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marta [7]
3 years ago
11

At a local clothing store, Morgan finds they are having a storewide 40% off sale. She also has a $15 coupon which applies to her

total purchase. When the sales clerk processes Morgan's order, she first applies the $15 off coupon, then takes the 40% off the remaining balance. Which order of the discounts is best for Morgan.
Mathematics
1 answer:
LuckyWell [14K]3 years ago
5 0

Morgan should first take the 40% off then apply the $15 coupon

Lets say her total was $150.

If you take the 40% off first, you get $90

150 * .6 = 90 (since you are taking off 40% you are still paying the rest of the 60% so you can just save extra steps by multiplying by .6 and not .4)

Now you subtract 15 from that value.

90 - 15 = 75 If Morgan takes the 40% off first and then applies the $15 dollar coupon, she has to pay $75.

If she applies the $15 coupon first, her total before the 40% is $135

150 - 15 = 135

The total will come out to be $81

$135 * .6 = 81

If Morgan takes the discount first before applying the coupon she has to pay less and saves the most money.

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Find an equation in standard form of the parabola passing through these points: (0,-6),(-1,-12),(3,0)
Elan Coil [88]
One form of the equation of a parabola is
y = ax² + bx + c

The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6                       (1)
a - b + c = -12            (2)
9a + 3b + c = 0         (3)

Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6                  (4)
9a + 3b - 6 = 0
9a + 3b = 6              (5)

Substitute a = b - 6 from (4) into (5).
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a = b - 6 = -1

The equation is
y = -x² + 5x - 6 

Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
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y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
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Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.

Answer: y = -(x - 2.5)² + 0.25

3 0
3 years ago
The diameters of ball bearings are distributed normally. The mean diameter is 107 millimeters and the population standard deviat
tensa zangetsu [6.8K]

Answer:

0.6710

Step-by-step explanation:

The diameters of ball bearings are distributed normally. The mean diameter is 107 millimeters and the population standard deviation is 5 millimeters.

Find the probability that the diameter of a selected bearing is between 104 and 115 millimeters. Round your answer to four decimal places.

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 107 mm

σ is the population standard deviation = 5 mm

For x = 104 mm

z = 104 - 107/5

z = -0.6

Probability value from Z-Table:

P(x = 104) = 0.27425

For x = 115 mm

z = 115 - 107/5

z = 1.6

Probability value from Z-Table:

P(x = 115) = 0.9452

The probability that the diameter of a selected bearing is between 104 and 115 millimeters is calculated as:

P(x = 115) - P(x = 104)

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