A school allots £1500 to spend on a trip to the theatre. Theatre tickets have a regular cost of £35 each and are for offer for 1/5 off. a train ticket for the day will cost £12 each. If 3 teachers and the maximum numbers of students attend how many students go on the trip?

Answer:

\(\frac{1}{9}\) , 3 , 10

Step-by-step explanation:

Using the rules of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

\(a^{\frac{m}{n} }\) = \(\sqrt[n]{a^m}\)

\(a^{0}\) = 1

(a)

\(6^{-x}\) = \(\frac{1}{6^{x} }\) = \(\frac{1}{9}\)

(b)

\(6^{\frac{x}{2} }\) = \(\sqrt{6^{x} }\) = \(\sqrt{9}\) = 3

(c)

\(6^{0}\) + \(6^{x}\) = 1 + 9 = 10

Answer: Measure of CED is: 212°

The production function is used to examine the relationship between inputs and outputs.

The production function is a fundamental concept in economics that represents the relationship between inputs and outputs in the production process. It helps us understand how much output can be produced with a given set of inputs.

In the production process, inputs such as labor, capital, raw materials, and technology are combined to produce goods or services. The production function captures the quantitative relationship between these inputs and the resulting output. It provides a framework to analyze how changes in input levels affect the output level.

The production function typically takes the form of a mathematical equation or a graphical representation. It shows how the quantity of output depends on the quantities of various inputs used in the production process.

By studying the production function, economists can analyze factors such as efficiency, productivity, and technological progress. It helps firms make decisions regarding the optimal combination of inputs to maximize output or minimize costs. Additionally, it allows policymakers to assess the impact of policies on production and economic growth.

Therefore, the production function primarily focuses on examining the relationship between inputs and outputs, rather than supply and demand, producers and consumers, or price and cost.

To learn more about function, click here: brainly.com/question/11624077

#SPJ11

61 matchsticks need to make 20 squares.

Given,

From the figure,

Matchsticks are used to make the pattern.

To make these 4 squares, you need 13 matchsticks.

To find the how many matchsticks do you need to make 20 squares?

Now, According to the question:

Let the need matchsticks be 'n'

The number of the squares to make 1 square , you need 4 matchsticks,

and when you need to add one square, you need three more matchsticks .

So , we have to make  n no. of squares you need

4 + 3(n - 1) matchsticks     (n \(\geq\) )

= 4 + 3n - 3

= 1 + 3n

When, n = 20

1 + 3 x 20

= 61

Hence, 61 matchsticks need to make 20 squares.

Learn more about Matchsticks Squares at:

https://brainly.com/question/583375

#SPJ1

Answer:

Step-by-step explanation:

Rationalization.  

                                                                              2 + i

For example:  " rationalize the denominator of ---------  "

                                                                               -3 + i

Given parameters:

Width  = 2x + 1

Length = 6x

Unknown:

Expression for the area = ?

Solution:

The area of a rectangle is the space it occupies,

        Area of rectangle  = length x width

Input the parameter and solve;

       Area of rectangle  = 6x(2x + 1)

                                       = 12x² + 6x

The area of the rectangle is 12x² + 6x

Answer:

68 quarters

Step-by-step explanation:

How many quarters are there in $17?

Each quarter is equivalent to 0.25 cents, 4 quarters makes up 1 dollar.

68 quarters is equivalent to $17.

Step-by-step explanation:

n < 4

Solution set =]_○○,4[

The derivative of the given expression `y=10 ∩_4^(x(x+1)(2x-1))` is `dy/dx = 4^(x(x+1)(2x-1)) * ln 4 * [(2x-1)(x+1) + 4x² - x]`.

Given, `y=10 ∩_4^(x(x+1)(2x-1))`

To find the derivative of the above expression, we can use the Chain rule of differentiation.

The Chain rule of differentiation is used to find the derivative of composite functions. This rule is also known as the function of a function rule.

The Chain Rule: If `f` and `g` are both differentiable functions, then the derivative of their composite is given by the product of the derivative of `g` with respect to `x` and the derivative of `f` with respect to `g`.

That is, if `y = f(g(x))`, then

`dy/dx = f'(g(x))g'(x)`

Hence, the derivative of the given expression `y=10 ∩_4^(x(x+1)(2x-1))` is given by:

dy/dx = d/dx [10 ∩_4^(x(x+1)(2x-1))]

dy/dx = 0 + d/dx [4^(x(x+1)(2x-1))] * d/dx [x(x+1)(2x-1)]

Now we need to find the derivative of the two terms separately.

(i) d/dx [4^(x(x+1)(2x-1))] = 4^(x(x+1)(2x-1)) * ln 4 * d/dx [x(x+1)(2x-1)]

(ii) d/dx [x(x+1)(2x-1)] = x'(x+1)(2x-1) + x(x+1)(2x-1)'= 1(x+1)(2x-1) + x(1)(4x-1)

So, dy/dx = 0 + 4^(x(x+1)(2x-1)) * ln 4 * [1(x+1)(2x-1) + x(1)(4x-1)]

Hence, dy/dx = 4^(x(x+1)(2x-1)) * ln 4 * [(2x-1)(x+1) + 4x² - x]

Learn more about Chain rule visit:

brainly.com/question/31585086

#SPJ11

Step-by-step explanation:

Hey, there!!

The given is a point (-6,8) through which a line passes. And is perpendicular to the line y = 2x-4

The equation for point (-6,8) is,

(y-8)= m1(x+6)...........(i)

and given equation is y = 2x-4............(ii)

Now, from equation (ii).

slope (m2)= 2 { as equation (ii) is in the form of y= mx+c where m is a slope}.

Now, For perpendicular,

m1×m2= -1

m1×2= -1

\(m1 = \frac{ - 1}{2} \)

Therefore, m1 = -1/2.

Putting, the value of m1 in equation (i).

(y-8) = -1/2×(x+6)

2(y-8)= -1(x+6)

2y - 16 = -x -6

x+2y-10 = 0......... is the required equation.

Hope it helps...

Answer:

b, quadratic with constant second difference of 96

Step-by-step explanation:

The function is cubic with a constant third difference of 96.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Using differences:

X            f(x)             first difference          second difference             third

3            39                        -                                    -                                -

5            187             (187-39)/2= 74                       -                                -

7            551            (551-187)/7-5 = 182     182 - 74/2 = 54                   -

9           1227          (1227-551)/(9-7)=338   338-182/2=78          78-54/2 = 12

11           2311           (2311-1227)/2=542      542-338/2=102       102-78/2 = 12

According to table,

The function is cubic, because the third average change rate is constant of 12.

12>0, so the third difference is >0 then -96 is false.

Thus, the function is cubic with a constant third difference of 96.

Learn more about function from:

https://brainly.com/question/12431044

#SPJ2

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

To know more about determinant visit

https://brainly.com/question/11841826

#SPJ11

We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

To know more about determinant visit

https://brainly.com/question/11843479

#SPJ11

Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

We are asked to determine the p-values for a proportion that is greater than 0.51. Since we are asked about the hypothesis being greater then the p-value is given by:

This is a right-tailed test. To determine this probability we need to use the fact that:

replacing we get:

Now, from the tables for z-scores in the normal distribution we get:

Therefore, the p-value is 0.0011

Step 1

Given; A graph

Required; To find f(-4)

Step 2

The graph at x=-4 has a removable discontinuity. Therefore we can then conclude that f(-4) is undefined.

Hence, f(-4) is undefined

A removable discontinuity is a point on the graph that is undefined or does not fit into the rest of the graph.

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

To know more about the expression:-

https://brainly.com/question/14083225

Answer:

Step-by-step explanation:

-7(1-10)

10-1=9

9 – -7=2

The rate at which the distance between the runner and second base changes is 28.71 ft/s.

Given, a batter hits the ball and runs toward first base at a speed of 28 ft/s. we have to find the rate (in ft/s) at which the distance between the runner and second base change when the runner has run 20 ft.

As, distance = speed × time

d = st

On differentiating both the sides

d' = s't + s

d' = 20/28 + 28

d' = 0.71 + 28

d' = 28.71

Hence, the rate at which the distance between the runner and second base changes is 28.71 ft/s.

Learn more about Application of Derivatives here https://brainly.com/question/25120629

#SPJ4

Answer:

Step-by-step explanation:

\((-1)^{n} = -1 , if \ n \ is \ a \ odd \ integer\\\\\\\\(-1)^{2003} =-1 \\\\(\dfrac{-3}{4)}^{2}=\dfrac{3}{4}, \ as \ 2 \ is \ even \ number.\\\\(\dfrac{2}{3})^{3}*(\dfrac{-3}{4})^{2}*(-1)^{2003}=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{4^{2}}*(-1)\\\\\\=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{2^{4}}*(-1)\\\\\\=\dfrac{-1}{3^{3-2}*2^{4-3}}\\\\\\=\dfrac{-1}{3^{1}*2^{1}}\\\\=\dfrac{-1}{6}\)

\((\dfrac{2}{5})^{2}*(\dfrac{-5}{12})^{3}=\dfrac{2^{2}}{5^{2}}*\dfrac{(-5)^{3}}{(2^{2}*3)^{3}}\\\\\\=\dfrac{2^{2}}{5^{2}}*\dfrac{- 5^{3}}{2^{6}*3^{3}}\\\\\\= -\dfrac{5^{3-2}}{2^{6-2}*3^{3}}\\\\\\= -\dfrac{5}{2^{4}3^{3}}\\\\= -\dfrac{5}{16*3}\\\\\\= \dfrac{-5}{48}\)\(HINT: \dfrac{a^{m}}{a^{n}}=a^{m-n}, m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}}, n >m\\\\\\(a^{m})^{n}=a^{m*n}\)

Answer:

Area ≈ 3077.68

Explanation:

See attached image for equation

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

<95141404393>

Answer: 28x+8y+2 .

= -2 (-14x-4y-1)

= 28x + 8y + 2

Step-by-step explanation:

Answer: 28x + 8y + 2

Step-by-step explanation:

-2(3x+12y-5-17x-16y+4)

= -2(3x-17x+12y-16y-5+4)

= -2(-14x-4y-1)

= -2(-14x) -2(-4y) -2(-1)

= 28x+8y+2

Answer:

im pretty sure its 2

Step-by-step explanation:

Answer:

4

Step-by-step explanaiton:

B is 4x bigger than A

Answer:

6 miles per hour or 6 miles

Step-by-step explanation:

If Karis can run 1 mile in 10 minutes, how many miles could he run in 1 hour at this same rate?

1 mile = 10 minutes

there are 60 minutes in 1 hour

10 minutes × 60 minutes = 6

6 × 1 mile = 6 miles so the answer is 6 mile per hour

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

To know more about the Area of the circle:

https://brainly.com/question/14738425

Among the given options, the values P = 8 and a = 9 will cause the function f(x) = Pa^x to be an exponential growth function. Option D

To determine which values of P and a will cause the function f(x) = Pa^x to be an exponential growth function, we need to consider the properties of exponential growth.

In an exponential growth function, the base (a) must be greater than 1. This is because the exponential function will continuously increase as x increases when a > 1.

Therefore, among the given options, the values P = 8 and a = 9 will cause the function f(x) = Pa^x to be an exponential growth function.

Learn more about exponential growth at https://brainly.com/question/13223520

#SPJ1

Answer:

Given that,

Margie is 4.25 feet tall

The maple tree in her backyard is 5.5 times taller than her.

To find the height of the maple tree.

we get,

Height of the maple tree is,

Maple tree is 23.375 feet tall.