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inn [45]
2 years ago
8

Given f(x) = 2 sin x, find the exact value of f (7pi/6) in simplest form with a rational denominator.​

Mathematics
1 answer:
IrinaVladis [17]2 years ago
6 0

Answer:

           \bold{f(\frac{7\pi}6)=-1}

Step-by-step explanation:

f(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\pi+\frac{\pi}6)=-2\sin(\frac{\pi}6)=-2\cdot\frac12=-1

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Bottle A contains 250 milliliters of juice. Bottle B contains at least 20% more juice than bottle A. What is the minimum amount
Serjik [45]

Answer:

300 milliliters of juice in bottle b

Step-by-step explanation:

250×0·2=50

250+50=300

8 0
3 years ago
The area of triangle AEB is 24.5 sq units. How long is `segment\ AE`?
RUDIKE [14]

Answer:

UGUDCRTSE5D

Step-by-step explanation:

7 0
3 years ago
A cereal manufacturer produces cereal in boxes having a labeled weight of 15.7 ounces. Suppose that a random sample of 31 boxes
taurus [48]

Answer:

t=\frac{16.14-15.7}{\frac{1.18}{\sqrt{31}}}=2.076    

p_v =P(t_{(30)}>2.076)=0.0233  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean for the weigths of cereal boxes is higher than 15.7 at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=16.14 represent the sample mean

s=1.18 represent the sample standard deviation

n=31 sample size  

\mu_o =15.7 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 15.7 or no, the system of hypothesis would be:  

Null hypothesis:\mu \leq 15.7  

Alternative hypothesis:\mu > 15.7  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{16.14-15.7}{\frac{1.18}{\sqrt{31}}}=2.076    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=31-1=30  

Since is a one side test the p value would be:  

p_v =P(t_{(30)}>2.076)=0.0233  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence toreject the null hypothesis, and we can conclude that the true mean for the weigths of cereal boxes is higher than 15.7 at 5% of signficance.  

4 0
3 years ago
Helpp me pleasse im going to cryy please respond asap
vodka [1.7K]

Answer:

4

Step-by-step explanation:

5 0
2 years ago
A father is now twice as old as his son. If the sum of their ages ten years ago was fifty two, how old are they today?​
Oliga [24]

Answer:

24 and 48

Today, the son is 24 years old, and the father is 48 years old.  

Step-by-step explanation:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

The father is 2 times his son's age.

2x

= 2(24)

= 48

So, the son is 24 and the father is 48.

10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.

3 0
3 years ago
Read 2 more answers
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