Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 78 degrees and the low temperature of 52 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. Use the minimum positive phase shift possible.

Answers

Answer 1

The equation for the temperature, D, in terms of t, with the minimum positive phase shift possible, is: D = 65 + 13 sin[(t - 4) * (2π / 24)].

The given information suggests that the temperature variation throughout the day follows a sinusoidal pattern. To find the equation for temperature, we need to consider the amplitude, period, and phase shift. The high temperature is 78 degrees, which corresponds to the midpoint of the sinusoidal function. The low temperature of 52 degrees occurs at 4 AM, which implies a phase shift to the right by four hours.

The general form of a sinusoidal function is D = A + B sin[(t - C) * (2π / P)], where A represents the midline (average temperature), B denotes the amplitude (half the difference between the high and low temperatures), C signifies the phase shift, and P is the period.

In this case, the midline temperature is (78 + 52) / 2 = 65 degrees. The amplitude is (78 - 52) / 2 = 13 degrees, as it is half the difference between the high and low temperatures. The phase shift, determined by the time at which the low temperature occurs, is 4 hours. The period, in this case, is 24 hours.

Substituting these values into the general equation, we obtain D = 65 + 13 sin[(t - 4) * (2π / 24)], which represents the temperature, D, as a function of time, t, with the minimum positive phase shift possible.

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Related Questions

What is the answer to this?

What is the answer to this?

Answers

Answer:

I think its A...

Step-by-step explanation:

It makes most sense

1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not simplify)

numbers on triangle:
77, 85, 36
(there is a right angle)

2. Decide which of the following statements are true based on the given triangle below. Assume the figure is drawn to scale such that angle A is greater than angle B

1. Using the right triangle above, fill in the correct ratios for each trigonometric function. (do not

Answers

Seventy seven can write.

Given f (x) = 2x² - 4x + 9 and g(x) = 4x +1:
Find (fog)(-1)

Answers

(fog)(-1) = f( g(-1) )

So the first step is to figure out g(-1) and then use that in f(x).

g(-1) = 4(-1) + 1

       = -3

f(-3) = 2(-3)^2 -4(-3) + 9

      = 2(9) + 12 + 9

      = 39

So, (f o g)(-1) = f(g(-1)) = f(-3) = 39

3 resistance 5Ω , 7Ω , 9Ω are connected in parallel with a power supply of 9 volt. Calculate its equivalent resistance current passing through each resistance and total current passing through the circuit.

Answers

The equivalent resistance currents passing through each resistance  are: 1.8 A , 1.29A , 1A.

The total current passing through the circuit is  19.83 A.

How can the current be calculated?

The resistance 5Ω , 7Ω , 9Ω  which are are connected in parallel, then,

R1 =5Ω,

R 2=7Ω,

R3 =9Ω; supply voltage V=9 volt.

Effective resistance of parallel combination can be calculated as :

1/RP = 1/R1 + 1/R2 + 1/R3

1/RP= 1/5 + 1/7 +1/9

Rp = 0.45397Ω

Then the Current through  resistors

are R1,  I1 = V/R1 = 9/5 = 1.8A

R2,  I2 = V/R2 = 9/7 = 1.29A

R3,  I3 = V/R3 = 9/9 = 1A

Then Total current I = V/Rp = 9/ 0.45397 = 19.83 A

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Stella wants to buy colored pencils that cost $3.50. She has 1 dollar, 5 quarters, 4 dimes, and 7 pennies. Does she have enough money to buy the colored pencils?

Answers

Answer:

no

Step-by-step explanation:

Lets she how much money she has

1.00   dollars

5 * .25 = 1.25 quarters

4 * .10 = .40 dimes

7 * .01 = .07 pennies

Add it all together

1 + 1.25+ .40 +.07 =2.72

3.50 - 2.72 =.78

She is 78 cents short

A gumball machine has 130 red gumballs. If the red gumballs are 25% of the total number of gumballs, how many gumballs are in the gumball machine?
A. 520
B. 32.5
C. 105
D.155

Answers

Answer:

A

Step-by-step explanation:

100/25=4

130x4=520

the answer is A 520.

What is the value of the missing angle?
a.120
b.130
c.155
d.720​

What is the value of the missing angle? a.120 b.130 c.155 d.720

Answers

Answer:

B.

Because the number of sides is 6 so the s go interior angles is 720. So if u want to get x u need to sum up the rest of the angles anf subtract from 720 giving an answer of 130

8/6 as a mixed number

Answers

Answer:

1  1/3

Step-by-step explanation:

Step 1: Find the whole number

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

8/6= 1.3333333333333 = 1

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (1) and multiply it by the original denominator (6). The result of that multiplication is then subtracted from the original numerator:

8 - (6 x 1) = 2

Step 3: Our mixed fraction

We've now simplified 8/6 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

1  2/6

Step 4: Simplifying our fraction

In this case, our fraction (2/6) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 2 and 6 is 2.

We can now divide both the new numerator and the denominator by 2 to simplify this fraction down to its lowest terms.

2/2 = 1

6/2 = 3

When we put that together, we can see that our complete answer is,

1  1/3

1
What is the radius of a circle with circumference 17 mm? Round to the nearest tenth. Use 3.14 for TT.

Answers

Answer: 2.7mm

Step-by-step explanation:

The formula for the circumference of a circle is given as 2πr. In thkw case, thw circumference is 17mm.

Therefore, 2πr = 17

2 × 3.14 × r = 17

6.28r = 17

r = 17/6.28

r = 2.7mm

Therefore the radius of the circle is 2.7mm

the solution to the system is (6,2). select the equations that could be the other in the system.

the solution to the system is (6,2). select the equations that could be the other in the system.

Answers

To find which could be the second equation to the system of equations, we insert the x part of the solution (6), if we obtain 2 as result then that equation could be since it has the same solution as the system.

\(\begin{gathered} y=-\frac{1}{6}x+3 \\ y=-\frac{1}{6}(6)+3 \\ y=-1+3 \\ y=2 \\ \text{second equation} \\ y=4x-2 \\ y=4(6)-2 \\ y=24-2 \\ y=22 \end{gathered}\)

The possible equation to the system is the first since the solution (6,2) belong to the line

39.54 divided by 3 please.

Answers

Answer: 13.18

Step-by-step explanation:

Answer: 13.18

Step-by-step explanation: But if rounded to the nearest tenth its 13.2

hope that helped

What symmetries have a parallelogram

Answers

Answer:

Rotational Symmetry

Step-by-step explanation:

Parallelograms have no lines of symmetry. But they do have rotational symmetry at 180°.

A Rotational Symmetry

Find -4- 2(1)/(2). Model the expression on the number line by drawing an arrow
I'm giving 30 points for this one

Find -4- 2(1)/(2). Model the expression on the number line by drawing an arrowI'm giving 30 points for

Answers

Answer:

Step-by-step explanation:

It would be the middle of the 6 and 5 because you go -4 plus to to the left and in half would be in the middle of that.

Find the measure of the missing angles

Find the measure of the missing angles

Answers

Answer:

m∠1 = 63

m∠2 = 49

m∠3 = 87

m∠4 = 44

Step-by-step explanation:

Angle 2 and 49 are similar

Angle 2 = 49

Angle 1 + 49 + 68 = 180

180 - 49 - 68 = Angle 1

180 - 49 - 68 = 63

Angle 1 = 63

Angle 3 + 93 = 180

180 - 93 = Angle 3

180 - 93 = 87

Angle 3 = 87

Angle 4 + 49 + 87 = 180

180 - 49 - 87 = Angle 4

180 - 49 - 87 = 44

Angle 4 = 44

Step-by-step explanation:

A straight angle measures 180°.

m∠3 = 180 - 93

m∠3 = 87

The sum of the three angles of any triangle is equal to 180°.

m∠4 = 180 - (49 + 87)

m∠4 = 180 - 136 = 44

The vertically opposite angle.

so m∠2 = 49

The sum of the three angles of any triangle is equal to 180°.

m∠1 = 180 - (68 + 49)

m∠1 = 180 - 117 = 63

please give me a brainliest answer

HELP PLS LOL !!!!!!!!!!!!!!

HELP PLS LOL !!!!!!!!!!!!!!

Answers

Answer:

try 137

Step-by-step explanation:

it may be congruent since they're parallel

x^2y+y^2-30x+221=0 find the radius ​

Answers

Answer:

2

Step-by-step explanation

Let's complete the square. We get:

(x^2-30x)+y^2+221=0

(x^2-30x+225)+y^2+221-225=0

(x-15)^2+y^2-4=0

(x-15)^2+y^2=4

By analyzing this, we see that the radius is just :\(\sqrt{4}\)=2

Multiply and express in the form of a complex number a + b i.
(-5 + 3i)(- 4 + 8i)

Answers

Answer:

-4 - 52 i

Step-by-step explanation:

Hope this helps :)

Mai had $14.50. She spent $5.25 at the arcade. What is the exact amount of money
Mai has left?

Answers

Answer:

nine dollars and 27 cents

Step-by-step explanation:

if u minus 14.50 minus 5.25 u get 9.27 9 dollars and 27 cents

Yw!

Answer:

9.25

Step-by-step explanation:

subtract 5.25 from 14.50

Is it B or C? I forgot for when you simplify if you either multiply or add.

Is it B or C? I forgot for when you simplify if you either multiply or add.

Answers

Answer:

B

Step-by-step explanation:

\((w^8)^8=w^{8\times8}=w^{64}\)

But,

\(w^8\times w^8=w^{8+8}=w^{16}\)

the dolphins at the washington aquarium are fed 1/2 of a bucket of fish each day. the sea otters are fed 2 1/3 times as much fish as the dolphins. how many buckets of fish are the sea otters fed each day?

Answers

The number of buckets of fish that the sea otters fed each day is  7/6 buckets .

In the question ,

it is given that ,

the number of buckets of fish that the dolphin are fed at the Washington aquarium = 1/2 bucket

the sea otters are fed \(2\frac{1}{3}\) times as many as fish .

So , the number of buckets that are fed to otters is = (7/3) × (number of buckets eaten by fish)

Substituting the values of number of buckets eaten by fish ,

we get

= (7/3) × (1/2)

Simplifying further ,

we get ,

= 7/6 buckets .

Therefore , the sea otters are fed 7/6 buckets of fish each day .

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evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m

Answers

The sum of the indicated variable is 23.

What is variable?

A variable is an  alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.

MAIN body:

the correct expression is as follows :

1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!)   where m = 3

for m= 3

the expression becomes:

=1(1!) +2(2!) +3(3!)

factorial means we need to multiply the number until it reaches 1.

= 1*1 + 2*2*1 + 3*3*2*1

= 1+ 4+ 18

= 23

Hence the sum of expression is 23.

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Work out the value of 5 to the power of a if it equal 1/125

Answers

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

I got the first part but i dont onow how to get the other ones

I got the first part but i dont onow how to get the other ones

Answers

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

m < CAB = 32º.m < FDE = 32º.

How to obtain the value of x?


We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

m < CAB = 7(5) - 3 = 35 - 3 = 32º.m < FDE = 5(5) + 7 = 32º.

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Generate a quadratic model with y=x+x^2+e. x and e are both vectors which are normal mean 0, variance 1. Generate a monte-carlo sample from this model with length m = 20. Use the functions train_test_split() to get training and test sets where the test set is 1/2 of the full sample size, m. Fit three different models, a linear model, a quadratic model, and a 7 degree polynomial.

Answers

Generate quadratic model: \(\(y = x + x^2 + e\)\) with \(\(x\) and \(e\)\) as normal variables. Perform train-test split and fit linear, quadratic, and 7th-degree polynomial models.

To generate a quadratic model with \(\(y = x + x^2 + e\)\), where \(\(x\) and \(e\)\) are both vectors following a normal distribution with mean 0 and variance 1, and to generate a Monte Carlo sample with a length of \(\(m = 20\)\), we can follow these steps:

1. Generate the vectors \(\(x\) and \(e\)\) using the normal distribution:

\(\[x \sim \mathcal{N}(0, 1), \quad e \sim \mathcal{N}(0, 1)\]\)

2. Calculate the dependent variable \(\(y\)\) using the quadratic model:

\(\[y = x + x^2 + e\]\)

3. Generate a Monte Carlo sample of length \(\(m = 20\)\) by repeating steps 1 and 2 \(\(m\)\) times.

Now, using the `train_test_split()` function, we can split the Monte Carlo sample into a training set and a test set. The test set will be half the size of the full sample \((\(m/2\)).\)

Next, we can fit three different models: a linear model, a quadratic model, and a 7th-degree polynomial. Let's denote the input variable as \(\(x\)\) and the dependent variable as \(\(y\).\)

1. Linear Model:

The linear model can be expressed as:

\(\[y = \beta_0 + \beta_1x\]\)

2. Quadratic Model:

The quadratic model can be expressed as:

\(\[y = \beta_0 + \beta_1x + \beta_2x^2\]\)

3. 7th-Degree Polynomial Model:

The 7th-degree polynomial model can be expressed as:

\(\[y = \beta_0 + \beta_1x + \beta_2x^2 + \beta_3x^3 + \beta_4x^4 + \beta_5x^5 + \beta_6x^6 + \beta_7x^7\]\)

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How do you add two mixed numbers with the same denominator?

Answers

Add the whole numbers first, then add the numerators, to get the sum of two mixed numbers integers with the same denominator. Finally, if necessary, simplify the outcome.

1. Add up all of the whole numbers.

2. Combine the numerators.

3. If necessary, simplify the result.

Start by adding the two whole numbers together in order to combine two mixed numbers with the same denominator. The final result will be a whole number equal to the sum of the two whole numbers. Next, combine the numerators of the two mixed integers. The final sum's numerator is this sum. Finally, simplify the fraction if the numerator is more than the denominator. The fraction is already in its simplest form if the numerator is less than the denominator. The sum of the two whole numbers and the sum of the two numerators, with the denominator staying the same, is the final sum of the two mixed numbers with the same denominator after completing these stages.

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2 1x - 2 = what is the value of |2x - 541

2 1x - 2 = what is the value of |2x - 541

Answers

First, we use the first expression to find x.

\(\frac{1}{3}x-2=\frac{1}{3}\)

We add 2 units on each side.

\(\begin{gathered} \frac{1}{3}x-2+2=\frac{1}{3}+2 \\ \frac{1}{3}x=\frac{1+6}{3} \\ \frac{1}{3}x=\frac{7}{3} \\ x=7 \end{gathered}\)

Then, we use this value to find absolute value.

\(|2x-5^2|=|2\cdot7-5^2|=|14-25|=|-11|=11\)Hence, the answer is 11.

The following measurements (in picocuries per liter) were recorded by a set of radon gas detectors installed in a laboratory facility: 684,684.4,677.1,680.6,671.5,657.1 Using these measurements, construct a 80% confidence interval for the mean level of radon gas present in the facility. Assume the population is approximately normal. Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to two decimal places.

Answers

Answer:

We get a sample mean of 675.78.

Step-by-step explanation:

To calculate the sample mean, we need to sum up all the measurements and divide by the total number of measurements:

Sample mean = (684 + 684.4 + 677.1 + 680.6 + 671.5 + 657.1) / 6 Sample mean = 4054.7 / 6 Sample mean = 675.78

Rounding this to two decimal places, we get a sample mean of 675.78.

The number of ways of arranging all trials to be failures in a binomial distribution is:?

Answers


In a binomial distribution, the number of ways of arranging all trials to be failures is 1. This means that there is only one way to have all trials result in failures, as each trial can only have one possible outcome - a failure.

1. In a binomial distribution, each trial can result in either a success or a failure. Let's assume that there are n trials in total.

2. To arrange all trials to be failures, we need to ensure that no trial results in a success. Therefore, for each trial, there is only one possible outcome - a failure.

3. The number of ways of arranging all trials to be failures can be calculated using combinations. In this case, we need to select 0 successes from n trials. The number of ways to do this is given by the combination formula: C(n, 0) = 1, where C represents the combination.

Therefore, the number of ways of arranging all trials to be failures in a binomial distribution is given by the combination formula, C(n, k) = n! / (k! * (n-k)!).

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The number of ways of arranging all trials to be failures in a binomial distribution is always 1. This is because there is only one way to have no successes in a set of trials.

Regardless of the number of trials or the probability of success, the number of ways of arranging all trials to be failures in a binomial distribution is always 1.

The number of ways of arranging all trials to be failures in a binomial distribution can be determined using the formula for the binomial coefficient.
The binomial coefficient, often denoted as nCk or n choose k, represents the number of ways to choose k items from a set of n items, without considering their order. In the context of a binomial distribution, n represents the total number of trials and k represents the number of successes (in this case, 0).
To find the number of ways of arranging all trials to be failures, we can use the binomial coefficient formula:
nCk = n! / (k!(n-k)!)
In this case, since we want all trials to be failures, k is equal to 0. Thus, the formula simplifies to:
nC0 = n! / (0!(n-0)!) = n! / (0! * n!) = 1

For example, if we have 5 trials and we want all of them to be failures, there is only one possible arrangement: FFFFF, where F represents a failure.

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Help algebra 2 please

Help algebra 2 please
Help algebra 2 please
Help algebra 2 please
Help algebra 2 please
Help algebra 2 please

Answers

Answer:

i just need point im so sorry only in Geomotry

Solve the equation:
10 In(100) – 3 = 117

Answers

Answer:

x = e^12/100

Step-by-step explanation:

Solve for x over the real numbers:

10 ln(100 x) - 3 = 117

Add 3 to both sides:

10 ln(100 x) = 120

Divide both sides by 10:

ln(100 x) = 12

Cancel logarithms by taking exp of both sides:

100 x = e^12

Divide both sides by 100:

Answer:  x = e^12/100

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