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
Stella [2.4K]
3 years ago
12

Find the start and end coordinates of y=2 sin x.

Mathematics
1 answer:
Fiesta28 [93]3 years ago
3 0

Answer:

Step-by-step explanation:

when x=0

y=2 sin 0=2×0=0

when x=π/2

y=2×sin (π/2)=2×1=2

when x=π

y=2 sin π=2×0=0

when x=3π/2

y=2 sin (3π/2)=2×-1=-2

when x=2π

y=2 sin (2π)=2×1=2

if ~0\leq x\leq 2\pi \\initial ~point~is ~(0,2)\\end~point~is ~(2\pi ,0)

You might be interested in
You're given a fraction in simplest form the numerator is not a zero when you write the fraction as a decimal it is a repeating
oksano4ka [1.4K]
The denominator can be 3 if the numerator is 1
3 0
3 years ago
What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}? 2r ≤ 3r – 8 A. {8, 9, 10}
TiliK225 [7]
2r\leq3r-8\\
r\geq8\\\Downarrow\\
\boxed{\{8,9,10\}}
8 0
3 years ago
"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0
3 years ago
If quadrilateral PQRS is a rectangle, then which of the following is true? ∠PSQ ≅ ∠QSR segment SR ≅ segment RQ segment PS ≅ segm
natima [27]

Answer:

Because the diagonals of a rectangle are congruent, the statement "segment SQ ≅ segment PR" is true.

5 0
3 years ago
What is 1/2+p=-3 i need help
son4ous [18]

Answr:

p=−7/2

Step-by-step explanation:

Simplify both sides of the equation.

p+

1

2

=−3

Step 2: Subtract 1/2 from both sides.

p+

1

2

−

1

2

=−3−

1

2

p=

−7

2

7 0
3 years ago
Read 2 more answers
Other questions:
  • Zoe has 8 cups of whole-wheat flous. If each loaf of her favourite graad requires 3/4 of a cup of whole wheat flour, how many wh
    5·2 answers
  • Samantha conjectures that for x &lt; -1, it is true that x5 - 2 &gt; x. Is her conjecture correct? Why or why not?
    12·1 answer
  • HELP WILL GIVE BRAINLIEST
    12·1 answer
  • Your uncle has 36 coins in nickels and quarters. The value of his nickels is 1/15 of the value of his quarters. Find the number
    6·1 answer
  • A rectangle has a length of 5^3 units and a width of 5^2 units. What is the area of the​ rectangle? Write your answer as a power
    13·1 answer
  • A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A
    7·2 answers
  • (Ill give brainliest :) )
    12·1 answer
  • In right triangle ABC, sin M = cos 61. If 0
    13·1 answer
  • (25x - 15)°<br> What is the value of x
    6·2 answers
  • Determine the number of crawlers and rovers to make,that will maximize the company profit in a given week
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!