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Tpy6a [65]
3 years ago
11

For the following paired data, (1) Calculate the correlation coefficient, r, and (2) at the 0.05 significance level, determine w

hether there exists a linear correlation.x | 2 4 5 6y | 6 9 8 10
Mathematics
1 answer:
expeople1 [14]3 years ago
7 0

Answer:

Linear correlation exists

Step-by-step explanation:

Given the data :

X : | 2 4 5 6

Y : | 6 9 8 10

Using technology to fit the data and obtain the correlation Coefficient of the regression model,

The Correlation Coefficient, r is 0.886

To test if there exists a linear correlation :

Test statistic :

T = r / √(1 - r²) / (n - 2)

n = number of observations

T = 0.886 / √(1 - 0.886²) / (4 - 2)

T = 0.866 / 0.3535845

T = 2.449

Comparing Pvalue with α

If Pvalue < α ; Reject H0

Pvalue = 0.1143

α = 0.05

Pvalue > α ; We reject the null and conclude that linear correlation exists

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Step-by-step explanation:

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3 years ago
2. Use the following picture for this question:
Art [367]

Answer:

a.  24\sqrt{3}  and 41.6

b.  52.1

Step-by-step explanation:

a.

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

<u>Note:</u> the exact value of tan 60 is \sqrt{3}

Thus, we can write Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}

Approximate value (rounded to nearest tenth):  24\sqrt{3} =41.6

b.

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1

4 0
3 years ago
Need all answers for 1, 2, 3, 4 , 5. Who ever answers them first will be mark brainliest!
Anettt [7]

answer

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EXPLANATION

5 0
3 years ago
Need an answer as soon as possible.
Elza [17]
Part A

Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
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Ashley made 2 out of 4 total shots. What percent of her shots did she make?
morpeh [17]

Answer:

50%

Step-by-step explanation:

4 is equal to 100

2 is half of 4

100 ÷ 2 = 50

3 0
3 years ago
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