I need help with this practice problem​

Answer:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values given we got:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

The confidence interval for the proportion is CI = 0.20 ± 0.0275.

The formula for calculating the confidence interval for proportion is expressed as:

[tex]CI=p \pm z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]

where:

Substitute into the formula;

[tex]CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(1-0.2)}{1400} }\\CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(0.8)}{1400} }\\CI = 0.20 \pm 0.0275\\[/tex]

Hence the confidence interval for the proportion is CI = 0.20 ± 0.0275.

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Answer:

  17

Step-by-step explanation:

For n cups, the height of the stack is ...

  4 + (1/4)(n -1)

For a height of 8 inches, we can find n from ...

  8 = 4 +(1/4)(n -1)

  4 = (1/4)(n -1) . . . . . . subtract 4

  16 = n -1 . . . . . . . . . .multiply by 4

  17 = n . . . . . . . . . . . .add 1

There are 17 cups in the stack.

Answer:

[tex]m\angle R=69.4^o[/tex]

Step-by-step explanation:

we know that

In the right triangle PQR

[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)

substitute the given values

[tex]tan(R)=\frac{8}{3}[/tex]

using a calculator

[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]

Answer: -6

Step-by-step explanation:

-4(3-1)+2

-12+4+2

-12+6

=-6

Hey there!

Just do PEMDAS

• Parentheses

• Exponents

• Multiplication

• Division

• Addition

• Subtraction

–4(3 – 1) + 2

= –4(2) + 2

= -–8 + 2

= –6

Therefore, your answer is: -6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

C(x) = 175√(x² + 360000) + 528000 - 100x

Step-by-step explanation:

See the attachment below (Line PR = 1mile)

C(x) = Cost of Distance across the river + Cost of Distance along the land

Calculating Distance Across the river:

In triangle OPQ,The distance across the river is represented by line y

Line y is the hypothenus of the triangle

Pythagoras theorem states that:

if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.

So,

y² = x² + 600²

y² = x² + 360000

y = √(x² + 360000)

If it costs $175 per foot across the river then It'll cost

175 * √(x² + 360000) to lay cables across the river.

Calculating Distance along the land

Distance along the land is represented by line QR

Line QR = Line PR - PQ.

Where PR = 1 Miles (1 mile = 5280 feet)

So, PR = 5280

Line PQ = x

So, QR = 5280 - x

If it costs $100 per foot along the land,then it'll cost

100 * (5280 - x) to lay cables along the land

= 528000 - 100x

C(x) = 175√(x² + 360000) + 528000 - 100x

Answer:

B and C.

Step-by-step explanation:

A prism can be constructed from 4 sided polygons like a rectangle.

A pyramid  (not including the vertex) can be constructed from  squares of diminishing size.

The piling method allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.

The piling method, also known as the additive method or stacking method, allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.

Prisms:

A prism is a three-dimensional shape with two congruent polygonal bases and rectangular lateral faces connecting the corresponding vertices of the bases. Examples of prisms include rectangular prisms (cuboids), triangular prisms, and hexagonal prisms.

Pyramids:

A pyramid is a three-dimensional shape with a polygonal base and triangular faces connecting the vertices of the base to a single point called the apex or vertex. Examples of pyramids include square pyramids, triangular pyramids, and pentagonal pyramids.

Cones:

A cone is a three-dimensional shape with a circular base and a curved surface that connects the base to a single point called the vertex. Cones can be constructed using polygons by approximating the curved surface with a series of smaller polygons.

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Know the properties of each shape:

A square has all sides of equal length plus all corners are right angles

A rectangle has all right angles, but has two pairs of parallel sides

A parallelogram is a quadrilateral that has two pairs of parallel sides

A rhombus is where all sides are equal length, but no right angles at all

So the best choice given the diagram is C: parallelogram

Hope this helped you to understand better.

Answer:

See answer below

Step-by-step explanation:

the ratio of pv against nrt is called compressibility Z and measures the deviation from an ideal gas behaviour . When Z is plotted against pressure for CH₄ for 0°C and 200°C the curves will differ because there are

- negative deviations ( Z decreases) due to intermolecular forces

- positive deviations (Z increases ) due to molecular size of gas particles

then

- at 0°C the negative deviations prevail  respect to positive deviations at lower pressures ( so Z drops below the horizontal line first ) and then Z increases when pressure increases since the effect of positive deviation is higher ( then Z increases)

- Nevertheless, at 200°C the effect of intermolecular forces is lower and thus the positive deviations always prevail ( thus you observe only Z increasing(

Answer:A)54 farms

B) 16 farms

Step-by-step explanation:

Y(1200) = (1200-1400)/100 = -200/100

Y(1200) = -2

Y(1600) = 1600-1400)/100

Y(1600) = 200/100 = 2

P(1200-1600) = (2y<-2)

2 standard deviation from the range = 68%=0.68

80 farms × 0.68 = 54 .4 approximately 54

B) 24× 0.68= 16.32 approximately 16

By using the empirical rule, it is expected that around 54 farms among the sample of 80 farms, as well as approximately 71 of 104 farms (after addition of 24 farms) will have land and building values per acre between 1300 and 1500.

The question deals with the concept of mean, standard deviation, and the empirical rule, specifically in the context of data relating to the values of land and buildings per acre on various farms.

A. Using the empirical rule, we know that approximately 68% of the population of a bell-curve distribution lies within one standard deviation from the mean. In this case, the mean is 1400 and the standard deviation is 100. So, one standard deviation above and below the mean is between 1300 and 1500. Therefore, approximately 68% of the 80 farms, or roughly 54 farms, have land and building values per acre between 1300 and 1500.

B. If we add 24 more farms to the sample, the total number of farms will be 104. Applying the same empirical rule, we'd expect approximately 68% of these, roughly 71 farms, to have land and building values per acre between 1300 and 1500.

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Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle

AC represents the hypotenuse of the right angle triangle.

With ∠A as the reference angle,

AB represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine the ratio of Tan A , we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan A = 28/45

Answer:

= 20.83%

Step-by-step explanation:

5/24 * 100

= 20.83%

To find what percent of people did not like the movie when 5 out of every 24 people did not, we calculate 5/24 as a percentage which is approximately 20.83%, rounded to about 21% of the people.

To calculate the percentage of people who did not like the movie, we need to set up a proportion where the number of people who did not like the movie is to the total number of people. Given that 5 out of every 24 people did not like the movie, we can express this as a fraction: 5/24. To find the equivalent percentage, we set up a fraction with 100 as the denominator and cross-multiply:

5/24 = x/100

Now we cross-multiply and solve for x:

24x = 5imes 100

x = (5 imes 100) / 24

x = 500 / 24

x = 20.833...

This equates to approximately 20.83%, which can be rounded to about 21%. Therefore, about 21% of the people did not like the movie.

Answer:

The answer to your question is 26

Step-by-step explanation:

Median is the middle number of a list order from lowest to highest.

Process

1.- Order the numbers from lowest to highest

              4   9   17   22   24   28   51   76   83   98

2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.

Middle numbers = 24 and 28

Median = (24 ´+ 28) / 2

Median = 52/2

Median = 26

Answer:

Step-by-step explanation:

First the numbers are arranged in ascending order from the least to the biggest number:

4 9 17 22 24 28 51 76 83 98

The numbers on the 5th and 6th position are in the middle

5th= 24

6th = 28

Since they are two numbers, we add them and divide by 2

= (24 + 28) / 2

= 52 / 2

= 26

Answer: she rented the car for 4 days.

Step-by-step explanation:

Let x represent the number of days for which Sonya rented the car.

She pays a fee of $50 for the rental plus $20 each day she had the car. This means that if she rents the car of x days, the total amount that she would pay is

20x + 50

Suppose she pays a total for $130, it means that the number of days for which she rented the car would be

20x + 50 = 130

Subtracting 50 from the left hand side and the right hand side of the equation, it becomes

20x + 50 - 50 = 130 - 50

20x = 80

x = 80/20 = 4

Answer: the small bottle holds 15 ounces while the large bottle holds 23 ounces.

Step-by-step explanation:

Let x represent the number of ounces that a small bottle holds.

Let y represent the number of ounces that a large bottle holds.

He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. It means that

2x + 2y = 76 - - - - - - - - - - - - 1

The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. This means that

4x + y = 83 - - - - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

4x + 4y = 152

4x + y = 83

Subtracting, it becomes

3y = 69

y = 69/3 = 23 ounces

Substituting y = 23 into equation 1, it becomes

2x + 2 × 23 = 76

2x + 46 = 76

2x = 76 - 46 = 30

x = 30/2 = 15 ounces

Answer:

its 15 and 19 ounces on IXL

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that you choose at random a real number X from the interval [2, 10].

a) Since this is a contnuous interval with all number in between equally likely

E = probability for choosing a real number is U(2,10)

pdf of E is [tex]\frac{1}{8}[/tex]

b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]

[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]

For

[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]

P(X<5 or x>7) = 1-P(5<x<7)

= [tex]\frac{3}{4}[/tex]

The density function of a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.

The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).

(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.

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Answer:

jursssursztsdigsdigssit

Step-by-step explanation:

hjnf

Answer: Lisa would need to serve 17 customers to attain the projected income.

Step-by-step explanation:

Their income on a certain day is projected to be $357.

This situation can be represented by the equation 21x + 17y = 357, where x is the number of Lisa's customers and y is the number of Daisy's customers.

On a day that Daisy is sick, the income from Daisy would be zero. For Lisa to attain the projected income of $357, the equation becomes

21x + 0 = 357

21x = 357

x = 357/21

x = 17

Answer:

16 women per 1 000

Step-by-step explanation:

The data was likely to be obtained from a survey. The question states how the information was gathered - most probably from questionnaires.

c. A simple model will be 16 women per 1 000 women. Proportion has been taken into account here.

Let 63 correspond with those that are going to get cancer out of 3980. The women have 63/3980 chance of getting cancer.

For 1 000 women that will be 1000/3980 × (63) = 16

Therefore the probability of a person getting cancer is 16 per 1 000 Ans

e. Large samples are essential to ensure that the results are representative of the actual population. In addition, large samples reduce inherent errors from deviations. Furthermore, useless data can be discarded and the remaining data still represent the actual population size. Lastly, large amounts of data are easy to scale up and use to develop models.

The two populations compared in the study were women whose mothers took the drug DES during pregnancy and those whose mothers did not. The data in the study were obtained through an observational study. A descriptive statistic can be used to estimate the number of women with tissue abnormalities out of 1000 in the population of women whose mothers took the drug DES during pregnancy.

a. The two populations in the study were: 1) women whose mothers took the drug DES during pregnancy and 2) women whose mothers did not take the drug.

b. The data in this study were obtained through an observational study, specifically a cohort study. This means that the researchers observed and compared the outcomes between the two groups of women without directly manipulating any variables.

c. A descriptive statistic that could be used to estimate the number of women out of 1000 in the population of women whose mothers took the drug DES during pregnancy and developed tissue abnormalities is:

Number of women with tissue abnormalities in the sample: 63

Descriptive statistic: (63 / 3980) * 1000 = 15.83

Therefore, an estimate is that 15.83 out of 1000 women in this population have tissue abnormalities that might lead to cancer.

d. Since the study only reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities, without providing an exact percentage, it is not possible to estimate the number of women without more specific information.

e. Medical studies often use a relatively large sample size, like 3980, to increase the reliability and representativeness of the findings. A larger sample size helps to reduce the chance of biased or random results and increases the generalizability of the findings to the larger population.

Answer: x = 3

Step-by-step explanation:

x^2 = 9

x = [tex]\sqrt{9}[/tex]

x = 3

Another way to think about it:

We think what number can be multiplied by itself to get 9.

since 3*3=9, our answer is 3

Matt paid $70 for mp3 player.

Step-by-step explanation:

Given,

Cost of mp3 player = $149.99

Discount = 20%

Amount of discount = 20% of 149.99

Amount of discount = [tex]\frac{20}{100}*149.99[/tex]

Amount of discount = 0.2*149.99

Amount of discount = $29.99

Sale price = Cost of mp3 - Amount of discount

Sale price = [tex]149.99 - 29.99 = \$120[/tex]

Rebate = $50

Amount paid by Matt = sale price - rebate

Amount paid by Matt = 120-50 =$70

Matt paid $70 for mp3 player.

Keywords: subtraction, percentage

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Answer:

Step-by-step explanation:

The formula for determining average is expressed as

Average = the total cost of the televisions/ the sum of the televisions

Total number of model A television that was sold is 21

Total cost of 21 televisions = 299 × 21 = $8671

Total number of model B television that was sold is 13

Total cost of 13 televisions = 549 × 13 = $7137

Total number of model C television that was sold is 6

Total cost of 6 televisions = 619 × 6 = $3714

Total number televisions sold is 21 + 13 + 6 = 40

Total cost of the televisions is 8671 + 7137 + 3714 = 19522

Therefore, the average price per TV Sold is

19522/40 = $488.05 per television

Final answer:

The work done against gravity in constructing the rectangular box is 3136000 J.

Explanation:

To calculate the work done against gravity in constructing the rectangular box, we need to first calculate the mass of the box. The density of the lightweight material is given as 800 kg/m³. Since the base of the box is a square with side lengths of 4 m and the height is 5 m, the volume of the box is V = (4 m)(4 m)(5 m) = 80 m³.

The mass of the box can be calculated using the formula mass = density × volume. Therefore, the mass of the box is [tex](800 kg/m^3)(80 m^3) = 64000 kg.[/tex]

The work done against gravity is given by the formula work = mass × gravity × height. Assuming the acceleration due to gravity is approximately 9.8 m/s², the work done against gravity is [tex](64000 kg)(9.8 m/s^2)(5 m) = 3136000 J.[/tex]

The composite shape's area is 61.12.

Step-by-step explanation:

Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.

Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.

Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.

Area of the composite shape = 36 + 25.12 = 61.12.

Yo sup??

This question can be solved by just imagining the object formed or practically trying it out.

Therefore the correct answer to this question is option 2 ie

a cylinder with a radius of 1 unit.

Hope this helps.

The figure created is a cone with a height of 2 units and a radius of 1 unit.

Notice that we have a triangle, so if we rotate it around the y-axis, we will get a cone.

Because the rotation is around the y-axis, the height of the cone will be equal to the side AB of the triangle, so the height of the cone is 2 units.

And the radius of the cone is equal to BC, then we can see that the radius measures 1 unit.

Then the figure created is a cone with a height of 2 units and a radius of 1 unit.

If you want to learn more about figures

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Answer: The length is 24 inches. The width is 7 inches.

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The length of the rectangle is to be 3 inches more than triple the width. This means that

L = 3W + 3

The diagonal of the rectangle divides it into two right angle triangles and the diagonal represents the hypotenuse. The length and width represents the opposite and adjacent side. Applying Pythagoras theorem,

Hypotenuse² = opposite side² + adjacent side²

Therefore,

25² = L² + W²

625 = L² + W² - - - - - - - - - -1

Substituting L = 3W into equation 1, it becomes

625 = (3W + 3)² + W²

625 = 9W² + 9W + 9W + 9 + W²

10W² + 18W - 625 + 9 = 0

10W² + 18W - 616 = 0

Dividing through by 2, it becomes

5W² + 9W - 308= 0

5W² + 44W - 35W - 308 = 0

W(5W + 44) - 7(5W + 44) = 0

W - 7 = 0 or 5W + 44 = 0

W = 7 or W = - 44/5

Since the width cannot be negative, then W = 7

L = 3W + 3 = 7 × 3 + 3

L = 24

Answer:

The answer to your question is it sold 7 cakes.

Step-by-step explanation:

Data

cakes = c = $5

pies = p = $7

total pieces = 15

total sell = $91

Process

1.- Write equations to solve this problem

                  c + p = 15      ------------ l

                5c + 7p = 91    ----------- ll

2.- Solve the system of equations by elimination

Multiply equation I by -5      

               -5c - 5p = -75

                 5c + 7p = 91

                 0   + 2p = 16

Solve for p

                            p = 16/2

                            p = 8

3.- Substitute p in equation l to find c

                 c + 8 = 15

solve for c

                 c = 15 - 8

                 c = 7

4.- Conclusion

It sold 7 cakes and 8 pies.

Answer: 7 cakes were sold.

Step-by-step explanation:

Let x represent the number of cakes that were sold.

Let y represent the number of cakes that were sold.

The cakes are $5 and the pies are $7. The store makes a total of $91. This means that

5x + 7y = 91- - - - - - -- -1

The store sold a total number of 15 goods. This means that

x + y = 15

Substituting x = 15 - y into equation 1, it becomes

5(15 - y) + 7y = 91

75 - 5y + 7y = 91

- 5y + 7y = 91 - 75

2y = 16

x = 16/2 = 8

x = 15 - y = 15 - 8

x = 7

Answer:the answer is life

Step-by-step explanation:

well life is life that you need

Answer:

$550 i think

Step-by-step explanation:

Answer:

15.6 liters

Step-by-step explanation:

Let the porridge eaten by Papa bear be 'x' liters.

Given:

Mama Bear ate 80% as much porridge as Papa Bear did.

Baby Bear ate as much as Mama Bear did.

Papa Bear ate 1.2 liters more porridge than Mama Bear did

So, porridge eaten by Mama Bear = 80% of 'x' = [tex]0.80x[/tex]

Now, Baby Bear eats same amount as Mama Bear. So,

Porridge eaten by Baby Bear = [tex]0.80x[/tex]

Papa Bear ate 1.2 liters more than Mama Bear.

Framing in equation form, we get:

[tex]x = 1.2 + 0.80x[/tex]

[tex]x-0.80x=1.2[/tex]

[tex]0.20x=1.2[/tex]

[tex]x=\frac{1.2}{0.20}=6\ liters[/tex]

So, Papa Bear ate 6 liters of porridge.

Mama Bear ate = 0.80 × 6 = 4.8 liters

Baby Bear ate = 4.8 liters.

So, total porridge = Papa Bear + Mama Bear + Baby Bear

Total porridge eaten = 6 + 4.8 + 4.8 = 15.6 liters

Answer:

Step-by-step explanation:answer is 20%

Step-by-step explanation:

[tex]m \angle \: WXZ = m \angle \: WYZ \\ ..(angles \: formed \: in \: same \: arc) \\ \therefore \: x \degree = (2x - 54)\degree \\ \therefore \: x = 2x - 54 \\ \therefore \: x - 2x = - 54 \\ \therefore \: - x = - 54 \\ \huge \purple{ \boxed{\therefore \: x = 54}}[/tex]

Answer:

The correct answer is D or 54.

Step-by-step explanation:

Answer: Coefficient of x²y² =5184

Step-by-step explanation:

18(3x + 4xy + y +3)*18(3x + 4xy + y + 3)

324( 9x² +12x²y + 3xy + 9x + 12x²y + 16x²y² + 4xy² +12xy + 3xy + 4xy² + y² + + 3y + 9x +12xy + 3y +9)

Already, x12y24x12y24 = 82944x²y²

From the expansion above, we have that: 324*16x²y²= 5184x²y²

Since, 82944x²y²/5184x²y² = 16

∴ Coefficient = 5184

Final answer:

To find the total number of possible license plates with two letters followed by five digits (with repetition allowed), multiply the number of options for each position: 26 letters and 10 digits result in 67,600,000 different license plates.

Explanation:

The question asks for the total number of license plates that can be produced when the first two symbols are letters from the alphabet and the following five symbols are digits from 0 to 9, with repetition allowed for both letters and digits. To find the number of possible license plates, we use the principle of counting, multiplying the number of choices for each position.

There are 26 possible letters for each of the first two positions (since there are 26 letters in the English alphabet) and 10 possible digits (0-9) for each of the last five positions.

Therefore, the total number of license plates that can be created is calculated as:26 * 26 * 10 * 10 * 10 * 10 * 10. This equals 67,600,000 possible license plates.

This calculation assumes that each symbol (letter or digit) can be repeated, meaning the same letter or digit can be used more than once in the license plate.