In Houston, Texas, at the spring equinox (March 21), there are 12 hours and 9 minutes of sunlight. The longest and shortest day of the year varies from the equinox by 1h 55 min . The amount of sunlight during the year can be modeled by a sine function.
c. Write a function that relates the number of days away from the spring equinox to the variation in hours of sunlight in Houston.
Answers
In Houston, Texas, the variation of sunlight during the year can be modeled by the sine function. Given that there are 12 hours and 9 minutes of sunlight during the spring equinox, and the longest and shortest day varies from the equinox by 1 hour and 55 minutes. Therefore, the variation of hours of sunlight in Houston, Texas, can be modeled using the sine function as follows: \(f(x) = Asin(B(x - C)) + D\)
where; A is the amplitude of the sine function, which is given by (Max - Min) / 2A = (Max - Min) / 2
= (13h 4m - 10h 14m) / 2 = 1h 25mB is the period of the sine function, which is given by 2π / B = 365 days
B = 2π / 365 ≈ 0.017
C is the horizontal shift of the function, which corresponds to the day of the year when the maximum or minimum daylight occurs. Since the longest and shortest day of the year varies from the equinox by 1 hour and 55 minutes, then the maximum and minimum daylight will occur on June 20th and December 22nd, respectively. Therefore, the horizontal shift can be found as follows:
C = 80D is the vertical shift of the function, which is the average daylight duration throughout the year.
Since there are 12 hours and 9 minutes of sunlight during the spring equinox, the vertical shift can be found as follows: \(D = (Max + Min) / 2\)
= (13h 4m + 10h 14m) / 2
= 11h 39m
Putting all the values together,
f(x) = Asin(B(x - C)) + D = 1h 25m
sin(0.017(x - 80)) + 11h 39m.
Therefore, this is the function that relates the number of days away from the spring equinox to the variation in hours of sunlight in Houston.
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Related Questions
We have a data set with 80 observations. If we use this data set to perform a 10-fold cross validation, how many observations are used for training at each iteration? A. 64 B. 72 C. 8 D. 16
Answers
At each iteration of a 10-fold cross-validation with a data set of 80 observations, 72 observations are used for training.
In a k-fold cross-validation, the data set is divided into k subsets or folds. Each fold is used as a validation set, and the remaining folds are used for training. The process is repeated k times, with each fold serving as the validation set once.
Given:
Number of observations in the data set = 80
Number of folds in cross-validation (k) = 10
To determine the number of observations used for training at each iteration, we need to calculate the size of each fold.
Number of observations in each fold = Total number of observations / Number of folds
Number of observations in each fold = 80 / 10
Number of observations in each fold = 8
Therefore, at each iteration of the 10-fold cross-validation, 8 observations are used for training.
However, we want to know the total number of observations used for training, so we need to multiply the number of observations in each fold by the number of folds minus one.
Total number of observations used for training = Number of observations in each fold * (Number of folds - 1)
Total number of observations used for training = 8 * (10 - 1)
Total number of observations used for training = 8 * 9
Total number of observations used for training = 72
In a 10-fold cross-validation with a data set of 80 observations, 72 observations are used for training at each iteration.
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help please asap lol thanks
Answers
Answer:
3.3
Step-by-step explanation:
Find all the numbers and find the mean
The x means that there are that many of each number
1 + 1 + 2 + 3 + 3 + 4 + 4+ 5 + 5 + 5
33
We have to divide that by the total amount of numbers present
33/10 = 3.3
Liza wants to have more than $750 in her
savings account before she will leave for college.
Right now she has $300, and she is going to
baby sit to earn $ 12.00 an hour. How many hours
will Liza need to babysit before she leaves for
college? What’s the inequality
Answers
Answer:
x is equal to or greater than 38.
Step-by-step explanation:
use the equation 300+12x to find the amount of money in total dependent on x, the number of hours she worked.
Step-by-step explanation:
750-300= $450 left that needs to be save to meet her goal.
set an equation to equal 450 that includes the next part of the information given which is $12 and hour
450=12x
isolate x by dividing 12 to both sides
x= 37.5 hrs
the inequality could be :
750<_ 300+ 12x
3 added to five times a number, and the result is multiplied by 4 . The final result is 72 . What is the number
Answers
Answer:
3
Step-by-step explanation:
72/4=18 18-3=15 15/5=3
If 3 added to five times a number, and the result is multiplied by 4, the number that satisfies the given conditions is x = 3.
Let's break down the problem step by step to find the number.
First, we start with a variable to represent the unknown number. Let's call it "x".
The problem states that "3 added to five times a number," which can be expressed as 5x + 3.
Next, it says that "the result is multiplied by 4," so we can write the equation as 4(5x + 3).
Finally, the problem states that "the final result is 72," so we set the equation equal to 72:
4(5x + 3) = 72
To solve for x, we simplify the equation:
20x + 12 = 72
Next, we subtract 12 from both sides:
20x = 60
Finally, we divide both sides by 20:
x = 3
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Tammy is mapping a portion of a fence line on her property. The fence runs along the property from point K to point L, and then turns at point L and runs directly to point M. Tammy has measured the lengths of AB and BC as well as AC and found the lengths to be 290 yards, 248 yards, and 499 yards respectively. By what angle does the fence line change direction? (Round your answer to the nearest degree if necessary. Do not include any units.)
Answers
Given the lengths of the three sides of the triangular fence, the angle by
which the fence line changes direction can be found by cosine rule.
The angle by which the fence line change direction is approximately 44
The given parameters are;
AB = 290 yards = LK
BC = 248 yards = ML
AC = 499 yards = MK
Let AB = a, BC = b, and AC = c, by cosine rule, we have;
c² = b² + a² - 2·b·a·cos(C)
Therefore;
499² = 248² + 290² - 2×248×290×cos(C)
2×248×290×cos(C) = 248² + 290² - 499² = -103397
143840×cos(C) = -103397
\(cos(C) = -\dfrac{103390}{143840}\)
\(\angle C = arccos \left( -\dfrac{103390}{143840} \right) \approx 135.95^{\circ}\)
∠C = ∠ABC = ∠MLK ≈ 135.95°
The angle by which the fence turns is a supplementary angle to angle
∠MLK, which is therefore;
?° + ∠MLK = 180°
?° = 180° - ∠MLK
∴ ?° ≈ 180° - 135.95° ≈ 44°
The angle by which the fence change direction is approximately 44
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5. Janet Gilbert is director of labs. She has some extra capacity and has contracted with some small neighboring hospitals to run some of their lab tests. She has recently had a study conducted and has determined that her costs of these contracts are $10,000 of which $7,000 are for supplies and items related to each test. She currently charges an average of $10.00 per lab test. She is thinking of lowering her price by 20 percent in hopes of raising her current volume of 10,000 tests by 15 percent.
Answers
Answer:
Check the explanation
Step-by-step explanation:
Present predicted
Revenue - per test 10000 8000
Variable cost - per test 7000 7000
Contribution – per test 3000 1000
Net income (10,000 test – 11,500 tests) 30,000,000 11,500,000
Which relationship is NOT a function?
Answers
Answer:
a
Step-by-step explanation:
Answer:
If it is possible to draw any vertical line (a line of constant x) which crosses the graph of the relation more than once, then the relation is not a function. If more than one intersection point exists, then the intersections correspond to multiple values of y for a single value of x (one-to-many).
Step-by-step explanation:
Where is the midpoint of AB if A(6, 4) and B(5, -2)?
Answers
Using the midpoint formula,
M(x3, y3) = [(x1+ x2)]/2, [(y1 + y2)]/2
M(x,y)=[(6+5)/2],[(4-2)/2]
after solving,
M(x,y)= (5.5,1)
HELP ME WITH THIS QUESTION PLESE!!
Answers
Answer:
See below for explanation since answer already provided along with question
Step-by-step explanation:
When adding binary numbers just add them as you would decimal numbers starting at the rightmost bit.
Note for bit addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 with a carry of 1 which is added to the next left column
When subtracting bits
0 - 0 = 0
0 - 1 = 1 but requires a carry from the next left column
1 - 0 = 0
1 - 1 = 0
First 11011₂ + 10011₂
Add the right most bits 1 + 1 = 0 with a carry of 1
The next left column has 1 + 1 = 10 + 1 = 11 that means 1 with a carry of 1
The next left column has 0 + 0 = 0; add the carry to get 0 + 1 = 1; no carry
The next left column has 1 + 0 = 1; no carry
The left most column has 1 + 1 = 0 with a carry of 1 which is appended to the left most position
Reading from left to right this would be 1 0 1 1 1 0
(This is the same as adding two 2-digit numbers with a carry. For example, 74 + 82 = 156)
In long addition format:
\(0 \quad 1 \quad 1 \quad 0 \quad 1 \quad 1\quad +\\0 \quad 1 \quad 0 \quad 0 \quad 1 \quad 1\quad \\---------\\1 \quad 0 \quad 1 \quad 1 \quad 1 \quad 0\quad\\---------\\\)
The leading zeros above are only for alignment and do not affect the values . Note the addition result has 6 places whereas the items being added have only 5 places
Subtracting 1 1 1 0 1 will give
\(1 \quad 0 \quad 1 \quad 1 \quad 1 \quad 0 \quad -\\\quad 0 \quad 1 \quad 1 \quad 1 \quad 0 \quad 1\\---------\\\quad 0 \quad 1 \quad 0\quad 0\quad 0\quad 1\\---------\\\)
Here, starting at the right most column we get 0 - 1 = 1 which requires a carry from the next left column. So the bit in the next left column becomes 1 - 1 = 0 which makes that column 0 - 0 = 0
The next two columns on the left have both 1 so it is just 1 - 1 = 0 in both
In the next to last left column we have 0 - 1, this requires a carry from the left most column so it becomes 0 - 1 with carry = 10 - 1 = 1
Hope that was comprehensible
The distance between two cities is 650 miles. A train travels between the two cities at a constant rate of 50 miles per hour. How many hours does it take the train to travel from one city to the other?
O:22
O:24
O:12
O:13
Answers
Answer:
The answer is 13
Step-by-step explanation:
Divide the distance by the rate to get your answer
EX. 650 ÷ 50 = 13
dum dum as heII
1/5 of 45 is what number?
Answers
Answer:
9
Step-by-step explanation:
1/5x45= 9
Triangle XYZ ~ triangle JKL. Use the image to answer the question.
a triangle XYZ with side XY labeled 8.7, side XZ labeled 8.2, and side YZ labeled 7.8 and a second triangle JKL with side JK labeled 12.18
Determine the measurement of KL.
KL = 9.29
KL = 10.92
KL = 10.78
KL = 11.48
Answers
The measurement of KL if triangles XYZ and JKL are similar is:
B. KL = 10.92
How to Find the Side Lengths of Similar Triangles?Where stated that two triangles are similar, it means they have the same shape but different sizes, and therefore, their pairs of corresponding sides will have proportional lengths.
Since Triangle XYZ and JKL are similar, therefore we will have:
XY/JK = YZ/KL
Substitute the given values:
8.7/12.18 = 7.8/KL
Cross multiply:
8.7 * KL = 7.8 * 12.18
Divide both sides by 8.7:
8.7 * KL / 8.7 = 7.8 * 12.18 / 8.7 [division property of equality]
KL = 10.92
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Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
Answers
(Equivalent Algebraic Expressions MC)
Which expression is equivalent to (m−2n−3)−4?
A m^-6 n^-7
B m^8 n^12
C m^-8 n^-12
D 1/m^6 n^7
Find the sum of the measures of the interior angles of each convex polygon.
23-gon
Answers
The sum of the measures of the interior angles of a 23-gon is 3780 degrees.
To find the sum of the measures of the interior angles of a convex polygon, we can use the formula:
Sum = (n - 2) * 180 degrees
where "n" represents the number of sides or vertices of the polygon.
For a 23-gon, substituting n = 23 into the formula, we have:
Sum = (23 - 2) * 180 degrees
= 21 * 180 degrees
= 3780 degrees
Thus, the obtained value of the angles is 3780 degrees.
Knowing the sum of the measures of the interior angles of a polygon is useful for various mathematical and geometric calculations. It helps in determining individual angle measures or comparing the angles of different polygons.
Additionally, it provides insight into the properties and characteristics of polygons, enabling deeper analysis and understanding of their structures and relationships.
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Jack puts 1/3 pounds of birdseed every time he fills his bird feeder up. How many times can jack fill his bird feeder with 4 pounds of birdseed
Answers
Answer:
He can fill his feeder 12 times
Step-by-step explanation:
If p = 2 3 , point b has a weight of 2, and point c has a weight of 4, find the weight of point a.
Answers
A fixed point Weight is the ideal weight for our bodies in order to function optimally and feel their best.
What are weighted points?"The set point is established over time," Harrison explains. "It's a complicated thing, but it appears to be your body's attempt to regulate itself, which results in a certain weight."
Even if set point theory is correct, it is possible to lose weight and keep it off. Avoiding fad diets and gradually losing weight may change your set point. It may allow your body to adjust to your new eating habits. You may be more successful if you seek the assistance of a therapist or a dietitian.
A fixed point Weight is the ideal weight for our bodies in order to function optimally and feel their best. It is the weight that our bodies can easily maintain—no micromanaging, counting calories, weighing food, and so on.
The point of weight A has been given in the figure.
The complete question is;
If p = 2/3, point b has a weight of 2, and point C has a weight of 4, find the weight of point A.
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Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)
Answers
Component 3 must be started on day 197 to meet the delivery date of day 200.
To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.
(a) Backward schedule:
Operation | Work Center | Time (hours) | Start Day
--------------------------------------------------------
Final Assembly | Work Center 1 | 1 | 200
Sub-assembly 1 | Work Center 2 | 2 | 199
Component 4 | Work Center 3 | 3 | 197
Component 2 | Work Center 4 | 4 | 196
Component 3 | Work Center 5 | 3 | ????
(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.
From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.
Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.
Hence, component 3 must be started on day 197 to meet the delivery date of day 200.
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5: 6 is 6. What is a of 5?
Answers
Can you please restate the problem in the comments and I will solve it.
Answer:
5/6
Step-by-step explanation:
Using the slope -intercept form
m=1/2 (-1,2)
Answers
Answer:
2 = 1/2(-1) + 2
Step-by-step explanation:
You first substitute the letters for the numbers and then to find (b) or y intercept, you change x to 0 and solve for y. The y intercept is 2
So the equation would be 2 = 1/2(-1) + 2
What is 35 divided by 22 in long division :)
Answers
Answer:
1 remainder 13
Step-by-step explanation:
:)
I need help with this please I’ve been stuck on this question for a week now
Answers
Answer:
32 degrees
Step-by-step explanation:
Answer:
55!
Step-by-step explanation:
y= 100-45!
exterior angle in equal to sum of interior angles 100° = y +45°
Which of the following measures of variability is used when the statistics having the greatest stability is sought?
•Mean Deviation
•Standard Deviation
•Quartile Deviation
•Range
Answers
The measure of variability that is used when the statistic with the greatest stability is sought is the Standard Deviation.
The Standard Deviation takes into account the dispersion of data points from the mean and provides a measure of the average distance between each data point and the mean. It is widely used in statistical analysis and is considered a robust measure of variability, providing a more precise and stable measure compared to other measures such as Mean Deviation, Quartile Deviation, or Range.
The Standard Deviation is a statistical measure that quantifies the dispersion or variability of a dataset. It takes into account the differences between individual data points and the mean of the dataset. By calculating the average distance between each data point and the mean, it provides a measure of how spread out the data is.
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Q2. (i) State the definition of the degree of precision of a quadrature formula (ii) Find the constants co, ci, and x1 so that the quadrature formula ∫ f(x) dx = c0 f(0) +c1 f(x1) has the highest possible degree of precision. what is that degree?
Answers
(i) The degree of precision of a quadrature formula is the highest degree of polynomial that the formula can exactly integrate.
(ii) To find the constants co, ci, and x1 that give the highest possible degree of precision, we need to choose a quadrature formula that is exact for polynomials of the highest possible degree.
Let's assume that we are trying to find a formula that is exact for polynomials of degree 1 (i.e., linear polynomials). We can set up two equations using this assumption:
∫ 1 dx = c0 + c1 (since the formula must be exact for constant functions)
∫ x dx = c0*0 + c1*x1 (since the formula must be exact for linear functions)
Solving for c0 and c1, we get:
c0 = 1/2
c1 = 1/2
x1 = 1
Therefore, the quadrature formula that has the highest possible degree of precision is:
∫ f(x) dx = (1/2) f(0) + (1/2) f(1)
This formula is exact for linear polynomials and has a degree of precision of 1.
(i) The degree of precision of a quadrature formula is the highest degree of a polynomial, p(x), for which the quadrature formula gives an exact result when applied to the integral of p(x) dx over a given interval.
(ii) To find the constants c0, c1, and x1 so that the quadrature formula ∫f(x)dx = c0f(0) + c1f(x1) has the highest possible degree of precision, we'll follow these steps:
Step 1: Start with the quadrature formula
∫₀¹ f(x)dx = c0f(0) + c1f(x1)
Step 2: Test polynomials of increasing degree until the formula fails to be exact.
For n=0: f(x) = 1
∫₀¹ 1 dx = c0(1) + c1(1) => 1 = c0 + c1
For n=1: f(x) = x
∫₀¹ x dx = c0(0) + c1(x1) => 1/2 = x1*c1
Step 3: Solve for the unknowns using the equations obtained from the test polynomials:
From the equation for n=0: c1 = 1 - c0
Substitute this expression for c1 in the equation for n=1:
1/2 = x1 * (1 - c0)
Step 4: Choose values that satisfy the above equation:
Let c0 = 1/2 and c1 = 1/2
1/2 = x1 * (1/2) => x1 = 1
So, the constants are c0 = 1/2, c1 = 1/2, and x1 = 1. The highest degree of precision achieved by this quadrature formula is 1 because the formula works exactly for polynomials of degree 0 and 1, but not for higher degrees.
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2(4 – 16) – (–30) 2(–12) – (–30) 24 – (–30) 54
Answers
Step-by-step explanation:
2(4 – 16) – (–30) 2(–12) – (–30) 24 – (–30) 54= 2×4-2×16 -×-30×2×-12-×-30×24-×-30= 8-32+30-24+30×24+30: 732
Answer:
2(4 - 16) - (-30) 2(-12) - (-30) 24 - (-30) 54
Solve the ones in the bracket first
Thus
2(-12) - 720 + 720 + 1620
= -24 + 1620
= 1596
Hope this helps
Which number line model represents the expression -2+(-7)?
Khan academy help!!!!!
Answers
Answer
is should be -9 but I dont see a model on your question.
Step-by-step explanation:
Ruby misses 10% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 70?
Answers
Answer:
700
Step-by-step explanation:
70x10 = 700
The total number of free throws she attempted is 700.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Missed free throws = 10%
Total free throws = 100%
10% = 70
Multiply 10 on both sides.
100% = 700
Thus,
Total free throws are 700.
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a=2bc
b=0.554 (3sf)
c=6000(1sf)
Work out the lower bound for the value of a.
Give your answer correct to 3 decimal places when appropriate.
Answers
The lower bound for the value of A is approximately 5535.
Given the equation A = 2bc and the values b = 0.554 (to 3 significant figures) and c = 6000 (to 1 significant figure), we can calculate the lower bound for the value of a.
To find the lower bound, we need to consider the maximum possible value for b and c within their respective rounding limits.
For b = 0.554 (to 3 significant figures), the lower bound would be the smallest value that is still within the range of possible values for b.
Since b is given to 3 significant figures, the lower bound can be considered as 0.5535, which retains the three significant figures.
For c = 6000 (to 1 significant figure), the lower bound would be the largest value that is still within the range of possible values for c.
Since c is given to 1 significant figure, the lower bound can be considered as 5000, which retains the one significant figure.
Now, we can substitute the lower bound values of b and c into the equation A = 2bc:
\(A = 2 \times 0.5535 \times 5000\)
A ≈ 5535
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.
What is the simplified form of this expression?
(4x - 4) - 8x
Answers
Answer:
-4x-4
Step-by-step explanation:
(4x-4) can't be combined so they are not relevant. 4x-8x = -4x and -4 is unchanged.
Answer:
X=-1
Step-by-step explanation:
(4x-4)-8x=0
4x-4-8x=0
-4x-4=0
-4(X+1)=0
X+1=0/-4
X+1=0
:.X= -1 .
The ratio of quarters to dimes in a money bag is 21:18. If the total number of coins is 147,how many dimes are there?
Answers
21 + 18 = 39
147/39 = 3.7692307692307
3.7692307692307 x 18 = 67.846153846152, round to 67.80 and that's your answer
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places. Use Table 1 in Appendix B. a. What is the probability of completing the exam in one hour or less (to 4 decimals)? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?
Answers
The probability that a student will finish the exam in one hour or less is 0.0228. The probability that a student will finish the exam in more than an hour but less than two hours is 0.2857. The number of students who won't finish the exam in the allocated time is 10.
Simply defined, probability estimates how probable something is to occur. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.
Data provided is,
mean = u = 80
departure from the mean = p = 10
a) The probability of finishing the test in an hour or less:
P(x 60) = (60 minutes in an hour)
= P[(x - u) /p< (60 - 80) / 10]
= P(z <-2.00)
in the z table,
= 0.0228
b) The likelihood that a student would finish the test in longer than 60 but shorter than 75 minutes:
P(60 x 75) = P[(60 - 80)/ 10) (x - u)/p (75 - 80)/ 10)]
= P(-2.00 < z < -0.50)
= P(z < -0.50) - P(z < -2.00)
based on z table,
= 0.3085 - 0.0228
= 0.2857
c) College students who won't be able to finish the test in the specified time
n = 60
P(x > 90) = 1 - p( x< 90)
=1- p P[(x - u) /p < (90 - 80) / 10]
P(z = 1.00)
= 1 - 0.8413
= 0.1587
= 60 * 0.1587
= 9.52
= 10 students.
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