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fomenos
2 years ago
14

Keith and Allison go out to eat their bill was 63.16$ they only paid 50.03$ what was the percent discount of their coupon

Mathematics
1 answer:
Aleonysh [2.5K]2 years ago
8 0

Answer:

16.04%

Step-by-step explanation:

53.03$- 63.16$= -10.13

-10.13$/63.16$=-0.16038

rounding 8 making the 3 a 4

16.04%

You might be interested in
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
Nora got an allowance of 50¢ each weekday and 75¢ each weekend altogether how much do they get in:
Furkat [3]
A) > since it is 50c per weekday and 75c each weekend assuming it allows for the 2 days each saturday/sunday.
50c * 5 = $2.50 since there are 5 days in weekdays
75c * 2 = $1.50 since there are 2 days in the weekend
Add $2.50 and $1.50 to get $4.00

b) For 3 school days we know it is a weekday on the school week.
So perform 50c * 3 which gives us <span>$1.50

</span>c) 12 days off from school is 10 weekdays and 1 weekend or 2 days of 75c
So now just do 50c * 10 which is $5.00 and 75c * 2 which is $1.50
Add $5.00 and $1.50 and we get $6.50

d) 4 weeks = 20 weekdays since 5 *4 = 20 and 8 days in each weekend since 2 * 4 = 8
Now that we have the amount of weekdays and weekend days we can multiply.
50c * 20 = $10.00
75c * 4 = $3.00
Add $10.00 and $3.00 to get $13.00 for 4 weeks.

e) We have 1 day of the weekend and 2 weekdays here.
50c * 2 = $1.00
75c * 1 = 75c
<span>$1.00 + 75c = $1.75 in those 3 days listed.
</span>
Add all these together to get your total value.
$4.00 + $1.50 + $6.50 + $13.00 + $1.75 = $26.75

7 0
3 years ago
A 4​-ft vertical post casts a 12​-in shadow at the same time a nearby cell phone tower casts a 122​-ft shadow. How tall is the c
zepelin [54]

Answer:

the cell phone tower is 488 ft

Step-by-step explanation:


change 12 in = 1ft

4ft                            x ft

------------------- =   ----------------

1ft  shadow           122 ft shadow


using cross products

4 * 122 = 1 * x

488 = x

3 0
3 years ago
Madison and Tanisha went out to lunch. The bill came to $18.94. Madison knows that her lunch cost 9.72. How much did Tanisha's l
Finger [1]

Answer:

Tanisha's lunch cost $9.22.

Step-by-step explanation:

Given that,

Total bill = $18.94

Cost for Madison cost = $9.72

Total cost = Tanisha's lunch + Madison's lunch

18.94 = Tanisha's lunch + 9.72

Tanisha's lunch = 18.94 - 9.72

Tanisha's lunch = 9.22

So, Tanisha's lunch cost $9.22.

4 0
2 years ago
10 points
Sergeu [11.5K]

Step-by-step explanation:

The mode is 7 because it is 5 times

8 0
3 years ago
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