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Naddika [18.5K]

3 years ago

8

A unit of gas costs 4.2 pence on averge ria uses 50.1 units of gas a week she pays for the gas she uses in 13 weeks work out an

estimsate for the amount ria pays

1 answer:

padilas [110]3 years ago

5 0

Answer:

Step-by-step explanation:

Cost per unit of gas = 4.2 pence

Average units of gas used per week = 50.1 units

Total cost of gas per week = Cost per unit of gas × Average units of gas used per week

= 4.2 pence × 50.1

= 210.42 pence

= £ 2.1042

Amount ria pays for gas for 13 weeks = cost of gas per week × number of weeks

= 210.42 pence × 13

= 2,735.46 pence

2,735.46 pence = £ 27.3546

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Step-by-step explanation:

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3 years ago

An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the ra

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Answer:

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Step-by-step explanation:

From the information given we know the probability mass function (pmf) of random variable X.

$\left|\begin{array}{c|ccc}x&16&18&20\\p(x)&0.3&0.1&0.6\end{array}\right|$

<em>Point a:</em>

The Expected value or the mean value of X with set of possible values D, denoted by <em>E(X)</em> or <em>μ </em>is

$E(X) = $\sum_{x\in D} x\cdot p(x)$

Therefore

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by <em>E[h(X)]</em> is computed by

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)$

So $h(X) = X^2$ and

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)\\E[X^2]=$\sum_{D}x^2\cdot p(x)\\ E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6\\E(X^2)=349.2$

The variance of X, denoted by V(X), is

$V(X) = $\sum_{D}E[(X-\mu)^2]=E(X^2)-[E(X)]^2$

Therefore

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<em>Point b:</em>

We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:

From the rules of expected value this proposition is true:

$E(aX+b)=a\cdot E(x)+b$

We have a = 60, b = -650, and <em>E(X)</em> = 18.6. Therefore

The expected price paid by the next customer is

$60\cdot E(X)-650=60\cdot 18.6-650=466$

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3 years ago