The vector [a², a] is in the span of [1, 1, 1] and [2, 1, 3] if and only if 'a' can be expressed as a linear combination of the given vectors. Thus, the vector [a², a] is in the span of [1, 1, 1] and [2, 1, 3] when a is either 0 or 2.
To determine the values of 'a' for which the vector [a², a] is in the span of [1, 1, 1] and [2, 1, 3], we need to check if there exist constants x and y such that:
x[1, 1, 1] + y[2, 1, 3] = [a², a]
This leads to the following system of equations:
x + 2y = a²
x + y = a
Solving this system, we find:
x = a - y
Substituting this value into the first equation:
a - y + 2y = a²
y = a² - a
Now, we substitute the value of y back into the equation for x:
x = a - (a² - a)
x = 2a - a²
Therefore, for the vector [a², a] to be in the span of [1, 1, 1] and [2, 1, 3], 'a' must satisfy the equation:
2a - a² = a(2 - a) = 0
This equation has two solutions: a = 0 and a = 2. Thus, the vector [a², a] is in the span of [1, 1, 1] and [2, 1, 3] when a is either 0 or 2.
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For what values of 'a', the vector a² a is in span 1 1 1 ELEME 2 1 3 3 4
5. Find the equation of the circle passing through three points (1,2), (3,-4), (5,-6).
The equation of the circle passing through the points (1,2), (3,-4), and (5,-6) is [tex]x^2 + y^2 - 6x - 4y + 7 = 0[/tex].
To find the equation of a circle passing through three non-collinear points, we can use the general form of the equation for a circle: (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is the radius.
To find the center and radius, we can form equations using the three given points. Substituting the coordinates of each point into the general equation, we get three equations:
[tex]\((1 - h)^2 + (2 - k)^2 = r^2\)\((3 - h)^2 + (-4 - k)^2 = r^2\)\((5 - h)^2 + (-6 - k)^2 = r^2\)[/tex]
Expanding these equations, we obtain three equations in terms of h, k, and r. By solving this system of equations simultaneously, we can determine the values of h, k, and r. However, in this case, it can be observed that the given points already satisfy the equation [tex]x^2 + y^2 - 6x - 4y + 7 = 0[/tex]. Hence, this is the equation of the circle passing through the given points.
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Help needed ASAP will give brainliest and 5 STARS RATE
Answer:
the 2nd answer choice
Answer:
Hey, its B. This ordinance made is so that new states could be added to the US.
Step-by-step explanation:
The law provided for the method by which new territories would be admitted to the United States. The government intended to encourage westward expansion.
Adition and subtraction of functions
f(x) = x^2 + 1. g(x)=5-x
(f + g)(x) =
x^2 + x -4
x^2+x+4
x^2-X+6
x^2 + x + 6
Answer:
(f + g)(x) = x² - x + 6
Step-by-step explanation:
Step 1: Define
f(x) = x² + 1
g(x) = 5 - x
Step 2: Find (f + g)(x)
(f + g)(x) = x² + 1 + 5 - x
(f + g)(x) = x² - x + 6
Answer:
(f + g)(x) = x² - x + 6
Step-by-step explanation:
What numbers come next in the pattern??
1, -3, 9, -27
Answer:
81
Step-by-step explanation:
You r multiplying by three's
Answer:
81.
Step-by-step explanation: The pattern in this scenario would be multiplying the previous number by -3. (1 x -3 = -3, -3 x -3 x 9, etc.). Using this information, we know that multiplying the last number (27) by -3 would be the correct equation, yielding 81. Hope this helps!
Raphael went to the store and bought 2 12 pounds of chicken breasts for $9.00. The chicken breasts cost $
per pound. Round your answer to the nearest cent, if necessary.
Answer:
Raphael spent $0.38 per pound of chicken
Step-by-step explanation:
Because Raphael bought 2 packages weighing 12 pounds each you have to multiply 2 by 12 to get the total weight which is 24.
the math would be for this equation $9.00/24=0.375
you round up the thousandths place and get $0.38 per pound of chicken
Problem 4(4×5=20 pts) During the Vancouver 2010 Olympics, in an effort to service the large inflow of tourists to the city, Translink set up a new route primarily for a fleet of Vancouver tour buses. The tours showcased popular Vancouver city highlights such as UBC, Stanley Park, Science World, and other popular attractions. You were hired as an expert for Translink to determine the number of buses that would be needed for this route. Before you began you needed to take into consideration several aspects of the process such as: - A single tour bus takes exactly 2 hours to complete the tour. - The tour starts and finishes at the UBC rose-garden pick-up point. - Each tour bus has seating for 50 passengers, and room for another 30 passengers to stand. This route is busy much of the day, because tourists prefer to visit sites and attractions early in the day and attend Olympic events in the evening. - Finally, Translink authorities want to show their Canadian hospitality and ensure they have enough capacity to handle peak customer loads so that no demand is unmet. a. Assuming there are only 2 buses servicing this new route, what is the cycle time between each completed tour? b. Translink does not want anybody to wait any longer than 6 minutes to catch a tour-bus. How many buses will be required to service this route to meet this requirement? c. Now assuming Translink wants to service the route with the number of buses that you have calculated in number 2 . What is the maximum amount of passengers that can be accommodated at a single point in time on the tour route? d. The buses operate from 8am to 8pm. The pick-up point for the tour is at UBC rose-garden, where the tour begins and ends. From 8am until noon, tourists arrive at a rate of 450 passengers per hour. From noon to 2pm tourists arrive at the rate of 1000 passengers per hour. From 2pm until 8pm, passengers arrive at a rate of 700 each hour. The tour-bus system can pick up tourists at a rate of 800 passengers per hour. How many tourists do you expect to see waiting to get on a tour-bus at the rose-garden at 10am? At 1:30pm? At 5:45pm? Hint: Create a plot/graph/diagram of the number of tourists waiting as a function of time.
At 10am, you would expect to see 350 tourists waiting to get on a tour-bus at the rose-garden. At 1:30pm, you would expect to see 650 tourists waiting, and at 5:45pm, you would expect to see 700 tourists waiting.
Let's consider the arrival and departure rates of tourists throughout the day. From 8am to noon, tourists arrive at a rate of 450 passengers per hour, while the tour-bus system can pick up tourists at a rate of 800 passengers per hour. This means that during this time, the tour-bus system can accommodate all arriving tourists, resulting in no waiting time. At 10am, two hours have passed since the start of the tour, and assuming each tour takes 2 hours, the first bus that started at 8am would have returned to the rose-garden. Hence, the number of tourists waiting at 10am would be 450 (arrival rate) - 800 (departure rate) = 350. Similarly, from noon to 2pm, tourists arrive at a rate of 1000 passengers per hour, and the tour-bus system can pick up tourists at a rate of 800 passengers per hour. This means that there is a waiting time for tourists during this period. At 1:30pm, three and a half hours have passed since the start of the tour, and assuming each tour takes 2 hours, one bus would have returned to the rose-garden, resulting in 800 passengers being picked up. Hence, the number of tourists waiting at 1:30pm would be 1000 (arrival rate) - 800 (departure rate) = 200, in addition to those who were waiting from the previous hours. Finally, from 2pm until 8pm, passengers arrive at a rate of 700 per hour, while the tour-bus system can pick up tourists at a rate of 800 per hour. This means that during this time, the tour-bus system can accommodate all arriving tourists, resulting in no waiting time. At 5:45pm, nine hours and forty-five minutes have passed since the start of the tour, and assuming each tour takes 2 hours, four buses would have returned to the rose-garden, resulting in 3200 passengers being picked up. Hence, the number of tourists waiting at 5:45pm would be 700 (arrival rate) - 3200 (departure rate) = 0, indicating no tourists waiting at that time.
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How are exponents related to multiplication?
Answer: Exponents are like the multiplication of a number against itself that many times.
Step-by-step explanation: 2^4=2x2x2x2
3^3=3x3x3
Answer: You use exponents when you want to wright a number that is
being multiplied by itself one or more times. The number 3 is the number being multiplied. The smaller number 2, near the top, means that there are two 3s that are being multiplied.
Step-by-step explanation:
6r + (r + 4)2
what is the answer to the equation above
Answer:
=8r+8
Step-by-step explanation:
The side s of a square carpet is measured at 2 ft. Estimate using the Linear Approximation the maximum error in the area A of the carpet if s is accurate to 0.7 inches. (Use decimal notation. Give your answer to three decimal places.)
To estimate the maximum error in the area A of the carpet, use the Linear Approximation. Let's use a differentiable function:
f(s) = s². When s = 2 feet, A = f(s) = s² = 4 square feet.
The change in s, Δs = 0.7 inches. We can convert that to feet and get the linear approximation:Δs = 0.7 in = 0.7/12 ft = 0.05833 ft.
A better approximation of the new area A is given by
ΔA = f′(s) Δs = 2s Δs
Since f′(s) = 2s,ΔA = 2s Δs = 4 Δs.
Since s = 2 ft and Δs = 0.05833 ft, we have that the maximum error in A is given by
|ΔA| ≤ 4 Δs = 4(0.05833) = 0.2333 square feet.
Therefore, the maximum error in the area of the carpet is 0.2333 square feet.
The side s of a square carpet is measured at 2 ft, and it's accurate to 0.7 inches. The maximum error in the area A of the carpet is 0.2333 square feet.
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An integer N is less than its opposite. Which of the
following must be true of the integer?
Answer:
N must a negitve number.
Step-by-step explanation:
They opposite would be positive. Anything positive is bigger than a negitve
Answer:
The integer must be negative (less than 0)
Step-by-step explanation:
The opposite of a number is the same number but but with the opposite sign (+/-). E. G. The opposite of (+)2 is -2.
If N is less than its opposite, than it means that it is negative as its opposite will be positive (greater than 0). E.g. If N=-2, its opposite would be 2.
2>-2
Hope this helped!
Ms. Vicker is trying to save enough money to buy her wedding dress at the cost of $1,200. She has $600 saved from her summer school job. To make the rest of the money, Ms. Vicker plans to tutor for Sylvan at a cost of $10 per hour. Write an inequality to determine how many hours Ms. Vicker must tutor to have enough money for the dress.
Answer:
The inequality to determine how many hours Ms. Vicker must tutor to have enough money for the dress.
$600 + 10x ≥ $1200
Step-by-step explanation:
From the question, we are told that:
Ms. Vicker is trying to save enough money to buy her wedding dress at the cost of $1,200. She has $600 saved from her summer school job.
The amount to make up to complete her wedding dress = $1200 - $600
= $600
To make the rest of the money, Ms. Vicker plans to tutor for Sylvan at a cost of $10 per hour.
= Number of hours Ms vicker must tutor Sylvan to make $600 is calculated as:
$600/$10 = 60 hours
The inequality to determine how many hours Ms. Vicker must tutor to have enough money for the dress is written as
$600 + 10x ≥ $1200
Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. х 0 1 2 3 4 5 P(x) 0.10 0.20 0.30 0.20 0.15 0.05 (g) If each customer takes 3 minutes to check out, what is the probability that it will take more than 6 minutes for all the customers currently in line to check out? The probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s
The probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.
The probability distribution of the number of customers in line at a supermarket express checkout counter is given as below: х 0 1 2 3 4 5
P(x) 0.10 0.20 0.30 0.20 0.15 0.05
Here, we have to find the probability that it will take more than 6 minutes for all the customers currently in line to check out if each customer takes 3 minutes to check out.
We know that time taken for one customer to check out is 3 minutes.
So, time taken for n customers to check out is 3n minutes.
The probability of more than 6 minutes is P(x>6) = P(x=4) + P(x=5)
On substituting the given probability distribution, we have: P(x>6) = 0.15 Х s
Therefore, the probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.
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In your reservoir, you have a production well which flows for 48 hours at 200 STB/day, and then shut-in for 24 hours. The following additional data are given : Pi = 3100 psi Ct = 15x10^-6 psi^-1 Bo = 1.3 bbl/STB ϕ = 15% μ=1.2 cp K = 45 md and h = 60 ft
a-) Calculate the pressure in this production well at 12 hours of shut in
b-) Explain how can you use superposition in time to analyze a pressure build-up test.
a) To calculate the pressure at 12 hours of shut-in:
substitute the given values into the pressure buildup equation and solve for P(t=12).
b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.
We have,
a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:
P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))
Where:
P(t) = Pressure at time t
Pi = Initial reservoir pressure
Q = Flow rate
K = Permeability
h = Reservoir thickness
ϕ = Porosity
μ = Viscosity
Ct = Total compressibility
t = Shut-in time (12 hours)
Δt = Time since the start of the flow period
Bo = Oil formation volume factor
ΔP = Pressure drop during the flow period
Given:
Pi = 3100 psi
Q = 200 STB/day
K = 45 md
h = 60 ft
ϕ = 15%
μ = 1.2 cp
Ct = 15x10^-6 psi^-1
Bo = 1.3 bbl/STB
t = 12 hours
Δt = 48 hours
ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))
Substituting the given values into the equation:
ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x[tex]10^{-6}[/tex] * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x [tex]10^{-6}[/tex] * (48 + 48)) / (1.3 * (0 + 48))))))
After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.
b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.
It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.
The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.
Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.
It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.
Thus,
a) To calculate the pressure at 12 hours of shut-in:
substitute the given values into the pressure buildup equation and solve for P(t=12).
b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.
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PLEASE HELP FOR BRAINLIEST:
if the system below has no solutions, what is the value of A?
4x-y=5
Ax+3y=-1
Answer:
Step-by-step explanation:
You have 2 equations and 3 unknowns (A, x, y). You could use any value for A and it would be correct because then you could solve for the other unknowns. See picture for many exampleS.
Please mark Brainliest when able.
Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC.Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC.
Explain why ABCD and ABEC are parallelograms.
Answer:
Because parallelograms can be divided into two equal triangles of different orientations.
Step-by-step explanation:
Rotation is a process in which a given shape or point is turned about a reference point or line to produce the image of the initial shape, both having different orientations. It is one of the types of solid transformation.
Since,
ΔCAD = ΔABC but of different orientations, then ABCD is a parallelogram.
Also,
ΔABC = ΔECB, so that ABEC is a parallelogram.
So then:
ΔCAD = ΔABC = ΔECB
Therefore, ABCD and ABEC are parallelograms.
Please help I’ll give brainiest.
Step-by-step explanation:
Simply replace X with 3 etc...
f (x) = 4x + 7
f (3) = 4 (3) + 7
f (3) = 12 + 7
f (3) = 19
f (2x) = 4 (2x) + 7
f (2x) = 8x + 7
Answer:
For the first one after F(3), write 4x + 7
4x + 7 12 + 7 = 19
For the second one after F(2x) write 4x + 7
24 + 7 = 31
Step-by-step explanation:
I believe the number after the f represents the x, so you put that into the original equation
The sum of two numbers is twenty-four. Four less than three times the
smaller is twelve less than twice the larger. Find the two numbers.
Answer:
Larger number: 16Smaller number: 8I hope this helps!
What is this? I need it please
1/3x+2=1/5x-8
Answer:
[tex]\boxed {x = -75}[/tex]
Step-by-step explanation:
Solve for the value of [tex]x[/tex]:
[tex]\frac{1}{3}x + 2 = \frac{1}{5}x - 8[/tex]
-Take [tex]\frac{1}{5}x[/tex] and subtract it from [tex]\frac{1}{3}x[/tex]:
[tex]\frac{1}{3}x + 2 - \frac{1}{5}x = \frac{1}{5}x - \frac{1}{5}x - 8[/tex]
[tex]\frac{2}{15}x + 2 = -8[/tex]
-Subtract [tex]2[/tex] to both sides:
[tex]\frac{2}{15}x + 2 - 2 = -8 - 2[/tex]
[tex]\frac{2}{15}x = -10[/tex]
-Multiply both sides by [tex]\frac{15}{2}[/tex], which is the reciprocal of [tex]\frac{2}{15}[/tex].
[tex]x = -10 \times (\frac{15}{2})[/tex]
[tex]x = \frac{-10 \times 15}{2}[/tex]
[tex]x = \frac{-150}{2}[/tex]
-Divide [tex]-150[/tex] by [tex]2[/tex]:
[tex]x = \frac{-150}{2}[/tex]
[tex]\boxed {x = -75}[/tex]
So, the value of [tex]x[/tex] is [tex]-75[/tex].
Find the value of x in this equation.
3 (6x-5) - x = 3 -2(x + 1)
Answer:
[tex]x = \frac{16}{19}[/tex]
Step-by-step explanation:
[tex]3 (6x-5) - x = 3 -2(x + 1) \\ 18x - 15 - x = 3 - 2x - 2 \\ 19x = 16 \\ \boxed{x = \frac{16}{19} }[/tex]
♨Rage♨
Triangle DEF has vertices D ( − 4 , 1 ) D-4, 1, E ( 2 , 3 ) E2, 3, and F ( 2 , 1 ) F2, 1 and is dilated by a factor of 3 using the point ( 1 , 1 ) 1, 1 as the point of dilation. The dilated triangle is named Δ D ' E ' F ' ΔD'E'F'. What are the coordinates of the vertices of the resulting triangle?
Answer:
D'(-14,1), F'(4,1) and E'(4,7)
Step-by-step explanation:
Let's take each point and dilate about the point (1,1) using rule (x,y)--->(kx,ky). Where 'k' is dilation factor
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
Answer:
C
Step-by-step explanation:
The equation for the red graph is,
⇒ 2y = f (x)
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
The black graph is the graph of,
⇒ y = f (x)
Now,
The red graph is spread out the function of blk graph.
Hence, We get;
The equation for the red graph is,
⇒ y = f (x) / 2
⇒ 2y = f (x)
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Two cars start traveling in the same direction around a circular road that is 80 km long. The speed of one car is 92 km/h and the sped of the other is 68 km/h. How many minutes after the two cars start traveling will one car lap the other for the second time?
PLEASE HELP! I WILL AWARD BRAINLIEST IF THERE ARE TWO ANSWERS!
Answer:
400 minutes
Step-by-step explanation:
The speed for car 1 is 92 km/h and the speed for car two is 68 km/h. The time is unknown but we know it has to be converted into minutes so the time for both cars will be x/60. Now we multiply speed by time and get distance. The first car is 92 x/60 and the second car is 68 x/60. Cross multiply and you get 92x/60 and 68 x/60 now we can make an equation. 92x/60 - 68 x/60 = 80, x = 200. We multiply x by 2 to get the second time which is 400 minutes.
do #11 and #12
(best answer gets brainliest!!)
Answer:
16cm, 37mm
Step-by-step explanation:
For number 11, the shape on the left is a square. This means all the sides are equal length, so the side shared with the triangle is also 12 cm. Using the pythagorean theorem, you will figure out that the unknown side is 16 (this is also another ratio of a 3-4-5 triangle).
For number 12, the side shared with the larger triangle must be 12 mm because of the pythagorean theorem once again (a^2+b^2=c^2). Then, you must use that same formula again to solve for x which is the hypotenuse. This turns out to be 37mm.
Side note**
in the pythagorean theorem, the c value is the hypotenuse and the a and b values are the legs of the triangle. it is probably best to use a calculator since you will be dealing with square roots.
how to do this question plz
Answer:
5.125 liters of his drink
Step-by-step explanation:
5 liters of water plus
100x2.5=250ml of juice Equals
5.125 liters of his drink
A recent study conducted by a health statistics center found that 27% of households in a certain country had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households va landlines Pick three households from this country at random Complete parts a) through c) below a) What is the probability that all three of them have a landline? 309 (Round to three decimal places as needed.) b) What is the probabilty that at leást one of them does not have a landline? 611 (Round to three decimal places as needed) c) What is the probability that at least one of them does have a landline? Round to three decimal places as needed.)
a) The probability that all three households have a landline can be calculated by multiplying the individual probabilities together. Since 27% of households do not have a landline, the probability that a randomly selected household has a landline is 1 - 0.27 = 0.73. Therefore, the probability that all three households have a landline is 0.73 * 0.73 * 0.73 = 0.389.
b) The probability that at least one household does not have a landline can be calculated by subtracting the probability that all three households have a landline from 1. So, 1 - 0.389 = 0.611. Therefore, the probability that at least one household does not have a landline is 0.611.
c) The probability that at least one household does have a landline can be calculated as the complement of the probability that all three households do not have a landline. Since 27% of households do not have a landline, the probability that a randomly selected household does not have a landline is 0.27. Therefore, the probability that at least one household does have a landline is 1 - 0.27 * 0.27 * 0.27 = 0.936.
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Yes or no? Please help
Answer:
yes
Step-by-step explanation:
Find the average rate of change in the simplest form
Rewrite the equation 4 x^2– 3x + 9 = 2x + 1 in standard form.
Answer:
this is quadratic equation
ax^2+bx+c=0
Step-by-step explanation:
4x^2-5x+8=0
Explain how would you select your sample to investigate the impact of a school nutrition program on grade performance of students at high school?
To select a sample for investigating the impact of a school nutrition program on grade performance of high school students, consider defining the target population, using random or stratified sampling methods, determining an appropriate sample size, and obtaining informed consent from participants.
To select a sample for investigating the impact of a school nutrition program on grade performance of high school students, there are several steps you can follow.
First, you would need to define your target population, which in this case would be high school students. This helps you determine the group you want to study and generalize your findings to.
Next, you can use random sampling to ensure that your sample is representative of the entire population. Randomly selecting students from different grades, genders, and socioeconomic backgrounds helps avoid bias and allows for more accurate results.
Another method is stratified sampling, where you divide the population into different groups or strata based on relevant characteristics such as grade level or socioeconomic status. You can then select a proportionate number of students from each stratum, ensuring representation from different groups within the population.
It is important to consider the sample size, as a larger sample can increase the reliability of the results. You can use statistical formulas or consult with a statistician to determine an appropriate sample size based on factors like desired level of accuracy and available resources.
Additionally, obtaining informed consent from the students and their parents or guardians is crucial. Explaining the purpose of the study, the benefits, and any potential risks will help ensure ethical considerations are met.
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!!POINTS!!
I need the answer to this, if you can show work that would be amazing!! if not, jsut send the equation
Answer:
so like would that be a cute
Step-by-step explanation:
because it's under 90 degrees
