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Ira Lisetskai [31]
2 years ago
8

6 is 4% of what number?

Mathematics
1 answer:
Ahat [919]2 years ago
8 0

Answer:

150

Step-by-step explanation:

since 4 percent would have to be multiplied by 25 to get 100 you have to multiply 6 by 25. This comes out to 150. You can even check this by doing 150 times 0.04 which is 6 so we are correct!

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g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur
sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

\displaystyle V = \pi r^2h

Substitute:

\displaystyle (300) = \pi r^2 h

Solve for <em>h: </em>

\displaystyle \frac{300}{\pi r^2} = h

Recall that the surface area of a cylinder is given by:

\displaystyle A = 2\pi r^2 + 2\pi rh

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for <em>h</em>.

\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r}  \end{aligned}

Find its derivative:

\displaystyle A' = 4\pi r - \frac{600}{r^2}

Solve for its zero(s):

\displaystyle \begin{aligned} (0) &= 4\pi r  - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

\displaystyle  \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2}  \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm}   \end{aligned}

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

7 0
3 years ago
Which expression is equivalent to 48 + 54?
Debora [2.8K]

48 + 54 = 102

102 / (8+9) = 6

48 + 54 = 6 x (8+9)

6 can be written on the blank line to make the expressions equivalent.

can i please get brainlist

6 0
2 years ago
Read 2 more answers
Mr Thompson plans to invest $7,500 in a savings account that earns 2.75% simple annual interest. If he makes no other deposits o
attashe74 [19]
Mr.Thompson's account will be worth $9,562.50 after 10 years.
3 0
2 years ago
Find the area of a circle whose circumference is 24 pi.
lozanna [386]

Answer:

452.39 sq.unit is the area of that circle.

6 0
3 years ago
Mr. Scruggs got some money for his birthday. He spent 1/5 of it on dog treats. Then, he divided the remainder equally among his
Mariulka [41]

Answer:

a. \frac{4a}{15}

b. $225

Step-by-step explanation:

Let Mr. Scruggs got money for his birthday be 'a'

He spent \frac{1}{5} of it on dog treats = a × \frac{1}{5}

                                                                      = \frac{1}{5}a

remainder amount would be = a - \frac{1}{5}a

                                                = \frac{4a}{5}

Then he divided the remainder money equally among 3 favorite charities.

\frac{\frac{4a}{5}}{3}

= \frac{4a}{15}

a. Each charity receive \frac{4a}{15}

b. If he donated $60 to each charity.

\frac{4a}{15}=60

a=\frac{15\times 60}{4}

a = $225

Mr. Scruggs received $225 for his birthday.

6 0
3 years ago
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