Help please inequalities are kicking my butt any help is greatly appreciated thank you in advance

Mathematics

1 answer:

Hitman42 [59]3 years ago

7 0

Answer:

Correct option is (C)

Step-by-step explanation:

we are given that -Tim design a pair of shorts,S, and T-shirts,t.

Tim sell Sorts for $12 and T-shirts for $8 each.

Tim can work atmost 18 hours a day so we can write $time\leq 18$

Time taken to design a T-shirt is 30 minutes and for Shorts, it is 45 minutes.

$\frac{30}{60}t+\frac{45}{60}s\leq 18\\\text{Multiply both the sides by 60}\\30t+45s\leq 1080\\\text{Divide both the sides by 45}\\s+0.66t\leq 24\\\text{Subtract 0.66t from both the sides}\\s\leq 24-0.66t$

He must design 12 itesm each day, so we can write $t+s\geq 12$

Further it can be written as

$t+s\geq 12\\\text{Subtract t from both the sides}\\s\geq 12-t$

Also Tim can not design more than 30 items in one day, so we can write

$t+s\leq 30\\\text{Subtsract t from both the sides}\\s\leq 30-t$

Hence from the above equations , its claer that

$s\geq 12-t,s\leq 30-t,s\leq 24-0.66t,s\geq 0,t\geq 0$

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Exact value of the function for the given x-value f(x) = 5x for x = -1

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Sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.

Mrrafil [7]

Answer:

C. 128/3 meters cubed

Step-by-step explanation:

The volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:

$V=\pi r^2h$

$64=\pi r^2h$

We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with 2r:

$64=\pi r^2h$

$64=\pi r^2*2r=2\pi r^3$

$\pi r^3=64/2=32$

Now, the volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius. From above, we know that $\pi r^3=32$ , so we can plug this into the equation: