The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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The growth of an investment is given by the formula A = 1200 × 1.3 n , where A is the amount the investment is worth and n is the number of years. Estimate how many days it would take for the investment to be valued at £3,800.
The number of days it would take for the investment to be valued at £3,800 is 4.4 days
Estimate the number of days it would takeFrom the question, we have the following parameters that can be used in our computation:
A = 1200 × 1.3^n
For the investment to be valued at £3,800, the value of A would be
A = 3800
Substitute the known values in the above equation, so, we have the following representation
1200 × 1.3^n = 3800
Divide both sides by 1200
1.3^n = 3800/1200
So, we have
n = ln(3800/1200)/ln(1.3)
Evaluate the quotient
n = 4.4
Hence, it would take 4.4 days
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I need help with these problems??
The value of the variable x;
1. x = -4, BC = 4x + 3 = -13
2. x = 72 degrees
3. x = 5/2, SV = 6.5, ZU = 6.4
4. x = 4
5. x = 5
6. x = 3
What are tangent lines?Tangent are simply described as any straight line that is drawn from the curve at a point but never reaches the center of the circle.
It is also important to note that tangent segments of a circle are equal.
From the information given, we have that;
1. The tangents are;
4x + 1 = 5x - 3
collect the like terms
-x = 4
x = -4
Then BC = 4x + 3 = -13
2. 2x - 1 = 143
collect the like terms
2x = 143 + 1
2x = 144
x = 72 degrees
3. 3x - 1 = 5x - 6
collect the like terms
-2x = -5
x = 5/2
Then,
SZ = ZU = 3(5/2) - 1 = 15/2 - 1 = 6.5
4. 5x² + 10 = x² + 74
collect the like terms
4x² = 64
x² = 16
x = 4
5. 2x + 7 = 5x - 8
collect the like terms
-3x = -15
divide the values
x = 5
6. 3x - 1.2 = 2x + 1.8
x = 3
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
V = 3 × 2 × 6 = 36 cubic centimeters
3x+9-8x=-31?????????????
How many times can u write your name in 12 minutes using variables Based on your recorded values, write an equation that represents the relationship between the time you spent doing the activity and the amount of the activity you completed. Make sure to define your variables
:D
The following equation denotes the correlation between the duration and output of an activity: A = kT
How to explain the equationIt should be noted that A represents the amount of production, T is the period of working on the task, and k consists of a constant ratio.
Therefore, it can be conclusively stated that the culminating yield is in direct correlation to the amount of effort contributed, as denoted by the factor of proportionality k, thus producing a linear relationship when displayed upon a graph.
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Mark bought 55 lbs of clay for his art projects. He used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug. How many mugs did Mark make if he had 32.85 lbs of clay left over?
If Mark used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.
Mark bought 55 lbs of clay for his art projects
He used 12.4 lbs to make a sculpture
The left over clay is 55-12.4 = 42.6
We know that 0.75 lbs for each mug
We have to find the number of mugs he can make from left over clay
To find this we have to divide 42.6 by 0.75
Number of mugs = 42.6/0.75
=56.8
=57
Hence, if Mark used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.
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Help help help hehehheheheh
Answer:
Step-by-step explanation:
your supposed to learn things in class pay attetion
pleas anwear fast
Graph the function.
�
(
�
)
=
4
⋅
(
3
2
)
�
f(x)=4⋅(
2
3
)
x
f, left parenthesis, x, right parenthesis, equals, 4, dot, left parenthesis, start fraction, 3, divided by, 2, end fraction, right parenthesis, start superscript, x, end superscript
The graph of the function f(x) = 4(2/3)^x is added as an attachment
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=4⋅(
2
3
)
x
Express the equation properly
So, we have
f(x) = 4(2/3)^x
The above expression is a an equation of a exponential function
Next, we plot the graph using a graphing tool
To plot the graph, we enter the equation in a graphing tool and attach the display
See attachment for the graph of the function
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PLS HELP LITERALLY HELP HELPL
[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]
Find the area of the trapezoid at the right 6 cm base 5 cm heights
Describe by a write up on how models can be used to express numbers of different bases to base 2 and base 5
Conversion models can be used to express numbers of different bases to base-2 and base-5. To convert a number from base-10 to base-2, we use division-by-2, and for base-5, we divide by 5. To convert between bases, we convert to base-10 first and then to the desired base. for example 25 in binary is 11001, 45 in base-5 is 104, 89 to base-2 is 1011001.
In computer science and mathematics, binary (base-2) and quinary (base-5) numbering systems are commonly used to represent numbers. However, it is often necessary to express numbers in other bases as well. This is where conversion models come into play.
To convert a number from base-10 to base-2, we can use the division-by-2 method.
The process involves repeatedly dividing the decimal number by 2 and keeping track of the remainders until the quotient becomes 0. We then write the remainders in reverse order to get the binary representation of the number.
For example, to convert the number 25 to binary
25 / 2 = 12 R1
12 / 2 = 6 R0
6 / 2 = 3 R0
3 / 2 = 1 R1
1 / 2 = 0 R1
Therefore, 25 in binary is 11001.
To convert a number from base-10 to base-5, we can use a similar method. Instead of dividing by 2, we divide by 5 and keep track of the remainders. For example, to convert the number 45 to base-5
45 / 5 = 9 R0
9 / 5 = 1 R4
1 / 5 = 0 R1
Therefore, 45 in base-5 is 104.
We can also convert a number from base-2 to base-5 or vice versa. To convert a number from base-2 to base-5, we can first convert it to base-10 and then to base-5. For example, to convert the binary number 101110 to base-5
1*2⁵ + 0*2⁴ + 1*2³ + 1*2² + 1*2¹ + 0*2⁰ = 46
46 to base-5 is 141
To convert a number from base-5 to base-2, we can first convert it to base-10 and then to base-2. For example, to convert the quinary number 324 to base-2
3*5² + 2*5¹ + 4*5⁰ = 89
89 to base-2 is 1011001
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Help I need to finish this before midnight
The correct statement regarding the graph is given as follows:
C. The graph is non-proportional and has the equation y = -2x + 18.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The slope and the intercept of the line in this problem are given as follows:
m = -2, as when x increases by 2, y decays by 4, m = -4/2 = -2.b = 18, as when x = 0, y = 18.Thus the equation is:
y = -2x + 18.
The equation is non-proportional, as it has an intercept which is different of zero.
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Need help now please!
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ at the given quadrant is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
The value of tan θ is calculated as follows;
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Complete the sentences to compare the intervals for which each function is decreasing
The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)
Completing the sentences to compare the intervalsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
From the graph of the functions, we can see that
The function g(x) decreases all through because it is a linear function with a negative slopeThe function f(x) decreases at [0, ∝) because it a quadratic function with a maximum vertex at (0, 5)Read more about functions at
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A lab technician has to fill the tank given below.
Find its volume.
Use
π=3.14 and round your answer to the nearest hundredth.
Answer:
π(5^2)(8) + (1/2)(4/3)π(5^3)
= 200π + 250π/3 = 850π/3 cubic meters
= about 889.67 cubic meters
I need help with these
Marques is going to invest in an account paying an interest rate of 2% compounded
daily. How much would Marques need to invest, to the nearest dollar, for the value of
the account to reach $28,000 in 6 years?
the permieter of object A is 94cm. What the value of x
The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The permieter of object A is 94cm
Assuming the object is a square
So, we have
4x = 94
Divide both sides by 4
So, we have
x = 94/4
Evaluate
x = 23.5
Hence, the value of x is 23.5cm
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what is the volume of a hemisphere with a diameter of 8ft (rounded to the nearest tenth of a cubic foot)
well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}[/tex]
Christina Sanders is concerned about the financing of a home. She saw a small Cape Cod–style house that sells for $90,000. If she puts 10% down, what will her monthly payment be at (a) 30 years, 5%; (b) 30 years, 512% ; (c) 30 years, 6%; and (d) 15 years, 378% ? What is the total cost of interest over the cost of the loan for each assumption? (Use Table 15.1.) Note: Round your answers to the nearest cent. Do not round intermediate calculations.
The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.
To calculate the monthly payments, we can use the formula for the present value of an annuity:
[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]
where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.
(a) 30 years, 5%:
PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)
r = 0.05 / 12 = 0.0125(monthly interest rate)
n = 30 * 12 = 360 (number of monthly payments)
Using the formula, we get:
PV = $81,000
Monthly payment = $436.82
Total cost of interest = $57,255.85
(b) 30 years, 5.12%:
r = 0.0512 / 12 = 0.00427 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $439.88
Total cost of interest = $59,956.19
(c) 30 years, 6%:
r = 0.06 / 12 = 0.005 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $485.24
Total cost of interest = $95,687.34
(d) 15 years, 3.78%:
n = 15 * 12 = 180 (number of monthly payments)
r = 0.0378 / 12 = 0.00315 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $591.93
Total cost of interest = $34,147.07
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Calculus help please, thank you
The limit as a definite integral is given as lim (n → ∞) Σ(8i²)/n³ = 8/3n³
What is a definite integra l?The area under the curve f(x) from x= a to x = b is represented by the definite integral of f(x )
There are 2 kinds of integrals
definite integrals (also known as Riemann integrals ) and indefinite integrals (also known as antiderivatives) .To express the limit as a definite integral, we can use the following formul
lim(n → ∞ ) Σf(i)/n = ∫ a^bf(x)dx
where....
a and b are the lower and upper limts of the definite integral
f (x) is the function being integrated
In this case, we have
lim(n → ∞) Σ(8i²)/n³
Let f (x) = x ²
So, f(i/n) = (i/n) ²
And, the sum can be written as
Σ(8i^2)/n³ = 8/n³ Σi²
= 8/n³ Σ(i/n)²
= 8/n³ Σ[f(i/n)]
= 8/n³ ∫0¹ f(x) dx (using the formula above)
Therefore, the limit can be expressed as
lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx
Simplifying the integral, we get....
8/n³ ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1
= 8/3n ³
Se we can say here that the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃
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Convert 135° from degrees to radians.
Answer: 2.35619
Step-by-step explanation: Hope this helps! :)
In an online game, you receive –3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most –27. When the character slips, it takes 2 seconds for him to resume the race. Write an inequality to find the least number of bananas your character slipped on.
An inequality to find the least number of bananas your character slipped on: -3x ≤ -27
And the least amount of race time character took to slip on bananas = 18 seconds.
Let us assume that x represents the number of bananas your character slipped on.
Here, based on the informtaion we get an inequality to find the least number of bananas your character slipped on -3x ≤ -27
We solve this inequality to find the least number of seconds of race time.
-3x ≤ -27
⇒ x ≥ 9
When the character slips, it takes 2 seconds for him to resume the race.
Therefore, the least amount of race time your character took to slip on bananas would be,
9 × 2 = 18 seconds
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The complete question is:
In an online game, you receive -3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most -27. When the character slips, it takes 2 seconds for him to resume the race. Write and solve an inequality to find the least number of bananas your character slipped on. At least how many seconds of race time
HELP 15 POINTS
Solve for x.
X
12 cm
x = [?] cm
Round to the nearest hundredth.
620
The opposite side of the right triangle is determined as 10.6 cm.
What is the value of x?The value of x is calculated by applying trigonometry ratio as shown below;
we will use the short form; SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.
sin (62) = x/12
x = 12 sin (62)
x = 10.6 cm
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Lesson 6.04
Comparing Data
Questions/Main Idea Notes
List the steps to compare two
representations of data
Example: use an example to show how to
compare data in two-line plots
Example: use an example to show how to
compare data displayed in a box plot
Example: use an example to show how to
compare data displayed in histograms
List the steps to create a back-to-back
stem-and-leaf plot
Include any examples here from the
lesson, that you would like.
Vocabulary Review:
Measures of center
Measures of variability
spread
Compare the data by observing the shape, center, and spread of the data in both representations.
1. Understand the data: Before comparing two representations of data, it is important to understand what the data represents and its context.
2. Identify the type of data: Identify the type of data represented in each representation to ensure the data is comparable.
3. Plot the data: Plot the data in each representation, such as a line plot, box plot, or histogram.
4. Compare the data: Compare the data by looking at the shape, center, and spread of the data in both representations.
Example: To compare data in two-line plots, plot the data as two lines on the same graph. Observe the difference in the shape of the two lines, the difference in center (the average value of the data), and the difference in spread (the range of the data).
Example: To compare data displayed in a box plot, plot the data as two box plots side by side. Observe the difference in the shape of the two box plots, the difference in center (the median value of the data), and the difference in spread (the interquartile range of the data).
Example: To compare data displayed in histograms, plot the data as two histograms side by side. Observe the difference in the shape of the two histograms, the difference in center (the mean value of the data), and the difference in spread (the standard deviation of the data).
List the steps to create a back-to-back stem-and-leaf plot:
1. Organize the data: Organize the data into two sets of numerical data.
2. Create stems: Create a stem for each set of data by dividing the values by a common multiple.
3. Create leaves: Create leaves for each set of data by recording the remainder of the original values after dividing them by the common multiple.
4. Plot the data: Arrange the stems and leaves into a back-to-back stem-and-leaf plot.
5. Compare the data: Compare the data by observing the shape, center, and spread of the data in both representations.
Therefore, compare the data by observing the shape, center, and spread of the data in both representations.
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A survey asked people of different ages whether they get their news by
reading the paper. What is the probability that a person surveyed is 40 or
above, given that he or she gets the news by reading the paper? If necessary,
round your answer to the nearest percent.
Don't read
Read paper
Total
Under 40
40 or older
Total
4
24
28
paper
36
16
52
40
40
80
The probability that a person surveyed is 40 or older and gets the news by reading the paper is 60%. The Option C is correct.
How do we find the reading for 40 or older?We must find the probability of a person getting their news by reading the paper and are given with a condition that the person must be 40 or older.
Data
The survey is conducted among 80 people.
Number of people aged 40 or older = 40
No of people aged 40 or older and read paper = 24
The probability of a person aged 40 or older reads a paper will be:
= (No. of People aged 40 or older and read paper)/(No. of people aged 40 or older)
= 24/40
= 0.6
= 60%
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Abbie needs to cover square pyramids with fabric. The dimensions of each pyramid are shown in the table. If the fabric costs $0.001 per square millimeter, what is the surface area and cost to cover each pyramid, rounded to the nearest whole cent?
PLEASE HELP !!!
The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2, 1285.8 and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10
To calculate the surface area of each pyramid, we need to use the formula
Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)
For the small pyramid, we have
Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)
Surface Area = 500 + 2 x 10 x 26.46
Surface Area = 1049.2 mm²
Cost to cover the small pyramid
Cost = Surface Area x 0.001
Cost = 1049.2 x 0.001
Cost = $1.05
For the medium pyramid, we have
Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)
Surface Area = 800 + 2 x 10 x 42.43
Surface Area = 1285.8 mm²
Cost to cover the medium pyramid
Cost = Surface Area x 0.001
Cost = 1285.8 x 0.001
Cost = $1.29
For the large pyramid, we have
Surface Area = 30 x 40 + 2 x ((30/2) x 50)
Surface Area = 1200 + 2 x 15 x 50
Surface Area = 2100 mm²
Cost to cover the large pyramid
Cost = Surface Area x 0.001
Cost = 2100 x 0.001
Cost = $2.10
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The wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, in
miles, that the tornado travels and S is the wind speed, in miles per hour.
If the wind speed was 130 miles per hour, which equation could be used to find the distance that the tornado traveled?
Select the correct answer below:
The equation that could be used to find the distance that the tornado traveled is: log d = 0.7
How to change the subject of the equation?We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,
where:
d is the distance, in miles, that the tornado travels.
S is the wind speed, in miles per hour.
When S = 130, we have:
130 = 93 log d + 65
93 log d = 130 - 65
93 log d = 65
log d = 65/93
log d = 0.7
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10 points. please answer
The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°
What are similar triangles?Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.
From the diagram shown:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
20 + 105 + ∠Z = 180
∠Z = 55°
Since triangle XYZ and triangle GHI are similar, hence:
∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°
The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°
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What will be the answer?
A symbolic representation of the contrapositive is
letter D
Answer:
b
Step-by-step explanation: