The number of days it will take the virus to grow from 90 to 410 is 15 days.
What is the growth rate of the virus?The growth rate of the virus is calculated as follows;
growth rate = (200 - 90) / 5
growth rate = 22 per day
The number of days it will take the virus to grow from 90 to 410 is calculated as follows;
growth = 410 - 90
growth = 320
Number of days = 320 / 22/day = 14.55 ≈ 15 days
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I need help I can't ask my teacher about this because I am sick so I need help learning to solve this.
Answer: x = 20
Step-by-step explanation:
[tex]\frac{3}{5} x - \frac{1}{4} x = 7\\12x-5x=140\\7x=140\\x=20[/tex]
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.
Given two points.
We have to find the slope of the line.
Slope of a line passing through (x, y) and (x', y') is,
Slope = (y' - y) / Ix' - x)
Here two points are,
(-3, -1) and (3, -10)
Slope = (-10 - -1) / (3 - -3)
= -9 / 6
= -3/2
Hence the slope of the line is -3/2.
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fv=100000, pmt=4000, i/y=5%, n=10, what is pv?
The Present value is $6,139.132.
We have,
FV=100000, pmt = 4000, I =5%, n=10
So, The present value formula is
PV=FV / (1 + [tex]i)^n[/tex]
So, PV = 100, 000 / (1+ 5/100[tex])^{10\\[/tex]
PV = 100,000 / (1+ 0.05[tex])^{10\\[/tex]
PV = 100, 000/ (1.05[tex])^{10\\[/tex]
PV = 100,000 / 1.6288946
PV= $6,139.132
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Find the volume of the sphere. Give the answer in terms of Pi and rounded to the nearest cubic foot. the radius is 5 ft.
The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.
Given a sphere.
Radius of the sphere = 5 feet
The formula to find the volume of the sphere is,
Volume of the sphere = 4/3 πr³,
where r is the radius of the sphere.
Substituting the given radius,
Volume of the sphere = 4/3 × π × (5)³
= 4/3 × π × 125
= 166.67π
Hence the volume of the sphere is 166.67π feet³.
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Here are two similar solid shapes.
and
A
surface area of shape A: surface area of shape B = 3:4
The volume of shape B is 10 cm³
Work out the volume of shape A.
Give your answer correct to 3 significant figures.
B
Step-by-step explanation:
Let the volume of shape A be V. Since the surface area of shape A is 3/4 times that of shape B, the surface area of shape A is 3/7 times the total surface area of the two shapes combined.
Therefore, the surface area of shape A is:
3/7 (surface area of shape A + surface area of shape B) = 3/7 (4/3 surface area of shape B) = 12/21 surface area of shape B
We know that the volume of shape B is 10 cm³, and we can find the volume of shape A by using the ratio of the volumes to the ratio of the surface areas:
V/10 = 3/4
V = 7.5 cm³ (to 3 significant figures)
Therefore, the volume of shape A is 7.5 cm³.
Bacteria was put in a petri dish with antibacterial soap. Determine the logarithmic regression of the bacteria. Use either a
calculator or spreadsheet program.
Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.
Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel
Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."
In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.
The resulting equation is
Bacteria = 447.91 * ln(Time) - 1733.1
This equation represents a logarithmic regression of the bacteria population over time.
To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation
Bacteria = 447.91 * ln(12) - 1733.1
Bacteria ≈ 44.1
So we would predict a bacteria population of about 44.1 at 12 hours.
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Study this table.
X
-3
-2
0
4
y
-2
0
4
12
Which best describes the function represented by the data in the table?
O linear with a common ratio of 2
Olinear with a common first difference of 2
O quadratic with a common ratio of 2
O quadratic with a common first difference of 2
The Function is linear with a common first difference of 2.
We have,
x y
-3 -2
-2 0
0 4
4 12
For the first set of points
m=(0-(-2))/(-2--3)
m = (0+2)/(-2+3)
m= 2/1 = 2
For the second set of points
m = (4-0)/(0-(-2))
m = 4/(0+2)
m = 4/2 = 2
For the third set of points
m = (12-4)/(4-0)
m = 8/4
m = 2
Thus, the function is linear with a common first difference of 2.
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Need help with 1 question for trig
The exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
The given trigonometric equation is cot²s=1 and the interval is [-2π, π).
The given equation can be rearranged as cot²s = 1, which can be written as cot s = ±1.
Using the inverse cotangent identity cot⁻¹(±1) = ±π/2, we can find the exact values of s in the interval [-2π, π) that satisfy the given condition:
s = ±π/2 + 2kπ, where k is an integer.
Therefore, the exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
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Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer. y = 12 x + 2 2y = x + 4 The system of equations has Choose... . The two equations represent Choose... .
Please help! I will mark brainiest! I do not understand the parenthesis being added.
Answer:
<4√97,-9√97>
Step-by-step explanation:
First, we need to find the values of A-C and B-D:
A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >
B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >
Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:
|A-C| = √((-4)^2 + 9^2) =√(97)
Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:
|A-C|(B-D) = √(97) * < 4, -9 >
= < 4√(97), -9√(97) >
So the final answer is < 4√(97), -9√(97) >.
A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, μ,
of babies born during the 24th week of the gestation period. She plans to select a random sample of birth
weights of such babies and use the mean of the sample to estimate μ. Assuming that the population of birth
weights of babies born during the 24th week has a standard deviation of 2.8 pounds, what is the minimum
sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number
(and make sure that it is the minimum whole number that satisfies the requirements).
The sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ is given as follows:
n = 189 babies.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is defined as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters are given as follows:
[tex]M = 0.4 \sigma = 2.8[/tex]
Then the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
0.4sqrt(n) = 1.96 x 2.8
sqrt(n) = (1.96 x 2.8/0.4)
n = (1.96 x 2.8/0.4)²
n = 189 babies. (rounded up).
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An unknown number w is 30 more than an unknown number p. The number w is also p less than 5. The equations to find p and w are shown below: w = p + 30 w = −p + 5 Which is a correct step to find p and w? (1 point) Add the equations to eliminate p. Multiply the equations to eliminate w. Write the points where the graphs of the equations intersect the x-axis. Write the points where the graphs of the equations intersect the y-axis.
The correct step find p and w is - add the equations to eliminate p. The correct option is the first option
Solving for variables in a system of linear equations: Determining the correct step to find p and wFrom the question, we are to determine which of the given steps is a correct step to find p and w.
The given system of equations is:
w = p + 30
w = −p + 5
From the above equation, we can easily add the equations to eliminate p
That is,
w = p + 30
+ w = −p + 5
------------------------
2w = 35
We can then solve for by dividing both sides by 2
2w / 2 = 35 / 2
w = 17.5
To determine the value of p, we can substitute the value of w into any of the equations
w = p + 30
17.5 = p + 30
p = 30 - 17.5
p = 12.5
Hence,
The correct step is add the equations to eliminate p
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gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
The amount of frosting in square centimeters it will take to cover the outside of the gingerbread house, pyramidal in shape, is about 12.65 square centimeters.
What is a the surface area of a square pyramid?The surface area of a square pyramid is the sum of the area of the four triangular faces.
The surface area of the gingerbread house can be found as follows;
The height of the pyramid and the square base indicates;
The slant height of a face of the pyramid = √(3² + 1²) = √(10)
The surface area of the pyramid = 4 × (1/2) × 2 × √(10) = 4·√(10)
4·√(10) ≈ 12.65
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The football players had to sell DEVIL FOOTBALL t-shirts to raise money for their next uniforms.They charged $14 for short sleeve shirts and $17 for long sleeve shirts. At the end of the fundraiser, they had sold 24 shirts and had made $378. How many of each type of shirt did they sell?
Use
S as the number of short sleeve shirts and
L as the number of long sleeve shirts.
PLS HELP
Answer:
Let's set up a system of equations to solve for S and L:
S + L = 24 (they sold a total of 24 shirts)
14S + 17L = 378 (the total amount made from selling the shirts was $378)
We can solve for one variable in the first equation and substitute it into the second equation:
S = 24 - L
14(24 - L) + 17L = 378
336 - 14L + 17L = 378
3L = 42
L = 14
So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:
S + 14 = 24
S = 10
Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.
The risk-free rate is 8%, and the expected return on the market is 16%. As an analyst, you are preparing a recommendation report on the following stock:
Stock S
Beta 0.85
Expected dividend next year $1.10
Growth rate (g) 8%
Current Price (p0) $22
Using the SML, would you recommend to buy or sell the stock?
A) Sell, because the required rate is greater than the expected rate.
B) Sell, because the expected rate is greater than the required rate.
C) Buy, because the required rate is greater than the expected rate.
D) Buy, because the expected rate is greater than the required rate.
Correct Option is,
D) Buy, because the expected rate is greater than the required rate.
Now, Based on the information you've provided,
To calculate the required rate of return, we can use the SML formula as;
Required rate of return = risk-free rate + beta x (expected market return - risk-free rate)
Plugging in the numbers, we get:
Required rate of return = 8% + 0.85 x (16% - 8%)
= 14.6%
Since the expected rate of return for Stock S is,
= dividend yield + growth rate
= (1.1 / 22 + 8%),
= 9.4%
which is higher than the required rate of return of 14.6%,
Here, the stock is undervalued and would be a good buy.
Therefore, the answer is, option D) Buy, because the expected rate is greater than the required rate.
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Simplify 6/15 x 55/10
2.2 in decimal form.
eleven fifths
Solve for x assume that lines which appear to be diameters are actual diameters
The value of x in the circle that shows diameter is calculated as:
x = -7
What is the Diameter of a Circle?In a circle, the line segment that divides the circle into two halves is the diameter. Half of the circle is a semicircle which has a measure of 180 degrees.
Note: The measure of a central angle is also the same measure with that of the arc it intercepts.
Therefore, we have:
-8x + 9 + 50 + 65 = 180
-8x + 124 = 180
-8x = 180 - 124
-8x = 56
x = 56/-8
x = -7
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Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?
Let c stand for the number of cousins Sawyer has.
Which bar model represents the problem?
Hazel C
Sawyer с с
Sawyer 8
8
Hazel 8 8
Sawyer C
Hazel
с с
8
Hazel 8
Sawyer 8 8
с
Sawyer has 4 cousins given that Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?From the question, we have the following parameters that can be used in our computation:
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.Using the above as a guide, we have the following:
Hazel = 2 * Sawyer
Let c stand for the number of cousins Sawyer has.
So, we have
Hazel = 2 * c
Substitute the known values in the above equation, so, we have the following representation
2 * c = 8
Divide by 2
c = 4
Hence, the number of cousins Sawyer has is 5
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How do I find the probability?
Answer:
To find the probability of an event occurring, you need to divide the number of ways the event can occur by the total number of possible outcomes. The probability is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
For example, if you want to find the probability of rolling a 3 on a standard six-sided die, there is only one way to roll a 3 and six possible outcomes (1, 2, 3, 4, 5, 6). So, the probability of rolling a 3 is 1/6 or approximately 0.17.
Keep in mind that the probability of an event occurring is not a guarantee that the event will happen. It only indicates the likelihood of the event happening based on the available information.
Given the figure below, find the values of x and z.
120°
(8x
+ 96).
Answer:
x = 3; z = 60°
Step-by-step explanation:
x:
The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.
Thus, we can solve for x by setting the two angles equal to each other and isolate x:
[tex]120=8x+96\\24=8x\\3=x[/tex]
We can check our answer by plugging in 3 for x and ensure that we get 120:
[tex]120=8(3)+96\\120=24+96\\120=120[/tex]
z:
We see that a horizontal straight line separates the angle measuring 120° and z°. Straight lines create straight angles, which equal 180°.
Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180. Then, we must isolate z:
[tex]120+z=180\\z=60[/tex]
How to solve for X and Y
The values of x and y are 4 and 2√2
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
In the triangle;
y is the opposite to angle 45 and x is the hypotenuse
cos 45° = 2√2/x
1/√2 = 2√2/x
x = 2√2 ×√2
x = 2 × 2 = 4
since the triangle is isosceles,
y = 2√2
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50 points. Out of 120 seventh and eighth grade CAVA students there were 30 students that chose Music as their elechive course and the rest chose World Language. There were a total of 60 eighth grade students and 40 of them chose
World Language as their elective.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table (6 pts)
Answer:
Based on the informtaion provided, the two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.
Total number of students = 120
This means that the number of students in 7th grade : 120- 60 = 60
Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.
This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.
Here, 40 eighth grade students chose World Language as their elective.
This means that out of total 90 students 90 - 40 = 50 students of 7th Grade chose World Language as their elective.
Now consider the 8th grade students,
Out of 60 students 40 chose World Language.
So, 60 - 40 = 20 must chose Music as their elective.
Now consider the 7th grade students,
Out of 60 students 50 chose World Language.
So, 60 - 50 = 10 students must chose Music as their elective.
Hence the required two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
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1. What would you get in your numerator when you multiply your terms together in the first step in simplifying?
2. What two terms would you combine in the numerator to simplify?
The step in simplifying the expression 3x/(x+5) - 3/(x+6) would result in 3x² + 18x - 3x - 15. The two terms that can be combined in the numerator to simplify are -3x and 18x. So, the correct answer is A), B) and D).
When multiplying the terms together in the first step of simplifying, we would get
3x - 3(x + 5)/(x + 6)
Simplifying this expression would lead to
3x² + 15x - 3x - 15/(x + 6)
Therefore, the answer is option (b): 3x² + 18x - 3x - 15
To simplify the numerator, we need to combine like terms.
To simplify the numerator, we need to combine like terms. The given expression is
3x² + 18x - 3x - 15
Here, the terms 18x and -3x have the same variable (x) and the same power (first power), but they have opposite signs. Therefore, we can combine them by subtracting the smaller value from the larger value. In this case, we have
18x - 3x = 15x
So, the expression simplifies to
3x² + 15x - 15
Therefore, the two terms that we would combine in the numerator to simplify are -3x and 18x, which give us 15x. So, the correct option is B) and D).
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cost minimal of logistic form factory to
warehouse mathematical problem
Answer:
To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.
To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.
Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.
Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:
C = 10x1 + 8x2 + 6x3
where C is the total cost of transportation.
Next, we would need to set up constraints based on the transportation options and the available resources. For example:
Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)
Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)
Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)
Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)
The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.
Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:
x1 >= 0, x2 >= 0, x3 >= 0
Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.
Step-by-step explanation:
if this helps, please mark my answer as brainliest
Activity
After an intensive search, Philip has narrowed his choices to four houses. Now he wants to buy the one that fits his budget. He has saved $40,000
for the down payment. Use the fixed-rate calculator to find the monthly payment for each house.
House Purchase Price Monthly Payment Affordability
A
$250,000
B
$200,000
C
$195,000
D
$180,000
Answer:
A
Step-by-step explanation:
A
A car is regularly passed through a traffic signal. Out of 100 times a car passed, it got a green signal 63 times. Find the maximum likelihood estimate of the probability p of green light on a single
The maximum likelihood estimate of the probability of getting a green light on a single pass through the traffic signal is 0.63.
To find the maximum likelihood estimate of the probability p of a green light on a single pass, we need to consider the observed frequency of green lights in the given data.
1. We are given that the car passed through the traffic signal 100 times and got a green light 63 times.
2. To find the maximum likelihood estimate (MLE) of the probability p of a green light, we need to divide the number of successful green light events (63) by the total number of passes (100).
3. Calculate the MLE: p = 63/100 = 0.63
The maximum likelihood estimate of the probability p of a green light on a single pass is 0.63.
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The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 5x + 12. Which of the following shows the area of the rectangle in terms of x? (L ⋅ W)(x) = 24x3 − 30x + 72 (L ⋅ W)(x) = 24x3 − 30x2 + 72x (L + W)(x) = 4x2 + x + 12 (L + W)(x) = 2x2 + x + 12
The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.
Given a rectangle.
Length of the rectangle, L(x) = 6x
Width of the rectangle, W(x) = 4x² − 5x + 12
The formula to find the area of the rectangle is,
Area = Length × Width
Substituting the given length and width,
Area of the rectangle = L(x) . W(x)
= (L . W)(x)
= (6x) (4x² − 5x + 12)
= 24x³ - 30x² + 72x
Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.
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Answer:
(L . W)(x) = 24x³ - 30x² + 72x.
Step-by-step explanation:
Use the figure below to answer the following questions.
Complete the statement: triangle AGC~triangle ___
Complete the statement: triangle CDE~triangle___
What is
What is
What is BC?
What is DE?
Complete sentence is,
⇒ ΔAGC ≈ ΔCDF
⇒ ΔCDE ≈ ΔCAB
And, The length of BC is, 51
The length of DE is, 132.7
We have to given that;
⇒ CF = 32
Hence, We get;
tan 24 = CF / DF
0.44 = 32 / DF
DF = 72.7
Thus, ΔAGC ≈ ΔCDF
Here, We have;
⇒ ΔCDE ≈ ΔCAB
In triangle BCG;
BC² = 24² + 45²
BC² = 576 + 2025
BC² = 2601
BC = 51
In triangle CEF;
⇒ EC² = CF² + EF²
⇒ 68² = 32² + EF²
⇒ 4624 = 1024 + EF²
⇒ EF² = 4624 - 1024
⇒ EF² = 3600
⇒ EF = 60
Thus, We get;
DE = DF + EF
DE = 72.7 + 60
DE = 132.7
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Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex] units. What is a simplified expression for the difference in the areas of Circle A and Circle B
The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²
Area of a Circle:The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.
We know that :
The formula of circle's circumference is = 2πr
We have :
Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units
and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]
Now, First we calculate the area of circle A is:
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
Area = πr² = (4/x+2)²π
Now, for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
Area =( 2/2x+2)²π
Simplified expression for the difference in the areas of Circle A and Circle B are:
(4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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Find the value of the trig function indicated.
3)
tan 0
13
12
0pls help
The value of the identities are;
1. tan θ = 5/12
2. cot θ = √7/3
How to determine the identitiesTo determine the value of the identities, we need to take note of the different identities;
sinetangentcotangentsecantcosecantcosineFrom the information given, we need to take note that;
tan θ = opposite/adjacent
cot θ = inverse of tangent identity
cot θ = adjacent/opposite
then,
1. tan θ =
Opposite = 5
Adjacent = 12
tan θ = 5/12
2. cot θ = 4√7/12 = √7/3
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