3. A man earns # 140 000 per annum. He is allowed a tax free pay of # 30 000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left as disposable income?

4. A discount of 15% is allowed on an article. If a customer received N600.00, find the actual amount paid on the article.​

The equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.

An equilateral triangle have all its sides and angle to be equal, and each interior angles is equal to 60°

using the trigonometric ratio of sin for the angle C;

recall sin 60° = √3/2

sin 60° = x/8 {opposite/hypotenuse}

√3/2 = x/8

x = 4√3 {cross multiplication}

angle B = 60° {one interior angle of an equilateral triangle}

area of triangle = 1/2 × base × height

area of triangle ABC = 1/2 × 8 × 4√3

area of triangle ABC = 16√3.

Therefore, the equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.

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Answer:

Step-by-step explanation:4(3x+y)+2(x-5y)+x²=12x+4y+2x-10y+x²

=14x-6y+x²

=x²+14x-6y

Answer:  [tex]a_n = 2n+11[/tex]

======================================

Explanation:

The gap between adjacent terms is 2.

We add 2 to each term to get the next. Therefore, d = 2 is the common difference.

The first term is [tex]a_1 = 13[/tex]

Use that and the value of d to determine the nth term formula of this arithmetic sequence.

[tex]a_n = a_1 + d(n-1)\\\\a_n = 13 + 2(n-1)\\\\a_n = 13 + 2n-2\\\\a_n = 2n+11 \textbf{ is the final answer}\\\\[/tex]

---------------

Check:

Plug in n = 1

[tex]a_n = 2n+11\\\\a_1 = 2*1+11\\\\a_1 = 2+11\\\\a_1 = 13\\\\[/tex]

That confirms 13 being the 1st term.

Now use n = 2

[tex]a_n = 2n+11\\\\a_2 = 2*2+11\\\\a_2 = 4+11\\\\a_2 = 15\\\\[/tex]

That matches with the fact 15 is the 2nd term.

I'll let you check the third term.

Answer:

- 40

Hope this helps!

Step-by-step explanation:

( 4d - 6 )( 4d - 4 )  :  Cross Multiply

( 4d × 4d ) + ( 4d × (-4)) + ((-6) × 4d ) + ((-6) × (-4))

[tex]16d^{2}[/tex] - 16d - 24d + 24  :  ( Combine like terms )

[tex]16d^{2}[/tex] - 40d + 24

There is no significant difference in the average scores of two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively, as per the two-sample t-test with a p-value of 0.388.

The average score of the spring group of 50 students in SOC 390 on Exam 1 was 80, with a standard deviation of 12, while the average score of the fall group of 52 students was 81, with a standard deviation of 6. To determine if the difference in the means of the two groups is statistically significant, we can use a two-sample t-test.

Assuming unequal variances, the t-value for the two groups is 0.87, with a corresponding p-value of 0.388. Since the p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis that the two groups have equal means.

Therefore, we can conclude that there is no significant difference in the average scores of the two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively.

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The complete question is :

What is the difference between the average scores of two groups of students who took Exam 1 in SOC 390 in the spring and fall semesters, respectively, given that the spring group consisted of 50 students who scored an average of 80 with a standard deviation of 12, and the fall group consisted of 52 students who scored an average of 81 with a standard deviation of 6?

With the help of the volume and radius of the cylinder, we know that the height is 18.01 in.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.

In elementary geometry, it is regarded as a prism with a circle as its basis.

A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.

So, in the given situation use the formula:

V=πr²h

Now, calculate as follows:

V=πr²h

h = V/πr²

h = 2772/π7²

h = 18.00724in

Rounding off: h = 18.01 in

Therefore, with the help of the volume and radius of the cylinder, we know that the height is 18.01 in.

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226 integers are present between 100 and 999, inclusive, and have the property that some permutation of its digits is a multiple of 11 between 100 and 999.

Here, we have,

The problem statement is to find the number of multiples of 11 between 100 and 999 inclusive, where some multiples may have digits repeated twice and some may not.

To solve this problem, we can first count the number of multiples of 11 between 100 and 999 inclusive, which is 81.

Some of these multiples may have digits repeated twice, and each of these can be arranged in 3 permutations.

Other multiples of 11 have no repeated digits, and each of these can be arranged in 6 permutations.

However, we must account for the fact that switching the hundreds and units digits of these multiples also yields a multiple of 11, so we must divide by 2, giving us 3 permutations for each of these multiples.

Thus, we have a total of 81 × 3 = 243 permutations.

However, we have overcounted because some multiples of 11 have 0 as a digit.

Since 0 cannot be the digit of the hundreds place, we must subtract a permutation for each of these multiples.

There are 9 such multiples (110, 220, 330, ..., 990), yielding 9 extra permutations.

Additionally, there are 8 multiples (209, 308, 407, ..., 902) that also have 0 as a digit, yielding 8 more permutations.

Therefore, we must subtract these 17 extra permutations from the total of 243, giving us 226 permutations in total.

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2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.

What are congruent angles?

Congruent angles are angles that have the same measure. Two angles are said to be congruent if they have the same degree measurement.

2x + 35 = 180 can be used to determine the degree measure of one of the congruent angles.

Let x be the degree measure of each of the two congruent angles.

Then, the sum of the interior angles of a triangle is 180 degrees, so we can set up the equation:

35 + x + x = 180

Simplifying and solving for x, we get:

2x + 35 = 180

Therefore, 2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.

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Answer:

2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.

Step-by-step explanation:

working on notes right now also the other guy is error free.

Answer:If 104° is a measure of one of the vertical angles formed by the intersection of two straight lines, then the measure of the other vertical angle would also be 104°. This is because vertical angles are always congruent, which means they have the same measure.

Step-by-step explanation:

There is No statisti-cally signi-ficant evidence against the teacher's-claim that Charlie is just guessing because the probability is very low.

The total number of True-false questions are = n = 201.

The probability of getting a correct answer by guessing is = p = 0.5,

Charlie answered 53.7% = 0.537 of the questions correctly,

So, P(p' ≥ 0.537)

⇒ P(z ≥ (0.537 - 0.5)/√(0.5×0.5)/201,

⇒ P(z ≥ 1.05) = 1 - P(z < 1.05)

⇒ 0.1469

Since, the probability is very low,

Therefore, there is not any significant evidence against the teachers claim.

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Matthew's family cannot drive for 25 days without the warning light coming on, and they will need to refill the tank before that point.

If the car uses 0.6 gallons of fuel per day, then in 25 days, it will use:

= 0.6 gallons/day × 25 days

= 15 gallons

This means that if Matthew's family starts with a full tank of 14 gallons, they will not be able to drive for 25 days without running out of fuel.

The question asks if they can drive for 25 days without the warning light coming on. If the warning light comes on when there is 1.5 gallons or less of fuel remaining, then Matthew's family can drive for:

= 14 gallons - 1.5 gallons

= 12.5 gallons before the warning light comes on.

Since they use 0.6 gallons of fuel per day, they can drive for:

= 12.5 gallons / 0.6 gallons/day

≈ 20.8 days without the warning light coming on.

Therefore, they cannot drive for 25 days without the warning light coming on, and they will need to refill the tank before that point.

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The conclusion of hypothesis testing through the t-test is that the technical engineer have not statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life. The p-value for t-test is equals to the 0.0074.

We have study related to battery life of two different laptops for student usage at a community college in california. There are two models, Krapple and Madroid. Engineer randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. Here we have paired data so paired t test should be used.

Let d = Krapple - Madroid ( Sample sum of difference). Above table shows the calculations, Sample size, n = 15

Sample sum of difference, d = 1243

Sample mean of differences: Σα

= 1243/15 = 82.87

Sample standard deviation = [tex]\sqrt{\frac{488317.73}{15-1}}[/tex]

= 186.76

The Null and alternative Hypotheses are defined as [tex]H_0 : \mu_1- \mu_2 = 0[/tex]

[tex]H_a : \mu_1 - \mu_2 < 0[/tex]

Level of significance, α = 0.05

Test is one tailed (right tailed) df = n- 1

=> Degree of freedom = 14

Using the t - test, [tex]t = \frac{\sum d }{ \sqrt{\frac{n\sum d² - (\sum d)²}{n - 1}}}[/tex]

so, [tex] t = \frac{ 1243}{\sqrt{\frac{15× 488317.73 - (1243)²}{ 15 -1}}}[/tex]

=> [tex]t =\frac{1243}{\sqrt{412836.925}}[/tex]

=> t = 1.93

Now, using distribution table, P- value for t = 1.93, is 0.074. See, p-value > 0.05 , so result is not statistically significant. So, there is no evidence to reject the null hypothesis.

Conclusion: The technical engineer do not have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life.

Hence, required p-value is 0.074.

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Complete question:

the above first figure complete the question.

a technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in california. the two models he has are madroid and krapple. he randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. use data file: laptops.csv download laptops.csv does the technical engineer have statistically significant evidence to present to the university budget committee to purchase krapple because it has, on average, a longer battery life? provide the p-value from your analysis.

Step-by-step explanation:

This is an ordinary annuity  type of question :

FV = C [  ((1+i)^n) -1 )/i ]   plug in the numbers

 FV = 25 000 [ (1+.08)^9 -1 ]/ .08  = ~ $ 312 189

Answer:

x =107+88 =195, 360 -195 =165

Answer:

73°

Step-by-step explanation:

In an inscribed quadrilateral opposite angles are supplementary( they add up to 180) so angle x and its opposite angle( which is 107°) are equal to 180.

x + 107 = 180

Subtract 107 from both sides to isolate the x

x = 73

(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes

a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.

z = (x - μ) / σ

where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes

Substituting the given values, we get

z = (65 - 70) / 20

z = -0.25

Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.

b) The standard deviation (standard error) of the sample mean can be calculated using the formula:

SE = σ/√n

where,σ = 20 minutes, n = 49

Substituting the given values, we get

SE = 20/√49

SE = 2.857 minutes

Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.

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Part A: compound inequality for the speed Shala's car: | x - 65 | ≤ 2.5

Part B: 67 mph < 67.5 (maximum value) Thus, she will not get the ticket.

Two or more inequalities are connected together with or or and to form a compound inequality (also described as a combined inequality). A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to succeed.

Speed limit set by car's cruise control function = 2.5 mph.

Speed limit set by Shala = 65 mph.

Thus,

Maximum speed of car = 65 + 2.5

Minimum speed of car = 65 - 2.5

Let x represents the current speed of car,

x ≤ 65 + 2.5 or x ≥ 65 - 2.5

x - 65 ≤ 2.5 or x - 65 ≥ - 2.5

x - 65 ≤ 2.5 or - (x-65) ≤ 2.5

| x - 65 | ≤ 2.5 ( required compound inequality)

Now,

65 - 2.5 ≤ x ≤ 65 + 2.5

62.5 ≤ x ≤ 67.5

In interval notation; [62.5, 67.5]

The inequality on the number is drawn.

If Shala goes with 7 mph over the speed limit.

60 + 7 = 67 mph < 67.5 (maximum value)

Thus, she will not get the ticket.

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When $2,000 is loaned for 5 years at 15% interest compounded monthly, the final amount (or future value) is $4,214.36.

The final amount is the future value of the present value investment.

The future value can be computed using the FV formula or an online finance calculator as follows:

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 15%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

Future Value (Final amount)) $4,214.36

Total Interest = $2,214.36

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From the sign chart, we can see that the solution set is x < -5 or -5 < x < 7. Therefore, the solution to the original inequality is:

x < -5 or -5 < x < 7

In order to solve an inequality, you need to isolate the variable on one side of the inequality symbol (i.e., <, >, ≤, ≥) and determine the range of values for which the inequality holds true.

The process for solving an inequality depends on the specific type of inequality. Here are the general steps for solving different types of inequalities:

Solving linear inequalities:

a. Move all variable terms to one side of the inequality and all constant terms to the other side.

b. Divide or multiply both sides by a positive constant (i.e. not zero) to isolate the variable.

c. If you multiply or divide by a negative constant, flip the inequality symbol to maintain the inequality.

Solving quadratic inequalities:So, the inequality can be written as:

[tex](x - 7) (x + 5) < 0[/tex]

To solve this inequality, we need to consider the sign of the expression on the left-hand side for different values of x. We can do this by creating a sign table:

x      |   x - 7   |   x + 5   | (x - 7) (x + 5)

----------|-----------|-----------|----------------

-6 | -13 | -1 | +13

-4 | -11 | +1 | -11

-1 | -8 | +4 | -32

6 | -1 | +11 | -11

8 | +1 | +13 | +13

From the sign table, we can see that the expression (x - 7)(x + 5) is negative (i.e., less than zero) for values of x between -5 and 7. Therefore, the solution to the inequality is:

[tex]-5 < x < 7[/tex]

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On solving the provided question we can say that

1. circle centered at the origin with a radius of 10 is:

[tex]x^{2} +y^{2} =100[/tex]

2. circle with center R(-1, 8) and a radius of 5 is:

[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]

3. center P(8, -5) and a radius of 24.5 is:

[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]

4. the origin and passing through the point (9, -2) is:

[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]

5. center B(0, -2) and passing through the point (-6, 0) is:

[tex](x )^2 + (y +2)^2 = 40[/tex]

6. center F(11, 4) and passing through the point (-2, 5) is:

[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

circle centered at the origin with a radius of 10 is:

[tex]x^{2} +y^{2} =100[/tex]

circle with center R(-1, 8) and a radius of 5 is:

[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]

center P(8, -5) and a radius of 24.5 is:

[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]

the origin and passing through the point (9, -2) is:

[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]

center B(0, -2) and passing through the point (-6, 0) is:

[tex](x )^2 + (y +2)^2 = 40[/tex]

center F(11, 4) and passing through the point (-2, 5) is:

[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]

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Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.

The shortest arc that connects two points on a circle is called a minor arc.

For the given figure:

Using the intersecting chord theorem:

m∠FED = 1/2(arc CG - arcFD)

39 = 1/2(arc CG - 48)

arc CG - 48 = 39*2

arc CG = 78 -  48

arc CG = 30°

Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.

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Complete question:

Find the measure of minor arc CG for the attached figure.

The missing value in the given figure is 120 degree.

An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.

The base angles of an isosceles trapezoid are congruent.

The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.

In CFED,

As it is and isosceles trapezoid,

m∠C=m∠F

m∠D=m∠E

∴m∠F = 60 degrees

Now

m∠D+m∠E+m∠F+m∠C = 360 degree

2m∠D+120=360

m∠D=(360-120)/2

∴m∠D=120 degree

Thus the value of missing angle is 120 degree.

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Answer: 3.45

Step-by-step explanation:

Answer:

aswer will be 11.25 hope this helps

Mrs. Hernandez's section has sold 12 fruit pies and Mr. Kane's class had sold 17 bottles of fruit juice.

Let's use the variables 'x' and 'y' to represent the number of fruit pies sold by Mrs. Hernandez's class and the number of bottles of fruit juice sold by Mr. Kane's class, respectively.

From the problem, we know that:

Each fruit pie sold for $5, so the revenue from Mrs. Hernandez's class is 5x.

Each bottle of fruit juice sold for $2, so the revenue from Mr. Kane's class is 2y.

The total number of items sold is 29, so x + y = 29.

The total revenue earned is $94, so 5x + 2y = 94.

Our system of equations is:

x + y = 29

5x + 2y = 94

To solve the system, we can use the substitution method. Solving the first equation for y, we get:

y = 29 - x

Substituting this expression for y into the second equation, we get:

5x + 2(29 - x) = 94

Simplifying and solving for x, we get:

3x = 36

x = 12

Substituting x = 12 into the equation y = 29 - x, we get:

y = 29 - 12 = 17

Therefore, it can be concluded that Mrs. Hernandez's class sold 12 fruit pies and Mr. Kane's class sold 17 bottles of fruit juice.

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Answer:

B 18√3

Step-by-step explanation: 1. Calculate the base and height of the triangle.

2. Multiply the base and height of the triangle.

3. Divide the result by 2.

4. Multiply the result by the square root of 3.

5. The answer is 18√3.

According to the question we can say that it will take the artist 72 hours to paint 9 pictures for the art show.

If the artist can draw one-eighth of a picture in one hour, then he can draw one complete picture in 8 hours (since 8 x 1/8 = 1).

Therefore, to draw 9 pictures, the artist will need 9 x 8 = <<9*8=72>>72 hours.

So, it will take the artist 72 hours to paint 9 pictures for the art show.

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Answer:

Step-by-step explanation:

Step 1:

Butterflies is greater than Snails

More=addition

GP: 28+9=B

Step 2:

28+2=30

30+7=37

Answer: 37 Butterflies

Hope this helps!

Given that,

Total butterflies = 28

Total snails = 9

More butterflies than snails are = butterflies + snails

[tex]\implies28+9[/tex]

[tex]\implies 37[/tex]

Therefore, there are 37 butterflies.

The probability that a uniformly distributed random variable between 12 and 41 is between 22 and 35 is 41.7%.

Since the random variable is uniformly distributed between 12 and 41, the probability density function (PDF) of the random variable is constant within that interval and zero outside of it. Let X be the random variable between 12 and 41. Then,

f(x) = 1/(41-12) = 1/29, for 12 ≤ x ≤ 41

The probability that the random variable is between 22 and 35 can be found by integrating the PDF over the interval [22, 35]:

P(22 ≤ X ≤ 35) = ∫(22 to 35) f(x) dx = ∫(22 to 35) 1/29 dx

Using the definite integral, we get:

P(22 ≤ X ≤ 35) = [x/29] from 22 to 35

P(22 ≤ X ≤ 35) = (35/29 - 22/29) = 13/29

So, the probability that the random variable is between 22 and 35 is 13/29, which is approximately 0.4483 or 44.8% when expressed as a percentage rounded to one decimal place.

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The length of other leg of the triangle is 64√2 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Base²+Height ²

Here we have a right angle triangle.

It is given that height and base of the triangle is 8 cm.

Now we want to find other leg of the triangle.

It is clear that other leg means hypotenuse here because this is a right angle triangle.

We know,

Hypotenuse ²= Base²+Height ²

[tex] = {64}^{2} + {64}^{2} \\ = 4096+ 4096 \\ = 2 \times 4096[/tex]

So,

[tex]hypotenuse = \sqrt{2 \times 4096} \\ = \sqrt{64 \times 64 \times2 } \\ = 64\sqrt{2} [/tex]

Therefore, length of the third leg is 64√2 cm.

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Correct question is " There is a right angle triangle. Height and base of the triangle is 8 cm.What is the length of other leg of the triangle?

64 cm

64√2 cm

128 cm

128√2 cm"

The area of the triangle is approximately 11.524 km²

What is an area?

We can find the area of the triangle using the formula:

Area = (1/2) * a * b * sin(C)

where a and b are the lengths of the two sides and C is the angle between them.

In this case, a = 5 km, b = 7 km, and C = 143°. However, before we can use this formula, we need to convert the angle to radians. We can do this by multiplying by pi/180:

C = 143 * pi/180

C ≈ 2.495 radians

Now we can substitute the values into the formula and calculate the area:

Area = (1/2) * 5 km * 7 km * sin(2.495)

Area ≈ 11.524 km²

Therefore, the area of the triangle is approximately 11.524 km².

What is triangle?

A triangle is a 2-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in various fields such as mathematics, engineering, architecture, and art. Triangles can be classified into different types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. The area of a triangle is calculated by using the formula A = 1/2 * base * height, where the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.

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Complete question is: The area of the triangle is approximately 11.524 km²