First we must calculate the volume of the tank in cubic feet. Converting the dimensions of the box to feet, we get $1\frac{1}{2}$ feet $\times$ $2\frac{2}{3}$ feet $\times$ $2\frac{1}{4}$ feet, so the total volume is $\frac{3}{2}\times \frac{8}{3}\times \frac{9}{4}$ , or 9, cubic feet. Thus, at a rate of 6 cubic feet per minute, it would take $\frac{9}{6}$, or $1\frac{1}{2}$ minutes to fill the tank.

Correct Answers is D. Dividing both sides of the equation $V=\frac{4}{3}\pi r^3$ by $\frac{4}{3}\pi$ results in $\frac{3V}{4\pi}=r^3$. Taking the cube root of both sides produces $\sqrt[3]{\frac{3V}{4\pi}}=r$. Therefore, $\sqrt[3]{\frac{3V}{4\pi}}$ gives the radius of the sphere in terms of the volume of the sphere. Choice A is incorrect. This expression is equivalent to the reciprocal of $r^3$. Choice B is incorrect. This expression is equivalent to $r^3$. Choice C is incorrect. This expression is equivalent to the reciprocal of $r$.

Correct Answer is A. By definition of segment bisector, $AD=CD=7$. By Pythagorean Theorem we have $AB^2=BD^2+AD^2$ or $AB^2=(4\sqrt{2})^2+7^2$ so $AB=\sqrt{81}=9$ Triangle ABC is isosceles so $AB=BC=9$ and perimeter of $\triangle ABC$ is $AB+BC+AC=9+9+14=32$

Correct Answer is A. In a right-angled isosceles triangle, the sides of the right angle are equal. Now, in the given rightangled isosceles triangle $\triangle ABC$, $\angle B$ is given to be the right angle. Hence, the sides of the angle, $AB$ and $BC$, are equal. Applying The Pythagorean Theorem to the triangle yields
$AB^2+BC^2=AC^2$
$BC^2+BC^2=(7\sqrt{2})^2$
$BC=7$
Hence, $AB = BC = 7$.

Correct answer is : A. Start by isolating the constant onto one side $x^2+12x+y^2-4y=-15$ then complete the squares for $x$ and $y$, we obtain $(x^2+12x+36)+(y^2-4y+4) =-15+36+4$ or $(x+6)+(y-2)^2=25$. The center of the circle $(-6,2)$ and the radius is $\sqrt{25}$ or $5$.