We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A
How to write a number in scientific notation ?First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:
3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)
However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.
Therefore, we can rewrite 3.1672 × 10¹² as:
3.1672 × 10²
So, the answer is (A).
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An isosceles triangle (two sides are the same length) has a base of 40 inches. The sides are 25 inches. Draw the height of the triangle from the top vertex perpendicular to the base. Find the height of the triangle.
The height οf the triangle is 15 inches. The diagram is attached belοw.
What is an isοsceles triangle?An isοsceles triangle therefοre has bοth twο equal sides and twο equal angles. The Greek wοrds isο (same) and skelοs are the sοurce οf the name. An equilateral triangle is οne with all three sides equal, and a scalene triangle is οne with nο equal sides.
Given that the length οf the base is 40 inches. The length οf equal sides is 25 inches.
The altitude οf an isοsceles triangle bisects the base.
The length οf BD = DC = 20 inches.
△ABD fοrms a right-angle triangle since AD is perpendicular tο BC.
Tο find the height apply Pythagοrean theοrem.
The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.
Cοnsider △ABD:
AB² = BD² + AD²
25² = 20² +AD²
625 = 400 +AD²
AD² = 625 - 400
AD² = 225
Take square rοοt οn bοth sides:
AD = 15
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Would a triangle with a vertical length of 6 and a horizontal length of 10 have the same slope as the blue and red triangles shown in the graph
A: yes, the slopes would be the same
B: No, the slope of the new triangle would be 2 : 4
C: no, the slope of the new triangle would be 2 : 5
D: no, the slope of the new triangle would be 3 : 5
Therefore , the solution of the given problem of slope comes out to be option D 3:5 is the correct slope.
Describe slope.The slope of a line determines how steep it is. Gradient overflow is a condition that can occur in equations based on gradients. By dividing the total of the run (width difference) and emergence (climbing distinction) among both two points, one can calculate the slope. The fixed path problem is modelled using the equation y = mx + b with the hill variant. where slope is millimeters, a = bc, and the location of the line's y-intercept.
Here,
Given :
Vertical length = 6
and
horizontal length = 10
=> Slope: Y/X=6/10=0.6
=> 6/10 = 3/5(D)
Thus , option D 3:5 is the correct slope.
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Answer:
A
Step-by-step explanation:
Likert scale A survey attempted to evaluate student interest about a range of classroom topics. Students were asked to rank their interest in various potential topics according to this scale: 10 if they felt a topic was very interesting if they felt a tapic was above average interest If they felt a topic was below average interest if they felt a topic was not worth studying in class 6 4 1 Please note that only four responses were permitted: 10, 6, 4, and 1. Is this an acceptable survey design? Explain your answer. Answer
The survey design that we have here is not an acceptable standard survey design for research.
Why is this not an acceptable survey design?This survey design has limitations and may not be the most optimal way to measure student interest in classroom topics. Here are some of the reasons why:
Limited response options: By only allowing four responses, the survey restricts the range of possible responses that students can give. For instance, some students may feel that a topic is somewhat interesting, but not interesting enough to warrant a score of 6. Similarly, some students may feel that a topic is not worth studying, but not to the extreme level of giving it a score of 1. This design does not account for such nuances in student opinions.
Lack of neutral option: The survey does not include a neutral option such as "no opinion" or "undecided". This means that students who do not have a strong opinion about a topic may be forced to pick a score that does not accurately reflect their level of interest.
Lack of context: The survey does not provide any context or information about the topics being evaluated. Without such information, students may base their scores on assumptions or incomplete knowledge about the topics, which may not accurately reflect their actual level of interest.
Lack of reliability and validity: The survey's reliability and validity may be questionable. The limited response options and lack of context may lead to responses that are not reliable or valid measures of student interest.
In conclusion, while this survey design may be simple and easy to administer, it has limitations that make it less than ideal for measuring student interest in classroom topics. A more comprehensive survey design that includes a wider range of response options and provides contextual information about the topics may provide more reliable and valid results.
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A(-4,-6) and B (3,2) find midpoint of AB
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -4}{2}~~~ ,~~~ \cfrac{ 2 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies \left(-\frac{1}{2}~~,~~-2 \right)[/tex]
(PLEASE HURRY!) A table giving various values of linear functions f(x) and g(x) is shown below. What is the solution to the system?
Answer:
A. (2, 1)
Step-by-step explanation:
You want the solution to the system of equations represented by the given table and graph.
SolutionWhen we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.
TableWhen you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...
(x, f(x)) = (2, 1)
Select which points are solutions to this inequality.
y ≥ 5x - 7
(-5, -3)
(-4, 2)
(1, -2)
(-1, 0)
(3, 0)
(4, 1)
The coefficient of variation for a poisson distribution with A=5 is
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2.
What is Poisson distribution?Poisson Distribution is a type of probability distribution used for independent events which occur at a known average rate within a given interval of time or space. It is used to model the number of times an event is likely to occur within a specified period of time or space. It is used in fields such as healthcare, quality control, finance, and engineering.
Coefficient of variation (CV) is a measure of relative variability or dispersion. It is a measure of the relative dispersion of a set of data points around its mean. It is calculated by dividing the standard deviation of the data points by the mean.
The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2. This means that the relative variability of a Poisson distribution with A=5 is 0.2. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean, and in this case, the mean is 5. Therefore, the standard deviation is the square root of 5, or 2.236. When divided by the mean, the coefficient of variation is 0.2.
In general, the coefficient of variation is used to compare the variability of two different datasets. A low coefficient of variation indicates that the data points are relatively close to the mean and that there is not much variability in the data. A high coefficient of variation indicates that the data points are further away from the mean and that there is a greater amount of variability in the data.
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Find the measure of
The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
How to evaluate for variable x of the adjacent anglesThe triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.
m∠SRA and m∠BAR are supplementary so;
(6x + 8)° + (9x + 7)° = 180°
15x + 15 = 180°
15x = 180° - 15 {subtract 15 from both sides}
15x = 165
x = 165/15 {divide through by 15}
x = 11
m∠A = 9(11) + 7 = 106°
m∠R = 6(11) + 8 = 74°
m∠S = 4(11) + 14 = 58°
Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°
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Possible question:
Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.
write an equation of vertical line through the point (9,-10)
Answer:
x = 9
Step-by-step explanation:
An equation for a vertical line is in the form:
x = anumber
The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!
x = 9
The equation of the vertical line through (9,-10) is
x = 9
This is an algebraic equation.
-12x^2/2x^2
Step-by-step explanation:
solving equipment step:
*SIMPLIFY THE EXPRESSION
- 12x² ÷(2x²²)
Rewrite
simply the equation
=12x² ÷ 2x²²
=-6x²÷x²²
Now cancel common factors
=-6x÷x^20
#Brainac
Solve for x, using a
tangent and a secant line.
?]°
x = [?
X
15°
40°
Remember : a = b
I think that the answer is 40 degreee
The required measure of section x on the circle is 95°.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property.
Here,
From the given we have,
a = 40,
c = x
b = 15
Now, put this value in the given formula,
a = c-b / 2
So,
40 = x - 15/2
x -15 = 80
x = 95°
Thus, the required measure of section x on the circle is 95°.
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Julie and Hammad each make a glass of orange drink. Julie uses 42ml of juice and 210ml of lemonade. Hammad uses 30ml of juice and 170ml of lemonade. Who has made their drink stronger in taste?
Answer:
Hammad has made his drink stronger in taste than Julie.
Step-by-step explanation:
We need to compare the ratio of juice to lemonade in each drink.
Julie's drink has a ratio of 42ml juice to 210ml lemonade, which simplifies to 1:5.
Hammad's drink has a ratio of 30ml juice to 170ml lemonade, which simplifies to 3:17.
To compare the strength of their drinks, we need to compare the ratios of juice to lemonade. Since a higher ratio of juice to lemonade indicates a stronger taste, we can see that Hammad's drink has a stronger taste, since his ratio of juice to lemonade is higher than Julie's.
Therefore, Hammad has made his drink stronger in taste than Julie.
Which is the bette buy 3 pints of
at $3.60 or 6 pints are all at $8.10
Answer:
It is better to buy 6 pints at $8.10
Step-by-step explanation:
To compare the cost per pint in each option, we can divide the total cost by the total number of pints.
For the first option, buying 3 pints at $3.60, the cost per pint is shown by the following:
3 pints ÷ $3.60 = $0.83 / pint
For the second option, buying 6 pints at $8.10, the cost per pint is shown by the following:
6 pints ÷ $8.10 = $0.74 / pint
Therefore, buying 6 pints at $8.10 is less expensive per pint than buying 3 pints at $3.60. Each pint when buying 3 at a time costs $0.83 whereas each pint when buying 6 at a time costs $0.74.
CAN U HELP ME ASAP ????????
The solution to the system of equations is given as follows:
(1,9).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection on the graph means that the two functions have the same numeric value, hence on a table we must identify the point which the functions have the same numeric value.
From the table, function f(x) and g(x) both contain the point (1,9), hence this is the point of intersection of the two lines, and the solution is given as follows:
(1,9).
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Use the diagram to name two points that are collinear with P, two planes that contain J, and all the points that are in more than one plane.
Step-by-step explanation:
colinear with P means they are in the same line as P.
that is K and N.
2 planes with J :
JKL (the ceiling) and JOKPN (the wall with J).
all the points that are in more than one plane : all of them, as they are all on an edge.
A neighborhood group goes to the movies every Saturday night. Last week, they purchased 29 adult tickets and 17 youth tickets for $254. This week they purchased 21 adult tickets and 22 youth tickets for $213. Find the cost of one adult ticket.
The cost of one adult ticket is $7.
What is the cost of one adult ticket?The first step is to set up a pair of linear equations that represent the information in the question.
29a + 17y = 254 equation 1
21a + 22y = 213 equation 2
Where:
a = cost of one adult tickety = cost of one youth ticketThe elimination method would be used to solve the equations
Multiply equation 1 by 22:
638a + 374y = 5588 equation 3
Multiply equation 2 by 17:
357a + 374y = 3621 equation 4
Subtract equation 4 from equation 3
1967 = 281a
Divide both sides of the equation by 281
1967 / 281 = a
a = 7
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Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Circle A has been transformed to circle B. What is the translation rule for these circles?
Answer choices are:
(x+4),(y+3)
(x-1),(y+4)
(x-2),(y+3)
(x+2),(y+3)
The translation rule for these circles is (x+2),(y+3).
What does translation mean?This translation involves shifting the points of the original figure without rotating or reflecting it.
In the given transformation, circle A has been transformed to circle B.
Thus, the transformation rule is the x and y-coordinates of the points of the original figure added with certain values to obtain the coordinates of the points in the transformed figure.
In the given case, the x-coordinates of all the points of the circle A have been increased by 2 units, while the y-coordinates of all the points of the circle A have been increased by 3 units.
Thus, the translation rule for these circles is (x+2),(y+3).
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What is the value of the next term in the geometric sequence graphed below?
O A. 6
B. 3
OC. 0.1875
OD. 0.375
Based on the readings from the graph, the sequence has a next term of the 16
How to determine the next term of the sequenceThe missing information is attached
The readings on the graph can be represented as
1, 2, 4, 8, .....
We can see that multiplying 2 to the previous term to gives the next term
Using the above parameters, we have the following equation
Next term = 2 * Current term
The current term in the graph is 8
So, we have
Next term = 2 * 8
Evaluate
Next term = 16
Hence, the next term is 16
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whats the slope of y=-4
Answer: The slope of y = -4 is 0.
Step-by-step explanation:
A triangle has a base of 8 cm and a height of 12 cm.
What is the area of the triangle?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
(No picture of the question was given)
________________________________
Answer:
A = 48 cm²
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(8 cm)(12 cm)
A = 48 cm²
Answer:
48cm^2
Step-by-step explanation:
8×12=96
96÷2=48cm^2
Part 1
The population of a small town can be modeled by Pt, where t is the number of years since 1975. Interpret the slope of the graph of this function as a rate of change.
The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
What is the slοpe?The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).
The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.
Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.
Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.
Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.
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Please help with this
a. The probability that a real number between 3 and 5 is picked is
b. The probability that a real number between 3 and 7 is picked is
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space / total outcome
The sample space is the area between the real numbers and the total outcome is the total area
Total area = 0.12 + 0.56+ 0.32
= 1
a. The probability a real number between 3 and 5 is picked = 0.56/1
= 0.56
b. The probability a real number between 3 and 7 is picked is( 0.56+0.32)/1
= 0.88
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16 lakh students in India use Khan Academy today. The number of users is expected to grow by 50% every year. How many students in India will be using Khan Academy two years from now?
Answer: Let's first calculate the number of users after one year:
Number of users after one year = 16 lakh + 50% of 16 lakh
= 16 lakh + 8 lakh
= 24 lakh
Now, we can calculate the number of users after two years by applying the same growth rate:
Number of users after two years = 24 lakh + 50% of 24 lakh
= 24 lakh + 12 lakh
= 36 lakh
Therefore, two years from now, it is expected that 36 lakh (3.6 million) students in India will be using Khan Academy.
Step-by-step explanation:
Answer:
36 Iakh Students
Step-by-step explanation:
Find the weight in pounds of a 140-kilagram person round to nearest hundredth
Answer: 308.65
:) Good luck
[tex]1 \ \text{lb} = 0.45359 \ \text{kg}[/tex]
[tex]140 \ \text{kg} \times (1 \ \text{lb})\div(0.45359 \ \text{kg}) = 308.65 \ \text{lb}[/tex]
[tex]\bold{140 \ kg=308.65 \ lb}[/tex]
Show that multiplication this following:
Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.
How to solveTo show that multiplication in M_n(R) is not commutative when n > 1, we need to find two matrices A and B in M_n(R) such that AB is not equal to BA.
Let's consider two matrices A and B in M_n(R) such that:
A = [a_ij], where a_ij = 1 if i=j, and a_ij = 0 otherwise.B = [b_ij], where b_ij = 1 if i+j = n+1, and b_ij = 0 otherwise.That is, A is the n x n identity matrix, and B is the matrix with 1's on the anti-diagonal and 0's elsewhere.
Now let's compute AB and BA:
AB = [c_ij], where c_ij = Σ_k=1^n a_ik * b_kj
If i+j = n+1, then b_kj = 1 only if k = i, and a_ik = 1 only if k = j.
Therefore,
c_ij = a_i1 * b_1j + a_i2 * b_2j + ... + a_in * b_nj = a_ii * b_jj = 1 * 1 = 1
If i+j ≠ n+1, then b_kj = 0 for all k, and hence c_ij = 0.
Therefore, AB is the matrix with 1's on the anti-diagonal and 0's elsewhere, just like B.
Now let's compute BA:
BA = [d_ij], where d_ij = Σ_k=1^n b_ik * a_kj
If i=j, then a_kj = 1 only if k = i, and b_ik = 1 only if k = i. Therefore,
d_ij = b_i1 * a_1j + b_i2 * a_2j + ... + b_in * a_nj = b_ii * a_jj = 1 * 1 = 1
If i ≠ j, then a_kj = 0 for all k, and hence d_ij = 0.
Therefore, BA is the matrix with 1's on the diagonal and 0's elsewhere, just like A.
Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.
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math proportion calculation
In respοnse tο the given questiοn, we can state that This signifies that 3 equatiοn οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
What is equatiοn?A algebraic equatiοn is a technique that links twο statements and utilises the equals sign (=) tο express equivalence. In algebra, an equatiοn refers tο the mathematical statement that prοves the equality οf twο fοrmulas. Fοr example, in the cοmputatiοn 3x + 5 = 14, a nοrmalise inserts a gap between the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο explain the link between the twο phrases written οn either side οf a letter. The emblem and the prοgramme are usually the same. Fοr example, 2x - 4 equals 2.
Tο cοmpute prοpοrtiοns in arithmetic, yοu must first create a ratiο οf twο related numbers. Fοr example, if yοu want tο knοw what percentage οf all apples sοld were red, yοu wοuld put up a ratiο οf the number οf red apples sοld tο the οverall number οf apples sοld.
Assume that 200 apples were sοld in tοtal, with 60 οf them being red. Tο get the prοpοrtiοn οf red apples, use the fοllοwing fοrmula:
60 / 200 = red apples / tοtal apples
3/10 = red apples / tοtal apples
This signifies that 3 οut οf every 10 apples sοld were red, οr that the red apple percentage was 3/10.
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Complete question:
Assume that 200 apples were sοld in tοtal, with 60 οf them being red.
What is proportion of red apples?
Plot the point where θ =
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+ g)(x).
O A. (f+ g)(x) = 3x + 2x+6
OB. (f+ g)(x) = -3* - 2x - 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x - 2x+14
S
Answer: C. (f+ g)(x) = 5x + 6
Step-by-step explanation:
C. (f+ g)(x) = 5x + 6
This is because when you add two functions together, you simply add their coefficients together and add the constants together. So, in this case, you add 3 and 2 to get 5 and add 10 and -4 to get 6. Therefore, the answer is 5x + 6.
Answer:
The correct answer is C. (f+ g)(x) = 5x + 6
In a pack of 36 trading cards, 1/4 of them are fire animals, 1/6 of them are water, animals, and the rest of them are grass animals, how many more cards are grass animals than fire animals?
Answer:
Fire animals = 36 * 1/4 = 9
Water animals = 36 * 1/6 = 6
Grass animals = 36 - (9 + 6) = 21
There are 21 - 9 = 12 more grass animals than fire animals
1. Solve the triangles:
2. Solve for x and y.
3. The Mighty Drop ski slope has an angle of elevation of 75°. If the top of the slope has an elevation of 800
feet, what is the length of the run?
4. Little Judy let go of her red balloon. The balloon is now 2240 feet up in the air and 350 feet to the west.
What is the angle of elevation when little Judy looks at her red balloon?
The answer of the given question is (3) the length of the run of the Mighty Drop ski slope is approximately 181.8 feet. (4) the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
What is Slope?A slope typically refers to the angle of an incline or ramp, or the ratio of vertical change to horizontal change of a straight line or curve on a graph. For an incline or ramp, the slope is the angle between the surface and the horizontal plane. It is defined as the ratio of the vertical rise to the horizontal run of the ramp.
In the context of a graph, slope refers to the steepness of a line or curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. The slope of a line can be positive (if the line goes up from left to right), negative (if the line goes down from left to right), or zero (if the line is horizontal).
(3) . To solve for the length of the run of the Mighty Drop ski slope, we can use the trigonometric function tangent, which relates angle of elevation to ratio of opposite and adjacent sides of right triangle.
Let x be the length of the run. Then we have:
tangent(75°) = opposite/adjacent
tangent(75°) = 800/x
Solving for x, we get:
x = 800 / tangent(75°)
x ≈ 181.8 feet
Therefore, the length of the run of the Mighty Drop ski slope is approximately 181.8 feet.
(4) . To solve for the angle of elevation when little Judy looks at her red balloon, we can use the trigonometric function arctangent.
Let θ be the angle of elevation. Then we have:
tangent(θ) = opposite/adjacent
tangent(θ) = 2240/350
Taking the arctangent on both sides, we will get:
θ = arctangent(2240/350)
θ ≈ 82.7°
Therefore, the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.
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