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2 years ago

Find the coordinates of the midpoint of a segment with the given endpoints W(-12, -7), T(-8, -4)

2 answers:

4 0

Finding the midpoint coordinates of any segment really boils down to finding the midpoints of each individual coordinate.

The x-coordinates of the two points are -12 and -8 - the number halfway between those two is -10, so that'll be the midpoint's x-coordinate. The y-coordinates are -7 and -4 - -5.5 is halfway between these two, so the y-coordinate will be 5.5.

Putting the two together, the midpoint of the segment WT has the coordinates (-10, -5.5).

Ludmilka [50]2 years ago

3 0

You can find the midpoint with the following formula:

$\frac{x1+x2}{2}$ , $\frac{y1+y2}{2}$

Substitute the corresponding values into the formula.

$\frac{(-12)+(-8)}{2}$ , $\frac{(-7)+(-4)}{2}$

$\frac{-20}{2}$ , $\frac{-11}{2}$

-10, -5.5

The coordinates of the midpoint are (-10, -5.5).

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The equation y = 15.7x + 459 can be used to predict the cost of renting a studio apartment in a certain housing complex, where x

ohaa [14]

The answer is C) 773.00

7 0

2 years ago

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What values of c and d make the equation true? RootIndex 3 StartRoot 162 x Superscript c Baseline y Superscript 5 Baseline EndRo

Reil [10]

Answer:

c=6, d=2

Step-by-step explanation:

Equations

We must find the values of c and d that make the below equation be true

$\sqrt[3]{162x^cy^5}=3x^2y \sqrt[3]{6y^d}$

Let's cube both sides of the equation:

$\left (\sqrt[3]{162x^cy^5}\right )^3=\left (3x^2y \sqrt[3]{6y^d}\right)^3$

The left side just simplifies the cubic root with the cube:

$162x^cy^5=\left (3x^2y \sqrt[3]{6y^d}\right)^3$

On the right side, we'll simplify the cubic root where possible and power what's outside of the root:

$162x^cy^5=3^3x^6y^3 (6y^d)$

Simplifying

$x^cy^5=x^6y^{3+d}$

Equating the powers of x and y separately we find

c=6

5=3+d

d=2

The values are

$\boxed{c=6,d=2}$

3 0

2 years ago

Read 2 more answers

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

Rearrange the formula F = mg + ma for a.

Ivan

draw out a triangle and then create three boxes inside by drawing a T. In each of the boxes you've created you need to put one of the letters from the equation. The equation you currently have is F= m*a. To rearrange this equation put the m and the a into the bottom boxes and the F above. Because there is a vertical line between the m and the a, this means you times them. If there is a horizonal line between two letters you divide them. So to find a, you must divide F by m.

4 0

1 year ago

Read 2 more answers

1,250 an 15% sale an 6.5 sales tax

eimsori [14]

Given:
price = 1,250
sales discount = 15%
sales tax = 6.5%

The problem is unclear whether the price is the original price or the discounted price. I am assuming that the price is the original price.

Original price times sales discount rate is the value of sales discount
1,250 x 15% = 187.50

Original price less the value of sales discount is the discounted price.
1,250 - 187.50 = 1,062.50

Discounted price times sales tax rate is the value of the sales tax
1,062.50 x 6.5% = 69.06

Discounted price plus sales tax is the total cost of the purchase
1,062.50 + 69.06 = 1,131.56

4 0

2 years ago