Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,699 was collected on the sale of 1,179 tickets. How many of each type of ticket were sold?

Recal the binomial theorem:

[tex]\displaystyle (a+b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

Then

[tex]\displaystyle (2q+p)^{21} = \sum_{k=0}^{21} \binom{21}k (2q)^{21-k} p^k = \sum_{k=0}^{21} \binom{21}k 2^{21-k} q^{21-k} p^k[/tex]

We get the q⁴p¹⁷ term when k = 17, and its coefficient would be

[tex]\dbinom{21}{17} 2^{21-17} = \dfrac{21!}{17!(21-17)!} 2^4 = \dfrac{21\cdot20\cdot19\cdot18}{4\cdot3\cdot2\cdot1}\cdot2^4 = \boxed{95,760}[/tex]

Answer:

y = (3/4)x + 17/4

Step-by-step explanation:

since we know the slope is 3/4, we have y = 3/4x + b. next plug in the point given. 5= 3/4(1) + b, simplify the equation to get 17/4=b, and now we have our equation: y = 3/4x + 17/4

Answer:

Square 2 and 4? sorry im not very good at this stuff but thats my guess goodluck

Step-by-step explanation:

I think the answer might be c

I think its 52 I'm not sure please dont get angry If I got it wrong

Answer:

The answer is a

Step-by-step explanation:

Like and give 5 star rating

Answer:

8/3 miles over 8miles

8 mi/3 hrs = 8/3 mi/hr = 2.66666.

Answer:

48 books

Step-by-step explanation:

Answer:

A = 18 in²

Step-by-step explanation:

The area of a triangle can be calculated using the formula A = (bh)/2

where b = base length and h = height

Fortunately for us, the variables are already defined and given to us in the problem

All we have to do is plug in the values of h and b into the formula for area of a triangle

A = (bh)/2

b = 3 and h = 12

A = ((12)(3))/2

multiply 12 and 3

A = 36/2

divide 36 by 2

A = 18 in²

Answer:

B) men are less likely to prefer driving trucks than women

Step-by-step explanation:

Using continuous compounding and compound interest, it is found that Matthew would have $17 more than Elizabeth in his account.

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

Continuous compounding:

[tex]A(t) = Pe^{rt}[/tex]

The parameters are:

For both of them:

Elizabeth:

Then:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(8) = 970\left(1 + \frac{0.06625}{365}\right)^{365(8)}[/tex]

[tex]A(8) = 1648[/tex]

Matthew:

Then:

[tex]A(t) = Pe^{rt}[/tex]

[tex]A(8) = 970e^{0.0675(8)}[/tex]

[tex]A(8) = 1665[/tex]

The difference is:

1665 - 1648 = 17

Hence, Matthew would have $17 more than Elizabeth in his account.

A similar problem is given at https://brainly.com/question/24507395

Answer:

14

Step-by-step explanation:

When there are 2 -, they both create a +. the brackets are removed and you get 4--10, which is equal to 4+10 which = 14

Answer:

x= -2

Step-by-step explanation:

y=x+4

y=2

2=x+4

-4+2=x

-2=x

x=-2

Answer:

x= -2

Step-by-step explanation:

Answer:

11, 15

Step-by-step explanation:

They both occur two times so they are tied for mode so both numbers is the answer

Answer:

  $169.33

Step-by-step explanation:

Each of the friends spent ...

  $14.95 +6.99 +2.25 = $24.19

The seven friends together spent ...

  7($24.19) = $169.33

Answer:

X+y over y

Step-by-step explanation:

X+y over y

Hope it helps

Answer:

going up by 2 numbers

Step-by-step explanation:

The resulting function is presented in the image attached below.

In this question we know the graphic of a function and we must draw a new function which is the reflection of the original one around the x-axis. Mathematically speaking, a reflection a around the x-axis is defined by the following operation:

[tex]f'(x) = f(x) - 2\cdot [f(x) - 0][/tex]

[tex]f'(x) = - f(x)[/tex] (1)

Which means that the reflected function is equal to the original function multiplied by -1.

Now, we proceed to represent the reflected function graphically.

We kindly invite to check this question on reflections: https://brainly.com/question/15487308

Answer: B

Step-by-step explanation:

The slope-intercept is usually written as y = mx + b form, where m is the slope, and b is the y-intercept. The y-intercept is the y value when x is equal to 0.

We can first eliminate C, because the y-intercept of the graph is 1.

To solve for slope, which is the m, choose two points, (-1, 5) and (1, -3).

Slope = (y2 - y1) / (x2 - x1)  

           = (-3 - 5) / (1 - (-1))

          = (-3 - 5) / (1 + 1)

          = -8/2

          = -4

Plug in the slope and y-intercept, we get y = -4x + 1

In a given permutation of 52 cards, if the 3 of spades is to follow all of the hearts, that means the 3 of spades must be at least the 14th card in the deck.

Consider some possible orderings of the deck:

• If the 3 of spades is the 14th card, then the deck looks like

[all 13 ♥] … 3 ♠ … [all other 38 cards]

There are 13! ways to arrange the 13 hearts at the beginning and 38! ways to arrange the tail of 38 cards. Hence there are 13! × 38! possible rearrangements of the deck where 3 ♠ is the 14th card.

• If 3 ♠ is the 15th card, then the deck looks like

[13 ♥ and 1 other] … 3 ♠ … [all other 37 cards]

and there would be 14! × 37! ways of arranging the cards in this order.

There are 39 possible positions for 3 ♠. Extrapolating, it follows that the total number of permutations of the deck in which all hearts occur before 3 ♠ is

[tex]\displaystyle \sum_{k=0}^{38} (13+k)! \times (38-k)![/tex]

There are 52! total possible ways of rearranging the deck. Then the probability of rearranging the deck so that all hearts are drawn before 3 ♠ is

[tex]\displaystyle \frac1{52!} \sum_{k=0}^{38} (13+k)! \times (38-k)! = \frac{87,031,512,096,420,449}{221,360,321,731,856,907,600} \approx \boxed{0.000393}[/tex]

Answer:

  B.  28.5

Step-by-step explanation:

Before you can use the Law of Sines, you need to know the measure of angle C. The sum of angles in a triangle is 180°, so you have ...

  A + B + C = 180°

  C = 180° -A -B = 180° -32° -25° = 123°

The Law of Sines tells you ...

  c/sin(C) = a/sin(A)

  c = sin(C)·a/sin(A) = sin(123°)·18/sin(32°)

  c ≈ 28.5

_____

Additional comment

The law of sines says the ratio of a side length to the sine of the opposite angle is a constant for any given triangle:

  a/sin(A) = b/sin(B) = c/sin(C)

In order to use this relationship, you need to have a side length and its opposite angle. If you're solving for a side length, as here, you need to know the angle opposite that side.

This problem gives you side 'a' and angle A, and it asks for side 'c'. That means you need to know angle C, which we found as part of our solution.

She spent 2 hours and 45 minutes.

Answer:

80

Step-by-step explanation:

honestly it depends on the question but if it's addition, this is the answer

Answer:

48 1/3 inches

Step-by-step explanation:

Each size 8 shoe measures 9 2/3 inches. If we line 5 of them together, the length of the entire thing will be 5 times the size of each shoe, 9 2/3 in. To write 5 as a fraction, put it over a denominator of 1. Then rewrite 9 2/3 as an improper fraction. Now you can multiply across and simplify as needed.

Answer:

the person below is correct

Step-by-step explanation:

hope this helps have a good rest of ur night :)❤

Answer:

There are none.

Step-by-step explanation:

No calculus involved:

The line, in slope-intercept form, has equation [tex]y=-10x+17[/tex], ie is always decreasing (easy to spot applying the definition)

Meanwhile, [tex]y=e^{5x}[/tex] is always increasing over its domain.

At no point the tangent will be decreasing.

Let's use calculus

We are to solve the equation [tex]y'(x) = -10 \rightarrow 5e^{5x} = -10 \rightarrow e^{5x}=-2[/tex] which has no real solutions.

Answer: isn't it 42÷7=6?

Answer:

42 / 7 = 6

Step-by-step explanation:

Just use a multiplication table.

Answer:

500 shots

Step-by-step explanation:

the question is 8% of what number is 40?

we can use this proportion:  is/of = %/100

let 'g' = number of goals

40/g = 8/100

cross-multiply to get:

8x = 4000

x = 500

Sum of x and 10 is (x+10)

Half of sum of x and 10 = [tex] \frac{x + 10}{2} \\ [/tex]