A school trip uses a 42-seater coach (excluding the driver’s seat).
36 students, 3 teachers and 3 parents go on the coach.
Each student pays £4.25 towards the cost of the coach. Each parent pays twice as much
as a student pays. The teachers travel for free.
The coach company charges £195 for the trip.
a Show that the money paid by the students and parents is not enough to pay for the
coach.
b How much should each teacher pay so that the cost of the coach is covered exactly?
c On the day of the trip, 8 students are ill and they get their money back. The
passengers on the coach share the extra cost equally. What is the extra payment for
each passenger?

The result of the expression -(3)⁰.⁵x for x = -2 is 3.4, for x = 0 is 0 and for x = 2 is - 3.4

The question states to evaluate the given expression, that is, -(3) ⁰.⁵ x for the given values of x, that are, x = -2, x = 0, and x = 2.

This question can be easily solved by using the concept of substitution. We have to substitute the given values of x in the given expression one after the other and note the answer.

For x = -2.

we get, -(3) ⁰.⁵ ( - 2) = - 1.7 * (-2) = 3.4

For x = 0.

we get, -(3) ⁰.⁵ ( 0 ) = - 1.7 * ( 0 ) = 0

For x = 2.

we get, -(3) ⁰.⁵ ( 2 ) = - 1.7 * ( 2 ) = - 3.4

Therefore, we get the result of the expression -(3)⁰.⁵ x for x = -2 as 3.4, for x = 0 as 0 and for x = 2 as - 3.4

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The value of test_val after the following code is executed is: 13.

Python can be defined as a high-level programming language that is designed and developed to build websites and software applications, especially through the use of dynamic commands (codes or semantics) and data structures.

A variable can be defined as a specific name which refers to a location in computer memory and it is typically used for storing a value such as an integer or string.

Based on the given Python code, we have:

if a * 2 == test_val:

if 12 * 2 ≠ 6:

Therefore, we have:

test_ val = a + 1

test_ val = 12 + 1

test_ val = 13.

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The value expression represents another method of computing the product given

Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.

-1.45*76 =-110.2

Now checking all the option one by one if any option has the value -110.2

then it is correct

A. (-1)((1 × 76) + (0.45 × 76))

   (-1)(76 + 34.2)

   =-110.2

B. (-1)(-1.45 - 76)

     (-1)(-77.5)

   = 77.5

C. (-1)(-1.45 + 76)

  (-1)(74.5)

  = -74.5

D. (-1)(-1.45 × 76)

   (-1)(-110.2)

= 110.2

Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.

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According to the question given that 6x +7 if x = 5 .If we put x=5 then we get the final answer i.e 37.

= 6x + 7

= 6×5 + 7 putting ( x=5)

= 30 + 7

= 37.

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, [tex]3^4[/tex] indicates that we are multiplying 3 by 4 times. Its full form is 3 3 3 3. Exponent is another name for a number's power.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent. For instance, if a-n is provided, it may be stretched to 1/an. It implies that we must multiply 1/a 'n' times, which is the reciprocal of a. When writing exponentiated fractions, negative exponents are employed.

A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. The square root of a base is a number having a power of half. The term "cube root of the base" is also used to describe a number with a power of 3.

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On solving the logarithmic function, 2 ln x+3 ln 4=4, we get value of x as is x = √e⁴ - 63.

In mathematics, the opposite of exponentiation is the logarithm. This means that the logarithm of a given number, base b, represents the exponent to which that number must be increased in order to get a certain number, x.

Given equation is -

2 ln x + 3 ln 4=4

⇒ ln x² + ln 4³ = 4

⇒ ln (x² + 4³) = 4

⇒ taking e

⇒ log e(x² + 4³) = 4

⇒ e⁴ = x² + 4³

⇒ e⁴ = x² + 63

⇒ x = √e⁴ - 63

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Answer:

the answer for this question is -3,248

The number of small smoothies sold is 26.

The number of large smoothies sold is 20.

The first step is to form a pair of simultaneous equations:

s + l = 46 equation 1

4s + 6.5l = 234 equation 2

Where:

s = number of small smoothies sold

l = e number of large smoothies sold

Multiply equation 1 by 4

4s + 4l = 184 equation 3

Subtract equation 3 from equation 2

2.5l = 50

Divide both sides of the equation by 2.5

l - 50 / 2.5

l =  20

Subtract 20 from 46

s = 46 - 20 = 26

Here is the complete question:

You collect $234 selling small and large smoothies. You sell a total of 46 smoothies. A small size is $4 and a large size is $6.50. How many of each size did you sell?

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The number of possible outcomes are 6 if we have 3 spinners labeled Red, Blue, Yellow by using permutations.

There are 3 spinners:

Red

Blue

and yellow.

Number of possible outcomes will be calculated by using permutation.

So, we get that:

Number of possible outcomes = 3 × 2

Number of possible outcomes = 6 ways.

Therefore, the number of possible outcomes are 6 if we have 3 spinners labeled Red, Blue, Yellow by using permutations.

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The distance value of the BD, CE, AC is 2 cm, 2 cm, 9cm.

According to the statement

We have to find that the distance between the given points.

So, For this purpose, we know that the

The distance between two points is the length of the path connecting them.

From the given information:

The given values of the points are:

Ab = 5 cm and AD = 7 cm and AE = 11 cm

Then we know that the

BD = AD -AB and

And the BD = CE and AC = AE - CE

Here we have to find the value of the BD, CE, AC .

Then

BD = AD -AB

BD = 7 -5

BD = 2

And

BD = CE

2 = CE

CE =  2cm

And

AC = AE - CE

AC = 11- 2

AC = 9cm.

So, The distance value of the BD, CE, AC is 2 cm, 2 cm, 9cm.

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Answer:

38.97 kilograms

Step-by-step explanation:

38 ones and 97 hundredths

38                  0.97

38.97

Expression as a single natural logarithm is 1.38629436112

ln 24- ln 6

ln(24/6)

ln 4 = 1.38629436112

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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If scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score you would need to be in the top 2% is equal to 88.929.

This type of problem can be referred to as a normal distribution problem.

It can be solved by using the z-score.

Formula;

Z = x - μ / σ

Here,

Z represents the standard score

x represents the observed value

μ represents the mean

σ represents the standard deviation

The z- score can be found by using the p-value on a standard table.

As the minimum score to be in the top 2% is needed to be found, p-value = 0.02

z- score that corresponds to the p-value of 0.02 in the standard table is equal to 2.054

Hence,

2.054 = x - 76.4 / 6.1

2.054(6.1) = x - 76.4

12.529 = x - 76.4

x = 12.529 + 76.4

x = 88.929

Hence the minimum score needed to be in the top 2% is calculated to be 88.929

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The correct option is D. V = 30-0.1t² ; represents the the volume of water in m³ after t minutes of pumping.

For the given question;

The values for the time of pumping and the volume of water is given;

use them to find the equation which represents their relation.

when, time t = 5

put the values in the options.

a. V = 30 - 2.5 × 5 = 17.5    .....(wrong)

b. V=30 - 0.5 × 5 = 27.5       .....(correct)

c. V = 30 - 0.5 × 25 = 17.5     ......(wrong)

d. V = 30 - 0.1 × 25 = 27.5      ........(correct)

Now, check at time t = 10 just for the correct value.

b. V = 30 - 0.5 × 10 = 25 .....incorrect

d. V = 30 - 0.1 × 100 = 20   ......correct

Therefore, the relation of the water pumped with time is given by the relation; V = 30-0.1t².

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The complete question is-

The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out for a certain number of minutes.

Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out?

A. V = 30-2.5t

B. V = 30-0.5t

C. V = 30-0.5t²

D. V = 30-0.1t²

Having 7 tiles named A to G in a bag and picking 3 of them have the probability that they'll spell BAG is 0.0050.

Probability is the chance of occurring a certain event out of the total possible events that can occur in a given scenario.

According to the given question you put 7 tiles with the letters A through G into a bag.

Total no. of sample space N(S) = 7.

∴ The probability of getting getting B named tile P(B) is = 1/7.

Now as we are not replacing the tiles there are 6 tiles now so probability of getting A named tile P(A) = 1/6 and in the same way probability of getting G named tile is P(G) = 1/5.

∴ The probability that they will spell BAG P(BAG) is = (1/7)×(1/6)×(1/5)                      = 0.0050.

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Answer:

Slope or (m) = 1           Give Brain

Damian should cut the ribbons into pieces of 21 meters.

To answer this, we need to find the maximum common factor between the two lengths of ribbon, which are 63 and 105.

If we rewrite both of these numbers as a product between prime factors we get.

63 = 3*3*7

105 = 3*5*7

Then the maximum common factor between these two numbers is 3*7 = 21

Then we conclude that Damian should cut the ribbons into pieces of 21 meters.

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The inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.

We are given the function:

f (x) = ∛x / 3

we need to find the inverse of the function.

First we will write the function in the form of x.

y = ∛x / 3

y³ =  x / 3

3 y³ =  x

x = 3 y³

So, the inverse function will be:

f ⁻¹ (x) = 3 x³

Therefore, the inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.

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Answer:

3h-6=d

Step-by-step explanation:

h=d/3 +2

take away 2 on both side this gives

h-2=d/3

multiply by 3 on each side which gives

3(h-2) =d

expand the brackets this gives

3h-6=d

so final answer is

3h-6=d

Answer:

The answer is d = 3h - 6........

The equation of the circle with center at (-1, 5) and passes through the point (2, 9) is equal to (x + 1)² + (y - 5)² = 25.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Next, we would determine the length of the radius (r) by using the distance formula. Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Substituting the given parameters into the formula, we have;

Radius = √[(2 - (-1))² + (9 - 5)²]

Radius = √[(2 + 1)² + (4)²]

Radius = √[3² + 4²]

Radius = √[9 + 16]

Radius = √25

Radius = 5 units.

For the equation of a circle, we have:

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 5)² = 25

(x + 1)² + (y - 5)² = 25

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Complete Question:

Write the equation of the circle with center at (-1, 5) and passes through the point (2, 9).

Answer:

A. Shawn's Poster

Step-by-step explanation:

It uses perimeter, and the formula is L*W.

Christie hiked 1/4 and Jackie hiked 3/5  MORE. More means Subtraction so it would be  [tex]\frac{3}{5} -\frac{1}{4}[/tex]

Same thing for the other two. They represent subtraction because of their keywords. Here is a list below of what you need to look for, for each control (+,-,x,÷)

Hope this helps

~R3VO

-10.27 is the value of x in  equation [tex]e^{\frac{x}{5} + 4}[/tex] = 7 solved by  using natural logarithms

We have been asked to find x in  [tex]e^{\frac{x}{5} + 4}[/tex] = 7 using natural logarithms

⇒   [tex]e^{\frac{x}{5} + 4}[/tex] = 7

⇒ [tex]\frac{x}{5}[/tex] + 4 = ㏑(7)

⇒  [tex]\frac{x}{5}[/tex] = ㏑(7) - 4

⇒ x = ㏑(16807) - 20

       = -10.27

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

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Use natural logarithms to solve each equation.

[tex]e^{\frac{x}{5} + 4}[/tex] = 7

Answer:

6x²+11x

Step-by-step explanation:

1. Group like terms

[tex]8x^2-2x^2+3x+8x-10+10[/tex]

2. Add like terms

[tex]6x^2+3x+8x-10+10[/tex]

3. Add the numbers

[tex]6x^2+11x[/tex]

The answer is. $1500.

Let x represent the amount invested at 5%, then  is the amount invested at 8%, and  is the amount invested at 6%. Since the total return is $1270:

let money invested at 5%= x

money invested at 6%

= 20000- (X+X-1500)

21500-2x

Total interest for 1 year.

x×5/100+ (x-1500)×8/100+(21500-2x)×6/100 = 1270

5x/100+8(x-1500)/100+(21500-2x)6/100=1270

5x+8x-12000+129000-12x = 127000

x+117000 = 127000

x = 10000

money invested at 8%

=21500-2×10000

= 1500.

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The values that satisfy the inequality are -3 , 0 , 14 .

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. On the number line, size comparisons between two numbers are typically conducted. Different notations can be used to represent various kinds of inequalities, including:

The symbol a <b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

Now the given inequality is of the form  -a < 4

solving we get:

a > - 4

Therefore the number which will satisfy this inequality are:

 -3 , 0 , 14 .

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The total simple interest paid by her is R6,600 and the rate of simple interest  is 22%.

Given that

To find

So, according to the question

We have,

After trading in and depositing, the balance was as follows:

= Cost of television - Selling price of old television - Deposit by her

= 20,000 - 3,000 - 2,000

= R15,000

The total simple interest paid by her in 2 years:

= (900 x 2 x 12months) - 15,000

= R6,600

The rate of simple interest given by her in 2 years:

= (6,600 / 2 years) / 15,000

= 22%

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Answer:

-1

Step-by-step explanation:

Use slope formula.

y2-y1/x2-x1

(2, -1) and (-3, 4)

4+1/-3-2=

=5/-5=-1

The slope is -1. The line is slanted down from left to right.

Hope this helps!

Please mark as brainliest if correct!

Answer:

y = - x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 1 ) and (x₂, y₂ ) = (- 3, 4 )

m = [tex]\frac{4-(-1)}{-3-2}[/tex] = [tex]\frac{4+1}{-5}[/tex] = [tex]\frac{5}{-5}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 3, 4 )

4 = 3 + c ⇒ c = 4 - 3 = 1

y = - x + 1 ← equation of line