What is the probability of landing on a 5 and then landing on an even number?
Write your answer as a percentage rounded to the nearest tenth.
Answers
The probability of landing on a 5 and then landing on an even number is 8.3%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The number of 5 on the dice is one.
Probability is the ratio of the number of favorable outcome to the total number of outcome.
The number of faces of dice is 6.
The probability of getting 5 is 1/6.
The even faces on the dice are 2, 4, 6.
The number of even number faces is 3.
The probability of getting even number is 3/6 = 1/2.
The probability of two independent event is the product of the probability of the events.
Therefore, the probability is (1/6) × (1/2)
= 1/12
= 0.083
= 8.3%
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Related Questions
B. compare his z-score in each event. c. compare his speed in each event. d. compare his pace in each event. questions 9-10 refer to the following situation: during a model railroad operating session, a model railroader must use the engine she is operating to move a pair of model cars through a series of track switches. her pair of cars consists of a boxcar and a flatcar. she knows that as the cars pass through the switches the boxcar has a 90% chance of getting through without derailing and the flatcar has an 80% chance of getting through without derailing. she also knows that whether either car derails or not is independent of the other car. 9. what is the probability that the flatcar derails? a. 10% b. 20% c. 28% d. 72% 10. what is the probability that both the boxcar and the flatcar get through without derailing? d. 72% c. 28% a. 10% b. 20%
Answers
To find the probability that the flatcar derails, we need to subtract the probability of it not derailing from 1. Since the flatcar has an 80% chance of getting through without derailing.
Therefore, the answer is b. 20%.
What is the probability that both the boxcar and the flatcar get through without derailing
Since the events of the boxcar and the flatcar derailing are independent, we can multiply their probabilities together.
The boxcar has a 90% chance of getting through without derailing (0.9) and the flatcar has an 80% chance (0.8), so the probability that both get through without derailing is
0.9 * 0.8 = 0.72 or 72%.
Therefore, the answer is d. 72%.
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Johnson’s table is represented by the vertices of rectangle KLMN. After a rotation 270° clockwise about the origin, the vertices of the rectangle are K'(−3,2) , L'(2,3) , M'(4,−2) , and N'(−2,−3). What were the original coordinates of rectangle KLMN ? Explain your reasoning.
Answers
We calculate the angle of rotation and rotate each vertex of the new rectangle by 90° anticlockwise to get the vertices of the original rectangle. Using the slope of a line, we find another equation relating the coordinates of the original rectangle. Solving these two equations simultaneously gives us the original coordinates of the rectangle.
We are given that Johnson’s table is represented by the vertices of rectangle KLMN. After a rotation 270° clockwise about the origin, the vertices of the rectangle are K'(−3,2), L'(2,3), M'(4,−2), and N'(−2,−3). We have to find the original coordinates of rectangle KLMN and explain our reasoning.Let's find the midpoint of the rectangle KLMN using the given coordinates:K = (x1, y1) = (x + a, y + b)L = (x2, y2) = (x + a, y + d)M = (x3, y3) = (x + c, y + d)N = (x4, y4) = (x + c, y + b)Midpoint of diagonal KM = (x + a + c) / 2, (y + d - b) / 2Midpoint of diagonal LN = (x + a + c) / 2, (y + b - d) / 2Since the midpoint of diagonal LN and KM are the same, we have:(x + a + c) / 2, (y + d - b) / 2 = (x + a + c) / 2, (y + b - d) / 2y + d - b = b - d2d = 2b - y ... Equation 1We know that, after rotating the rectangle KLMN by 270°, K’(−3, 2), L’(2, 3), M’(4, −2), and N’(−2, −3) are the vertices of the new rectangle.
Let us first find the new coordinates of the midpoint of diagonal KM and LN using the given coordinates:Midpoint of diagonal K'M' = (x' + a' + c') / 2, (y' + d' - b') / 2Midpoint of diagonal L'N' = (x' + a' + c') / 2, (y' + b' - d') / 2Since the midpoint of diagonal L'N' and K'M' are the same, we have:(x' + a' + c') / 2, (y' + d' - b') / 2 = (x' + a' + c') / 2, (y' + b' - d') / 2y' + d' - b' = b' - d'2d' = 2b' - y' ... Equation 2Now, let us calculate the angle of rotation. We have rotated the given rectangle 270° clockwise about the origin. Hence, we need to rotate it 90° anticlockwise to bring it back to the original position.Since 90° anticlockwise is the same as 270° clockwise, we can use the formulas for rotating a point 90° anticlockwise about the origin. A point (x, y) rotated 90° anticlockwise about the origin becomes (-y, x).So, applying this formula to each vertex of the rectangle, we get:K'' = (-2, -3)L'' = (-3, 2)M'' = (2, 3)N'' = (3, -2)Now, we need to find the coordinates of the original rectangle KLMN using these coordinates.
Since the diagonals of a rectangle are equal and bisect each other, we know that:KM = LNK'M'' = (-2, -3)L'N'' = (3, -2)Equating the slopes of K'M'' and LN'', we get:(y' + 3) / (x' + 2) = (y' + 2) / (x' - 3)y' = -x'This is the equation of the line K'M'' in terms of x'.Putting the value of y' in the equation of L'N'', we get:3 = -x' + 2x' / (x' - 3)x' = 3Hence, the coordinates of K'' are (-2, -3) and the coordinates of K are obtained by rotating this point 90° clockwise. So, we get:K = (3, -2)Similarly, we can find the coordinates of the other vertices of the rectangle. Hence, the original coordinates of the rectangle KLMN are:K = (3, -2)L = (2, 3)M = (-4, 2)N = (-3, -3)Therefore, the original coordinates of the rectangle KLMN are K(3, -2), L(2, 3), M(-4, 2), and N(-3, -3).Reasoning: The approach used here is to find the midpoint of the diagonal of the original rectangle KLMN and the new rectangle K'M'N'L'. Since a rotation preserves the midpoint of a line segment, we can equate the midpoints of the diagonal of the original rectangle and the new rectangle. This gives us one equation relating the original coordinates of the rectangle. Next, we calculate the angle of rotation and rotate each vertex of the new rectangle by 90° anticlockwise to get the vertices of the original rectangle. Using the slope of a line, we find another equation relating the coordinates of the original rectangle. Solving these two equations simultaneously gives us the original coordinates of the rectangle.
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Find the distance between each pair of points, to the nearest tenth. (-5,-5),(1,3)
Answers
The distance between the points (-5, -5) and (1, 3) is 10 units.
To find the distance between the points (-5, -5) and (1, 3), we can use the distance formula.
The distance formula is:
\(d = \sqrt{((x_2 - x_1)^2+ (y_2 - y_1)^2)}\)
Let's substitute the values into the formula:
\(d = \sqrt{((1 - (-5))^2 + (3 - (-5))^2)}\\d = \sqrt{((1 + 5)^2 + (3 + 5)^2}\\d = \sqrt{(6^2 + 8^2)}\\d = \sqrt{(36 + 64)}\\d = \sqrt{100}\\d = 10\)
Therefore, the distance between the points (-5, -5) and (1, 3) is 10 units.
Explanation:
The distance formula is derived from the Pythagorean theorem.
It calculates the length of the hypotenuse of a right triangle formed by the coordinates of two points.
In this case, we have a right triangle with legs of length 6 and 8.
Using the Pythagorean theorem, we find that the hypotenuse (the distance between the two points) is 10 units.
Remember to round your answer to the nearest tenth, so the final answer is 10 units.
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11r ≥ 220
how to solve? and what are the steps to solve
Answers
Answer:
r ≥ 220/11
Step-by-step explanation:
To solve for r, you first need to isolate r. To do that, divide both sides by 11. Therefore, you get r ≥ 220/11. 220/11 is the most simplified form of that fraction, so r ≥ 220/11 is the answer.
common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 74 cells. Find the relative growth rate.
Answers
The
relative growth rate
is 0.481\(e^{0.0065t}\).
What is growth rate?
The
growth rate
refers to any growth that occurs over time; its formula takes time into consideration and provides information on the rate and quantity of growths that occur after a specific time period. The formula of growth is
P(t)=\(P_{0}\)\(e^{kt}\) where,
P(t)= Population after time t,
\(P_{0}\)= initial population , t= time and
K= growth constant.
Initial population of culture is 74 Cell.
Two cells in every 20 Min.
The
relative growth rate
is:
If the population growth is P(T) Then the growth rate is P′(T).
P(t)= \(P_{0}e^{kt}\)
P’(t)= k\(P_{0}e^{kt}\)
P(t)= Population after time t,
\(P_{0}\)=74
t=20
k= growth constant
If the cells double every 20 Minutes then:
P(t)= \(P_{0}e^{kt}\)
100= 74\(e^{20k}\)
20k=ln (100/74)
k= 0.0065
So, the
relative growth rate
is:
P’(t)= k\(P_{0}e^{kt}\)
P’(t)= 0.0065×74(\(e^{0.0065t}\))
P’(t)=0.481\(e^{0.0065t}\)
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what is the equation of the line? please help !!!! first and correct answer will get brainesttt
Answers
Answer:
y=1/2x-4
Step-by-step explanation
A town’s population has been increasing at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070 people. Assume this trend continues and type your answer without any commas.The population in 2016 will be?
Answers
ANSWER
64170
EXPLANATION
Step 1: Given that:
The population was 46020 in 2010 and 52070 in 2012
Step 2: Determine the slope of the trend
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how much is ( ( (13 x 3) - 3) / 3)?
Answers
Let's simplify the expression step by step. The value of the expression ((13 x 3) - 3) / 3 is 12.
Step 1: Multiply 13 by 3
13 x 3 = 39
Step 2: Subtract 3 from the result of Step 1
39 - 3 = 36
Step 3: Divide the result of Step 2 by 3
36 / 3 = 12
To explain the calculations further, we follow the order of operations (also known as PEMDAS/BODMAS) to ensure the correct sequence of calculations:
Parentheses: There are no parentheses in the expression.
Exponents: There are no exponents in the expression.
Multiplication and Division: We perform the multiplication of 13 and 3 first, as indicated by the multiplication symbol (x). This gives us the intermediate result of 39. Then, we subtract 3 from 39.
Addition and Subtraction: Since there are no addition or subtraction operations in the expression beyond the subtraction of 3 from 39, we move to the next step.
Finally, we divide the result of the subtraction (36) by 3, which gives us the final result of 12.
It's important to follow the order of operations to ensure accurate calculations and obtain the correct answer.
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An insect population after x months can be modeled by
the function g(x) = 11(1.2). Which statement is the
best interpretation of one of the values in this function?
A. The insect population increased by 12 insects each month
B. The insect population decreased by 12 insects each month
C. The insect population increased at a rate of 20% each month
D. The insect population decreased at a rate of 20% each
month
Answers
The given function is g(x) = 11(1.2), where x is the number of months that have passed since the start of the model.\
What is function?a function is a relation between two sets, known as the domain and the range, that assigns to each element of the domain a unique element of the range. The domain is the set of all possible inputs or arguments for the function, and the range is the set of all possible outputs or values that the function can produce.
The given function is g(x) = 11(1.2), where x is the number of months that have passed since the start of the model. The function does not have a variable that changes with time, which suggests that the insect population is not affected by any external factors such as predation or migration. Instead, the function has a constant value of 11(1.2) that represents the insect population at any time x.
The value 1.2 in the function represents the growth factor, which is a multiplier applied to the initial population of 11 insects. This growth factor indicates the rate at which the insect population increases over time. Specifically, the growth factor of 1.2 means that the insect population increases by 20% each month, since:
new population = initial population + (growth factor) * initial population
new population = 11 + (1.2) * 11
new population = 11 + 13.2
new population = 24.2
This means that after one month, the insect population would be 24.2, which is an increase of 13.2 insects or approximately 20%. Therefore, the best interpretation of the value 1.2 in the function is that it represents the rate of increase of the insect population, and the correct answer is C.
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(35+4n)−(15+3n)
pls answer asap
Answers
Answer:
20 - n
Step-by-step explanation:
Subtract like-terms:
35 + 4n - 15 - 3n = 20 - n
2737÷13 full workingout
Answers
210.53846
×wwwwwwwwwwwwwwwww
\(2737/13=\frac{2737}{13}\)
This is because division is always the same as a fraction
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?a. The sampling distribution of d hat is normal.b. The sampling distribution of d hat is binomial.c. The sampling distribution of d hat is uniform.d. d hat is unbiased.e. d hat is biased.
Answers
The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
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pls help me. show the steps too
\(3x {}^{2} - 27\)=0
Answers
Answer:
x = ± 3
Step-by-step explanation:
3x² - 27 = 0 ( add 27 to both sides )
3x² = 27 ( divide both sides by 3 )
x² = 9 ( take square root of both sides )
x = ± \(\sqrt{9}\) = ± 3
PLEASE HELP I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
correct option is A
Step-by-step explanation:
mark me
Hope this helps!!!!!!
If a data set has a standard deviation of 4 units and a mean of 10 units, the coefficient of variation is
Answers
According to the question The coefficient of variation for the given data set is 40%.
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation (SD) by the mean (μ) and expressing the result as a percentage.
The formula for the coefficient of variation is:
\(\[ CV = \left(\frac{SD}{\mu}\right) \times 100 \]\)
In this case, the standard deviation is 4 units and the mean is 10 units. Plugging these values into the formula, we get:
\(\[ CV = \left(\frac{4}{10}\right) \times 100 \]\)
\(\[ CV = 0.4 \times 100 \]\)
\(\[ CV = 40 \]\)
Therefore, the coefficient of variation for the given data set is 40%.
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Which equation is the slope-intercept form of the equation of the line that passes through (1, 2) and is parallel to 4x - 2y = 6?
Answers
Answer:
The equation of the parallel line is y = 2x
Step-by-step explanation:
The slope-intercept form of the linear equation is:
y = m x + b, where
m is the slope of the line b is the y-intercept (value y at x = 0)Parallel lines have the same slopes and different y-intercepts
∵ The equation of the given line is 4x - 2y = 6
→ To find the slope of this line re-arrange it to be in the
slope-intercept form Subtract 4x from both sides to move x to
the right side
∵ 4x - 4x - 2y = 6 - 4x
∴ -2y = 6 - 4x
→ Divide both sides by -2 to make the coefficient of y = 1
∵ \(\frac{-2y}{-2}=\frac{6}{-2}-\frac{4x}{-2}\)
∴ y = -3 - (-2x)
∴ y = -3 + 2x
→ Swithch -3 and 2x
∴ y = 2x - 3
→ Compare it by the form of the equation above to find m
∴ m = 2
∴ The slope of the given line is 2
∵ The two lines are parallel
∴ The slope of the parallel line is 2
→ Substitute it in the form of the equation above
∴ y = 2x + b
→ To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The line passes through the point (1, 2)
∴ x = 1 and y = 2
∵ 2 = 2(1) + b
∴ 2 = 2 + b
→ Subtract 2 from both sides to find b
∴ 2 - 2 = 2 - 2 + b
∴ 0 = b
∴ y = 2x
The equation of the parallel line is y = 2x
T/F regardless of whether a distribution of scores that is symmetrically shaped has one mode or two modes, the mean value tends to be similar to the median value.
Answers
True
In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.
When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.
The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.
If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.
If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.
In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.
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answer this and u a big W if u dont ur a L
Answers
Answer:
Part A. (4,5)
Part B. (9,7)
Step-by-step explanation:
Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.
n his road trip, Leon stops to refuel and get some snacks. He has the following purchases:
12 gallons of gas at $2.89 per gallon
2 granola bars for $1.59 each
1 apple for $0.89
2 bottles of vitamin water for $1.39 each
Leon must pay 7.5% sales tax on everything but the gas, which already has tax included in the per gallon price. If Leon paid $44.64, then he _____ for his purchase.
a.
did not pay enough
b.
paid the correct amount
c.
paid $2.60 too much
d.
paid $3.11 too much
Answers
Answer:
C. Paid $2.60 too much
Step-by-step explanation:
Gas 12 x 2.89 = 34.68
granola 2 x 1.59 = 3.18 x 1.075 = 3.4185
apple .89 x 1.075 = 0.95675
vitamin water 2 x 1.39 = 2.78 x 1.075 = 2.9885
34.68
3.4185
0.95675
+ 2.9885
---------------------
$42.04
$44.64
- $42.04
---------------------
$2.60
What determines whether a certain welding process can be used for workpieces in horizontal, vertical, or upsidedown positions-or, for that matter, in any position? (See Table 30.1.) Explain and give examples of appropriate applications.
Answers
The positions of a workpiece in the welding process. It is a crucial step in determining whether a certain welding process can be used for workpieces in horizontal, vertical, or upside-down positions, or in any position. It is the degree of weld penetration, the direction of welding, and the metal transfer mode, among other factors, that are influenced by the position of the workpiece.
A welding technique should be chosen to optimize the penetration depth and direction of the weld, as well as to ensure that the metal is deposited in a stable and controllable manner, in order to provide the desired results for a given welding situation. Certain welding processes, such as gas metal arc welding (GMAW), are more flexible than others and can be used in various positions with little to no modifications.
Nonetheless, some welding techniques may need the use of specific equipment or modifications to function properly in particular positions. For example, a gas tungsten arc welding (GTAW) technique may require the addition of a backing plate to ensure proper penetration in the vertical position.
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what is the equation of the line in slope-inr except form.write your answer using integers proper fractions and improper fractions in simplest form
Answers
Answer:
Figure it out yourself loser
Step-by-step explanation:
Find the measure of arc FGH given measure of angle FGH = 21x – 2 degrees and messure of angle FAH = 38x + 5 degrees.
Answers
Answer:
there is actually a secret degree in science
Step-by-step explanation:
it's called
ur mom
Question: help me on this problem :
Which two angles measures can u add to find the Measure of angle FMH? Pls
Pls help
D = 0.25 (36950 - 0.02p^3)^2. Find the unit price that maximizes revenue. Enter your answer as a number (no units) rounded appropriately.
Answers
To find the unit price that maximizes revenue, we need to maximize the given revenue function: \(R = 0.25(36950 - 0.02p^3)^2\). The revenue function R is dependent on the unit price p.
To maximize the revenue, we need to find the value of p that corresponds to the maximum point on the revenue curve.
To determine this, we can take the derivative of the revenue function with respect to p and set it equal to zero to find the critical points. Let's calculate the derivative:
\(dR/dp = 2 * 0.25 * (36950 - 0.02p^3) * (-0.02) * 3p^2 = -0.015 * p^2 * (36950 - 0.02p^3)\)
Setting this derivative equal to zero, we have:
\(-0.015 * p^2 * (36950 - 0.02p^3) = 0\)
Since we are interested in finding the unit price, we can solve this equation numerically using methods like graphing, Newton's method, or a calculator. The resulting value of p will be the unit price that maximizes revenue. Remember to round the answer appropriately based on the precision required.
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What is the optimal choice when pı = 3, P2 = 5 and I = 20 and utility is (a) u(x1, x2) = min{2x1, x2} (b) u(x^2 1, x^2 2) = x} + x3 (c) u(x1, x2) = In(xi) + In(x2) (d) u(x1, x2) = x x = (e) u(x1, x2) = -(x1 - 1)^2 – (x2 - 1)^2
Answers
Using the Lagrange method, the optimal choice is therefore (x1, x2) = (20/9, 4/3).
The optimal choice when pı = 3, P2 = 5 and I = 20 and utility is u(x1, x2) = min{2x1, x2} can be found using the Lagrange method .Lagrange method: This method involves formulating a function (the Lagrange function) which should be optimized with constraints, i.e. the optimal result should be produced while adhering to the constraints provided. The Lagrange function is given by: L(x1, x2, λ) = u(x1, x2) - λ(I - p1x1 - p2x2)
Where L is the Lagrange function, λ is the Lagrange multiplier, I is the budget, p1 is the price of good 1, p2 is the price of good 2.The optimal choice can be determined by the partial derivatives of L with respect to x1, x2, and λ, and setting them to zero to get the critical points. Then, the second partial derivative test is used to determine if the critical points are maxima, minima, or saddle points. The critical points of the Lagrange function L are:
∂L/∂x1 = 2λ - 2p1 = 0 ∂L/∂x2 = λ - p2 = 0 ∂L/∂λ = I - p1x1 - p2x2 = 0
Substitute the first equation into the second equation to get:λ = p2,2λ = 2p1 ⇒ p2 = 2p1,
Substitute the first two equations into the third equation to get: x1 = I/3p1,x2 = I/5p2
Substitute p2 = 2p1 into the above to get:x1 = I/3p1,x2 = I/10p1.Substitute the values of p1, p2 and I into the above to get:x1 = 20/9,x2 = 4/3.The optimal choice is therefore (x1, x2) = (20/9, 4/3).
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LaShea would like to invest her $100 in birthday money. Which option will give her the most money at the end of the investment period?
1 year at 8 percent
1.5 years at 7 percent
2 years at 6.5 percent
3 years at 4 percent
Answers
Answer:
1 year at 8 percent
Step-by-step explanation:
i took the test
Simplify -5(20 + 3).
85
-115
-97
-103
ill give brainliest
Answers
Answer:
The answer is -115
Step-by-step explanation:
Answer:
-115
Step-by-step explanation:
Ur welcome
What is the temperature, in degrees Fahrenheit, shown on the thermometer to the nearest integer? Enter your integer answer in the box.
Answers
Find the equation of the line that passes through the point (2, 1) and is perpendicular to y=(−2/5)x+3.
Answers
Answer:
Step-by-step explanation:
perp. 5/2
y - 1 = 5/2(x - 2)
y - 1 = 5/2x - 5
y = 5/2x - 4
Answer:
The answer is
\(y = \frac{5}{2} x - 4\)Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
The original line is y = - 2/5x + 3
Comparing with the general equation above
Slope/m = - 2/5
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
So we have
\(m \times m _1 = - 1 \\ - \frac{2}{5} m _1 = - 1 \\ = - 2m _1 = - 5 \\ = m _1 = \frac{5}{2} \)
So the slope of the perpendicular line is
5/2
So the equation of the line using point
(2, 1) and slope 5/2 is
\(y - 1 = \frac{5}{2} (x - 2) \\ y - 1 = \frac{5}{2} x - 5 \\ y = \frac{5}{2} x - 5 + 1\)
We have the final answer as
\(y = \frac{5}{2} x - 4\)
Hope this helps you
TRANSAMERICA BUILDINGThe TransAmerica building in San Francisco is built of concrete and is shaped like a square-based pyramid. The building is periodically power-washed using one gallon of cleaning solution for every 250 square meters of surface. As the new building manager, you need to order the cleaning supplies for this large task. The problem is that you do not know the height of each triangular face of the building; you only know the vertical height of the building from the base to the top vertex.Your Task: Determine the amount of cleaning solution needed to wash the TransAmerica building if an edge of the square base is meters and the height of the building is meters. Include a sketch in your solution.
Answers
we know that
The surface area of a square pyramid is given by the formula
\(SA=B+LA\)where
B is the area of the square base
LA is the lateral area (area of the four triangular faces)
step 1
Find out the area of the square base B
\(\begin{gathered} B=96^2 \\ B=9,216\text{ m}^2 \end{gathered}\)step 2
Find out the area of one triangular face
the area of one triangular face is given by the formula
\(A=\frac{1}{2}*b*h\)where
b=96 m
h=?
Applying the Pythagorean Theorem, find out the value of h
\(h^2=H^2+(\frac{b}{2})^2\)where
H=220 m (height of the building)
b/2=96/2=48 m
substitute
\(\begin{gathered} h^2=220^2+(48)^2 \\ h^2=50,704 \\ h=225.18\text{ m} \end{gathered}\)substitute
\(\begin{gathered} A=\frac{1}{2}*96*225.18 \\ A=10,808.64\text{ m}^2 \end{gathered}\)Multiply by 4 to obtain the Lateral Area
\(\begin{gathered} LA=4*10,808.64 \\ LA=43,234.56\text{ m}^2 \end{gathered}\)The surface area of the building is equal to
\(\begin{gathered} SA=9,216+43,234.56 \\ SA=52,450.56\text{ m}^2 \end{gathered}\)step 3
we know that
one gallon of cleaning solution -----> for every 250 square meters of surface
Applying proportion
1/250=x/52,450.56
solve for x
x=52,450.56/250
x=210 gallons
The answer is 210 gallonssee the figure below to better understand the calculation to obtain the value of
h (the height of each triangular face)
What are 10 words that can be used to explain what a right triangle is? 10 points for 10 words
Answers
Answer:
A triangle with one of the angles being ninety degrees.
Step-by-step explanation: