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tia_tia [17]
3 years ago
6

An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured

the amount of natural gas used y y ( in cubic feet) to heat the home and outside temperature x x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oF o F ) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be: yˆ= y ^ = 85 + 13x. How much, on average, does gas used increase for each additional degree-day?
Mathematics
1 answer:
astraxan [27]3 years ago
6 0

Answer:

13

Step-by-step explanation:

The slope of the regression shows the average increase in response variable due to unit increase in explanatory variable. The regression equation of structure y=a+bx has slope=b.

The given regression equation y^=85+13x shows that the slope in the given equation is b=13. The response variable is amount of natural gas is used and explanatory variable is outside temperature in this case.

So, we can say that on increase of every unit of degree day the amount of gas used increase by 13 cubic feet.

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Jessamine wants to ride her bike at least 85 miles per week. She rides to and from school 5 days per week. Her house is 6.25 mil
aalyn [17]

Step-by-step explanation:

Let's translate the verbal language to algebraic language.

She rides to and from school 5 days per week, 6.25 miles each route => 5*2*6.25 miles = 62.5 miles.

She rides additioanly around the park 2.5 miles for each trip t => 2.5*t = 2.5t

Total miles of her rides per week: 62.5 miles + 2.5t

She wants to ride minimum 85 miles => 62.5 + 2.5t ≥ 85

Then, the situation is represented by this inequality:

2.5t + 62.5 ≥ 85

You can develop it and get to several equivalent inequalities, for example:

2.5t ≥ 85 - 62.5

2.5t ≥ 22.5

t ≥ 9

Any of the four forms are equivalent and a valid answer.

4 0
4 years ago
Read 2 more answers
The temperature, T, of a given mass of gas varies inversely with its Volume,V. The temperature of 98 cm ³ of a certain gas is 28
Naily [24]

Answer:

T₂ = 421.4 K

Step-by-step explanation:

The temperature, T, of a given mass of gas varies inversely with its Volume,V.

T\propto \dfrac{1}{V}\\\\V_1T_1=V_2T_2

We have,

V₁ = 98 cm³, T₁ = 28° C = (28+273) K = 301 K

V₂ = 70 cm₃

We need to find the new temperature of the gas. Using the above relation to find T₂.

T_2=\dfrac{V_1T_1}{V_2}\\\\T_2=\dfrac{98\times 301}{70}\\\\T_2=421.4\ K

Hence, the required temperature of the gas is 421.4 K.

4 0
3 years ago
0.5 and 9/18 greater than, less than, or equal
bezimeni [28]
It would be equal i think 
3 0
3 years ago
Using complete sentences, discuss the different kinds of real numbers. In your answer, glve an example of each type and discuss
Nadya [2.5K]

Answer:

Different type of real numbers include natural numbers, whole numbers, integers, irrational numbers, and rational numbers. Natural numbers are the set of numbers (1, 2, 3, 4...) also known as counting numbers. Whole numbers are natural numbers including zero (0, 1, 2, 3, 4...). Integers are the set of whole numbers and their opposites (-3, -2, -1, 0, 1, 2, 3...). Irrational numbers are numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating. An example of an irrational number is pi (3.14). A rational number is a number that can be written as a fraction. It includes integers, terminating decimals, and repeating decimals. An example of a rational number is the number 214.

Step-by-step explanation:

7 0
3 years ago
4. Christine's pet bunny ate 0.513 pounds of carrots on Friday. What is this number in word form?
kupik [55]

Answer:

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Step-by-step explanation:

It is decimals so it ends in ths and it has 3 places so it ends in thousandth. it is five hundred 13 so it is five thirteen thousandths

4 0
3 years ago
Read 2 more answers
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