Does the residual plot suggest a linear relationship?

Answer:

94 cm2

Step-by-step explanation:

Base x Width x height

4 x 5 x 3

Answer:

A: 94 cm2

Step-by-step explanation:

the surface area is 94 cm2

Answer:

45 sides

Step-by-step explanation:

If each of the interior angles is 172 degrees, then each of the exterior angles is 8 degrees. Since the sum of the exterior angles of any polygon is 360 degrees, there are 360 / 8 = 45 exterior angles and 45 sides.

Answer:

645/100 = 129/20 or 6.45

645/50 = 129/10 or 12.9

48.6/30 = 1.62

48 divided by x = 48.6/x

Step-by-step explanation:

645/100

Factor the number:

= 5*129/100

Factor the number:

= 5*129/5*20

Cancel the common factor:

= 129/20

645/50

Factor the number:

5*129/50

Factor the number:

5*129 / 5*10

Cancel the common factor:

= 129/10

48.6/30

Write the problem in long division format

Multiply the quotient digit (1) by the divisor (30)

Subtract 30 from 48

Add a decimal and bring down the next number

Divide 186 by 30 to get 6

Continue...A few steps later...

Subtract 60 from 60

Solution is 1.62

48.6/x

Re-write division as a fraction:

48.6/x

Answer:

There are 14 horses and 21 chickens.

Step-by-step explanation:

First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :

(horse has 4 feet and chicken has 2 feet)

There are a total of 35 heads so the other equation will be :

Lastly, you have to solve it :

Final answer:

The equation 'M = 0.6666 log x - 3.2' describes the relationship between the energy produced by an earthquake (x) and its resulting magnitude (M). The 0.6666 in the formula is the growth factor. To get a magnitude for a specific energy level, we plug the energy value into the formula, and solve.

Explanation:

The equation given represents the relationship between the magnitude of an earthquake (M) and the energy it produces (x), with M being the earthquake's magnitude and x being the energy produced by the earthquake. This equation is a logarithmic model with a base of 10 (without the base explicitly stated, we assume it to be 10).

1. The curve representing the relationship includes the point: To identify a point, we need a specific x-value for the energy level. For instance, for x=1000, we can plug it into the equation to get the magnitude M = 0.6666 log(1000) - 3.2.
2. The growth factor is: In this context, the growth factor refers to the constant 0.6666 which is multiplied by the logarithm. This factor impacts the rate at which the magnitude of the earthquake grows for a given increase in energy.
3. An earthquake with an energy level of (an x-value should be inserted here) has a magnitude of: We would again plug the energy value (x-value) into the formula, compute the expression to determine the corresponding magnitude.

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Answer:

Step-by-step explanation:

(a) For n = 6, CL = 90%,  

The degrees of freedom: 5, Critical t-value: 2.571

(b) For n = 21, CL = 98%,

The degrees of freedom: 20, Critical t-value: 2.845

(c) For n = 29, CL = 95%,

The degrees of freedom: 28, Critical t-value: 2.048

(d) For n = 12, CL = 99%,

The degrees of freedom: 11, Critical t-value: 3.106

Use the concept of critical t- value defined as:

A critical value is a number that is used in hypothesis testing to compare to a test statistic and evaluate whether or not the null hypothesis should be rejected. The null hypothesis cannot be rejected if the test statistic's value is less extreme than the crucial value.

(a) Given that,

n = 6 and a confidence level of 90%,

The degrees of freedom are,

n-1 = 6-1

The degrees of freedom = 5.

To find the critical t-value,

Look it up in the t-distribution table using a confidence level of 90% and a degree of freedom of 5.

From the table,

The critical t-value is approximately 2.571.

(b) Given that,

n = 21 and a confidence level of 98%,

The degrees of freedom are,

n-1 = 21-1

The degrees of freedom = 20.

By referring to the t-distribution table with a confidence level of 98% and degrees of freedom of 20,

The critical t-value is approximately 2.845.

(c) Given that,

n = 29 and a confidence level of 95%,

The degrees of freedom are,

n-1 = 29-1

The degrees of freedom = 28

Using the t-distribution table with a confidence level of 95% and degrees of freedom of 28,

The critical t-value is approximately 2.048.

(d) Given that,

n = 12 and a confidence level of 99%,

The degrees of freedom are,

n-1 = 12-1

The degrees of freedom = 11

By consulting the t-distribution table with a confidence level of 99% and degrees of freedom of 11,

The critical t-value is approximately 3.106.

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Final answer:

To find the degrees of freedom and critical t-value for each given sample size and confidence level, we can use the t-distribution and a t-table. The degrees of freedom (df) for each sample is equal to the sample size minus 1. The critical t-value can be found using the t-table with the corresponding degrees of freedom and the confidence level.

Explanation:

To find the degrees of freedom and critical t-value for each given sample size and confidence level, we can use the t-distribution and a t-table. The degrees of freedom (df) for each sample is equal to the sample size minus 1. For example, for (a) n = 6, df = 6 - 1 = 5. The critical t-value can be found using the t-table with the corresponding degrees of freedom and the confidence level.

For (a) n = 6, CL = 90%, the critical t-value is approximately 1.943.

For (b) n = 21, CL = 98%, the critical t-value is approximately 2.861.

For (c) n = 29, CL = 95%, the critical t-value is approximately 2.045.

For (d) n = 12, CL = 99%, the critical t-value is approximately 3.106.

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