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romanna [79]
3 years ago
7

Dean needs 6060 inches of wood to build a rectangular picture frame.

Mathematics
1 answer:
Hitman42 [59]3 years ago
5 0
What we know:
Perimeter=60
Perimeter formula=2l+2w
l=2w

This perimeter has the following set up using p=60 and l=2w:
perimeter =2(l)+2w
60=2(2w)+2w 
60=4w+2w
60=6w

Now that we know how many w's we need to have we can use this information to find which equations have 6 w's and which one does not.
Look at the first equation:
2(2w+w)=60         distributive power
4w+2w=60               like terms
6w=60                       correct

second equation:
w+2w+w+2w=60
6w=60              like terms, correct

third equation:
2w+2x2w=60            multiplication property
2w+4w=60                  like terms
6w=60                          correct

fourth equation:
w+2w=60                     like terms
3w=60                              not correct

Fourth equation is not correct.
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A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to
Fantom [35]
A geometry program can show you the total displacement is about 10.14 miles.

_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
   4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

_____
If you want to do it by hand, you can recognize the sum will be
   7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by 
   displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
   = (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
   = (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
   = (7, -3) + 0.707107*(-1, -7)
   = (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
   d = √(6.2929² +(-7.9497)²) ≈ √102.7990
   d ≈ 10.1390 . . . . miles

4 0
3 years ago
What is the experamental probability that the coin lands on heads?
sammy [17]

Answer:

The experamental probability that the coin lands on head is 50 %

Step-by-step explanation:

Given:

Experiment:

A coin is Toss

Let the Sample Space be 'S' that is total number of outcomes for a coin has been tossed = { Head, Tail }

∴ n ( S ) =  2

Let A be the event of getting a Head on tossing a coin i.e  { Head }

∴ n( A ) = 1

Now,

\textrm{Probability} =\frac{\textrm{outcomes for the experiment}}{\textrm{total number of outcomes}}

Substituting the values we get

P(A) = \frac{n(A)}{n(S)} \\\\P(A) = \frac{1}{2} \\\\P(A) = 0.5\\\\P(A) = 50\%

The experamental probability that the coin lands on head is 50 %

5 0
3 years ago
Graph the line with slope<br> −1/2<br> and y-intercept 3.
joja [24]

Step-by-step explanation:

m=-1/2

b(0,3)

mark (0,3)then go down 1 and 2 to the right as in positive side

6 0
3 years ago
A term account earns 3.6%, compounded daily for 3 years. If the amount is $8411.02 at the end of the 3 year period, what was the
ValentinkaMS [17]

Answer:

7550

Step-by-step explanation:

AV=PV(1+\frac{i}{n} )^{nt}\\8411.02=PV(1+\frac{.036}{365})^{365*3}\\8411.02= PV*1.114\\PV= 7550

5 0
3 years ago
Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]
insens350 [35]
The given function is 
f(x) =  x - ln(8x), on the interval [1/2, 2].

The derivative of f is
f'(x) = 1 - 1/x
The second derivative is 
f''(x) = 1/x²

A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0  => 1/x = 1  => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079

The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2)  = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.

Answer: 
Minimum value  = 1 - ln(8)
Maximum value = 2 - ln(16)


4 0
3 years ago
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