What is 19% of 103?

(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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The distance covered by the train in 3.5 seconds will be 1575 feet.

What is speed?

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A train travels 45 feet in 1/10 in a second.

Then the speed will be

Speed = 45 / (1/10)

Speed = 45 x 10

Speed = 450 feet per second

The distance covered by the train in 3.5 seconds will be

Distance = 450 x 3.5

Distance = 1575 feet

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Answer:

1575 ft

Step-by-step explanation:

Convert 1/10 to decimal to make the math simpler.

1/10 = 0.1

Divide 3.5 by 0.1.

3.5/0.1 = 35

Multiply 35 by 45.

35 × 45 = 1575

The train will travel 1575 feet in 3.5 seconds.

Answer:

(a) 1 - (15 C 6) / (30 C 6)

(b)  (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Step-by-step explanation:

Number of  nickels = 5

Number of dimes = 10

Number of quarters = 15

(a) The probability of getting 6 quarters  

= (15 C 6) / (30 C 6)

So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)

(b) Probability of getting 2 nickels , 2 dimes and 2 quarters

= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

We have been given that Catherine's employer matches 25% of her 401(k) contributions or a maximum of $2000. Further we are given that Catherine's salary is $50,000 and she contributed $10,000 to her 401(k) plan.

Let the contribution form her employer be $x. We are given that her employer matches 25% of Catherine's contribution under 401(k) plan. Therefore, contribution made by employer would be either 25% of 10,000 or 2000, whichever is lesser.

Let us find 25% of 10,000.

Since 25% of 10,000 is more than 2000, therefore, Catherine's employer would make a contribution of $2000.