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postnew [5]
3 years ago
7

2 What is the period of f(x) = sin(x)? € O 2 O 20

Mathematics
1 answer:
Ad libitum [116K]3 years ago
8 0

Answer:

Period: 2\pi

Step-by-step explanation:

The function f(x)=asin(bx-c)+d has a period of \frac{2\pi}{|b|}, therefore f(x)=sinx has a period of 2\pi, where the wave cycle of the function repeats every 2\pi units. See the attached graph for a visual.

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Find the gradient of the line 2x+7y=14
Alex777 [14]

Answer:

-2/7

Step-by-step explanation:

2x+7y=14

7y=-2x+14

divide by 7

y=-2/7 x+2

4 0
3 years ago
The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, al
Valentin [98]

Answer:

a) p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation  

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \geq 0

Alternative hypothesis: \mu_y -\mu_x

The first step is calculate the difference d_i=y_i-x_i and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451

The 4 step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679

The next step is calculate the degrees of freedom given by:

df=n-1=10-1=9

Now we can calculate the p value, since we have a left tailed test the p value is given by:

p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The confidence interval for the mean is given by the following formula:  

\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that t_{\alpha/2}=3.25  

Now we have everything in order to replace into formula (1):  

-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469  

-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069  

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0
3 years ago
The function f(x) is represented by this table of values.
Darya [45]
The average slope (s) on the interval [a, b] is given by
  s = (f(b) -f(a))/(b -a)

When there are a lot of computations to do, it is convenient to let a machine do them. The intervals and slopes are ...
  [0, 5] : 5
  [-3, 3] : 0
  [-5, 3] : -2
  [-3, 5] : 2

6 0
4 years ago
The sales tax rate is 3%. If Tanvi buys a balance beam priced at $648, how much tax will she pay?
lesya [120]
She will pay $19.44

I asked Siri, "what is 3% of $648"
4 0
3 years ago
A triangle has vertices at (-4,-6),(3,3), (7,2). Rounded to two decimal places, which of the following is the closest approximat
Cerrena [4.2K]

Answer:

Hey there!

The perimeter of the triangle is the distance around it.

We can find the distance of two points using the distance formula, and add up all the distances to find the total distance.

-4, -6 to 3, 3 is 2

3, 3 to 7, 2 is 5

7, 2 to -4, -6 is about 5.4

2+5+5.39=12.4, which is closest to 12.36.

Let me know if this helps :)

6 0
3 years ago
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