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Questions in mathematics

[Jawaban] If [tex]s(x)=x-7[/tex] and [tex]t(x)=4 x^2-x+3[/tex], which expression is equivalent to [tex](t \circ s)(x)[/tex]? A. [tex]4(x-7)^2-x-7+3[/tex] B. [tex]4(x-7)^2-(x-7)+3[/tex] C. [tex](4 x^2-x+3)-7[/tex] D. [tex](4 x^2-x+3)(x-7)[/tex]

[Jawaban] In a survey of 2035 workers, $73\%$ reported working out 3 or more days a week. What is the margin of error? What is the interval that is likely to contain the exact percent of all people who work out 3 or more days a week? Show all work. Use this formula: $\pm \frac{1}{\sqrt{n}}$

[Jawaban] If $3, x, y, 24$ are in AP, find $x+y$.

[Jawaban] Which of the following are simple equations? (i) 3x + 5 = 14 (ii) 3x - 6 = x + 2 (iii) 3 = 2x + y (iv) (x/3) + 5 = 0 (v) x² + 5x + 3 = 0 (vi) 5m - 6n = 0 (vii) 7p + 6q + 13s = 11 (viii) 13t - 26 = 39

[Jawaban] Fill in the blanks to summarize how to add, subtract, multiply, and divide integers. Addition 1. If the two integers being added have the same sign, - add their absolute values. - use their sign for the answer. 2. If the two integers being added have different signs, - find the difference of their absolute values. - use the sign of the number with the greater absolute value. Subtraction 1. While subtracting one number from another, find the additive inverse of the second number and add it to the first using the rule of addition. Multiplication and Division 1. While multiplying or dividing two integers, - find the product or quotient of the absolute values. - identify the sign of the result by following the rules below: - positive x positive = positive - positive x negative = negative - negative x positive = negative - negative x negative = positive - When the signs are the same, the answer is positive. - When the signs are different, the answer is negative. - positive ÷ positive = positive - positive ÷ negative = negative - negative ÷ positive = negative - negative ÷ negative = positive Fill in the blanks with 'Yes' or 'No' to summarize the properties of integers. | Property/Operation | Addition | Subtraction | Multiplication | Division | |-------------------|----------|-------------|----------------|----------| | Closure Property | Yes | No | Yes | No | | Commutative Property | Yes | No | Yes | No | | Associative Property | Yes | No | Yes | No |

[Jawaban] 14. What are the degrees of freedom for each of the following situations? a. N=28, C=6, Goodness of fit test b. N=200, K=10, R=2, Test of independence c. N=130, C=5, Test of homogeneity 15. A researcher selects a sample of 40 people to investigate the relationship between brand preference (Brand A or Brand B) and gender (Male or Female). Of the 20 males in the sample, five prefer Brand A. Of the 20 females in the sample, 12 prefer Brand A. Based on this scenario: | Preference | Male | Female | Total | |------------|------|--------|-------| | Brand A | 5 | 12 | | | Brand B | | | | | Total | 20 | 20 | 40 | a. What is the expected frequency for females who prefer Brand A? b. What is the expected frequency for females who prefer Brand B? c. What is the observed frequency for females who prefer Brand B?

[Jawaban] What is the center of a circle whose equation is $x^2+y^2+4 x-8 y+11=0$? A. $(-2,4)$ B. $(-4,8)$ C. $(2,-4)$ D. $(4,-8)$

[Jawaban] Which is the solution set of the compound inequality [tex]$3.5 x-10>-3$[/tex] and [tex]$8 x-9<39$[/tex]? A. [tex]$-2<x<6$[/tex] B. [tex]$-2 \leq x < 6$[/tex] C. [tex]$2<x<6$[/tex] D. [tex]$2 \leq x < 6$[/tex]

[Jawaban] Factor: $x^2+4 x+3$ A. $(x+2)(x+2)$ B. $(x+3)(x+1)$ C. $(x+4)(x-1)$ D. Cannot be factored

[Jawaban] Factor a number, variable, or expression out of the trinomial shown below: [tex]$5 x^2-25 x+10$[/tex] A. [tex]$2\left(x^2-5 x+5\right)$[/tex] B. [tex]$5\left(x^2-5 x+2\right)$[/tex] C. [tex]$5\left(x^2-20 x+5\right)$[/tex] D. [tex]$5\left(x^2-10 x+2\right)$[/tex]