monthly mortgage payments can be found using the formula below, where $m$ is the monthly payment, $p$ is the…

monthly mortgage payments can be found using the formula below, where $m$ is the monthly payment, $p$ is the amount borrowed, $r$ is the annual interest rate, and $n$ is the total number of monthly payments.\nm=\frac{p\frac{r}{12}(1 + \frac{r}{12})^n}{(1+\frac{r}{12})^n - 1}\nif adam takes out a 15 - year mortgage, borrowing $240,000 at an annual interest rate of 4.5%, his monthly payment would be\na) $9011.94$ b) $1179.09$ c) $1835.98$ d) $1604.80$\n14) given that $i$ is the imaginary unit, the expression $(x - 2i)^2$ is equivalent to\na) $x^2-2xi - 4$ b) $x^2 - 4$ c) $x^2+4$ d) $x^2-4xi - 4$\n15) which situation best describes conditional probability?\na) finding the probability of an event occurring two or more times\nb) finding the probability of an event occurring only once\nc) finding the probability of an event occurring given another event has already occurred\nd) finding the probability of two independent events occurring at the same time\n16) a parabola has a directrix of $y = 3$ and a vertex at $(2,1)$. which ordered pair is the focus of the parabola?\na) $(2,2)$ b) $(2,-1)$ c) $(2,0)$ d) $(2,5)$\n17) which sketch could represent the function $m(x)=-log_{10}(x - 2)$?

monthly mortgage payments can be found using the formula below, where $m$ is the monthly payment, $p$ is the amount borrowed, $r$ is the annual interest rate, and $n$ is the total number of monthly payments.\nm=\frac{p\frac{r}{12}(1 + \frac{r}{12})^n}{(1+\frac{r}{12})^n - 1}\nif adam takes out a 15 - year mortgage, borrowing $240,000 at an annual interest rate of 4.5%, his monthly payment would be\na) $9011.94$ b) $1179.09$ c) $1835.98$ d) $1604.80$\n14) given that $i$ is the imaginary unit, the expression $(x - 2i)^2$ is equivalent to\na) $x^2-2xi - 4$ b) $x^2 - 4$ c) $x^2+4$ d) $x^2-4xi - 4$\n15) which situation best describes conditional probability?\na) finding the probability of an event occurring two or more times\nb) finding the probability of an event occurring only once\nc) finding the probability of an event occurring given another event has already occurred\nd) finding the probability of two independent events occurring at the same time\n16) a parabola has a directrix of $y = 3$ and a vertex at $(2,1)$. which ordered pair is the focus of the parabola?\na) $(2,2)$ b) $(2,-1)$ c) $(2,0)$ d) $(2,5)$\n17) which sketch could represent the function $m(x)=-log_{10}(x - 2)$?

Answer

Explanation:

Step1: Calculate values for mortgage formula

For the mortgage problem, $P = 240000$, $r=0.045$, and $n = 15\times12=180$. First, find $\frac{r}{12}= \frac{0.045}{12}=0.00375$.

Step2: Calculate numerator of mortgage formula

The numerator is $P\times\frac{r}{12}\times(1 + \frac{r}{12})^{n}=240000\times0.00375\times(1 + 0.00375)^{180}$. $(1 + 0.00375)^{180}\approx1.9479$. So the numerator is $240000\times0.00375\times1.9479 = 240000\times0.007290375=1749.69$.

Step3: Calculate denominator of mortgage formula

The denominator is $(1+\frac{r}{12})^{n}-1=(1 + 0.00375)^{180}-1\approx1.9479 - 1=0.9479$.

Step4: Calculate monthly payment

$M=\frac{1749.69}{0.9479}\approx1845.85$ (There may be some rounding - off differences in the options).

For the complex - number problem:

$(x - 2i)^{2}=x^{2}-4xi+(2i)^{2}=x^{2}-4xi - 4$.

For the probability problem:

The definition of conditional probability is the probability of an event occurring given that another event has already occurred.

For the parabola problem:

The vertex of the parabola is $(h,k)=(2,1)$ and the directrix is $y = 3$. The distance from the vertex to the directrix is $d=|1 - 3| = 2$. The focus of a parabola is at a distance $d$ from the vertex in the opposite direction of the directrix. So the focus is at $(2,-1)$.

For the function - graph problem:

The function $y=-\log_{10}(x - 2)$ has a vertical asymptote at $x = 2$ and is a reflection of the basic logarithmic function $y=\log_{10}(x)$ about the $x$ - axis and shifted 2 units to the right.

Answer:

  1. C
  2. D
  3. D
  4. B
  5. (description of the correct graph based on the above analysis)