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3 years ago

Solve the system by the substitution method. x + y = 2 y= x2 - 6x + 8

Mathematics

1 answer:

ruslelena [56]3 years ago

8 0

Answer:

The solution of the given system is (2,0)

Step-by-step explanation:

Here, the given system of equations is:

x + y = 2 .............. (1)

$y= x^2 - 6x + 8$ ........ (2)

Now from (1) x = 2 - y

Substitute this value of x = 2- y in (2) ,we get:

$y= (2-y)^2 - 6(2-y) + 8\\\implies y = 4 + y^2 - 4y - 12 + 6y + 8\\or, y^2 + y = 0\\\implies y(y +1) = 0$

⇒ y = 0 or, y = -1

Now, if y = 0, x = 2

and if x= -1, y = 2-(-1) = 2+1 = 3, or y = 3

But (x = -1 , y = 3 )is NOT a solution of (2).

Hence, the solution of the given system is (2,0)

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A cashier checks the price of a leather wallet that is marked $7.41, because it usually rings up to $9.88. What is the discount

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3 years ago

The Nelson Company makes the machines that automatically dispense soft drinks into cups. Many national fast food chains such as

Vika [28.1K]

Answer:

a) There is a 2.28% probability that a new cup will overflow when filled by the automatic dispenser.

b) The mean amount dispensed by the machine should be set at 16.14 ounces to satisfy this wish.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Normal model with mean 16 ounces and standard deviation 0.31 ounces. This means that $\mu = 16, \sigma = 0.31$ .

A new 16-ounce cup that is being considered for use actually holds 16.62 ounces of drink.

a. What is the probability that a new cup will overflow when filled by the automatic dispenser?

This probability is 1 subtracted by the pvalue of Z when $X = 16.62$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16.62 - 16}{0.31}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772. This means that there is a 1-0.9772 = 0.0228 = 2.28% probability that a new cup will overflow when filled by the automatic dispenser.

b. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish?

This is the value of $\mu$ , with $X = 16.62$ when Z has a pvalue of 0.94. It is between $Z = 1.55$ and $Z = 1.56$ , so we use $Z = 1.555$ .