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2 years ago

6

Toby is making a picture graph. each picture of a book is equal to 2 bookso he has read. the row for month 1 has 3 pictures of b

ooks. how many books did Toby read during month 1

2 answers:

lozanna [386]2 years ago

8 0

It has to be nine because 2 times 3 is 9

Nata [24]2 years ago

3 0

The answer is 6 because in adding 2+2+2=6 and in multiplicating is 2*3=6

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A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

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

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

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Imagine you conducted a study to look at the association between whether an expectant mother eats breakfast (or not) and the gen

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Answer:

: The percentage of newborn infants who are exclusively breastfed at the time of hospital discharge.

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Footnotes: The year indicated is the mid-year of a five-year period of data.

Step-by-step explanation:

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The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304

shtirl [24]

Answer:

B. 152 cm²

Step-by-step explanation:

To find the surface area using a net, do this:

Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ( $A=l*w$ ) and then add the values together:

The first rectangle on the left is the same as the one on the right.

$5*8=40$

Two measures are 40 cm².

The middle rectangle is:

$6*8=48$

48 cm²

The formula for the area of a triangle is $A=\frac{1}{2}*b*h$ :

$A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12$

The area of the two triangles is 12 cm².

Now add the values:

$40+40+48+12+12=152$

The area of the figure is 152 cm².

:Done

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A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground. If it goes 12

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Answer:

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