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The real number x satisfies log_2 x + log_2 (x - 6) = 4 . What is the value of x ? [1]
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014.8: Sampling and statistical inference
3 questionsPractice
021.1: Scientific notation and significant figures
2 questionsPractice
031.4: Financial applications of arithmetic and geometric sequences and series (loan repayments compound interest)
2 questionsPractice
041.5: Amortization
2 questionsPractice
052.2: Function notation; composite functions; inverse functions
2 questionsPractice
062.5: Linear models: formulating and interpreting linear models
2 questionsPractice
073.3: Applications of right and non-right triangle trigonometry
2 questionsPractice
083.9: Scale drawings and similarity
2 questionsPractice
094.1: Collection of data; types of data: discrete continuous qualitative quantitative
2 questionsPractice
101.2: Arithmetic sequences and series
1 questionsPractice
111.3: Geometric sequences and series
1 questionsPractice
121.7: Use of technology for numerical calculations including rounding to a specified number of decimal places or significant figures
1 questionsPractice
131.8: Use of calculator functions
1 questionsPractice
141.9: Properties of exponents and logarithms
1 questionsPractice
152.11: Piecewise functions
1 questionsPractice
162.4: Graphical representation of functions; equation of a line in the form y = mx + c
1 questionsPractice
172.6: Quadratic functions; the general form y = ax^2 + bx + c
1 questionsPractice
182.8: Exponential functions and their graphs
1 questionsPractice
192.9: Logarithmic functions and their graphs
1 questionsPractice
203.1: Right-angle trigonometry
1 questionsPractice
213.4: Geometric transformations of figures: reflections rotations translations dilations
1 questionsPractice
223.6: Area and perimeter of complex shapes
1 questionsPractice
234.5: Correlation and regression
1 questionsPractice
245.5: Antiderivatives indefinite integrals
1 questionsPractice
255.7: Applications of integration including kinematics
1 questionsPractice
265.8: Numerical solutions of equations using iteration
1 questionsPractice
275.9: Use of technology for calculus problems
1 questionsPractice

02 Questions

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A calculator is used to evaluate dfrac12π × 0.025 . The brackets are omitted, so the calculator computes dfrac12π × 0.025 . What is the difference between the correct value and...MCQA radioactive sample has mass M(t)=250× 0.94^ t grams, where t is in years. The mass first falls below 80 grams after T years. Which equation is solved on a calculator to find T ?MCQThe real number x satisfies log_2 x + log_2 (x - 6) = 4 . What is the value of x ?MCQA function is defined by f(x)=3x+1 for 0≤ x<4 , and f(x)=x^2-5 for 4≤ x≤ 8 . Which branch is used to evaluate f(4) , and what is the value of f(4) ?MCQThe function f(x)=dfrac2x+5x-3 has domain xinmathbbR, x≠ 3 . The inverse function f^-1 is defined for all real x except one value. Which expression gives the value excluded from...MCQThe function f is defined by f(x)=5x-2/3 . Which expression gives f(4) ?MCQThe cost C , in dollars, of hiring a machine for t hours is modelled by C = 18t + 45 . In this model the gradient representsMCQA printing firm charges a setup fee of 24 dollars plus 0.65 dollars per poster. The cost C in dollars for n posters is modeled by C = mn + c . What are the values of m and c ?MCQA printing service charges a fixed set-up fee plus a constant amount per poster. The total cost for 20 posters is 74 dollars and for 50 posters is 149 dollars. Which expression...MCQA quadratic function is given by f(x) = 3x^2 - 12x + 7 . The equation of the axis of symmetry of the graph of f is x =MCQThe function f(x) = 5 ln(2x) - 8 is defined for x > 0 . The graph of f crosses the x -axis at one point. What is the exact x -coordinate of this point?MCQA vertical mast TB stands at corner B of a horizontal rectangular field ABCD . The mast is 25 m tall, AB = 40 m and BC = 30 m. The angle between TA and the horizontal field is θ...MCQA ship sails from port P on a bearing of 040^° for 12 km to point Q , then on a bearing of 155^° for 9 km to point R . What is the equation giving the distance PR ?MCQA triangle of area 5 cm^2 is mapped onto its image by the matrix M = beginpmatrix 3 & 1 \ 4 & 2 endpmatrix . The inverse transformation M^-1 is then applied to a square of area...MCQA school has 400 students in Year 12 and 200 students in Year 13. A sample of 60 students is required. Twenty Year 12 students and 40 Year 13 students are chosen at random from...MCQFor a set of bivariate data, the coefficient of determination for the linear regression of y on x is R^2 = 0.64 . The regression line has a negative gradient. What is the value...MCQA population has standard deviation σ = 12 grams. A random sample of 36 items has mean 84 grams. What is the width of the 95% confidence interval for the population mean?MCQA machine fills bottles with volume normally distributed with mean μ and standard deviation 4.0 ml . A sample of 16 bottles is used to test H_0: μ = 500 against H_1: μ < 500 at...MCQA data set has lower quartile 24 g and upper quartile 40 g. An outlier is any value more than 1.5 interquartile ranges from the nearest quartile. What is the smallest mass that...MCQA curve has gradient function dfracdydx = 4e^2x + dfrac3x . An expression for y in terms of x isMCQA particle moves in a straight line with velocity v(t) = t^2 - 4t m s^-1 for 0 ≤ t ≤ 6 . What is the total distance travelled by the particle?MCQThe trapezoidal rule with two strips of width 1 is used to estimate int_0^2 x^2 dx . The exact value of the integral is 8/3 . What is the difference between the trapezoidal esti...MCQEuler's method with step length h = 0.5 is used for dfracdydx = x + y , with y = 2 when x = 0 . A spreadsheet column contains the recursion for y . What is the value of y when x...MCQA sum of 5000 dollars is invested at a nominal annual interest rate of 6%, compounded monthly. At the end of each month, immediately after interest is added, a payment of 100 do...MCQThe mass of a decaying sample is modelled by M(t) = 12 + 48e^-0.2t , where M is in grams and t is in years. According to this model the mass never falls below a limiting value....MCQA sector of a circle has area 45 cm^2 and central angle 100^° . What is the radius of the sector?MCQA map is drawn to a scale of 1 : 150 000 . A straight road is 18 km long. What is the length of this road on the map?MCQ
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