7x+4y=−8;−8x−5y=13

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)'

7x+4y=−8;−8x−5y=13

Step: Solve 7x+4y=−8 for x:

7x+4y+−4y=−8+−4y(Add -4y to both sides)

7x=−4y−8

7x/7 =  -4y-8/7 (Divide both sides by 7)

x=-4/7y + -8/7

Step: Substitute -4/7y + -8/7 for x in −8x−5y=13:

−8x−5y=13

-8(-4/7y + -8/7) −5y=13

-3/7y + 64/7 =13(Simplify both sides of the equation)

-3/7y + 64/7 + -64/7 = 13 + -64/7 (Add (-64)/7 to both sides)

-3/7y = 27/7

-3/7y/-3/7 = 27/7/-3/7 (Divide both sides by (-3)/7)

y=−9

Step: Substitute −9 for y in x= -4/7y + -8/7:

x = -4/7y + -8/7

x = -4/7 (-9) + -8/7

x=4(Simplify both sides of the equation)

Answer:

x=4 and y=−9

Aiden evaluated the expression to find the volume of a cylinder. What could be dimensions of the cylinder

Answers

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).

Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.

Assuming the units to be cm, we can say that:

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

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The complete question is:

Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?

The height is 12 cm, and the diameter of the base is 8 cm.

The height is 12 cm, and the area of the base is 16 cm².

The height is 16 cm, and the diameter of the base is 6 cm.

The height is 16 cm, and the area of the base is 12 cm².

This question is down below. The picture attached below.
Thanks.

Answers

The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Given an equation showing profits of A Christmas vendor as

P=-0.1[tex]g^{2}[/tex]+30g-1200.

We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.

To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.

665.60=-0.1[tex]g^{2}[/tex]+30g-1200

0.1[tex]g^{2}[/tex]-30g+1200+665.60=0

0.1[tex]g^{2}[/tex]-30g+1865.60=0

Divide the above equation by 0.1.

[tex]g^{2}[/tex]-300g+18656=0

Solving for g we get,

g=[300±[tex]\sqrt{(300)^{2}-4*1*18656 }[/tex]]/2*1

g=[300±[tex]\sqrt{90000-74624}]/2[/tex]

g=[300±[tex]\sqrt{15376}[/tex]]/2

g=(300±124)/2

g=(300+124)/2       , g=(300-124)/2

g=424/2,  g=176/2

g=212,88

Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.

Put the value of P=1500 in equation P=-0.1[tex]g^{2}[/tex]+30g-1200.

-0.1[tex]g^{2}[/tex]+30g-1200=1500

0.1[tex]g^{2}[/tex]-30g+1500+1200=0

0.1[tex]g^{2}[/tex]-30g+2700=0

Dividing equation by 0.1.

[tex]g^{2}[/tex]-300g+27000=0

Solving the equation for finding value of g.

g=[300±[tex]\sqrt{300^{2} -4*1*27000}[/tex]]/2*1

=[300±[tex]\sqrt{90000-108000}] /2[/tex]

=[300±[tex]\sqrt{-18000}[/tex]]/2

Because [tex]\sqrt{-18000}[/tex] comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.

Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

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In which of these situations do the quantities combine to make 0?
A. Kathy receives $20 as a gift. She gives half of her $20 to a friend and keeps the rest for herself.
B. A player in a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board. C. In the morning, the temperature rises 30 degrees. In the evening, it falls by 30 degrees.
D. A hot air balloon rises 40 feet. It then rises another 40 feet.​

Answers

Answer:

C

Step-by-step explanation:

The temperature rises by 30 degrees, so lets say that it goes from 0 to 30.

The temperature is now 30. But then, it falls by 30 degrees. It is now 0 again. The quantities even out, or make 0.

X+y=5 7x+37=27 solve the system of equations: x=3; y=2 x=4; y=4 x=6;y=1 x=3; y=5

Answers

Answer:

  (a)  (x, y) = (3, 2)

Step-by-step explanation:

The correct answer to the given system of equations can be found by trying the offered choices.

The equations are ...

x + y = 57x +3y = 27

Evaluating "solutions"

The first equation tells you the sum of the x and y values is 5. Here's what we get for a sum from the different answer choices:

  A: 3 +2 = 5 . . . . a viable choice

  B: 4 +4 = 8 . . . . doesn't work

  C: 6 +1 = 7 . . . . doesn't work

  D: 3 +5 = 8 . . . . doesn't work

__

Checking (x, y) = (3, 2) in the other equation, we have ...

  7(3) +3(2) = 21 +6 = 27 . . . . as required

The solution is x = 3; y = 2.

__

Additional comment

Often, the easiest way to find the answer to a multiple-choice question is to see which answer works to solve the problem. It can sometimes be easier to check the answer than to develop it in the first place.

Substitution can work for this problem to find the correct y-value. (The answer choices differ by y-values, so knowing y tells the answer.)

  7(5 -y) +3y = 27 . . . . substitute x=5-y

  35 -4y = 27 . . . . . . simplify

  8 = 4y . . . . . . . . . add 4y-27

  2 = y . . . . . . . . . divide by 2. Matches the first answer choice.

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