In a school canteen, a cup of tea costs 60p.
(a) Write down an expression for the cost, in pence, of y cups of tea.

answer:

16.24 or 12 square root of 18

Answer:

13

Step-by-step explanation:

180-96=84

(4x-10)+(4x-10)= 84

X=13

The solution to the system of equations is x = 1 and y = 5. The coordinate of the solution is (1, 5).

The system of equations consists of y = 2x + 3 and -y + 7 = -2. To find the coordinate of the solution, we need to solve the equations simultaneously.

To solve the system of equations, we can start by solving the second equation for y:

-y + 7 = -2

Adding y and subtracting 7 from both sides, we get:

y = 7 - 2

Simplifying, we find:

y = 5

Now that we know the value of y, we can substitute it into the first equation:

y = 2x + 3

5 = 2x + 3

Subtracting 3 from both sides, we have:

2 = 2x

Dividing both sides by 2, we find:

x = 1

Therefore, the solution to the system of equations is x = 1 and y = 5. The coordinate of the solution is (1, 5).

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Answer:

C=2v

Step-by-step explanation:

because 0*2=0 1*2=2 2*2=4 3*2=6 4*2=8 5*2=10 so C=2v

Answer:

21

Step-by-step explanation:

x = -3 1/9

took the quiz lol

Answers:

========================================

Work Shown:

To find the scale factor, we divide a side of triangle MNO over a corresponding side of triangle FGH. We can only pick the horizontal bottom sides since we don't know what x is yet.

scale factor = ON/HG = 15/9 = (5*3)/(3*3) = 5/3

In decimal form, this is approximately 5/3 = 1.67; however, I find it's better to stick with the fraction since it's exact.

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

Let's solve for x

One way to do so is to follow these steps

(FG)/(MN) = (HG)/(ON)

6/x = 9/15

6*15 = x*9 ..... cross multiply

90 = 9x

9x = 90

x = 90/9

x = 10

Or we could solve like this

(FG)/(HG) = (MN)/(ON)

6/9 = x/15

6*15 = 9x

90 = 9x

9x = 90

x = 90/9

x = 10

We end up with the same result because we got to 90 = 9x after cross multiplying, which was found in the previous set of steps as well. There are other ways to solve using a proportion. But they should all lead to x = 10.

Note how,

MN/FG = 10/6 = (5*2)/(3*2) = 5/3

which was the scale factor we found earlier

5/3 is going to be your answer.

Answer:

Answer is C

Andy's Y value increases 2 times more

Answer:

B)

Step-by-step explanation:

If you look at Kate's y column, you will see that her pattern goes by 2,4,6 and 8.

It increases by 2.

At the same rate, Andy's increases by 4.

Therefore, B would be the correct answer.

Answer:

V=785.4

Step-by-step explanation:

V=pi*r^2*h

V=pi*5^2*10

V=pi*25*10

V=pi250

V=785.39=785.4

The sample points in event E are 1, 3, 5, 7, and 9.

The outcome of some experiments cannot be predicted before they have been performed. There is a well-defined procedure that produces an observable outcome and it is known as a random experiment. These experiments can be repeated several times under similar conditions.

Our experiment is to choose a number between 1 and 10. The numbers between 1 and 10 are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. So, the total number of outcomes is 10.  

An event is the set of specific outcomes of a random experiment. The event in this case is to choose an odd number out of those 10 outcomes.

E = Odd number chosen

Odd numbers from 1 to 10 are 1, 3, 5, 7, and 9. So, there are a total of 5 sample points in event E.

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The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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Pete relies on personal observations and experiences as empirical evidence to support his belief about the automatic carwash damaging cars.

In this scenario, Pete is relying on empirical evidence as his source of knowledge. Empirical evidence is based on direct observation or experience. Pete's belief that the automatic carwash damages cars stems from the repeated occurrences of finding new dings in his car after each visit. He has personally observed this cause-and-effect relationship, leading him to conclude that the automatic carwash is responsible for the damages.

Pete's reliance on empirical evidence is grounded in his own experiences and perceptions. It is important to note that while empirical evidence can be valuable in forming beliefs and drawing conclusions, it is also limited. Pete's individual experiences may not necessarily reflect the broader truth. Other factors such as the specific carwash he visits, the condition of his car prior to the wash, or even coincidental events could contribute to the dings on his car.

To validate his conclusion, Pete could consider gathering additional evidence from other car owners who use the same automatic carwash or seek expert opinions from professionals in the automotive industry. This would provide a more comprehensive and reliable understanding of the situation.  

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Answer:

13 pounds

Step-by-step explanation:

volume = base area × height

area of a rectangular triangle = a×b/2

Vp = (2×3/2) × 5 = 3×5 = 15 ft³

weight of contents = 15 × 0.84 = 12.6 pounds = 13 pounds rounded.

Answer:

g = 93

Step-by-step explanation:

distribute -3 by g and 69

-3g-(-207) = -72

-3g + 207 = -72

-3g = -279

g = 93

Answer:

xx

Step-by-step explanation:

Answer:

X=15.5 °

Step-by-step explanation:

AOB is an isosceles triangle since AO=BO (radius of the circle), to angle OAB=OBA= (180-53)/2= 63.5 °

Angle CAB=63.5+11=74.5 °

And the angle ACB=53/2= 26.5° (inscribed angle)

so in the triangle ABC: the angle ABC= 180- angle CBA + angle ACB =180-(74.5+26.5 )= 79 °

so x= angle ABC - angle OBA = 79 - 63.5 = 15.5 °

Answer: t = 7°

Step-by-step explanation:

        We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. Using this information we can create an equation to solve for t.

   Given:

180° = 90° + 6t° + 6° + 7t° - 7°

   Combine like terms:

180° = 89° + 13t°

   Subtract 89 from both sides of the equation:

91° = 13t°

   Divide both sides of the equation by 13:

t = 7°

Answer:

\( s = 6.1~cm \)

Step-by-step explanation:

\( s = \dfrac{n}{360^\circ} \times \pi d \)

\( s = \dfrac{50^\circ}{360^\circ} \times \pi \times 14~cm \)

\( s = 6.1~cm \)

Answer:

12.2 cm

Step-by-step explanation:

Since the circle has a diameter of 14cm, its radius is 7cm.

Using the formula s=rθ where s is the arc length of the circle, r is the radius of the circle, and θ is the central angle of the circle in radians, then the arc length is s = (14)(50°)(π/180) = (14)(50π/180) = 700π/180 ≈ 12.2 cm

Answer:

f= 1.3s - 8.7

Step-by-step explanation:

Slope is M

M = 1.3 feet per second

y=mx+ b your b= 8.7ft

your equation is

f= 1.3s - 8.7

Answer:

The dimensions of a matrix are the number of rows by the number of columns.

Answer:

Each country will have a representative of 565 people in that political gathering.

Step-by-step explanation:

Answer:

x=   \(\frac{9}{2} y\) or  y=  \(\frac{2}{9} x\)

Step-by-step explanation:

Solving for (x)

Step 1: Add -3y to both sides.

2x+3y+−3y=12y+−3y

2x=9y

Step 2: Divide both sides by 2.

\(\frac{2x}{2} = \frac{9y}{2}\)

Solving for (y)

Step 1: Add -12y to both sides.

2x+3y+−12y=12y+−12y

2x−9y=0

Step 2: Add -2x to both sides.

2x−9y+−2x=0+−2x

−9y=−2x

Step 3: Divide both sides by -9.

\(\frac{-9y}{9} = \frac{-2x}{9}\)

The “yearly tuition costs” as an independent variable which should be plotted on X-axis and “mid-career salary” as a dependent variable on Y-axis. The scatterplot is made of them.

Based on the table provided, it is possible to observe that there is not necessarily a clear relationship between the cost of tuition and mid-career salary.

While some of the colleges with higher tuition costs (such as MIT and Stanford) have high mid-career salaries, others (such as Harvey Mudd and Caltech) also have high mid-career salaries despite lower tuition costs. Additionally, some colleges with low or zero tuition costs (such as the US Naval Academy and West Point) also have high mid-career salaries.

Therefore, it is not safe to assume that a higher cost of tuition will necessarily translate into higher-paying jobs. The scatter plot of yearly tuition costs and mid-career salary is made.

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The volume of the sample of gas is 0.0032661 cubic meters (m³).

To convert the volume from cubic centimeters (cm³) to cubic meters (m³), you need to understand the relationship between the two units. There are 1,000,000 cubic centimeters in one cubic meter.

So, to convert the given volume of 3266.1 cm³ to cubic meters, you divide it by the conversion factor:

3266.1 cm³ ÷ 1,000,000 = 0.0032661 m³

This means that the given sample of gas has a volume of approximately 0.0032661 cubic meters.

When converting between cubic centimeters and cubic meters, you are scaling the volume by a factor of 1,000,000.

Since a cubic meter is much larger than a cubic centimeter, dividing the volume by 1,000,000 results in a smaller value expressed in cubic meters.

Therefore, the volume of the sample of gas is approximately 0.0032661 cubic meters (m³).

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The get valid input function prompts the user for the number of hours a paddle board was rented for. If the user enters a valid number of hours (between 0 and 10 inclusive), the function returns the number of hours as a float.

If the user enters a value that is not a valid numeric value or not within the range, the function displays an error and prompts the user to try again. This function is called by the main program until a valid input is received.

def get_valid_input():
   while True:
       try:
           hours = float(input("Enter the number of hours the paddle board was rented for (0-10): "))
           if hours < 0 or hours > 10:
               print("Error: Input out of range. Please try again.")
           else:
               return hours
       except ValueError:
           print("Error: Invalid input. Please enter a number.")

Calculate Charge Function
The calculate charge function takes the number of hours a paddle board was rented for as input and returns the total charge for that rental. The minimum charge is $35 for up to 2 hours, and then an additional $10 is added for every hour over two hours. The maximum charge for the day is $75.

def calculate_charge(hours):
   if hours <= 2:
       return 35
   elif hours > 2 and hours <= 10:
       return min(75, 35 + (hours - 2) * 10)
   else:
       return 75

Display Summary Function
The display summary function takes three input parameters: total_number_of_boards, total_number_of_hours, and total_charge. It then displays a summary of the total number of boards rented, the total number of hours rented, and the total charge collected for the day.

def display_summary(total_number_of_boards, total_number_of_hours, total_charge):
   print("Total number of paddle boards rented: ", total_number_of_boards)
   print("Total number of hours rented: ", total_number_of_hours)
   print("Total amount collected: $", total_charge).

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Answer:

10:30

Step-by-step explanation:

Since it is asking for the ratio of 6th grade students to all you need to put the amount of 6th grade students first. Then you add the amount of 6th and 5th grade students to get 30. and so the ratio would be 10:30. Hope it helped! :)