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-Dominant- [34]
2 years ago
10

A classic children's toy consists of 13 different blocks that combine to form a rectangle showing a man's face. Each block has f

our sides with alternatives for that part of the face; for example, the block for the right eye might have a closed eye on one side, a partially open eye on another, and so on. A child can turn any block and so change that part of the face, and in this way many different faces can be formed.
How many different faces can be formed by the children's toy?
Mathematics
1 answer:
Gwar [14]2 years ago
8 0

Answer: 67,108,863 combinations.

Step-by-step explanation:

We have 13 blocks.

Each block has 4 differet options.

The total number of combinations is equal to the product of the options for each variable (the variables are the 13 blocks) so we have that the number of combinations is:

C = 4*4*4*4*4*4*4*4*4*4*4*4*4 = 4^13 = 67,108,863

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A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (80
miskamm [114]

Answer:

\epsilon = 3.958\times 10^{-3}

Step-by-step explanation:

The Young's Module of Aluminium is E = 69\times 10^{9}\,Pa. The axial stress on the specimen is:

\sigma = \frac{F}{A_{t}}

\sigma = \frac{35500\,N}{(0.01\,m)\cdot (0.013\,m)}

\sigma = 2.731\times 10^{8}\,Pa

The strain is derived of following expression:

\epsilon = \frac{\sigma}{E}

\epsilon = \frac{2.731\times 10^{8}\,Pa}{69\times 10^{9}\,Pa}

\epsilon = 3.958\times 10^{-3}

4 0
2 years ago
Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly
eimsori [14]

Answer:

11.58%

Step-by-step explanation:

The initial volume if blood flowing through the artery is given by

V=kr^4

To achieve a new volume of 155% (55% increase) of the initial volume, the new radius must be:

V'= 1.55V\\1.55V=k(r')^4\\1.55kr^4 = k(r')^4\\(\sqrt[4]{1.55}*r)^4=(r')^4 \\(1.1158*r)^4=(r')^4 \\r'=1.1158*r

Since the new radius is 1.1158 times larger than the initial radius, the percentage increased is:

I=(1.1158 - 1)*100\%\\I= 11.58\%

7 0
2 years ago
A woman's weekly salary is increased from $350 to $380. The percent of increase is most nearly
Kay [80]

Find the amount of the difference and then divide it by the original amount:


380 - 350 = 30


30 / 350 = 0.0857 = 8.6% increase.  Round the answer as needed.



3 0
2 years ago
In △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP . Find the area of △ABC if the area of △BMP
ddd [48]

M is mid point of CP. M will divide the \Delta BPC in two equal parts \Delta BMC and    \Delta BMP.

Area of \Delta BMP is equal to 21m^2

Since, \Delta BMC = \Delta BMP

Area of  \Delta BPC = Area of  \Delta BMC +Area of \Delta BMP =  21 + 21 = 42m^2

and since ratio of AP:BP =1:3  so the area of \Delta BMP will be 1/3 of Area of \Delta ABC

hence, Area of \Delta ABC = 63m^2

5 0
1 year ago
Read 2 more answers
A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft, and it weighs 50 lbs. T
Lady_Fox [76]

Answer:

116 units of the first product

380 units of the second product

Step-by-step explanation:

Product 1 has a unit volume of  10 cu ft

Product 2 has a unit volume of 3 cu ft

The truck has 2300 cu ft of space

Product 1 weighs 50 lbs

Product 2 weighs 40 lbs

The truck can carry 21000 lbs

Let X be the units of product 1

Let Y be the units of product 2

The given information can be expressed as:

10X+3Y=2300...(1)

50X+40Y=21000...(2)

Solving the system of equations:

10X+3Y=2300...(1)

10X=2300-3Y

X=(2300-3Y)/10

Substituting X in (2) we have:

50X+40Y=21000

50[(2300-3Y)/10]+40Y=21000

50[(2300/10)-(3Y/10)]+40Y=21000

50[230-(3Y/10)+40Y=21000

11500-(150Y/10)+40Y=21000

11500-15Y+40Y=21000

11500+25Y=21000

25Y=21000-11500

25Y=9500

Y=380

Substituting Y in (1) we have:

10X+3Y=2300...(1)

10X+3(380)=2300

10X+1140=2300

10X=2300-1140

10X=1160

X=116

So 116 units of the first product and 380 units of the second product can be transported in a single shipment with one truck.

8 0
2 years ago
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