Suppose that there are two types of tickets to a show: advance and same-day, Advance tickets cost $20 and same-day tickets cost $35. For one performance,
there were 45 tickets sold in all, and the total amount paid for them was $1200. How many tickets of each type were sold?
Number of advance tickets sold:
Number of same-day tickets sold:

The quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]

The coordinates of the vertex of the graph = (-3, 8)

The coordinates of the point on the parabola = (0, -19)

The quadratic function of the form

f(x) = [tex]a(x-h)^2+k[/tex]

Where (h, k) is the coordinates of the vertex of parabola

y = [tex]a(x-(-3))^2+8[/tex]

y = [tex]a(x+3)^2+8[/tex]

The coordinates of the point = (0, -19)

-19 = [tex]a(0+3)^2+8[/tex]

Take the square of the number

-19 = a × 9 +8

Multiply the terms

-19 = 9a + 8

9a = -19 - 8

Subtract the terms

9a = -27

a = -27 / 9

Divide the terms

a = -3

Hence, the quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]

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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.

Given is each student in Ms. Lee's class is either a junior or a senior. Ms. Lee took some students from her class on a field trip. Of the 18 juniors in her class, 5/6 went on the trip, and 17 seniors from her class also went on the trip.

[A] - Juniors that did not went are -

18 - (5/6 x 18)

18 - 15

3

[B] - Juniors that went are -

(5/6 x 18)

15

[C] - Not enough information

Therefore -

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The temperature of City A and City B on that day was 4° C respectively.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

WE have been given system of equations as;

5x = 8 + 3y

x − 2y = −4

Now we can multiply equation B by -5 to eliminate the x variable in both equations.

Add them together;

5x = 8 + 3y

-5x + 10y = 20

Then add both of them A + B:

-5x + 10y + 5x - 3y = 20 + 8

7y = 28

y = 4

To solve for x;

5x = 8 + 3y

5(x) = 8 + 3(4)

x = 4

Hence, the temperature of City A and City B on that day was 4° C respectively.

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Answer:

B. City A was 4° C, and City B was 4° C.

Step-by-step explanation:

It is right i did it on the test

The maximum income is Maximum cost C is $19740

Let Q represent the number of cars rented per day and P the rate.

To form the demand equation;

Q = a - bP

A car rental agency rents 440 cars per day at a rate of ​$40 per day

440 = a - 40b ......1

For each ​$1 increase in​ rate, 10 fewer cars are rented

(440-10) = a - (40+1)b

430 = a - 41b ......2

Subtracting equation 2 from 1

10 = b

From equation 1;

440 = a - 10(40)

a = 440 + 400 = 840

So;

Q = 840 - 10P

Cost C = Q×P = P (840-10P) = 840P - 10P^2

Maximum cost is at dC/dP = 0

dC/dP = 840 - 20P = 0

P = 840/20 = $42

Maximum cost C is

C = P(840-10P) = 42(840-370) = 42 × 470 = $19740

The maximum income is Maximum cost C is $19740

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Step-by-step explanation:

For Part A:

Refer to the photo for an explanation on how to graph z=x+y+24 and how to set up the first integral. I will not explain how to do the other five but I have placed them beneath....

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]

Where limits are, [tex]0\leq x\leq z-y-24\\0\leq y\leq z-24\\0\leq z\leq 24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{y+24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdzdy\\\\[/tex]

Where limits are, [tex]0\leq x\leq z-y-24\\0\leq z\leq y+24\\0\leq y\leq -24[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydxdz\\\\[/tex]

Where limits are,[tex]0\leq y\leq z-x-24\\0\leq x\leq z-24\\0\leq z\leq 24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{x+24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydzdx\\\\[/tex]

Where limits are, [tex]0\leq y\leq z-x-24\\0\leq z\leq x+24\\0\leq x\leq -24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{-y-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdxdy\\\\[/tex]

Where limits are, [tex]0\leq z\leq x+y+24\\0\leq x\leq -y-24\\0\leq y\leq -24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{-x-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdydx[/tex]

Where Limits are, [tex]0\leq z\leq x+y+24\\0\leq y\leq -x-24\\0\leq x\leq -24[/tex]

For Part B:

All the above limits equal the same volume. So I will just solve for one of the limits.

Evaluate, [tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, (x]^{z-y-24} _0){} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, [(z-y-24)-0]{} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,z-y-24{} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[0-\frac{y^{2} }{2} -0]{} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\frac{y^{2} }{2} ]^{z-24} _{0} {} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[(\frac{(z-24)^{2}}{2})-0] {} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[\frac{z^2}{2}-288] {} dz \\\\[/tex]

[tex][\frac{z^3}{6}-288z]^{24} _{0} {} \\\\[/tex]

[tex][(\frac{24^3}{6}-288(24))-0] {}[/tex]

[tex](4608-6912)=-2304\\[/tex]

Answer: -2304

Answer:

x = 55

x = 13

Step-by-step explanation:

Use the distributive property to solve.

0.5(x+9)=32

0.5x + 4.5 = 32

0.5x = 27.5

x = 55

Solve by dividing first

0.5(x+9)=32

x + 9 = 32/0.5

x + 9 = 64

x = 55

Use the distributive property to solve.

2(x+12)=50

2x + 24 = 50

2x = 26

x = 13

Solve by dividing first

2(x+12)=50

x + 12 = 50/2

x  + 12 = 25

x = 13

Answer:

4x[tex]\sqrt{6x}[/tex]

Step-by-step explanation:

This can be written:

[tex]\sqrt{(3)(2)(2)(2)(2)xxx}[/tex]  Pull out all the pairs. There are 2 pairs of 2 and 1 pair of x's

(2)(2)x[tex]\sqrt{(3)(2)x}[/tex]  Clean up

4x[tex]\sqrt{6x}[/tex]

As per the concept of matrix multiplication, the value AB is [tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

Matrix multiplication:

Matrix multiplication states that "The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix."

Given,

Here we have the matrix A and B.

And we have to perform the multiplication operation on it.

The value of matrix A is written as,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}[/tex]

And the value of the matrix B is written as,

[tex]\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

Now, we have to multiply these two matrix, then we get the following,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}\times\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

And the multiplication of the matrix is written as,

[tex]\begin{bmatrix} -4\times-4+1\times3-4\times2& -4\times-4+1\times3-4\times2 &-4\times4+1\times-5-4\times-1 \\3\times-4+3\times3+1\times2 & 3\times-5+3\times3+1\times2 & 3\times4+3\times-5+1\times-1 \\2\times-4+5\times3+5\times2 & 2\times-5+5\times3+5\times2 & 2\times4+5\times-5+5\times-1\end{bmatrix}[/tex]

When we simplify this one then we get the value of AB is,

[tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

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Answer:

Step-by-step explanation

Initial amount = $85

Final amount = $110

percentage error = ((Final amount - Initial amount)*100)/Final amount

= (25*100)/110

=22.7272

=22.7 (to the nearest tenth of a percent, which is 1 decimal place)

The solution is 22.7 %

The percentage error in the estimation of donations at the pet store by Jenny is 22.7 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the percentage error be represented as A

Now , the value of A is

The estimated donation amount by Jenny = $ 85

The actual donation amount collected by Jenny = $ 110

Now , the percentage error in the estimation of Jenny A is calculated by the equation ,

Percentage error in the estimation of Jenny A = ( ( | estimated donation amount - actual donation amount collected by Jenny ) | / actual donation amount collected by Jenny ) ) x 100

Substituting the values in the equation , we get

Percentage error in the estimation of Jenny A = ( | 85 - 110 | / 110 ) x 100

On simplifying the equation , we get

Percentage error in the estimation of Jenny A = ( 25/110 ) x 100

Percentage error in the estimation of Jenny A = 2500 / 110

Percentage error in the estimation of Jenny A = 22.72 %

Therefore , the value of A is 22.7 %

Hence , the percentage error in the estimation is 22.7 %

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From the position of the metals on the electrochemical series, there would be no reaction of the solution with iron and copper.

We know that a reaction is said to have occurred between a metal and a solution if the metal is able to displace the cation that is in the solution. This displacement would in turn have a lot to do with the position of the metals in the electrochemical series.

Given that iron and copper are all less than aluminum which is the cation in the solution in the electrochemical series then it would not be possible for these metals to displace it in solution thus there would be no reaction.

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Answer:

[tex]\huge\boxed{\sf x = 1}[/tex]

Step-by-step explanation:

g(x) = 5x + 4

Given that, g(x) = 9

So,

9 = 5x + 4

Subtract 4 to both sides

9 - 4 = 5x

5 = 5x

Divide 5 to both sides

1 = x

OR

x = 1

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = 1

Step-by-step explanation:

The given information is,

→ g(x) = 5x + 4

→ g(x) = 9

Now the value of x will be,

→ 5x + 4 = g(x)

→ 5x + 4 = 9

→ 5x = 9 - 4

→ x = 5/5

→ [ x = 1 ]

Hence, the value of x is 1.

Answer:

328,000-49,000= 279000

the amount of mortgage they paid

15 x 2354.37= 35315.55

Step-by-step explanation:

The test statistic for the hypothesis test using the parameters is 2.05

A test statistic is used to access how consistent  sample data are with the null hypothesis in a hypothesis test.

How to calculate test hypothesis of  given parameters?

Using the parameters

Hₙ: ц=12.5, x=14.1, s=2.7, and n=12

The test statistic (t) is given by the formula

t=[tex]\frac{x-U}{s/\sqrt{n} }[/tex]

Substituting the given parameters;

t=[tex]\frac{14.1-12.5}{2.7/\sqrt{12} }[/tex]

t=[tex]\frac{1.6}{2.7/3.46}[/tex]

t=[tex]\frac{1.6}{0.78}[/tex]

t=2.05

This figure is round up to 2 decimal places

The test statistic using the parameters is 2.05

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The number of pupils altogether that said cola was their favorite is 26.

From the question:

The total number in pupils in the class = 60

Number of  Boys in the  classroom =32

Number of Girls in the classroom=Total number of pupils - Number of  Boys in the  classroom

Number of Girls in the classroom= 60-32

                                                       = 28

Number of Boys that like Cola only= 12

Number of Boys that like water best = 4

Number of Girls that like water best = 9

 The number of pupils altogether that said Milk was their favorite =21

The number of pupils altogether that said Water was their favorite =  9 boys+  4girls

The number of pupils altogether that said Water was their favorite =13

Thus,

The number of pupils altogether that said cola was their favorite =Total number of pupils  -The number of pupils altogether that said Water was their favorite -  The number of pupils altogether that said Milk was their favorite

= 60 - 21 - 13

=26

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The error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close brackets the close brackets mean the value at the close bracket is also included, and the open bracket means the value at the open bracket does not include.

It is given that, the number is 3.7.

We have to find the error interval for x rounded to 1 decimal place for the number 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

When a number has been rounded or truncated, error intervals are the upper bounds of accuracy. They represent the range of values that a number might have had before being rounded or truncated.

This is so that we may round the range of 3.65 to 3.75 to one decimal place, and as 3.74 or less is considered to be below 3.75, rounding to one decimal place gives us 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

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The system of equations given have infinite number of solutions

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.

In the equations given;

4x + y = 10 ...eq(i)

16x + 4y = 40 ...eq(ii)

Solving both equations;

The value of x and y is

y = 10 - 4x

This shows that the system has infinite number of solutions.

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Answer:

[tex]0.4514 = 45.14%[/tex]

Step-by-step explanation:

Use the equation:
[tex]Z=\frac{X-u}{a}[/tex]

Given:

[tex]u=159, o=13,n=60,s=1.68[/tex]

This is the pvalue of Z when [tex]X = 159+1 = 160[/tex]  subtracted by the pvalue of Z when [tex]X = 159-1 = 158[/tex]

[tex]x = 160[/tex]

[tex]Z=\frac{X-u}{o}[/tex]

Central Limit Theorem  applied:

[tex]Z=\frac{X-u}{o}[/tex]

[tex]Z=\frac{160-159}{1.68}[/tex]

[tex]Z=0.6[/tex]

[tex]Z=0.6(\text{P-value}:0.7257)[/tex]

[tex]X=150[/tex]

[tex]Z=\frac{X-u}{o}[/tex]

[tex]Z=\frac{158-159}{1.68}[/tex]

[tex]Z=-0.6[/tex]

[tex]Z=-6(\text{P-value}:0.2743[/tex]

[tex]0.7257-0.2743=0.4514[/tex]

This means that there is a 45.14% probability.

The conversion of 33 kilo to pounds using unit fractions is given by 72.765 pounds

There are several units used by scientist to measure different things such as weight, temperature, mass, length etc. Units can be converted from one form to another.

Kilograms written as kg is a unit of mass

Milligrams written as mg is also a unit of mass.

Convert kilo to pounds:

1 kilo = 2.205 pounds

33 kilo = 2.205 × 33

= 72.765 pounds

That is,

A kilo is equivalent to 2.205 pounds

In conclusion, the conversion of 33 kill to pounds is 72.765 pounds.

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Answer:

E $80

Step-by-step explanation:

This would be like paying for 9 lessons

9 x 40 is 360

The first lesson costs twice as much, so it costs 80.

Answer: not 100% but i think its A

Step-by-step explanation:

The equation that can be used to determine the number of plates used is p = 48 / 6.

In order to determine the number of plates that Jim used, divide the total number of carrots by the number of carrots used for each plate.

Division is the mathematical process used to put a number into equal groups using another number. The sign that represents division is ÷.

Total number of plates used = total number of carrots / carrot used per plate

Total number of plates used = 48 / 6

Total number of plates used = 8

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Answer:

---------------------------------------

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

The required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

The number is given in the question as:

(9 × 100) + (5 × 10) + (4 × 1/100) + (8 × 1/1000)

900 + 50 + 4/100 + 8/1000

1040 + 1/25 + 1/125

118756/125

950.048

As per the requierd place values in the chart are:

Hundred: 9

Tens: 5

Ones: 0

Tenths: 0

Hundredths: 4

Thousandths: 8

Now, the number in standard form is 950.048.

Thus, the required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

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The function notations that could represent the variable, w, are:

f(v) = 2v - 1

f(v) = 1 - 8v

For example, if we are given the function notation as f(b) = b, where a and b are the variables, it means that:

In the same vein, if v is an independent variable and w is a dependent variable, it means that:

w which is the dependent variable is equivalent to f(v)

The value of f(v) is dependent on the value of v.

The function notation can therefore be:

f(v) = 2v - 1

f(v) = 1 - 8v

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Answer:

The answer is answer choice E.

Step-by-step explanation:

Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees

Answer: -11

(absolute value) (15 - 6) x -1 = 11 x -1 = -11

Answer:

6 on edge

Step-by-step explanation:

The evaluation of the fraction (5/6 + 2/3) - (3/4 + 1/12) in its simplest form is 2/3

A fraction is a number which consists of a numerator and a denominator.

A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

(5/6 + 2/3) - (3/4 + 1/12)

= (5+4)/ 6 - (9+1) / 12

= 9/6 - 10/12

= 3/2 - 5/6

= (9-5) / 6

= 4/6

= 2/3

Consequently, the answer to the given fraction in its simplest form is 2/3

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Answer:

8

Step-by-step explanation:

Multiply the two radicals and then square it.

The volume V generated by rotating the region bounded by the given curves is V = 960π/7.

Given:

the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.

27y= x³, y=0, x=6

dV = π(8^2-(8-y)^2)dx

y = [tex]x^{3} /27[/tex]

= π*([tex]8^2-(8-(x^3/27)^2)dx[/tex]

= π(64 - 64+16*[tex]x^3/27[/tex]-[tex]x^6/729[/tex])dx

[tex]= \int\limits^6_0 {16x^3/27-x^6/729} \, dx[/tex]

= π(4.[tex]6^6/27 - 6^7/7.729[/tex])

= π(5184/27 - 384/7)

= π(960)/7

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