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4 years ago

13

A marble is selected at random from a jar containing 50 red marbles, 30

1 answer:

Nikolay [14]4 years ago

7 0

Answer:

7/10 or 70%

Step-by-step explanation: There is 100 marbles in total and 70 red and green marbles, 70 times out of 100 is the same as 7 times out of 10. Thus, 7/10 or 70%.

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Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 288 cub

ratelena [41]

Answer:

The minimum cost is $17.30c

Step-by-step explanation:

Given

$V = 288$ --- Volume

$C_1 = 0.06$ --- cost of wall paint

$C_2 = 0.16$ ---cost of ceiling paint

Required

Minimum cost of paint

The volume is calculated as:

$V =xyz$

Substitute 288 for V

$288 =xyz$

Make z the subject

$z = \frac{288}{xy}$

The surface area is calculated as:

$Area = 2(yz + xz) + xy$

Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2

The cost is:

$C = 0.06 * 2(yz + xz) + 0.16 * xy$

Substitute $z = \frac{288}{xy}$

$C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy$

$C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy$

$C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy$

$C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy$

$C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy$

Differentiate w.r.t x and y

$C_x = -\frac{34.56}{x^2} + 0.16y$

$C_y = -\frac{34.56}{y^2} + 0.16x$

By comparison: $x = y$

Set them equal to 0

$C_y = -\frac{34.56}{y^2} + 0.16x=0$

$-\frac{34.56}{y^2} + 0.16x=0\\$

Substitute x for y

$-\frac{34.56}{x^2} + 0.16x=0$

$0.16x=\frac{34.56}{x^2}$

Cross multiply

$0.16x^3 = 34.56$

$x^3 = \frac{34.56}{0.16}$

$x^3 = 216$

Take the cube root of both sides

$x = \sqrt[3]{216}$

$x = 6$

$x=y= 6$

Substitute 6 for x and for y in $C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy$

$C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6$

$C = (\frac{2*34.56}{6}) + 5.76$

$C = 11.52 + 5.76$

$C = 17.28$

$C = 17.3$ --- approximated

8 0

3 years ago

Help. As usual i suck at math.

Blababa [14]

Answer:

(4,6) is the solution.

Step-by-step explanation:

Given $4x + y = 10$

Let the solution be $(a,-6)$ .

The solution to this line means it should satisfy the equation. Therefore, substituting this we get,

$4(a) - 6 = 10$

$\implies 4a = 16$

Dividing by 4 throughout we get,

$a = 4$

Therefore, the solution is: (4,6)

6 0

3 years ago

How does the graph of g(x) = (x + 4)3 − 6 compare to the parent function f(x) = x3?

Solnce55 [7]

Answer:

g(x) is shifted 6 units to the left

Step-by-step explanation:

Lets try to simplify g(x) since has a few extra terms:

g(x)= 3x+12-6=3x+6

Now it is easier to compare the two functions.

We can tell that they both have the same slope, both differs on a extra term

This term tell us that the g(x) is shifted to the left (it is positive 6)

Another approach to the solution is to plot the two functions together by obtaining the crossing points with the 'y' axis and with the 'x' axis

the result is shown in the attached picture

4 0

4 years ago

Read 2 more answers

Benito wants to buy a car. He is considering two different models, Model Ais 5 ft wide. Model B is 87 in, wide. Express the widt

enyata [817]

Model B is wider Bc it’s 7.25 ft

6 0

4 years ago

1. What is the greatest number that can be rounde<br>to the nearest thousands?

Xelga [282]

Answer:

10000.

Step-by-step explanation:

i think.. i may be wrong.

4 0

3 years ago