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andre [41]
3 years ago
5

The table of vaules represents a linear function g(x) where X is the number of days that have passed and g(x) is the blance in t

he bank account x vaules 0,3,6 G(x) vaules $600,$720,840
Part A Find the interpert the slope of the function

Part B write equation of the line in point slope, slope - intercept and standard forms

Part C write equation of the line using function notation

Mathematics
1 answer:
Step2247 [10]3 years ago
8 0

Answer:

Step-by-step explanation:

The slope formula is

m=\frac{y_2-y_1}{x_2-x_1}

Filling in this formula with 2 different points 2 times will ensure that this is fact a linear function. In other words, if the slope comes up the same between points 1 and 2 and then between points 2 and 3, this is linear.

Between (0, 600) and (3, 720) the slope formula is

m=\frac{720-600}{3-0}=\frac{120}{3}=40  and

m=\frac{840-720}{6-3}=\frac{120}{3}=40 So this is in fact linear because the slopes are the same.

Interpreting a slope is similar to interpreting a unit ratio. In our case, the slope means that after the initial investment in the account, $40 per day (there's the unit rate I was referring to) is deposited into the account.

Using that slope to write first the point-slope form of the line allows us to use any one of the 3 coordinates to write the equation. I use (0, 600). In point-slope form:

y-600=40(x-0)

That's point-slope form. Now for slope-intercept form, which is the same as solving for y.

y - 600 = 40x - 0 and

y = 40x + 600. That's slope-intercept, and now for standard form. Standard form follows the format of a. No fractions and b. Both the x and y terms go on the same side of the equals sign and the constant on the other.

We move the x term over to the y side:

-40x + y = 600. But a lot of textbooks don't like to lead with a negative, so the equivalent form of this with a positive leading coefficient is

40x - y = -600 (notice that all we did was change ALL the signs to the opposite of what they were, not just the sign on the x term. Very important!!)

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An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 51% of passengers have no c
Orlov [11]

Answer:

The average revenue per passenger is about $13.85

μ = $13.85

The corresponding standard deviation is $14.51

σ = $14.51

The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Expected revenue = $1,662 ± 14.51

Step-by-step explanation:

An airline charges the following baggage fees:

$25 for the first bag and $35 for the second

Suppose 51% of passengers have no checked luggage,

P(0) = 0.51

33% have one piece of checked luggage and 16% have two pieces.

P(1) = 0.33

P(2) = 0.16

a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.

The average revenue per passenger is given by

μ = 0×P(0) + 25×P(1) + 35×P(2)

μ = 0×0.51 + 25×0.33 + 35×0.16

μ = 0 + 8.25 + 5.6

μ = $13.85

Therefore, the average revenue per passenger is about $13.85

The corresponding standard deviation is given by

σ = √σ²

Where σ² is the variance and is given by

σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16

σ² = 97.83 + 41.03 + 71.57

σ² = 210.43

So,

σ = √210.43

σ = $14.51

Therefore, the corresponding standard deviation is $14.51

b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?

For 120 passengers,

Expected revenue = 120×$13.85

Expected revenue = $1,662 ± 14.51

Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

6 0
2 years ago
Enter the symbol (&lt;, &gt;, or =) that correctly completes this comparison.<br> 0.147 0 0.174
prohojiy [21]

Answer:

<

Step-by-step explanation:

.174 is greater than .147

6 0
2 years ago
A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat.If the mixture is to be made from milk containing
3241004551 [841]

Answer:

<u>800 pints</u> of 5% butterfat and <u>200 pints</u> of 20% butterfat is needed.

Step-by-step explanation:

Given:

A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat.

If the mixture is to be made from milk containing 5% butterfat, and cream

containing 20% butterfat.

Now, to find the pints of each is needed.

Let the pints of 5% butterfat be x.

And the pints of 20% butterfat be y.

<em>So, the total pints of milk:</em>

x+y=1000

x=1000-y  ......(1)

<em>As, given:</em>

<em>1,000 pints of milk that contains 8% butterfat.</em>

<em>The mixture of milk containing 5% butterfat, and cream containing 20% butterfat.</em>

According to question:

5(x)+20(y)=8(1000)

5x+20y=8000

Substituting the value of x from equation (1):

5(1000-y)+20y=8000

5000-5y+20y=8000

5000+15y=8000

<em>Subtracting both sides by 5000 we get:</em>

15y=3000

<em>Dividing both sides by 15 we get:</em>

y=200.

<em>The pints of 20% butterfat = 200 pints.</em>

Now, to get the pints of 5% butterfat we put the value of y in equation (1):

x=1000-y

x=1000-200

x=800.

<em>The pints of 5% butterfat = 800 pints.</em>

Therefore, 800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.

8 0
2 years ago
What is the length of AD?
Setler [38]
We find the length of AD using the similarity of right triangle property. See image attached.

AD² = BD × CD
AD² = 9 × 36
AD² = 324
AD² = 18²
AD = 18

The length of AD is 18 units

7 0
3 years ago
Nicole is half as old as Donald. The sum of their ages is 72. <br><br> How old is Nicole, in years?
bixtya [17]
Your gonna divide 72 by 2 so therefore you get 36
So that equals to Nicole’s age
6 0
3 years ago
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