Answer: The dimensions of the rectangular part of the Norman window that would allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.
Explanation:
Let's assume that the height of the rectangular part of the Norman window is "h" and the width is "w". Then the diameter of the semicircle is also "w". The total amount of framing material needed is the sum of the perimeter of the rectangular part and half the circumference of the semicircle:
Perimeter of rectangular part = 2h + 2w
Circumference of semicircle = 1/2πw
Total framing material = 2h + 2w + 1/2πw
We want to maximize the amount of light entering the window, which is proportional to the area of the rectangular part of the window. The area of the rectangular part is given by:
Area of rectangular part = hw
Now we can use the constraint that there is only 12 feet of framing material available:
2h + 2w + 1/2πw = 12
Solving for h in terms of w:
h = (12 - 2w - 1/2πw)/2
Substituting this expression for h into the formula for the area of the rectangular part:
Area of rectangular part = w(12 - 2w - 1/2πw)/2
We can now use calculus to find the value of w that maximizes this area. Taking the derivative of the area with respect to w and setting it equal to zero:
d/dw[w(12 - 2w - 1/2πw)/2] = 0
Simplifying and solving for w:
w = 4π/(4 + π)
Substituting this value of w into the expression for h:
h = (12 - 2w - 1/2πw)/2
h ≈ 8
Therefore, the dimensions of the rectangular part of the Norman window that allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.
Chandler earns $15.25 an hour as a hostess at a local restaurant. She
earns an additional $25 in tips each night from take-out orders.
Determine if this linear relationship is proportional. Explain.
No, this linear relationship is not proportional, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes
Proportional relationships are those wherein the ratio between the two portions being as compared stays constant, no matter the values of those quantities.
In this case, we're evaluating Chandler's earnings primarily based on her hourly wage and her hints from take-out orders.
But, the ratio between Chandler's hourly wage of $15.25 and her tips of $25 per night varies relying on the number of hours she works.
For example, if Chandler works for 2 hours, her total income could be $30.50 (2 x $15.25) + $25 = $55.50.
If she works for four hours, her total earnings would be $61 (4 x $15.25) + $25 = $86. In this example, the ratio among her hourly salary and tips adjustments as her income increase with more hours worked.
Therefore, because the ratio between Chandler's hourly wage and tips changes because the number of hours worked changes, this linear relationship is not proportional.
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Cardine company acquired and placed into use equipment on 2009 january 2, at a cash cost of 935,000. transportation charges amounted to 7,500, and installation and testing costs totaled 55,000. the equipment was estimated to have a useful life of nine years and a salvage value of 37,500 at the end of its life. it was further estimated that the equipment would be used in the production of 1,920,000 units of product during its life. during 2009, 426,000 units of product were produced. compute the depreciation if the year ended december 31, using straight line method.
t\The depreciation expense for the year ended December 31, 2009 using the straight-line method is $23,333.33.
The total cost of the equipment is $997,500 ($935,000 + $7,500 + $55,000). The depreciable cost is calculated by subtracting the salvage value from the total cost, which is $960,000 ($997,500 - $37,500).
To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment. The annual depreciation expense is $106,666.67 ($960,000 ÷ 9).
Since the equipment was only used for a portion of the year, we need to prorate the annual depreciation expense based on the number of units produced.
The depreciation expense for the year ended December 31, 2009 is calculated as follows:
Depreciation Expense = (Annual Depreciation Expense ÷ Total Units of Production) x Units Produced in 2009
Depreciation Expense = ($106,666.67 ÷ 1,920,000) x 426,000
Depreciation Expense = $23,333.33
Therefore, the depreciation expense for the year ended December 31, 2009 using the straight-line method is $23,333.33.
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1. Write a function of × that performs the following operations: Raise x to the ninth
power, multiply by 6, and then add 4.
y = f(x) = _____
2. Find the inverse to the function you found in
part (a).
x = g (y) =
A function of x that performs the operations y = f(x) = 6x^9 + 4, the inverse to the function found in part (a). x = g (y) = ((y - 4) / 6)^(1/9)
The function that performs the operations of raising x to the ninth power, multiplying by 6, and adding 4 is
f(x) = 6x^9 + 4
To find the inverse function, we need to solve for x in terms of y
y = 6x^9 + 4
Subtract 4 from both sides
y - 4 = 6x^9
Divide both sides by 6
(x^9) = (y - 4) / 6
Take the ninth root of both sides
x = ((y - 4) / 6)^(1/9)
Therefore, the inverse function is
g(y) = ((y - 4) / 6)^(1/9)
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Solve for X pleaseee!!!
part of a multiplication table is below. complete the pattern in the multiplication table. click each dot on the image to select an answer. a partial multiplication table with 3 rows and 3 columns. the first row reads 40, 45, 50. the second row reads an unknown number, 54, 60. the third row reads 56, an unknown number, 70. stuck?.
the completed multiplication table is: 40 45 50 ,72 54 60 and 56 90 70 .by using common factor logic we can solve this question.
what is common factor ?
A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.
In the given question,
From the given table, we can see that:
The first row reads 40, 45, 50 (which are multiples of 5).
The second row has an unknown number (let's call it x), 54, and 60.
The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).
To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.
Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.
Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.
Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.
Therefore, the completed multiplication table is:
40 45 50
72 54 60
56 90 70
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A cyclist went out for a solo ride but has become lost. He knows from his inexpensive cycletracker GPS the distance he has traveled and in which direction, but he has no idea how to get home short of retracing his path. The different legs of his trip are listed below.
Determine in which direction and how far he needs to ride to get back where he started in the shortest distance possible. (assume there are no obstacles in his way and he can travel in a straight line) (5 marks)
Leg #1-8 km [North]
Leg #2-10 km [East]
Leg #3-12 km [15 S of East]
Leg #4-14 km [South]
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
How to solve for the distanceWe can use trigonometry to find the x and y components.
x3 = 12 * cos(15°) ≈ 11.59 km (east)
y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)
Leg #4: 14 km [South]
x4 = 0 km (no east/west movement)
y4 = -14 km (south, hence the negative sign)
Now, let's find the total x and y displacements:
x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km
y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km
Now, we can find the distance and direction he needs to ride to get back to the starting point:
Distance=
[tex]\sqrt{21.59^2 + (-9.10)^2}[/tex])
23.21 km
Direction:
angle =
arctan(9.10 / 21.59)
= 23.13°
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
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There are 250 students who went to the homecoming dance, 300 students who went to the prom and 200 students who went to both dances. find the probability that someone went to homecoming or prom.
The probability that someone went to either homecoming or prom is 1, or 100%.
To find the probability that someone went to either homecoming or prom, we need to add the number of students who went to each dance and then subtract the number of students who went to both dances (as they would have been counted twice in the first step).
So, the total number of students who went to either homecoming or prom is:
250 + 300 - 200 = 350
Now, we can calculate the probability that someone went to either dance by dividing this number by the total number of students:
P(homecoming or prom) = 350 / (250 + 300 - 200) = 350 / 300 = 1.17
However, probabilities are typically expressed as decimals or percentages between 0 and 1. Since it's impossible for someone to have a probability greater than 1, we can conclude that there is an error in our calculation. This is likely because we made a mistake when adding or subtracting the number of students.
To correct this, we need to double-check our work and make sure we have the correct numbers. Assuming that the numbers provided are correct, the probability that someone went to either homecoming or prom is:
P(homecoming or prom) = 350 / (250 + 300 - 200) = 350 / 350 = 1
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Can you use addition or mulipulcation for solving 100000 x 1/100000
Using multiplication to solve 100000 x 1/100000, the answer would be 1.
You should use multiplication to solve the problem 100000 x 1/100000.
When you multiply 100000 by 1/100000, you're essentially multiplying 100000 by a fraction that represents "one part out of 100000.". The step by step explanation is:
1. Write down the given problem: 100000 x 1/100000
2. Perform the multiplication: 100000 x (1/100000)
3. Simplify the expression: 1
Mathematically, this can be written as:
So, 100000 x 1/100000 equals 1.
You wouldn't typically use addition to solve this particular problem, as it involves multiplication of a fraction rather than adding two numbers together. However, you could use addition to solve related problems.
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La literatura consiste en una forma de escribir en la cual se violenta organizadamente el lenguaje ordinario.
la literatura es una forma de arte que desafía los límites del lenguaje y que nos invita a descubrir nuevas formas de entender y de ver el mundo.
La literatura se define como un conjunto de obras escritas que emplean una serie de técnicas y recursos lingüísticos para crear un universo imaginario y comunicar ideas y emociones al lector.
Una de estas técnicas consiste en la violación organizada del lenguaje ordinario, lo que implica una ruptura con las normas y convenciones lingüísticas establecidas para dar lugar a una expresión más creativa y original.
Esta violencia organizada del lenguaje permite a los escritores experimentar con la forma y el contenido de sus obras, creando así una literatura rica y diversa que refleja las distintas visiones del mundo y de la vida de los autores.
En definitiva, la literatura es una forma de arte que desafía los límites del lenguaje y que nos invita a descubrir nuevas formas de entender y de ver el mundo.
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Help there is a picture of it
Answer:
5 19/20 miles
what is 1/10 of 1.65
I will mark you brainliysit help
WHAT IS 2X36 DIVED BY 3 PLUS 9 -4=
HEEELPPP
Answer:
Step-by-step explanation:
2 x 36 ÷ 3 + 9 - 4
= 72 ÷ 3 + 9 - 4 (perform multiplication first)
= 24 + 9 - 4 (perform division)
= 29 (perform addition and subtraction)
Therefore, 2x36 ÷ 3 + 9 - 4 = 29.
Answer:
29
Step-by-step explanation:
2×36=72
72/3=24
24+9=33
33-4=29
8.Soloman attempts to construct a triangle similar to triangle XYZ.
Soloman constructs his triangle X'Y'Z' by making angles X' and Y' half the measures of
angles X and Y, respectively. Is his triangle X'Y'Z' similar to triangle XYZ? If so, name the
theorem that indicates similarity. If not, explain why not.
Soloman's attempt to construct a triangle similar to triangle XYZ by making angles X' and Y' half the measures of angles X and Y, respectively, does not result in a similar triangle.
Why are the triangles not similar ?For two triangles to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be equal. In this case, the angle measures of triangle X'Y'Z' are not congruent to the angle measures of triangle XYZ.
Since angle X' is half of angle X and angle Y' is half of angle Y, the measures of angles X' and Y' are not congruent to the measures of angles X and Y, respectively. Therefore, the triangles are not similar.
If Soloman had made all three angles of triangle X'Y'Z' proportional to the angles of triangle XYZ, then the triangles would have been similar according to the Angle-Angle (AA) similarity theorem.
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A trip to white mountains of new hampshire from boston will take you 2 3/4 hours. assume you have traveled 1/11 of the way. how much longer will the trip take?
The trip will take another 1 hour to complete.
If a trip from Boston to the White Mountains of New Hampshire takes 2 3/4 hours, and you have already traveled 1/11 of the way, then the remaining distance is:
1 - 1/11 = 10/11 of the total distance.
To find how much longer the trip will take, we can use the proportion:
time taken for 10/11 of the trip = x (time taken for the whole trip)
distance traveled for 10/11 of the trip = 1 - 1/11 = 10/11 of the total distance
Since the time taken is proportional to the distance traveled, we can set up the following equation:
2 3/4 hours / (1 - 1/11) = x
where x is the time it will take for the whole trip.
Simplifying the left side of the equation, we get:
2 3/4 hours / (10/11) = x
Multiplying both sides by (11/10), we get:
x = (2 3/4 hours) × (11/10) = 3 1/4 hours
Therefore, the remaining time to complete the trip is:
3 1/4 hours - 2 3/4 hours = 1 hour
So the trip will take another 1 hour to complete.
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What is the probability of selecting an Ace, not replacing it, and then selecting a King?
The probability of selecting an Ace, not replacing it, and then selecting a King is 4/663 or approximately 0.006 or 0.6%.
The probability of selecting an Ace, not replacing it, and then selecting a King can be calculated using the rules of conditional probability.
First, we need to determine the probability of selecting an Ace from a standard deck of 52 cards. There are four Aces in the deck, so the probability of selecting an Ace is 4/52, which can be simplified to 1/13.
Next, we need to consider the fact that the Ace is not replaced before selecting the King. This means that the deck now contains 51 cards, with only three remaining Aces. Therefore, the probability of selecting a King after selecting an Ace without replacement is 4/51.
To determine the overall probability of selecting an Ace and then a King, we multiply the probability of selecting an Ace (1/13) by the probability of selecting a King after selecting an Ace without replacement (4/51).
The calculation is as follows:
(1/13) x (4/51) = 4/663
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0= pi/6 radians. Identify the terminal point and tan θ
The terminal point is (0.866025, 0.5) and the tangent of θ is 0.55735 for θ = π/6 radians.
When the angle is given as 0 radians (0 = π/6 radians), the terminal point of the angle is on the positive x-axis.
The terminal point represents the point in the coordinate system where a given angle and distance (or magnitude) from the origin are located.
For any angle a, the coordinates of the terminal point are given by:
x = cos(a)
y = sin(a).
In this case, the angle is a = π/6
Then the coordinates of the terminal point are:
x = cos(π/6) = 0.5
= 0.866025
y = sin(π/6)
= 0.5
So the terminal point is (0.866025, 0.5)
The quotient of the y-component and the x-component is the tangent of that angle:
tan(π/6) = 0.5/ 0.866025
= 0.57735
Therefore, the terminal is (0.866025, 0.5) and the tangent is 0.55735.
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The question attached here seems to be incomplete, the complete question is:
If θ= π/6 radians then Identify the terminal point and tan θ.
A rectangle has vertices located at the points: A(-1 1/4,3 1/2), B(2 2/3,3 1/2), C(2 2/3,-1 3/4), D(-1 1/4,-1 3/4). Find the length of BC
The length of BC is 5.25 units. when the rectangle has vertices located at the points: B is ( 2 2/3,3 1/2) and C is (2 2/3,-1 3/4).
We need to find the length of BC. The length of a line segment BC can be calculated using the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given as :
d = √(x2−x1)²+(y2−y1)²
Given data:
A = (-1 1/4,3 1/2)
B = ( 2 2/3,3 1/2)
C = (2 2/3,-1 3/4)
D = (-1 1/4,-1 3/4)
We need to Convert the B and C mixed numbers to improper fractions, we get,
B = (2+2/3), (3 + 1/2)
= (8/3, 7/2)
C = (2+2/3) , (-1 + 3/4)
= (8/3, -7/4).
Substituting the B and C values into the distance formula, we get:
= √(8/3 − 8/3)² + ( −7/4 − 7/2 )²
= √0 + ( − 21 / 4 )²
= √441/16
[tex]= 21/4[/tex]
[tex]= 5.25[/tex]
Therefore, the length of BC is 5.25 units.
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Cuánto interés ganará lesli si presta l 5000 a pagar en 3años? al:5%simple anual. 10%simple anual. 5%compuesto anual
The interest gained by Lesli is if she lends $5000 for 3 years at 5% simple interest annually is $750, 10% simple interest annually is $1500, and on 5% compound interest annually is $790
The simple interest is calculated by
I = P * r * t
where P is the principal
r is the rate of interest
t is the time
I is the simple interest
The compound interest is calculated by:
I = P[tex](1 +r)^t[/tex] - P
where I is the compound interest
P is the principal
r is the rate of interest
t is the time
According to the question,
P = $5000
t = 3 years
1. r = 5% simple interest
I = 5000 * 3 * 0.05
= $750
2. r = 10% simple interest
I = 5000 * 3 * 0.10
= $1500
3. r = 5% compounded annually
I = 5000 [tex](1+0.05)^3[/tex] - 5000
= 5000 * 1.158 - 5000
= $790
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The question is in Spanish, and the question in English is:
How much interest will Lesli earn if she lends 15,000 to be paid in 3 years? at: 5% annual simple. 10% simple annual. 5% compounded annually
simplify, please, and thank you!
Answer:
(3x+4) ÷ (x+6)
Step-by-step explanation:
3x²-14x-24 = (3x+4) (x-6)
x²-36 = (x+6) (x-6)
= (3x+4) (x-6) ÷ (x+6) (x-6)
Eliminate the (x-6)
= (3x+4) ÷ (x+6)
A right square pyramid is shown. A plane intersects the pyramid through the apex and is perpendicular to the base.
Answer:
Trapezoid.
Step-by-step explanation:
If st - sv, m∠sut - w + °10, and m∠suv =3w, what is m∠sut
If st - sv, m∠sut - w + °10, and m∠suv =3w, the measure of angle SUT is 52.5°.
Given the information provided, we can set up the following equations:
1) m∠SUT + m∠SUV = 180° (since they are supplementary angles)
2) m∠SUT = w + 10°
3) m∠SUV = 3w
Now we can substitute equations (2) and (3) into equation (1):
(w + 10°) + (3w) = 180°
Combining like terms, we get:
4w + 10° = 180°
Now, subtract 10° from both sides:
4w = 170°
Finally, divide both sides by 4:
w = 42.5°
Now we can find m∠SUT by substituting the value of w back into equation (2):
m∠SUT = 42.5° + 10°
m∠SUT = 52.5°
So, the measure of angle SUT is 52.5°.
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A video game player is creating a user identification to play a game. The identification must consist of one vowel (A, E, I, O, U) followed by any one number (2, 4, 6, 8). What is the probability that the user identification will contain both an E and an 8?
The probability that the user identification will contain both an E and an 8 is 1/20, or 5%.
To determine the probability of a user identification containing both an E and an 8, we will break down the problem step-by-step.
1. Identify the total number of possibilities:
There are 5 vowels (A, E, I, O, U) and 4 even numbers (2, 4, 6, 8). To calculate the total number of possible user identifications, multiply the number of vowels by the number of even numbers:
Total possibilities = 5 vowels × 4 even numbers = 20 combinations
2. Determine the desired outcome:
In this case, we are interested in the combination that has an E followed by an 8. There is only one such combination: E8.
3. Calculate the probability:
To find the probability of the desired outcome, divide the number of desired outcomes by the total number of possible outcomes:
Probability = Desired outcomes / Total possibilities
Probability = 1 / 20
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150 miles 3/4 tank of gas 3 hours how far can you drive on one tank of gas?
The car can travel for 4 hours on one full tank of gas.
150 miles 3/4 tank gas 3 hours how can you drive one tank of gas?Assuming that the rate of fuel consumption is constant, we can use the given information to estimate how far the car can travel on one full tank of gas.
First, we need to find the capacity of the gas tank. Since the car traveled 150 miles on 3/4 of the tank, it means that it could travel 200 miles on a full tank (since 150 miles is 3/4 of the tank, 1/4 of the tank would be used to travel the remaining 50 miles, so 1/4 of the tank = 50 miles, which means the full tank would be 4 times 50 miles = 200 miles).
Next, we need to find the car's average speed. Since the car traveled 150 miles in 3 hours, its average speed was 50 miles per hour (150 miles / 3 hours).
Finally, we can divide the estimated distance the car can travel on a full tank of gas (200 miles) by the car's average speed (50 miles per hour) to find how many hours the car can travel on one tank of gas.
200 miles / 50 miles per hour = 4 hours
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Medical records at a doctor’s office reveal that 12% of adult patients have seasonal allergies. Select a random sample of 100 adult patients and let p^ = the proportion of individuals in the sample who have allergies.
(a) Calculate the mean and standard deviation of the sampling distribution of p^.
(b) Interpret the standard deviation from part (a).
(c) Would it be appropriate to use a normal distribution to model the sampling distribution of p^ ? Justify your answer
The mean of the sampling distribution is 0.12 and the standard deviation is 0.033
(a) The mean of the sampling distribution of p^ is equal to the population proportion, which is p = 0.12. The standard deviation of the sampling distribution of p^ is given by the formula:
σ = sqrt[(p(1-p))/n]
where n is the sample size. Plugging in the values, we get:
σ = sqrt[(0.12)(0.88)/100] = 0.033
Therefore, the mean of the sampling distribution is 0.12 and the standard deviation is 0.033.
(b) The standard deviation from part (a) represents the amount of variability we expect to see in the sampling distribution of p^ due to chance.
It tells us how much we would expect p^ to vary from sample to sample, if we were to repeat the sampling process many times.
(c) Yes, it would be appropriate to use a normal distribution to model the sampling distribution of p^, because the sample size n is large enough (n=100) for the Central Limit Theorem to apply.
According to the Central Limit Theorem, the sampling distribution of p^ will be approximately normal with mean p and standard deviation σ/sqrt(n), as long as the sample size is sufficiently large.
In this case, the sample size is large enough, so we can use a normal distribution to model the sampling distribution of p^.
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Dante has a tent shaped like a triangular prism. The tent has an equilateral base that measures 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall.
101. 5ft
120 ft.
141. 5 ft.
184 ft
What is the surface area of the tent
The surface area of Dante's tent is approximately 180 square feet.
To find the surface area of Dante's tent, we need to find the area of each of its faces and then add them up. Since the tent is in the shape of a triangular prism, it has three rectangular faces and two triangular faces.
First, let's find the area of each rectangular face. We know that the tent is 8 feet long and 4.3 feet tall. To find the width of each face, we need to use the Pythagorean theorem since the base of the tent is equilateral. So, we can use a triangle with sides of 5 feet (the base of the tent) and 4.3 feet (the height of the triangular face) to find the width of each rectangular face.
a^2 + b^2 = c^2
5^2 + 4.3^2 = c^2
25 + 18.49 = c^2
43.49 = c^2
c = √43.49
c ≈ 6.6 feet
Now that we know the width of each rectangular face, we can find the area of each face:
Area of rectangular face = length x width
Area of rectangular face = 8 x 6.6
Area of rectangular face ≈ 52.8 square feet
Next, let's find the area of each triangular face. Since the base of the tent is equilateral, each triangular face has a base of 5 feet and a height of 4.3 feet. The area of each triangular face is:
Area of triangular face = (base x height) / 2
Area of triangular face = (5 x 4.3) / 2
Area of triangular face ≈ 10.8 square feet
Now we can add up the areas of all five faces to find the total surface area of the tent:
Surface area of tent = 3 x area of rectangular face + 2 x area of triangular face
Surface area of tent = 3 x 52.8 + 2 x 10.8
Surface area of tent = 158.4 + 21.6
Surface area of tent ≈ 180 square feet
Therefore, the surface area of Dante's tent is approximately 180 square feet.
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Offering brainiest to whoever can give me the answer fastest, a nice explanation, and the correct answer!
Box C has the smallest volume, followed by Box A, and Box B has the largest volume.
Explanation on how to get the least volumeFirst, we need to find the volume of each box.
Recall that the formula for volume of a box is given as:
V = length x height x width
For Box A,
V = 3 cm x 2 cm x 4 1/2 cm = 27 cm³
For Box B,
V = 2 1/3 cm x 3 cm x 5 cm = 7/3 cm x 3 cm x 5 cm = 35 cm³
For Box C,
V = 4 cm x 3 cm x 1 1/4 cm = 4 cm x 3 cm x 5/4 cm = 15 cm³
So, the order of the boxes by volume from least to greatest is: Box C, Box A, and Box B.
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a chain letter starts when a person sends it to 7 others. these people either ignore it or send it to 7 more. if 211 are involved in this chain letter (including the sender), (1) how many sent the letter? (2) how many did not continue the chain?
There are 22 people who sent the chain letter, and 189 people did not continue the chain.
We know that the chain started with one person who sent it to 7 others, so that makes a total of 8 people in the first round. In the second round, each of those 7 people could either send it to 7 more people or ignore it, so there are two possibilities for each of those 7 people: they either continue the chain or they don't.
Therefore, there are 2⁷ = 128 possible outcomes for the second round.
If we assume that everyone who received the letter in the second round sent it to 7 more people, then there would be 7 x 128 = 896 people in the third round.
Continuing this pattern, we can see that the number of people in each round is given by the formula of combination 8 x 7ⁿ⁻¹, where n is the round number (starting with n = 1 for the first round).
We want to find the round number such that the total number of people in the chain is 211. Setting the formula above equal to 211 and solving for n gives
8 x 7ⁿ⁻¹ = 211
7ⁿ⁻¹ = 26.375
n - 1 = log_7(26.375)
n = 2.78 (rounded to two decimal places)
Since we can't have a fractional round number, we can assume that the chain ended after the second round (since the third round would have too many people). Therefore, the total number of people who sent the letter is
8 + 7(2) = 22
To find the number of people who did not continue the chain, we can subtract the number of people who sent the letter from the total number of people in the chain
211 - 22 = 189
Therefore, 189 people did not continue the chain.
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Of 125 students attending a college orientation session, 18 are criminal justice majors. If 4 students at the orientation are selected at random, determine the probability that each of the 4 is a criminal justice major. Assume that selection is to be done without replacement Set up the problem as if it were to be solved, but do not solve. P(4 criminal justice majors selected) N
The probability that each of the 4 is a criminal justice major is equal to 0.0003 (rounded to four decimal places).
The probability of selecting 4 criminal justice majors from a group of 125 students, without replacement,
Using the hypergeometric probability distribution.
Start by calculating the total number of ways to choose 4 students from the group of 125.
C(125,4) = 125! / (4! (125-4)!)
= 125 x 124 x 123 x 122 / (4 x 3 x 2 x 1)
= 9,691,375
Next, calculate the number of ways to choose 4 criminal justice majors from the group of 18.
C(18,4) = 18! / (4! (18-4)!)
= 18 x 17 x 16 x 15 / (4 x 3 x 2 x 1)
= 3060
Finally,
Probability of selecting 4 criminal justice majors
= number of ways to choose 4 criminal justice majors / total number of ways to choose 4 students:
P(4 criminal justice majors selected) = C(18,4) / C(125,4)
⇒P(4 criminal justice majors selected) = 3060 / 9,691,375
= 0.0003157
Therefore, probability that each of the 4 students selected at random from the group of 125 students are criminal justice majors, without replacement is 0.0003 (rounded to four decimal places).
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Nora signed up for a streaming music service that costs $5 per month. The service allows Nora to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0. 75 per song. How much total money would Nora have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
cost of 30 songs:
cost of s songs:
Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
The cost for downloading 30 songs would be:
$0.75 per song × 30 songs = $22.50
Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.
If she downloaded "s" songs, the cost would be:
$0.75 per song × s songs = $0.75s
Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
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PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Based on the information, statement (A) False is correct.
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
How to calculate the probabilityIt should be noted that since the proportion of females who work part-time only in the summer (84%) is greater than the overall proportion of students who work part-time only in the summer (80%), we can conclude that gender and working part-time only in the summer are dependent. This means that knowing someone's gender gives us information about the likelihood that they work part-time only in the summer.
Therefore, statement (A) False is correct.
The probability will be:
0.80 x 0.50 x 0.84 = 0.336
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
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