Dominic is a server at a restaurant. Each dish at the restaurant costs $8. A sales tax of 8% is charged. The total bill amount includes the sales tax of the meal. Dominic earns tips left by customers. The amount of money tipped can be represented by a percentage of the total bill. Order the tip amounts from least to greatest tip, in dollars. 4 dishes 20% tip 6 dishes 14% tip 7 dishes 11% tip

For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

To know more about probability,

https://brainly.com/question/18849307

#SPJ4

Answer:

i think

the answer is A. 4.9

Using the GREAT decision-making model, one could consider telling the driver not to drive after drink, getting out of the car and looking for another, or riding in the same car while ignoring the situation.

The options we have in this situation are:

Option 1:

Option 2:

Option 3:

Learn more about GREAT decision making model in: https://brainly.com/question/18066206

#SPJ1

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

To know more about point , visit:

https://brainly.com/question/26310043

#SPJ1

Answer:

I think it might be option 3

Step-by-step explanation:

sorry if I’m wrong

Answer:

82 degrees

Step-by-step explanation:

LA= 180 degrees -140 degrees =37degrees

LB 180 degrees - LA - LC

180 degrees - 37 dgrees - 61 degrees

Using the binomial distribution, it is found that the expected frequency would be of:

d. 160

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has expected value given by:

\(E(X) = np\)

In this problem:

Then, the expected frequency is:

\(E(X) = np = 800(0.2) = 160\)

And the correct option is d.

A similar problem is given at https://brainly.com/question/24261244

The present age of Mohan is 55.

Let the present age of Mohan be x.

Mohan's age 10 years ago = (x-10)

Given, the ratio of Mohan's and Suman's ages 10 years ago = 3:5

⇒ Mohan's age 10 years ago/ Suman's age 10 years ago = 3/5

⇒ Suman's age 10 years ago = Mohan's age 10 years ago × 5/3

                          = (x-10)×5/3

Again, Mohan's age after 11 years = (x+11)

Given, the ratio of Mohan's and Suman's ages after 11 years = 11:16

⇒ Mohan's age after 11 years/Suman's age after 11 years = 11/16

⇒ Suman's age after 11 years = Mohan's age after 11 years × 16/11

                                                 = (x+11)×16/11

But, the Difference between Suman's age 10 years ago and after 11 years                      = 21

⇒ (x+11)×16/11 - (x-10)×5/3 = 21

⇒  (x+11)×48 - (x-10)×55 = 693

⇒ 48x+528-55x+550=693

⇒ 7x=385

∴ x = 55

Hence, the present age of Mohan is 55.

For more questions on linear equation word problems,

https://brainly.in/question/18679846

The value of x is \( \frac{1}{4} \)

Step-by-step explanation:

Given:

\( \sqrt{x} + \sqrt{x + 2} = 2\)

Rearranging the radical on left side,

\(\sqrt{x + 2} = 2 - \sqrt{x}\)

Power on both sides,

\((\sqrt{x + 2})^{2} = (2 - \sqrt{x})^{2} \)

Simplifying the left,

\(x + 2 = (2 - \sqrt{x} )^{2}\)

For the RHS equation, use the property of (a-b)² = (a²-2ab+b²),

\( = > x + 2 = {2}^{2} - (2 \times 2 \sqrt{x}) + ( \sqrt{x})^{2} \)

Now calculating its powers,

\( = > x + 2 = 4 - 4\sqrt{x} + x\)

Now sending -4√x to the LHS (left side), its sign becomes plus (+),

\( = > 4 \sqrt{x} = 4 + x - x - 2\)

Now the +x and -x will be cancelled,

\( = > 4 \sqrt{x} = 4 - 2\)

\( = > 4 \sqrt{x} = 2\)

Bringing 4 to the right side, it becomes the denominator,

\( = > \sqrt{x} = \frac{2}{4} \)

\( = > \sqrt{x} = \frac{1}{4} \)

Now powering both sides,

\( = > ( \sqrt{x})^{2} = ( \frac{1}{2})^{2}\)

\( = > x = \frac{1}{4} \)

Answer:

$0.10

Step-by-step explanation:

Divide 2 million by 20 million:

2,000,000/20,000,000

= 0.1

So, each meal costs $0.10

Answer:

$24 is her allowance. 1/3 of her allowance is $8. So you would multiply 8 times 3 because 8 is just 1/3 of her allowance and you want to find her total weekly allowance. 8 x 3 = 24

Step-by-step explanation:

Answer:

fx inverse is (x+3)^1/3+2

Step-by-step explanation:

y=(x-2)^3 -3

y+3=(x-2)^3

(y+3)^1/3=x-2

(y+3)^1/3 +2=x

fx inverse is (y+3)^1/3

The equivalent expression of 21√(3)(15) - 9√(3)(15) is 36√5

The expression is given as:

21√(3)(15) - 9√(3)(15)

Express 15 as 3 * 5

21√(3)(15) - 9√(3)(15) = 21√(3)(3 * 5) - 9√(3)(3 * 5)

Evaluate the product of 3 and 3

21√(3)(15) - 9√(3)(15) = 21√(9 * 5) - 9√(9 * 5)

Take the square root of 9

21√(3)(15) - 9√(3)(15) = 21*3√(5) - 9*3√5)

Evaluate the product

21√(3)(15) - 9√(3)(15) = 63√(5) - 27√5)

Evaluate the difference

21√(3)(15) - 9√(3)(15) = 36√5

Hence, the equivalent expression of 21√(3)(15) - 9√(3)(15) is 36√5

Read more about equivalent expression at

https://brainly.com/question/2972832

#SPJ1

Answer:

27units

Step-by-step explanation:

volume of a rectangular prism v=sh

s=v/h = 278.1/10.3 =27 units

so the area of its base is 27 units

The probability that a randomly selected person is infected with disease D is 11%. This is calculated based on the given information regarding the occurrence of minor cold-like symptoms and the associated probabilities of being infected with D.

Let's denote the event of experiencing minor cold-like symptoms as S, and the event of being infected with disease D as D. We are given that P(S) = 0.2 (20% of people experience these symptoms).

We also know that within the group of people experiencing symptoms (S), P(D|S) = 0.35 (35% chance they are infected with D), and within the group of people not experiencing symptoms (~S), P(D|~S) = 0.05 (5% chance they are infected with D).

To find the probability of being infected with D, we can use Bayes' theorem:

P(D) = P(D|S) * P(S) + P(D|~S) * P(~S)

Substituting the given values:

P(D) = 0.35 * 0.2 + 0.05 * (1 - 0.2)

Simplifying:

P(D) = 0.07 + 0.05 * 0.8
P(D) = 0.07 + 0.04
P(D) = 0.11

Therefore, the probability that a randomly selected person is infected with disease D is 0.11, or 11%.

To learn more about Probability, visit:

https://brainly.com/question/6649771

#SPJ11

Answer:

A, B, and E

Step-by-step explanation:

A function has only ONE out put for each input. For example in C 12 has two outputs, -18 and 5 so that set is NOT a function.

The population of the next year will be, 108,864.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are just temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The population of a city increases by 0. 8% per year.

This year's population is 108,000.

0.8% of 108,000 is,

108,000 x 0.008 = 864

The population increased by 864 people.

So, the next year's population will be,

108,000 + 864 = 108,864.

Hence, the next year's population will be 108,864.

To know more about population, click on the link

https://brainly.com/question/25630111

#SPJ4

Answer:

3/6 and 2/6

4/6 and 1/6

Step-by-step explanation:

The fraction of crackers Nina got is 5/6.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, Mariana fed 1/6 of a box of crackers to the birds outside her house. She shared the rest with Nina.

Fraction of crackers Nina got = 1 -1/6

= (6-1)/6

= 5/6

Therefore, the fraction of crackers Nina got is 5/6.

To learn more about the fraction visit:

brainly.com/question/1301963.

#SPJ2

Answer:

\(g=\frac{9}{2}, \\x=-6\)

Step-by-step explanation:

Step-by-step explanation:

the formular we're to use is the point slope formula

SLOPE = -3

and x1= -5 y1 = -6

HENCE

Y - Y1 = M (X- X1)

y-(-6) = -3( x--5)

y+ 6 = -3 (x+5 )

y+6 = -3x -15

y= -3x-15-6

y= -3x -21

Answer:

negative

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

The initial amount, a, in the exponential function g(x) = 14 × 2x is 14, and the growth factor, b, is 2.

This can be determined by looking at the equation and noting that the coefficient of x is 2, which indicates that the base of the exponential is 2. We can also calculate the initial amount and growth factor mathematically.

To calculate the initial amount, a, we can take the equation g(x) = 14 × 2x and set x = 0, yielding g(0) = 14 × 20, which simplifies to 14. To calculate the growth factor, b, we can take the natural log of both sides of the equation to yield ln(g(x)) = ln(14 × 2x).

Simplifying this gives

ln(g(x)) = ln(14) + ln(2x).

We can then divide both sides by x to yield

ln(g(x))/x = ln(14) + ln(2)/x.

We can then take the limit as x approaches 0, which yields

ln(g(0))/0 = ln(14) + ln(2)/0.

This simplifies to

ln(g(0)) = ln(14) + ln(2), which can be rearranged to

ln(2) = ln(g(0)) - ln(14).

Taking the exponential of both sides gives us

2 = e^(ln(g(0)) - ln(14)), which simplifies to

2 = g(0)/14, or b = g(0)/14 = 2.

This shows that the initial amount, a, is 14, and the growth factor, b, is 2.

Learn more about exponential function:

https://brainly.com/question/30241796

#SPJ4

We use the quadratic formula to find the roots of the quadratic equation.

The quadratic equation is given below:

f(x) = a\(x^{2}\) + bx + c = 0 where a, b, c

The system of equations used to find roots of equation is y = 12\(x^{3}\)-5x and y=2\(x^{2}\)+x+6.The given equation will be,12\(x^{3}\)-5x=2\(x^{2}\) + x + 6.

Now we take the root of equation into two parts:

1. Left-hand side

2. Right-hand side

Equation no.1 : 12\(x^{3}\)-5x=0

Equation no.2: 2\(x^{2}\)+x+6=0

Now we contains system of equation 0 with y.

So, the equation will be:

12\(x^{3}\)-5x=y

2\(x^{2}\)+x+6=y

However,system of equations can be used to find the roots of the equation 12\(x^{3}\)-5x=2\(x^{2}\)+x+6 is:
y = 12\(x^{3}\)-5x and y = 2\(x^{2}\)+x+6

To learn more about roots of equation, click here

brainly.com/question/28034005

#SPJ4

The sampling frame is: All adults with residential telephones

An opinion poll calls 2000 randomly chosen residential telephone numbers, then asks to speak with an adult member of the household. The interviewer asks, "How many movies have you watched in a movie theater in the past 12 months?"The question is asking for the sampling frame which means it is looking for the subset of the population from which the sample is selected. It is important to define the sampling frame because it is necessary to determine how to obtain a representative sample.Here in the given statement, the sampling frame would be All adults with residential telephones. This is because the poll calls randomly chosen residential telephone numbers and then asks to speak with an adult member of the household. It is unclear whether the poll only includes adults who have watched movies in the past 12 months.

Know more about  sampling frame here:

https://brainly.com/question/31448091

#SPJ11

The general process of finding the number of days when there will be 20 g remaining, given the decay function.

Let's assume the decay function is represented by:

M(t) = M₀ * e^(kt),

where M(t) is the mass remaining after t days, M₀ is the initial mass (35 g in this case), e is the base of the natural logarithm (approximately 2.71828), k is the decay constant, and t is the time in days.

To find the number of days when there will be 20 g remaining, we need to solve the equation M(t) = 20 for t.

M(t) = 20 can be rewritten as:

35 * e^(kt) = 20.

To solve for t, we need to know the value of the decay constant (k). Without this information, we cannot provide a specific answer.

If you have the value of the decay constant (k) or any additional information, please provide it, and I'll be happy to help you find the number of days when there will be 20 g remaining.

To know more about Value visit-

brainly.com/question/30760879

#SPJ11

Using metric system , we have cοme tο find that Bucky walked 25.908 meter.

Metric system is a prοcess οf measuring things. It is used tο measure length, vοlume , weight , capacity etc. In metric system οne unit can be cοnverted intο anοther unit.

Given that Bucky walked 85 feet. His friend in Canada wanted tο

knοw hοw many meters he walked.

Given that 1 fοοt = .3048 meter

Tο cοnvert 85 feet tο meter we are gοing tο use the metric system.

1 fοοt = 0.3048 meter

85 fοοt = 85 × 0.3048 meter [ Since in metric system , tο cοvert a unit frοm anοther unit either have tο multiply οr have tο divide the unit]

By multiplying we get 25.908 meter.

Hence, Bucky walked 25.908 meter.

To know more about metric system

https://brainly.com/question/30386511

#SPJ1