Two secant segments intersect outside a circle as shown. What is the value of x?

26. Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics

hjlf

The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

$\mu _d = \mu _{post} - \mu _{pre}$

Then the null hypotheses and alternative hypotheses will be

H₀: $\mu _d = 0$

Hₐ: $\mu _d > 0$

Then the test statistic will be

$\rm \overline{x} _d = \dfrac{\Sigma x_d}{n} = \dfrac{15+12+10+1}{4}\\\\\overline{x} _d = 9.5$

Then

$\rm S_d = 6.02$

The test statistic value is given by

$\rm t = \dfrac{\overline{x} _d }{\dfrac{S_d}{\sqrtn}} \\\\t = \dfrac{9.5}{\dfrac{6.02}{\sqrt4}}\\\\t = 3.16$

Since this is a right-tailed test, so the critical value is given by

$\rm t_{n-1}(\alpha ) = t_3 (0.05) = 2.353$

Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that $\mu _d > 0$ that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

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7 0

2 years ago

The difference between two numbers is 25. The smaller number us 1/6th of the larger number. What is the value of the smaller num

Nataliya [291]

Answer:

5

Step-by-step explanation:

Let L be the larger number and s be the smaller one.

Then we have two equations.

(1) L – s = 25

(2) s = L/6 Multiply both sides by 6

6s = L Substitute the value for L in Equation(1)

6s – s = 25 Combine like terms

5s = 25 Divide both sides by 5

s = 5

The value of the smaller number is 5.

7 0

4 years ago

Help pls i don’t know how to do this

Vlada [557]

Answer:

m∠1= 79

Step-by-step explanation:

What we have here is two vertical lines and one intersecting point.

The m∠1 and m∠6 are vertical angles, which means that they equal to each other. So, the equation would be: 6x+25= 10x-11.

Step 1- Subtract 6x to both sides.

6x+25= 10x-11

-6x -6x

25= 4x-11

Step 2- Add 11 to both sides.

25= 4x-11

+11 +11

36= 4x

Step 3- Divide both sides by 4.

4 4

x= 9

Now that we know the value of the variable x, substitute it into the equation for m∠1.

m∠1= 10(9)-11

m∠1= 90-11

m∠= 79

<u>Check </u>

m∠6= 6(9)+25

m∠6= 54+25

m∠6= 79

Since m∠1 and m∠6 are vertical angles, they should equal each other.

4 0

3 years ago

Amanda bought a 6 cup bag of shredded cheese for $6.89. She used 2.25 cups to make lasagna and 1.25 cups to make pizza. How much

Anna11 [10]

Answer:

3.50 cups

Step-by-step explanation:

6-2.25=4.75

4.75-1.25=3.50

5 0

3 years ago

What is the horizontal displacement of the basic graph to produce a graph of

chubhunter [2.5K]

Since the equation says "cos(x-2)", we know that the horizontal displacement is 2 units.

3 0

3 years ago