When Jennifer spent 3/7 of her money, she has $72 left. How much money did Jennifer start with?

2. A boy and his father played 26 games of checkers. For every game the boy lost, he gave his father 5 cents. For every game the

trasher [3.6K]

Answer: the boy won 10 games

Step-by-step explanation:

Let's call B as the number of games won by the boy, and F as the number of games won by the father.

We know that, there is a total of 26 games:

B + F = 26.

We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:

B*8 + F*(-5) = 0.

Then we have a system of equations:

B + F = 26

8*B - 5*F = 0.

The first step is isolating one of the variables. Let's start isolating F in the first equation:

B + F = 26

F = 26 - B.

Now we can replace this in the second equation:

8*B - 5*F = 0

8*B - 5*(26 - B) = 0

8*B + 5*B - 5*26 = 0

13*B = 5*26

B = 5*26/13 = 5*2 = 10

So the boy won 10 games (then the father won the other 16 games)

7 0

2 years ago

A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies'

Sindrei [870]

Answer:

(i) The estimated regression equation is;

$\hat y$ ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that $\hat y$ increase by a multiple of 0.0604 for each million dollar increase in sales, X

(ii) The estimated earnings for the company is approximately $4.7096 million

(iii) The standard error of estimate is approximately 29.34

The high standard error of estimate indicates that individual mean do not accurately represent the population mean

(iv) The coefficient of determination is approximately 0.57925

The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925

Step-by-step explanation:

The given data is presented as follows;

$\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}$

(i) From the data, we have;

The regression equation can be presented as follows;

$\hat y$ = b₀ + b₁·x

Where;

b₁ = The slope given as follows;

$b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}$

b₀ = $\overline y$ - b₁· $\overline x$

From the data, we have;

${\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}$ = 364.05

$\Sigma(x_i - \overline x)^2}$ = 6,027.259

$\overline y$ = 4.2

$\overline x$ = 41.5625

∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005

b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69

Therefore, we have the regression equation as follows;

$\hat y$ ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales

(ii) For the small company, we have;

X = $50.0 million, therefore, we get;

$\hat y$ = 1.6896 + 0.0604 × 50 = 4.7096

The estimated earnings for the company, $\hat y$ = 4.7096 million

(iii) The standard error of estimate, σ, is given by the following formula;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}$

Where;

n = The sample size

Therefore, we have;

$\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34$

The standard error of estimate, σ ≈ 29.34

The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean

(iv) The coefficient of determination (R Square) is given as follows;

$R^2 = \dfrac{SSR}{SST}$