Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.

6 0

2 years ago

A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation

postnew [5]

Answer: P(22 ≤ x ≤ 29) = 0.703

Step-by-step explanation:

Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = output of the machine in ounces per cup.

µ = mean output

σ = standard deviation

From the information given,

µ = 27

σ = 3

The probability of filling a cup between 22 and 29 ounces is expressed as

P(22 ≤ x ≤ 29)

For x = 22,

z = (22 - 27)/3 = - 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.047

For x = 29,

z = (29 - 27)/3 = 0.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.75

Therefore,

P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703

6 0

3 years ago

PLEASE HELP ASAP GIVING BRAINLIEST

Lady_Fox [76]

Answer:

Part 1) $y=32.5x+11.95$

Par 2) see the explanation

Part 3) $\$401.95$

Step-by-step explanation:

Part 1) Write an equation in slope intercept form to represent this problem

Let

x ----> the number of tickets

y ---> the total cost

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept (one-time processing fee)

In this problem we have

$b=\$11.95$

ordered pairs (4,141.95) and (7,239.45)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values in the formula

$m=\frac{239.45-141.95}{7-4}$

$m=\frac{97.5}{3}$

$m=32.5$

substitute the values in the linear equation

$y=32.5x+11.95$

Part 2) What does your slope represent in this problem? What does your y-intercept represent in this problem?

a) The slope of the linear equation represent the unit rate, so the slope represents the cost of one ticket

$m=\$32.5\ per\ ticket$

b) The y-intercept is the value of y when the value of x is equal to zero

In this context, the y-intercept represent the one-time processing fee

$b=\$11.95$

Part 3) Use the equation to find how much Alan would have to pay for 12 tickets

For x=12 tickets

substitute in the linear equation

$y=32.5(12)+11.95$

$y=\$401.95$

3 0

3 years ago

amanda read 15 pages of her 150-page book in 2 hours. At this rate, how long will it take her to read the entire book?

irina [24]

20 hours. You find this by dividing 150 by 10 and then multiplying that by 2.

7 0

3 years ago

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