All categories

3 years ago

If the volume is 56 1/4 cubic feet and the length is 7 1/2ft and the width is 3 3/4ft what is the height?

1 answer:

3 0

The height is 2. Multiply 7.5 by 3.75 and you should get 28.125. Divide 56.25 by 28.125 and you will get 2. If you want to check, multiply 2 by 7.5 by 3.75 and you will get 56.25.

You might be interested in

Ask me whatever you want

AnnZ [28]

Answer:

how life

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

With a short time remaining in the day a delivery driver has to make deliveries at 5 locations among the 6 locations remaining.

nika2105 [10]

The delivery driver has to make deliveries at 5 locations <span>among the 6 locations. </span>This means the order of the probability is important because the route he will take from A to B is different with A to C.
So, you need to use permutation for this problem. The calculation would be:
6P5= 6!/ (6-5)!= 720 different routes

6 0

3 years ago

If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.

klio [65]

<h3>Answer:</h3>

±12 (two answers)

<h3>Explanation:</h3>

Suppose one root is <em>a</em>. Then the other root will be -3<em>a</em>. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:

(<em>a</em>)(-3<em>a</em>) = -27/4

<em>a</em>² = -27/(4·(-3)) = 9/4

<em>a</em> = ±√(9/4) = ±3/2

Then the other root is

-3<em>a</em> = -3(±3/2) = ±9/2 . . . . . . the roots will have opposite signs

We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...

-(a + (-3a)) = b/4

2a = b/4

b = 8a = 8·(±3/2)

b = ±12

_____

<em>Check</em>

For b = 12, the equation factors as ...

4x² +12x -27 = (2x -3)(2x +9) = 0

It has roots -9/2 and +3/2, the ratio of which is -3.

For b = -12, the equation factors as ...

4x² -12x -27 = (2x +3)(2x -9) = 0

It has roots 9/2 and -3/2, the ratio of which is -3.

4 0

3 years ago

There are 15 cherry, 17 grape, and 14 orange juice boxes in the cooler. What is the probability of randomly selecting a cherry t

Art [367]

15 cherry, 17 grape, and 14 orange....total of 46 juice boxes

P(cherry) = 15/46
without replacing
P(grape) = 17/45 (I put it over 45 because since the 1st was not replaced, we have 1 less juice box)

P (both events happening) = 15/46 * 17/45 = 17/138 <==

3 0

3 years ago

Read 2 more answers

How do I find the integral<br> ∫10(x−1)(x2+9)dxint10/((x-1)(x^2+9))dx ?

defon

$\int\frac{10}{(x-1)(x^2+9)}\ dx=(*)\\\\\frac{10}{(x-1)(x^2+9)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+9}=\frac{A(x^2+9)+(Bx+C)(x-1)}{(x-1)(x^2+9)}\\\\=\frac{Ax^2+9A+Bx^2-Bx+Cx-C}{(x-1)(x^2+9)}=\frac{(A+B)x^2+(-B+C)x+(9A-C)}{(x-1)(x^2+9)}\\\Updownarrow\\10=(A+B)x^2+(-B+C)x+(9A-C)\\\Updownarrow\\A+B=0\ and\ -B+C=0\ and\ 9A-C=10\\A=-B\ and\ C=B\to9(-B)-B=10\to-10B=10\to B=-1\\A=-(-1)=1\ and\ C=-1$

$(*)=\int\left(\frac{1}{x-1}+\frac{-x-1}{x^2+9}\right)\ dx=\int\left(\frac{1}{x-1}-\frac{x+1}{x^2+9}\right)\ dx\\\\=\int\frac{1}{x-1}\ dx-\int\frac{x+1}{x^2+9}\ dx=\int\frac{1}{x-1}-\int\frac{x}{x^2+9}\ dx-\int\frac{1}{x^2+9}\ dx=(**)\\\\\#1\ \int\frac{1}{x-1}\ dx\Rightarrow\left|\begin{array}{ccc}x-1=t\\dx=dt\end{array}\right|\Rightarrow\int\frac{1}{t}\ dt=lnt+C_1=ln(x-1)+C_1$

$\#2\ \int\frac{x}{x^2+9}\ dx\Rightarrow \left|\begin{array}{ccc}x^2+9=u\\2x\ dx=du\\x\ dx=\frac{1}{2}\ du\end{array}\right|\Rightarrow\int\left(\frac{1}{2}\cdot\frac{1}{u}\right)\ du=\frac{1}{2}\int\frac{1}{u}\ du\\\\\\=\frac{1}{2}ln(u)+C_2=\frac{1}{2}ln(x^2+9)+C_2$

$\#3\ \int\frac{1}{x^2+9}\ dx=\int\frac{1}{x^2+3^2}\ dx=\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3\\\\therefore:\\\\\#1;\ \#2;\ \#3\Rightarrow(**)=ln(x-1)+C_1-\frac{1}{2}ln(x^2+9)+C_2-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3$

$\boxed{=ln(x-1)-\frac{1}{2}ln(x^2+9)-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C}$

4 0

3 years ago