A straw is placed inside a rectangular box that is 6 inches by 8 inches by 5 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.
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both clocks ring toget (b) Two bells hanged at a school were adjusted at 10:00 am in such a way th one of them rings at the interval of every 45 minutes and another at every minutes. At what time will both bells ring together ?
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The Least common multiple (LCM) The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.
The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.
The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.
To find the LCM, we can list the multiples of each interval until we find a common multiple.
Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.
Thus, the two bells will ring together every 45 minutes.
If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.
Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.
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I need to understand the steps and why. ty. \(\sqrt{y} ^4\)
Answers
Answer: \(y^2\)
Reason:
A square root represents an exponent of 1/2
So \(\sqrt{y} = y^{1/2}\)
Raising that to the fourth power gets us this,
\((\sqrt{y})^4 = (y^{1/2})^4\\\\ (\sqrt{y})^4 = y^{(1/2)*4}\\\\ (\sqrt{y})^4 = y^{2}\\\\\)
----------------
Edit: Here's an alternative route
\((\sqrt{y})^4 = (\sqrt{y})*(\sqrt{y})*(\sqrt{y})*(\sqrt{y})\\\\ (\sqrt{y})^4 = (\sqrt{y})^2*(\sqrt{y})^2\\\\ (\sqrt{y})^4 = y*y\\\\ (\sqrt{y})^4 = y^2\\\\\)
The first line is possible because raising anything to the 4th power is the same as having 4 copies of it multiplied out (eg: 3^4 = 3*3*3*3 = 81).
Then in the second line, I collected the terms into pairs
By line 3, the square root and squaring exponent cancel each other out. This only works if y is not negative.
Fifty-six and forty-2 hundredths in standard form can someone please help me
Answers
Answer:
Fifty-six and forty-two hundredths in standard form is 56.042
Hope this helps!!
The rear windshield wiper of a car rotated 120 degrees,as shown. Find the area cleared by the wiper. 25inch,120 degrees, 14inch
Answers
The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.
The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.
The wiper's arm is represented by a line segment and has a length of 14 inches.
The wiper's blade is perpendicular to the arm and has a length of 25 inches.
Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.
As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.
The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.
In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.
Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
The statements that are always true are:
i. m∠5 + m∠6 = 180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
What is a triangle?A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.
From the given question and information, the statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
The required diagram is attached to this answer as a guide
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A random sample of five Galaxy 8 smartphones is selected from the production line after final assembly, and the result of the weight control measurement is (in grams) 155.1, 154.8, 155.5, 155.3, and 154.6.What are the average weight, its uncertainty (i.e. the standard deviation of the mean), and the fractional uncertainty
Answers
Answer:
a. Mean = 155.1 grams
b. Standard deviation = 0.37
c. Fractional uncertainty = 0.074
Step-by-step explanation:
a. Average weight
This is same as the mean weight;
Mathematically, that would be; sum of the weights/ the number of weights
= (155.1 + 154.8 + 155.5 + 155.3 + 154.6)/5 = 775.3/5 = 155.06 which is approximately 155.1
b. Standard deviation
Mathematically; we calculate that using the formula;
√{(x-mean)^2/(N-1)}
Please check attachment for for the complete breakdown of this
c. Fractional uncertainty
= Standard deviation/number of measurements = 0.37/5 = 0.074
Gretchen is delivering boxes of cookies to her neighbors. Her wagon itself weighs 12 pounds when empty and will hold up to 9 boxes. If each box of cookies weighs 1 pound, what is the range of the total weight of her wagon while she is delivering cookies?
Answers
Answer:
21
Step-by-step explanation:
12 plus 9
QUESTION 1 Determine the general solution of: 2 sin x. cos x = COS X
Answers
Starting with the given equation: 2 sin x cos x = cos x
By dividing both sides by cos x, we may simplify: 2 sin x = 1
Dividing both sides by 2:
sin x = 1/2
The values of x that fulfil sin x = 1/2 must now be found, and they are:
x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.
Therefore, the general solution is:
x = π/6 + 2πn or
x = 5π/6 + 2πn, where n is any integer.
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plz help me im struggling hard
Answers
Answer:
0.20 × 65 is what you would do for the second
Step-by-step explanation:
btw listen to yungblud
Note that the cost for the rent is a function of the amount of the miles you drove. Let's call that \(C(m)\).
Also note that the amount you pay will linearly increase, in other words, the increase in cost will always be the same for each mile. This tells us that our function is indeed a line, a first order polynomial of the form \(C(m) = am+b\)
What would happen if you were to rent a truck and not drive it at all? You would pay only the one-time fee.
Therefore, \(C(0)=55\)
So, \(C(m) = am + 50\)
The cost will increase by $0.20 for each mile, wich tells us that \(a=0.20\)
Finally, our expression is \(\boxed{C(m) = 0.2m+55}\)
If we want to know how much would you pay if you drove 65 miles, we want to know what \(C(65)\) is.
By plugging \(m=65\) in the expression, we get
\(C(65) =68\)
So you would pay $68
How do you convert 72 kilograms to pounds? show the mathmatical steps
Answers
1 kilogram = 2.20462 pounds
To convert 72 kilograms to pounds, you can multiply 72 by 2.20462 as follows:
72 kilograms = 72 x 2.20462 pounds
72 kilograms = 158.73264 pounds (rounded to five decimal places)
Therefore, 72 kilograms is equal to approximately 158.73264 pounds.
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50 POINTSSS!!!!!! PLS HURRRYYYYY!!!!!!! A set of data includes 98 data points ranging from 0 – 160. If the data is split into classes with a range of 10 (1 – 10, 11 – 20, etc), and there are no values that fall in the class 81 – 90, what can you say about the data?
1 The mean of the data will not be between 81 – 90.
2 All the data lies below 80.
3 The relative frequency of the class 81 – 90 is 0.
4 The median could be in the range 81 – 90
Answers
Answer:
3
Step-by-step explanation:
What are the answers to these questions?
Answers
Step-by-step explanation:
the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.
therefore, for our example here the negative case would be
2.5x - 6.8 = -12.9
which gives us
2.5x = -6.1
x = -6.1/2.5 = -2.44
and the positive case would be
2.5x - 6.8 = 12.9
and that gives us
2.5x = 19.7
x = 19.7/2.5 = 7.88
A red and a blue die are thrown. Both dice are fair. The events A, B, and C are defined as follows: A: The sum on the two dice is even
B: The sum on the two dice is at least 10
C. The red die comes up 5
Answers
The probability of event A occurring is 1/2, the probability of event B occurring is 1/3, and the probability of event C occurring is 1/6.
in order for a sum of two dice to be even, the numbers on the two dice must add up to an even number. The possible combinations of two dice that add up to an even number are (1,3), (3,1), (2,4), (4,2), (5,5). Therefore, the probability of event A occurring is 1/2.
In order for the sum of two dice to be at least 10, the numbers on the two dice must add up to 10, 11, 12. The possible combinations of two dice that add up to 10, 11, 12 are (4,6), (6,4), (5,5), (5,6), (6,5). Therefore, the probability of event B occurring is 1/3.
In order for the red die to come up 5, the number on the other die does not matter. Therefore, the probability of event C occurring is 1/6.
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In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
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The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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A child’s pool is in the shape of a rectangular prism with a height of 2 ft and a base that is 4 ft wide by 5 ft long. During the course of the summer, the child’s pool needed to be filled 3 times. How many cubic feet of water were needed to fill the pool during the summer? Responses 40 ft³ 40 ft³ 80 ft³ 80 ft³ 120 ft³ 120 ft³ 160 ft³ 160 ft³
Answers
The requried, 120 ft³ of water was needed to fill the pool during the summer.
The volume of the child's pool is given by multiplying its length, width, and height.
The volume of the pool = Length x Width x Height
= 5 ft x 4 ft x 2 ft
= 40 cubic feet
Since the pool was filled 3 times during the summer, the total amount of water needed is:
The total volume of water = Volume of pool x Number of times filled
= 40 ft³ x 3
= 120 ft³
Therefore, 120 ft³ of water was needed to fill the pool during the summer.
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The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answers
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
Sarah is looking to take out a mortgage for $300, 000 from a bank offering a monthly
interest rate of 0.525 %. If Sarah makes monthly payments of $1925, determine how
long it will take her to pay off the loan, to the nearest tenth of a year, using the
formula below.
Answers
It will take Sarah approximately 15.9 years to pay off the loan.
To determine how long it will take Sarah to pay off the loan, we can use the formula for the number of periods required to pay off a loan:
\(\(n = \frac{{\log\left(\frac{{P \cdot r}}{{P - M \cdot r}}\right)}}{{\log(1 + r)}}\)\)
Where:
n is the number of periods (in this case, the number of months)
P is the principal amount (loan amount), which is $300,000
r is the monthly interest rate, which is 0.525% or 0.00525 (expressed as a decimal)
M is the monthly payment, which is $1,925
Substituting the values into the formula, we have:
\(\(n = \frac{{\log\left(\frac{{300,000 \cdot 0.00525}}{{300,000 - 1,925 \cdot 0.00525}}\right)}}{{\log(1 + 0.00525)}}\)\)
Using a calculator to evaluate the logarithms and perform the division, we find that \(\(n \approx 190.6\)\) months.
Since we are asked to determine the time to the nearest tenth of a year, we divide 190.6 by 12 to convert it into years:
\(\(\frac{{190.6}}{{12}} \approx 15.9\) years\)
Therefore, it will take Sarah approximately 15.9 years to pay off the loan.
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HELPPP ASAPPPP PLEASEEE
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Answer:
with the years labeled on the horizontal axis and the number of hours labeled on the vertical axis. The graph shows that the number of hours spent watching TV declined steadily over the 5-year period, starting at around 1750 hours in Year 1 and falling to around 1300 hours in Year 5. The graph also shows a clear, downward-sloping trend from Year 1 to Year 5.
Step-by-step explanation:
help with his math question please
Answers
Answer:
Exact: -41/20 Decimal: -2.05
Step-by-step explanation:
Answer:
41
----------_______
20
Decimal: :-2.05
A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 9. Compute the raw, x-value associated with a Z-score of 0.21. Round to two decimal places, as needed.
Answers
The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.
To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:
Z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = Zσ + μ
Substituting the given values, we get:
x = 0.21(9) + 144
Simplifying the expression, we get:
x = 145.89
A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.
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What is 147.15 rounded to the nearest hundredth
Answers
Answer:
147.15
Step-by-step explanation:
There ya go, mate.
To round 147.15 to the nearest hundredth consider the thousandths’ value of 147.15, which is 0 and less than 5. Therefore, the hundredths’ value of 147.15 remains 5.
147.15 rounded to the nearest hundredth = 147.15
Is the following statement true or false? the mean of a random sample equals the mean of the population from which it was drawn.
Answers
The claim that the average of a random sample is the same as the average of the population from which it was taken is False.
Is the sample mean the same as the population mean?The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.
Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.
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Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
Answers
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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a rectangle with a width of 30 centimeters has a perimiter of 100 centimeters to 160 centimeters graph a compound inequality
Answers
Answer:
5 ≤ L ≤ 35
Step-by-step explanation:
Let w represent the width of the rectangle.
The perimeter (P) of the rectangle is given by:
P = 2w + 2L
Where L is the length of the rectangle.
We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:
100 ≤ 2(30) + 2L ≤ 160
100 ≤ 90 + 2L ≤ 160
10 ≤ 2L ≤ 70
We can now divide both sides by 2 to solve for L:
5 ≤ L ≤ 35
Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is: 5 ≤ L ≤ 35
A can contains 24 fluid ounces of fruit juice. How many pints of fruit juice does the can contain? HELP ASAP FREE BRAINLEST IF ANSWER CORRECTLY.I will be ur gf for a day if u answer this correctly
Answers
Answer:1.5 pints
Step-by-step explanation: I only want Brainliest and 5 star. Thank u
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
The domain of the function f(x)=−3x is restricted to the negative integers. Which values are elements of the range?
Answers
answer
\(fx = - 3x \\ \frac{fx}{x} = - \frac{3x}{x} \\ f = - 3\)
Answer:
learning only kang po yan
Step-by-step explanation:
basa lang
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
Answers
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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Trees in a landscaping company's warehouse are being sold at a monthly rate of 7.3%. This situation can be modeled by an exponential function. The warehouse initially contained 45,000 trees.
Which function can be used to find the number of trees in the warehouse at the end of m months?
Answers
An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.
The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:
N(m) = 45,000(1.073)^m
Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.
For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)^5 = 60,731. Thus, the warehouse will contain 60,731 trees at the end of 5 months.
In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
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An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
What is function?
A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.
The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:
\(N(m) = 45,000(1.073)^m\)
Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.
For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)⁵ =60,731.
Thus, the warehouse will contain 60,731 trees at the end of 5 months.
In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
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Determine the amplitude of function
Answers
The amplitudes of functions are a) 8 and b) 6.
Given are the functions we need to determine the amplitude of function,
a) y = 8 Sin (x/2) + 3
b) y = 6 Cos x + 2
So,
To determine the amplitude of a trigonometric function, you can follow these steps:
For a sine function of the form y = A×sin(Bx + C) + D:
The amplitude is equal to the absolute value of the coefficient A.
For a cosine function of the form y = A×cos(Bx + C) + D:
The amplitude is equal to the absolute value of the coefficient A.
Let's apply these steps to the given functions:
a) y = 8×sin(x/2) + 3
The coefficient of sin in this function is 8, so the amplitude is |8| = 8.
Therefore, the amplitude of function a) is 8.
b) y = 6×cos(x) + 2
The coefficient of cos in this function is 6, so the amplitude is |6| = 6.
Therefore, the amplitude of function b) is 6.
Hence the amplitudes of functions are a) 8 and b) 6.
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