Answer:
First, we need to find out how many people are male and female in the town:
Step-by-step explanation:
Male population = 48% of 42800 = 20544
Female population = 100% - 48% = 52% of 42800 = 22256
To find out how many more females there are than males, we need to subtract the male population from the female population:
Female population - Male population = 22256 - 20544 = 1712
Therefore, there are 1712 more females than males in the town.
Aisha spent $120.94 to buy 2 wheelbarrows. The wheelbarrows both had the same price. How much did each wheelbarrow cost?
PLEASE SOLVE THIS....I WILL GIVE BRAINLIEST!!!
Answer:
Give me a sec
Step-by-step explanation:
Given that sin theta = 15/17 with theta quadrant 1 , find cos 2theta
[tex]\textit{Double Angle Identities} \\\\ \cos(2\theta)= \begin{cases} \cos^2(\theta)-\sin^2(\theta)\\ 1-2\sin^2(\theta)&\leftarrow \textit{we'll use this one}\\ 2\cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 1-2\sin^2(\theta)\implies 1-2\left( \cfrac{15}{17} \right)^2\implies 1-2\left( \cfrac{225}{289} \right) \\\\\\ 1-\cfrac{450}{289}\implies \cfrac{289-450}{289}\implies -\cfrac{161}{289}[/tex]
I NEED HELP ASAP PLEASE HELP!!!!!!
#9 75% of 1
#10 50% of 350 is
#11 What percent of 450 is 50
#9 75% of 1.
#10 50% of 350.
#11
To find out what percent of 450 is 50, we can set up a proportion
x/100 = 50/450
Simplifying the right-hand side of the equation by dividing both numerator and denominator by 50 gives
x/100 = 1/9
Multiplying both sides by 100 gives
x = 100/9
Hence, 50 is approximately 11.1% of 450.
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a tree in lamar’s backyard has been growing for 4 1/2 years. the tree is 4/5 meters tall. what is the unit rate in meters per year? write your answer as a fraction or pixies number in simplest form.
As the tree is 4/5 meters tall the unit rate in meters per year is 8/45 or approximately 0.177 meters per year.
To find the unit rate in meters per year, we need to divide the height of the tree by the time it took to grow.
Height of the tree = 4/5 meters
Time taken to grow = 4 1/2 years = 9/2 years
Unit rate = Height/Time = (4/5)/(9/2) meters per year
To divide by a fraction, we can multiply by its reciprocal:
Unit rate = (4/5) * (2/9) meters per year
Unit rate = 8/45 meters per year
Therefore, the unit rate of the tree in meters per year is 8/45 or approximately 0.177 meters per year.
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Is anyone here looking for a personal tutor?????
meAnswer: me
Step-by-step explanation: I need help
5. Shanequa graphed a triangle with the coordinates R(-2, 1), S(2, 1) and T(0, -3). She wanted to graph
a dilation of the figure with a scale factor of 2 centered at the origin so she graphed the points
R'(-2, 2), S'(2, 2) and T'(0, -6).
a. Is AR'S'T' a dilation of ARST? Why or why not?
b. If Shanequa was wrong, correct her answer by giving the correct coordinates for AR'S'T'.
c. Shanequa's teacher said Shanequa had made a common mistake. Explain her mistake.
a) No , it is not a dilation
b) The coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)
c) Shanequa's mistake is that she incorrectly applied the dilation transformation
Given data ,
a)
In ARST, the coordinates of the original triangle are given by R(-2, 1), S(2, 1), and T(0, -3), and in AR'S'T', the coordinates are R'(-2, 2), S'(2, 2), and T'(0, -6)
So , the dilated triangle is R'(-2, 2), S'(2, 2), and T'(0, -6)
b)
The coordinates for AR'S'T' can be calculated by multiplying the original coordinates of ARST by the scale factor of 2, centered at the origin.
R'(-4, 2), S'(4, 2), and T'(0, -6)
c)
The dilation transformation was applied wrongly by Shanequa. The coordinates of the original points in a dilation centred at the origin with a scale factor of two should be multiplied by the scale factor to obtain the coordinates of the dilated points.
Hence , the dilation is solved
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there are 105 days until basketball season starts. Melanie says the season starts in 15 weeks. Is this reasonable? Use estimation to justify your answer.
Answer:
Yes, Melanie's statement that the basketball season starts in 15 weeks is reasonable.
To see why, we can estimate the number of days in 15 weeks. Since 1 week is equal to 7 days, 15 weeks would be approximately equal to:
15 weeks x 7 days/week = 105 days
Solve the following system of linear equations 3x₁ + x₂ + 2x3= 6
4x₁ - 3x₂ + 5x3 = 8,
2x₁ + x₂ + 3x3 = 10
Okay, here are the steps to solve this system of linear equations:
3x1 + x2 + 2x3= 6
4x1 - 3x2 + 5x3 = 8,
2x1 + x2 + 3x3 = 10
1) Add 4 times the first equation to the second equation:
7x1 + 2x2 + 7x3 = 22
2) Add -2 times the first equation to the third equation:
5x1 - x2 + 5x3 = 12
3) Divide both sides by 5 to get:
x1 = 2
x2 = -2
x3 = 1
Therefore, the solution to the system is:
x1 = 2
x2 = -2
x3 = 1
Let me know if you have any other questions!
Winnie and Vanessa Co Ltd. borrowed an amount of money (P) from a rural bank in Miotso at i% p.a simply interest. The company paid A amount of money as well as the total amount of interest (I) to the bank at the end of n- years. Show that, p= A(1+in)-1
The amount of money borrowed by the company from the rural bank is:
P = [tex]A(1 + in)^{-1}[/tex]
What is Amount?
Amount is a term used to describe the total quantity or value of something. It can refer to a quantity of a physical substance or object, such as the amount of water in a bottle or the amount of money in a bank account.
Let P be the amount of money borrowed by Winnie and Vanessa Co Ltd from the rural bank at an interest rate of i% per annum.
The simple interest on this amount after n years will be:
I = P * i * n
The total amount to be paid by the company after n years will be:
A = P + I = P + P * i * n
We can simplify this expression by factoring out P:
A = P(1 + i * n)
Dividing both sides of this equation by (1 + i * n), we get:
P = A / (1 + i * n)
Therefore, the amount of money borrowed by the company from the rural bank is:
P = [tex]A(1 + in)^{-1}[/tex]
This is the desired result.
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For questions 4 – 7, find the value of x.
The values of x in the isosceles trapezoids x = 32, x = 10.9 and x = 41
Calculating the values of x in the figuresAn isosceles trapezoid is a four-sided geometric shape that has two parallel sides and two non-parallel sides that are of equal length.
The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs and the angles in the same base are equal in measure
Using the above as a guide, we have the following:
2x + 14 = 78
x = 32
2 * (6x +32 + 4x + 39) = 360
x = 10.9
4x = 164
x = 41
The last details are not clear
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5x+3y=4 -2x-8y=6 Which strategy can you use to eliminate a variable.
The strategy that could be used to eliminate a variable is:
Multiply the first equation by 2 and multiply the second equation by 5. Then, add the resulting equations
Solving system of linear equations using the elimination method: Determining a strategy to eliminateFrom the question, we are to determine a strategy that could be used to eliminate a variable in the given system of equations
From the given information,
The system of linear equations is
5x + 3y = 4
-2x - 8y = 6
To eliminate the variable x, we can multiply the first equation by 2 and then multiply the second equation by 5. After that, we will add the resulting equations
2 × [ 5x + 3y = 4
5 × [-2x - 8y = 6
10x + 6y = 8
-10x - 40y = 30
Add the resulting equations
10x + 6y = 8
+ (-10x - 40y = 30
------------------------
-34y = 38
This way we have eliminated x
Hence,
The above strategy can be used to eliminate a variable
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Need to solve some questions can you Help me?
2nd Question
6 ÷ 2 ( 1 + 2 ) = ?
Answer:
Step-by-step explanation:
[tex]6/2 ( 1 + 2 ) = 3(3) = 9[/tex]
A caterer made a sandwich 6' 6" long for a party. by request 3' 8" were added to the sandwich. what was the total length of the sandwich?
The total length of the sandwich, given the addition to the sandwich, would be 10. 17 feet.
How to find the length of the sandwich ?In order to accurately add lengths measured in feet and inches, it is necessary to transform the unit type prior to adding them together. As an example, take a sandwich that originally measured 6 feet 6 inches long with 3 feet 8 inches being added into it.
To combine these measurements, we must first convert inches to feet or vice versa for optimal results. Let's begin with transforming the inches to feet:
6 feet 6 inches = 6 + ( 6 / 12 ) feet = 6. 5 feet
3 feet 8 inches = 3 + ( 8 / 12 ) feet = 3. 67 feet
Then add the lengths to become :
6. 5 feet + 3. 67 feet = 10. 17 feet
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What is the unit sales of product A at the monthly break even point?
The unit sales of product A at the monthly break-even point is 193,750 units.
What is the unit sales of product A at the monthly break even point?To determine the unit sales of product A at the monthly break-even point, we need to calculate the total contribution margin that covers the monthly fixed costs of $387,500.
Given that the unit contribution margin for product A is $2 and the unit selling price for product A is $5, we can calculate the contribution margin ratio for product A as follows:
Contribution Margin Ratio for Product A:
= (Unit Contribution Margin for Product A) / (Unit Selling Price for Product A)
= $2 / $5
= 0.4
40%
Now, let's consider the sales ratios given in the problem statement. It states that the company sells two units of A for each unit of B, and three units of B for each unit of C. This means that the sales ratio for product A to product B is 2:1, and the sales ratio for product B to product C is 3:1.
Let's assume that the unit sales of product A at the monthly break-even point is "x". Then, the unit sales of product B would be "2x" (based on the sales ratio of 2:1 between A and B), and the unit sales of product C would be "6x" (based on the sales ratio of 3:1 between B and C).
The total contribution margin for product A at the monthly break-even point can be calculated as follows:
Total Contribution Margin for Product A = (Unit Contribution Margin for Product A) * (Unit Sales of Product A at Break-Even Point)
= $2 * x
Since the monthly fixed costs are $387,500, we can set up the equation for the break-even point as follows:
Total Contribution Margin for Product A = Monthly Fixed Costs
$2 * x = $387,500
Now we can solve for x, the unit sales of product A at the monthly break-even point:
$2 * x = $387,500
x = $387,500 / $2
x = 193,750
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what is true about the modeling equation that best fits the data?
• It captures the overall trends and patterns in the data points. It does not necessarily pass through every single data point but approximates the shape and trajectory of the data.
• It has parameters that can be adjusted to optimize how well the model fits the data. Things like coefficients, exponents, intercepts, etc. The good parameter values will depend on the specific data set and model.
• It has an appropriate level of complexity for the data. It does not overfit or underfit the data. An overfit model captures every detail and noise, while an underfit model fails to capture the key dynamics.
• Key features like slope, curvature, periodicity, thresholds, etc. in the data are properly represented in the model.
• It provides insights or useful information, not just a mathematical abstraction of the data. A good model opens the black box and provides interpretable knowledge about the system or phenomenon that generated the data.
• Predictions or extrapolations from the model align well with any additional data points beyond the original data set. The model generalizes purposefully.
• There are objective metrics that can evaluate how good a particular model is for a data set, like R2, mean absolute error, Akaike information criterion, etc. The best model will optimize such metrics.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three (3) true statements about the quadratic function and its graph include the following:
A. The value of f(–10) = 82
B. The graph of the function is a parabola.
D. The graph contains the point (20, –8).
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the other true statements about the graph of this quadratic function:
At point (-10, 82), we have:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(-10) = -10²/5 – 5(-10) + 12
Quadratic function, f(-10) = 82
At point (20, -8), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(20) = 20²/5 – 5(20) + 12
Quadratic function, f(20) = -8
In conclusion, we can logically deduce that the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.
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For a certain set of five numbers, the mean of all but the largest number is 80 and the
mean of all but the smallest number is 90. What is the range of the set of five numbers?
Thus, the range of the set of five numbers (a,b,c,d,e) is found as : 40.
Explain about the range of set:The difference in between highest and lowest numbers in a piece of data is known as the range. To locate it, sort the data first from least to greatest. Then take the difference between the least and largest number in the set.
The range is a straightforward assessment of the variation in values within a dataset. Simply take the difference between the two values, ignoring the others, to determine the range.
Let the 5 numbers be: (a,b,c,d,e)
a < b < c < d < e
Mean = sum of all observation / total number of observations
Equation for the mean except the largest number.
(a+b+c+d)/4 = 80
Now, Equation for the mean except the smallest number.
(b+c+d+e)/4 = 90
On simplifying each:
a + b + c + d = 320 ...eq 1
b + c + d + e = 360 ..eq 2
Range = max - min
Subtract eq 1 from eq 2
e - a = 40
Thus, the range of the set of five numbers (a,b,c,d,e) is found as : 40.
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Please help, ASAP! This is for a College Algebra Class, No wrong answer.
The value of x in the equation is 2.10.
How to solve exponential equation?The exponential equation above can be solved as follows:
[tex]8^{\frac{4}{x} } = 53[/tex]
Therefore, let's log both sides
log [tex]8^{\frac{4}{x} }[/tex] = log 53
Hence,
4 / x log 8 = log 53
divide both sides by log 8
4 / x = log 53 / log 8
4 / x = 1.7242758696 / 0.90308998699
4 / x = 1.9092439208
cross multiply
1.902x = 4
x = 4 / 1.902
x = 2.09511837419
Therefore,
x = 2.10
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For the rotation -757°, find the coterminal angle from 0° ≤ 0 < 360°, the
quadrant, and the reference angle.
To find the coterminal angle for a rotation of -757°, we can add or subtract multiples of 360° until we find an angle between 0° and 360° that is coterminal with -757°.
Adding 360° multiple times:
-757° + 360° = -397° (not coterminal)
-397° + 360° = -37° (not coterminal)
-37° + 360° = 323°
Therefore, the coterminal angle for -757° is 323°.
To find the quadrant in which 323° lies, we can note that 323° is between 270° and 360°, which means it lies in the fourth quadrant.
To find the reference angle for 323°, we can subtract 360° from 323° until we get an angle between 0° and 90°:
323° - 360° = -37° (not in the correct range)
-37° + 360° = 323°
So the reference angle for 323° is 37°.
The garment factory plans to make 690 sets of garments. It has been done for 5 days, with an average of 75 sets per day. The rest needs to be completed in 2.5 days, how many sets are done on average per day (step-by-step answer)
For the remaining set of garments, the average per day that they need to be completed would be = 126 sets/day.
How to calculate the average set made per day?The quantity of garments planned to be made by the factory = 690sets.
The rate of coverage for 5 days = 75sets/day.
That is for 5 days the number of garments covered = 75×5 = 375
The remaining sets = 690-375 = 315
The average per day to cover the remaining sets of garment = 315/2.5 = 126 sets/day
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answer:
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartR…
✓ Answer:8(x2 + 2x) = –3 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRootStep-by-step explanation:S…
Plot the numbers -1 1/2 and 2 3/4 on the number line below.
For the second number 2 3/4 you will find the 2 points, to the right from 0. Now count three small points to the left to get the 3/4 part
How to solveTo locate the value of -1 1/2 on the number line, first locate the point denoting -1 to the left of 0. Progressing to the second minor point on the right immediately after -1 will indicate this position.
For the second figure of 2 3/4, identify the point at 2 by moving to the right from 0. An additional count of three minor points towards the left reveals where the fraction of 3/4 is located. The exact spot is depicted here.
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I am in need of this to be answered~
Transform this sentence into NNF:
~(~(P&~Q)v(R&~S))
Please answer, step by step to the answer.
Thank you!
~(~(P&~Q)v(R&~S)) transformation of this statment into NNF is ((~P v Q) & (~R v S))
How to transform the statement by using NNF?The transformations used to turn the given sentence into NNF:
Using the equivalence, remove the implication: p → q ≡ ~p ∨ q
≡ (((P&~Q)) & ~(R&~S))
Use De Morgan's law: ~(p ∨ q) ≡ ~p & ~q, and ~(p & q) ≡ ~p ∨ ~q
≡ ((~P v Q) & (~R v S))
Elimination by double negation:~~p ≡ p
≡ ((~P v Q) & (~R v S))
The resulting sentence, ~(~(P&~Q)v(R&~S)) is in NNF (Negation Normal Form), which limits negations to atomic propositions (P, Q, R, S) and logical connectives ¬, ∧, and ∨.
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A sports statistician determined that the probability of a certain rugby team winning its next match is 11/23. Find the odds against the team winning its next match.
The probability of the odds of the rugby team winning its next match is
12 to 11.
We have,
The probability of an event happening is defined as the ratio of the number of favorable outcomes to the total number of outcomes.
The odds against an event happening are defined as the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
If the probability of the rugby team winning its next match is 11/23, then the probability of the team losing its next match is:
= 1 - 11/23
= 12/23.
The odds against the rugby team winning its next match are the ratio of the number of unfavorable outcomes (losing the match) to the number of favorable outcomes (winning the match), which is:
12/23 : 11/23
We can simplify this ratio by dividing both the numerator and denominator by 11:
(12/23) ÷ (11/23) : (11/23) ÷ (11/23)
Simplifying.
12/11 : 1/1
Therefore,
The probability of the odds of the rugby team winning its next match is
12 to 11.
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Please help me
Decide the type of transformation and state the rule
The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Comparing the equivalent vertices, the translations are given as follows:
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Let = {1, 2, 3, 4, 5} be a set. Consider the functions = {(1,3), (2,5), (3,3), (4,1), (5,2)} and = {(1,4), (2,1), (3,1), (4,2), (5,3)} From into . (i) Determine the range of and (ii) Find the composition functions ∘ and ∘ .
g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}. And the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.
How to solve the problem?
(i) To determine the range of a function, we need to find all the possible output values of the function. In other words, we need to find the set of all second elements in the ordered pairs of the function. For the function f, the set of all second elements is {3, 5, 1, 2}. For the function g, the set of all second elements is {4, 1, 2, 3}. Therefore, the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.
(ii) To find the composition functions f ∘ g and g ∘ f, we need to apply the functions in the correct order. The composition function f ∘ g means that we first apply g and then apply f to the result. The composition function g ∘ f means that we first apply f and then apply g to the result.
For f ∘ g:
First, we apply g to the domain of f.
(1,3) is mapped to (4,2) by g
(2,5) is mapped to (1,4) by g
(3,3) is mapped to (1,4) by g
(4,1) is mapped to (2,1) by g
(5,2) is mapped to (3,1) by g
Now we apply f to the result of g.
(4,2) is mapped to 2 by f
(1,4) is mapped to 4 by f
Therefore, f ∘ g is the function {(1,4), (4,2)}.
For g ∘ f:
First, we apply f to the domain of g.
(1,4) is mapped to 3 by f
(2,1) is mapped to 5 by f
(3,1) is mapped to 3 by f
(4,2) is mapped to 1 by f
(5,3) is mapped to 2 by f
Now we apply g to the result of f.
3 is mapped to (1,2) by g
5 is mapped to (2,1) by g
1 is mapped to (4,2) by g
2 is mapped to (5,3) by g
Therefore, g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}.
Note that the composition functions f ∘ g and g ∘ f are not the same. In general, composition of functions is not commutative, i.e., f ∘ g is not equal to g ∘ f.
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The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:
98 97.9 99 97.3 98.9 99.6 97.8 99.8 99.1 98.4 98.7 97.6 96.5
Assume body temperatures of adults are normally distributed. Based on this data, find the 95% confidence
interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,
parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.
95% C.I. =
The 95% confidence interval of the mean body temperature of adults in the town is (97.584, 98.876)°F (open-interval notation), accurate to 3 decimal places.
What is the 95% confidence interval of the mean body temperature of adults in the town?To find the 95% confidence interval (C.I.) of the mean body temperature, we need to use the formula:
C.I. = x ± z*(σ/√n)
Where:
x is the sample mean
σ is the population standard deviation (unknown, but we can estimate it using the sample standard deviation)
n is the sample size
z is the critical value for the desired confidence level (95% in this case)
First, we need to calculate the sample mean, sample standard deviation, and sample size:
x = (98 + 97.9 + 99 + 97.3 + 98.9 + 99.6 + 97.8 + 99.8 + 99.1 + 98.4 + 98.7 + 97.6 + 96.5) / 13 = 98.23
s = √((1/(n-1)) * Σ(xi - x)²)
s = 1.339
n = 13
Next, we need to find the critical value, z, for a 95% confidence level. We can look this up in a standard normal distribution table or use a calculator. For a 95% confidence level, z = 1.96.
Now we can plug in the values into the formula to get the 95% confidence interval:
C.I. = 98.23 ± 1.96*(1.339/√13) = (97.584, 98.876)
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Math: please answer this question very important for me, I’ll give brainliest if it’s correct!!
Q2. The average depth of the water in a port on a tidal river is 4 m. At low tide, the depth of the water is 2 m. One cycle is completed approximately every 12h.
(a) [4 marks] Find an equation of the depth, d(t) meters, with respect to the average depth, as a function of the time, t hours, after low tide, which occurred at 15: 00.
(b) [2 marks] Draw a graph of the function for 48 h after low tide.