Suppose you measured a boiling temperature (in Cº) for a liquid 6 times and observed. the following results:
Sample mean: 101.82, sample variance (biased): 0.81
a. You are given that σ^2 = 1.2 for the population distribution. What is the confidence interval for the mean at 95% confidence level?
b. Assuming σ is unknown, what is the confidence interval for the population mean at 95% confidence level?
Please round your answers to 2 decimal digits.

Both the classical method and the p-value method lead to the conclusion that the average distance cars travel per year is less than 20,000 kilometers,

a) t =  -2.564

b)  t = -2.564

To test the claim that the average distance cars travel per year is less than 20,000 kilometers, we can conduct a hypothesis test using the classical method and the p-value method.

a) The steps we need to follow are:

Step 1: Formulate the null and alternative hypotheses:

Null hypothesis (H₀): The average distance cars travel per year is 20,000 kilometers.

Alternative hypothesis (H₁): The average distance cars travel per year is less than 20,000 kilometers.

Step 2: Determine the test statistic:

Since we know the sample size (n = 100), the sample mean (x = 19,000 kilometers), and the sample standard deviation (s = 3900 kilometers), we can use the t-test statistic.

t = (x - μ₀) / (s / √n)

where μ₀ is the assumed population mean under the null hypothesis.

Step 3: Set the significance level:

The significance level is given as 0.05, which means we want to be 95% confident in our conclusion.

Step 4: Calculate the critical value:

Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value corresponding to a 0.05 significance level and degrees of freedom (df) = n - 1 = 99. From the t-distribution table or calculator, the critical t-value is approximately -1.660.

Step 5: Calculate the test statistic:

t = (19,000 - 20,000) / (3900 / √100)

t = -10 / (3900 / 10)

t ≈ -2.564

Step 6: Compare the test statistic with the critical value:

Since -2.564 is less than -1.660, the test statistic falls in the rejection region. We reject the null hypothesis.

Step 7: Make a conclusion:

Based on the classical method, since the test statistic falls in the rejection region, we conclude that the average distance cars travel per year is significantly less than 20,000 kilometers.

b) The P-value method:

Using the same test statistic t = -2.564 and the degrees of freedom (df) = 99, we can calculate the p-value. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

From a t-distribution table or calculator, the p-value corresponding to t = -2.564 and df = 99 is approximately 0.0075 (or 0.75% if multiplied by 100).

Since the p-value (0.0075) is less than the significance level (0.05), we reject the null hypothesis. This suggests strong evidence that the average distance cars travel per year is significantly less than 20,000 kilometers.

Learn more about standard deviation at:

https://brainly.com/question/475676

#SPJ4

The steps necessary for graphing parametric equations include creating a table, solving the equations for t and plotting those points, connecting the points with a smooth curve, and setting up the coordinate plane with t on the horizontal axis (c, d, f, h).

Create a table: Choose a range of values for t and calculate the corresponding values for x and y using the parametric equations. List these values in a table.

Solve the equations for t and plot those points: Solve the parametric equations separately for t to obtain the x and y coordinates. Plot these points on the coordinate plane.

Connect the points with a smooth curve: Once all the points are plotted, connect them with a smooth curve. This curve represents the graph of the parametric equations.

Set up the coordinate plane with t on the horizontal axis: Label the horizontal axis as t and the vertical axis as either x or y. This allows you to visualize how the x and y values change with respect to the parameter t.

For more questions like Curve click the link below:

https://brainly.com/question/28793630

#SPJ11

Answer:

3:1 (Girls:Boys)

6 divided by 2

Answer:

48 is the answer

Step-by-step explanation:

9*4 +. 6*2

36 + 12

48

Answer:

47

Step-by-step explanation:

^

all i know is that it would not be 13.9

Answer:

12in

Step-by-step explanation:

this is the only subject i'm good at in math XDDD.

Answer: 140,  220,  220,  140

Step-by-step explanation:

All you have to do is double the numbers.

Answer:

3. The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4.  The equivalent fractions are presented as follows;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The reason why it works is because [tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Step-by-step explanation:

3. Based on the shaded region of the given figures, the two fractions are equivalent

Mathematically, we can show the equivalency of the two fractions as follows;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{2 \times 2}{3 \times 2} =\dfrac{4}{6}[/tex]

4. From the shaded region of the given figure, the fractions are equivalent

Mathematically, we have;

[tex]\dfrac{2}{3} =\dfrac{2}{3} \times 1 = \dfrac{4}{4} \times \dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

Therefore;

[tex]\dfrac{2}{3} = \dfrac{4 \times 2}{4 \times 3} =\dfrac{8}{12}[/tex]

5. The amount of salt required by the recipe = 1/4 teaspoon of salt

The measure of the spoon Jonas has = 1/8 teaspoon

When Jonas adds two 1/8 teaspoons, he gets;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1 + 1}{8} = \dfrac{2}{8} = \dfrac{2 \times 1}{2 \times 4} = \dfrac{2}{2} \times \dfrac{1}{4} = 1 \times \dfrac{1}{4} = \dfrac{1}{4}[/tex]

Therefore;

[tex]\dfrac{1}{8} + \dfrac{1}{8} = \dfrac{1}{4}[/tex]

Two 1/8 measuring teaspoons are equivalent to one 1/4 teaspoons and therefore Jonas is able to get the 1/4 teaspoons of salt the recipe asks for b combining two 1/8 measuring teaspoons of salt he has because 1/8 + 1/8 = 1/4.

Answer

6 and 2/3 percent of an hour OR 6.666.... hour

I don’t know if you have to round or not but if it does just round

Step-by-step explanation:

Well 4 minutes of an hour is basically 4/60

4/60=1/15

1/15=x/100

solve the proportion by cross multiplying

100=15x

x=6.66666666

That is yoru percent

Answer:

a = 15

t = 5

Step-by-step explanation:

[tex] \frac{12}{a} = \frac{16}{20} \\ \\ 16a = 12 \times 20 \\ \\16 a = 240 \\ \\ a = \frac{240}{16} \\ \\ a = 15 \\ \\ \\ \frac{2}{8} = \frac{t}{20} \\ \\ 8t = 40 \\ \\ t = \frac{40}{8} \\ \\ t = 5[/tex]

By applying the principle of inclusion-exclusion, we can show that for any events E1, E2,..., EM, the inequality P(E1 or E2 or ... or EM) < P(EM) holds. This result holds true for any integer M ≥ 1.

To prove the statement by induction, we will assume that for M = 1, the inequality holds true. Then we will show that if the statement holds for M, it also holds for M + 1.

Base case (M = 1):

For M = 1, we have P(E1) ≤ P(E1), which is true.

Inductive step:

Assuming that the inequality holds for M, we need to show that it holds for M + 1. That is, we need to prove P(E1 or E2 or ... or EM or EM+1) < P(EM+1).

Using the principle of inclusion-exclusion, we can express the probability of the union of events as follows: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1) - P((E1 or E2 or ... or EM) and EM+1). Since events E1, E2, ..., EM, and EM+1 are mutually exclusive, the last term on the right-hand side becomes zero: P(E1 or E2 or ... or EM or EM+1) = P(E1 or E2 or ... or EM) + P(EM+1)

Since we assumed that P(E1 or E2 or ... or EM) < P(EM), we can rewrite the inequality as: P(E1 or E2 or ... or EM or EM+1) < P(EM) + P(EM+1)

Now we need to show that P(EM) + P(EM+1) < P(EM+1) for the inequality to hold. Simplifying the expression, we have: P(EM) + P(EM+1) < P(EM+1)

Since P(EM+1) is a probability and is always non-negative, this inequality holds true. Therefore, by the principle of mathematical induction, we have shown that for any integer M ≥ 1, the inequality P(E1 or E2 or ... or EM) < P(EM) holds.

to learn more about  principle of inclusion-exclusion, click: brainly.com/question/32097111

#SPJ11

Answer:

Step-by-step explanation:

1. Write the equation.

y = -2x

y = 5x - 21

2. Substitute the values.

(-2x) = 5x - 21

3. Solve the equation.

-2x = 5x - 21

-5x    - 5x

-7x = -21

4. Both negatives cancel

7x = 21

5. Divide both sides by 7

7x = 21

/7      /7

6. x = 3

7. Check the answer.

-2(3) = 5(3) - 21

-6 = 15 - 21

-6 = -6

Hope this helped,

Kavitha

P.S Sorry for taking so long.

The sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

What is sum of series?

A series' sum is the sum of the words or list of numbers that make up the series. If a series has a sum, it will be one integer (or fraction), such as 0, 1/2, or 99.

As given series is,

f(x) = sinx + sin(2x)/3 + sin(3x)/5+.....

The series function is trigonometric function such as sinx, sin(2x), sin(3x).

The nth term of series is sin(nx).

The coefficient of series is 1, 1/3, 1/5.

The coefficient of nth terms is 1/(2n - 1).

Sum of series is,

= infinity ∑(n = 1) sin(nx)/(2n - 1).

Hence, the sum of given series is infinity ∑(n = 1) sin(nx)/(2n - 1).

To learn more about trigonometric function from the given link.

https://brainly.com/question/28386323

#SPJ4

Answer:

area = 164.52 cm²

Step-by-step explanation:

area = (12x6) + (12x3x0.5x2) + (3.14)(0.5)(6²) = 164.52 cm²

Answer:

3

Step-by-step explanation:

dude kinda obv that its 3

Answer:

answer would be 3

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

Using the Pythagorean theorem

a^2+b^2 = c^2

20^2 + 48^2 = c^2

400 +2304=c^2

2704=c^2

Taking the square root of each side

sqrt(2704) = sqrt(c^2)

52 = c

Answer:

[tex]hypotenuse^{2}[/tex] = [tex]altitude^{2}[/tex] + [tex]base^{2}[/tex]

[tex]hyp^{2}[/tex] = [tex]48^{2}[/tex] + [tex]20^{2}[/tex]

       = 2304 + 400

       = 2704

∴[tex]hyp[/tex] = [tex]\sqrt{2704}[/tex]

       = 52

hope this answer helps you....

Answer:

5. B

6. A

7. C

Step-by-step explanation:

Answer:

5.) b. 12 - 2x

6.) a. 8x

7.) c. 5d + 3c = 66

Step-by-step explanation:

uhm, I don't really have proof, i've just been doing this for a long time, you're just gonna have to trust me on this one

Answer:

5/11 is 0.4555555555555555555555555

so basically the first option out of the two.

U do know you can just calculate this with the calculator right?

Answer:

Step-by-step explanation:

59 apples two times = 59 x 2 = 118 apples

Total apples = 118 + 60 = 178 apples

Answer:

Step-by-step explanation:

a = 32 ÷ 4

a = 8

Answer:

(-13,-20)

Step-by-step explanation:

We know that the graph with x-intercept at (7,0) and y-intercept at (0,-7) is y = x-7

and the second equation is y = 2x+6

Therefore, we have two equations.

[tex] \large{ \begin{cases} y = x - 7 \\ y = 2x + 6 \end{cases}}[/tex]

Because both equations are equal (y=y)

x-7=2x+6

-7-6=2x-x

-13=x

We know the value of x, but not y-value. We substitute the value of x to get the value of y.

Substitute in any given equations which I will be substituting in the first equation.

y=-13-7

y = -20

Therefore when x = -13, y = -20

In coordinate form, we can write as (-13,-20).

If you have any questions, feel free to ask.

Answer:

E

Step-by-step explanation:

The solution to the system of differential equations is x₁(t) = e⁻⁵ˣ + 3e³ˣ and x₂(t) = 2e⁻⁵ˣ + 5e³ˣ

Let's solve the given system of differential equations: x₁' = -5x₁ + 0x₂ ...(1) x₂' = -16x₁ + 3x₂ ...(2)

To solve this system, we can rewrite it in matrix form. Let's define the vector X = [x₁, x₂] and the matrix A as:

A = [[-5, 0], [-16, 3]]

The system can then be written as X' = AX, where X' is the derivative of X with respect to time.

Now, let's find the eigenvalues and eigenvectors of matrix A. The eigenvalues are obtained by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix.

A - λI = [[-5 - λ, 0], [-16, 3 - λ]]

det(A - λI) = (-5 - λ)(3 - λ) - 0(-16) = λ² + 2λ - 15 = (λ + 5)(λ - 3)

Setting the characteristic equation equal to zero, we find the eigenvalues: λ₁ = -5 λ₂ = 3

To find the corresponding eigenvectors, we substitute each eigenvalue back into the matrix A - λI and solve the system of equations (A - λI)v = 0, where v is the eigenvector.

For λ₁ = -5: A - (-5)I = [[0, 0], [-16, 8]]

Using Gaussian elimination, we can solve the system of equations to find the eigenvector corresponding to λ₁: -16v₁ + 8v₂ = 0 => -2v₁ + v₂ = 0 => v₁ = (1/2)v₂

Let v₂ = 2, then v₁ = 1. Therefore, the eigenvector corresponding to λ₁ is v₁ = [1, 2].

For λ₂ = 3: A - 3I = [[-8, 0], [-16, 0]]

Solving the system of equations, we find: -8v₁ = 0 => v₁ = 0

Thus, the eigenvector corresponding to λ₂ is v₂ = [0, 1].

Now, let's express the solution of the system in terms of the eigenvalues and eigenvectors.

X(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂

Substituting the eigenvalues and eigenvectors we found earlier, we have: X(t) = c₁e⁻⁵ˣ[1, 2] + c₂e³ˣ[0, 1]

Using the initial conditions, x₁(0) = 1 and x₂(0) = 5, we can find the values of c₁ and c₂.

At t = 0: [1, 5] = c₁[1, 2] + c₂[0, 1] 1 = c₁ 5 = 2c₁ + c₂

Solving these equations, we find: c₁ = 1 c₂ = 3

To know more about differential equation here

https://brainly.com/question/30074964

#SPJ4

Complete Question:

Solve the system of differential equations

x₁' = – 5x₁ + 0x₂

x₂' = – 16x₁ + 3x₂

x₁(0) = 1, x₂(0) = 5

Answer:

27.

Step-by-step explanation:

3^3 = 3 * 3 * 3

= 9 * 3

= 27.

Answer:

IMAO YOU GAVE UP, PSY

Step-by-step explanation:

Answer:

Each cereal bar weighs 16.8 oz

Step-by-step explanation:

Multiply 12 times 1.4 to get 16.8

Add 16.8 and 1.75 to get 18.55

Hope this helps! Pls mark brainliest

Answer:

2,125,760

Step-by-step explanation:

The first term (a) is 8

The fourth term is 216

Hence the sum of the first 12 term can be calculated as follows

= 8-8(3)^12/1-3

= 8-24^12/-2

= 2,125,760

The sum of first 12 terms is 2,125,760

Sum of the first 12 term  =  2,125,760

For geometric sequence,

aₙ = arⁿ⁻¹

where

a = first term

r = common ratio

n = number of terms

Therefore,

a = 8

a₄ = 216

let's find the common ratio

216 = 8 × r⁴⁻¹

216 = 8 × r³

r³ = 216 / 8

r³ = 27

r = [tex]\sqrt[3]{27}[/tex]

r = 3

Let's find sum of the first 12 terms.

Sₙ = a (rⁿ - 1) / r - 1

S₁₂ = 8(3¹² - 1) / 3 - 1

S₁₂ = 8(531440) / 2

S₁₂ = 4251520 / 2

S₁₂ = 2,125,760

read more here: https://brainly.com/question/3498087?referrer=searchResults