Question 1

A student picks the first 20 students that enter the cafeteria at eight in the morning. Is this a random sample of students at the college?

Accepted Answer

The answer of A student picks the first 20 students...

Question 2

For the function $f(x)$ graphed below, which of the following is the $\lim _{x \rightarrow 3} f(x)$

Accepted Answer

A)  $\lim _{x \rightarrow 3} f(x)=2$ 
B)  $\lim _{x \rightarrow 3} f(x)=1 / 2$ 
C)  $\lim _{x \rightarrow 3} f(x)=1$ 
D)  $\lim _{x \rightarrow 3} f(x) \text { does not exist }$ 
A)  $\lim _{x \rightarrow 3} f(x)=2$ 
B)  $\lim _{x \rightarrow 3} f(x)=1 / 2$ 
C)  $\lim _{x \rightarrow 3} f(x)=1$ 
D)  $\lim _{x \rightarrow 3} f(x) \text { does not exist }$

Question 3

Find a polynomial of degree 3 with real number coefficients that has $8+2 i \text { and } 5$ as zeros.

Accepted Answer

The answer of Find a polynomial of degree 3 with...

Question 4

Simplify: 
$(\sec x-\csc x) \sin x \cos x=$

Accepted Answer

A)  $\sin x-\cos x$ 
B) $\cos x-\sin x$ 
C)  $\sin x+\cos x$ 
D)  $\cos x+\sin x$ 
A)  $\sin x-\cos x$ 
B) $\cos x-\sin x$ 
C)  $\sin x+\cos x$ 
D)  $\cos x+\sin x$

Question 5

Rewrite the expression using a single radical.
$\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}$

Accepted Answer

The answer of Rewrite the expression using a single radical.
$\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}$...

Question 6

Write the parametric form of the equation of the line through the points  (2,-1,5)  and  (-3,1,0).

Accepted Answer

x= 2-5t,

Question 7

At the top a radio signal tower there is an antenna with a light on the end of it. From a point on the ground 800 feet from the base of the tower, the angle of elevation to the tip of the light is $48.8^{\circ}$ and the angle of elevation to the bottom of the antenna is $42.7^{\circ}$ . What is the height of the antenna, including the light?

Accepted Answer

The answer of At the top a radio signal tower...

Question 8

Find the angle between vector $ \mathbf{u}=\langle-2,5\rangle $ and vector $ \mathbf{v}=\langle-1,3\rangle $

Accepted Answer

The answer of Find the angle between vector \( \mathbf{u}=\langle-2,5\rangle...

Question 9

Solve the equation  log (x-6)+log (x-3)=1 .
List any extraneous roots and explain.

Accepted Answer

Solution: @#LAT-DLM& Extraneous root: @#LAT-DLM&.

Question 10

Jose deposits $ \$ 200 $ at the end of each month into an account that pays $ 5 \% $ interest compounded monthly. After 7 years of deposits, what is the account balance?

Accepted Answer

The answer of Jose deposits $ \$ 200 $ at...

Question 11

There are 10 balls in a box that are numbered 1 through 10. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 3 and the second ball selected will not be a 9 ?

Accepted Answer

The answer of There are 10 balls in a box...

Question 12

Which of the following could represent a complete graph of $f(x)=a x+x^{3}$ where a is a real number?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

In a certain national forest, the number of moose present after  t  years is modeled by the function 
$P(t)=\frac{1518}{1+65 e^{-0.05 t}}$
(a) What was the initial population of moose?
(b) When will the number of moose be 850 ?
(c) What is the maximum number of moose possible in the forest?

Accepted Answer

(a) 23
(b)

Question 14

For the function $f(x)=\frac{1}{x}$ what is the equation of the tangent line at  x=1  ?

Accepted Answer

The answer of For the function $f(x)=\frac{1}{x}$ what is the...

Question 15

Use the discriminant to identify the graph of 
$2 x^{2}+4 x y-2 y^{2}-3 x-y=8$

Accepted Answer

A)  The graph is a circle. 
B)  The graph is a hyperbola. 
C)  The graph is an ellipse. 
D)  The graph is a parabola. 
A)  The graph is a circle. 
B)  The graph is a hyperbola. 
C)  The graph is an ellipse. 
D)  The graph is a parabola.

Question 16

Solve the equation graphically. $|5 x-4|=(\sqrt{x+3}) 5$

Accepted Answer

x @#LAT-DLM& -0.71

Question 17

Martha invests $6,000 at 7.5% for 8 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 8 years?

Accepted Answer

The answer of Martha invests $6,000 at 7.5% for 8...

Question 18

Find the angle between vector $\mathbf{u}=\langle 5,-2\rangle$ and vector $\mathbf{v}=\langle 1,-3\rangle$

Accepted Answer

The answer of Find the angle between vector $\mathbf{u}=\langle 5,-2\rangle$...

Question 19

Evaluate all six trigonometric functions of the angle $\theta$ for the traingle given below.
 
$\begin{array}{lccc}
\sin \theta=& ----------------\
\tan \theta= & ----------------\
 \csc \theta= & ----------------\
\cos \theta= & ----------------\
 \sec \theta= & ----------------\
\cot \theta= & ----------------\
\end{array}$

Accepted Answer

None

Question 20

Solve the right triangle $\triangle A B C$ for all its unknown parts if  $\beta=38^{\circ}$ and b= 4.5.

Accepted Answer

The answer of Solve the right triangle \(\triangle A B...

A student picks the first 20 students that enter the cafeteria at eight in the morning. Is this a random sample of students at the college?

For the function $f(x)$ graphed below, which of the following is the $\lim _{x \rightarrow 3} f(x)$ $For the function f(x) graphed below, which of the following is the \lim _{x \rightarrow 3} f(x)$

Find a polynomial of degree 3 with real number coefficients that has $8+2 i \text { and } 5$ as zeros.

Simplify: $(\sec x-\csc x) \sin x \cos x=$

Rewrite the expression using a single radical. $\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}$

Write the parametric form of the equation of the line through the points (2,-1,5) and (-3,1,0).

Find the angle between vector $\mathbf{u}=\langle-2,5\rangle$ and vector $\mathbf{v}=\langle-1,3\rangle$

Solve the equation log (x-6)+log (x-3)=1 . List any extraneous roots and explain.

Jose deposits $\$ 200$ at the end of each month into an account that pays $5 \%$ interest compounded monthly. After 7 years of deposits, what is the account balance?

There are 10 balls in a box that are numbered 1 through 10. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 3 and the second ball selected will not be a 9 ?

Which of the following could represent a complete graph of $f(x)=a x+x^{3}$ where a is a real number?

In a certain national forest, the number of moose present after t years is modeled by the function $P(t)=\frac{1518}{1+65 e^{-0.05 t}}$ (a) What was the initial population of moose? (b) When will the number of moose be 850 ? (c) What is the maximum number of moose possible in the forest?

For the function $f(x)=\frac{1}{x}$ what is the equation of the tangent line at x=1 ?

Use the discriminant to identify the graph of $2 x^{2}+4 x y-2 y^{2}-3 x-y=8$

Solve the equation graphically. $|5 x-4|=(\sqrt{x+3}) 5$

Martha invests $6,000 at 7.5% for 8 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 8 years?

Find the angle between vector $\mathbf{u}=\langle 5,-2\rangle$ and vector $\mathbf{v}=\langle 1,-3\rangle$

Solve the right triangle $\triangle A B C$ for all its unknown parts if $\beta=38^{\circ}$ and b= 4.5. $Solve the right triangle \triangle A B C for all its unknown parts if \beta=38^{\circ} and b= 4.5.$

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

A student picks the first 20 students that enter the cafeteria at eight in the morning. Is this a random sample of students at the college?

For the function f(x)f(x)f(x) graphed below, which of the following is the lim⁡x→3f(x)\lim _{x \rightarrow 3} f(x)limx→3​f(x)

Find a polynomial of degree 3 with real number coefficients that has 8+2i and 58+2 i \text { and } 58+2i and 5 as zeros.

Simplify: (sec⁡x−csc⁡x)sin⁡xcos⁡x=(\sec x-\csc x) \sin x \cos x=(secx−cscx)sinxcosx=

Rewrite the expression using a single radical. x97x65\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}5x6​7x9​​

Write the parametric form of the equation of the line through the points (2,-1,5) and (-3,1,0).

Find the angle between vector u=⟨−2,5⟩ \mathbf{u}=\langle-2,5\rangle u=⟨−2,5⟩ and vector v=⟨−1,3⟩ \mathbf{v}=\langle-1,3\rangle v=⟨−1,3⟩

Solve the equation log (x-6)+log (x-3)=1 . List any extraneous roots and explain.

Jose deposits $200 \$ 200 $200 at the end of each month into an account that pays 5% 5 \% 5% interest compounded monthly. After 7 years of deposits, what is the account balance?

There are 10 balls in a box that are numbered 1 through 10. A ball is selected and replaced, then a second ball is selected. What is the probability that the first ball selected will be a 3 and the second ball selected will not be a 9 ?

Which of the following could represent a complete graph of f(x)=ax+x3f(x)=a x+x^{3}f(x)=ax+x3 where a is a real number?

For the function f(x)=1xf(x)=\frac{1}{x}f(x)=x1​ what is the equation of the tangent line at x=1 ?

Use the discriminant to identify the graph of 2x2+4xy−2y2−3x−y=82 x^{2}+4 x y-2 y^{2}-3 x-y=82x2+4xy−2y2−3x−y=8

Solve the equation graphically. ∣5x−4∣=(x+3)5|5 x-4|=(\sqrt{x+3}) 5∣5x−4∣=(x+3​)5

Martha invests $6,000 at 7.5% for 8 years. If the interest is compounded daily (use 360 days for the year), what will the investment be worth in 8 years?

Find the angle between vector u=⟨5,−2⟩\mathbf{u}=\langle 5,-2\rangleu=⟨5,−2⟩ and vector v=⟨1,−3⟩\mathbf{v}=\langle 1,-3\ranglev=⟨1,−3⟩

Evaluate all six trigonometric functions of the angle θ\thetaθ for the traingle given below. \theta= ---------------- \theta= ---------------- \theta= ---------------- \theta= ---------------- \theta= ---------------- \theta= ----------------

Solve the right triangle △ABC\triangle A B C△ABC for all its unknown parts if β=38∘\beta=38^{\circ}β=38∘ and b= 4.5.

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

For the function $f(x)$ graphed below, which of the following is the $\lim _{x \rightarrow 3} f(x)$ $For the function f(x) graphed below, which of the following is the \lim _{x \rightarrow 3} f(x)$

Find a polynomial of degree 3 with real number coefficients that has $8+2 i \text { and } 5$ as zeros.

Simplify: $(\sec x-\csc x) \sin x \cos x=$

Rewrite the expression using a single radical. $\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}$

Find the angle between vector $\mathbf{u}=\langle-2,5\rangle$ and vector $\mathbf{v}=\langle-1,3\rangle$

Jose deposits $\$ 200$ at the end of each month into an account that pays $5 \%$ interest compounded monthly. After 7 years of deposits, what is the account balance?

Which of the following could represent a complete graph of $f(x)=a x+x^{3}$ where a is a real number?

For the function $f(x)=\frac{1}{x}$ what is the equation of the tangent line at x=1 ?

Use the discriminant to identify the graph of $2 x^{2}+4 x y-2 y^{2}-3 x-y=8$

Solve the equation graphically. $|5 x-4|=(\sqrt{x+3}) 5$

Find the angle between vector $\mathbf{u}=\langle 5,-2\rangle$ and vector $\mathbf{v}=\langle 1,-3\rangle$

Solve the right triangle $\triangle A B C$ for all its unknown parts if $\beta=38^{\circ}$ and b= 4.5. $Solve the right triangle \triangle A B C for all its unknown parts if \beta=38^{\circ} and b= 4.5.$