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\( 21 \div \square=7 \).
(A) 1
(B) 3
(C) 7
(D) 9
Pre Algebra
\begin{tabular}{l} Question \\ A deck of cards contains RED cards numbered \( 1,2,3,4,5 \) and BLUE cards numbered 1,2 . Let \( R \) be the event of drawing a \\ red card, \( B \) the event of drawing a blue card, \( E \) the event of drawing an even numbered card, and \( O \) the event of drawing \\ an odd card. \\ Drawing the Red 1 is one outcome of which of the following events? Select all correct answers. \\ Select all that apply: \\ B AND \( O \) \\ \( \square B \) OR \( E \) \\ \( \square B \) OR \( O \) \\ \( \square O^{\prime} \) \\ \( \square E^{\prime} \) \\ \( \square R \) AND \( E \) \\ \hline\end{tabular}
Probability
La longitud de la curva determinada por la función vectorial
\( \mathbf{r}(t)=\left\langle 10 e^{t} \cos (t), 10 e^{t} \sin (t), 6 e^{t}\right\rangle \operatorname{con} t \in[0,2 \pi] \) es
De ser necesario redondee su respuesta con dos cifras decimales
Calculus
Find the location of the local extrema of the following function.
\( f(x)=3-x^{\frac{2}{9}} \)
Calculus
\begin{tabular}{|l} Determine if the side lengths could form a triangl \\ \hline \( 1.16 \mathrm{~m}, 21 \mathrm{~m}, 39 \mathrm{~m} \) \\ 3\end{tabular}
Geometry
La longitud de la curva \( C \) determinada por \( \mathbf{r}(t)=\left\langle e^{t}, \frac{35}{2} e^{-t}, \sqrt{35} t\right\rangle \)
Para \( t \in[-1,1] \). La longitud de Ces: 43.49
Calculus
A deck of cards contains RED cards numbered \( 1,2,3,4 \) and BLUE cards numbered \( 1,2,3,4,5,6 \). Let \( R \) be the event of
drawing a red card, \( B \) the event of drawing a blue card, \( E \) the event of drawing an even numbered card, and \( O \) the event of
drawing an odd numbered card.
Drawing the Red 3 is an outcome in which of the following events? Select all correct answers.
Select all that apply:
\( \square R \) AND \( O \)
\( \square B \) OR \( E \)
\( \square \cdot R^{\prime} \)
\( \square E^{\prime} \)
\( \square E \) OR \( R \)
Probability
A bank features a savings account that has an annual percentage rate of \( 3.3 \% \) with interest
compounded semi-annually. Riley deposits \( \$ 11,000 \) into the account.
What is the annual percentage yield (APY) for the savings account?
\( A P Y=\square \% \) Round to the nearest hundredth of a percent.
Arithmetic
A bank features a savings account that has an annual percentage rate of \( 3.4 \% \) with interest
compounded annually. Maurice deposits \( \$ 3,000 \) into the account.
How much money will Maurice have in the account in 1 year?
Answer \( =\$ \). Round onswer to the nearest penny.
What is the annual percentage yield (APY for the savings account?
APY \( =\square \% \) Round to the nearest hundredth of a percent.
Arithmetic
Solve the given equation for \( d \)
\( \frac{3}{4}(2 d-3)=3(d+2)-\frac{1}{4} d \)
Algebra
Find the location of the local extrema of the following function.
\( f(x)=3-x^{\frac{2}{9}} \)
Calculus
A bank features a savings account that has an annual percentage rate of \( 4 \% \) with interest
compounded quarterly. Enzo deposits \( \$ 2,000 \) into the account.
How much money will Enzo have in the account in 1 year?
Answer \( =\$ \) Round answer to the nearest penny.
What is the annual percentage yield (APY) for the savings account?
APY \( =\square \) Round to the nearest hundredth of a percent.
Arithmetic
A bank features a savings account that has an annual percentage rate of \( 5.8 \% \) with interest
compounded semiannually. Laila deposits \( \$ 10,000 \) into the account.
How much money will Laila have in the account in 1 year?
Answer = \( \$ \square \)
What is the annual percentage yield (APY) for the savings account?
APY \( =\square \). Round to the nearest hundredth of a percent.
Arithmetic
La longitud de la curva \( C \) determinada por \( \mathbf{r}(t)=\left\langle e^{t}, \frac{35}{2} e^{-t}, \sqrt{35} t\right\rangle \)
Parat \( \in[-1,1] \). La longitud de \( C \) es:
De ser necesario redondee su respuesta con dos cifras decimales
Calculus
La longitud de la curva \( C \) determinada por \( \mathrm{r}(t)=\left\langle e^{t}, \frac{33}{2} e^{-t}, \sqrt{35} t\right) \)
Parat \( \in[-1,1] \). La longitud de Ces:
Deser necesario redondee su respuesta con dos cifras decimales
Calculus
7. Determine cual o cuales es o son paralelos a \( \boldsymbol{w} \)
\[ \boldsymbol{w}=\frac{1}{2} i-\frac{2}{3} j+\frac{3}{4} k \text { : } \]
a. \( 6 i-4 j+9 k \)
b. \( 12 i+9 k \)
c. \( -1 i+\frac{4}{3} j+\frac{3}{2} k \)
d. \( \frac{3}{4} i-j+\frac{9}{8} k \)
Geometry
\( P(x)=x^{3}+6 x^{2}-32 \)
All the real zeros of the given polynomlal are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
Write the polynomial in factored form.
\( P(x)=\square \)
Algebra
Determine the location of each local extremum of the function.
\( f(x)=\frac{4}{3} x^{3}-2 x^{2}-80 x+5 \)
Calculus
6. How much kinetic energy does a 160 gm cricket ball have when it is thrown with velocity of \( 22 \mathrm{n} / \mathrm{sec} \) ?
(a) 176 J
(b) 1.76 J
(c) 3872 J
(d) 38.72 J
7. Which of the following is a wrong example of friction? (a) washing machine pushed along a floor, (b) Sled sliding across snow, (c ) A person sliding down a slide (d) A person lifting a heavy object.
8. The moment of Inertia of a body is \( 100 \mathrm{Kg}-\mathrm{m}^{2} \). If Torque of \( 50 \mathrm{~N}=\mathrm{m} \). is applied on this body, the tangular acceleration produced in the is given by (a) \( 2 \mathrm{rad} / \mathrm{s}^{2} \) (b) \( 1.5 \mathrm{rad} / \mathrm{s}^{2} \) (c) 1 \( \mathrm{rad} / \mathrm{s}^{2} \)
(d) \( 0.5 \mathrm{rad} / \mathrm{s}^{2} \)
9. Find the capillary rise of water in a glass tube is 29.4 cm . When the tube radius is doubled, the capillary rise will be equal to (a) 14.7 cm (b) 29.4 cm . (c) 43.1 (d) 7.35 cm
10 The difference of temperature between two bodies is \( 15^{\circ} \mathrm{C} \). The difference in temperature in Kutvin scale is (a) \( 27^{\circ \prime} \) (b) \( 36^{\circ} \) (c) \( 45^{\circ} \). (d) none of these..
Physics
Sea \( \Gamma \), la curva parametrizada por \( \vec{r}(t)=\langle\cos t, t, \sin t\rangle \). El vector binormal unitario \( \vec{B} \) de \( \Gamma \), enel punto \( \left(0, \frac{\pi}{2}, 1\right) \), es:
Seleccione una:
( a. \( \frac{\sqrt{2}}{2}\langle-1,-1,0\rangle \)
b. \( \frac{\sqrt{2}}{2}\langle 1,-1,1\rangle \)
c. \( \frac{\sqrt{1}}{14}\langle-1,2,-3\rangle \)
od. \( \frac{\sqrt{1}}{3}\langle 1,2,-2\rangle \)
Calculus
A bank features a savings account that has an annual percentage rate of \( 3 \% \) with interest
compounded monthly. Marissa deposits \( \$ 9,000 \) into the account.
How much money will Marissa have in the account in 1 year?
Answer \( =\$ \square \). Round answer to the nearest penny.
What is the annual percentage yield (Apy for the savings account?
APY \( =3.04 \)
Question Help:
Giin Calculator
Arithmetic
Let's find \( \frac{2}{3}+\frac{1}{4} \).
\( \begin{array}{l}\text { First write the addition with a common denominator, } \\ \text { Then add, } \\ \frac{2}{3}+\frac{1}{4}=\frac{\square}{\square}+\frac{\square}{\square}=\frac{\square}{\square}\end{array} \)
Arithmetic
phrase
I. The difference between three times \( x \) and fifteen is greater than or equal to five
2. Five more than sixteen times \( x \) is less than or equal to six
3. Three more than two times \( x \) is less than seven \( \square \)
4. Five less than four times \( x \) is less than or equal to sixteen
5. Six times the sum of \( x \) and twelve is less than fourteen
6. The difference between fifteen and two times \( x \) is greater than five
7. The difference between eleven and four times \( x \) is greater than or equal to three
8. The sum of negative three times \( x \) and five is less than or equal to negative four
9. Fourteen less than five times \( x \) is at most eleven \( \qquad \)
10. Twice the sum of nine and \( x \) is greater than twenty
II. Ten less than three times \( x \) is greater than eleven
12. Thirteen plus five times \( x \) is no more than
thirty
13. Thirteen more than three times \( x \) is no more than the opposite of eleven
14. Half of the sum of \( x \) and six is no less than twenty
15. The difference between negative five times \( x \) and eight is greater than twelve.
Solve only your inequalities! Look for your answer at the bottom.
\[
\begin{array}{ll}
N \quad 2 x+3 \leq 7 & E \\
C & 14-5 x \leq 11 \\
\text { C } 15-2 x>5 & \text { R } \\
F(9+x)>20 \\
E \quad 1 / 2 x+6 x \leq 30 & \text { D }
\end{array} 6(x+12)<141
\]
\[
\text { L } 5 x-14 \leq 11 \quad H \quad-3 x-5<-4
\]
\[
\text { U } 3 x-15 \geq 5 \quad \text { A } 1 / 2(x+6) \geq 20
\]
\[
E \quad 6(x-12)>14 \backslash \text { H } \quad 11-4 x \geq 3
\]
\[
3 x-10>11 \quad 0 \quad-5 x-8>12
\]
\[
\vee 16 x+5<6 \quad \& \quad 3 x+13 \leq-11
\]
\[
\text { Y } 4 x-5 \geq 16 \quad \text { \& } 16 x+5 \leq 6
\]
Algebra
Find the quotient and remainder using synthetic division.
\[ \frac{3 x^{4}+8 x^{3}+5 x^{2}+x+1}{x+\frac{2}{3}} \]
quotient
remainder
Algebra
Determine the location of each local extremum of the function.
\( f(x)=x^{3}+3 x^{2}-9 x+1 \)
Calculus
A bank features a savings account that has an annual percentage rate of \( 3 \% \) with interest
compounded monthly. Marissa deposits \( \$ 9,000 \) into the account.
How much money will Marissa have in the account in 1 year?
Answer \( =\$ \square \) Round answer to the nearest penny.
What is the annual percentage yield (APY) for the savings account?
APY \( =\square \% \) Round to the nearest hundredth of a percent.
Question Help: Message instructor
Qilculator
Economics
Use the remainder theorem to find the remainder when \( f(x) \) is divided by \( x+2 \). Then use the factor theorem to determine whether \( x+2 \) is a factor of \( f(x) \).
\( f(x)=2 x^{6}-8 x^{4}+x^{3}-9 \)
The remainder is
Algebra
\( ( x - y ) d x + ( x + y ) d y = 0 \)
Calculus
\( 2^{\text {ND }} \) ASSIGNMENI
Subject: Applied Physics-1 ( 2024-2025), Semester I
NAME :
REGISTRATION NUMBER :
BRANCH :
Choose correct answer (put \( \checkmark \) ) of the following questions. ( \( 1 \times 10 \) )
1 A copper rod of length 1 m and cross-sectional area \( 0.005 \mathrm{~m}^{\mathbf{2}} \) has its ends maintained at \( 100^{\circ} \mathrm{C} \) and \( 0^{\circ} \mathrm{C} \). If the thermal conductivity of copper is \( \mathbf{4 0 0} \mathrm{W} / \mathrm{m} \cdot \mathrm{K} \). The rate of heat transfer is (a) 200 Watt (b) 1470 watt (c) 1050 Watt (d) 1260 Watt .
Physics
\( \left\{\begin{array}{l}\text { (1) Hâlan lá ecuacion de la recta que pasa par } \\ \text { a) drumto } A(3,-2) \text { y es prrancicular. } \\ \text { la ructa } y=-\frac{1}{5} x+2 \text { Grahicar. }\end{array}\right. \)
Geometry
Find the quotient and remainder using synthetic division.
\[ \frac{x^{3}-4 x^{2}+8 x-8}{x-2} \]
quotient
remainder
Algebra
A deck of cards contains RED cards numbered \( 1,2,3 \) and BLUE cards numbered \( 1,2,3,4,5,6 \). Let \( R \) be the event of
drawing a red card, \( B \) the event of drawing a blue card, \( E \) the event of drawing an even numbered card, and \( O \) the event of
drawing an odd card.
Drawing the Blue 4 is an example of which of the following events? Select all correct answers.
Select all that apply:
\( \square R \) OR \( O \)
\( \square B \) AND \( O \)
\( \square R \) OR \( E \)
\( \square R^{\prime} \)
\( \square E^{\prime} \)
Probability
8. Test Practice Which expression will have the same sum as \( \frac{3}{8}+\frac{1}{4} \) ?
\( \begin{array}{ll}\text { (A) } \frac{3}{8}+\frac{1}{8} & \text { (C) } \frac{3}{4}+\frac{1}{4} \\ \text { (B) }\left(\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\right)+\frac{1}{4} & \text { (a) }\left(\frac{1}{8}+\frac{1}{8}\right)+\frac{1}{8}\end{array} \)
Arithmetic
Determine the location of each local extremum of the function.
\( f(x)=x^{3}+3 x^{2}-9 x+1 \)
Calculus
Solve the equation using the zero-product property
\[ (x-7)(5 x+9)=0 \]
Algebra
Find a polynomial of the specified degree that has the given zeros.
Degree \( 3 ; \) zeros \( -2,2,4 \)
\( P(x)=\square \)
Algebra
NAME
FEGITRATION NUMBER
terfall.
BRAVCH
Choose correct answer (put / ) of the following questions. ( \( 1 \times 10 \) )
| A copper rod of lingeh I m and crosu-sectional area \( 0.005 \mathrm{~m}^{2} \) has its ends maintained at \( 190^{\circ} \mathrm{C} \) and \( 0^{\circ} \mathrm{C} \) If the thermal conductonाy of copper is \( 400 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K} \). The rate of heat tramier is (a) 200 Wath (b) 1470 wall (c) 1050 W att (d) 1260 War
2. A stecl wirc of tength 3 m and crons-sectaunal arca \( 2 \times 10^{*} \mathrm{~m}^{2} \) as atretehed by 1.5 mm under a force of 200 N . The Young's modulus of the material. (a) 200 GPa (b) 100 GPa (c) 300 GPa (d) 150 GPa
3 A cricket ball of mans 0.5 hy is moving with a wolocity of \( 10 \mathrm{~m} / \mathrm{s} \) After being hit by a bat. it moves in the opponice dirction with a velocity of -15 m . The change in mernentum is equal ts (a) (b) \( -125 \mathrm{~kg} m / \mathrm{s} \) (c) \( 12.5 \mathrm{~kg} \mathrm{~m} / \mathrm{s} \) (d) \( 625 \mathrm{~kg} \mathrm{~m} / \mathrm{s} \)
4 The value of \( \frac{6}{c t} \) for air is (d) 14, (b) 1.33 , (c) 1 , (d) 0.8 .
Physics
ómo crees que se calculó el perímetro del círculo?
Geometry
\( 187 \int e^{x} \sin x d x \) T \( A T E \)
\[
\begin{array}{ll}
u=\sin x & d u=e^{x} d x \\
d u=\cos x d x & u=e^{x}
\end{array}
\]
\[
\int u d u=u-\int u d u
\]
\[
\begin{aligned}
=\int e^{x} \sin x d x & =\sin \cos \left(e^{x}\right)-\int e^{x}(\cos x) d x \\
& =e^{x} \sin (x)-\int e^{x} \cos x d x \\
& =\int e^{x} \cos x d x
\end{aligned}
\]
\[
\begin{array}{ll}
u=\cos x & d u=e^{x} \\
d u=-\operatorname{sen} x & v=e^{x}
\end{array}
\]
\[
\begin{aligned}
\int e^{x} \sin x d x & =e^{x} \sin x-\left[\cos x\left(e^{x}\right)-\int e^{x}(-\operatorname{sen} x) d x\right] \\
& =e^{x} \sin x-\left[e^{x} \cos x-\int-e^{x} \operatorname{sen} x d x\right] \\
& =e^{x} \sin x-e^{x} \cos x+\left[\int-e^{x} \operatorname{sen} x d x\right] \\
-2 \int e^{x} \sin x d x & =e^{x} \sin x-e^{x} \cos x+c \\
& =-\frac{1}{2} e^{x}[\sin x-\cos x]+c
\end{aligned}
\]
Calculus
Dit word gegee dat: \( m=x(x-y)^{2} \)
Bereken die waarde van \( m \) indien \( x y^{2}=4 \) en \( x^{3}-2 x^{2} y=3 \)
Algebra
7. En semana santa se va a instalar la feria, para instalar un juego en una
feria Juan puso \( \$ 4000 \) y Pedro \( \$ 6000 \). Las gananclas que se obtengan las
repartirán de acuerdo con lo que cada uno aportó.
a) Si en un día de feria ganaron \( \$ 1600 \), ¿Cuál es el reparto proporcional
de Juan y Pedro?
b) Considera que la ganancia por dia es la misma y calcula cuanto
ganara Juan en la estancia de la feria.
8. Gabriel, Raúl y Alberto son hermanos y sus familias tienen 4 , 7 y 3
integrantes, respectivamente. Harán una fiesta de fin de año y pagar:
los gastos según el número de integrantes de cada familia.
a) ¿Cuánto debe pagar cada hermano? Si el total de los gastos fue
\( \$ 3,646 \).
Arithmetic
\[
P(x)=x^{3}+2 x^{2}-6 x-4, \quad c=2
\]
Evaluate \( D(x) \) for the given value of c, (Simplify your answers completely,)
\[
\begin{aligned}
P(2) & =(2)^{3}+2(\square)-6(2)-4 \\
& =8+2(\square)-6(2)-4 \\
& =8+(\square)=12-4 \\
& =\square \square \square)
\end{aligned}
\]
Since? \( \square \) is 3 zero of \( P(x), x=2 \) \( \square \) is a factor of \( P(x) \),
Algebra
3. Basir took a science test on Friday. One-eighth of the questions were multiple choice,
and \( \frac{3}{4} \) of the questions were true-false questions. What part of the total number of
questions were either multiple choice or true-false questions?
Arithmetic
Question 2 of 14 (1 polity 1 Question Athenpt 1 of 1
Time Remainty ze29
MeriaKindal
1
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3
4
5
6
7
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Esato
13
Amy received a \( \$ 1300 \) bonus. She decided to invest it in a 2 -year certificate of deposit (CD) with an annual interest rate of \( 1.23 \% \) compounded quarterly.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If nececcary refer to the list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Amy's account after 2 years?
\( \square \)
\( \square \)
(b) How much interest is earned on Amy's investment after 2 years?
©?
\( \square \)
Calculator
Economics
For the following function, find the intervals on which the function is increasing or decreasing.
\( f(x)=\sqrt{x^{2}+7} \)
Calculus
6 The magnitude of \( \overrightarrow{\mathrm{PQ}} \) is 20 units. Given that \( \overrightarrow{\mathrm{OP}}=\binom{5}{0} \) and \( \overrightarrow{\mathrm{OQ}}=\binom{17}{y} \), find the positive
value of \( y \).
Geometry
\[ \begin{array}{l}x=5 \\ 25+5\end{array} \begin{array}{l}25+5=4^{2}+5\end{array} \]
22) Andullah claims that as \( n \) approaches infinity, the expressions \( \frac{1}{n+5} \) and \( \frac{1}{n}+5 \) approach
same value. Is Abdullah's claim correct? Explain.
Calculus
If \( \$ 26,000 \) is invested in an account for 20 years. Calculate the total interest earned at the end
of 20 years if the interest is:
(a) \( 8 \% \) simple interest: \( \$ 41,600 \)
(b) \( 8 \% \) compounded annually: \( \$ \)
(c) \( 8 \% \) compounded quarterly: \( \$ \)
(d) \( 8 \% \) compounded monthly: \( \$ \)
Round your answers to the nearest cent.
Arithmetic
Add the fifths, then the sevenths.
\[ \begin{aligned} & \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\ = & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\ = & \square+\square\end{aligned} \]
Arithmetic
Solve the polynomial equation
\[ 4 x^{3}+x^{2}-36 x-9=0 \]
Algebra
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Add the fifths, then the sevenths.
\[
\begin{aligned}
& \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\
= & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\
= & \square+\square
\end{aligned}
\]
(1) 2
3
4
5
6
7
8
9
0
Enter
Arithmetic
2. Simplify the expression shown below:
\( 6 \sqrt{10} \cdot \sqrt{2} \)
Pre Algebra
a) \( 10^{9} \cdot 10^{(-4)}= \)
b) \( \left(-8^{5}\right) \cdot(-8) \cdot\left(-8^{(-4)}=\right. \)
c) \( \frac{13}{13^{17}}= \)
Algebra
Work each problem according to the instructions given.
a. Evaluate when \( x=0:-2 x-7 \)
b. Solve: \( -2 x-7=5 \)
\( x=\square \)
c. Is 0 a solution to \( -2 x-7 \geq 5 \) ?
? \( v \)
d. Solve: \( -2 x-7 \geq 5 \)
Algebra
3. \( V_{1}^{2} x^{2}+V_{2} x^{2}=d^{2} \)
4. \( 5^{2}=x^{2}+4^{2} \)
5. \( \frac{30}{21}=2 x+ \)
Algebra
The life (in months) of a certain computer component has a CDF given by
\( P(x)=\left\{\begin{array}{ll}1-e^{-z / 4} & \text { if } x>0 \\ 0 & \text { if otherwise }\end{array}\right. \)
Let the random variable \( X \) represent the time (in months) that a randomly selected component lasts.
a) Find \( P(X \leq 11) \).
b) Find \( P(X>16) \). 0.0183
Round your answers to 4 decimals.
Probability
For the following function, find the intervals on which the function is increasing or decreasing.
\( f(x)=\sqrt{x^{2}+4} \)
Calculus
Unit 9: Linear, Quadratic, \& Exp. Functions
Homework 1: Identifying Functions
Algebra
Factorizar agrupando (también llamado el método ac).
\[ 10 x^{2}-x-2 \]
Primero, seleccionar una forma con los signos apropiados.
Luego, llenar los blancos con los números que va a utilizar para agrupar.
Finalmente, mostrar la factorización.
Algebra
Solve the following inequality for \( y \).
\[ 4 x-2 y \leq 8 \]
Algebra
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