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Questions in mathematics

[Jawaban] Solve \(\ln (5 x+1)=3\) Round to the nearest thousandth.

[Jawaban] Please select the best answer from the choices provided. A B D

[Jawaban] Consider the equation [tex]0.75 \cdot 10^{\frac{w}{3}}=30[/tex]. Solve the equation for [tex]w[/tex]. Express the solution as a logarithm in base-10. [tex]w=\square[/tex] Approximate the value of [tex]w[/tex]. Round your answer to the nearest thousandth. [tex]w \approx \square[/tex]

[Jawaban] Select the correct answer. Which function is decreasing and approaches negative infinity as $x$ increases? A. $f(x)=3(0.6)^x-1$ B. $f(x)=-3(0.6)^x+1$ C. $f(x)=3(6)^x-2$ D. $f(x)=-3(6)^x+2

[Jawaban] Lily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find $b$, the number of bracelets she sold, and $n$, the number of necklaces she sold? $\begin{array}{l} b+n=101 \\ 6 b+5 n=18 \end{array}$ $\begin{array}{l} b+n=101 \\ 5 b+6 n=18 \end{array}$ $b+n=18$ $6 b+5 n=101$ $b+n=18$ $5 b+6 n=101$

[Jawaban] The measure of angle BAC can be calculated using the equation $\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x$. [Not drawn to scale] What is the measure of angle BAC? Round to the nearest whole degree. A. $0^{\circ}$ B. $1^{\circ}$ C. $44^{\circ}$ D. $48^{\circ}$

[Jawaban] A random sample of students at North High School were polled on whether they prefer a 15-minute break between classes in the morning or in the afternoon. The results are shown in the frequency table. | | Morning | Afternoon | Total | | :---- | :------ | :-------- | :---- | | 10th | 21 | 17 | 38 | | 11th | 16 | 25 | 41 | | 12th | 19 | 20 | 39 | | Total | 56 | 62 | 118 | What is the joint relative frequency for 11th graders who want the break in the afternoon? Round to the nearest percent. A. 21% B. 25% C. 40% D. 61%

[Jawaban] True or False: Analyze the statement below and tell whether the statement about polygons is true or false. Reason why? 1. A regular pentagon has five equal sides. 2. A rectangle is a regular quadrilateral. 3. A triangle is always a convex polygon. 4. All convex polygons are regular polygons. 5. All regular polygons are convex.

[Jawaban] 5. If P(E) = 0.05, what is the probability of 'not E'? 6. A bag contains lemon flavored candies only. What is the probability that she: (i) draws an orange flavored candy? (ii) draws a lemon flavored candy? 7. It is given that in a group of 3 students, the probability of having the same birthday is 0.992. What is the probability that they do not have the same birthday? 8. A bag contains 3 red balls and 5 black balls. What is the probability that the ball drawn is: (i) red?

[Jawaban] Jonny makes a sequence of patterns using matchsticks. He adds the same number of matchsticks each time. How many matchsticks does he add each time? | Pattern number | 1 | 2 | 3 | ... | |---|---|---|---|---| | Number of matchsticks | 5 | 9 | 13 | ... |