ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY DISTRIBUTED WITH A MEAN OF 16 MINUTES AND STANDARD DEVIAITON OF 4 MINUTES.1. IN A RANDOM SAMPLE OF 1000 CUSTOMERS, HOW MANY WAIT 18 MINUTES OR MORE BEFORE BEING SEATED.2. IN A RANDOM SAMPLE OF 500 CUSTOMERS, HOW MANY WAIT LESS THAN 9 MINUTES BEFORE BEING SEATED

Answers

Answer 1

Solution.

Calculate the z-score

The formula is shown below

[tex]\begin{gathered} \sigma=4 \\ \mu=16 \\ \end{gathered}[/tex][tex]\begin{gathered} Z_{18}=\frac{18-16}{4}=0.5 \\ P\left(x>0.5\right)=0.30854 \\ n=0.30854\text{ x 1000} \\ n=308.54 \\ n=309(nearest\text{ whole number\rparen} \end{gathered}[/tex]

Thus, 309 customers (to nearest whole number) wait 18 minutes or more before being seated

(ii)

[tex]\begin{gathered} Z_9=\frac{9-16}{4} \\ Z_9=-1.75 \\ P\left(x<-1.75\right)=0.040059 \\ n=0.040059\text{ x 500} \\ n=20.03 \\ n=20(nearest\text{ whole number\rparen} \end{gathered}[/tex]

Thus, 20 customers (to nearest whole number) wait less than 9 minutes before being seated

ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY

Related Questions

Which of the following describes the graph of h(x)= -2^(x+3)-4. Thanks for the help!

Answers

SOLUTION:

Case: Graphs

Method:

The equation:

[tex]h(x)=-2^{(x+3)}-4[/tex]

We will plug in several values of x

(-3, ?), (0, ?)

[tex]\begin{gathered} (-5,?) \\ h(-3)=-2^{(-3+3)}-4 \\ h(-3)=-2^0-4 \\ h(-3)=-1-4 \\ h(-3)=-5 \\ (-3,-5) \end{gathered}[/tex]

And

[tex]\begin{gathered} (0,?) \\ h(0)=-2^{(0+3)}-4 \\ h(0)=-2^3-4 \\ h(0)=-8-4 \\ h(0)=-12 \\ (0,-12) \end{gathered}[/tex]

Final answer: 3rd Option

The graph:

[tex] \frac{1}{2} {x}^{2} + 1 = 2 \times - 1[/tex]Solve the equation

Answers

Solve the system of equations:

4x-2y=10 (1)

y=2x-5 (2)

We can substitute 2 in 1:

4x-2(2x-5)=10

4x-4x+10=10

0=0

Since the solution of the system of equation is 0=0 we can say that it has infinite solutions.

I need help with 3 , 7 ,4 and 8

Answers

Solution:

Question 3:

The image below gives a vivid explanation of the question

Concept:

The sum of angles in a triangle is

[tex]=180^0[/tex][tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ \angle A=61^0 \\ \angle B=90^0 \\ \angle C=4f+1 \end{gathered}[/tex]

By substituting the values, we will have

[tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ 61^0+90^0+4f+1=180^0 \\ \text{collect similar terms, we will have} \\ 61+90+1+4f=180^0 \\ 152^0+4f=180^0 \\ 4f=180-152^0 \\ 4f=28^0 \\ \text{Divide both sides by 4} \\ \frac{4f}{4}=\frac{28}{4} \\ f=7^0 \end{gathered}[/tex]

Hence,

The final answer is f = 7°

Max is scuba diving at elevation of -64.5 feet, when friend signals to come higher. Max makes 2 ascents, each an equal distance to reach an elevation of -21.4 feet, where his friend is located. What was max’s elevation after his first ascent?I come up with -43.1

Answers

Answer: - 42.95 feet

Explanation:

Let each ascent be x. Thus,

2 equal ascents = 2x

From the information given,

initial position = - 64.5 feet

Final position after 2 ascents = - 21.4 feet

This means that

- 64.5 + 2x = - 21.4

2x = - 21.4 + 64.5

2x = 43.1

x = 43.1/2

x = 21.55

Thus, Max's elevation after the first ascent is

- 64.5 + 21.55

= - 42.95 feet

Find the measure of angle A associated with the following ratios and round to the nearest degree.

Answers

For, CosA = 0.2785 value of angle m∠A = 73.8293°   ≈ 74°

Inverse Cosine function:

                                       The inverse cosine function is written as cos^-1(x) or arccos(x).

CosA = 0.2785

         A = [tex]Cos^{-1}[/tex](0.2785)

         A = 73.8293°

                   thus by calculation we can say,

                 m∠A = 73.8293°

                          ≈ 74°

Thus,

           For, CosA = 0.2785 value of angle m∠A = 73.8293°

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A department store is having a clothing sale. If a $35.00 pair of pants has a discount tag of 25% off, what is the sale price? 

Answers

Given Data:

The prise of the pair of the pant is: p= 35

the percentage of discount is: 25%

The expression to calculate the discount sale price is,

[tex]d=p\times\frac{25}{100}[/tex]

Substitute values in the above expression.

[tex]\begin{gathered} d=35\times\frac{25}{100} \\ =35\times0.25 \\ =8.75\text{ } \end{gathered}[/tex]

Thus, the discount price of the pant is $8.75.

00:00Drag a tile to each number to classify it as rational or irrational.rationalirrational9.682.010010001...✓ 64-57

Answers

the numbers are

[tex]undefined[/tex]

How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?

Answers

Solution

We need to remember that in a standard deck we have 4 aces and 48 other types of cards

For this case we can solve the problem with the follwoing operation:

[tex](4C2)\cdot(48C3)=\frac{4!}{2!2!}\cdot\frac{48!}{45!3!}=6\cdot17296=103776[/tex]

So then we have 103776 ways to create the combination required


If we start with 5 people that have the coronavirus, and the number of cases increases by 26% each week. How many cases of coronavirus will there be
in 36 weeks?

Answers

Answer:

6600 new cases

Step-by-step explanation:

17 people fit comfortably in a 7 feet by 7 feet area. Use this value to estimate the size of a crowd that is 21 feet deep on both sides of the street along a 3-mile section of a parade route. (Hint: 1mile= 5,280ft) Draw a diagram

Answers

In order to estimate the size of the crowd, let's find the area of the parade route.

The length is 3 miles, that is, 3 * 5280 = 15840 ft.

The width is 2 times 21, so 42 ft.

Therefore the area is:

[tex]A=15840\cdot42=665280[/tex]

Now, to estimate the size of the crowd, let's use a rule of three, knowing that the area for 17 people is 7 * 7 = 49 ft²:

[tex]\begin{gathered} 17\text{ people}\to49\text{ ft}^2 \\ x\text{ people}\to665280\text{ ft}^2 \\ \\ \frac{17}{x}=\frac{49}{665280} \\ x=\frac{665280\cdot17}{49} \\ x=230811.43 \end{gathered}[/tex]

Rounding to the nearest integer, we have 230,881 people.

Joe’s parents are making sandwiches for the class picnic they have 7230 size is 48 two slices and 96 tomato sauce is Y

Answers

We have to calculate the maximum common divisor of these 3 numbers in order to know what is the maximum ammount of sandwiches they can make.

We can list the factors of each number:

72: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 72.

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96.

To calculate this factors, we start by dividing by 2 and 3, and so on, and checking if the result is a whole number. If it is, the denominator is a factor.

The maximum common divisor is 24, so they can make 24 sandwichs, each one with 72/24=3 slices of turkey, 48/24=2 slices of cheese and 96/24=4 slices of tomatoes.

George's boxes

He has bought boxes at different prices.

3 boxes at $3.50 and 4 boxes at $3.00.

The cost of the first group of boxes is 3 boxes x 3.50 $/boxes = $10.50.

The cost of the second group is 4 boxes x 3.00 $/boxes = $12.

Then, if we add the cost, it is 10.50 + 12 = $22.50.

If we write it in the blanks we have:

3 boxes * 3.50 = 3 * 3.50

4 boxes * 3.00 = 4 * 3.00

(3 * 3.50) + (4 * 3.00) = 22.50

(underlined is what goes in the blanks)

1. A function is given by the set of ordered pairs {(2,5),(4,9), (6,13), (8,17)). Write its domain and rangein roster form.Domain:Range:

Answers

The domains are:

{2, 4, 6, and 8}

The range are {5, 9, 13 and 17}

EXPLANATION

Given:

{(2,5),(4,9), (6,13), (8,17))

The above is given in the form (x, y)

where x is the domain and y is the range.

The domains are:

{2, 4, 6, and 8}

The range are {5, 9, 13 and 17}

-8x+3y= 313x-3y= -18x=y=

Answers

Given the pair of simultaneous equation;

[tex]\begin{gathered} -8x+3y=3 \\ 13x-3y=-18 \end{gathered}[/tex]

We are going to use the method of elimination to solve this.

We will be eliminating the variable y first, since it has the same co-efficient in the two(2) equations.

Thus, we have:

[tex]\begin{gathered} -8x+13x=3-18 \\ 5x=-15 \\ x=-\frac{15}{5} \\ x=-3 \end{gathered}[/tex]

To solve for y, we are going to substitute for x = -3 into any of the two(2) equations.

Thus, we have:

[tex]\begin{gathered} \text{from equation i}i) \\ 13x-3y=-18 \\ 13(-3)-3y=-18 \\ -39-3y=-18 \\ -3y=-18+39 \\ -3y=21 \\ y=-\frac{21}{3} \\ y=-7 \end{gathered}[/tex]

If the scale factor is 5:8, and the actual width of the model is 20 feet, what is the model width?

Answers

If the scale factor is 5:8, it is the same as 5/8.

In order to calculate the width of the model, just multiply its actual width by the scale factor, as follow:

width of the model = (20 ft)(5/8) = 12.5 feet

Hence, the width of the model is 12.5 feet

Let X represent number of sundaes sold and y represent the number of banana splits sold.Sundaes are sold for $2 each and banana splits for $3 each. They made a total of $150. Equation____________The number of sundaes sold is 5 times more than the number of banana splits sold. Equation________Solve the system of problem questions by substitution

Answers

Given that the total income was $150 by selling 'x' sundaes and 'y' banana splits,

[tex]\begin{gathered} \text{Total Cost}=\text{ Cost per sundae}\cdot\text{ Number of sundae}+\text{ Cost per banana splits}\cdot\text{ Number of banana splits} \\ 150=2x+3y \\ 2x+3y=150\ldots(1) \end{gathered}[/tex]

Also given that the number of sundaes sold is 5 times more than the number of banana splits sold,

[tex]\begin{gathered} x=y+5y \\ x=6y\ldots(2) \end{gathered}[/tex]

Substitute this value in equation (1),

[tex]\begin{gathered} 2(6y)+3y=150 \\ 12y+3y=150 \\ 15y=150 \\ y=10 \end{gathered}[/tex]

The corresponding value of 'x' is calculated by using equation (2) as,

[tex]\begin{gathered} x=6(10) \\ x=60 \end{gathered}[/tex]

Thus, the solution to the system of problem

Give the domain and range of a quadratic function whose graph as described. The vertex is (-5,-6) and the parabola opens up. The domain of f is ___

Answers

We will have that it's domain goes from -infinity to infinity.

It's range, goes from infinity to -6.

Look at the graphs and their equations below. Then in the information about the ABCand D

Answers

Given:

Given a graph and their equations. Then in the information about the A,B, Cand D

Required:

To fill the blanks.

Explanation:

(a) For each coefficient choose whether it is positive or negative :

A : It has positive coefficient.

B : It has positive coefficient.

C : It has negative coefficient.

D : It has negative coefficient.

(b) Choose the coefficient with the least value:

The graph D.

(c)

6.[–/1 Points]DETAILSALEXGEOM7 8.3.006.MY NOTESASK YOUR TEACHERIn a regular polygon, each interior angle measures 120°. If each side of the regular polygon measures 4.6 cm, find the perimeter of the polygon in centimeters. cm

Answers

Given:

Measure of each interior angle = 120 degrees

Length of each side = 4.6 cm

Let's find the perimeter of the polygon.

Since the measure of each interior angle is 120 degrees, let's find the number of sides of the polygon using the formula below:

[tex]120=\frac{(n-2)*180}{n}[/tex]

Let's solve for n.

We have:

[tex]\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}[/tex]

Divide both sides by 60:

[tex]\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}[/tex]

Therefore, the polygon has 6 sides.

To find the perimeter, apply the formula:

Perimeter = number of sides x length of each side

Perimeter = 6 x 4.6

Perimeter = 27.6 cm

Therefore, the perimeter of the polygon is 27.6 cm

ANSWER:

27.6 cm

What is the area of rectangle with a length of 24 meters and a height of 7 meters?A84 square meters84 square metersB600 square meters600 square metersC168 square meters168 square metersD300 square meters

Answers

Answer: C. 168 m²

Explanation

The area of a rectangle (A) is given by:

[tex]A=l\cdot h[/tex]

where l represents the length and h represents the height.

Then, in our case, l = 24m and h = 7m. By replacing the values and simplifying we get:

[tex]A=24m\cdot7m[/tex][tex]A=168m^2[/tex]

What are the roots for the trinomial below? *x2 – 2x – 15O x=-5,x=-3Ox=5,x=-3Ox=3,x=5O x=-5,x=3

Answers

ANSWER:

[tex]x=5,=-3[/tex]

STEP-BY-STEP EXPLANATION:

We have the following equation:

[tex]x^2-2x-15[/tex]

We solve by factoring. We look for two numbers that product -15 and the sum is equal to -2:

[tex]\begin{gathered} 3\cdot-5=-15 \\ 3+(-5)=-2 \\ \text{Therefore:} \\ (x+3)\cdot(x-5)=0 \\ x+3=0\rightarrow x=-3 \\ x-5=0\rightarrow x=5 \end{gathered}[/tex]

A garden table and a bench cost $669 combined. The garden table costs $81 less than the bench. What is the cost of the bench?

Answers

Given:

The cost of garden table and bench is, 669.

The garden table costs 81 less than bench.

Let us take x as the cost of the bench and y as the cost of the table. Then we have,

[tex]\begin{gathered} x+y=669\ldots\text{.}.(1) \\ y=x-81\ldots.(2) \end{gathered}[/tex]

Now, substituting the value of y in equation 1, we get,

[tex]\begin{gathered} x+x-81=669 \\ 2x=669+81 \\ 2x=750 \\ x=\frac{750}{2}=375 \end{gathered}[/tex]

Thus, the cost of bench is 375.

Michelle sells new and used kayaks. She makes a 10.5% commission on every kayak she sells and she also gets paid $495.50 per week. a) Develop an equation for the way Michelle is paid. b) Last month, the total value of the kayaks she sold was $19 425. Use the equation you’ve developed to find out how much Michelle was paid for that month.

Answers

Michelle was paid for that month is $ 4021.625

A linear equation is an algebraic equation of the form y=mx+b. regarding only a regular and a first-order (linear) time period, in which m is the slope and b is the y-intercept. on occasion, the above is called a "linear equation of two variables," where y and x are the variables.

Calculation:-

Percentage of commission = 10.5%

per week paid = $495.50

a. Equation of Michelle paid = 10.5/100X + 495.50

b. The total value of the kayaks she sold was $19 425.

  Michelle was paid for that month = 19 425 × 10.5/100 + 4 × 495.50

                                                          = 2039.625 + 1982

                                                          = $ 4021.625

A linear equation bureaucracy is an immediate line on a graph. A nonlinear equation paperwork an S-curve, bell curve, or any other nonlinear form on a graph. experts in mathematics and physics view linear equations as simple. specialists in mathematics and physics view nonlinear equations as complex.

A linear equation in a single variable is an equation wherein there is handiest one variable present. it is of the form Ax + B = 0, wherein A and B are any real numbers and x is an unknown variable that has the handiest one answer. for instance, 9x + 78 = 18 is a linear equation in one variable.

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2. A blanket is 4 feet wide. It is 3 times as long as it is wide. Draw a diagram of the blanket, and label its dimensions. b. Find the perimeter and area of the blanket.

Answers

the width of the blanket is 4 ft

it is given that length is 3 times of width so the length is 3 * 4 = 12 ft

part b)

so the blanket is rectangular.

the perimeter of the blanket is

2(4+12) = 32

area of the blanket is

length x width

12 x 4 = 48 square ft

part a)

the diagram of the blanket is given as follows,

Solve for x.
11x=2=8x+26

Answers

Answer:

X=8

Step-by-step explanation:

11x=2=8x=+26

11x -8x = -2 +26

3x=24

X=8

find the prime factorization ofa) 2205 and b)2525

Answers

(a) 2205.

The prime factorization consist in finding prime numbers which multiplication gives the initial number, to find those prime numbers, we divide the number by 2, 3, or 5, depending on the case. Let's do it.

2205 | 5

441 | 3

147 | 3

49 | 7

7 | 7

1

So, the prime factorization is

[tex]2205=5\times3\times3\times7\times7[/tex]

(b) 2525.

Let's repeat the process as we did with (a).

2525 | 5

505 | 5

101 | 101

1

So, the prime factorization is

[tex]2525=5\times5\times101[/tex]

Find the volume of this right rectangularprism.3 ft15 ft10 ft[? ]ft3

Answers

Given the following question:

[tex]\begin{gathered} volume=l\times b\times h \\ l=15 \\ b=10 \\ h=3 \end{gathered}[/tex][tex]\begin{gathered} volume=l\times b\times h \\ volume=15\times10\times3 \\ 15\times10=150 \\ 150\times3=450 \\ v=450ft^3 \end{gathered}[/tex]

Volume is equal to 450 feet^3.

Marshall has a rectangular garden that he wants to enclose with a fence. To calculate the perimeter, he used the expression below; where w represents the width and I represents the length of the garden. 2w + 2L Which other expression could Marshall use to calculate the perimeter?A. wLB.2wLC.2(w+2L)D.2(w+L)

Answers

by factoring the expression, you can also write

[tex]\begin{gathered} 2w+2l \\ 2(w+l) \end{gathered}[/tex]

graph the inequality x-2y less than or equal to 0

Answers

To graph the inequality, we can do the following steps.

Step 1: We rearrange the equation so y is on the left and everything else is on the right.

[tex]\begin{gathered} x-2y\le0 \\ \text{ Subtract x from both sides} \\ x-2y-x\le0-x \\ -2y\le-x \\ \text{ Divide by -2 from both sides} \\ \frac{-2y}{-2}\le\frac{-x}{-2} \\ y\ge\frac{x}{2} \end{gathered}[/tex]

Step 2: We plot the line associated with the inequality. For this, we choose two values of x and replace them in the below equation.

[tex]\begin{gathered} x=2 \\ $$\boldsymbol{y=\frac{x}{2}}$$ \\ y=\frac{2}{2} \\ y=1 \\ \text{ Then, the lines passes through the point (2,1).} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ y=\frac{x}{2} \\ y=\frac{4}{2} \\ y=2 \\ \text{ Then, the lines passes through the point (4,2).} \end{gathered}[/tex]

Since inequality has the symbol ≥, we make a solid line.

Step 3: Since inequality has the symbol ≥, we shade above the line. Therefore, the graph of the inequality is:

Figure 2 is the image of Figure 1. What is the scale factor?

Answers

Answer

Scale factor = (2/5)

Explanation

The scale factor shows the extent to which the original image has been dilated (enlarged or reduced). It is given mathematically as

[tex]\text{Scale factor = }\frac{Length\text{ of a side of the image}}{Length\text{ of the corresponding side of the original figure}}[/tex]

From the image attached we can see that

Length of a side of the image = 4 dots

Length of the corresponding side of the original image = 10 dots

Scale factor = (4/10) = (2/5)

Hope this Helps!!!

would the answer be written as 47 ¹¹⁰/¹⁷³? my daughter has to write the answer as the remainder as a fraction. 8241 ÷ 173

Answers

8241 ÷ 173

173 will go into 8241 47 times an we will have a remainder of 110

So, it will be written as;

8241 ÷ 173

[tex]=47\text{ }\frac{110}{173}[/tex]

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