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Annette [7]
3 years ago
11

NASA performed aerodynamic and acoustic tests of two and three-dimensional airfoil blade sections. These tests were conducted in

an anechoic wind tunnel. One input (X) measured was the free-stream velocity, in meters per second. The output (Y ) was scaled sound pressure level, in decibels. From this data, we found the following values: µX = 50.86; µY = 124.8; σXY = 13.44; σX = 15.57; σY = 6.90. (a) Find the value of the correlation coefficient to 3 decimals. (b) Is the linear relationship / association between X and Y strong, weak, or is there no relationship? (c) Is there a positive linear relationship, negative linear relationship, or no linear relationship?
Mathematics
1 answer:
Svetlanka [38]3 years ago
4 0

Answer:

a) ρ (X,Y) = 0.125

b)  The linear relationship is weak because ρ (X,Y) is almost 0

c) There is a positive linear relationship because ρ (X,Y) > 0

Step-by-step explanation:

The Pearson correlation coefficient is calculate as :

ρ (X,Y) = (σXY) / (σX)(σY)

-1 ≤ ρ ≤ 1

When ρ = 0 there is no linear relationship between the variables. This does not mean that the variables are independent.

When ρ = 1 the linear relationship is perfect positive. ρ = 1 means a direct relation between X and Y : When X increases also Y increases in constant proportion. When Y increases also X increases in constant proportion.

When ρ = -1 the linear relationship is perfect negative. ρ = -1 means a inverse relation between X and Y : When X increases Y decreases in constant proportion. When Y increases X decreases in constant proportion.

In our exercise ρ (X,Y) = 13.44 / (15.57)(6.90) = 0.125

a) ρ (X,Y) = 0.125

b)  The linear relationship is weak because ρ (X,Y) is almost 0

c) There is a positive linear relationship because ρ (X,Y) > 0

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skelet666 [1.2K]
Answer: 8 m/s

First let’s convert the time to seconds. There are 69 seconds in a minute so 1 minute and 40 seconds is 60 +40 second which totals to 100 seconds
Now to get the speed in meters per second we divide the total meters run by the total seconds
So the speed will be 800m/100s = 8m/s
7 0
3 years ago
Find the indicated term of the given arithmetic sequence. a1=45, d= -3, n=10
klasskru [66]

In this sequence, we're given the first term, which is 45.

The difference between each term is -3, which means 3 will be subtracted in each term.

We're asked to find the value of the tenth term, and we can do so by using this formula:

a(n) = a(1) + d(n - 1)

Replace values.

a(10) = 45 + -3(9)

a(10) = 18

<h3>The value of the tenth term is 18.</h3>
3 0
3 years ago
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A wooden board 100 centimeters long is cut into two pieces. One piece is 16 centimeters longer than the other. What are the leng
Bezzdna [24]

x = the length of one piece

y = the length of the other piece


the total length is 100 cm this means 


x + y = 100


one piece is 16 inches longer than the other


first we need to convert inches to cm: 


1 in = 2.54 cm

16 in = 2.54*16 = 40.64


now we can write


x = y + 40.64


by solving the system of equations


x + y = 100

x = y + 40.64


we find


x = 70.32 cm


y = 29.68 cm


the lengths of the two pieces are 70.32 cm and 29.68 cm.

4 0
3 years ago
What is the answer to this sum 5/6 of 120
ELEN [110]
100 is the correct answer
6 0
3 years ago
Please help me in this questions....​
Ivahew [28]

Part (i)

I'm going to use the notation T(n) instead of T_n

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

<h3>Answers: -1, -4</h3>

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer:  21st term</h3>

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>
4 0
3 years ago
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