Find the equation of the line.

An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the

nalin [4]

Answer:

$z=\frac{9.25-10}{\frac{2}{\sqrt{35}}}=-2.219$

$p_v =P(z$

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, so we can conclude that the true mean is significantly lower than 10 minutes.

Step-by-step explanation:

Data given and notation

$\bar X=9.25$ represent the sample mean

$\sigma=2$ represent the population standard deviation

$n=35$ sample size

$\mu_o =10$ represent the value that we want to test

$\alpha=0.05$ 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 less than 10 minutes, the system of hypothesis would be:

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{9.25-10}{\frac{2}{\sqrt{35}}}=-2.219$

P-value

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

$p_v =P(z$

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 to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.

6 0

4 years ago

10 to the power of 2 +10 to the powers of three

yulyashka [42]

10x10= 100
10x10x10=1000
100+1000=10,000

4 0

3 years ago

Read 2 more answers

How do I solve a given right triangle to find Cos, Sin, and Tan. How do I solve for a missing adjacent side? (For Example: Imagi

Sphinxa [80]

The steps to find cos, sin, and tan and missing adjacent side of a given right angle triangle is explained.

<u>Solution:</u>

Given, a right triangle with A, B, and C.

Opposite side = 70 inches

Hypotenuse = 12 feet = 12 $\times$ 12 inches = 144 inches

Adjacent side = "x" inches.

We are not given angle, so we have to use the hypotenuse theorem

Hypotenuse theorem means square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

$\text { hypotenuse }^{2}=(\text { opposite side })^{2}+(\text { adjacent side })^{2}$

Substituting the values we get,

$\begin{array}{l}{\rightarrow 144^{2}=70^{2}+x^{2}} \\\\ {\rightarrow x^{2}=20736-4900} \\\\ {\rightarrow x^{2}=15836} \\\\ {\rightarrow x=\sqrt{15836}} \\\\ {\rightarrow x=125.841}\end{array}$

So, the adjacent side value is 125.8 inches approximately.

Hence the steps to find adjacent side is shown above

Now let us find cos, sin and tan

$\begin{aligned} \sin \theta &=\frac{\text {opposite side}}{\text {hypotenuse}} \\\\ \cos \theta &=\frac{\text {adjacent side}}{\text {hypotenuse}} \\\\ \tan \theta &=\frac{\text {opposite side}}{\text {adjacent side}} \end{aligned}$

By substituting the required values, we can find cos, sin and tan

$\begin{array}{l}{\sin \theta=\frac{70}{144}=\frac{35}{122}} \\\\ {\cos \theta=\frac{125.8}{144}=\frac{62.9}{122}} \\\\ {\tan \theta=\frac{70}{125.8}=\frac{35}{62.9}}\end{array}$

5 0

3 years ago

Given that x= -3, what is the value of 2×² - x + 5?

Roman55 [17]

Answer:

26

Step-by-step explanation:

2(9)-(-3)+5

2(9)+3+5

18+8

26

3 0

3 years ago

Read 2 more answers

Find the missing length indicated. x=

guapka [62]

Answer: x = 120

Step-by-step explanation:

Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.

Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)

Cos(A) = 64/Z

Cos(A) = Z/(64 +225)

We can take the quotient of those two equations and get:

$1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}$

Then:

Z = √(18,496) = 136.

now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.

Then, using the Pythagorean theorem:

64^2 + x^2 = 136^2

x = √(136^2 - 64^2) = 120

5 0

3 years ago