The probability is P(k) = (q^(k-1)) * p for k>=1, and P(0) = q. The expected number of times the loop will be executed is 1/p.The expected number of times that the repeat loop will be executed is 1/p.
To find the probability that the loop will be executed k times, we can consider the probability of the event that B is false k-1 times followed by B being true. This probability is q^(k-1) * p.
The event of the loop not being executed at all corresponds to B being true in the first trial, which has a probability of q. Therefore, the probability that the loop will be executed k times is P(k) = (q^(k-1)) * p for k>=1, and P(0) = q.
The expected number of times the loop will be executed is the sum of the probabilities of executing the loop k times, weighted by k, i.e., E = Sum(kP(k)) for k>=1, and E = 0 if P(0) = q.
By using the expression for P(k), we can simplify this to E = Sum(kq^(k-1)*p) for k>=1, and E = 0 if P(0) = q. By applying the formula for the sum of a geometric series, we get E = 1/p.
For the "repeat S until B" loop, the expected number of times that the loop will be executed is the expected number of trials in a Bernoulli process until the first success, where the success probability is p. By using the formula for the expected value of a geometric distribution, we get E = 1/p.
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Pls answer!! A scanner takes 6 minutes to scan 4 pages. How many pages can it scan in 15 minutes?
The reader can scan 10 sheets in 15 minutes, according to the claim.
What does math's multiple mean?One of the four fundamental math processes, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual adding of sets of identical size.
If a scanner can scan 4 pages in 6 minutes, then we can set up the following ratio:
4 pages / 6 minutes = x pages / 15 minutes
where x is the number of pages that the scanner can scan in 15 minutes.
To solve for x, we can cross-multiply and simplify:
4 pages × 15 minutes = 6 minutes × x pages
60 pages = 6x
x = 60 pages / 6
x = 10 pages
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if three letter of the alphabet are slected at random find the porbability of getting all vowels letters are relaced each time before selection
The probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.
There are 5 vowels in the English alphabet (a, e, i, o, and u) and 26 letters in total. If we select three letters at random with replacement, we have 5 options for each selection.
The probability of getting a vowel on any one selection is 5/26. Since we are replacing the letter each time, the probability of getting three vowels in a row is:
(5/26) × (5/26) × (5/26) = 1/125
Therefore, the probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.
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A school district has 20 elementary schools, and each school has 12 classes that can be used for a study.
a. Using schools as blocks, describe a randomized block design to compare three teaching methods.
b. Explain why schools should be used as blocks.
By using schools as blocks, any variability between schools can be controlled for and the results of the study can be more accurately interpreted and by controlling for these differences between schools, the results of the study will more accurately reflect the effects of the teaching methods being compared, rather than the effects of other factors.
Given,
A school district has 20 elementary schools, and each school has 12 classes that can be used for a study
a. In a randomized block design to compare three teaching methods, schools can be used as blocks. The goal is to control for any variability between schools that could affect the results of the study. To do this, each of the 20 schools is considered a block and the 12 classes in each school are used as the experimental units.
To implement the randomized block design, you would first randomly assign each of the teaching methods to one of the 12 classes in each school.
For example,
method A could be assigned to four classes in school 1,
method B to four classes in school 2,
method C to four classes in school 3.
This random assignment process would be repeated for each of the 20 schools, so that each method is assigned to 4 classes in each of the 20 schools.
Once the methods have been assigned, the study can be conducted in each of the 12 classes within each school, and the results can be compared between the methods.
By using schools as blocks, any variability between schools can be controlled for and the results of the study can be more accurately interpreted.
b. Schools should be used as blocks because there may be differences between schools that could affect the results of the study, such as socio-economic factors, teacher experience, or prior test scores. By using schools as blocks, any variability between schools can be controlled for and the results of the study can be more accurately interpreted. By controlling for these differences between schools, the results of the study will more accurately reflect the effects of the teaching methods being compared, rather than the effects of other factors.
By using schools as blocks, any variability between schools can be controlled for and the results of the study can be more accurately interpreted and by controlling for these differences between schools, the results of the study will more accurately reflect the effects of the teaching methods being compared, rather than the effects of other factors.
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If IJ=16 and JK=16, what is the length of HK?
The length of HK is approximately 20.17 units.
what Pythagorean theorem ?
The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in a right triangle, 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.
The theorem is usually written in the form of an equation:
[tex]a^2 + b^2 = c^2[/tex]
According to the questions :
First, we can use the fact that HJ is perpendicular to the base IK to determine the height of triangle HKI. Since J is the midpoint of the hypotenuse IK, we know that HJ is also the median of the hypotenuse, and it divides the hypotenuse into two equal segments of length 16.
Therefore, we can use the Pythagorean theorem to find the height HK of triangle HKI:
[tex]HK^2 = IK^2 - HI^2[/tex]
Since triangle HKI is a right triangle, we know that HI is the height of the triangle, and IK is the hypotenuse. Using the Pythagorean theorem again, we can find the length of IK:
[tex]IK^2 = IJ^2 + JK^2[/tex]
Substituting the given values, we get:
[tex]IK^2 = 16^2 + 16^2[/tex]
[tex]IK^2 = 5123[/tex]
Taking the square root of both sides, we get:
[tex]IK = sqrt(512) ≈ 22.63[/tex]
Now we can use this value to find the height HK:
[tex]HK^2 = IK^2 - HI^2[/tex]
[tex]HK^2 = 22.63^2 - (16/2)^2[/tex]
[tex]HK^2 = 512 - 64[/tex]
[tex]HK^2 = 448[/tex]
Taking the square root of both sides, we get:
[tex]HK = sqrt(448) ≈ 20[/tex]
Therefore, the length of HK is approximately 20 units.
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Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car?
Therefore, when the tyer pressure goes below 21.9 psi, the TPMS will sound an alarm.
What is an illustration of pressure?By pressing a knife against some produce, one can see a straightforward illustration of pressure. The surface won't be sliced if you press the smooth portion of the scalpel against by the fruit. The army is dispersed over a wide region (low pressure).
If the target tire pressure is 30 psi, 27% below that value is:
0.27 × 30 psi = 8.1 psi
So the TPMS will trigger a warning when the tire pressure is 30 psi - 8.1 psi = 21.9 psi.
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A random rectangle is formed in the following way: The base, X, is chosen to be a uniform [0, 1] random variable and after having generated the base, the height is chosen to be uniform on [0, X]. Use the law of total expectation, Theorem A of Section 4.4.1, to find the expected circumference and area of the rectangle.
Using the law of total expectation, the expected circumference of the rectangle is 3/2, and the expected area of the rectangle is 1/6.
Let C and A denote the circumference and area of the rectangle, respectively. Then we have:
E[C] = E[C|X] * P(X) + E[C|X'] * P(X')
where X' is the complement of X, and P(X) and P(X') are the probabilities of X and X' respectively. Since X is a uniform [0, 1] random variable, we have P(X) = 1 and P(X') = 0.
Therefore, we can simplify the above expression to:
E[C] = E[C|X]
To find E[C|X], we can use the formula for the circumference of a rectangle:
C = 2 * (base + height)
Substituting in the values for the base and height of the rectangle, we get:
C = 2 * (X + U[0, X])
where U[0, X] denotes a uniform random variable on [0, X].
Then, we can find the expected value of C given X as follows:
E[C|X] = E[2*(X+U[0,X])|X]
= 2*(X+E[U[0,X]|X])
where we have used the linearity of expectation. Note that E[U[0,X]|X] is simply the expected value of a uniform random variable on [0, X], which is X/2.
Therefore, we have:
E[C|X] = 2*(X+X/2) = 3X
Substituting this back into the expression for E[C], we get:
E[C] = E[3X] = 3E[X]
Since X is a uniform [0, 1] random variable, we have E[X] = 1/2. Therefore, the expected circumference of the rectangle is:
E[C] = 3E[X] = 3/2
Similarly, we can use the Law of Total Expectation to find the expected area of the rectangle by conditioning on X:
E[A] = E[A|X] * P(X) + E[A|X'] * P(X')
where, again, we have P(X) = 1 and P(X') = 0. Therefore, we can simplify the expression to:
E[A] = E[A|X]
To find E[A|X], we can use the formula for the area of a rectangle:
A = base * height
Substituting in the values for the base and height of the rectangle, we get:
A = X * U[0, X]
where U[0, X] denotes a uniform random variable on [0, X].
Then, we can find the expected value of A given X as follows:
E[A|X] = E[XU[0,X]|X]
= XE[U[0,X]|X]
where we have again used the linearity of expectation. Note that E[U[0,X]|X] is X/2, as before.
Therefore, we have:
E[A|X] = X * (X/2) = X^2/2
Substituting this back into the expression for E[A], we get,
E[A] = E[X^2/2] = 1/2 * E[X^2]
To find E[X^2], we can use the formula for the variance of a uniform [0, 1] random variable:
Var(X) = E[X^2] - (E[X])^2 = 1/12
Solving for E[X^2], we get:
E[X^2] = Var(X) + (E[X])^2 = 1/12 + (1/2)^2 = 1/3
Substituting this back into the expression for E[A], we get:
E[A] = 1/2 * E[X^2] = 1/6
Therefore, the expected area of the rectangle is:
E[A] = 1/6
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can you plese do this
The vector is (-3, 4) and its x and y components are -3 and 4.
What are Vectors?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.
Given:
Vector v have an initial point at (3, -5) and a terminal point at (0, -1).
It initial point of a vector is (a, b) and terminal point is (c, d), then the vector is
v= (c-a, d-b)
We have (a, b) = (3, -5) and (c, d) = (0, -1)
Then, vector v is defied as
v = (0 - 3, -1 - (-5))
v = (-3, -1+5)
v = (-3, 4)
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A wrecking ball is suspended on a chain from a crane. The chain is 25 feet long, and the distance from the bottom of the wrecking ball to the crane is 8 feet. What is the length of the crane? Round to the nearest tenth. ft
The length of the crane is given as follows:
23.7 feet.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
In the context of this problem, the parameters are given as follows:
The sides are the length of the crane and 8 feet.The hypotenuse is of 25 feet.Hence the length of the crane is obtained as follows:
l² + 8² = 25²
l = sqrt(25² - 8²)
l = 23.7 feet.
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5) h(x) = -2x² - 5
g(x) = 2x - 1
Find (h•g)(x)
The value of of function is -8x² + 8x - 7.
What is a function?
Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function h(x) = -2x² - 5 and g(x) = 2x - 1
Now,
To find (h•g)(x), we need to first evaluate the composition of functions h(g(x)):
h(g(x)) = -2(2x - 1)² - 5 [substituting g(x) into h(x)]
= -2(4x² - 4x + 1) - 5
= -8x² + 8x - 7
Therefore, the function (h•g)(x) will be equal to -8x² + 8x - 7.
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Referring to the figure, evaluate the expression shown
when a = 3, b = 7, c = 2
Answer:
5
Step-by-step explanation:
The Garcia family drew a circle graph of their budget that contained the following: Taxes, 20% Rent, 32% Food, 20% Utilities, 5% Gas, 13% Miscellaneous, 12% What would you tell the family concerning the data?
If the Garcia family drew a circle graph of their budget I would tell the Garcia family that the circle graph shows the percentage breakdown of their budget.
What would you tell the family concerning the data?The largest portion of their budget is going towards rent, followed by taxes and food. Utilities, gas, and miscellaneous expenses make up smaller portions of their budget.
It may be helpful for the family to further analyze their spending in each category to see if any adjustments can be made to better align with their financial goals.
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Suppose that 20 randomly selected customers give the following satisfaction ratings (on a scale of 1 to 10) for a DVD recorder N 1 1 4 4 4 4 7 7 6 8 8 8 8 9 9 9 10 10 10 Find the first quartile, the median, and the third quartile for these data (Round your answers to 1 decimal place.), Q1 Median Q3
From the given information provided, the first quartile (Q₁) is 4, the median is 8, and the third quartile (Q₃) is 9.
To find the first quartile, median, and third quartile for the given data set, we first need to arrange the data in ascending order:
1 1 4 4 4 4 6 7 7 8 8 8 8 9 9 9 10 10 10
There are 20 data points in the set, so the median is the average of the 10th and 11th values:
Median = (8 + 8) / 2 = 8
To find the first quartile (Q₁), we need to find the median of the lower half of the data set. There are 10 data points in the lower half, so the median is the average of the 5th and 6th values:
Q₁ = (4 + 4) / 2 = 4
To find the third quartile (Q₃), we need to find the median of the upper half of the data set. There are 10 data points in the upper half, so the median is the average of the 15th and 16th values:
Q₃ = (9 + 9) / 2 = 9
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Please help me I’m so lost
The remaining side lengths of triangle B are given as follows:
25 cm and 30 cm.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering that the smallest side of triangle B has a length of 20 cm, while for triangle A it has a length of 24, the scale factor is given as follows:
k = 20/24
k = 5/6.
Hence the remaining side lengths of triangle B are given as follows:
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Hello please help me w this question
Answer: so u do the e then f to get z
Step-by-step explanation:
Determine whether ZY || VX If WY=5, YX 12.5, WV=15, and WZ=4. Justify your answer.
V
N
W
Y
X
4
→>>>
wv
wv equals x because the hypotenuse of rhe quadrilateral is congruent to the pathagoreum theorum
Answer: wv
Step-by-step explanation:
Decide how many solutions this equation has:
x2 + 3 = 0
Decide how many solutions this equation has:
x2 - 2x + 1 = 0
how many solutions this equation has:
x2 + 3 = 0
answer : no real solution
x = + i√3
x = - i√3
Decide how many solutions this equation has:
x2 - 2x + 1 = 0
answer : has 1 solution
x=1
chatgpt
Identify the vertex of the function graphed below. -6 -5 -4 -3 -2 -1 y 6 5 4 3 2 -2 Far -5 -6 2 3 4 5 6 X
The vertex of the parabola is in the form of coordinates is (h, k). The standard equation can be used to find the vertex.
What is Parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curvesGiven is to find the vertex of the parabola.
The vertex of the parabola is the point of intersection of the parabola and the axis of symmetry.
The Standard Form of a Parabola is y = a(x-h)² + k. To find the vertex in this form, you will use identify h and k from the standard form and put it into the vertex point (h, k).
Therefore, the vertex of the parabola is in the form of coordinates is (h, k). The standard equation can be used to find the vertex.
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which of the following is always true for all probability density functions of continuous random variables? group of answer choices they are symmetrical they are bell-shaped the area under the curve is 1.0 they have the same height
True, for all probability density functions of continuous random variables that the area under the curve is 1.0, but they do not have to be symmetrical or bell-shaped, and they do not have the same height.
A continuous random variable is a random variable that can take any value within a certain range, such as time or distance. Probability density functions (PDFs) describe the probability distribution of continuous random variables, and they have some important properties that hold true for all of them.
The first property of a PDF is that the area under the curve is always equal to 1.0. This means that the total probability of all possible outcomes of the random variable is equal to 1.0.
The second property is that PDFs do not have to be symmetrical or bell-shaped. The shape of the PDF depends on the distribution of the data.
The third property is that PDFs do not have the same height. The height of the PDF depends on the distribution of the data and the range of values that the random variable can take. The height of the PDF represents the density of the probability distribution for a given value.
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2π + 5π= 7π proposition or not?
The statement 2π + 5π = 7π is always a proposition.
What is a proposition?A proposition is a statement that is either right or wrong. Both results can not be possible for a statement. Only one result occurs at a time.
Clearly, the value of the addition 2π + 5π is 7π. So, the statement 2π + 5π = 7π is always true.
Therefore, the obtained answer is a proposition.
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Eniki has a sequence of numbers given by the formula t (n) = 4(5^n). a. What are the first three terms of Eniki's sequence? Hint (a):
b. Chelita thinks the number 312.500 is a term in Eniki's sequence. Is she correct? Justify your answer by either giving the term number or explaining why it is not in the sequence. Hint (b):
c. Elisa thinks the number 94.500 is a term in Eniki's sequence. Is she correct? Explain. Hint (c):
a) The first three terms of Eniki's sequence are 20, 100, and 500.
b) The number 312,500 is the 7th term in Eniki's sequence.
c) The number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.
The term 'n' in the formula represents the position of the number in the sequence, starting from the first term.
Enoki's also has a sequence of numbers, which is given by the formula (n) = 4(5ⁿ). Let's break down this formula to understand what it means.
a. To find the first three terms of Eniki's sequence, we substitute the values 1, 2, and 3 for 'n' in the formula. This gives us:
n = 1: 4(5¹) = 20
n = 2: 4(5²) = 100
n = 3: 4(5³) = 500
Therefore, the first three terms of Eniki's s sequence are 20, 100, and 500.
b. Chelita thinks that the number 312,500 is a term in Eniki's sequence. To determine whether she is correct or not, we need to find the value of 'n' that corresponds to this number. We can rearrange the formula to solve for 'n' as follows:
n = log base 5 (312,500/4)
Using a calculator, we find that n is approximately equal to 7. Therefore, the number 312,500 is the 7th term in Eniki's sequence.
c. Elisa thinks that the number 94,500 is a term in Eniki's sequence. To verify this, we can once again solve for 'n' in the formula:
n = log base 5 (94,500/4)
Using a calculator, we find that n is approximately equal to 6. Therefore, the number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.
In summary, Eniki's sequence is defined by the formula
=> f(n) = 4(5ⁿ),
where 'n' represents the position of the number in the sequence.
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What is the product of 2/5 and 4/5
How do you find the length of a side of a square with a given area?
To find the length of a side of a square with a given area, you need to take the square of side value.
The area of a square is the product of its two adjacent sides.
In other words, if you know the length of one side of a square, you can find its area by multiplying it by itself (squared). The formula for finding the area of a square is:
Area = side x side or Area = side²
So, if you have a square with an area of 16 square units, you can find the length of its sides by taking the square root of the area. This is because the square root of a number gives you the length of the side that, when multiplied by itself, gives you that number.
Using the formula, we get:
Area = side²
16 = side²
To solve for side, we need to take the square root of both sides of the equation:
√16 = √side²
4 = side
Therefore, the length of the side of the square with an area of 16 square units is 4 units.
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Element X decays radioactively with a half life of 9 minutes. If there are 850 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 301 grams?
The time to the nearest tenth of a minute, it would take the element to
decay to 301 grams is; 13.1 minutes
How to solve Radioactive decay problems?The number of grams of element x, after t minutes, is given by the following equation:
X(t) = X(0)(1 - r)^(t)
In which X(0) is the initial amount and r is the decay rate.
There are 850 grams of Element X
This means that X(0) = 850
So;
X(t) = 850(1 - r)^(t)
Half life of 9 minutes.
This means that X(9) = 0.5 * X(0) = 0.5 * 850 = 425. So;
425 = 850(1 - r)^(9)
(1 - r)^(9) = 0.5
1 - r = (0.5)^(1/9)
1 - r = 0.9259
r = 1 - 0.9259
r = 0.0741
X(t) = 850(0.9259)^(t)
Thus, at X(T) = 301, we have;
310 = 850(0.9259)^(t)
310/850 = (0.9259)^(t)
In 0.3647 = t In 0.9259
t = (In 0.3647 )/(In 0.9259)
t = 13.1 minutes
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Ron started with $15 in his savings account. After a short amount of time, his balance was $100. What is the percent of change?
pls, help!!!
To calculate the percent of change, we can use the following formula:
Percent of change = (final value - initial value) / initial value x 100%
In this case, the initial value is $15 and the final value is $100. Plugging these values into the formula, we get:
Percent of change = ($100 - $15) / $15 x 100% = 567%
So the percent of change in Ron's savings account balance is 567%. This means that Ron's balance increased by 567% from its initial value of $15 to its final value of $100.
Which rational number is greatest in-10/11,-19/22,-23/33,-39/44
The Greatest Number is -10/11.
What is Ascending Order?Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right.
Given:
Rational Number: 10/11,-19/22,-23/33,-39/44
The LCM of 11.22,33,44 is 132
-10/11×12/12=-120/132
-19/22×6/6=-114/132
-23/33×4/4=-92/132
-39/44×3/3=-117/132
In ascending order
-120/132,-117/132,-114/132,-92/132
= -10/11,-39/44,-19/22,-23/33
In descending order
-92/132,-114/132,-117/132,-120/132
= -23/33,-19/22,-39/44,-10/11
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A special truck cleans the surface of the ice rink shown below.
The figure is composed of a square and two semicircles.
30 m
30 m
If the truck cleans the entire surface, how many square meters of
ice will the truck
clean? Use 3.14 for p. Round your answer to the nearest tenth.
Answer: The area is 1660.41.
Geometry
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Given
The combination of circle and rectangle of length, width, and radius are 30.5, 30.5, and 15.25.
To find
The area of the geometry.
How to find the area of geometry?
Area = Area of rectangle and area of two semi-circle
Length = 30.5
Width = 30.5
Radius = 15.25
Then
Thus the area is 1660.41.
Two events are mutually exclusive:
a. if their intersection is 1
b. if they have no sample points in common
c. if their intersection is 0.5
d. Both a and c are correct
e. None of the above
option (b) if they have no sample points in common, then the two events are mutually exclusive
Probability is an essential concept in statistics and other related fields. It deals with the chance or likelihood of an event happening. In this context, we will discuss the concept of mutually exclusive events.
Two events are considered mutually exclusive if they cannot happen at the same time. That is, if one event occurs, the other cannot occur. For instance, if we flip a coin, it can either come up heads or tails, but not both at the same time. In mathematical terms, we can represent mutually exclusive events using the intersection of sets.
Suppose we have two events A and B. Their intersection is the set of all sample points that are common to both events. If the intersection of A and B is equal to 1, then the two events are not mutually exclusive. This means that both events can happen at the same time. On the other hand, if the intersection is equal to zero, the two events have no sample points in common. This implies that the events cannot happen together and are mutually exclusive.
Therefore the correct option is (b).
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What is the Pythagorean theorem formula?
Answer:
a^2 +b^2=c^2
Step-by-step explanation:
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I have attached and image of the equation! Please explain it to me step by step! Thank you!
The expression that gives the formula of the volume of a cone is interchanged for π, is given by, π = 3V/hr²
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, the formula for the volume of a cone, the expression is,
V = 1/3 πr²h
Where, r and h are radius and height of the cone respectively.
We are asked to interchange the expression to give a formula for, π
Therefore, the given expression,
V = 1/3 πr²h
Multiplying by 3 to each side,
3V = πr²h
Divide by r² to both sides,
3V/r² = πh
Divide by h to both sides,
3V/hr² = π
or,
π = 3V/hr²
Hence, the expression that gives the formula of the volume of a cone is interchanged for π, is given by, π = 3V/hr²
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Q9. A triangular prism has a volume of 480 cm³. The cross section of the prism is an isosceles triangle with base 6 cm. The depth of the prism is 20 cm. Find the length of the longest side of the triangular cross section. (Answer correct to 2 d.p.)
Answer:
Step 1: The volume of a prism is determined by the area of the cross section multiplied by the height of the prism.
Step 2: The area of an isosceles triangle can be calculated by A = (base x height)/2.
Step 3: Substituting values, we get A = (6 cm * h)/2.
Step 4: Since the volume of the triangular prism is 480 cm3, substituting in the formula V = A * height, we get 480 cm3 = (6 cm * h)/2 * 20 cm.
Step 5: Solving for h, we get h = 16 cm.
Step 6: Since it is an isosceles triangle, the longest side of the cross section is also 16 cm.
Answer: The length of the longest side of the triangular cross section is 16 cm.