Use the trigonometric functions to find the value of x.
Write your answer as a decimal rounded to the nearest tenth.

The simplified expression is 9j¹⁴k⁹ + 9j¹¹k⁶ - 72j⁶k².

When you use operations like addition, subtraction, multiplication, division, exponentiation, and other operations to combine numbers and variables.

Expressiοns in math are mathematical statements that have a minimum οf twο terms cοntaining numbers οr variables, οr bοth, cοnnected by an οperatοr in between. The mathematical οperatοrs can be οf additiοn, subtractiοn, multiplicatiοn, οr divisiοn. Fοr example, x + y is an expressiοn, where x and y are terms having an additiοn οperatοr in between. In math, there are twο types οf expressiοns, numerical expressiοns - that cοntain οnly numbers; and algebraic expressiοns- that cοntain bοth numbers and variables.

To simplify the expression 9j⁶k²(j⁸k⁷ + j⁵k⁴ - 8j²k), we need to distribute the factors and simplify the resulting terms:

9j⁶k²(j⁸k⁷ + j⁵k⁴ - 8j²k)

= 9j⁶k²j⁸k⁷ + 9j⁶k²j⁵k⁴ - 72j⁸k³

= \(9j^{(6+8)}k^{(2+7)} + 9j^{(6+5)}k^{(2+4)} - 72j^{(8-2)}k^{(3-1)\)

= \(9j^{14}k^9 + 9j^{11}k^6 - 72j^6k^2\)

Therefore, the simplified expression is 9j¹⁴k⁹ + 9j¹¹k⁶ - 72j⁶k².

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Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

1.  You should use the median to describe the measure of the center of a data set when an outlier is present in a data set.

 Having an outlier will skew the mean of the data.

This means it will adjust the average to be smaller or greater than what the actual numbers are showing.  

The median should be used as the measure of center in these circumstances.

2) Using a box plot, you can find the range and interquartile range.  

The range is the distance from the smallest number to the largest.  The interquartile range is the distance from the first quartile to the third quartile.

All these values are found on a box plot.

3)The best measure of spread to describe symmetrical data sets is the mean absolute deviation.

This tells us how far on average the numbers are spread out from the mean.

4) See the answer given in 1 for the explanation.  An example would be a student who scores 8, 9, 10, 9, 10, and 2 on 6 quizzes.

The mean would be an average of 8, which is not a good number to represent the score this student normally gets.

The median of 9 is a better number to show how this student normally performs.

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Answer:

its d

Step-by-step explanation:

x is the number of hours he charges for

Answer:

Slope = 2

Y intercept = 4

Step-by-step explanation:

This is of the form y = mx + k

where m is the slope

K = y intercept

Hello! (:

y=2x+4

This equation is written in slope-intercept form:

y=mx+b

m is the slope (2) and b is the y-intercept (4)

Hope it helps!

If you have any question or query, feel free to ask! (:

~An excited gal

\(SparklingFlower\)

The required volume of the given composite space figure is 1512 \(cm^3\).

Given that, the rectangular pyramid fits exactly on top of a rectangular prism. The length of the prism is 18 cm, width is 6 cm and height is 9 cm. The length of the pyramid is 18 cm, width is 6 cm and height is 15 cm.

To find the volume of the composite figure formed by the rectangular pyramid on top of the prism, find the volume of prism and pyramid and then add it .

The volume of the prism is given by V1 = length × width × height.

The volume of the pyramid is given by V2 = length × width × height.

The volume of the composite figure is V = V1 +V2.

By using the given data and formula, find the volume of the prism,

Volume of prism V1 = length × width × height.

Volume of prism V1 = 18 × 6 × 9.

Thus, Volume of prism V1 = 972 \(cm^3\) .

By using the given data and formula, find the volume of the pyramid,

Volume of pyramid V2 = (length × width × height)/3.

Volume of pyramid V2 = (18 × 6 × 15)/3.

Thus, Volume of pyramid V2 =  1620/3= 540 \(cm^3\) .

By using above volumes, find the volume of the composite figure.

V = V1 +V2.

V = 972 + 540.

V = 1512 \(cm^3\) .

Hence, the required volume of the given composite space figure is

1512 \(cm^3\)

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The conversion from mililitres to litre will be done using the relation between the two, where 1 liter has 1000 mililitres.

Firstly know the abbreviations. In this question, ml represents mililitres. Now, The mentioned problem is from unit conversion. As we know the relation, that one litre contains 1000 milliliters of any fluid. So, this is the method of conversion from mililitres to litre.

We can understand given conversion through example. Let us say Zainab has a bottle of 2000 mililitres. Now how many litres of liquid can this bottle contain?

1000 mililitres is present in 1 liter

So, 2000 mililitres will contain = 2000/1000

Performing division

2,000 mililitres will contain 2 litre liquid.

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Answer:

A coin toss

Step-by-step explanation:

if you flip one coin repeatedly like 10 to 10000 it can be 0.5

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

r³ + 15r² - 10r - 4

Step-by-step explanation:

First, note you can remove the brackets, in this case they contribute nothing at all.

Then, group the like terms and add them, e.g., we have 3r³ and -2r², they add up to r³.

Finally, order them from greatest power of r to smallest power of r.

That's all!

The solution for \($r$\) is approximately 0.0572 or 5.72% (rounded to four decimal places). This indicates that the loan receives an annual rate of return of approximately 5.72%.

To solve for the rate of return \(($r$)\) of the loan, we can use the present value formula for an annuity. The formula is given by: value formula for an annuity. The formula is given by:

\(\[PV = \frac{P \left(1 - (1 + r)^{-n}\right)}{r}\]\)

where \($PV$\) is the present value (loan amount), \($P$\) is the periodic payment, \($r$\) is the interest rate, and \($n$\) is the number of periods.

Let's assume the present value \(($PV$)\) is $30000, the periodic payment \(($P$)\) is $5000$, and the number of periods \(($n$) \ is\ $13$\). Plugging in these values into the formula, we get:

\(\[30000 = \frac{5000 \left(1 - (1 + r)^{-13}\right)}{r}\]\)

Solving this equation for \($r$\) will give us the rate of return of the loan.

The solution for \($r$\) is approximately 0.0572 or 5.72% (rounded to four decimal places). This indicates that the loan receives an annual rate of return of approximately 5.72%.

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When you multiply a negative number by another negative number, the result is always a positive number.

This rule is based on the properties of multiplication and the concept of negative numbers.

When two negatives are multiplied, the negative signs "cancel out" each other. Mathematically, if you have -a multiplied by -b, where a and b are positive values, the result is given by ab.

For example, if you multiply -2 by -3, the product is 6, which is a positive number. This can be explained by the idea that multiplying two numbers with opposite signs results in a negative product, while multiplying two numbers with the same sign (both negative) produces a positive product.

Therefore, when you multiply a negative by a negative, the outcome is a positive number.

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Answer:

27.6%

Step-by-step explanation:

See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%.  (8/29)*(100%) = 27.6% to the nearest tenth.

The probability of getting a result as extreme or more extreme than 8 heads in one flip of 10 unbiased coins is 0.0547.

To solve the problem, we can use the binomial probability formula:

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

where X is the number of heads obtained in the flip of 10 coins.

Using the binomial probability formula, we can calculate:

P(X = 8) = (10 choose 8) * (0.5)^10 ≈ 0.044

P(X = 9) = (10 choose 9) * (0.5)^10 ≈ 0.0098

P(X = 10) = (10 choose 10) * (0.5)^10 ≈ 0.00098

Therefore,

P(X ≥ 8) = 0.044 + 0.0098 + 0.00098 ≈ 0.0547

Thus, the probability of getting a result as extreme or more extreme than 8 heads in one flip of 10 unbiased coins is approximately 0.0547. Therefore, the correct answer is option A.

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Answer: letter B. -2,-1.5,0

Step-by-step explanation: hope it helps

The order from least to greatest are;

⇒ -2, -2, -2, -2, -1.5, -1.5, -1.5, 0, 0, 0, 0, |-1.5|

Here,

The list of ordered pair are;

−1.5, −2, 0, , −2, −1.5, 0, , |−1.5|, −2, 0, , −2, −1.5, 0, ,

We have to arrange it from least to greatest.

What is Modulus function?

The modulus function give the absolute value of a number irrespective of the number being positive or negative.

Now,

The list of ordered pair are;

−1.5, −2, 0, , −2, −1.5, 0, , |−1.5|, −2, 0, , −2, −1.5, 0.

Since, |-1.5| = 1.5

And, -2 < -1.5

So, The order from least to greatest are;

⇒ -2, -2, -2, -2, -1.5, -1.5, -1.5, 0, 0, 0, 0, |-1.5|

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a and b must be chosen in such a way that the resulting function f(x) has real coefficients.

From the given graph, it can be observed that the zero is located at x = 2, and the other two roots are non-real and conjugate pairs.

Let these two roots be represented by a + bi and a - bi, respectively.

The function can be expressed in factored form as follows:

f(x) = k (x - 2) (x - (a + bi)) (x - (a - bi))

Where k is a constant.

Since the leading coefficient of the polynomial is not given, let us assume k = 1 for simplicity.

Thus:

f(x) = (x - 2) (x - (a + bi)) (x - (a - bi))f(x)

= (x - 2) ((x - a) - bi) ((x - a) + bi)

Now, we simplify the expression:

f(x) = (x - 2) ((x - a)² - b²i²)f(x)

= (x - 2) ((x - a)² + b²)f(x)

= (x - 2) (x² - 2ax + a² + b²)

Now, we expand the product:f(x) = x³ - 2ax² + (a² + b² - 2) x + 2a² - 2ab²

The required third-degree polynomial function f(x), with real coefficients sketched here given that 2i is a zero, is:

x³ - 2ax² + (a² + b² - 2) x + 2a² - 2ab² = 0

We have shown that two non-real roots of the polynomial are a + bi and a - bi, which are complex conjugates.

Therefore, a and b must be chosen in such a way that the resulting function f(x) has real coefficients.

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If the 14 billion year history of the universe were compressed to one year, and "now" is exactly midnight December 31, one's grandparents would have have born 0.15 seconds ago. Correct option is D.

If the 14 billion year history of the universe were compressed to one year, then one day in this compressed timeline would represent approximately 38 million years of actual time. Therefore, midnight on December 31 would represent the end of the 14 billion year timeline.

Assuming an average lifespan of around 75 years, the birth of one's grandparents would have occurred approximately two generations ago. If we estimate the length of a generation to be around 30 years, then the birth of one's grandparents would have occurred approximately 60 years ago in actual time.

In the compressed timeline, one year would represent 14 billion years, so one hour would represent approximately 583 million years. Therefore, the birth of one's grandparents would have occurred approximately 0.1 seconds ago on this compressed timeline, which is equivalent to 0.15 seconds ago when rounded to the nearest hundredth of a second.

So, the answer is option D.

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Complete question is:

If the 14 billion year history of the universe were compressed to one year, and "now" is exactly midnight December 31, approximately how long ago were your grandparents born, they are 75 years?

-1 hour ago

-1 minute ago

-1 second ago

-0.15 second ago

Answer:

in one minute they rake \(\frac{y+x}{xy}\) leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes \(\frac{1}{x}\) leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes \(\frac{1}{y}\) leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: \(\frac{1}{x}+ \frac{1}{y}\)

Now, to simplify this expression:

\(\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}\)

Thus, in one minute they rake \(\frac{y+x}{xy}\) leaves.

The inverse Laplace transform of \(X(s) = (s+1)/(s^2 + 4s + 4)\) is \(x(t) = e^-^t * (t + 1)\). The poles are located at s = -2, and the region of convergence (ROC) includes all values of s to the right of -2 on the real axis. This means that the Laplace transform is valid for all values of s greater than -2.

To find the inverse Laplace transform, we can use partial fraction decomposition. The denominator of X(s) factors as \((s + 2)^2\), indicating a repeated pole at s = -2. The numerator is (s + 1), which is a first-order polynomial.

Applying partial fraction decomposition, we can express X(s) as \((A/(s + 2)) + (B/(s + 2)^2)\). Solving for A and B, we find A = 1 and B = -1.

Now, we can take the inverse Laplace transform of each term. The inverse Laplace transform of A/(s + 2) is \(e^-^2^t\), and the inverse Laplace transform of \(B/(s + 2)^2\) is \(t * e^-^2^t\).

Thus, the inverse Laplace transform of X(s) is \(x(t) = e^-^t * (t + 1)\).

The poles of X(s) are located at s = -2. The region of convergence (ROC) can be determined by examining the values of s for which X(s) converges. In this case, since the poles are at s = -2, the ROC includes all values of s to the right of -2 on the real axis.

In summary, the inverse Laplace transform of X(s) = \((s+1)/(s^2 + 4s + 4)\) is \(x(t) = e^-^t * (t + 1)\). The poles are located at s = -2, and the ROC includes all values of s to the right of -2 on the real axis.

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Answer:

One solution

Step-by-step explanation:

3x+x+2=8x-4x+2

Combine like terms.

4x+2=4x+2

Solve for x

4x+(-4x)+2=4x+(-4x)+2

2=2

This equation has one solution because 2 only equals 2 and will not equal any other number.

using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to  ∫u+2 /5 du/5

What is Derivative?

Calculus defines a derivative as the rate at which one quantity, y, changes in relation to another, x. The differential coefficient of y with respect to x is another name for it. Finding a function's derivative is the process of differentiation. A function's derivative is typically represented by d/dx (f(x)) (or df/dx (or Df(x) (or f')). Let's examine the technical definition of a derivative. Two points on a function f(x) curve are (x, f(x)) and ((x + h), f(x + h)), respectively. If so, [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h] will be the slope of the secant line through these points. The second point overlaps the first point in the figure below when the distance between two points is nearly equal to 0 (i.e., as h approaches 0), and the secant line turns into the tangent line. Calculus refers to the slope of the tangent line as the function's derivative.

x = 1/y + 1

y + 1 = 1/x

y = 1/x - 1

differentiating y w.r.t to x

dy/dx=-1/x^2

using subsitution u= 5x-2

then x= u+2/5

∫u+2 /5 du/5

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The solution for x is x ∈ (-∞, 11] ∪ (9, ∞)

We are given that;

The inequality − 36 < − 3− 9 or −36<−3x−9or − 42 ≥ − 3 − 9 −42≥−3x−9

Now,

You can solve this inequality by first adding 9 to both sides of each inequality to get:

-27 < -3x or -33 >= -3x

Then, divide both sides of each inequality by -3, remembering to reverse the inequality symbol when dividing by a negative number:

9 > x or 11 <= x

Therefore, by inequality the answer will be x ∈ (-∞, 11] ∪ (9, ∞).

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The answers are (a) 1.5 orders (b) 0.5  (c)-1

a. Probability that a faxed order will arrive within the next 9 minutes:

Since there are 24 hours in a day, and we receive an average of 20 orders every two hours, this means we receive an average of 10 orders per hour. We can assume that orders arrive uniformly throughout the hour. To find the probability that a faxed order will arrive within the next 9 minutes, we can convert the time to hours. 9 minutes is \(\frac{9}{60} = 0.15\) hours. The probability of an order arriving within the next 9 minutes is equal to the average rate of orders per hour multiplied by the time interval:

Probability = (10 orders/hour) * (0.15 hours) = 1.5 orders.

b. Probability that the time between two faxed orders will be between 3 and 6 minutes. Again, we need to convert the time interval to hours. 3 minutes is \(\frac{3}{60}=0.05\) hours, and 6 minutes is \(\frac{6}{60} = 0.1\).

The probability of the time between two orders being between 3 and 6 minutes can be calculated as the difference between the probabilities of an order arriving within the next 3 minutes and an order arriving within the next 6 minutes:

Probability = (10 orders/hour)  (0.1 hours) - (10 orders/hour) (0.05 hours)

= 1 - 0.5

= 0.5.

c. Probability that 12 or more minutes will elapse between faxed orders:

Similar to the previous calculations, we convert the time to hours. 12 minutes is \(\frac{12}{60} = 0.2\) hours.

The probability that 12 or more minutes will elapse between faxed orders can be calculated as the probability of no orders arriving within the next 12 minutes:

Probability = 1 - (10 orders/hour) (0.2 hours)

= 1 - 2

= -1.

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The missing elements are:
C = 40° (angle opposite side c)
a = 2.31 (length of side opposite angle A)
c = 5.63 (length of side opposite angle C)

To find the missing elements, we can use the properties of triangles and trigonometry. Here's how:

1. Identify the type of triangle: From the given information, we can see that we have a triangle with two known angles: 40° and 120°. Since the sum of angles in a triangle is always 180°, we can find the third angle by subtracting the sum of the other two angles from 180°.

A = 180° - 40° - 120° = 20°

Therefore, we have a triangle with angles of 40°, 20°, and 120°.

2. Use the Law of Sines: The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. We can use this property to find the missing sides of the triangle.

a/sin(A) = b/sin(B) = c/sin(C)

We already know the angles A, B, and C, and we are given the length of side b (8). We can use this information to find the missing sides:

a/sin(20°) = 8/sin(120°) => a = 8*sin(20°)/sin(120°) ≈ 2.31

c/sin(40°) = 8/sin(120°) => c = 8*sin(40°)/sin(120°) ≈ 5.63

Therefore, the missing elements are:

C = 40° (angle opposite side c)

a = 2.31 (length of side opposite angle A)

c = 5.63 (length of side opposite angle C)

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Answer:

\(x=3c\sqrt{a} -b^2\)

Step-by-step explanation:

\(\sqrt{a} =\dfrac{x+b^2}{3c}\)

Multiply both sides by 3c:

\(\implies \sqrt{a} \cdot 3c=\dfrac{(x+b^2) \cdot 3c}{3c}\)

\(\implies 3c\sqrt{a} =x+b^2\)

Subtract \(b^2\) from both sides:

\(\implies 3c\sqrt{a} -b^2=x+b^2-b^2\)

\(\implies 3c\sqrt{a}-b^2=x\)

Switch sides:

\(\implies x=3c\sqrt{a} -b^2\)

Answer:

Only J) is true

The probability that exactly 12 recover is 0.1797, the probability that at most 11 will recover is 0.040440  the probability that at least 12 but not more than 17 recover is 0.5070 and he probability that at most 16 recover is 0.9840.

Based on the given information, the probability that a patient recovers from a stomach disease is 0.6.

Now, let's answer the questions:

A. the probability that exactly 12 recover is
Using the binomial probability formula, we can calculate the probability as follows:
P(X=12) = (20 choose 12) * 0.6^12 * (1-0.6)^(20-12)
= 0.1797 (rounded to 3 decimal places)

B. the probability that at most 11 recover is
This is the same as asking for the probability that less than or equal to 11 recovers.

We can calculate it by adding up the probabilities for X=0,1,2,...,11.
P(X<=11) = Σ (20 choose x) * 0.6^x * (1-0.6)^(20-x) for x=0 to 11
= 0.040440 (rounded to 3 decimal places)

C.the probability that at least 12 but not more than 17 recover is
This is the same as asking for the probability that X is between 12 and 17 inclusive.

We can calculate it by adding up the probabilities for X=12,13,14,15,16,17.
P(12<=X<=17) = Σ (20 choose x) * 0.6^x * (1-0.6)^(20-x) for x=12 to 17
= 0.5070 (rounded to 3 decimal places)

D. the probability that at most 16 recover is
This is the same as asking for the probability that X is less than or equal to 16.

We can calculate it by adding up the probabilities for X=0,1,2,...,16.
P(X<=16) = Σ (20 choose x) * 0.6^x * (1-0.6)^(20-x) for x=0 to 16
= 0.9840 (rounded to 3 decimal places)
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Inferential Statistics

Inferential Statistics is the part of statistical analysis that helps you to determine or predict further steps from the data studied according to Statistical methods. It is helpful in understanding people's perspectives or analyzing data from the samples obtained from it. It can be defined as the analytical tool used to draw conclusions about a population by analyzing random samples.

Descriptive Statistics are used to describe the data and make generalizations about the studies. It is used the define the characteristics of the data obtained.

In the given situation, the statistical analysis is done and it has been inferred from the studies that 67% of people check their cell phone even when it is not ringing or vibrating.

Hence, It is a case of Inferential Statistics.

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The surface area of a triangular prism is 288 square inches. If the triangle base is 8 inches, each rectangular face will be 8 inches broad and 10 inches long. The height of the triangular prism is 16 inches.

To find the height of the triangular prism, we need to use the formula for the surface area of a triangular prism:

Surface Area = 2(Area of the rectangular face) + (Perimeter of the base) x (Height)

We know that the rectangular face has a width of 8 inches and a length of 10 inches, so its area is:

Area of the rectangular face = 8 x 10 = 80 square inches

We also know that the surface area of the triangular prism is 288 square inches. Substituting these values into the formula, we get:

288 = 2(80) + (Perimeter of the base) x (Height)

Simplifying this equation, we get:

288 = 160 + 8(Height)

128 = 8(Height)

Height = 16 inches

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