After the modification, the maximum amount of medical costs in the sample must have stayed the same.
After the wrongly recorded medical expense was repaired, the adjusted amount remained more than or equal to every other medical expense in the sample. This suggests that the sample statistic linked to the highest value must have remained unchanged after the modification.
The highest value, also known as the maximum or largest value, of the medical expenses in the sample, had to have remained constant. Even though the real quantity was mistakenly recorded as being 10 times its value, the rectified amount still had the highest value in the sample.
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How do you find the third side of an isosceles triangle when given the angle?
The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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Help please I don't really understand
Answer:i need to know what youre trying to find first
Step-by-step explanation:
In the 2-man bobsled competiton in the olympics, the gold medalists were about 0.2 seconds faster than the silver medalists, and the silver medalists were about 0.14 seconds faster than the bronze medalists. Which gap in time was larger? By how much?
The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.
what is unitary method ?The unit technique is a strategy for addressing issues that entails first figuring out the value of a specific unit, then dividing that value to figure out the needed value. Simply put, the unit method is employed to derive a single system value from a multiple that is supplied. For example, 40 pens might cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, computational equations, or algebra of matrices or operators.
given
time separation of gold medalists by silver medalists is equal to 0.14 minus 0.2, or 0.11.
The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.
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A right pyramid has a square base with perimeter 24 inches. Its apex is 9 inches from each of the other vertices. What is the height of the pyramid from its peak to the center of its square base, in inches
If the square base with perimeter 24 inches then the height of the right pyramid be 8.485 - inches.
What is meant by right pyramid?A right pyramid is one whose apex is located exactly above the centroid of the base. As a result, a right pyramid is a special instance of a regular pyramid.
It is referred to as the right pyramid if the pyramid's apex lies immediately above the base's center. If not, the pyramid is known as the oblique pyramid.
A right-triangular pyramid is a three-dimensional object that has a base that is a right-angle triangle and extends up to a single point.
Right pyramids have apex points that are immediately above the centroid of their base. Oblique pyramids are referred to as non right pyramids. An implied right pyramid is a regular pyramid since it has a regular polygon base.
24 / 4 = 6 inches - the edge length of the square base
9² = 3² + Height²
simplifying the above equation, we get
Height² = 9² - 3²
Height² = 72 take the square root of both sides
Height = ~8.485 - inches - the height of the pyramid.
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If the square base with perimeter 24 inches then the height of the right pyramid be 8.485 - inches.
What is meant by right pyramid?The centroid of the base is exactly where the top of a right pyramid sits. Consequently, a right pyramid is a unique example of a standard pyramid.
If the top of the pyramid sits directly above the centre of the base, it is referred to as the right pyramid. If not, the structure is referred to as an oblique pyramid.
A right-triangular pyramid is a three-dimensional object with a base that rises to a single point from a right-angle triangle.
Apex points of right pyramids are located directly above the centroid of their base. Non-right pyramids are another name for oblique pyramids. Given that its base is a regular polygon, an implied right pyramid is a typical pyramid.
24 / 4 = 6 inches - the edge length of the square base
9² = 3² + Height²
simplifying the above equation, we get
Height² = 9² - 3²
Height² = 72 take the square root of both sides
Height = ~8.485 - inches - the height of the pyramid.
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A palindrome is an integer that reads the same forwards and backwards. How many positive 3-digit palindromes are multiples of $3$
There are total 30 positive 3-digit palindromes are multiples of 3.
The numbers are as follows,
111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999.
Palindrome numbers
A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis.
A palindrome number is a number that is same after reverse.
For example - 121, 34543, 343, 131, 48984 are the palindrome numbers.
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When x²+(1/x)=3 find x⁴-2x³-x²-2x+1=
(without using calculator)
so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
we can start by squaring the equation x²+(1/x)=3
so we have x⁴ + 2x² + (1/x)² = 9
x⁴ + 2x² + 1 = 9x²
x⁴ - 7x² + 1 = 0
Now we can factor it
(x²-1)(x²-1) = 0
so x² = 1
now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1
x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1
= x⁴-2x³-2x-1
= (x⁴-2x³) - (2x+1)
= x⁴-2x³-2x-1
= (x²-x)² - (2x+1)
= (x-1)² - (2x+1)
so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
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The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 486 cars traveling east and 189 cars traveling west. What percentage of the cars were traveling east?
The percentage of cars traveling east is 28% of the total number of cars.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The commission counted 486 cars traveling east and 189 cars traveling west.
We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.
From this concept, the percentage of the cars were traveling east would be
The cars traveling east divided by the total numbers of cars time s100%.
= (189/486 + 189)×100%.
= (189/675)×100%.
= 0.28×100%.
= 28%.
So, 28% of the total cars traveling east.
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please answer **ASAP** (WORTH 50pts)
in a sequence the first term of 4 and the common difference is 8 find a fifth term
EXPLAIN
The fifth term of the given arithmetic sequence is 36.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d
Given that, in a sequence the first term of 4 and the common difference is 8.
Here, a=4 and d=8
Now, the fifth term is
a₅=4+(5-1)×8
= 4+32
= 36
Therefore, the fifth term of the given arithmetic sequence is 36.
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54. Suppose the population of a country is currently 8,100,000. Studies show this
country's population is increasing 2% each year.
a. What exponential function would be a good model for this country's
population?
b. Using the equation you found in part (a), how many years will it take for the
country's population to reach 9 million? Round your answer to the nearest
hundredth.
a. The exponential function that is good model for the country population is:
Pₙ = 8100000(1.02)ⁿ ,
b. It will take 5.27 years to reach 9 million.
What is exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Exponential Function Formula
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.
a. Given, initial population P₀ = 8100000, Rate of increase R = 2%.
If a constant rate of growth be R% per annum,
then function for population after n years
Pₙ = P₀ x (1+R/100)ⁿ
Population Pₙ = 8100000 × (1+2/100)ⁿ
Pₙ = 8100000(1.02)ⁿ
b. Let after x years population will be 9 million.
then,
9000000 = 8100000 (1 + 2/100)ˣ
(1 + 2/100)ˣ = 9000000/8100000
(1.02)ˣ = 90/81
(1.02)ˣ = 1.11
Taking log on both sides
ln (1.02)ˣ = ln (1.11)
ln(a)ⁿ = n ln(a)
x ln(1.02) = ln (1.11)
x = ln(1.11)/ln(1.02)
x = 5.27 years
Hence, the population will reach 9 million in 5.27 years.
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Mia is taller than Gage. If m represents Mia’s height and g represents Gages hight write an inequity that shows the relationship between their heights. Answer plsssssssss
The inequality that shows the relationship between thier heights is; g < r or r > g
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Now we have the following parameters that can be used in our computation:
Reese is taller than Gage.
Also, we have
Reeses's height = r
Gage's height = g
Since Reese is taller than Gage, then it means that
The value of r is greater than the value of g
So, we have the following inequality expression;
r > g
Also, we have;
g < r
Hence, the inequality is g < r
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Expectation 2 Suppose that X is log-normal. For example log(x) follows a normal distribution with mean m and standard deviation k. What is the expectation of X? Pick ONE option exp(m - k2/2) exp(m + k²/2) exp(m) m
The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).
Therefore the answer is exp(m + k²/2).
The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.
The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.
The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.
For log-normal distribution, the expectation of X is calculated as follows:
E(X) = exp(m + k²/2)
where m is the mean of log(X) and k is the standard deviation of log(X).
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The function f is defined by f(x) = x^2 + 3x - 10. If f(x-2) = x^2 + bx + c, what are the values of b and c?
______________________________
When you put the answer could you put the steps that you took, so I could use it on other problems
Thanks
Distributive Property
Factoring
FOIL (First Outside Inside Last)Functions
Function NotationApplicationStep 1: DefineLet's organize what is given to us in the problem.
We are given a function f, defined as f(x) = x² + 3x - 10.
We are asked to find the values of b and c in f(x - 2) = x² + bx + c.
Step 2: SolveIn order to solve the question, we first must find the full function of f(x - 2):
[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]
∴ [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]
Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:
[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]
∴ we have found the values of b and c.
Answer∴ the value of b is equal to -1 and the value of c is equal to -12.
___
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Topic: Algebra I
Unit: Factoring
The triangular symbol for "play" on many electronic devices has
the shape of an isosceles triangle. Find the other two angles
if angle P measures 30°.
A triangle that is equilateral has three equal sides and three equal angles.
Find the other two angles if angle P measures 30°?The angles are all 60 degrees each. Two 90-degree angles are formed when the height of an equilateral triangle is drawn to the base of the triangle, and the top angle is divided into two 30-degree angles. A triangle with sides of 30-60-90 always has sides that are 1:3:2.
The 30-60-90 triangle formula for sides y is also known as y3: 2y. The angles of the triangle are always 30, 60, and 90 degrees. Given that one of the angles is 90 degrees, this triangle is always a right triangle. These angles come together to form a right-angled triangle. Furthermore, the right angle is equivalent to the sum of two sharp angles, which will have the ratios of 1: 2 or 2: 1.
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5. The population of a town went from
100,000 to 137,000 in 5 years. What was
the percent increase in the town's
population
over that time?
A 7.4%
B 37%
C 73%
D 137%
Answer:B or A depending on if it went per year or overall
Step-by-step explanation:100 137, 137-100=37
37/5=7.4
pls i need to know what the answer is!!!
The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.
What are inequalities?A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.
The given inequality is 3(2m - 1) ≤ 4m + 7
Remove the brackets by multiplying 3 with each term inside it:
6m - 3 ≤ 4m + 7
Subtract 4m from both sides of the equation.
6m - 3 - 4m ≤ 4m + 7 - 4m
2m -3 ≤ 7
Add 3 to both sides of the equation.
2m - 3 + 3 ≤ 7 + 3
2m ≤ 10
Divide both sides of the equation with 2.
2m/2 ≤ 10/2
m ≤ 5
Hence the solution of the equation is m ≤ 5, that is option A.
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Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart. A linear model of this situation contains the values (25 , 1,167) and (41 , 1,407), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year. What is the flat fee for the annual golf pass? A. $15 B. $1,032 C. $792 D. $807
To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.
Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.
The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.
5 multiply by c 24-47-48 divide 24
Answer:
70
Step-by-step explanation:
nk
what is 5 2/3 x 3/4 equal?
Answer: 4 1/4
Step-by-step explanation: Decimal= 4.25
Answer:
Exact form: 17/4
Decimal Form: 4.25
Mixed number form: 4 1/4
what is the distance between (-3,5) and (4,5)
Answer: 7
Step-by-step explanation:
Distance (d) = √(4 - -3)2 + (5 - 5)2
= √(7)2 + (0)2
= √49
= 7
ΔX = 4 – -3 = 7
ΔY = 5 – 5 = 0
y = 0x + 5
When x=0, y = 5
Answer:
Step-by-step explanation:
D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2
X2 Y2
(-3,5)
X1 Y1
(4,5)
D= SQRT (-3-4)^2 + (5-5)^2
D= SQRT 49
D=7
You are conducting a survey on the number of pets per household in your region. From a sample with n = 40, the mean number of pets per household is 2 pets and the standard deviation is 1 pet. Using chebyshev's theorem, determine at least how many of the households have 0 to 4 pets
At least 30 of the households have 0 to 4 pets.
What is Chebyshev's theorem?
The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied to this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Here,
we have a sample size of n = 40.
The mean number of pets per household is 2 and the standard deviation is 1.
We need to determine at least how many of the households have 0 to 4 pets.
By using Chebyshev’s inequality rule with k = 2(that is ) then,
= 100(1- (1/k²))%
= 100 (1- (1/2²))%
= 100 (1- (1/4))%
= 75%
The corresponding number of households is the percentage multiplied by the sample size.
= 75% × 40 = 30
Hence, at least 30 of the households have 0 to 4 pets.
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How many solutions exist for the given equation 3 x 10 6 3 x 12?
There are no solutions for the equation 3x106 3x12.
The equation 3x106 3x12 can be rearranged to 3x106 - 3x12 = 0. This is a linear equation and can be solved using the equation ax+b=0, where a is the coefficient of the variable and b is the constant.
In this case, a = 3 and b = -3x106. To solve this equation, we can use the quadratic formula, which states that x = -b ± √b2 - 4ac / 2a.
Substituting the values for a, b, and c yields x = -(-3x106) ± √(3x106)2 - 4(3)(-3x106)/2(3). Simplifying this yields x = 3x106 ± √9x1012 - 36x1012/6.
This simplifies to x = 3x106 ± √-27x1012/6. Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, there are no solutions for the equation 3x106 3x12.
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A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descends
in the first 4 minutes. How many feet must the submarine descend in the fifth minute?
Answer:
Submarine must descend by 12 feet in the fifth minute.Average of the data:Average of a data set is calculated by dividing the sum of terms by the number of the terms of the set.From the table given in picture,Let the distance descended by submarine in 5th minute = x feetAverage distance descended by the submarine = = = feet per minuteStatement given in the question → "Submarine must descend at an average rate of at least 10 feet per minute"So the inequality for the statement will be,38 + x ≥ 50x ≥ 50 - 38x ≥ 12 Therefore, submarine must descend 12 feet in the 5th minute.
Step-by-step explanation:
What is a algebraic expression for 1,10,19
The algebraic expression for the sequence 1, 10, 19, is given as a(n) = 1 + (n-1) 9.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
For the given sequence the common difference between two consecutive terms is 19 - 10 = 9.
The general form of the nth term of an arithmetic sequence is given as:
a(n) = a + (n-1) d
Since, the value of a = 1 and the common difference d =9, the resulting expression is:
a(n) = 1 + (n - 1) 9
Hence, the algebraic expression for the given sequence is a(n) = 1 + (n - 1) 9.
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A large shipping container holds 1,512 ft3. The base measures 12 ft by 14 ft. What is the height of the shipping container?
Answer:
9 ft
Step-by-step explanation:
assuming the 3 was a mistake T'T volume is l x w x h so if the base is l x w then 12 x 14 (168) is the base then divide the volume from the base (1512 / 168) the answer is 9 ft
How to solve 40 50 90 triangles
The 40 50 90 triangle can be solved using Pythagoras theorem.
What is the 40 50 90 triangle?A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.
Given:
We have 40 50 90 triangles.
A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.
Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.
So, Such type of Triangles can be solved using Pythagoras theorem.
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A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error
The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.
What is a confidence interval with an example?In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
First we need to name some of the variables we are given:
n = 38 the sample size
x = 6.88 the sample mean
= 1.86 the population standard deviation
We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:
= 1-.90 = .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
This can give us a probability expression:
P(-1.645 < z < 1.645) = .90
The margin of error is calculated with the formula: E = z(/2)(/√n)
E = 1.645(1.86/√38) = $.4963(300) = $148.89
Then to calculate the upper and lower limit we add and subtract E from x:
lower limit = 6.88 - .4963 = $7.38(300) = $2214
upper limit = 6.88 + .4963 = $6.38(300) = $1914
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Find the median of data 1/3 3/2 1/6 1/4 2/3
Answer:
median= 1/3
Step-by-step explanation:
A car moving at a constant speed passed a timing device at t=0. After 9 seconds the car has traveled 1,053ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Answer:
d = 117t
Step-by-step explanation:
The equation is
y = mx + b
Here m is the function's slope, and b is the y-intercept.
We know
As the car moves at a constant speed passes a timing device at t=0.
After 9 seconds, the car traveled 1053ft.
We have to find the slope
Slope = rise/run or (y2 - y1) / (x2 - x1)
We have the slope is
m = 1053/ 9 = 117
So, the equationn is d = 117t
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PLEASE HELPP
If A and B are supplementary angles and
m/B = 54, find m/A.
Answer:
m∠A=126°
Step-by-step explanation:
Supplementary means that they add up to 180°.
Therefore we can do 180-54 to get 126° for the m∠A.
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If police and fire are already on an accident scene, how many feet away should you park your ambulance
It is recommended that when an ambulance arrives at an accident scene, it should park a safe distance away from the scene, at least 500 feet away.
This is to ensure the safety of the paramedics and other emergency responders, as well as to ensure that the ambulance does not impede the movement of other emergency vehicles. Additionally, it is also to protect the privacy of the individuals involved in the accident and ensure that the scene is not tampered with.
It is also important to follow any additional instructions given by the police or fire department at the scene, as they may have specific parking instructions based on the situation.
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