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Paul [167]
3 years ago
10

You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You al

so know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
Mathematics
1 answer:
Naddika [18.5K]3 years ago
5 0

Answer:

y = 7.8x + 26

Step-by-step explanation:

Given the following :

Pearson's r = 0.78

Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams

Average weight = 65 kg with standard deviation of 15kg

Formular for the regression line :

General regression formula :

y = mx + c

y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept

Gradient (m) = change in y / change in x

m = (sd y / sd x) * r

m = (sd weight / sd ice cream) × r

m = (15 / 1.5) × r

m = 10 × 0.78 = 7.8

Intercept:

mean of weight(y) - [Slope×mean of icecream(x)]

65 - [7.8 × 5]

65 - 39 = 26

Hence,

y = 7.8x + 26

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The shape below is a composite figure made up of two rectangular prisms, what is the volume of the figure?
gregori [183]

Answer:

<u>11098 cm³</u>

Step-by-step explanation:

<u>Volume of top prism</u>

  • V = 62 x 3 x (13 - 7)
  • V = 186 x 6
  • V = 1116 cm³

<u>Volume of bottom prism</u>

  • V = 62 x 23 x 7
  • V = 1426 x 7
  • V = 9982 cm³

⇒ Total volume = Volume (top) + Volume (bottom)

⇒ Total volume = 1116 + 9982

⇒ Total volume = <u>11098 cm³</u>

5 0
2 years ago
Read 2 more answers
Help help help help help ASAP
Rufina [12.5K]

Answer:

No, it is much too low

5 0
3 years ago
How do you solve this?
puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let x represent the width.

Since the length is 7 feet longer, we can represent the length by x+7.

Now that we have our values for the length and the width we can multiply them together to find our area.

(x)(x+7)=x^{2} +7x

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

(x+7)(x+14)

And multiply our area by 3.

3(x^{2} +7x)

set these equal to each other to find your new equation.

(x+7)(x+14)=3(x^{2} +7x)

Now you need to solve for x. To do this first muliply (x+7) and (x+14).

(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98

Then multiply 3(x^{2} +7x)

3(x^{2} +7x)=\\3x^{2} +21x

Now you can begin solving for x.

x^{2} +21x+98=3x^{2} +21x

Subtract x^{2} from both sides.

21x+98=2x^{2} +21x

Subtract 21x from both sides.

98=2x^{2}

Divide by 2.

49=x^{2}

And finally take the sqaure root of both sides.

\sqrt{x^{2} }=\sqrt{49}\\x=7

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of x, we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

7 0
3 years ago
F(x) = x2. What is g(x)?
vladimir1956 [14]

Answer:

Step-by-step explanation:

C

5 0
3 years ago
Is there an.expert answerer who can help me with this
nlexa [21]
I think the answer is 2,612.48 because if you multiply the radius, 80 by itself you get 640. Then if you multiply 640 by 3.14 and then multiply the product by 1.3 you get 2,612.48.
4 0
3 years ago
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