Tickets to the college basketball game are $2.50 for students and $3 for general admission. If 58 people attended the last game and the box office collected $162, how many of each type of ticket did they sell?

The box office sold _____ general admission tickets and _____ student tickets.

Answer:

The x-intercept is (7,0).

Step-by-step explanation:

See the graph below for explanation

Answer:

(x+1) (x^2+6)

Step-by-step explanation:

x^3+6x+x^2+6

Rearranging the order

x^3+x^2 + 6x+6

We can factor by grouping

Taking an x^2 from the first two terms and a 6 from the last two terms

x^2(x+1) +6(x+1)

Now we can factor out an (x+1)

(x+1) (x^2+6)

Answer:

I

Step-by-step explanation:

At least means greater than or equal to

a ≥ 10

That is a closed circle

We have a closed circle at 10

We have to be at least 10 years old

Closed circle at 10, line going to the right

Answer:

D. (4, -4)

Step-by-step explanation:

Convert to vertex form by completing the square.

For a polynomial y = x² + bx + c, first add and subtract (b/2)² to the polynomial.  Then factor.

Here, b = -8.  So (b/2)² = (-8/2)² = 16.

y = x² − 8x + 12

y = x²− 8x + 16 − 16 + 12

y = (x − 4)² − 16 + 12

y = (x − 4)² − 4

The vertex is (4, -4).

The vertex of the function y = x2 - 8x + 12 is found by first using the formula -b/2a to find the x-coordinate of the vertex, and then substituting that value into the equation to find the y-coordinate. This results in the vertex being at the point (4,-4).

The vertex of a quadratic function given in the form y = ax2 + bx + c is found using the formula -b/(2a) for the x-coordinate, and substituting that value into the equation to find the y-coordinate. In the given function y = x2 - 8x + 12, a is equal to 1, and b is equal to -8.

Using the vertex form, the x-coordinate of the vertex can be found by using -b/2a, or --8/(2*1), which equals 4. This becomes the x-coordinate of our vertex. Substituting x = 4 into our equation, we find y = (4)2 - 8*4 + 12 = -4. Therefore, the vertex of the given graph is at the point (4,-4), which corresponds to option D.

https://brainly.com/question/31410496

#SPJ2

Answer:

The answer is an attachment I hope it helps!!!

Based on these first few terms, we can deduce that the next term is computed by switching the sign of the previous one, and multiplying it by 3: we start with -1, we switch the sign (1) and multiply by 3 (3); then again we switch the sign (-3) and multiply by 3 (-9), and so on.

Since switching sign is the same as multiplying by -1, we can compute every next term by multiplying the previous one by -3:

[tex]a_1 = -1\\a_2 = a_1\cdot(-3) = (-1)\cdot(-3)=3\\a_3 =a_2\cdot(-3)=3\cdot(-3)=-9[/tex]

So, the recursive formula is

[tex]a_n = -3a_{n-1}[/tex]

because it states precisely that the next term is -3 times the previous one.

Answer:

=136

Step-by-step explanation:

Lets solve the triangle using the sine formula.

c/sine C=a/sine A

C= 180-(72+16)

=92°

61/Sin 92=a/sin 72

a=(61 sin 72)/sin 92

=58.0

Solving for b:

c/sin C= b/Sin B

61/sin 92= b/Sin 16

b=(61 Sin 16)/Sin 92

=16.82

Perimeter = 61 +58+ 16.82 = 135.82

Answer =136 to the nearest whole number.

Answer:

Some part of the question is missing , you are requested to kindly recheck it once. There must be some time provided in the problem

Step-by-step explanation:

Answer:

slope = 7/2

y-int = 4

Step-by-step explanation:

parent formula is y=mx+b ; where m is slope and b is y-int.

begin by rewriting formula to isolate y ; 7x+8=2y ; divide bothe sides by 2 ; so

7/2 x+4=y. slope/m=7/2 and y-int/b=4

Both 3 and 24 have 3 in common.  This means that you can factor a three out of this equation like so:

3(x + 8y)

If you distribute the three back into the equation then you would then get 3x + 24y (the equation before factoring)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3 ( x + 8 y )

Step-by-step explanation:

Since 3 is the LCM ( lowest common multiple ) which goes into both numbers, it will go on the outside of the brackets. To get the insides of the brackets you have to divide the original expression by 3

3 ÷ 3 x = x

24 y ÷ 3 = 8 y

And our final factored form is 3 ( x + 8 y )

Answer:

A

Step-by-step explanation:

The following ratio is true for any circle

[tex]\frac{arc}{C}[/tex] = [tex]\frac{centralangle}{360}[/tex] ← C is circumference

[tex]\frac{4}{C}[/tex] = [tex]\frac{30}{360}[/tex] ( cross- multiply )

30C = 1440 ( divide both sides by 30 )

C = 48 → A

Answer:48

Step-by-step explanation:i got it right

Answer:

8x^3-46x^2-5x+18

Step-by-step explanation:

The volume of a rectangular prism is L*W*H where

L=length

W=width

H=height.

So we want to probably find the standard form of this multiplication because writing (4x+3)(x-6)(2x-1) is too easy.

Let's multiply (4x+3) and (x-6), then take that result and multiply it to (2x-1).

(4x+3)(x-6)

I'm going to use FOIL here.

First:  4x(x)=4x^2

Outer:  4x(-6)=-24x

Inner:  3(x)=3x

Last:   3(-6)=-18

---------------------------Add.

4x^2-21x-18

So we now have to multiply (4x^2-21x-18) and (2x-1).

We will not be able to use FOIL here because we are not doing a binomial times a binomial.

We can still use distributive property though.

(4x^2-21x-18)(2x-1)

=

4x^2(2x-1)-21x(2x-1)-18(2x-1)

=

8x^3-4x^2-42x^2+21x-36x+18

Now the like terms are actually already paired up we just need to combine them:

8x^3-46x^2-5x+18

Answer:

[tex]\large\boxed{8x^3-46x^2-15x+18}[/tex]

Step-by-step explanation:

The formula of a volume of a rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have l = 4x + 3, w = x - 6 and h = 2x - 1.

Substitute:

[tex]V=(4x+3)(x-6)(2x-1)[/tex]

use FOIL: (a + b)(c + d)

[tex]V=\bigg[(4x)(x)+(4x)(-6)+(3)(x)+(3)(-6)\bigg](2x-1)\\\\=(4x^2-24x+3x-18)(2x-1)\qquad\text{combine like terms}\\\\=(4x^2-21x-18)(2x-1)[/tex]

use the distributive property: a(b + c) = ab + ac

[tex]V=(4x^2-21x-18)(2x)+(4x^2-21x-18)(-1)\\\\=(4x^2)(2x)+(-21x)(2x)+(-18)(2x)+(4x^2)(-1)+(-21x)(-1)+(-18)(-1)\\\\=8x^3-42x^2-36x-4x^2+21x+18[/tex]

combine like terms

[tex]V=8x^3+(-42x^2-4x^2)+(-36x+21x)+18\\\\=8x^3-46x^2-15x+18[/tex]

Answer:

2x^3 + x^2 - 9x + 6

Step-by-step explanation:

(2x^2 + 3x - 6)(x - 1)

2x^3 + 3x^2 - 6x - 2x^2 - 3x + 6

2x^3 + x^2 - 9x + 6

Answer:

(21, 80)

Step-by-step explanation:

We have the two lines y = 4x -4  and y = 3x + 17. The point 'C' will be given by the interception of them, as follows:

4x -4 = 3x + 17

Solving for 'x':

x = 21

Now, to find 'y' we have:

y = 4(21) -4 = 80

Therefore, they intercept at: (21, 80)

For this case we must find the value of "x":

We have that, by definition:

[tex]4x-4 = 3x + 17[/tex]

Because they are opposite the vertex.

Then, subtracting[tex]3x[/tex] on both sides we have:

[tex]4x-3x-4 = 3x-3x + 17\\x-4 = 17[/tex]

Adding 4 to both sides:

[tex]x = 17 + 4\\x = 21[/tex]

So, the value of x is 21

Answer:

[tex]x = 21[/tex]

Answer:

1) (2x - 3)(x + 5)

2) 1.5, -5

3) Open upwards from both ends

4) Minimum

Step-by-step explanation:

Step 1:

The given polynomial is:

[tex]2x^{2}+10x-3x-15[/tex]

Taking out commons, we get:

[tex]2x(x+5)-3(x+5)\\\\ =(2x-3)(x+5)[/tex]

This is the factorized form of the polynomial.

Step 2:

The zeros of the functions occur when the function is equal to zero.

i.e.

[tex](2x-3)(x+5)=0\\\\ \text{According to the zero product property}\\\\ 2x-3=0, x+5=0\\\\ x =\frac{3}{2}=1.5, x = -5[/tex]

This means, the zeros of the polynomial are 1.5 and -5

Step 3:

The end behavior of a graph depends on its degree and the sign of leading coefficient. Since the degree is even and the coefficient is positive the graph of the polynomial will opens upwards from left and right side.

Step 4:

The given polynomial is a quadratic function with positive leading coefficient. Since it open vertically upwards, its vertex will be the lowest most point. So, the vertex will be the minimum of the function.

Answer:

0.9317

Step-by-step explanation:

Standard deviation of the weights = [tex]\sigma[/tex]=100 lbs

Mean weight = u = 1200 lbs

We need to find the probability that the weight(x) of a randomly selected steer is between 1000 lbs and 1369 lbs i.e. P(1000 < x < 1369)

Since, weights follow the normal distribution we can use the z values to find the required weight. For this we have to convert both the values to z score. The formula for z scores is:

[tex]z=\frac{x-u}{\sigma}[/tex]

1000 converted to z scores is:

[tex]z=\frac{1000-1200}{100}=-2[/tex]

1369 converted to z scores is:

[tex]z=\frac{1369-1200}{100}=1.69[/tex]

So, we have to find the values from z table that lie between -2 to 1.69

P( 1000 < x < 1369 ) = P(-2 < z < 1.69)

P(-2 < z < 1.69) = P(z < 1.69) - P(z < -2)

From the z table:

P(z < 1.69) = 0.9545

P(z < -2) = 0.0228

So,

P(-2 < z < 1.69) = 0.9545 - 0.0228 = 0.9317

Thus,

P( 1000 < x < 1369 ) = 0.9317

From this we can conclude that:

The probability that the weight of a randomly selected steer is between 1000 lbs and 1369 lbs is 0.9317

Final answer:

The probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean of 1200lbs and standard deviation of 100lbs, is approximately 0.9326 or 93.26%.

Explanation:

To find the probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean (μ) of 1200lbs and a standard deviation (σ) of 100lbs, we first convert the weights into z-scores.

The z-score for a value x is given by the formula:

z = (x - μ) / σ

Calculating the z-scores for both weights:

For 1000lbs: z = (1000 - 1200) / 100 = -2

For 1369lbs: z = (1369 - 1200) / 100 = 1.69

We then look up these z-scores in a standard normal distribution table or use a calculator with statistical functions to find the probabilities for each. The probability for a z-score less than -2 is approximately 0.0228, and for a z-score less than 1.69 is approximately 0.9554.

To find the probability that a steer's weight falls between 1000lbs and 1369lbs, we subtract the smaller probability from the larger probability:

Probability = P(z < 1.69) - P(z < -2) = 0.9554 - 0.0228 = 0.9326

Therefore, the probability that a steer weighs between 1000 and 1369lbs is 0.9326, or 93.26% when rounded to four decimal places.

Answer:

4 , 2 , 10 , 5

Step-by-step explanation:

46,880

Since this is an even number, we can divide by 2

46,880/2 =23440

Since this number ends in either a 0 or a 5 we can divide by 5

46880/5 =9376

Since the number is divisible by 2 and 5, we know it is divisible by 10

46880/10 =4688

The only number we need to check is 4

If the last 2 numbers are divisible by 4 then the number is divisible by 4

80/4 = 20  so the number is divisible by 4

46880/4 =11720

46880 is divisible by 4,2,10,5

Answer:

all of the are correct

Answer:

Answer in factored form: [tex]P(x)=(x+2)(x-7)(x-5)^2[/tex]

Answer in standard form: [tex]P(x)=x^4-15x^3+61x^2+15x-350[/tex]

Step-by-step explanation:

I don't see your choices but I can still give you a polynomial fitting your criteria. I will give the answer in both factored form and standard form.

The following results are by factor theorem:

So if x=-2 is a zero then x+2 is a factor.

If x=7 is a zero then x-7 is a factor.

If x=5 is a zero then x-5 is a factor.  It says we have this factor twice.  I know this because it says with multiplicity 2.

So let's put this together.  The factored form of the polynomial is

A(x+2)(x-7)(x-5)(x-5)

or

[tex]A(x+2)(x-7)(x-5)^2[/tex]

Now A can be any number satisfying a polynomial with zeros -2 and 7 with multiplicity 1, and 5 with multiplicity 5.

However, it does say we are looking for a polynomial function with leading coefficient 1 which means A=1.

[tex](x+2)(x-7)(x-5)^2[/tex]

Now the factored form is easy.

The standard form requires more work (multiplying to be exact).

I'm going to multiply (x+2)(x-7) using foil.

First: x(x)=x^2

Outer: x(-7)=-7x

Inner: 2(x)=2x

Last: 2(-7)=-14

--------------------Adding.

[tex]x^2-5x-14[/tex]

I'm going to multiply [tex](x-5)^2[/tex] using formula [tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](x-5)^2=x^2-10x+25[/tex].

So now we have to multiply these products.

That is we need to do:

[tex](x^2-5x-14)(x^2-10x+25)[/tex]

I'm going to distribute every term in the first ( ) to

every term in the second ( ).

[tex]x^2(x^2-10x+25)[/tex]

[tex]+-5x(x^2-10x+25)[/tex]

[tex]+-14(x^2-10x+25)[/tex]

------------------------------------------ Distributing:

[tex]x^4-10x^3+25x^2[/tex]

[tex]+-5x^3+50x^2-125x[/tex]

[tex]+-14x^2+140x-350[/tex]

-------------------------------------------Adding like terms:

[tex]x^4-15x^3+61x^2+15x-350[/tex]

Answer:

f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Step-by-step explanation:

Answer:

с. х = 26

Step-by-step explanation:

x – 9 = 17

Add 9 to each side

x – 9+9 = 17+9

x = 26

Answer:

4/7

Step-by-step explanation:

P(A or B) when A and B are disjointed is P(A)+P(B)

P(A or B)=P(A)+P(B)

P(A or B)=1/7 +3/7

P(A or B)=4/7

The value of P(A or B) is 4/7 (3rd option)

Let A and B be two disjoint events.

Then, probability of A is P(A) & probability of B is P(B).

In this case, the probability of A or B is the sum of P(A) & P(B)

∴ P(A or B) = P(A) + P(B)

Given, P(A) = 1/7 & P(B) = 3/7

So, P(A or B) = P(A) + P(B)

                     = 1/7 + 3/7

                     = (1+3)/7

                     = 4/7

Required value of P(A or B) is 4/7

Learn more about disjoint events here :

https://brainly.com/question/8639736

#SPJ2

Answer:

$13,795

Step-by-step explanation:

15500/x=100/11

(15500/x)*x=(100/11)*x       - we multiply both sides of the equation by x

15500=9.0909090909091*x       - we divide both sides of the equation by (9.0909090909091) to get x

15500/9.0909090909091=x  

1705=x  

x=1705

now we have:  

11% of 15500=1705

Answer:

C. [tex]0\le x\le55,-1.45[/tex]

Step-by-step explanation:

The domain of the function refers to all values of x for which the function is defined.

From the diagram the graph of the function exist on the interval [tex]x=0[/tex] to [tex]x=55[/tex].

The average rate of change is the slope of the secant line joining the points (0,f(0)) and (55,f(55)).

The average rate of change of this function f(x) on this interval is

[tex]\frac{f(55)-f(0)}{55-0}[/tex]

From the graph, [tex]f(0)=80[/tex] and [tex]f(55)=0[/tex].

The average rate of change becomes:

[tex]\frac{0-80}{55-0}=\frac{-80}{55}=-1.45[/tex] to the nearest hundredth.

The correct answer is: C

Answer: The correct answer would be C

Step-by-step explanation:

Answer:

GCF = 4ab

Step-by-step explanation:

We need to factor the GCF of

12a^3b+8a^2b^2-20ab^3

Finding the common term: 4ab

So, GCF = 4ab

Factoring the common term

12a^3b+8a^2b^2-20ab^3= 4ab(3a^2+2ab-5b^2)

Answer:

(2,0)

Step-by-step explanation:

y> -3x + 2

Substitute the points into the inequality to see if they are a solution

(0,2)

2 > -3(0)+2

2 > 2  False

(2,0)

0> -3(2) + 2

0>-6+2

0> -4   True

(1,-2)

-2> -3(1) + 2

-2 > -3+2

-2 >-1  False

(-2,1)

1> -3(-2) + 2

1 >6+2

1>8  False

Answer:

49π cm²

Step-by-step explanation:

area = πr²

fill in r=7cm

Answer:

Tenth:-42.8

Hundredth: -42.85

To explain:

To the right of the decimal point every name of the place ends with -th.

If a number is bigger than 5 you round the number left to it by 1

If it's 4 or smaller you don't do anything.

Answer: 226.8

Step-by-step explanation:  Find the number in the tenth place 8 and look one place to the right for the rounding digit 4 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .

Answer:

List the letters in alphabetical order

Step-by-step explanation:

ABC,ACB

BAC,BCA

CAB,CBA

Answer: 6 permutations

Step-by-step explanation: A permutation is an arrangement of objects in which order is important. In this problem, to find the number of permutations of the letters A, B, and C, we find the number of ways we can arrange the order of the letters A, B, and C.

Image provided.

Therefore, there are 6 permutations of the letters A, B, and C.

Answer:

the answer to this question is b.

Answer:

The correct option is B.

Step-by-step explanation:

It is given that In a population of 1000 individuals, 100 new individuals were born and 200 individuals died over the course of 1 year.

We need to find the population growth rate of this population.

Rate of birth = [tex]\frac{100}{1000}=0.10[/tex]

Rate of death = [tex]\frac{200}{1000}=0.20[/tex]

The formula for rate of change is

Rate of change = Rate of birth - Rate of death

Rate of change = 0.10 - 0.20

Rate of change = -0.10

The required equation is 0.10 - 0.20 = -0.10.

Therefore, the correct option is B.

Answer: x = 41

Step-by-step explanation: You need to isolate x. First, subtract x from each side. You will get:

-2 = 2x - 84

Next, add 84 to each side.

82 = 2x

Divide by 2 on each side.

X = 41

Answer:41

Step-by-step explanation:x-3x=-84+2

-2x=-82

X=-82/-2

X=41