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1 year ago

You buy a new laptop for $300. The sales tax is 6%. What is the total cost for the laptop including the sales tax?

Mathematics

1 answer:

ladessa [460]1 year ago

6 0

Answer: Total cost incurred on new laptop is $318.

Explanation:

Since we have given that

Cost price of new laptop = $300

Sales tax = 6%

total cost of laptop including the sales tax is given by

$Cost\times \frac{100+\text{ sales tax}}{100}$

so,

$\text{ Cost price including the sales tax }\\\\=300\times \frac{100+6}{100}\\\\=300\times \frac{106}{100}\\\\=\$318$

So, total cost incurred on new laptop is $318.

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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;

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

Where;

SSR = The Sum of Squared Regression ≈ 21.9884

SST = The total variation in the sample ≈ 37.96

Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925

The coefficient of determination, R² ≈ 0.57925.

Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925

6 0

2 years ago

In the figure, polygon ABCD is transformed to create polygon A’B’C’D’. This transformation is a

BartSMP [9]

reflection transformation i believe. Correct me if im wrong im not that smart lol.

6 0

2 years ago

If a large cylinder has a volume of 28260 cubic cm, how many cylinders can be filled out of the large cylinder if the small cyli

inysia [295]

Hi,

To find the number of small cylinders that fit inside the big cylinder. You need to divide volume of small cylinder with the volume of big cylinder. We do this by using formula to calculate volume of cylinder:

$v = \pi \times {r}^{2} \times h$

To find radius just divide diameter with 2.

$v = \pi \times {2}^{2} \times 6 \\ v = \pi \times 4 \times 6 \\ v = \pi \times 24 \\ v = 3.14 \times 24 \\ v = 75.4 {cm}^{3}$

Now just division:

$28260 \div 75.4 = 374.8$

Answer: You could fit 374.8 smaller cylinders inside a big cylinder.

Hope this helps.
r3t40

7 0

2 years ago

Peter mixes 4 1/2 cups of orange juice, 2 1/4 of ginger ale and 6 1/3 cups of strawberry lemonade to make some punch. What is th

ruslelena [56]

To add these amounts together, we must first find their least common multiple in order to get common denominators (b/c when you add fractions, the denominators must be the same).

We'll start by listing some of their multiples.
To do this, count by whatever the denominator is:
4 1/2 (denominator is 2): 2 4 6 8 10 12 14
2 1/4 (denominator is 4): 4 8 12 16
6 1/3 (denominator is 3): 3 6 9 12 15

Look and see which is the first multiple that all three denominators have. Circle them if it helps you. In this case, it's 12.

So now we have to multiply the denominators by whatever number it takes to reach 12, and multiply by the same number to the numerator:

4 1/2 (times 6 to both top and bottom) =
4 6/12

2 1/4 (times 3) = 2 3/12

6 1/3 (times 4) = 6 4/12

Add all these fractions together, and you get 12 13/12, which is equal to 13 1/12.

Thus, Peter makes a total of 13 1/2 cups.

Hope this made sense! tell me if anything is confusing/incorrect :))

8 0

2 years ago

Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all T-shirts are $10 each. He has $100 to spend and w

Tatiana [17]

Answer:32

Step-by-step explanation:

8 0

2 years ago