How many lines of symmetry does the figure have?

Use the quadratic formula to solve. Round to the nearest tenth if necessary.<br> 2x^2 -3x -7 = 0

abruzzese [7]

The quadratic formula is:

$\frac{-b + \sqrt{b^2 - 4ac} }{2a}$ and $\frac{-b - \sqrt{b^2 - 4ac} }{2a}$

In this case, a = 2, b = -3, and c = -7

So, we can plug in the numbers to get:

$\frac{-(-3) + \sqrt{(-3)^2 - 4(2)(-7)} }{2(2)}$ and $\frac{-(-3) - \sqrt{(-3)^2 - 4(2)(-7)} }{2(2)}$

Simplifying, we get:

$\frac{3 + \sqrt{65} }{4}$ and $\frac{3 - \sqrt{65} }{4}$

You need to use a calculator to find what these would be in decimal form. The answer, rounded to the nearest tenth, is: x = 2.8, x = -1.3

8 0

2 years ago

The bottom layer of a rectangular prism contains 15 unit cubes The prism is made up of 5 equal-size layers what is the volume of

borishaifa [10]

Answer:

75 cubic units

Step-by-step explanation:

Bottom layer of a rectangular prism is made up of 15 unit cubes.

Therefore, area of the 15 unit cubes = 15(area of the base of one unit cube)

= 15(1)²

= 15 unit²

Number of layers of unit cubes in the rectangular prism = 5

So the height of the prism = 5 units

Volume of the prism = (Area of the base) × Height

= 15 × 5

= 75 cubic unit

6 0

2 years ago

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$