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GalinKa [24]
3 years ago
5

Angel borrowed $141 to buy a stereo. He pays backs $14 each week. How much does he still owes after each week? Use a graph if yo

u can
Mathematics
1 answer:
Harrizon [31]3 years ago
3 0

Logically, he would owe 14 less each week

Let x = # of weeks passed

Algebraic Expression: 141 - 14x =

Week 1: 141 - 14 = 127

Week 2: 141 - 14(2) = 113

Week 3: 141 - 14(3) = 99

etc.....

Hope this helps


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A researcher collected data on the hours of TV watched per day from a sample of five people of different ages. Here are the resu
frozen [14]

Answer:

1. The least squares regression is y = -0.1015·x + 6.51

2. The independent variable is b) age

Please see attached table

Step-by-step explanation:

The least squares regression formula is given as follows;

\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y}  \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}

We have;

\bar x = 24

\bar y = 4

\Sigma (x_i - \bar x) (y_i - \bar y) = -79

\Sigma (x_i - \bar x)^2 = 778

\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y}  \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015

The least squares regression is y = -0.1015·x + α

∴ α = y  -0.1015·x = 6 - (-0.1015 × 5) = 6.51

The least squares regression is thus;

y = -0.1015·x + 6.51

2. The independent variable is the age b)

3. Steps to create an ANOVA table with α = 0.05

The overall mean = (43  + 30  + 22  + 20  + 5  + 1  + 6  + 4  + 3  + 6 )/10 = 14

There are 2 different treatment = df_{treat} = 2 - 1 = 1

There are 10 different treatment measurement = df_{tot} = 10 - 1 = 9

df_{res} = 9 - 1 = 8

df_{treat} + df_{res} = df_{tot}

The estimated effects are;

\hat A_1 = 24 - 14 = 10

\hat A_2 = 4 - 14 = -10

SS_{treat} = 10^2 \times 5 + (-10)^2 \times 5 =1000

\sum_{i}\SS_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y)= [(1 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2] = 18

\sum_{i} S S_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y) ^2= [(43 - 24)^2 + (30 - 24)^2 + (22 - 24)^2 + (20 - 24)^2 + (5 - 24)^2] = 778

S S_{res} = \sum_{i} S S_{row}_i = 778 + 18 = 796

SS_{tot} = (43  - 14)² + (30  - 14)² + (22  - 14)² + (20  - 14)² + (5  - 14)² + (1 - 14)1² + (6  - 4 )² + (3  - 14)² + (6  - 14)² = 1796

MS_{treat} = \dfrac{SS_{treat} }{df_{treat} } = \dfrac{1000}{1} = 1000

MS_{res} = \dfrac{SS_{res} }{df_{res} } = \dfrac{796}{8} = 99.5

F- value is given by the relation;

F = \dfrac{MS_{treat} }{MS_{res} } = \frac{1000}{99.5} = 10.05

We then look for the critical values at degrees of freedom 1 and 8 at α = 0.05 on the F-distribution tables 5.3177

Hence; F = 10.05 > F_{1,8}^{Krit}(5\%) = 5.3177, we reject the null hypothesis.

7 0
3 years ago
Full explanation please<br> Will mark brainlist :)
Afina-wow [57]

Answer:B

Step-by-step explanation:

3 0
2 years ago
Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount os money on shirts.
beks73 [17]

Answer: 24$


Step-by-step explanation:

24 is the smallest common factor between 6 and 8. So to get 24 you would simply multiply 6 by 4 and 8 by 3. So Jodie bought 4 shirts while Marge bought 3.

7 0
3 years ago
Read 2 more answers
What is the slope of a line perpendicular to this line
Fynjy0 [20]

The slope of a line perpendicular to another line is the opposite reciprocal of the slope of that line. Basically, the slopes of two perpendicular lines multiply to -1. The slope of this line is -1/5. To find the slope of a line perpendicular, we need to find out what number, multiplied by -1/5, would make -1. Or, we can take the opposite reciprocal (it's the same answer). This number is 5, so the slope of a line perpendicular to this line is 5.

4 0
3 years ago
Are the two functions parallel, perpendicular, the same equation, or none of these choices? -x-3y= -18 9x-3y= -27
Dahasolnce [82]
They are perpendicular. If you normalize both functions into y=ax + b form, you get:

-x-3y=-18 => -3y = -18+x => y= 6 - 1/3 x
9x-3y=-27 -> -3y = -27-9x => y= 9 + 3 x

Just comparing the slopes, you see they are -1/3 and 3, which are each other's negative reciprokes. Negative reciprocal slopes are perpendicular.
8 0
3 years ago
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