1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
EastWind [94]
3 years ago
11

Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of105°Foccur

s at 5PM and the average temperature for the day is85°F.Find the temperature, to the nearest degree, at 9AM.
Mathematics
1 answer:
mafiozo [28]3 years ago
3 0

Answer:

The temperature at 9AM = 75°F

Step-by-step explanation:

Consider D(t) be the temperature in Fahrenheit at time t, where t is measured in hours since midnight. It knows when the maximum temperature occurs. Then it can create a model using a cosine curve.

Vertical shift, D = 85°F

Amplitude, A = (105-85)°F = 20°F

Horizontal stretch factor, B = 2π/24 = π/12

Horizontal shift = -(12+5) = -17

Using the information, we have this model

D(t) = 20cos [π/12(t-17)] + 85

D(9) = 20cos [π/12(9-17)] + 85

       = 20cos [-2π/3] + 85

       = -20 x 1/2 + 85

       = 75°

You might be interested in
Janna jumped 156 inches in the long jump competition at the high school track meeting . how many feet did janna jump?
Fiesta28 [93]
Janna jumped 13 feet. Hope it help!
4 0
3 years ago
A ladder is leaning against a wall that is 20 ft tall. The base of the ladder is 30 ft from the wall. How long is the ladder?
creativ13 [48]
15 ft. so bruh i hope this helps you
3 0
3 years ago
Read 2 more answers
One measure of an athlete’s ability is the height of his or her vertical leap. Many professional basketball players are known fo
almond37 [142]

Answer:

(1) P(\bar X < 26 inches) = 0.0436

(2) P(27.5 inches < \bar X < 28.5 inches) = 0.2812

Step-by-step explanation:

We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

Firstly, Let \bar X = mean vertical leap for the 36 players

Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;

            Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean vertical  leap = 28 inches

            \sigma = standard deviation = 7 inches

            n = sample of NBA player = 36

(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P(\bar X < 26 inches)

   P(\bar X < 26) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{26-28}{\frac{7}{\sqrt{36} } } ) = P(Z < -1.71) = 1 - P(Z \leq 1.71)

                                                 = 1 - 0.95637 = 0.0436

(2) <em>Now, here sample of NBA players is 26 so n = 26.</em>

Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < \bar X < 28.5 inches) = P(\bar X < 28.5 inches) - P(\bar X \leq 27.5 inches)

    P(\bar X < 28.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{28.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z < 0.36) = 0.64058 {using z table}                      

    P(\bar X \leq 27.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{27.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z \leq -0.36) = 1 - P(Z < 0.36)

                                                        = 1 - 0.64058 = 0.35942

Therefore, P(27.5 inches < \bar X < 28.5 inches) = 0.64058 - 0.35942 = 0.2812

6 0
3 years ago
A company manufactures televisions. The average weight of the televisions is 5 pounds with a standard deviation of 0.1 pound. As
Semenov [28]

Answer:

0.2564\text{ pounds}

Step-by-step explanation:

The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.

To find the X percentile for the television weights, use the formula:

X=\mu +k\sigma, where \mu is the average of the set, k is some constant relevant to the percentile you're finding, and \sigma is one standard deviation.

As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute \mu=5, k=1.282, and \sigma=0.1:

X=5+(1.282)(0.1)=5.1282

Therefore, the 90th percentile weight is 5.1282 pounds.

Repeat the process for calculating the 10th percentile weight:

X=5+(-1.282)(0.1)=4.8718

The difference between these two weights is 5.1282-4.8718=\boxed{0.2564\text{ pounds}}.

8 0
3 years ago
Read 2 more answers
How to draw the angles and how did you fine the angle.
nadezda [96]
I think it's option c. 
8 0
3 years ago
Other questions:
  • For breakfast, Clarissa can choose from oatmeal, cereal, french toast, or scrambled eggs. She thinks that if she selects a break
    10·2 answers
  • 867,000 rounded to the nearest hundred thousand
    8·1 answer
  • HELP ME ASAP!!!! PLEASE HELP I AM DESPERATE!!!!!!!
    5·1 answer
  • The Jackson family went out to dinner
    11·1 answer
  • Kevin says that lines p and m will eventually intersect.
    13·2 answers
  • PLEEEEASS HELP QUICKLY!!!!!!
    7·1 answer
  • Work out the area of this circle. Take to be 3.142 and give your answer to 2 decimal places. 11.2 cm
    7·1 answer
  • Solve. <br><br> −5.1p + 3.8 = 86.93
    12·1 answer
  • Solve. Graph the solution and write the solution in interval notation.<br> 2x+4≤3(x+2)
    15·2 answers
  • Find the equation of the line that passes through point a and b
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!