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3 years ago

Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5

Mathematics

1 answer:

adell [148]3 years ago

8 0

Answer:

The solution for the inequality is $x \leq 6$ .

Step-by-step explanation:

Consider the provided inequality.

$2x - 1 \leq x + 5$

Subtract x from both the sides.

$2x -x- 1 \leq x-x + 5$

$x- 1 \leq 5$

Add 1 to both the sides.

$x- 1+1 \leq 5+1$

$x \leq 6$

Hence the solution for the inequality is $x \leq 6$ .

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Help. How do u convert units within a measurement system

Triss [41]

Step 1. Identify the unit you have
Step 2. Identify the unit you want to covert to
Step 3. Count the number of units between them

(If you are going from a larger unit to a smaller unit, you multiply by 10 successively.)

4 0

3 years ago

The table showing the stock price changes for a sample of 12 companies on a day is contained in the Excel file below.

AfilCa [17]

Answer:

(a) The sample variance for the daily price change is 0.2501.

(b) The sample standard deviation for the daily price change is 0.5001.

Step-by-step explanation:

Let the random variable X denote the stock price changes for a sample of 12 companies on a day.

The data provided is:

X = {0.82 , 1.44 , -0.07 , 0.41 , 0.21 , 1.33 , 0.97 , 0.30 , 0.14 , 0.12 , 0.42 , 0.15}

(a)

The formula to compute the sample variance for the daily price change is:

$s^{2}=\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}$

The sample mean is computed using the formula:

$\bar X=\frac{1}{n}\sum\limits^{12}_{i=1}{X_{i}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample mean and sample variance are:

$\bar X$ =AVERAGE(A2:A13)

$s^{2}$ =VAR.S(A2:A13)

Thus, the sample variance for the daily price change is 0.2501.

(b)

The formula to compute the sample standard deviation for the daily price change is:

$s=\sqrt{\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample standard deviation is:

$s$ =STDEV.S(A2:A13)

Thus, the sample standard deviation for the daily price change is 0.5001.

(c)

The (1 - α)% confidence interval for population variance is:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

Compute the critical value of Chi-square for α = 0.05 and (n - 1) = (12 - 1) = 11 degrees of freedom as follows:

$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2,11}=21.920$

$\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{(1-0.05/2),11}=\chi^{2}_{0.975,11}=3.816$

*Use a Chi-square table.

Compute the 95% confidence interval estimates of the population variance as follows:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

$=[\frac{(12-1)\times 0.2501}{21.920 } \leq \sigma^{2}\leq \frac{(12-1)\times 0.2501}{3.816} ]$

$=[0.125506\leq \sigma^{2}\leq 0.720938]\\\approx [0.1255, 0.7210]$

Thus, the 95% confidence interval estimates of the population variance is (0.1255, 0.7210).

7 0

4 years ago

Terri is starting a babysitting service to make some extra money. She plans to charge a base fee of $10 plus $7 per hour. Write

antoniya [11.8K]

Given:

Terri plans to charge a base fee of $10 plus $7 per hour for babysitting.

To find:

The function that could be used to represent her total charge for the babysitting service, y, as a function of the number of hours she babysits, x.

Solution:

Let y be the total charge for the babysitting service for x hours.

Base fee = $10

Additional fee for one hour = $7

Additional fee for x hour = $7x

Total fee = Base fee + Additional fee for x hours

$y=10+7x$

Therefore, the equation of required function is $y=10+7x$ .

6 0

3 years ago

Anyone know #3 for me I’m stuck

steposvetlana [31]

<h3>Answers: 4, 3, 2</h3>

Each number gets its own box, and the values are entered in that exact order.

============================================================

Explanation:

x and y are placeholders for numbers.

If we replace x with -1, then we get

y = -x+3

y = -(x)+3

y = -(-1)+3 ... replace x with -1

y = 1+3

y = 4

This means that x = -1 leads to y = 4. So we'll write 4 underneath the "-1" in the y row.

------------------------

Similarly, if x = 0, then

y = -x+3

y = -0+3

y = 0+3

y = 3

Leading to 3 being the next item we input.

------------------------

Finally, if x = 1, we get this y value

y = -x+3

y = -1+3

y = 2

Which is the last value in the bottom row.

------------------------

The order of the y values in the bottom row is therefore: 4, 3, 2

This means the points (-1, 4), (0, 3), and (1, 2) are on the line y = -x+3.

Side note: The equation y = -x+3 has slope -1 and y intercept 3.

5 0

3 years ago

Somebody please help me

Art [367]

Answer:

66°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°.

79° +x +35° = 180°

x = 180° -114° . . . . . . . . subtract 114° from both sides

x = 66° . . . . . simplify

8 0

2 years ago

Read 2 more answers