A rectangular sheet of paper had a width of 841 millimetres.

A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00. If we wa

Sedbober [7]

Answer:

The t-score is 1.96

Step-by-step explanation:

The margin of error is given as

(Margin of Error) = (critical value) × (standard deviation of the sample mean)

The critical value is usually obtained from the t-score or the z-score at the given confidence level.

With small sample sizes (sample sizes less than 30) and/or information about the population standard deviation is not known, the t-distribution is used to find critical values.

We convert the confidence level to significance level and use the sample size to trace out the t-score.

Significance level = (1 - confidence level)/2

For example, a confidence level of 95% mean that 5% (spread equally at the top and bottom of the distribution as 2.5% and 2.5%) is still room for error, hence, the significance level = (5%/2) = 2.5%

This information, with the sample size, directs one exactly to where to obtain the t-score for the distribution on the t-score table.

But, with large sample sizes, with known information about its standard deviation, we typically use critical values on the Z-distribution to obtain the margin of error.

And as the sample size increases, the t-score approximates the z-score.

So, for a sample size of 100, the t-score can be simply obtained from the z-score table for a confidence level of 95%; and that is 1.96.

Hope this Helps!!!

6 0

3 years ago

Simplify by combining like terms. 2(3y − 5) + 8 − 6y

Romashka-Z-Leto [24]

Answer:

-2

Step-by-step explanation:

8 0

4 years ago

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Palindrome numbers are numbers that read the same foward or backward. Here are some palindrome numbers: 11, 121, 75257, and 1234

KatRina [158]

Answer:

99.

Step-by-step explanation:

A palindrome number is one that can be read in the same way both from the front and from the back. A clear example is the number 242, which starts and ends in the same way from the front or back.

Between 10 and 100, there are 9 palindromes, from 11 to 99. In turn, between 100 and 200, 200 and 300 and so on, each hundred has within it 10 palindromes (101, 111, 121, 131, 141 , 151, 161, 171, 181 and 191, for example).

Therefore, considering the 9 hundreds between 100 and 1000, there will be 90 palindromes, which added to the 9 between 10 and 100 give a total of 99 palindromes.

6 0

3 years ago

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its x-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the x-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

3 0

3 years ago

The thrift store is selling their old DVDs. When the DVDs first came out, they sold for $19. They have now been marked down by 7

Luda [366]

Step-by-step explanation:

original price (100%) → $19

discounted price ((100-75)%) = (25%) → 25% x $19 = $4.75

8 0

3 years ago

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