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4 years ago

In the formation of the four basic conics, the intersecting plane

Mathematics

1 answer:

Damm [24]4 years ago

5 0

Answer:

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According to industry sources, online banking is expected to take off in the near future. The projected number of households (in

Airida [17]

Answer:

(a) The least-square regression line is: $y=4.662+2.709x$ .

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

$y=\alpha +\beta x$

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

(a)

The formula to compute intercept and slope is:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}$

The values of ∑X, ∑Y, ∑XY and ∑X² are computed in the table below.

Compute the value of intercept and slope as follows:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}$

The least-square regression line is:

$y=4.662+2.709x$

(b)

For the year 2007 the value of x is 10.

Compute the value of y for x = 10 as follows:

$y=4.662+2.709x$

$=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8$

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

5 0

3 years ago

Order the group of quadratic functions from widest to narrowest graph y=3^2, y=5^2, y=7^2

Sedbober [7]

Y = 7^2
y = 5^2
y = 3^2

if wide is the greatest and narrow means smallest then i hope its right

Ur Welcome and if its wrong plz let me know and i will fix it,
xXharleyquinn04Xx

7 0

3 years ago

Is anyone good at geometry if so can you help me please ?

Pachacha [2.7K]

The arcs FA, AB, and BF make up the entire circle, so their measures sum to 360°:

arcFA + arcAB + arcBF = 360° → arcBF = 360° - 160° - 140° = 60°

By the inscribed angle theorem, angle BAF has measure equal to half of that of arc BF, so

angleBAF = 30°

By the secant-tangent theorem (not sure if there's an official name for it), the measure of angle ACF is equal to half the difference of the arcs it intercepts, namely BF and FA, so that

angleACF = 1/2 (arcFA - arcBF) = 1/2 (160° - 60°) = 50°

Now use the law of sines for solve for FA:

sin(angleACF) / FA = sin(angleBAF) / FC

sin(50°) / FA = sin(30°) / 10

FA = 10 sin(50°) / sin(30°) ≈ 15.3

3 0

3 years ago

What is 5/8 as a mixed number

Paul [167]

It can’t be a mixed number

3 0

3 years ago