The medicine capsule consists of a cylinder with a hemisphere at each end. The total length of the capsule is 18 millimeters. The diameter is 7 millimeters. Which choice is the best approximation of the total surface area of the capsule? Use 3.14 to approximate pi. possible answers a)396 square millimeters b)550 square millimeters c)1,407 square millimeters d)1,099 square millimeters

Answers

Answer 1

Answer: Given:
diameter: 7 mm
total length = 18 mm

There are two shapes in this problem.
1) a sphere
2) a rectangle shaped cylinder

We need to get the area of both shapes to have the best approximation of the total surface area of the capsule.

Area of a sphere = 4 π r² = 4 * 3.14 * (3.5mm)² = 12.56 * 12.25mm²
Area of a sphere = 153.86 mm²

Area of a rectangle = length * width
*in this case, we need to compute for the circumference of the circle to get the measure of the width

Area of a rectangle = (18-7mm) * 7 * 3.14
Area of a rectangle = 11mm * 7mm * 3.14
Area of a rectagnle = 241.78 mm²

Total surface area = 153.86 mm² + 241.78 mm² = 395.64 mm²

Choice A.) 396 square millimeters.

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Answers

Answer:

Factor $x^(4)$ −2401

$x^(4)$ −2401

=( $x^(2)$ +49)(x+7)(x−7)

it takes 1 gallon of diesel 1 fuel for a cruise ship to trarel 6 inches how many gallons will it take for the cruise ship to travel 1 mile

Answers

considering that there are 63360 inches in one mile I can divide that by 6 inches to get 10560 gallons of diesel fuel

Which correctly describes how the graph of the inequality 5x + 2y ≥ 13 is shaded? (1 point) Above the solid line Below the solid line Above the dashed line Below the dashed line

Answers

Answer:

The graph of inequality $5x+2y\geq 13$ is above the solid line.

Step-by-step explanation:

Step-by-step explanation:

An inequality on a coordinate plane consist of a boundary line and an area in which each point is a possible solution.

* If the inequality has a sign or , then the line will be a solid line and its point are included in the solution.

* If the inequality has a sign '>' or '<' , then the line will be a dotted line and its point are not included in the solution.

Given: The linear inequality: $5x+2y\geq 13$

Then, the equation of the boundary line is; 5x+2y =13 ......[1]

we can write this as;

$2y = -5x+13$

Divide by 2 we get;

$y = -(5)/(2) x + (13)/(2)$ ......[2]

Compare this boundary line equation with the general point slope intercept line i.e, y = mx+b where m is the slope and b is the y-intercept.

Therefore, the slope of the this line is, m = $-(5)/(2)$

and a y-intercept (b) = $(13)/(2)$ = 6.5

To find x -intercept:

Substitute y =0 in to solve for x;

$5x+0 =13$

Simplify:

$x =(13)/(5) = 2.6$

Therefore, the x-intercept is 2.6

Now,

Plot $y = -(5)/(2) x + (13)/(2)$ ( as a solid line because $y\geq$ included equal to)

and shade the area above as $5x+2y\geq 13$ as shown below in the graph

The answer is above the solid line.
Tip: On problems like these, go to the website, desmos.com, press the big red button that says "Start Graphing", and you can graph any equation by typing it in on the side and it show you the graph to get the answer!

A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers. The margin of error for the population proportion is ± _____%.

Answers

In a survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employer, the margin of error for the population proportion is ± seventeen (17) or ± 5.67%.

Answer:

Step-by-step explanation:

Given that A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers

i.e. sample size n =300

Sample proportion p = 0.10

q=1-p=0.9

Std error = $\sqrt{(pq)/(n) } =\sqrt{(x0.1(0.9))/(300) } \n=0.01732$