Question 1

Arturo invests  $2700  in a savings account that pays  9%  interest, compounded quarterly. If there are no other transactions, when will his balance reach  $4550?

Accepted Answer

$\text { After } 6 \text { years }$

Question 2

A ball is thrown from the ground with initial velocity  35ft/sec  at an angle of elevation of $75^{\circ}$. Let  t=0  be the time when the ball is thrown. Using the position function in parametric form, what is the maximum height of the ball if air resistance is neglected?A ball is thrown from the ground with initial velocity  35ft/sec  at an angle of elevation of $75^{\circ}$. Let  t=0  be the time when the ball is thrown. Using the position function in parametric form, what is the maximum height of the ball if air resistance is neglected?

Accepted Answer

About 17.86 ft

Question 3

Determine the range of $f(x)=3+15 x-x^{3}-2 x^{4}$
Express your answer in interval notation.

Accepted Answer

Approximately $(-\infty, 15.25]$

Question 4

Three sides of a fence and a wall form a rectangular enclosure. The total length of a fence used for the three sides is 160 feet. Let  x  be the length of the two sides perpendicular to the wall as shown.
 
Write the area  A  of the enclosure as a function of the length  x . For what values of  x  will the area be 5,500 square feet?

Accepted Answer

The answer of Three sides of a fence and a...

Question 5

Find the equation of the parabola that passes through  (4,7)  and has vertex  (2,-5) . Express your answer in the standard form for a quadratic function.

Accepted Answer

The answer of Find the equation of the parabola that...

Question 6

Which transformation was not performed on  y=sin x  to obtain $y=-2 \sin (3 x+\pi / 3) ?$

Accepted Answer

A)  Horizontal shift left by $\pi / 9$ units 
B)  Horizontal stretch by a factor of 3 
C)  Vertical stretch by a factor of 2 
D)  Reflection through the  x -axis 
A)  Horizontal shift left by $\pi / 9$ units 
B)  Horizontal stretch by a factor of 3 
C)  Vertical stretch by a factor of 2 
D)  Reflection through the  x -axis

Question 7

An airplane is flying on a bearing $ 23^{\circ} $ east of north at $ 650 \mathrm{mph} $. Express the velocity of the airplane as a vector.

Accepted Answer

The answer of An airplane is flying on a bearing...

Question 8

Graph the relation defined by the parametric equations when $-3 \leq t \leq 2$
$x(t)=5-r^{2}$ y(t)=t+2 .

Accepted Answer

The answer of Graph the relation defined by the parametric...

Question 9

For the function $f(x)=\frac{3\left(x^{2}-25\right)}{x^{2}-4}$
what are the intercepts and what are the asymptotes?

Accepted Answer

x -intercepts:  (5,

Question 10

Find two complex number roots for the equation 
$x^{2}-4 x+21=0$

Accepted Answer

The answer of Find two complex number roots for the...

Question 11

Accepted Answer

The answer of  ...

Question 12

Melanie invests $ \$ 3,500 $ in a savings account that pays $ 8 \% $ interest, compounded monthly. If there are no other transactions, when will her balance reach $ \$ 4,300? $

Accepted Answer

The answer of Melanie invests $ \$ 3,500 $ in...

Question 13

Solve the system by any method.
x-3 z=0 
x-y=4 
x+2 y-z=0

Accepted Answer

The answer of Solve the system by any method.
x-3 z=0...

Question 14

Geoff invests  $5,000  at  8.2%  for 12 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 12 years?

Accepted Answer

The answer of Geoff invests  $5,000  at ...

Question 15

Solve the inequality  |x-8|>4 . Express your answer in interval notation.

Accepted Answer

The answer of Solve the inequality  |x-8|>4 . Express...

Question 16

What are the four roots of $16\left(\cos \frac{8 \pi}{15}+i \sin \frac{8 \pi}{15}\right) ?$
Express the answers in trigonometric form.

Accepted Answer

None

Question 17

Sketch the region of feasible points and solve the linear programming problem.
Maximize  C=-3 x+2 y , subject to:
$\begin{array}{r}
x \geq 0 \
y \geq 3 \
x+3 y \leq 18 \
x+y \geq 8
\end{array}$

Accepted Answer

C=-21 (9,3)

11ec74

Question 18

Find the partial fraction decomposition of $\frac{2-3 x}{x^{2}}$

Accepted Answer

The answer of Find the partial fraction decomposition of \(\frac{2-3...

Question 19

Use synthetic division to show that the number  c=-3  is a lower bound for the zeros of $f(x)=x^{4}-2 x^{3}-8 x^{2}+3 x-10$
Be sure to reference any properties, theorems or tests used.

Accepted Answer

Sample answer: According to the lower bo

Question 20

There are 12 balls in a box that are numbered 1 through 12. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 7 and the second ball selected will not be a 2 ?

Accepted Answer

The answer of There are 12 balls in a box...

Arturo invests $2700 in a savings account that pays 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550?

Determine the range of $f(x)=3+15 x-x^{3}-2 x^{4}$ Express your answer in interval notation.

Find the equation of the parabola that passes through (4,7) and has vertex (2,-5) . Express your answer in the standard form for a quadratic function.

Which transformation was not performed on y=sin x to obtain $y=-2 \sin (3 x+\pi / 3) ?$

An airplane is flying on a bearing $23^{\circ}$ east of north at $650 \mathrm{mph}$ . Express the velocity of the airplane as a vector.

Graph the relation defined by the parametric equations when $-3 \leq t \leq 2$ $x(t)=5-r^{2}$ y(t)=t+2 .

For the function $f(x)=\frac{3\left(x^{2}-25\right)}{x^{2}-4}$ what are the intercepts and what are the asymptotes?

Find two complex number roots for the equation $x^{2}-4 x+21=0$

Melanie invests $\$ 3,500$ in a savings account that pays $8 \%$ interest, compounded monthly. If there are no other transactions, when will her balance reach $\$ 4,300?$

Solve the system by any method. x-3 z=0 x-y=4 x+2 y-z=0

Geoff invests $5,000 at 8.2% for 12 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 12 years?

Solve the inequality |x-8|>4 . Express your answer in interval notation.

What are the four roots of $16\left(\cos \frac{8 \pi}{15}+i \sin \frac{8 \pi}{15}\right) ?$ Express the answers in trigonometric form.

Sketch the region of feasible points and solve the linear programming problem. Maximize C=-3 x+2 y , subject to: x\geq0 y\geq3 x+3y\leq18 x+y\geq8

Find the partial fraction decomposition of $\frac{2-3 x}{x^{2}}$

Use synthetic division to show that the number c=-3 is a lower bound for the zeros of $f(x)=x^{4}-2 x^{3}-8 x^{2}+3 x-10$ Be sure to reference any properties, theorems or tests used.

There are 12 balls in a box that are numbered 1 through 12. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 7 and the second ball selected will not be a 2 ?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Filters

Exam 12: Mathematical Problem Set

Arturo invests $2700 in a savings account that pays 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550?

Determine the range of f(x)=3+15x−x3−2x4f(x)=3+15 x-x^{3}-2 x^{4}f(x)=3+15x−x3−2x4 Express your answer in interval notation.

Find the equation of the parabola that passes through (4,7) and has vertex (2,-5) . Express your answer in the standard form for a quadratic function.

Which transformation was not performed on y=sin x to obtain y=−2sin⁡(3x+π/3)?y=-2 \sin (3 x+\pi / 3) ?y=−2sin(3x+π/3)?

An airplane is flying on a bearing 23∘ 23^{\circ} 23∘ east of north at 650mph 650 \mathrm{mph} 650mph . Express the velocity of the airplane as a vector.

Graph the relation defined by the parametric equations when −3≤t≤2-3 \leq t \leq 2−3≤t≤2 x(t)=5−r2x(t)=5-r^{2}x(t)=5−r2 y(t)=t+2 .

For the function f(x)=3(x2−25)x2−4f(x)=\frac{3\left(x^{2}-25\right)}{x^{2}-4}f(x)=x2−43(x2−25)​ what are the intercepts and what are the asymptotes?

Find two complex number roots for the equation x2−4x+21=0x^{2}-4 x+21=0x2−4x+21=0

Melanie invests $3,500 \$ 3,500 $3,500 in a savings account that pays 8% 8 \% 8% interest, compounded monthly. If there are no other transactions, when will her balance reach $4,300? \$ 4,300? $4,300?

Solve the system by any method. x-3 z=0 x-y=4 x+2 y-z=0

Geoff invests $5,000 at 8.2% for 12 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 12 years?

Solve the inequality |x-8|>4 . Express your answer in interval notation.

What are the four roots of 16(cos⁡8π15+isin⁡8π15)?16\left(\cos \frac{8 \pi}{15}+i \sin \frac{8 \pi}{15}\right) ?16(cos158π​+isin158π​)? Express the answers in trigonometric form.

Sketch the region of feasible points and solve the linear programming problem. Maximize C=-3 x+2 y , subject to: x\geq0 y\geq3 x+3y\leq18 x+y\geq8

Find the partial fraction decomposition of 2−3xx2\frac{2-3 x}{x^{2}}x22−3x​

Use synthetic division to show that the number c=-3 is a lower bound for the zeros of f(x)=x4−2x3−8x2+3x−10f(x)=x^{4}-2 x^{3}-8 x^{2}+3 x-10f(x)=x4−2x3−8x2+3x−10 Be sure to reference any properties, theorems or tests used.

There are 12 balls in a box that are numbered 1 through 12. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 7 and the second ball selected will not be a 2 ?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Filters

Determine the range of $f(x)=3+15 x-x^{3}-2 x^{4}$ Express your answer in interval notation.

Which transformation was not performed on y=sin x to obtain $y=-2 \sin (3 x+\pi / 3) ?$

An airplane is flying on a bearing $23^{\circ}$ east of north at $650 \mathrm{mph}$ . Express the velocity of the airplane as a vector.

Graph the relation defined by the parametric equations when $-3 \leq t \leq 2$ $x(t)=5-r^{2}$ y(t)=t+2 .

For the function $f(x)=\frac{3\left(x^{2}-25\right)}{x^{2}-4}$ what are the intercepts and what are the asymptotes?

Find two complex number roots for the equation $x^{2}-4 x+21=0$

Melanie invests $\$ 3,500$ in a savings account that pays $8 \%$ interest, compounded monthly. If there are no other transactions, when will her balance reach $\$ 4,300?$

What are the four roots of $16\left(\cos \frac{8 \pi}{15}+i \sin \frac{8 \pi}{15}\right) ?$ Express the answers in trigonometric form.

Find the partial fraction decomposition of $\frac{2-3 x}{x^{2}}$

Use synthetic division to show that the number c=-3 is a lower bound for the zeros of $f(x)=x^{4}-2 x^{3}-8 x^{2}+3 x-10$ Be sure to reference any properties, theorems or tests used.