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Hatshy [7]
3 years ago
7

Why is the - sin of x the same as the sin of -x?

Mathematics
1 answer:
Neko [114]3 years ago
3 0

Answer:

Sine is an odd function and presents positive values in the 1st and 2nd quadrants and negative values in the 3rd and 4th quadrants.

Step-by-step explanation:

-sin(x) = sin(-x)

This property is valid because the sine trigonometric function presents positive values in the first two quadrants and negative values in the third and fourth quadrants. The sine function is an odd function with symmetry with respect to the origin, which means that sin(x) and sin(-x) will always present opposite signs.

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A newspaper poll asked respondents if they trusted "eco friendly" labels on cleaning products. Out of 1000 adults surveyed, 498
Paul [167]

Answer:

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.  

Step-by-step explanation:

1) Data given and notation

n=1000 represent the random sample taken

X=498 represent the adults that trust these labels

\hat p=\frac{498}{1000}=0.498 estimated proportion of respondents that trust these labels

p_o=0.5 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of respondents that trust these labels is at least 50%:  

Null hypothesis:p\geq 0.5  

Alternative hypothesis:p < 0.5  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.498 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-0.126  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level is not provided but we can assume it as \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

So the p value obtained was a very high value and using the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of respondents that trust these labels is not significanlty less than 0.5 or 50%.  

7 0
3 years ago
If 2a - 8 = 4 and 3b - 8 = 10, what is the value of a + b?
barxatty [35]
A+B=22 is your answer
7 0
3 years ago
HELLLLPPPPPLPPOOLL no fake answers pls
stepan [7]

Answer:

x = 11

Step-by-step explanation:

(3x + 28) + (5x + 52) + ( 2x - 10) = 180

(3x + 5x + 2x) + (28 + 52 - 10) = 180

10x + 70 = 180

10x = 180 - 70

10x = 110

x = 11

6 0
2 years ago
Read 2 more answers
Please help me thank you.
Alona [7]

Answer:

\large\boxed{1.\ (4)^{-3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}}

\large\boxed{2.\ ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x}

Step-by-step explanation:

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\------------\\\\(4)^{-3x^2}=\left[(4)^{-1}\right]^{3x^2}=\left(\dfrac{1}{4}\right)^{3x^2}

Use:\ a^{-n}=\left(\dfrac{1}{a}\right)^n\ and\ (a^n)^m=a^{nm}\\--------------------\\\\ab^{-3x}=a\cdot b^{-3x}=a\left[(b)^{-1}\right]^{3x}=a\left(\dfrac{1}{b}\right)^{3x}\\\\ab^{-3x}=a\left(\dfrac{1}{b}\right)^{3x}=a\left[\left(\dfrac{1}{b}\right)^3\right]^x

8 0
2 years ago
Find the mean of the data in the dot plot below
Firdavs [7]
The mean would be 5
Reason for this is that the mean is when all data is summed up then divided by how many data points there are
So 4+4+7=15
Then divide by 3 would equal 5
I hope this helps!
4 0
3 years ago
Read 2 more answers
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