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3 years ago

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The sum of Kyra's and Caleb's ages is 37. Caleb's age is equal to twice the quantity of Kyra's age decreased by 4. Let k represe

nt Kyra's age.
Complete each expression to represent the situation.

Kyra's age: , 1 of 3.
Select Choice
years

Caleb's age: , 2 of 3.
Select Choice
(k − , 3 of 3.
Select Choice
) years

Part B
Add the two expressions and set this sum equal to 37 to model the situation with an equation. Solve for k. How old is Kyra?

1 answer:

frosja888 [35]3 years ago

7 0

Based on the given conditions, formulate:
Rearrange unknown terms to the left side of the equation:
Combine like terms:
Calculate the sum or difference:
Divide both sides of the equation by the coefficient of variable:
Answer: k=41/3

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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