A sphere and cylinder have the same radius and height. The volume of the cylinder is 30m^3. What is the volume of the sphere?

Screen-printing a batch of shirts requires 3 minutes per shirt in addition to 12 minutes of initial set-up time. If it takes 45

Furkat [3]

Answer:

11 shirts

Step-by-step explanation:

Since 12 of the 45 minute are devoted to setup, the actual printing time is 33 minutes. At 3 minutes per shirt, that's enough time for ...

(33 min)/(3 min/shirt) = 11 shirts

A batch consists of 11 shirts.

_____

<em>Alternate solution</em>

Another way to consider this is to realize that the setup time is the time required to print 4 shirts. 45 minutes would be enough time to print 45/3 = 15 shirts, but the time for 4 shirts is spent setting up. That leaves the batch size at 15 -4 = 11 shirts.

4 0

3 years ago

please help me figure out how to determine the range of the following graph (the line y=5 is a horizontal asymptote)

prisoha [69]

we are given the graph of the function and we are interested in finding the range of the function. Recall that the range of a graph is simply the set of values on the y axis, for which there is a point on the graph that has that y coordinate.

One easy way to spot this set, is by taking any point on the graph and then drawing a horizontal line. Wherever the line crosses the y axis, that point is included in the range.

From the graph, we can see that no part of the graph has values with y coordinate less than 5. That is, any number less than 5 in the y coordinate would indicate that there is no point on the graph at that "height". So every number less than 5 is excluded from the range.

We are also told that line y=5 is a horizontal asymptote. This means that despite the graph is really close to the line y=5 (and it keeps getting closer and closer as x increases), it never touches the line. This means that the point 5 is excluded from the range.

Finally, we can see that above the horizontal line y=5, if we draw a horizontal line on the graph, it will touch the y axis. This means that every number greater than 5 is part of the range. Then, the set of numbers that represent the range is

$(5,\text{infinity)}$

4 0

1 year ago

Find the perimeter of the figure below composed of an isoceles trapezoid and one semicircle rounded to the nearest tenth place.

MArishka [77]

Answer:

πr + (4+6+6+8) = 2π+24=30.28

8 0

3 years ago

You operate a non-profit foodbank that accepts food donations and packages them into meals for local families who are food insec

Fofino [41]

Answer:

Step-by-step explanation:

Binomial distribution is to be used here due to following reasons.

(a)

Probability of sending a box to an experienced inspector

= Probability of getting non-zero unacceptable cans

= 1 - Probability of getting zero unacceptable cans

=1- P(X = 0) = 1 - 10.08^0 *(1 – 0.08)^(4-0) = 0.283607

(b)

Expected cost per inspector in an hour in case of 8% unacceptable cans

= {(1-0.283607)*16+0.283607*22} = $ 17.70164

If groceries reduce their unacceptable rate to 4% then X - Bin(4, 0.04) .

In this scenario,

Probability of sending a box to an experienced inspector

= Probability of getting non-zero unacceptable cans

= 1 - Probability of getting zero unacceptable cans

=1- P(X = 0) = 1 - 0.04^0 * (1 – 0.04)*(4-0) = 0.150653

Expected cost per inspector in an hour in case of 4% unacceptable cans

= {(1-0.150653)*16+0.150653*22} = $ 16.90392

Percentage of savings realized = (17.70164-16.90392)/17.70164*100% = 4.506475%

7 0

3 years ago

What is the constant of proportionality in the equation y=3xy=3xy, equals, 3, x?

snow_lady [41]

Answer:

k=3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In this problem we have

$y=3x$

therefore

The constant of proportionality is k=3

6 0

3 years ago