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katovenus [111]
3 years ago
9

You originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to

be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.
Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer:

  the other dimension is 4.2 inches

Step-by-step explanation:

The scale factor from 5 inches to 10.5 inches is ...

  10.5/5 = 2.1

Then the other dimension is 2 inches times that scale factor:

  2.1×(2 in) = 4.2 in

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard dev
Vladimir [108]

Answer:

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

                Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean = 30.05 inches

           \sigma   = standard deviation = 0.2 inches

             n = sample of sheets = 4

So, Probability that average length of a sheet is between 30.25 and 30.35 inches long is given by = P(30.25 inches < X bar < 30.35 inches)

P(30.25 inches < X bar < 30.35 inches)  = P(X bar < 30.35) - P(X bar <= 30.25)

P(X bar < 30.35) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{30.35-30.05}{\frac{0.2}{\sqrt{4} } } ) = P(Z < 3) = 0.99865

 P(X bar <= 30.25) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } <= \frac{30.25-30.05}{\frac{0.2}{\sqrt{4} } } ) = P(Z <= 2) = 0.97725

Therefore, P(30.25 inches < X bar < 30.35 inches)  = 0.99865 - 0.97725

                                                                                       = 0.0214

                                       

7 0
3 years ago
Let v be an eigenvector of a matrix A with a corresponding eigenvalue ?=2. Find one solution x of the system Ax=v.
Murljashka [212]

Answer with explanation:

For, a Matrix A , having eigenvector 'v' has eigenvalue =2

 The order of matrix is not given.

It has one eigenvalue it means it is of order , 1×1.

→A=[a]

Determinant [a-k I]=0, where k is eigenvalue of the given matrix.

It is given that,

k=2

For, k=2, the matrix [a-2 I] will become singular,that is

→ Determinant |a-2 I|=0

→I=[1]

→a=2

Let , v be the corresponding eigenvector of the given eigenvalue.

→[a-I] v=0

→[2-1] v=[0]

→[v]=[0]

→v=0

Now, corresponding eigenvector(v), when eigenvalue is 2 =0

 We have to find solution of the system

→Ax=v

→[2] x=0

→[2 x] =[0]

→x=0, is one solution of the system.

5 0
3 years ago
I need help!!!!!!!!!!!!!
never [62]

Answer:

The perimeter is 38 but it gets rounded to 40

Step-by-step explanation:

7 0
2 years ago
23) m 2 = 7x + 6<br>70°​
lakkis [162]

Answer:

∠2 = 55°

Step-by-step explanation:

Given that the triangle has 2 congruent sides then the triangle is isosceles.

Thus the 2 base angle are congruent, both equal to ∠2

The sum of the 3 angles in a triangle = 180

7x + 6 + 7x + 6 + 70 = 180, that is

14x + 82 = 180 ( subtract 82 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

Hence

∠2 = 7x + 6 = (7 × 7) + 6 = 49 + 6 = 55°

3 0
3 years ago
How many letters are in this sentence that you are reading right now?
Mila [183]

Answer:

56 letters

Step-by-step explanation:

6 0
2 years ago
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