Solve For X: 12 * X+3=51

[(e^x -e^-x)/(e^x + e^-x)] = 1/3

mr_godi [17]

Answer:

x ≈ 0.34657359

Step-by-step explanation:

5 0

3 years ago

Some research suggests that police officers are more likely to make an arrest in the presence of bystanders. If mentally disorde

zmey [24]

Answer:

$t=\frac{7.03-3.58}{\frac{9.42}{\sqrt{20}}}=1.638$

$p_v =P(t_{(19)}>1.638)=0.0589$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that the true mean is not significantly higher than 3.58 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=7.03$ represent the sample mean

$s=9.42$ represent the sample standard deviation

$n=20$ sample size

$\mu_o =3.58$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z 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 mean is higher than 3.58 :

Null hypothesis: $\mu \leq 3.58$

Alternative hypothesis: $\mu > 3.58$

Since we don't know the population deviation, 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)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{7.03-3.58}{\frac{9.42}{\sqrt{20}}}=1.638$

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

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

$p_v =P(t_{(19)}>1.638)=0.0589$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can conclude that the true mean is not significantly higher than 3.58 at 5% of signficance.

7 0

3 years ago

A varsity boy's basketball team has ratio of seniors to juniors that is 7:4. The varsity girl's basketball team has a ratio of s

valentina_108 [34]

Answer:

Girl's basketball team has more seniors

Step-by-step explanation:

A varsity boy's basketball team has ratio of seniors to juniors that is 7:4.

Let there are 7x seniors and 4x juniors in boy's basketball team.

ATQ,

7x+4x = 12

11x = 12

x = 12/11

Seniors = $7\times \dfrac{12}{11}=7.63$

The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2.

Let there are 7x seniors and 4x juniors in girl's basketball team.

3x+2x = 12

5x = 12

x = 12/5

Seniors = $7\times \dfrac{12}{5}=16.8$

As we can see that girl's basketball team has more seniors as compared to the boy's team.

4 0

3 years ago

A survey indicated that 2 out of 4 doctors used brand X aspirin. If 1000 doctors used brand X, how many doctors were surveyed? P

Ratling [72]

We can set this up as a proportion.

Since 2 is proportional to 1000, then 4 is proportional to "doctors surveyed".

$\frac{2}{4} = \frac{1000}{d}$ where d is the doctors surveyed.

Cross multiply.

2d = 4000
d=2000

2000 doctors were surveyed.

8 0

3 years ago

What is one factor of 30x2 − 33x + 3?

olganol [36]

Answer:

10x - 1

Step-by-step explanation:

30x^2 − 33x + 3 =

= 3(10x^2 - 11x + 1)

= 3(10x - 1)(x - 1)

Answer: 10x - 1

8 0

3 years ago