The units of a and b are m/sec³ and m/sec⁴
Given :v = at² + bt³
The dimension of velocity v = [L] [T]⁻¹
According to the Principle of Homogeneity of Dimension, "the terms combining the equation must have the same dimensions for the equation to have any physical meaning."
So, Dimensiona of v = Dimensions of at²
[L][T]⁻¹ = a[T]²
a = [L][T]⁻³ = m/sec³
Similarly, we can say
Dimension of v = Dimension of bt³
[L][T]⁻¹ = b[T]³
b = [L][T]⁻⁴ = m/sec⁴
Hence, the unit of a is m/sec³ and the unit of b is m/sec⁴
The question is incomplete, the complete question is
"During a short interval of time, the speed v in m/s of an automobile is given by v = at² + bt³ where the time t is in seconds the units of a and b are respectively:"
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tv screens are measured on the diagonal. if we have a tv-cabinet that is 66 inches long and 54 inches high, how large a tv could we put in the space (leave 2-inches on all sides for the edging of the tv)? round your answer to the nearest tenth.
Using Pythagoras' theorem, we can conclude that we can put a 79.65 inches TV in the TV cabinet.
We have been given that a TV -cabinet is 64 inches long and 52 inches high.
After leaving 2 inches on all sides, our new dimensions would be:
Length = 66 - 2 - 2 = 66 - 4 = 62 inches
Height = 54 - 2 - 2 = 54 - 4 = 50 inches
Using Pythagoras' theorem, we can find the diagonal of the television
Diagonal² = 62² + 50²
Diagonal² = 3844 + 2500
Diagonal² = 6344
Take square root of both sides:
Diagonal = √6344
Diagonal = 79.65 inches
Hence, we can put a 79.65 inches TV
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What is the rule for an exponential graph?
One significant mathematical function that has the form is the exponential function, f(x) = [tex]$$a^x[/tex].
What is meant by exponential graph?If f(x) = [tex]$$a^x[/tex], where x is the input variable and is expressed as an exponent, is the formula for an exponential function. In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. One significant mathematical function that has the form is the exponential function. f(x) = [tex]$$a^x[/tex].
The four fundamental characteristics of exponential functions are their y-intercept, horizontal asymptote, domain (the range of x values at which the function occurs), and constant growth factor, b.
Calculating the exponential growth or decay of a set of given data is done using an exponential function. According to the power to the power rule, "If the base increased to a power is being raised to another power, then the two powers are multiplied and the base remains the same."
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Use the Box plot below
By using the box plots, each statistical value should be completed as follows;
Mean: cannot be determined.
Median: equal for data sets X and Y.
Range: greater for data set X.
Interquartile range: greater for data set Y.
How to calculate the range?Mathematically, the range of a data set can be calculated by using this formula;
Range of X = Highest number - Lowest number
Range of X = 65 - 20
Range of X = 45.
Range of Y = Highest number - Lowest number
Range of Y = 55 - 20
Range of Y = 35.
How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of X = Q₃ - Q₁
Interquartile range (IQR) of X = 55 - 35
Interquartile range (IQR) of X = 20.
Interquartile range (IQR) of Y = Q₃ - Q₁
Interquartile range (IQR) of Y = 50 - 25
Interquartile range (IQR) of Y = 25.
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alice is holding up the top vertex of a triangular banner attached to the ground by two anchors on the bottom vertices. what is the area of the banner of alice reaches her arm up above the ground and the anchors on the bottom are apart?
Let's call the length of the bottom side of the triangular banner "b". When Alice reaches her arm up above the ground, the height of the banner changes from its original height of "h" to a new height of "h'". The area of the banner can be calculated using the formula:
A = (b * h') / 2
The new height "h'", can be calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the two shorter sides are the original height "h" and the difference between the length of Alice's arm and the original height, which we will call "d". The longest side is the distance between the two anchors, which we will call "a".
So:
h^2 + d^2 = a^2
We can solve for "d" using this equation:
d = sqrt(a^2 - h^2)
And then we can find "h'" using:
h' = h + d
So the area of the banner can be calculated as:
A = (b * (h + sqrt(a^2 - h^2))) / 2
The solution assumes that the banner is a right triangle, with one vertex at the top, one vertex at the bottom, and a straight side along the ground connecting the two bottom vertices.
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an experiment requires a measurement before and after the presentation of a stimulus to 20 subjects. in the analysis of the data collected from this experiment, how many degrees of freedom are there in the test?
In a repeated measures design with 20 subjects, each subjected to 2 measurements (before and after stimulus presentation), the degrees of freedom in the test would be 19.
DF in Repeated Measures ExperimentThe problem is about an experiment in which a measurement is taken before and after a stimulus is presented to 20 subjects. The aim is to determine the number of degrees of freedom in the data analysis of the experiment.
Degrees of freedom (df) are a measure of the amount of variability in a set of data that is free to vary in the calculation of a statistical test. In a repeated measures design, the degrees of freedom are calculated as the number of subjects minus 1. In this case, with 20 subjects, the degrees of freedom would be 19.
The concept of degrees of freedom is used in both mathematics and physics, but the specific context of a t-test for dependent samples is commonly used in statistical analysis, particularly in the social sciences, psychology, and education research. So, it is more related to mathematics.
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find an equation of the sphere with center (−4, 2, 6) and radius 7. correct: your answer is correct. what is the intersection of this sphere with the yz-plane? incorrect: your answer is incorrect.
The equation of sphere is (x + 4)² + (y - 2)² + (z - 6)² = 49 and the intersection is a circle of radius √33 on yz - plane.
A sphere, like a ball, is defined as a perfectly spherical geometrical entity in three dimensions.
the general equation of a sphere is (x – a)² + (y – b)² + (z – c)² = r² where (a, b, c) is the centre of the sphere and r is the radius of the sphere.
Given, the centre of the sphere C(−4, 2, 6) and radius of sphere 7 units
Equation of sphere: (x - (-4))² + (y - 2)² + (z - 6)² = 7²
(x + 4)² + (y - 2)² + (z - 6)² = 49
It is given that the sphere is intersecting with yz - plane which means x = 0
so, (0 + 4)² + (y - 2)² + (z - 6)² = 49
(y - 2)² + (z - 6)² = 33
The intersection is a circle of radius √33 on yz - plane.
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A parabola can be drawn given a focus of (-7, 9) and a directrix of y = 11. Write
the equation of the parabola in any form.
The equation of the parabola with focus at (-7,9) and directrix at y = 11 is given as follows:
(x + 7)² = -4(y - 10)
How to obtain the equation of the parabola?The equation of a vertical parabola is given as follows:
(x - h)² = 4p(y - k)
In which:
(h,k) are the coordinates of the vertex.y = k - p are the coordinates of the directrix.(h, k + p) are the coordinates of the focus.A parabola can be drawn given a focus of (-7, 9), hence:
h = -7.k + p = 9.Directrix of y = 11, hence:
k - p = 11.
Adding the equations of the y-coordinate of the focus and of the directrix, the value of k is obtained as follows:
2k = 20
k = 20/2
k = 10.
Hence the value of p is of:
p = k - 11
p = -1.
Meaning that the equation is:
(x + 7)² = -4(y - 10)
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DeAndre has 190 square inches of plastic to make a cylindrical bird feeder. Which design should he choose? Explain.
DeAndre should select the shape that satisfy the equation -
r(2h + r) = (190/π).
What is cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology.Given is that DeAndre has 190 square inches of plastic to make a cylindrical bird feeder.
He should choose the design whose total surface area is equivalent to 190 square inches. We can write the total surface area as -
2πrh + πr² = 190
πr(2h + r) = 190
r(2h + r) = (190/π)
Therefore, DeAndre should select the shape that satisfy the equation -
r(2h + r) = (190/π).
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solve the simultaneous equation. y=5-x ,x^2-2y^2-1=0
In the given simultaneous linear equation, the value for x is 3 and the value for y is 2.
Explain simultaneous linear equation.A system of simultaneous linear equations is any set of two or more linear equations that share the same variables involved. Obtaining values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.
In the given question,
x + y = 5.......(i)
x2 - 2y2 = 1.......(ii)
x = 5 - y.........(iii)
Substituting x in equation(ii) = (5 - y)2 - 2y2 = 1
25- 10y + y2 - 2y2 = 1
25 - 1 = y2 + 10y
y2 + 10y2 - 24 = 0
(y + 12)(y - 2) = 0
Then Either y + 12 = 0 or y - 2 = 0
= (-12, 2)
Thus, y = 2
Now, substituting the value of y in equation (i),
x + y = 5
x + 2 = 5
x = 5 - 2
x = 3
Therefore x = 3 and y = 2.
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A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries. Assume that all schedules are equally likely. Determine the probability for each of the following: (a) All hip surgeries are completed before another type of surgery (b) The schedule begins with a hip surgery (c) The first and last surgeries are hip surgeries. (d) The first two surgeries are hip surgeries.
To calculate the probability a) P = (4C4 x 3C3)/(12C12) = 1/12. (b) P = (4C1 x 3C3 x 5C5)/(12C12) = 1/12. (c) P= (4C1 x 3C3 x 4C3 x 5C4)/(12C12) = 1/9. (d) P= (4C2 x 3C3 x 5C5)/(12C12) = 1/36.
(a) To calculate the probability that all hip surgeries are completed before another type of surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with four hip surgeries and three knee surgeries (4C4 x 3C3). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (b) To calculate the probability that the schedule begins with a hip surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery, three knee surgeries, and five shoulder surgeries (4C1 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (c) To calculate the probability that the first and last surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery at the start, three knee surgeries, three hip surgeries, and four shoulder surgeries (4C1 x 3C3 x 4C3 x 5C4). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/9). (d) To calculate the probability that the first two surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with two hip surgeries, three knee surgeries, and five shoulder surgeries (4C2 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/36).
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A 75 kg box is being pulled across the floor with a force of 465 N. If the kinetic coefficient of friction is 0.57, what is the acceleration of the box?
The acceleration of an object is interpreted as the rate of change at which its speed varies with time. When the motion is vertical, the object has an acceleration when its speed varies, while when the speed is constant, the acceleration is equal to zero. The acceleration of the box is 0.614 m/s.
What is acceleration?In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.Deceleration occurs when acceleration is directed in the opposite direction as the velocity of an object.Deceleration is always defined in physics as the slowing down of an object, which means that the magnitude of the velocity decreases.The rate of change of displacement is defined as velocity. The rate of change of velocity is defined as acceleration. Because it includes both magnitude and direction, velocity is a vector quantity. Because it is simply the rate of change of velocity, acceleration is also a vector quantity.To learn more about acceleration refer to:
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can someone pls help
The required area of the parallelogram and pentagon is 91 unit² and 75 unit².
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram = 13 × 7 = 91 unit²
Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
= 5 [1/2 × 5 × 6]
= 75 suqare units.
Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².
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Name a pair of adjacent angles in this figure. N
Answer:
Step-by-step explanation:
angleNOP AND anglePOQ
anglePOQ AND angleQOR
a box containis some chocolate. thw weight of the box and chocolate 360g. Alex eats 2/5 of the chocolate. the weight of the box and chocolate is now 248g. how much does the box weigh?
Answer: 80g
Step-by-step explanation:
we can write an equation for the weight of chocolate; 360-(2/5)x=248
when we solve that equation, we get x=280
since the total weight is 360, we can minus 280 from it to get the weight of the box
360-280=80
A car moving at a constant speed passed a timing device at t=0. After 6 seconds, the car has traveled 684 ft. 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.
The linear function rule is d = ?
Answer:
Step-by-step explanation:
219y+608=−121156 219y+608=−121156 219y+608=−121156 v 219y+608=−121156v219y+608=−121156vvv219y+608=−121156= 365
Answer:
d = 114t
Step-by-step explanation:
distance = rate * time
therefore, rate = distance/time
684 ft in 6 sec = 114 ft per sec (this is the 'rate')
so the distance can be calculated by multiplying time in seconds to get distance in feet
d = 114t
Simplify the expression please. See image for problem
Answer:
answer is 1
Step-by-step explanation:
12-y/6y-36
and other you can see by photo
Adrian is going to an amusement park. The price of admission into the park is $35, and once he is inside the park, he will have to pay $3 for every ride he rides on. How much money would Adrian have to pay in total if he goes on 12 rides? How much would he have to pay if he goes on r rides?
The amount of money that Adrian will pay if he goes on the given amount of ride would be =$71
How to calculate the cost per ride?An amusement park is defined as the park where different recreational activities are being carried out.
The price of admission in the park = $35
The amount he pays for each ride at the amusement park= $3.
The amount for 12 rides= 3×12 = $36
Therefore the total amount of money that Adrian will pay if he goes to the amusement park for 12 rides would be = $36 + $35 =$71
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Paul wins 1500metres in 4,67metres .(c) write down his average in metres per minutes correct to: (I) The nearest Whole number ( ii ) One decimal place ( iii ) Two decimal places ( iv ) Three significant figures
Answer:
(I) The nearest whole number is 317.5 meters per minute.
(ii) One decimal place is 317.5 meters per minute.
(iii) Two decimal places is 317.47 meters per minute.
(iv) Three significant figures is 317 meters per minute.
Note: To find the average velocity, divide the distance traveled by the time it took to travel that distance. 1500 meters / 4.67 minutes = 322.2 m/min. But since you want the answer rounded to different degrees, you can round the answer accordingly.
The differential equation xydx + (x^2 + y^2)dy = 0 is Select the correct answer.
a. exact with solution x^2y/2 + y^3/3 =c b. exact wiih solution x^2y/2 + y^2/2 = c c. exact with solution x^2y/2 + y^3/3+c d. not d: not exact but having an integrating factor x c e. not exact but having an integrating factor y
The correct answer is option is option d) not exact but having an integrating factor x c e.
Integrating factor is defined as the function which is selected in order to solve the given differential equation. It is most commonly used in ordinary linear differential equations of the first order. When the given differential equation is of the form; dy/dx + P(x) y = Q(x)
We have, (x2+y2)dy= -xydx
⇒dxdy= -(x2+y2xy)
Substitute y=vx
⇒ - dxdy=v+xdxdv
⇒v+xdxdv= -(1+v2v)
⇒ xdxdv= -(1+v2v−v)
= -(−1+v2v3)
⇒v31+v2dv =xdx
Integrating both sides we get, −2v21+logv= logx-logc, where c is constant
⇒−2v21+log(cvx)=0
⇒y=cex2/2y2
Now using y(1)=1⇒c=e−1/2
Also y(x0)=e
⇒e=e−1/2+x02/2e2⇒1=−1/2+x02/2e2
⇒x02=3e2
⇒x0=[tex]\sqrt{3}[/tex]e
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In this figure, a || b || c and m/5 = 155°
What is m/3 ?
25°
65°
155°
I don't know.
25 Degres it is a obtuse angle using the dewy decimal system
Answer:
The person above me is correct
25
Step-by-step explanation:
Kendra watches the moon change from a new moon to a full moon. Which of the following descriptions is accurate? (Select all that apply.)
Responses
The moon is waxing.
The moon is waxing.
The moon is waning.
The moon is waning., ,
The moon appears to get smaller.
The moon appears to get smaller.
The moon appears to get bigger.
The moon appears to get bigger.
The moon does not change.
The correct description is that moon is waxing.
Which of the following descriptions is accurate?The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.
The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.
The waning phase is when the moon is gradually getting smaller and less illuminated.
The moon is waxing:
This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.
This means that the moon is gradually getting bigger, and its illuminated side is increasing.
This process is called the waxing phase of the moon's cycle.
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what 26789 divide 43
What is the weight in lbs of a 75-kg person?
Hence, we can say that the weight of a person of 75 Kg in lbs will be equal to 165.3465lbs.
Define weight?The weight of an object is the force acting on it due to gravity in science and engineering.Weight is defined as a vector quantity in some standard textbooks, as the gravitational force acting on the object.Others define weight as a scalar quantity, the magnitude of gravity.We know that the conversion factor for lbs to kg is
1 kg = 2.20462lbs
Now, to convert 75 Kg into lbs, we need to multiply the 75 with the conversion factor. That is,
75kg = 75×2.20462lbs = 165.3465lbs
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3. What is the probability an individual student likes between 5.5 and 8.5 songs from Eminem?
This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.
Explain about the probability?The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.
There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.
How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
To find:
P(X < 5.5)
Z = -1.0
However;
P(X< 5.5) = P(Z < -1.0)
P(X< 5.5) = 0.1587
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At the end of any year a car is worth 5% less than what is was worth at the beginning of the year. if a car was brought for 10 000 in January 2009, its value in December 2009 was
Answer:If at the end of any year a car is worth 5% less than what it was worth at the beginning of the year, we can say that the car's value decreases by a factor of 0.95 (1 - 0.05) every year.
To find the car's value in December 2009, we can use the formula:
Car value at end of year = Car value at beginning of year * (1 - 0.05)^(number of years)
Plugging in the given values, we get:
Car value in December 2009 = 10,000 * (1 - 0.05)^1 = 9,500
So the car's value in December 2009 is 9,500 dollars.
Step-by-step explanation:
Answer:
9500
Step-by-step explanation:
If you didn't understand that one (which I personally found a little complicated) the answer can be found like this.
1. You firstly find the decrease which is 5/100 × 10000 (5/100 can also be written as 5%) and the answer will be 500
2. Then you take the original value and you minus the loss in worth of the car —> 10000-500 = 9500
Exponential growth: what it is, why it matters, and how to spot it
An expansion within a population that happens at the same pace across time is represented by the function of exponential growth.
What is exponential growth?It is reasonable to suppose that data grows exponentially as populations double or triple in size. Exponentially decaying data is the reverse of exponentially growing data. When your data are visualized on a graph, the pattern an exponential function displays appears as an ascending curve. f(x) = a(1 + r)x is another formula you may use to compute exponential growth.F(x) stands for the function and is a term.The starting value of your data is indicated by the a variable.Growth rate is indicated by the variable r.Period of time is represented by the x variable.Examples :
The analyst can determine the possible returns after three, five, and ten years if the customer deposits an initial starting capital of $5,000 into their compound savings account. The analyst decides: Using a 5% interest rate
Upon completion of three years: ($5,000)(1 + 0.05)(3) = $5,788
Upon completion of five years: ($5,000)(1 + 0.05)(5) = $6,381
A decade later, ($5,000)(1 + 0.05)(10) = $8,144
The Complete Question is exponential growth.
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Three boys shared D 10,500.00 in the ratio 6:7: 8. Find the largest share.
Answer:
Step-by-step explanation:
let the common ratio be x.
boy 1 share= 6x
boy 2 share= 7x
boy 3 share= 8x
-------------------------------
21x= 10500.00
=> x= 10500/21
x= 500
6 x 500= $3000
7x 500= $3500
8 x 500= $28000
therefore, boy 3 has the largest share of $28000.
Four research teams each used a different method to collect data on how fast a new iron skillet rusts. Assume that they all agree on the sample size and the sample mean (in days). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation
The smallest sample standard deviation
Confidence Level: 95%; Confidence Interval: 42 to 48.
How to interpret the confidence interval?Assume that x ± y represents the confidence interval at P% for the values of some parameter.
In other words, the parameter's projected value is P% likely to fall within the range.
[x - y, x + y]
Data on how quickly a brand-new iron skillet rusts were gathered by four research teams using various techniques.
Assume that everyone is in agreement with the sample size and sample mean (in days).
Choose the team with the smallest sample standard deviation using the (confidence level; confidence interval) pairs below.
Then we have
= 48 - 42 = 6
Then we have
= 6/2
=3, which is smallest
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The question you have uploaded is seems to be incomplete, the complete question is
A. Confidence Level: 99.7%; Confidence Interval: 40 to 40
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Need answer soon thank you
The translation needed to obtain the graph of g(x) = [tex]9^{x}-4[/tex] from the graph of f(x) = [tex]9^{x}[/tex] is a shift down 4 units.
What is graph?Graph is a type of data structure that is used to store and organize data in a visual representation. It consists of nodes, which store the data, and edges that connect the nodes. Graphs can be used to represent networks, relationships between different entities, or even mathematical equations. Graphs are versatile and can be used in many different applications, from engineering to data science. Graphs are also used to represent complex data structures and are often used to simplify and organize data for easier analysis.
This is because subtracting 4 from [tex]9^{x}[/tex] is the same as shifting the graph of f(x) down 4 units on the y-axis, resulting in the graph of g(x).
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What is 32(4x+6) in simplified form
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING:}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\huge\textbf{If so, distribute \boxed{\rm{\bf \dfrac{3}{2}}} within the}\\\\\huge\textbf{parentheses}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}(4x) + \dfrac{3}{2}(6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}\times \dfrac{4}{1}x + \dfrac{3}{2} \times \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{3\times4}{2\times1}x +\dfrac{3\times6}{2\times1}}[/tex]
[tex]\mathsf{= \dfrac{12}{2}x +\dfrac{18}{2}}[/tex]
[tex]\mathsf{= 6x + 9}[/tex]
[tex]\huge\textbf{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{6x + 9}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
