Questions in mathematics

Questions in mathematics

📝 Answered - Each equation given below describes a parabola. Which statement best compares their graphs? x=5y² x=3y² A. Both parabolas open upward, and x = 5y² is wider than x = 3y². B. Both parabolas open to the right, and x = 5y² is wider than x = 3y². C. Both parabolas open to the right, and x = 3y² is wider than x = 5y². D. Both parabolas open upward, and x = 3y² is wider than x = 5y².

📝 Answered - Sports car or convertible? The following table presents the fuel efficiency, in miles per gallon, for a sample of convertibles and a sample of sports cars. | Convertible Model | MPG | Sports Model | MPG | |---|---|---|---| | Ford Mustang V6 | 20 | Honda Civic Si | 27 | | Volkswagen Eos | 25 | BMW 135i | 23 | | Mini Cooper | 25 | Mazda3 Mazdaspeed | 24 | | Saab 9-3 | 24 | Subaru Impreza WRX STi | 21 | | BMW 328 i | 21 | Mazda RX-8 | 18 | | Toyota Camry Solara | 21 | Mitsubishi Lancer Evolution | 21 | Part 1 of 2 (a) Find the sample standard deviation of the mileage for the sample of convertibles. Round the answer to one decimal place. The sample standard deviation for the convertibles, in miles per gallon, is $\square$ .

📝 Answered - When graphing $3x + 5y > 20$, the boundary line is A. solid B. dotted

📝 Answered - Simplify. $\frac{x^2-9 x+14}{x^2+5 x-14}$

📝 Answered - Rewrite $256^{-\frac{1}{4}}$ with a positive exponent, then simplify. $256^{-\frac{1}{4}}=\square$

📝 Answered - Solve the equation algebraically and check graphically. $6300=300\left(10^x\right)$ $x \approx$ $\square$ (Round to three decimal places as needed.)

📝 Answered - Given that [tex]$U = \{1,2, \ldots, 10\}$[/tex] is a universal set, [tex]$A = \{x: x \leq 5, x \in U[/tex] odd number, [tex]$y \in U\}$[/tex] and [tex]$C = \{z: z[/tex] is a prime number, [tex]$z \in U\}$[/tex]. (i) What is the cardinality of set A? (ii) How many elements are there in [tex]$A \cap B \cap C$[/tex]? (iii) Show the relation of the sets U, A, B, and C in a Venn-diagram. (iv) Find the percentage of [tex]$n _{ o }( A )$[/tex].

📝 Answered - Given two dependent random samples with the following results: | Population 1 | 22 | 39 | 20 | 34 | 43 | 17 | 45 | |---|---|---|---|---|---|---|---| | Population 2 | 33 | 45 | 35 | 46 | 35 | 27 | 37 | Use this data to find the $98 \%$ confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4 : Find the point estimate for the population mean of the paired differences. Let $x_1$ be the value from Population 1 and $x_2$ be the value from Population 2 and use the formula $d=x_2-x_1$ to calculate the paired differences. Round your answer to one decimal place.

📝 Answered - Form a fifth-degree polynomial function with real coefficients such that [tex]$i, 1-2 i$[/tex], and -5 are zeros and [tex]$f(0)=75$[/tex]. [tex]$f(x)= \square$[/tex] (Simplify your answer. Type an expression using [tex]$x$[/tex] as the variable.)

📝 Answered - Simplify $9 m^3 y^2 \div 3 m^2 y$