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Charra [1.4K]
3 years ago
13

Four friends go out to eat and their meal costs $86.50. The sales tax is 6.75% and they should tip the waiter 20%. How much shou

ld each person pay to the nearest cent?
Mathematics
2 answers:
GenaCL600 [577]3 years ago
8 0
If the tax is placed on the roigial price, they should each pay around 49 dollars and 3 cents.
sattari [20]3 years ago
6 0

Answer:

Each person should pay 27.7$

Step-by-step explanation:

The meal costs 86.50$. When the sales tax is added to meal cost total amount of money that restaurant will receive:

M=86.5*10675/10000=92.34

92.34$ and total amount of money that 4 friends will give included waiter tip is:

T=92.35*120/100=110.80

and each person need to give 110.8/4=27.7$

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What is the equation of the quadratic graph with a focus of (1 ,3) and a directrix of y=1?
zimovet [89]
Check the picture below.

now, we know the directrix is at y = 1, and the focus point is at 1,3, well, notice the picture, the distance between those fellows is just 2 units.

the vertex is half-way between those fellows, therefore, the vertex will be at 1,2.

the distance "p", from the vertex to either the directrix or focus, is really just 1 unit.  Since the focus point is above the directrix, is a vertical parabola, and it opens upwards, like in the picture, and since it opens up, the "p" value is positive, or +1.

\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
4p(x- h)=(y- k)^2
\\\\
\boxed{4p(y- k)=(x- h)^2}
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ( h, k)\\\\
 p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=1\\
k=2\\
p=1
\end{cases}\implies 4(1)(y-2)=(x-1)^2\implies 4(y-2)=(x-1)^2
\\\\\\
y-2=\cfrac{1}{4}(x-1)^2\implies y=\cfrac{1}{4}(x-1)^2+2

4 0
3 years ago
Simplify.<br> 12<br> 24<br> A) 3<br> 2<br> B) 6<br> 2<br> C) <br> 1<br> 2<br> D) <br> 2<br> 2
AleksandrR [38]
12/24 simplifies to 1/2, seeing as 12 is half of 24. :) Your answer is C.
5 0
3 years ago
Find the perimeter of the following triangle. Round your answer to the nearest hundredth.
vladimir2022 [97]

Step-by-step explanation:

step 1. The perimeter (P) is the length around the triangle.

step 2. P = 6 + 5 + L (the length of the hypotenuse)

step 3. L = sqrt(6^2 + 5^2) = sqrt(61) where sqrt is the square root

step 4. P = 11 + sqrt(61) = 18.81.

5 0
2 years ago
If two distinct lines intersect, which MUST be true?
emmainna [20.7K]

Answer:

Answer options

A) the lines are parallel

B) the lines are perpendicular

C) the lines form angles at the intersection

D) the lines form right angles at the intersection

the answer is C

Step-by-step explanation:

I got it right on my test

7 0
2 years ago
Ryan has $3$ red lava lamps and $3$ blue lava lamps. He arranges them in a row on a shelf randomly, then turns $3$ random lamps
hjlf

There are 6! = 720 ways of arranging the lamps.

If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.

Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.

Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.

Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So

P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4

7 0
2 years ago
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