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shutvik [7]
3 years ago
8

An umbrella sprinkler is positioned on a ceiling at a point whose x- coordinate is 0. Negative values of a indicate distances, i

n meters, to the left of the position of the sprinkler, and positive values indicate distances to the right. The path of water from the sprinkler can be modeled by the quadratic function
w(x) = -1/4(x^2 -12 ) where w(x) is the height of the water, in meters, at position x.

Required:
Which equivalent expressions displays the height of the ceiling as a constant or coefficient?
Mathematics
1 answer:
vodka [1.7K]3 years ago
8 0

Answer:

-1/4x² + 3

Step-by-step explanation:

Given that:

Path of sprinkler is modeled by the quadratic function :

w(x) = -1/4(x^2 -12 )

w(x) = height of the water, in meters, at position x

The height of ceiling as a constant or Coefficient = w(x)

Expanding w(x)

-1/4(x^2 -12 )

-1/4 * x² + 1/4 * 12

-1/4x² + 3

The height of ceiling is -1/4x² + 3

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jorge measured his heart rate after jogging he counted 11 beats during 6 second interval what was the unit rate of jorges heart
defon

Answer: 66

Step-by-step explanation:

11 beats in 6 seconds means you mulitiply the beats times the seconds

6 0
3 years ago
At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with
MatroZZZ [7]

Answer:

a)Slope: \hat \beta_1 =\frac{7625.9}{1248.9}=6.106

Intercept: \hat \beta_o = 157.955 -6.106 (69.686)=-267.548

b) r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"    

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

\sum Y_i =17375 , \sum X_i = 7665.5

Part a

The slope is given by this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

If we replace we got:

\hat \beta_1 =\frac{7625.9}{1248.9}=6.106

We can find the intercept with the following formula

\hat \beta_o = \bar y -\hat \beta_1 \bar x

We can find the average for x and y like this:

\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955

And replacing we got:

\hat \beta_o = 157.955 -6.106 (69.686)=-267.548

Part b

In order to calculate the correlation coefficient we can use this formula:  

r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}  

For our case we have this:  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

So we can find the correlation coefficient replacing like this:

r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

6 0
3 years ago
The equation P= 21 + 2w models the perimeter, P, of a rectangle with a length of / units and a width of w units.
natima [27]

Answer:

width = 10 units and length = 20 units

Step-by-step explanation:

Let the width be w

so Length will be 2w

using the rectangle formula:

\sf Perimeter \ of \ rectangle= 2L + 2W

\sf 60= 2(2w) + 2w

\sf 60= 4w + 2w

\sf 60= 6w

\sf w = 10 \ units

Find length:

\sf length = 2w

\sf length = 2(10)

\sf length = 20 \ units

5 0
2 years ago
Read 2 more answers
Alyssa had Pokemon cards. she gave 8 to her friends she now has 5 Pokemon cards left how many Pokemon cards did she have to star
Stolb23 [73]

Answer:

She had 13 pokemon

Step-by-step explanation:

5 + 8 is 13

7 0
3 years ago
Read 2 more answers
three consecutive intergers have a sum of 30. Which equation can be used to find x, the value of the smallest of three numbers
prohojiy [21]

Answer:

x+ x+1 + x+2 = 30

3x+3 =30

Step-by-step explanation:

Let x be the smallest integer

x+1 be the next smallest

x+2 be the third

x+ x+1 + x+2 = 30

Combine like terms

3x+3 =30

8 0
3 years ago
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