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Katena32 [7]
3 years ago
8

1. Which of the following triangles is classified as a right triangle?

Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

a triangle witih side lengths of 12,16,20

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A person measured the depth of water in a bathtub at two minute intervals after the tap was turned on. Use the line of best fit
Leto [7]

Answer:

The Depth of water in the bathtub initially = 2 cm

Step-by-step explanation:

For this question, we want to f8nd the amount of water present in the bathtub at time t = 0 using line of best fit, that is, linear regression analysis.

The table provided shows that the depth of water in the bathtub (y) changes as time (x) progresses.

Time (min) (x) | 2 | 4 | 6 | 8 | 10 | 12 | | 14

Depth (cm) (y) | 8 | 15 | 29 | 37 | 39 | 49 | 55

Running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.

Σxᵢ = sum of all the independent variables (sum of all the time data)

Σyᵢ = sum of all the dependent variables (sum of all the depth data)

Σxᵢyᵢ = sum of the product of each dependent variable and its corresponding independent variable

Σxᵢ² = sum of the square of each independent variable (time data)

Σyᵢ² = sum of the square of each dependent variable (depth data)

n = number of variables = 7

The scatter plot and the line of best fit is presented in the second attached image to this solution

Then the regression analysis is then done

Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]

Intercept b = [Σyᵢ - m×(Σxᵢ)] / n

Mean of x = (Σxᵢ)/n

Mean of y = (Σyᵢ) / n

Sample correlation coefficient r: r =

[n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}

And -1 ≤ r ≤ +1

All of these formulas are properly presented in the third attached image to this answer

The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.

The linear regression equation obtained is then

y = 3.911x + 1.857

at a regression coefficient of 0.987 (the closer the value is to 1, the more accurate the equation obtained)

So, the Depth of water in the bathtub initially, that is, when t = x= 0,

y = 3.911x + 1.857

y = 3.911(0) + 1.857 = 1.857 cm = 2 cm to the nearest integer.

Hope this Helps!!!

3 0
3 years ago
What is the value of Y ?
gtnhenbr [62]

Answer:

y=7

Step-by-step explanation:

Since y "b" of the triangle is x and the hypotenuse is 2x, you can divide 14 by 2 and get 7, the answer.

7 0
3 years ago
Solve the following equation:<br> 1/3(y - 2) -5/6 (y + 1) =3/ 4(0 - 3) - 2
Evgesh-ka [11]

Answer:

11/5

Step-by-step explanation:

If you need help with more problems like this you can use m a t h w a y. (remove the spaces)  :)

8 0
3 years ago
In a class of 40 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose
ladessa [460]

Answer:3

Step-by-step explanation:

Given

There are total 40 students in a class

No of students with Pierced Nose n(N)=7

No of students with Pierced ear n(E)=36

and we know using sets

n\left ( N\cup E\right )=n\left ( E\right )+n\left ( N\right )-n\left ( N\cap E\right )

where n\left ( N\cup E\right )=Students either nose or ear Pierced

n\left ( N\cap E\right )=no of students having both nose and ear pierced

40=7+36-n\left ( N\cap E\right )

n\left ( N\cap E\right )=43-40=3

3 0
3 years ago
The area of a circular place is 45 square inches. Estimate the radius to the nearest integer
GREYUIT [131]
The radius to the nearest integer is 22.5 square inches
7 0
3 years ago
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