amelia and 2 of her friends went out to lunch. each girl ordered exactly the same meal. the total cost 55.08, which included 8% sales tax. what was the price of each meal, not including tax?


Answer 1



Step-by-step explanation:

We are given that Amelia and her  two friends went out to lunch.

If each girl ordered exactly the same meal.

We have to find out the value of price of  each meal without tax.

Total cost of meals=$55.08

Cost of 3 meals with tax=$55.08

Sales tax=8% of $55.08

8% of 55.08=(8)/(100)*55.08

8% of 55.08= $4.4064

Cost of 3 meals without tax=$55.08-$4.4064=$50.6736

Cost of each meal=(50.6736)/(3)=$16.8912

Hence, the cost of each meal without tax=$16.8912

Answer 2
Answer: Cost of the meal with tax = 108% = $55.08

108% = 55.08
1% = 55.08 ÷ 108 = $0.51
100% = $51

3 meals = $51
1 meal = $51 ÷ 3 = $17

Answer: $17

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Consider the daily market for hot dogs in a small city. Suppose that this market is in long-run competitive equilibrium with many hot dog stands in the city, each one selling the same kind of hot dogs. Therefore, each vendor is a price taker and possesses no market power.


The graph show\ing the demand (D) and supply (S = MC) curves in the market for hot dogs indicate: Competitive market.

Competitive market

In a market were their is competition, when demand and supply curves intersect this indicate market equilibrium.

Based on the graph the market equilibrium price will be $1.50 per hot dog while on the other hand the market equilibrium quantity will be 250 hot dogs which  is the point were demand and supply intersect.

Inconclusion the market for hot dogs indicate: Competitive market.

Learn more about competitve market

Answer:IF each vendor has his own price or (ppower) so far every single vendor will have his own price.

Step-by-step explanation:

In a recent survey it was found that Americans drink an average of 23.2 gallons of bottled water in a year. If the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year. What is the probability that the selected person drinks between 22 and 30 gallons



a) 0.25249

b) 0.66575

Step-by-step explanation:

We solve this question using z score formula

= z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 23.2 gallons

σ is the population standard deviation = 2.7 gallons

a) Find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year.

For x = 25 gallons

z = 25 - 23.2/2.7

z = 0.66667

Probability value from Z-Table:

P(x<25) = 0.74751

P(x>25) = 1 - P(x<25)

1 - 0.74751

= 0.25249

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is 0.25249

2) What is the probability that the selected person drinks between 22 and 30 gallons

For x = 22 gallons

z = 22 - 23.2/2.7

z = -0.44444

Probability value from Z-Table:

P(x = 22) = 0.32836

For x = 30 gallons

z = 30 - 23.2/2.7

z =2.51852

Probability value from Z-Table:

P(x = 30) = 0.99411

The probability that the selected person drinks between 22 and 30 gallons is

P(x = 30) - P(x = 22)

= 0.99411 - 0.32836

= 0.66575

Final answer:

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is approximately 0.2514, while the probability that they will drink between 22 and 30 gallons is approximately 0.6643.


This is a statistics question about probability distribution, specifically, normal distribution. You need to find the z-scores and use the standard normal distribution table to find the probabilities.

The average or mean (μ) consumption is 23.2 gallons and standard deviation (σ) is 2.7 gallons.

First, we use the z-score formula: z = (X - μ) / σ

To find out the probability that a selected American drinks more than 25 gallons annually, we substitute X = 25, μ = 23.2 and σ = 2.7 into the z-score formula to get z = (25 - 23.2) / 2.7 ≈ 0.67. Z value of 0.67 corresponds to the probability of 0.7486 in standard normal distribution table, but this is the opposite of what we want. We need to subtract this probability from 1 to find the probability that a person drinks more than 25 gallons annually. So 1 - 0.7486 = 0.2514.

Second, to find the probability an individual drinks between 22 and 30 gallons, we calculate two z-scores: For X = 22, z = (22 - 23.2) / 2.7 ≈ -0.44 with corresponding probability 0.3300, and for X = 30, z = (30 - 23.2) / 2.7 ≈ 2.52 with corresponding probability 0.9943. We find the probability of someone drinking between these quantities by subtracting the smaller probability from the larger, 0.9943 - 0.3300 = 0.6643.

Learn more about Normal Distribution here:


Use the GCF and the distributive property to find the expression that isequivalent to 36 - 48
A 6(6+8)
B. 12(3+4)
C. 2(18-24)
D. 419-12


The answer is 2(18-24) or C.
It’s c! Make sure to do the problems and remember when a problem has () these you do that problem first then the rest!

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 4640 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize the cost. (Round your answers to three decimal places.)


The dimensions that minimize the cost of building the tank are r\approx 6.5ft \text{ and } h \approx 26.0ft .


h=\text{the height of the cylindrical sides}\nr=\text{the radius of the hemispheres and the cylindrical sides}


T=\text{the total cost}\nu_c=\text{the unit cost of building the cylindrical sides}\nu_h=\text{the unit cost of building the hemispherical surfaces}


S_c=\text{the surface area of the cylinder}\n=2\pi rh\n\nS_h=\text{the total surface area of both hemispheres}\n=4\pi r^2



From the question


The total cost becomes

T=u_cSc+2u_cSh\n=2u_c \pi rh+8u_c \pi r^2

We need to eliminate h. The volume from the question gives a way out

4640=(4)/(3)\pi r^3 +\pi r^2h\n\nh=(4640)/(\pi r^2)-(4r)/(3)

substitute into the formula for total cost gives, after simplifying

T=(16u_c\pi r^2)/(3)+(9280u_c)/(r^2)

differentiating with respect to r, we get

(dT)/(dr)=(32)/(3)u_c\pi r-(9280u_c)/(r^2)

at extrema

(dT)/(dr)=0\n\n\implies (32)/(3)u_c\pi r=(9280u_c)/(r^2)\n\nr=\sqrt[3]{(870)/(\pi)}\approx 6.5ft

To confirm that r is a minimum value, carry out the second derivative test


substituting r=\sqrt[3]{(870)/(\pi)}, we get that (d^2T)/(dr^2) > 0, confirming that minimum value

To find h, recall that

h=(4640)/(\pi r^2)-(4r)/(3)

substituting r, we get h\approx 26.0ft as the corresponding minimum height

Therefore, r\approx 6.5ft \text{ and } h \approx 26.0ftminimize the total cost of building the tank.

Learn more about minimizing dimensions to reduce costs here:

Final answer:

The problem involves finding the dimensions of a cylinder and two hemispheres that minimize the cost to build an industrial tank of a specific volume. This involves setting up equations for the volume and cost, and then using calculus to find the dimensions that minimize the cost.


This problem can be solved using calculus. Let's denote the radius of both the hemispheres and the cylinder as r and the height of the cylinder as h. The total volume of the solid is the sum of the volume of the cylinder and the two hemispheres. Using the formulas for the volumes of a cylinder and hemisphere, we have:

V = (πr²h) + 2*(2/3πr³) = 4640 cubic feet.

The total cost of the material is proportional to the surface area. The surface area of the two hemispheres is twice as expensive as that of the sides of the cylinder, so we have:

Cost = 2*(2πr²) + πrh.

To minimize the cost, we can take the derivative of the Cost function with respect to r and h, set them equal to zero, and solve for r and h.

This problem involves calculus, the volume of cylinders and spheres, and optimization, which are topics covered in high school mathematics.

Learn more about Mathematics Optimization Problems here:


Plz help I don’t get it


Answer:there is nothing attached

Step-by-step explanation:

Write an inequality for a game that allows 2 and not more than 4 players




Step-by-step explanation:

2 is less than/equal to x; x is less than/equal to 4