What is the value of x?
A) 80 degrees
B) 50 degrees
C) 90 degrees
D) 65 degrees
The value of x is 80 degrees.
The correct answer is an option (A)
Consider the following figure.
Let us assume that the upper triangle be ABC and the lower triangle be NMC.
We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.
Consider triangle ABC.
As the triangle is isosceles triangle, from the definition of isosceles triangle ∠A = ∠B
So, ∠A = 65°
We know that the sum of all the angles of triangle is 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠C = 180° - (65° + 65°)
⇒ ∠C = 180° - 130°
⇒ ∠C = 50°
We can observe that ∠ACB and ∠MCN are opposite angles.
So, ∠MCN = 50°
Also, triangle MNC is also an isosceles triangle.
so, ∠C = ∠N
⇒∠N = 50°
We know that the sum of all the angles of triangle is 180°
⇒ ∠M + ∠N + ∠C = 180°
⇒ ∠M = 180° - (50° + 50°)
⇒ ∠M = 180° - 100°
⇒ ∠M = 80°
Therefore, x = 80°
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A hospital has a nursing staff of 250 nurses, working four shifts: A (7:00 AM to 1:00 PM); B (1:00 PM to 7:00 PM); C (7:00 PM to 1:00 AM); D (1:00 AM to 7:00 AM)
The number of nurses apportioned to each shift is based on the average number of patients, per shift, given the following table:
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.
What is number?Number mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.
Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.
The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.
In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.
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Huw investigates the opinion of the public about their local primary schools. He visits his town centre and administers a questionnaire to 120 people over the course of several days.
What type of sampling is this?
The type of sampling that Huw is using is called Convenience Sampling.
Explanation:
Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.
since the mode is the most frequently occurring data value, it group of answer choices is always larger than the mean can never be larger than the mean none of these alternatives is correct. is always larger than the median
Since the mode is the most frequently occurring data value so -
Option D : None of the alternatives is correct.
What is mode?
A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.
The distribution of the mean, median, and mode values will depend on how skewed the distribution is.
The total dependency of mean, median and mode of data is on the asymmetric form of the data.
As a result, mean or mode may be larger than or less than mode.
Therefore, the mode is neither large than mean or median and can never be larger than mean.
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GUYS I NEED HELP ASAP
An individual who files a local income tax return has a probability of the return being audited. If 12,000 tax returns are received by the city, which of the following is the best prediction of the number of income tax returns that were audited?
A.3,000
B.2,000
C.3,500
D.2,500
The matrix 1 −1 ]5
0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter. (If an answer does not exist, enter DNE.)
The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.
The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).
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The complete question is
The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).
3.8 liters = ____ deciliters?
Answer:
Step-by-step explanation:
3.8 liters = 38deciliters
Answer:
3.8 litres =38 deciliters
Three numbers are in the ratio 2:3:5. The sum of their
cube is 34560. Find the numbers
In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are 12, 18, and 30.
How can the numbers be determined?The given Ratio of three numbers can be expressed as 2:3:5
Then we can represent the three numbers as: 2x, 3x, and 5x.
We were given the Sum of their cubes as 34560
Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560
The we will have 8x^3 + 27x^3 + 125x^3 =34560
Then we have 160x^3 = 34560
x^3 =34560/160
x= 6.
then we can find the values of the ratio as :
2x =( 2×6)
= 12
3x = (3×6 )
= 18
5x = (5×6 )
= 30
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Mr P’s had some car issues and he took it into the car shop. The mechanic told him that it will cost 50$ an hour to fix his car. How much it will it cost?
If the mechanic told Mr P that it will cost 50$ an hour to fix his car, then 50x will be the cost which Mr P has to pay.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Mr P’s had some car issues and he took it into the car shop.
The mechanic told him that it will cost 50$ an hour to fix his car.
We need to find Mr P has to pay for car.
Let x represents the number of hours.
$50x represents the amount Mr P has to pay for car.
Hence, the expression 50x represents the cost Mr P has to pay for car.
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In 1980 the population of alligators in a particular region was estimated to be 1200. In 2008 the population had grown to an estimated 7500. Using the Malthusian law for population growth, estimate the alligator population in this region in the year 2020.
The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.
Mathematically, we can express this as:
dP/dt = rP
where P is the population size, t is time, and r is the growth rate.
Assuming a constant growth rate, we can integrate this equation to get:
ln(P) = rt + C
where C is an integration constant. We can solve for C using the initial population estimate:
ln(1200) = r(1980) + C
C = ln(1200) - r(1980)
Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:
ln(7500) = r(2008) + ln(1200) - r(1980)
Solving for r, we get:
r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496
Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:
ln(P) = rt + ln(7500)
ln(P) = 0.0496(12) + ln(7500) = 9.058
P = e^9.058 = 8656
Therefore, the estimated alligator population in the region in the year 2020 is 8656.
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I WILL GIVE BRAINLY
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 $1,500
2 $1,350
4 $1,200
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 5 days? (2 points)
Answer:
Part A: Slope (m) = -75
Part B:
Point-slope form --- y - 1350 = -75(x - 2)
Slope-intercept form --- y = -75x + 1500
Standard form --- 75x + 1y = 1500
Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').
Part D: The balance in the bank account after 5 days equals $1,125.
Step-by-step explanation:
(Pertaining to Part D --- Plugging in variables):
To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.
Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.
Hope that helps!!
Answer:
Part A: Slope (m) = -75
Part B:
Point-slope form --- y - 1350 = -75(x - 2)
Slope-intercept form --- y = -75x + 1500
Standard form --- 75x + 1y = 1500
Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').
Part D: The balance in the bank account after 5 days equals $1,125.
Alexa, Ashton, and Morgan are working on a project. They
want to know who types the fastest so that person can type
the report. The equation y=39x models the total number of
words Alexa can type, where y is the number of words typed
and x is the time in minutes. The table shows the
relationship between words typed and minutes for Ashton.
The graph shows the relationship for Morgan. Who types the
fastest?
Who types the fastest?
OA. Morgan types the fastest.
OB. Ashton types the fastest.
OC. Alexa types the fastest.
OD. They all type equally fast
The one who types the fastest is Morgan. hence, the correct option is A.
What is an equation?An equation is defined as an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation , the instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We have been given that equation y=39x
Which models the total number of words Alexa can type, where y is the number of words typed and x is the time in minutes.
The data shows the relationship for Morgan.
Then we can conclude that Morgan types the fastest.
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Mathematics: What is a mean
Harry is a Wizard. He brought 4 new cloaks and 2 wands. Each cloak and each wand is the same price. If he paid Hogwarts gift-shop $498, how much does each wand cost?
Each wand costs $83, found by dividing the total cost of $498 by the total number of items, 6 (4 cloaks and 2 wands), resulting in $498 / 6 = $83.
To solve for the cost of each wand, we first need to determine the cost of each item (cloak and wand) that Harry bought. We can represent the cost of each item as "x". Since Harry bought 4 cloaks, the total cost of the cloaks is 4 * x. Similarly, since he bought 2 wands, the total cost of the wands is 2 * x.
The total cost of the cloaks and wands that Harry bought was $498, so we can write the equation: 4 * x + 2 * x = $498. This equation represents the total cost of the 4 cloaks plus the 2 wands, which must equal $498.
Next, we can simplify the equation by combining like terms: 4 * x + 2 * x = 6 * x = $498.
Finally, we can find the cost of each item by dividing both sides of the equation by 6: x = $498 / 6 = $83.
Therefore, each wand costs $83.
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a roll of ribbion is 12 meter long. Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. He then used the remaining ribbion to make some wreaths. Each wreath requried 0.6 meter. Foe each question, explain your reasoning.
After cutting 9 pieces of ribbons, Diego made 14 pieces of wreaths with the remaining roll of ribbon.
For finding the pieces of wreaths we will first obtain the total meter required for 9 pieces of ribbon by multiplying 9 with 0.4 meter and then subtract it from the total meters of the roll of ribbons i.e., 12 meters and then divide the result with 0.6 meter.
Total meter required for 9 pieces of ribbon = 9x0.4 meter
= 3.6 meters
Total meter of the roll of ribbon = 12 meters
Meter required per wreath = 0.6 meter per wreath
Meter of roll remaining for making wreaths = 12-3.6
= 8.4 meters
Total number of wreath made from the remaining roll
= 8.4 meter / 0.6 meter
= 14 Wreaths
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12. Trystan and Kendall have decided to buy a new home that costs $300,000. They want to make a 20% down payment and
finance the rest. Their bank has offered an opportunity to buy down the quoted interest rate of 4.75% by 0.125% per point
purchased. Each point will cost 1% of the amount borrowed. Trystan and Kendall were hoping the interest rate was no more than
4.5% What will it cost to buy down the quoted interest rate to 4.5%?
To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.
What is the down payment?The down payment refers to the initial cash payment for the purchase of an item on mortgage.
The down payment is required by the financier to evaluate the buyer's financial readiness.
The cost of the new home = $300,000
Down payment = 20% or $60,000 ($300,000 x 20%)
Mortgage loan required = $240,000 ($300,000 - $60,000)
Bank quoted interest rate = 4.75%
Desired interest rate = 4.5%
Difference in interest rate = 0.25% (4.75% - 4.5%)
Rate of buy down of the quoted interest per point = 0.125%
The number of points to buy down the interest rate = 2 (0.25/0.125)
The cost of each point = 1% of $240,000 = $2,400
The total cost of 2 points = $4,800 ($2,400 x 2)
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Question 12Miple Choice Worth 4 pores)
(08.02 MC)
The expression 4x+13 represents the time it takes a commuter to travel in the morning to work. The expression 10x-2 represents the time it takes a commuter to
havel in the evening from work What is the total travel time?
Otx+18
Ox+11
06+21
Ox+15
If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.
What is meant by functions?A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
Given f(x) = 4x + 13 and g(x) = 10x − 2
We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.
Let the equation be (f + g)(x) = f(x) + g(x)
substitute the values in the above equation, we get
= (4x + 13) + (10x − 2)
simplifying the above equation, we get
= 4x + 13 + 10x − 2
= 4x + 10x − 2 + 13
= 4x + 11
Therefore, the expression (f + g)(x) be 4x + 11.
The completed question is:
The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.
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What is y=2x?
what is 12 x 12 in like righting
Answer:
Step-by-step explanation:
y = 2x:
This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.
12 x 12:
This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".
1004.8 into 3 significant figures
Rounding off the 1004.8 into 3 significant figures will give 1000.
Significant Figures:Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.
For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.
Here we have a number
1004.8 need to be rounded off for 3 significant figures
Since 4 is less than 5 then the resultant number = 1000
[ 4 and 8 neglected since 4 < 5]
Therefore,
Rounding off the 1004.8 into 3 significant figures will give 1000.
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which number can each term of the equation be multiplied by to eliminate the decimals before solving?
The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100
The equation is
5.6j + 0.12 = 4 + 1.1j
The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication
The equation is
5.6j + 0.12 = 4 + 1.1j
Here three term has fractional part.
In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .
Then the equation will become
560j + 12 = 400 + 110j
Therefore, the number is 100
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The given question is incomplete, the complete question is
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
5.6j + 0.12 = 4 + 1.1j
Factor 80+60. Write your answer in the form a(b+c) where a is the GCF of 80 and 60.
Answer:
20(4+3)
Step-by-step explanation:
GCF of 80 and 60 = 20
20*4=80
20*3=60
20(4+3)
hope this helps! :)
A carnival charges $6 to enter and $. 75 per ticket. Write a function rule that models this situation
A function rule, if a carnival charges $6 to enter and $. 75 per ticket is f(x) = $6 + .75x
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
According to the question,
carnival charges is $6
cost per ticket is $0.75
Let the number of person/tickets be x
and f(x) be the total cost
therefore the function is f(x) = $6 + 0.75x
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You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?
The required we can save $13.86 annually by buying all your turkey at the discount store.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.
Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.
And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.
Therefore, the amount you would save annually by buying all your turkey at the discount store is,
= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86
So, we would save $13.86 annually by buying all your turkey at the discount store.
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What is 4 3/5+5/6 as a mixed number in simplest form
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
163/30
Step-by-step explanation:
4 3/5 in mixed number form would be 23/5
5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.
23/5 + 5/6
in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.
23 times 6 = 138
5 times 6 = 30
5 times 5 = 25
5 times 6 = 30
138/30 + 25/30
at this point, we can simply just add the numerators
163/30
i hope this helps
HELLPP my mom said ill get ungrounded if I get a good grade SOMEONE HELLLPPP
Answer:The price of 10 pounds of cheese is 15.84$
Step-by-step explanation:
It's simple
Which parallelogram has the greatest area?
Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To find the area of a parallelogram, we use this equation:
Base × height = areaNow that we have this equation, we can apply it to each parallelogram.
3 × 5 = 155 × 3 = 154 × 4 = 164 × 3 = 12Now, we can figure out which has the greatest area.
Therefore, the parallelogram that has the greatest area is 3, or III.
Answer:
III
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
I
A = 3 × 5 = 15 units²
II
A = 5 × 3 = 15 units²
III
A = 4 × 4 = 16 units²
IV
A = 4 × 3 = 12 units²
parallelogram III has the greatest area
Given the following segment lengths,
find the length of segment AB
The measure of side AB of the triangle is given by equation AB = 3.5 cm
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔACE
Let the second triangle be represented as ΔBCD
The measure of side AC = 14 cm
The measure of side EC = 84 cm
The measure of side ED = 21 cm
Now , ΔACE is similar to ΔBCD
So , corresponding sides of similar triangles are in the same ratio
Substituting the values in the equation , we get
AB / AC = ED / EC
AB / 14 = 21 / 84
Multiply by 14 on both sides of the equation , we get
AB = ( 1/4 ) 14
AB = 3.5 cm
Therefore , the value of AB is 3.5 cm
Hence , the measure of side AB of triangle is 3.5 cm
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Segment EF has endpoints E(-7, 14) and F(11, 5). Point P lies on EF at P(-3, 12).
What is the ratio of EP to PF?
I’m trying again. Brainly did it again
The ratio of EP to PF is given as follows:
EP : PF = 2 : 7.
How to obtain the ratio of EP to PF?The ratio of EP to PF is obtained applying the proportions in the context of the problem.
Looking at the x-coordinates, we have that:
|P - E| = 4.|F - P| = 14.The ratio must necessarily be the same for the y-coordinates, hence the ratio is given as follows:
EP : PF = 4 : 14.
EP : PF = 2 : 7.
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Use the law of sines to find each missing side or angle
15
12
128
X
The missing angle is approximately 108.5 degrees.
What is the law of sines?Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, 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 sides and angles in the triangle.
Using the law of sines:
sin(128°)/15 = sin(x)/12
Multiplying both sides by 12:
sin(x) = 12sin(128°)/15
Taking the inverse sine of both sides:
x = sin^-1(12sin(128°)/15)
x ≈ 108.5°
Therefore, the missing angle is approximately 108.5 degrees.
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estimate how much ke is there in an average size helium balloon, the kind you would see at a kid's birthday party.
We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.
The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.
Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.
Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).
Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:
KE = (3/2)kT * N
where N is the number of helium atoms in the balloon.
Plugging in the estimated values, we get:
KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23
KE ≈ 9.95 x 10^2 J
Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.
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