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United Kingdom
The value of a painting \( n \) years after it was painted is given by this formula: value in pounds \( (£)=300 \times 1.24^{n} \) a) What was the original value of the painting? b) By what percentage does the value of the painting increase each year?
Algebra Jan 20, 2025
Using the quadratic formula, solve the equation below to find the two possible values of \( x \). \[ 6 x^{2}-21=-5 x \] Give each value as a fraction in its simplest form.
Algebra Jan 20, 2025
Using the quadratic formula, solve \[ 0=2 x^{2}-14 x+9 \] Give each of your answers to 2 d.p.
Algebra Jan 20, 2025
Using the quadratic formula, solve \[ 4 x^{2}+16 x+15=0 \] to find the two possible values of \( x \). Give any decimal answers to 1 d.p. \[ \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=0 \] \[ \boldsymbol{x}=\frac{-\boldsymbol{b} \pm \sqrt{\boldsymbol{b}^{2}-4 a \boldsymbol{c}}}{2 \boldsymbol{a}} \]
Algebra Jan 20, 2025
WE DO l 1(a). A fast food restaurant offers half-price meals if the customer is a student or has a discount card. The offer is not valid on Saturdays. The restaurant needs an algorithm designing to help employees work out if a customer can have a half price meal or not. It should: I input required data decide if the customer is entitled to a discount output the result of the calculation. Design the algorithm using a flowchart.
Computer Technology Jan 20, 2025
\begin{tabular}{|l|l}\hline 9. Create a grading & \\ A score out of 100 is entered. & Copy and paste the Python code here. \# \\ Score between 90 and 100 is A & \\ Score between 80 and 89 is a B & \\ Score lesson than 80 is a C \\ Score less than 70 is D \\ Score lesson 50 and greater or & \\ equal to 40 is an E & \\ Score below 40 is an F. & \end{tabular}
Computer Technology Jan 20, 2025
3 Calculate \( \frac{\mathrm{d} y}{\mathrm{~d} x} \) when \( y= \) \( \begin{array}{ll}\text { a } \quad x^{2}+2 x-3 & \text { b } \quad 1-2 x-5 x^{2} \\ \text { c } \quad x^{3}+2 x^{2}-3 x+1 & \text { d } \\ x^{2}-x^{4}+\pi \\ \text { e } \quad x-\frac{1}{x} & \text { f } \\ 3+x+\frac{2}{x^{2}} \\ \text { g } \quad x^{3}-\frac{1}{x^{3}}+\frac{3}{x}+5 & \text { h } \\ \frac{10}{x}-1-\frac{x}{10} \\ \text { i } \sqrt{x}+\frac{1}{\sqrt{x}} & \text { j } \\ x^{5}-\frac{5}{\sqrt[3]{x}} \\ \text { k } 3+\frac{2}{\sqrt{x}}-\frac{5}{\sqrt[3]{x^{2}}} & \text { i } \frac{3}{\pi}-\frac{2}{x^{2}}-x^{\frac{3}{2}}\end{array} \)
Calculus Jan 20, 2025
b) \( 25 p^{2}+8 q^{2}-8 q^{2}-6 p^{2}= \)
Algebra Jan 20, 2025
Simplify fully: a) \( 6 a b-7 b+18 a b-9 b \)
Algebra Jan 20, 2025
Maddie had a six-sided dice numbered from 1 to 6 . She rolled it a to of 50 times. It landed on an even number 24 times. a) Work out the relative frequency of the dice landing on an even number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probability of it landing on an even number be? Give your answer as a decimal. c) Is the dice definitely biased or definitely not biased, or is it impossible to tell? Write a sentence to explain your answer.
Probability Jan 20, 2025
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