Questions in mathematics

Questions in mathematics

[Free] A newly married couple bought a stove by paying 30 monthly instalments of RM60. The cash price of the stove is RM1,230. However, the couple decides to settle the balance immediately after paying for 2 years. How much should the couple pay using the Rule of 78?

[Free] Which of the following statements about a 95% confidence interval is true? Select 2 correct answers. A. There is a 95% chance the population mean lies within the interval. B. If we were to take many samples, approximately 95% of the calculated intervals would contain the population mean. C. The sample mean will always fall within the confidence interval. D. The interval width can change based on sample size and confidence level.

[Free] Prove that: [tex]8 \cos 10^{\circ} \cdot \cos 50^{\circ} \cdot \cos 70^{\circ}=\sqrt{3}[/tex].

[Free] What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point $(-4,-3)$? A. $y+3=-4(x+4)$ B. $y+3=-\frac{1}{4}(x+4)$ C. $y+3=\frac{1}{4}(x+4)$ D. $y+3=4(x+4)$

[Free] \left(\frac{13}{18} \times \frac{-12}{39}\right)-\left(\frac{8}{9} \times \frac{-3}{4}\right)+\left[-\frac{7}{-9} \div \frac{63}{-36}\right]

[Free] What is the third step in proving by mathematical induction that for every positive integer $n , 11^n-6$ is divisible by 5, is true? A. Assume that $11^{k+1}-6$ is divisible by 5. B. Show that $11^{k+1}-6$ is divisible by 5. C. Assume that $11^1-6$ is divisible by 5. D. Show that $11^k-6$ is divisible by 5.

[Free] Annual expenses for an individual are shown in the table. To prorate the annual costs into a monthly budget, how much money per month should be budgeted for car registration? | | | | :-------------------- | :-------- | | Annual Expenses | | | Car Registration | $84.00 | | Car Insurance | $565.00 | | Home Insurance | $1,070.00 | Round to the nearest cent.

[Free] A right triangle has side lengths [tex]$A C=7$[/tex] inches, [tex]$B C=24$[/tex] inches, and [tex]$AB =25$[/tex] inches. What are the measures of the angles in triangle [tex]$A B C$[/tex]? [tex]$m \angle A \approx 46.2^{\circ}, m \angle B \approx 43.8^{\circ}, m \angle C \approx 90^{\circ}$[/tex] [tex]$m \angle A \approx 73.0^{\circ}, m \angle B \approx 17.0^{\circ}, m \angle C \approx 90^{\circ}$[/tex] [tex]$m \angle A \approx 73.7^{\circ}, m \angle B \approx 16.3^{\circ}, m \angle C \approx 90^{\circ}$[/tex] [tex]$m \angle A \approx 74.4^{\circ}, m \angle B \approx 15.6^{\circ}, m \angle C \approx 90^{\circ}$[/tex]

[Free] What value of [tex]$x$[/tex] would make [tex]$\overline{ KM } / / \overline{ JN }$[/tex]? Complete the statements to solve for [tex]$x$[/tex]. By the converse of the side-splitter theorem, if JK/KL = [$\square$] then KM // JN. Substitute the expressions into the proportion: [tex]$\frac{x-5}{x}=\frac{x-3}{x+4}$[/tex]. Cross-multiply: [tex]$(x-5)$[/tex] ([$\square$] [tex]$=x(x-3)$[/tex]. Distribute: [tex]$x(x)+x(4)$[/tex] Multiply and simplify: [tex]$x^{ X }$[/tex] Solve for [tex]$x: x=$[/tex] [$\square$] [tex]$x+4$[/tex] [tex]$x-3$[/tex]

[Free] e) [tex]\left[\frac{\left(4^2\right)^{-1}}{16^{-9}}\right]^{-3}[/tex] f) [tex]\frac{\left(\frac{2}{5}\right)^{-2}}{\left(\frac{5}{2}\right)\left(\frac{5}{2}\right)} \times 2[/tex] g) [tex]\frac{25^{-1}}{5^{-2}}+\frac{0,05^{-2}}{0,1^{-3}}[/tex]