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2 years ago

7

Mrs. Winter's students reported the amount of time they spent reading last night. The line plot shows the fraction of an hour ea

ch student spent reading. How much total time did Mrs. Winter's students spend reading last night?

1 answer:

ad-work [718]2 years ago

5 0

Answer:

A. 10:45 HOURS

Step-by-step explanation:

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A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

2 years ago

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!!

Over [174]

9514 1404 393

Answer:

b. -150

Step-by-step explanation:

We usually take elevation to be positive above sea level, and negative below sea level. If the elevation is below sea level, it is negative. If it is within 200 ft of sea level, the magnitude of the negative number is 200 or less. That is, the elevation must satisfy ...

-200 ≤ elevation < 0

The only answer choice in that range is -150.

Ethan's elevation in feet could be -150.

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2 years ago

What amount of money will accumulate to $192,400 in 6 years and 11 months at the interest rate of 5.36% compounded semi-annually

MaRussiya [10]

We will have the following:

$\begin{gathered} 192400=A(1+\frac{0.0536}{2})^{(11/12)(2)}\Rightarrow A=\frac{192400}{(1+0.0536/2)^{(11/12)(2)}} \\ \\ \Rightarrow A=183293.7505...\Rightarrow A\approx18329375 \end{gathered}$

So, the original quantity was approximately $183 293.75.

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5 months ago

Which equation represents this situation?

Anika [276]

Answer:

I would say...

C.)x - 5 = 3 (x + 2)

Really really sorry if I'm wrong...

One thing I can say is that when it says 5 less than a #, that means the # is being subtracted from another #...

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2 years ago

List the ordered pairs and determine whether or not this is a function

Ahat [919]

The ordered pairs are (1,-1) (1,-2) (2,-3) (2,-4).

This is not a function because in order to be a function, every x value needs to have one and only one y value. You can see here that the x values have two y values, so it is not a function.

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2 years ago