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Questions in mathematics

[Free] One model of Earth's population growth is [tex]$P(t)=\frac{64}{\left(1+11 e^{-.08 t}\right)}$[/tex] measured in years since 1990, and P is measured in billions of people. Which of the following statements are true? Check all that apply. A. The population of Earth is increasing by a steady rate of [tex]$8 \%$[/tex] per year. B. The population of Earth will grow exponentially for a while but then start to slow down its growth. C. In 1990, there were 5.33 billion people. D. The carrying capacity of Earth is 5.33 billion people.

[Free] For what values of [tex]$x$[/tex] does [tex]$25^x=5^{x^2-3}$[/tex]? A. [tex]$x=-3, x=1$[/tex] B. [tex]$x=-1, x=3$[/tex] C. [tex]$x=-\frac{3}{2}, x-2$[/tex] D. [tex]$x=-2, x=\frac{3}{2}$[/tex]

[Free] Solve on the interval $\left[0^{\circ}, 360^{\circ}\right)$. Hint: Use an Identity! $2 \sec ^2 x+\tan ^2 x=3$

[Free] What is $7 / 8 \div 7 / 16$ reduced to the lowest term? A. 1 B. 2 C. $7 / 2$ D. $7^{1 / 32}$

[Free] Solve the following equation algebraically: [tex]2 x^2=50[/tex] A. [tex]\pm 0.2[/tex] B. [tex]\pm 7.07[/tex] C. [tex]\pm 5[/tex] D. [tex]\pm 12.5[/tex]

[Free] Pam is preparing for a trip to the Philippines. She has set aside money for everything that she needs to have, but there are several other items which, while not strictly necessary, she would like to take with her. The following table shows the money that Pam has already spent or allocated, with prices listed in Philippine pesos (P). | Expense | Cost (P) | | :------------ | :------------- | | Transportation | 10,804 | | Hostel | 9,773 | | Food budget | 11,229 | | Sightseeing budget | 24,615 | Pam's total budget is P 77,500. Which of the following additional items can Pam afford? I. brand-new walking shoes, P 6,865 II. ticket upgrade to first class, P 15,149 III. electronic Tagalog/English dictionary, P 13,255 A. only I B. I or III, but not both

[Free] The sum of two polynomials is $10 a^2 b^2-8 a^2 b+6 a b^2-4 a b+2$. If one addend is $-5 a^2 b^2+12 a^2 b-5$, what is the other addend?

[Free] The table given below shows the number of pens owned by each student in a class. | No. of pens | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---|---|---| | No. of students | 6 | 2 | 9 | 9 | r | 2 | 2 | If the mean is 2.5, find the value of r?

[Free] The table represents a linear equation. | x | y | | --- | --- | | -10 | 8 | | -5 | 7 | | 10 | 4 | | 15 | 3 | Which equation shows how $(-10,8)$ can be used to write the equation of this line in point-slope form? A. $y-8=-0.15(x-10)$ B. $y+8=-0.15(x-10)$ C. $y-8=-0.2(x+10)$ D. $y+8=-0.2(x-10)$

[Free] Line $CD$ passes through points $C(1,3)$ and $D(4,-3)$. If the equation of the line is written in slope-intercept form, $y=mx+b$, what is the value of $b$?