MATHEMATICS COLLEGE

There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees can he choose, assuming that the order of the entrees chosen does not matter ?

Answers

Answer 1

Answer:

Answer: 8008

Step-by-step explanation:

Total entrees = 16

Number of entrees to choose = 6

Since order does not matter , so we combinations .

Number of combinations to choose r things out of n = $C(n,r)=(n!)/(r!(n-r)!)$

Then, total ways to choose 6 entrees = $C(16,6)=(16!)/(6!10!)$

$=(16*15*14*13*12*11*10!)/((720)10!)\n\n= 8008$

Hence, the required number of ways= 8008

Related Questions

Select the correct answer. Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second? O A. 15+ d = 100 B. 100 + d = 15 O c. dx 15 = 100 D. d x 100 = 15
Last question if ya don’t mind giving me a help
Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ θ < π. Enter your answers as a comma-separated list of ordered pairs.)r = 6 cos(θ)
Find the y-intercept and x-intercept of the line -x+2y=4
In tilapia, an important freshwater food fish from Africa, the males actively court females. They have more incentive to court a female who has already laid all of her eggs, but can they tell the difference? an experiment was done to measure the male tilapia's response to the smell of female fish. Water containing feces from females that were either pre-ovulatory (they still had eggs) or post-ovulatory (they had already laid their eggs) was washed over the gills of males hooked up to an electro-olfactogram machine which measured when the senses of the males were excited. The amplitude of the electro-olfactogram was used as a measure of the excitability of the males in the two different circumstances. Six males were exposed to the scent of pre-ovulatory females; their readings average 1.51 with a standard deviation of .25. Six different males were exposed to post-ovulatory females; their average readings of 0.87 with standard deviation is .31. Assume that the electro-olfactogram readings were approximately normally distributed within the groups.(A) test for a difference in the excitability of the males with exposure to these two types of females(B) what is the estimated average difference in electro-olfactogram readings between the two groups? What is the 95% confidnece limit for the difference between population means?

Line A y= 2x + 3 is parallel to another line B, what is the slope of the line B?

Answers

Answer:

Step-by-step explanation:

Since the lines are parallel, then the slope of line B would be the same as line A.

Use the inner product〈f,g〉=∫10f(x)g(x)dxin the vector space C0[0,1] of continuous functions on the domain [0,1] to find 〈f,g〉, ∥f∥, ∥g∥, and the angle αf,g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f,g〉= ,∥f∥= ,∥g∥= ,αf,g .

Answers

Answer:

a) <f,g> = 2605/3

b) ∥f∥ = 960

c) ∥g∥ = 790

d) α = 90

Explanation

a) We calculate <f,g> using the definition of the inner product:

$<f,g> = \int\limits^1_0 {10(-10x^(2) -6)(-9x-4)} \, dx \n \n =\int\limits^1_0 {900x^(3)+400x^(2) +540x+240 } \, dx\n \n = (225x^(4) + (400x^(3) )/(3) + 270x^(2) +240x)\n = (2605)/(3)$

b) How

∥f∥ = <f,f> then:

∥f∥ = $<f,f> = \int\limits^1_0 {10(-10x^(2) -6)(-10x^(2) -6)} \, dx \n \n =\int\limits^1_0 {1000x^(4)+1200x^(2) + 360} \, dx\n \n = (200x^(5) + 400x^(3) + 360x)\n = 960$

∥g∥ = <g,g>

∥g∥ = $<g,g> = \int\limits^1_0 {10(-9x-4)(-9x-4)} \, dx \n \n =\int\limits^1_0 {810x^(2)+720x + 160} \, dx\n \n = (270x^(3) + 360x^(2) + 160x)\n = 790$

d) Angle between f and g

<f,g> = ∥f∥∥g∥cosα

Thus

$\alpha = cos^(-1)((2605/3)/((790)(960)) )\n\n\alpha = 90$

Final answer:

The answer to this problem involves applying integrals, norms, and concepts of angles between vectors to the functions f(x) and g(x). The INNER PRODUCT is the integral of the products of the two functions, the norms are the square roots of the inner products of the functions with themselves, and the angle between the functions is calculated using the dot product and norms.

Explanation:

To find the inner product 〈f,g〉, the norms ∥f∥ and ∥g∥, and the angle αf,g between the functions f(x)=−10x2−6 and g(x)=−9x−4, we'll apply concepts from vector calculus. The inner product (also known as the dot product) is the integral from 0 to 1 of the products of the two functions. The norm of a function is the square root of the inner product of the function with itself. The angle between two vectors in a Vector Space, in this case the space of continuous functions C0[0,1], is given by cos(α) = 〈f,g〉/( ∥f∥∙ ∥g∥). Integrating and solving these equations will give us the desired values.

Learn more about Vector Calculus here:

brainly.com/question/10164701

#SPJ11

5628763672÷7727467828

Answers

0.72840984877 is the answer :)

A portrait without its frame has a height 1.5 times its width w, in inches. The width of the frame is 3 inches. Which of the following is an expression for the area of the framed portrait in terms of w

Answers

Answer:

Area = $1.5w^2+15w+36$

Step-by-step explanation:

Let the width of portrait be 'w'

Given:

Height of portrait without frame (h) = 1.5 times its width = $1.5w$

Width of the frame is 3 inches on all sides.

Area of the framed portrait is the total area of the portrait plus the area of the frame.

The figure representing the above scenario is shown below.

From the figure, area of rectangle ABCD is the area of the framed portrait.

From the figure,

AB = $3 + w + 3 = w + 6$

BC = $3 + h + 3 = h + 6 = 1.5w + 6$

Now, area of the rectangle ABCD is given as the product of the length AB and width BC. Therefore,

$Area=AB* BC\n\nArea=(w+6)(1.5w+6)\n\nArea=(w* 1.5w)+(w* 6)+(6* 1.5w)+(6* 6)\n\nArea=1.5w^2+6w+9w+36\n\nArea=1.5w^2+15w+36$

Therefore, the expression for the area of the framed portrait in terms of the width 'w' is given as:

Area = $1.5w^2+15w+36$

The area of the portrait without the frame will be $A=13.5=1.5w^2$ .

Given information:

A portrait without its frame has a height 1.5 times its width w, in inches.

The width of the frame is 3 inches.

Length of the frame will be,

$l=1.5w\nl=1.5* 3\nl=4.5$

So, the area of portrait without frame will be,

$A=l* w\nA=1.5w* w\nA=1.5w^2\nA=1.5* 9=13.5=1.5w^2$

Therefore, the area of the portrait without the frame will be $A=13.5=1.5w^2$ .

For more details, refer to the link:

brainly.com/question/15218510

.
What is the y intercept of the line represented by the equation
3x+2y = 6?

Answers

Answer:

Step-by-step explanation:

To identify the y-intercept represented by the given equation, we need to get the equation into slope-intercept from:

$y=mx+b$

$m=slope$

$b=y-intercept$

Start with:

$3x+2y=6$

Subtract $3x$ from both sides of the equation:

$2y=-3x+6$

Divide both sides of the equation by the coefficient of $y$ , which is $2$ :

$y=-1.5x+3$

Identify the y-intercept:

$b=3$

Determine the next step for solving the quadratic equation by completing the square. 0 = –2x2 + 2x + 3

Answers

Answer:

-1/2, 1/4, 1/2 on edge

The next step is to divide the equation by -2

-2(x^2 - x) + 3 = 0

Other Questions

Order of operations (41-3^2)-(4+4)

8=16-8n Solve for NN=

Using the table of ordered pairs, which equation shows the linear relationship between the x and y values? ---- ---- x|y-2|2 1|5 3|7---- ----A. y = x + 4 B. y = -x C. y = x - 4 D. y = 4 - x

Maggie rewrote the expression 36 + 27 as two factors using the greatest common factor and the distributive property. Write the expression Maggie created.