17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.
1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon
46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69°
1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight
72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°
a. Find the amplitude of a sinusoidal function that models this temperature variation.
b. Find the vertical shift of a sinusoidal function that models this temperature variation.
c. What is the period of a sinusoidal function that models this temperature variation?
d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.
e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?
Answers
Answer:
a. Amplitude: 19.65446
b. Vertical Shift: 58.00713
c. Period: 2/0.22797 = 27.56146
d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713
e. Model's Temperature at 10 A.M.: f(-7) = 61.91
This value is 9.91 degrees higher than the actual value.
Step-by-step explanation:
With 1 am being timed as t = 1, we fitted the temperature data collected at different points during the day in Portland, Oregon using sine regression. After receiving the sine function, we respond to the many questions connected to the sine function's properties.
What is sinusoidal Function?A smooth, repeating oscillation characterizes a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that may be described by sinusoidal functions.
Given, The hourly temperature at Portland, Oregon, on a particular day is recorded.
Using sine regression on the given data with t = 1 being the hour 1 am etc, we get the following sine regression formula using the TI-83 Graphing Calculator where T is the temperature:
T = a sin(bt + c) + d
Where a = 19.65, b = 0.28, c = -2.93, d = 58.01
From the sine regression function above:
a. The amplitude of the sinusoidal function is a = 19.65.
b. The vertical shift is d = 58.01.
c. The period is 2*pi /b = 2*pi/ 0.28 = 22.44
d. At 5 PM, the time value is t = 17. Hence the temperature distribution with 5 PM being t = 0 will be
t = asin[b(t - 17) + c] +d.
e. From the table, at 10 AM, the actual value of the temperature is 52 degrees.
Using the model in part a., at 10 AM, with t = 10, the temperature will be
T = a sin(10b + c) + d
T = 55.46 degrees
Learn more about sinusoidal functions here:c. The period is
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Complete question:
Related Questions
How many pies are there if someone eats 2 and then someone else eats 4 then I eat 13? We started with 200 pies.
Answers
Answer:
183
Step-by-step explanation: 13+4=17 200-17=183
Answer:
181
Step-by-step explanation:
Which of the following is equal to the fraction below?
(5/9)^8
Answers
Hope I’m right I don’t really know this stuff
A famous recipe for New Orleans jambalaya calls for 1 1/4 cups of Gulf shrimp. The recipe serves 5 people. Trinetta and Agnes want to serve 12 people, so they increase all the ingredients proportionally. How much Gulf shrimp is required for the new recipe?
A. 1 2/5
B. 5/12
C. 3 cups
D. 4/5 cups
E. 7 cups
Answers
Answer: C. 3 cups
Step-by-step explanation:
Given: In recipe for 5 people, Required Gulf shrimp = [tex]1\dfrac14[/tex] cups
Since, [tex]1\dfrac14=\dfrac{5}{4}[/tex]
Required Gulf shrimp = [tex]\dfrac54[/tex] cups
Then, for 1 people Gulf shrimp required = [tex]\dfrac{5}{4}\div 5[/tex]
[tex]=\dfrac54\times\dfrac{1}{5}[/tex]
[tex]=\dfrac14[/tex] cup
For 12 people, it is required = [tex]12\times\dfrac14 = 3\text{ cups}[/tex]
Hence, 3 cups of gulf shrimp is required for new recipe.
So, correct option is C. 3 cups
−126 = 14k
MAKE SURE TO SHOW YOUR WORK PLEASE HURRY
Answers
Answer:
k = -9
Step-by-step explanation:
When a number (coefficient) is next to a letter (variable) that means you multiply. To solve you would to the opposite, which is to divide.
-126 ÷ 14 = -9
So -9 is equal to k.
Hope that helps and have a great day!
If X is a random variable with expected value 2, then the expected value of 5X will be:______
Answers
Answer:
E(5X) = 10
Step-by-step explanation:
The expected value of a random variable X is denoted as; E(X)
Now we are told it's equal to 2.
Thus;
E(X) = 2
Now, we want to find the expected value of 5X
We will use the principle from expected value derivations below;
E(cX + d) = cE(X) + d
Also;
If E(X) = z
Then;
E(aX) will give; aE(X) = az
From our question, we have;
E(X) = 2
Thus;
E(5X) = 5E(X) = 5 × 2 = 10
Provide the correct justifications for each statement in the derivation of the tangent difference identity.
1.
identity
2. Trigonometric
identities
3. Divide numerator and denominator by
4. Factor out common factors using the quotient identity.
Answers
Answer:
1: Quotient
2: Difference
3: cos(x)cos(y)
Step-by-step explanation:
I just did it on Edge :)
Answer:
Step-by-step explanation:
it's right here lol
In an office building, 39 offices are currently being rented. This represents 30% of the total units. How many offices are there in the building?
There are __ offices in the building
Answers
Answer:
130 offices are in the building
Step-by-step explanation:
first 39/x = 30/100
secondly, you cross multiply 39 x 100 and 30 x x
100 x 39= 3900
3900/30 = 130
Answer:
ANS. = 130
30% or 30/100=39offices
use cross multiplication
100/30 x 39/1 (note 30/100 is inversed to 100/30) math. law
10/3 x 39/1 (using divisor 10)
10/1 x 13/1 (using divisor 3)
10 x 13 = 130
Ans = 130 offices
Ans.Checked
30% of 130 offices
30/100 x 130/1
3/10 x 130/1 (10 as divisor)
3/1 x 13/1 (10 as divisor)
3 x 13 = 39
39 offices
Q.E.D
Which inequality is represented by the graph?
A. y > -2/3x+1
B.y < -2/3x +1
C.y < -3/2x +1
D.y> -3/2x +1
Answers
Answer:C
Step-by-step explanation:
Four more than twice a number is -10.
Answers
Answer:
4 + ( -7 X 2 ) = -10
Step-by-step explanation:
Check work:
-7 times 2 is -14.
4 + -14 = -10
The Diameter Of a circle is 10 cm. find its area in terms of pi
Answers
A = 1/2 x 3.14 x 10^2
Answer = 78.54
Hope this helps. If it’s too confusing, I can simplify it.
Combine like terms 17y-15y
Answers
17-15 = 2 now just add y 17y-15y = 2y
Answer:
2y
Step-by-step explanation:
Since 17y and 15y both have a y, you can combine it. You can subtract 17-15 to get 2, so the answer is 2y.
What is the product of -3(-6r+6)
Answers
Step-by-step explanation:
-3 times -6r= 18r
-3 times 6 =-18
18r=-18
R=-1
If the answer is wrong try just 1
Answer:
0
Step-by-step explanation:
remove r first
-3(-6+6)
-3x-6= 18 -3x6|=-18
18-18=0
or
-3(-6+6)
=-3(0)
=-3x0
=0
don't forget the r you removed which equals to one
so you got 1
-3(-6r+6)=1
wish it could help
The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is requested to send three employees who have positive indications of asbestos to a medical center for further testing. If 30% of the employees have positive indications of asbestos in their lungs, find the probability that eleven employees must be tested in order to find three positives. (Round your answer to three decimal places.)
Answers
Answer:
0.070
Step-by-step explanation:
Y = number on trial
Y has a negative binomial distribution
r = 3
P = 30% = 0.3 probability of positive indication.
P(Y = 11) probability of 11 employees that must be tested to get 3 positives
Y-1Cr-1*p^r*q^(y-r)
Y-1 = 11-1 = 10
r-1 = 3 -1 = 2
10C2 x 0.3³x0.7⁸
45x0.027x0.05764801
= 0.070
This is the probability that 11 employees must be tested to get 3 positives.
Sandra has $32 in her purse. She $15 for a CD.Which expression represents this situation.
32+15
-32+15
-32+(-15)
32+(-15)
Answers
Write the whole number 7 as an improper fraction.
Answers
Improper Fractions means
The numerator is greater than (or equal to) the denominator.Then the Answer is :
[tex] = \dfrac{21}{3} [/tex]What is the reciprocal of 7/11 in simpliest form
Answers
Answer:
11/7is your answer ....
Step-by-step explanation:
hope its help you
Select the correct answer from the drop-down menu.
A company sells its products to distributors and boxes of 10 units each. it's profits can be modeled by this equation, where p is the profit after selling n boxes.
p = -n² + 300n + 100,000
Use this equation to complete the statement.
The company breaks even, meaning the profits are only $0, when it sells _____ boxes.
Options for Blank:
A: 200 or 500
B: 500
C: 150
D: 200
Answers
Answer:
B. 500Step-by-step explanation:
Given the profit made by a company modeled by the function
p = -n² + 300n + 100,000
The company breaks even when p = 0
To get the number of boxes sold when the company breaks even, we will substitute p = 0 into the equation.
0 = -n² + 300n + 100,000
multiply through by -1
0 = n² - 300n - 100,000
n² - 300n - 100,000 = 0
(n² - 500n) + (200n - 100,000) = 0
n(n-500)+200(n-500) = 0
(n+200)(n-500) = 0
n+200 = 0 and n-500 = 0
n = -200 and n = 500
Since n cannot be negative
Hence n = 500
This means that the company breaks even when it sells 500 boxes
solve ??? If any1 can
Answers
Answer:
125
Step-by-step explanation:
180-75-50=55 180-55=125
Answer:
s=130
Step-by-step explanation:
the flat line is 180 so to find out S you have to subtract 50 from 180
hope this helps:)
Can someone please help me with this, I will mark you as brainliest
Answers
Answer:
1st answer is 1/2x^5
2nd answer is m^3/16p^2q^2
3rd answer is 2r^4+9r^3
56x + 40 = 48x + 104
Answers
Answer:
56x-48x=104-40
8x=24
X=3
Step-by-step explanation:
the answer is 8
]explanation subtract 56-48 and 104-40 you should get 8x=64
divide 8/8 and 64/8 and the answer is 8
Gordon types 2,448 words in 36 minutes. Find the unit rate.
Answers
Answer: 68 words
Step-by-step explanation: 2448 / 36 = 68
Answer:
68 Words
Step-by-step explanation:
68 words in a minute if you divide 2448 by 36
karla sings for 45 mins for y days each week. on the other days of the week, she plays piano for 1.5 hours. Write an expression for the total number of hours kara sings and plays the piano each week.
Answers
Answer:
(10.5 - 0.75y) hours
Step-by-step explanation:
Number of days in 1 week = 7 .
Number of days in a week Karla sings = y
Number of days Karla plays piano in a week = Number of days in 1 week - Number of days in a week Karla sings
Number of days Karla plays piano in a week = 7 - y
In 1 day Karla sings for = 45 minutes
60 minutes = 1hour
45 minutes = 1/60 * 45 = 3/4 hours = 0.75 hours
In y days time for which Karla sings = y *0.75 hours= 0.75y hours
Time for which Karla plays piano in 1 day = 1.5 hours
Time for which Karla plays piano in (7-y) day = 1.5*(7-y) hours
Total time in hours for which karla sings and plays the piano each week
= 0.75y + 1.5*(7-y)
= 0.75 y + 10.5 - 1.5y
= 10.5 - 0.75y
Thus, total number of hours karla sings and plays the piano each week is 10.5 - 0.75y hours
Your computer supply store sells two types of inkjet printers. The first, type A, costs $241 and you make a $25 profit on each one. The second, type B, costs $103 and you make an $11 profit on each one. You can order no more than 140 printers this month, and you need to make at least $2660 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost?
Answers
Answer:
The number of printers for type A = x = 80 printers
The number of printers for type B = y = 60 printers
Step-by-step explanation:
Let the number of printers for type A = x
Let the number of printers for type B = y
You can order no more than 140 printers this month
x + y ≤ 140
x + y = 140
x = 140 - y
Profit for type A = $25
Profit for type B = $11
You need to make at least $2660 profit
25x + 11y ≥ 2660
25x + 11y = 2660
Substitute 140 - y = x
25(140 - y ) + 11y = 2660
3500 - 25y + 11y = 2660
3500 - 2660 = 25y - 11y
840 = 14y
y = 840/14
y = 60 printers
x = 140 - y
x = 140 - 60
x = 80 printers
To minimize cost :
The number of printers for type A = x = 80 printers
The number of printers for type B = y = 60 printers
How many numbers are 10 units from 0 on the number line?
Answers
Answer:
2 Numbers; -10, and 10.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
10 and -10
Jim is an archaeologist who wants to determine the age of a fossil. The half-life of Carbon-14 is 5730 years. Jim determines there must have been 6.6 grams of Carbon-14 in the fossil when the animal was alive. Now there is only 1.2 grams of Carbon-14 remaining. What is the age of the fossil?
14,092.54
13,119.45
16,345.18
15,540.97
Answers
Answer:
14,092.54
Step-by-step explanation:
I just had this question and got it right.
Order from least to greatest:
-5/6,0.567,-0.11,-1/4
Answers
Answer:
-5/6,-1/4,-0.11,0.567
Step-by-step explanation:
What is the value of y=-1/2x +5
Answers
There are three possible answers
Slope = -1.000/2.000 = -0.500
x-intercept = 10/1 = 10.00000
y-intercept = 10/2 = 5
If this is helpful please mark brainliest. Have a great day
Constance will win 500 in a savings account which option should she choose so that she will have the most money
Answers
Answer:
2 years at 7%
Step-by-step explanation:
Answer:
2 years at 7 percent
Step-by-step explanation:
I got it right on the quiz, I just took it.
Hope this helps! ^^
-9 - 11 = 2q + 4
Solve?
Answers
Answer:
q = -12
Step-by-step explanation:
-9 - 11 can be written as -9 + (-11)
-20 = 2q + 4
Subtract 4 from both sides.
-24 = 2q
Divide both sides by 2
-12 = q
Hope I helped :)
Please consider Brainliest :)
Alondra is training for a 5 mile race. The table below shows how many strides Alondra takes as she builds up to running 5 miles. How many strides will Alondra take to run 4 miles? Exercise Log Miles 1 2 4 5. Strides 2,640 5,280 13,200
Answers
Answer:
7920
Step-by-step explanation: