7 Question Find the value of x.

What are the formulas to calculate acceleration A. velocity and time B. displacement and time C. Change in distance and time D.

scZoUnD [109]

The correct choice is A

6 0

3 years ago

A lidless box is to be made with a volume of 256256 ft cubed 3. Find the dimensions of the box that requires the least amount of

sveta [45]

The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.

The dimensions of your box will be 8 ft square by 4 ft high.

_____

If the base dimension is x ft, the area (quantity of material) is

... a = x² + 4x(256/x²)

... a = x² + 1024x⁻¹

Then the derivative of area with respect to x is

... a' = 2x -1024x⁻²

Setting this derivative to zero and solving for x gives the value of x for minimum area.

... 0 = 2x -1024/x²

... 512 = x³

... x = 8 . . . . . . . . same as above.

7 0

2 years ago

Need help please! Will give it to the brainliest. Which expression models the bacterium's volume? Picture is below.

Tomtit [17]

The expression C. $\pi (1)^{2} (0.5)$ cubic $\mu \mathrm{m}$ represents the bacterium's volume.

Step-by-step explanation:

Step 1:

The E. Coli bacterium is in the shape of a cylinder.

The volume of a cylinder is given by multiplying π with the square of the radius (r²) and the height of the cylinder.

The volume of a cylinder, $V=\pi r^{2} h.$

In the given diagram, E. Coli has a radius of 1 $\mu \mathrm{m}$ and a height of 0.5 $\mu \mathrm{m}$ .

Step 2:

By substituting the values in the equation, we get

The volume of the E. Coli bacterium $= \pi (1)^{2} (0.5)$ cubic $\mu \mathrm{m}$ .

This is option C.

7 0

3 years ago

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

attashe74 [19]

Answer:

$0.424 - 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.286$

$0.424 + 2.58\sqrt{\frac{0.424(1-0.424)}{85}}=0.562$

The 99% confidence interval would be given by (0.286;0.562)

Step-by-step explanation:

Information given:

$X= 36$ represent the families owned at least one DVD player

$n= 85$ represent the total number of families

$\hat p=\frac{36}{85}= 0.424$ represent the estimated proportion of families owned at least one DVD player

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by: