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2 years ago

The variance Var(x) for the binomial distribution is given by equation :

Mathematics

1 answer:

aliina [53]2 years ago

6 0

Answer: d. np(1 - p).

Step-by-step explanation:

Let x be any binomial variable which represents the number of success such that $X\sim B(n, p)$ , where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Then, the mean E(x) and the variance Var(x) for the binomial distribution is given by equation :

$E(x)=\mu=np$

$Var (x)=\sigma^2=np(1-p)$

where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Therefore , the correct option is option d. np(1 - p) .

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The manufacturer's suggested retail price (MSRP) for a particular car is $25,425, and it is expected to be

arsen [322]

Answer:

(a) The linear depreciation function of the car which gives the worth of the car y after a number of years, t is given as follows;

y = 25,425 - 2,739 × t

(b) The value of the car 7 years from now is $6,252

Step-by-step explanation:

The manufacture's suggested retail price (MSRP) for the car = $25,425

The amount the car is expected to be worth in 5 years = $11,730

(a) The linear depreciation is given as follows;

$Depreciation \ Per \ Year \ = \dfrac{Cost \ of \, Asset - Salvage \ Value}{Life \ of \, Asset \ in \ use}$

Where;

Cost of Asset = $25,425

Salvage Value = $11,730

Life of Asset in use = 5 years

We get;

$Depreciation \ Per \ Year \ = \dfrac{\$ 25,425 - \$11,730}{5} = \$2,739/year$

Therefore, the linear depreciation function, can be written as follows;

y - 25,425 = -2,739×(t - 0)

y = -2,739·t + 0 + 25,425 = 25,425 -2,739·t

y = 25,425 - 2,739 × t

Where;

y = The expected worth of the car after a given number of years

t = The number of years used for the calculation of the depreciation

(b) The value of the car 7 years from now is given by substitution as follows;

Whet t = 7, we have;

y = 25,425 -2,739·t = y = 25,425 -2,739 × 7 = $6,252

The value of the car 7 years from now = $6,252

The car is depreciating at a rate of $2,739 per year.

3 0

1 year ago

(i)Express 2x² – 4x + 1 in the form a(x+ b)² + c and hence state the coordinates of the minimum point, A, on the curve y= 2x² 4x

earnstyle [38]

Answer:

(i). $y = 2\, x^2 - 4\, x + 1 = 2\, (x - 1)^2 - 1$ . Point $A$ is at $(1, \, -1)$ .

(ii). Point $Q$ is at $\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)$ .

(iii). $\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}$ (slope-intercept form) or equivalently $x + 5\, y - 17 = 0$ (standard form.)

Step-by-step explanation:

<h3>Coordinates of the Extrema</h3>

Note, that when $a(x + b)^2 + c$ is expanded, the expression would become $a\, x^2 + 2\, a\, b\, x + a\, b^2 + c$ .

Compare this expression to the original $2\, x^2 - 4\, x + 1$ . In particular, try to match the coefficients of the $x^2$ terms and the $x$ terms, as well as the constant terms.

For the $x^2$ coefficients: $a = 2$ .
For the $x$ coefficients: $2\, a\, b = - 4$ . Since $a = 2$ , solving for $b$ gives $b = -1$ .
For the constant terms: $a \, b^2 + c = 1$ . Since $a = 2$ and $b = -1$ , solving for $c$ gives $c =-1$ .

Hence, the original expression for the parabola is equivalent to $y = 2\, (x - 1)^2 - 1$ .

For a parabola in the vertex form $y = a\, (x + b)^2 + c$ , the vertex (which, depending on $a$ , can either be a minimum or a maximum,) would be $(-b,\, c)$ . For this parabola, that point would be $(1,\, -1)$ .

<h3>Coordinates of the Two Intersections</h3>

Assume $(m,\, n)$ is an intersection of the graphs of the two functions $y = 2\, x^2- 4\, x + 1$ and $x -y + 4 = 0$ . Setting $x$ to $m$ , and $y$ to $n$ should make sure that both equations still hold. That is:

$\displaystyle \left\lbrace \begin{aligned}& n = 2\, m^2 - 4\, m + 1 \\ & m - n + 4 = 0\end{aligned}\right.$ .

Take the sum of these two equations to eliminate the variable $n$ :

$n + (m - n + 4) = 2\, m^2 - 4\, m + 1$ .

Simplify and solve for $m$ :

$2\, m^2 - 5\, m -3 = 0$ .

$(2\, m + 1)\, (m - 3) = 0$ .

There are two possible solutions: $m = -1/2$ and $m = 3$ . For each possible $m$ , substitute back to either of the two equations to find the value of $n$ .

$\displaystyle m = -\frac{1}{2}$ corresponds to $n = \displaystyle \frac{7}{2}$ .
$m = 3$ corresponds to $n = 7$ .

Hence, the two intersections are at $\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)$ and $(3,\, 7)$ , respectively.

<h3>Line Joining Point Q and the Midpoint of Segment AP</h3>

The coordinates of point $A$ and point $P$ each have two components.

For point $A$ , the $x$ -component is $1$ while the $y$ -component is $(-1)$ .
For point $P$ , the $x$ -component is $3$ while the $y$ -component is $7$ .

Let $M$ denote the midpoint of segment $AP$ . The $x$ -component of point $M$ would be $(1 + 3) / 2 = 2$ , the average of the $x$ -components of point $A$ and point $P$ .

Similarly, the $y$ -component of point $M$ would be $((-1) + 7) / 2 = 3$ , the average of the $y\!$ -components of point $A$ and point $P$ .

Hence, the midpoint of segment $AP$ would be at $(2,\, 3)$ .

The slope of the line joining $\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)$ (the coordinates of point $Q$ ) and $(2,\, 3)$ (the midpoint of segment $AP$ ) would be:

$\displaystyle \frac{\text{Change in $y$}}{\text{Change in $x$}} = \frac{3 - (7/2)}{2 - (-1/2)} = \frac{1}{5}$ .

Point $(2,\, 3)$ (the midpoint of segment $AP$ ) is a point on that line. The point-slope form of this line would be:

$\displaystyle \left( y - \frac{7}{2}\right) = \frac{1}{5}\, \left(x - \frac{1}{2} \right)$ .

Rearrange to obtain the slope-intercept form, as well as the standard form of this line:

$\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}$ .

$x + 5\, y - 17 = 0$ .

7 0

2 years ago

An angle passes through the point (-7,-5). What is the compass heading of this angle?

umka21 [38]

To find the angle use arc tan (-5/-7) which simplifies tips arctan(5/7). arc tan is tan to the power -1, which is also called inverse tan. The heading of the angle, if you drew this out on a graph your angle would be in the third quadrant and therefore the heading is south of west.

3 0

1 year ago

What is the multiplicative rate of change of the exponential function represented in the table? 1.5 2.25 3.0 4.5

Sati [7]

Use the geometric sequence formula to solve for rate:
an=a1r^(n-1)

6.75=4.5r^(2-1)
6.75=4.5r
6.75/4.5=r
r= 1.5
and if you want to make sure just multiply each number by 1.5 and see if it gets you the next number
4.5 4.5×1.5=6.75 (holds true)
6.75 6.75×1.5=10.125 (holds true)
10.125 10.125×1.5=15.1875 (holds true)
15.1875

1.5 is the multiplicatice rate hope that helps :)

8 0

2 years ago

Read 2 more answers

3.4.4 Journal: Exponential vs. Quadratic

zysi [14]

Answer:

what's the question your asking for?

5 0

2 years ago