A world-famous prix fixe menu includes the following choices.

Beverage (choose one): wine, soft drink, coffee, tea, milk, juice, or cappuccino

First course (no choice): baguette, bruschetta, whole roasted garlic, and butter

Second course (choose one): quesadilla, onion soup, salad, Caesar salad, lettuce wedge, spinach salad, or romaine salad

Third course (choose one): rib eye steak, swordfish, rack of lamb, whitefish, grilled chicken, southern fried chicken, lobster, or vegetarian plate
if you choose steak, then choose one of the following: fries, mashed potatoes, creamed corn, spinach, broccoli, or grilled onions

Fourth course (choose one): chocolate cake, cinnamon tart, apple tart, pecan tart, creme brulee, mango sorbet, or chocolate tart

How many different choices are possible?

Answers

Answer 1

Using the fundamental counting theorem, it is found that 107,016 different choices are possible.

Fundamental counting theorem:

States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

For the beverage, there are 7 options, hence [tex]n_1 = 7[/tex]For the first course, there are no choice, hence an arrangement of 4 options, that is, [tex]n_2 = 4! = 24[/tex]For the second course, there are 7 options, hence [tex]n_3 = 7[/tex]For the third course, there are 7 non-steak options, plus 6 steak options, hence [tex]n_4 = 13[/tex]For the fourth course, there are 7 choices, hence [tex]n_4 = 7[/tex]

Then, applying the theorem:

[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]

107,016 different choices are possible.

A similar problem is given at https://brainly.com/question/19022577


Related Questions

If the side of a square is increased by 25%, then by how much is its area increased?

Answers

Answer:

56.25%

Step-by-step explanation:

If a variable X changes by A% and another variable Y changes by B%, then overall net change when the two variables are multiplied is given by :

A + B + AB/100

If the change is “increase” it is positive & if the change is “decrease” it is negative.

In the given question, A = B = 25% ( Both positive as length increase )

And area = Side x Side

Applying our versatile relation :

Net increase in area = 25 + 25 + (25x25)/100 = 56.25%

Determine the intercepts of the line.
Do not round your answers.
y = 4r +7

Answers

Answer:

(-7/4, 0) (0, 7)

Step-by-step explanation:

I'm assuming r is x

0=4r+7

r=-7/4

y=0r+7

y=7

25 points! Help (Vectors)

Answers

Answer:

[tex]7\cos(30^{\circ})[/tex]

Step-by-step explanation:

if y=x^3+3 find the value of y when x=2

Answers

Answer:

11

Step-by-step explanation:

Substitute [tex]x=2:[/tex]

[tex]y=x^3+3[/tex]

[tex]y=2^3+3\\ =8+3\\ =11[/tex]

Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truck (not the least of which is that it runs). The new truck would cost $55,440. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,400. At the end of 8 years, the company will sell the truck for an estimated $27,700. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset’s estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company’s cost of capital is 8%.

Answers

The payback period of the investment is 6.6 years.

The net present value is $7,797.22.

The payback period calculates the amount of time it takes to recover the amount invested from the cumulative cashflows.

Payback period = Amount invested / cost saving

$55,440 / $8,400 = 6.6 years

Net present value is the present value of after-tax cash flows from an investment less the amount invested.  

NPV can be determined using a financial calculator

Cash flow in year 0 = $-55440

Cash flow in year 1 to 7 = $8,400

Cash flow in year 8 = $8400 + $27,700

I = 8%

NPV = $7,797.22

To learn more about net present value, please check: https://brainly.com/question/13739943?referrer=searchResult

Mr. Walthour is building a storage in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth.

Answers

5.06(repeating) pi or approx 15.917
meters cubed

The formula for volume of a cone is 1/3 area of base times height

We can find the r of the base by dividing the diameter by 2 which can then be used in pi r squared to find the area of the base. Now we just have to multiply this by the height (which is 3.8) and then divide by 3

4. Ms. Bragg is giving a test worth 100 points. The test contains a total of 40 questions. Some questions are worth 2 points and some questions are worth 4 points on the test. Write a system of equations to determine how many of each type of question are on the test. A) Define your variables. You can use any letters you want) B) Write your system of equations. (There should be 2 separate equations)​

Answers

9514 1404 393

Explanation:

A)

Let t and f represent the numbers of two-point and four-point questions, respectively.

__

B) The number of points for each type of question is the product of the point-value per question and the number of questions of that type.

  2t + 4f = 100 . . . . . the test is worth 100 points

  t + f = 40 . . . . . . . . there are 40 questions on the test

_____

Additional comment

The test will have 30 two-point questions and 10 four-point questions.

What is the solution to
4
+ 5 = 2 ?
X-3

Answers

Answer:

what you men

Step-by-step explanation:

Answer:

This may not be right, but I tried! I believe its 6.

Step-by-step explanation:

Explain the meaning of 5?
a. 1 + 2 + 3 + 4 + 5
b. 5-4-3-2-1-0
c. 0 x 1 x 2 x 3 x 4 x 5
d. 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1​

Answers

A. 5 is being added

B. 5 is being subtracted

C. 5 is being multiplied

D. 5 is being multiplied

I hope these answers are correct

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y2; about y = 1

Answers

We have y = 22
D? y
= VE
Now we find the points of intersection first: 27?
-
VE
2 = 0, 1 so when x is O y is also 0
and when x is 1, y is also 1
Hence the points of intersection are (0,0) and (1,1)
Given it is rotated about y
=1
So using disk method, the volume is given by:

The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.

Procedure - Determination of the volume of a solid of revolution

Let [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].

The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:

[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)

After substituting on each function and simplifying terms we get the following integral:

[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]

[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]

And the volume of the solid of revolution is:

[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]

[tex]V = \frac{11\pi}{30} [/tex]

The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]

To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504

Please hurry will mark brainliest if you answer correctly

Answers

Answer:

24.3

Step-by-step explanation:

Answer:

The answer would be 24.3

Consider the following equation.

x+2y=4
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,12) so that it will satisfy the given equation.

Answers

X= -20

Substitute the value of y, which is 12, into the equation and solve for x.

X+2y=4
X+2(12)=4
X+24=4
-24 -24
——————
X=-20

Richard purchases a box of 12 cookies and Meghan purchases a bag of 10 cookies. Richard ate x amount of cookies from his box while Meagan ate half the number of cookies Richard ate. How many cookies did Richard eat if they had the same number of cookies left

Answers

Richard: 12 cookies

Meghan: 10 cookies

If Richard eats 4 cookies, then Meghan would eat half, or 2. So Richard would have 8 cookies, and Meghan would also have 8 cookies.

12 - x = 10 - x/2

If x = 4

12 - 4 = 10 - 4/2

8 = 8

Which confirms that Richard would have to eat 4 cookies for them to have the same amount.

I hope this helps! :)

What is the gradient of the graph shown ? Give your answer in its simplest form

Answers

Answer:

-2

Step-by-step explanation:

choose any point on the graph

Answer:

Step-by-step explanation:

Yo you man its 3

f(x)=(1/7)^x then what is f(-3)​

Answers

Answer:

[tex]f(-3)=343[/tex]

Step-by-step explanation:

[tex]f(x)=(\frac{1}{7} )^x[/tex]

Plug -3 into x and solve using the negative power rule:

[tex]x^{-a}=\frac{1}{x^a}[/tex]

[tex]f(-3)=(\frac{1}{7} )^{-3} \\\\f(-3)=\frac{1}{\frac{1}{7}^3 } \\\\f(-3)=\frac{1}{\frac{1}{343} } \\\\f(-3)=343[/tex]

Sorry, those fractions got very small. Let me know if I need to clarify anything there

Faktor dari bilangan 18 adalah....

Answers

Step-by-step explanation:

1 x 18, 2 x 9, dan 3 x 6. Jadi, faktor dari 18 adalah 1, 2, 3, 6, 9, dan 18.

What is the prime factorization of 270?

Answers

270 = 2 x 3 x 3 x 3 x 5 = 2 x 3^3 x 5

ok done. Thank to me :>

Answer:

2x3x3x3x5

Step-by-step explanation:

if your doing this on time4learning lesson type 5x2x3x3x3 to get it right it worked for me but it didnt work in any other order

A company borrows $50,000 for 8 years at a simple interest rate of 13.5%. Find the interest paid on the loan and the total amount paid

The interest paid on the loan is $

The total amount paid is $

Answers

Answer:

13.5%×50000=6750

this is interest paid on loan 6750

50000+6750=56750

The total amount paid

Hello i need some help here the answer
A.x−3y=6 5x−y=10

B.3x−4y=24 2x+3y=−6

C.2x−9y=18 7x−2y=14

D.x−8y=16 5x+2y=20

Answers

The answer is A i took the test last week

9514 1404 393

Answer:

  A.  x −3y = 6; 5x −y = 10

Step-by-step explanation:

The first table gives the x- and y-intercepts, so you can write the equation for the line in intercept form as ...

  x/a +y/b = 1 . . . . . . x-intercept = a; y-intercept = b

The x-value with y=0 is a=6; the y-value with x=0 is b=-2. So, the equation of the line for the first table is ...

  x/6 +y/-2 = 1

Multiplying by 6 gives ...

  x -3y = 6

The only matching equation is in answer choice A.

__

You can check that the second given equation in choice A matches the second table:

for (x, y) = (-3, -25), you have ...

  5(-3) -(-25) = -15 +25 = 10 . . . . as required

Use set builder notation to write the set E= {1, 3, 9, 27}

PLEASE NO SPAMMING I NEED AN ANSWER NOW​

Answers

Answer:

E = { x | x = 3ⁿ, n ∈ N, and 0 ≤ n ≤ 3 }

Step-by-step explanation:

Given set:

E = {1, 3, 9, 27}

We observe that:

1 = 3⁰, 3 = 3¹, 9 = 3², 27 = 3³

Each term can be shown as 3ⁿ, where n is natural number between 0 and 3.

Set builder notation:

E = { x | x = 3ⁿ, n ∈ N, and 0 ≤ n ≤ 3 }
E={1,3,9,27}

Here let's observe

1=3^03=3^19=3^227=3^3

So set builder form:-

[tex]\\ \sf\longmapsto E=\{x|x=3^n,n\in N,0\leqslant n\leqslant 3\}[/tex]

can someone pls help me with dis ill give brainliest​

Answers

9514 1404 393

Answer:

  a) 9×10⁶ +1×10³ +1×10²

  b) 8×10⁷ +7×10⁶ +9×10⁴ +6×10³ +1×10² +4×10¹ +2×10⁰

Step-by-step explanation:

The place value of each digit is 10 to a power equal to the number of places the digit is to the left of the units (ones) place. That is, the exponent of 10 is the number of zeros in the multiplier for place value.

a)

9,001,100 = 9×1,000,000 +1×1,000 +1×100 = 9×10⁶ +1×10³ +1×10²

__

b)

87,096,142 = 80,000,000 +7,000,000 +90,000 +6,000 +100 +40 +2

  = 8×10⁷ +7×10⁶ +9×10⁴ +6×10³ +1×10² +4×10¹ +2×10⁰

_____

Additional comment

It is useful to learn to think of place value in this way, because it helps immensely when you convert numbers to or from scientific notation.

You may notice the powers of ten count up for places to the left of the decimal point. They count down for places to the right. That is, the tenths place has a place value that is the inverse of the tens place: 1/10 = 10⁻¹.

3. Marilyn hit a golf ball on the ground with her driver. Use

the general function for a projectile to write a function

that shows the height in feet of her golf ball as a function

of time. The ball was hit with an initial vertical velocity of

130 feet per second.

h(t) = -16t2 + 130t


a) How long will Marilyn's ball stay in the air?


b) What was the maximum height of the ball?

Answers

It will take the ball 4.0625secs to stay in the air

The maximum height of the ball is 264.0625m

Given the function representing the height reached by the golf expressed as;

h(t) = -16t^2 + 130t

The velocity function is expressed as:

v(t) = -32t + 130

At maximum height, the velocity of the ball will be zero, i.e v(t) = 0

0 = -32t + 130

32t = 130

t = 130/32

t = 4.0625

Hence it will take the ball 4.0625secs to stay in the air

b) Substitute t = 4.0625 into the height function to have:

h(t) = -16t^2 + 130t

h(t) = -16(4.0625)^2 + 130(4.0625)

h(4.0625) = -264.0625 + 528.125

h(t) = 264.0625m

Hence the maximum height of the ball is 264.0625m

Learn more on velocity function here: https://brainly.com/question/10962624

I need help really bad! I have literally no clue what the answer is to this question

Answers

Answer: C is the answer

Answer:

The second answer: {(-1, 4),(2, 7),(3,7)} because every x value has one y value

Scores in the first and final round for a sample of 8 golfers who completed golf tournament as shown below. Golfer First Round Final Round 1 73 78 2 68 75 3 70 66 4 67 71 5 71 73 6 70 68 7 68 65 8 73 72 a. State any appropriate hypothesis that can be tested for the above data. Use 2% level of significance to test the stated hypothesis. Use p-value approach

Answers

Answer:

golfing is fun but not to fun

Step-by-step explanation:

Given that m||n, find the value of x.

Answers

Answer:

[tex] \boxed{ \sf{x = 65 \degree}}[/tex]

Step-by-step explanation:

In the given figure we have two corresponding angles.

We know that corresponding angles are equal to each other

So,

2x+5 = 1352x = 135 - 52x = 130x = 130/2x = 65

Therefore, x = 65°

Corresponding angles are same

[tex]\\ \sf\longmapsto 2x+5=135[/tex]

[tex]\\ \sf\longmapsto 2x=135-5[/tex]

[tex]\\ \sf\longmapsto 2x=130[/tex]

[tex]\\ \sf\longmapsto x=130/2[/tex]

[tex]\\ \sf\longmapsto x=65°[/tex]

What is the solution of this inequality?

r−10>−7

Drag and drop the choices to correctly complete the inequality.

r Response area Response area

Answers

Answer:

=r-10+10>-7+10

=r>3

first add +10 to the both sides so as to balance the inequality then do a simple calculation which results you to the final answer.

For r > 3, the inequality r - 10 > -7 is satisfied.

What is a expression? What is a mathematical equation? What is Equation Modelling? What is inequality?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. An inequality is a relation comparing two expressions. For example -

3x + 4 > 5

ax + b < c

We have the following inequality -

r - 10 > -7

We can write -

r - 10 > -7

r - 10 + 10 > - 7 + 10

r > 3

Therefore, for r > 3, the inequality r - 10 > -7 is satisfied.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Plz solve. The question is in the picture. 100 points and brainliest.

Answers

Answer:

A

Step-by-step explanation:

At a coffee shop, a latte costs $5.50 and
hot tea costs $1.75. Each day, Parker
buys 2 hot teas and several lattes for
his office staff. Which equation can be
used to find y, Parker's total cost, if x
represents the number of lattes? (7.1A,
7.1B, 7.1D, 7.1F)
A y = 5.50x + 3.50
BY 5.50x + 1.75
C y = 1.75x + 5.50
Dy = 3.50x + 5.50

Answers

Answer:

A) y = 5.50x + 3.50

Step-by-step explanation:

2 x 1.75 = 3.50 + x number of lattes $5.50 each.

if someone helps me with dis ill give u brainliest​

Answers

Answer:

4 different answers

Step-by-step explanation:

1.

[(24/3) + (5*2^2)] = 28

2.

[(3 + 5) * 2^2 )]/24 = 32/24 = 4/3

3.

[(24/3 + 5)*2^2] = 52

4.

[(3 + 5*2^2)/24] = 23/24

Answer:

Step-by-step explanation:

1 - 2 + 10 o lw. First find a common denominator. 3 * 5 ... Divide the fraction to get a decimal answer. 21 into a an. Jinit. 5 = 1.25. Find a common.

The figure below is a square with an area of 625 square centimeters. The length of a rectangle is 40% more than the length of the square. Find the length of the rectangle.

Answers

For a square:

A = s2, where s = side (the length and the width are the same)

625 = s2

±25 = s

length of rectangle = 1.4 · length of square

length of rectangle = 1.4(25)

length of rectangle = 35

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