Browse Math problems Studdy Solved!

Problem 51501

12. $\begin{array}{l} 18 x+12 y=24 \\ 3 x+2 y=6 \end{array}$

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Problem 51502

10. Find the quotient of the expression $(-864.3) \div(-3)$
Type a response Show Your Work

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Problem 51503

8 Prove that $\frac{1+\cos \theta}{1-\cos \theta} \equiv(\operatorname{cosec} \theta+\cot \theta)^{2}$

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Problem 51504

Evaluate the integral. $\int_{-7}^{7} e d x$

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Problem 51505

Convert the following equation to polar coordinates. $y=4 x^{2}$
The polar form of $y=4 x^{2}$ is $\square$ (Type an exact answer.)

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Problem 51506

Suppose that a simple random sample of size $n=315$ selected from a population has $x=185$ successes. Calculate the margin of error for a $95 \%$ confidence interval for the proportion of successes for the population, $p$ . Compute the sample proportion, $\hat{p}$ , standard error estimate, SE, critical value, $z$ , and the margin of error, $m$ . Use a $z$ -distribution table to determine the critical value. Give all of your answers to three decimal places except give the critical value, $z$ , to two decimal places. $\hat{p}=$ $\square$ $\mathrm{SE}=$ $\square$ $z=$ $\square$ $m=$ $\square$

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Problem 51507

Solve the inequality: $-2(x+2)<14$ $x<-5$ $x<-9$ $x>-5$ $x>-9$

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Problem 51508

Is there a mistake on the equation solved? If so where was the mistake made? $\begin{array}{c} 3(2 x-5)=4-6 x \\ 6 x-15=4-6 x \\ -15=4 \end{array}$ no solution The mistake was made on the second step of moving the variable The mistake was made on the first step of doing the distributive property $-15=4$ should not be interpreted as "no solution" This equation is solved correctly

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Problem 51509

3. Construct Arguments Gene stated that finding $25 \%$ of a number is the same as dividing the number by $\frac{1}{4}$ . Is Gene correct? Explain.

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Problem 51510

For a given geometric sequence, the $10^{\text {th }}$ term, $a_{10}$ , is equal to $\frac{19}{16}$ , and the $13^{\text {th }}$ term, $a_{13}$ , is equal to -76 . Find the value of the $17^{\text {th }}$ term, $a_{17} \cdot 1 f$ applicable, write your answer as a fraction. $a_{17}=$ $\square$

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Problem 51511

Use the Venn diagram and find $B^{\prime}$ . $B^{\prime}=\{\mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{x}, \mathrm{y}\}$ $B^{\prime}=\{\mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}\}$ $B^{\prime}=\{\mathrm{q}, \mathrm{r}, \mathrm{s}\}$ $B^{\prime}=\{\mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{x}, \mathrm{y}\}$

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Problem 51512

9. $\frac{p}{p-2}+2=\frac{8}{p^{2}-4}$
10. $\frac{13}{3 w-3}-\frac{1}{w-1}=\frac{w}{9}$
11. $\frac{x+6}{x+3}=2-\frac{5 x+12}{x+3}$
12. $\frac{3 c-2}{c^{2}-4 c}=\frac{c}{c-4}-1$

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Problem 51513

1. Let $F(x)=\int_{-1}^{x} f(t) d t,-1 \leq x \leq 4$ , where $f$ is the function graphed in the figure. a) Complete the following table of values for $F$ . \begin{tabular}{|c|c|c|c|c|c|c|} \hline $x$ & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline $F(x)$ & & & & & & \\ \hline \end{tabular}

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Problem 51514

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ , where $h \neq 0$ , for the function below. $f(x)=\frac{x}{x+1}$
Simplify your answer as much as possible. $\frac{f(x+h)-f(x)}{h}=$ $\square$

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Problem 51515

The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the $\begin{array}{l} (8,15) \\ \sin \theta=\square \\ \cos \theta=\square \\ \tan \theta=\square \\ \csc \theta=\square \\ \sec \theta=\square \\ \cot \theta=\square \end{array}$

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Problem 51516

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) $\sec \left(\arcsin \left(\frac{3}{5}\right)\right)$

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Problem 51517

Find the value of the constant $\boldsymbol{k}$ such that integral has the prescribec value: $\int_{1}^{4} \frac{3 x+k}{\sqrt{x}} d x=8$

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Problem 51518

System A Line 1: $y=-\frac{1}{2} x-\frac{5}{2}$
Line 2: $y=x-1$
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: $\square$ $\square$ no solution infinitely many solutions
System B Line 1: $y=\frac{1}{2} x+3$ Line 2: $y=\frac{1}{2} x-1$
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: $\square$ $\square$ no solution infinitely many solutions
System C Line 1: $y=-\frac{5}{2} x+3$
Line 2: $5 x+2 y=6$
This system of equations is: inconsistent consistent independent consistent dependent This means the system has: a unique solution Solution: $\square$ D no solution infinitely many solutions Explanation Check

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Problem 51519

24. 求微分方程 $y^{\prime \prime}+4 y^{\prime}-12 y=0$ 的通解.
25. 计算不定积分 $\int x \arctan x \mathrm{~d} x$ 。

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Problem 51520

Consider the following integral. $\int t^{6} e^{-t^{7}} d t$
Find a substitution to rewrite the integrand as $-\frac{1}{7} e^{u} d u$ . $\begin{aligned} u & =\boxed{-t^{7}} \\ d u & =(\square) d t \end{aligned}$
Evaluate the given integral. (Use $C$ for the constant of integration.) $\square$ Remember to use capital C.

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Problem 51521

Consider the following integral. $\int \cos (4 x) d x$
Given the substitution $u=4 x$ , find $d u$ . $d u=$ $\square$ $\int d x$
Rewrite the given integral in terms of $u$ . $\square$ $\int(\square) d u$
Evaluate the integral by making the given substitution. (Use C for the constant of integration.) $\square$ Need Help? Roadin Submit Answer

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Problem 51522

Solve this system of equations by using graphing. $\left\{\begin{array}{l} y=\frac{1}{2} x+1 \\ y=-x-2 \end{array}\right.$ ([?], $\square$ Enter

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Problem 51523

How many real zeros does the following quadratic function have? $y=5 x^{2}+2 x+4$
Use the Discriminant: b² - 4ac no real zeros two real zeros one real zero

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Problem 51524

IdyBuddy NEW Help Center Search
Find the intervals on which the function is concave up or down, the points of inflection, and the critical points, and determine whether each critical point corresponds to a local minimum or maximum (or neither). Let $f(x)=5 x+5 \sin (x), 0 \leq x \leq 2 \pi$
What are the critical point(s)= $\square$ What does the Second Derivative Test tell about the first critical point: $\square$ ? What does the Second Derivative Test tell about the second critical point: $\square$ ?
What are the inflection Point $(\mathrm{s})=$ $\square$ On the interval $\square$ to the left of the critical point, $f$ is $\square$ and $f^{\prime}$ is $\square$ (Include all points where $f^{\prime}$ has this sign in the interval.) On the interval $\square$ to the right of the critical point, $f$ is $\square$ and $f^{\prime}$ is $\square$ - (Include all points where $f^{\prime}$ has this sign in the interval.)
On the interval $\square$ to the left of the inflection point $f$ is $\square$ ? . (Include only points where $f$ has this concavity in the interval.) On the interval $\square$ to the right of the inflection point $f$ is $\square$ . (Include only points where $f$ has this concavity in the interval.)

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Problem 51525

Solve the equation. $\frac{3}{w^{2}+2 w-8}+\frac{3}{w^{2}+w-6}=\frac{5}{w^{2}+7 w+12}$

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Problem 51526

What is the present value of $\$ 3780$ due in nine months if simple interest rate is $5 \%$ ?
The present value is $\$$ $\square$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

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Problem 51527

Evaluate the expression for the given value of the variable. $\sqrt{x-4}+3 \text { for } x=68$

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Problem 51528

Graph the inequality $4 x-5 y>20$ .

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Problem 51529

Find the sales tax. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Sales Tax } \\ \hline Selling Price & Rate of Sales Tax & Sales Tax \\ \hline $\$ 90.00$ & $5 \%$ & $?$ \\ \hline \end{tabular}
The sales tax is $\$$ $\square$

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Problem 51530

2. ${ }^{2}$ Evaluate the following integrals. (a) $\int \frac{2}{(x-4)\left(x^{2}+2 x+6\right)} d x$ , (b) $\int \frac{x^{2}}{x^{3}-x^{2}+4 x-4} d x$ , (c) $\int \frac{x^{3}+6 x^{2}+3 x+6}{x^{3}+2 x^{2}} d x$ , (d) $\int \frac{x}{(x-1)\left(x^{2}+2 x+2\right)} d x$ ,

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Problem 51531

The expression $\log \left(\frac{x^{10} y^{7}}{z^{10}}\right)$ can be written in the form $A \log (x)+B \log (y)+C \log (z)$ where $A=$ $\square$ $B=$ $\square$ $\sigma^{\infty}$ , and $C=$ $\square$ Question Help: Video Read
Message instructor Submit Question

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Problem 51532

Find the commission. \begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{ Earning Commission } \\ \hline Sales & Commision Rate & Commission \\ \hline $\$ 540$ & $7 \%$ & $?$ \\ \hline \end{tabular}
The commission is $\$ \square$ .

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Problem 51533

Simplify. Enter the result as a single logarithm with a coefficient of 1. $\log _{7}\left(6 x^{6}\right)-\log _{7}\left(7 x^{7}\right)$ $\square$ Question Help: Video Message instructor Submit Question

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Problem 51534

Given $M$ , find $\mathrm{M}^{-1}$ and show that $\mathrm{M}^{-1} \mathrm{M}=\mathrm{I}$ . $M=\left[\begin{array}{rrr} 1 & 2 & 0 \\ 0 & 1 & 3 \\ -1 & -1 & 4 \end{array}\right]$
Find the value in the first row and first column of the product $M^{-1} M$ using matrix multiplication. Select the correct expression below and fill in the answer box to complete your selection. A. $(-3 \cdot 1)+(4 \cdot 0)+(-3 \cdot-1)=$ $\square$ (Simplify your answer.) B. $(7 \cdot 1)+(-8 \cdot 0)+(6 \cdot-1)=$ $\square$ (Simplify your answer.) C. $(7 \cdot 0)+(-8 \cdot 3)+(6 \cdot 4)=$ $\square$ (Simplify your answer.) D. $(7 \cdot 2)+(-8 \cdot 1)+(6 \cdot-1)=$ $\square$ (Simplify your answer.)

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Problem 51535

Mental Math A typical tip in a restaurant is $15 \%$ of the total bill. If the bill is $\$ 140$ , what would the typical tip be?
The typical tip would be \\square$

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Problem 51536

Section 4.4 Score: 9.5/12 Answered: 10/12
Question 3
Simplify. Enter the result as a sing Next $\begin{array}{l} \log _{8}\left(4 x^{7}\right)-\log _{8}\left(5 x^{4}\right) \\ = \end{array}$ Question Help: Video Message instructor

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Problem 51537

Question 3
Find the domain of $y=\log (3+3 x)$ . The domain is: $\square$ Question Help: Video Message instructor Submit Question

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Problem 51538

Question 4
Write an equation for the transformed logarithm shown below, that passes through $(2,0)$ and $(1$ , $f(x)=$ $\square$ Question Help: Video 1 Video 2 Video 3 Message instructor Submit Question

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Problem 51539

Solve this system of equations by using elimination. $\begin{array}{c} \left\{\begin{array}{l} 3 x+5 y=-2 \\ -x+2 y=8 \end{array}\right. \\ ([?] \end{array}$ Enter

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Problem 51540

Listen
Brody loves to read, and he counts the number of books he reads each year. This year, he used a graph to keep track of the books he read. By his birthday, he read 15 books. The following graph shows how many books he read for the months following his birthday.
C 2017 StrongMind. Created using GeoGebra.
How many books does Brody read each month? Enter your answer as a number, like this: 42 $\square$ ch/assessment/e03deb2f-ad09-427d-a4b2-42e737f1864c?revisionid=70061\&smcatalogid=1826\&label=376d7f54-922c-40f2-haco

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Problem 51541

$\sqrt{x-111}=-21$

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Problem 51542

3. $f(x)=x^{4}-4 x^{2}$

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Problem 51543

A relation in $x$ and $y$ is given. Determine if the relation defines $y$ as a one-to-one function of $x$ . $\{(13,5),(-7,3),(-1,-1),(-8,4)\}$ The relation defines $y$ as a one-to-one function of $x$ . The relation does not define $y$ as a one-to-one function of $x$ .

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Problem 51544

2 Rajah 2 menunjukkan graf jarak-masa bagi pergerakan dua buah objek dalam tempoh 80 minit.
Diagram 2 shows the distance-time graph of the motion of two objects for a period of 80 minutes.
Graf $E F G H$ mewakili pergerakan objek $A$ dari titik $Y$ ke titik $Z$ . Graf $L H$ mewakili pergerakan objek $B$ dari titik $X$ ke titik $\dot{Z}$ . Graph EFGH represents the motion of object A from point $Y$ to point $Z$ . Graph LH represents the motion of object B from point X to point Z. (a) Nyatakan jarak, dalam km, dari titik $X$ ke titik $Y$ .
State the distance, in km, from point $X$ to point $Y$ . [2 markah/marks] (b) Hitung masa $t$ , dalam minit, apabila dua objek itu bertemu.
Calculate the time $t$ , in minutes, when the two objects meet. [3 markah/marks]

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Problem 51545

A relation in $x$ and $y$ is given. Determine if the relation defines $y$ as a one-to-one function of $x$ . \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 5.5 & -1.5 \\ \hline 2.15 & 2.5 \\ \hline-1.02 & 1.5 \\ \hline 11.43 & -0.5 \\ \hline \end{tabular} The relation defines $y$ as a one-to-one function of $x$ . The relation does not define $y$ as a one-to-one function of $x$ .

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Problem 51546

2 Rajah 2 menunjukkan graf jarak-masa bagi pergerakan dua buah objek dalam tempoh 80 minit.
Diagram 2 shows the distance-time graph of the motion of two objects for a period of 80 minutes.
Graf $E F G H$ mewakili pergerakan objek $A$ dari titik $Y$ ke titik $Z$ . Graf $L H$ mewakili pergerakan objek $B$ dari titik $X$ ke titik $\dot{Z}$ . Graph EFGH represents the motion of object A from point $Y$ to point $Z$ . Graph LH represents the motion of object B from point X to point Z. (a) Nyatakan jarak, dalam km, dari titik $X$ ke titik $Y$ .
State the distance, in km, from point $X$ to point $Y$ . [2 markah/marks] (b) Hitung masa $t$ , dalam minit, apabila dua objek itu bertemu.
Calculate the time $t$ , in minutes, when the two objects meet. [3 markah/marks]

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Problem 51547

Wodurch ist eine Ebene festgelegt? - Auftrag 3 Eine Ebene kann nicht nur durch drei geeignete Punkte festgelegt werden, sondern auch durch zwei Geraden. a). Begründe: Zwei verschiedene, zueinander parallele Geraden legen eine Ebene fest.
Im Folgenden sind zwei Geraden gegeben: $g: \vec{x}=\left(\begin{array}{l} 3 \\ 2 \\ 1 \end{array}\right)+t \cdot\left(\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right) \quad h: \vec{x}=\left(\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right)+s \cdot\left(\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right)$ b) Diese zwei verschiedenen, parallelen Geraden legen eine Ebene fest. Bestimmen eine Parametergleichung der Ebene.

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Problem 51548

Use the definition of a one-to-one function to determine if the function is one-to-one. $f(x)=x^{2}-1$
Part 1 of 5
To show a function $f$ is a one-to-one function using the definition, it must be shown that if $f(a)=f(b)$ , then $a=b$ .
Part: $1 / 5$
Part 2 of 5
For the given function $f(x)=x^{2}-1$ , we begin by assuming that (Choose one) $\nabla$ .

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Problem 51549

$\frac{\tan 45^{\circ}+\tan 300^{\circ}}{1-\tan 45^{\circ} \tan 300^{\circ}}$

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Problem 51550

Describe and correct the error in solving the equation. $\begin{aligned} x^{2} & +10 x+74=0 \\ x & =\frac{-10 \pm \sqrt{10^{2}-4(1)(74)}}{2(1)} \\ & =\frac{-10 \pm \sqrt{-196}}{2} \\ & =\frac{-10 \pm 14}{2} \end{aligned}$

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Problem 51551

This is similar to Section 4.5 Problem 6:
Determine the indefinite integral $\int \frac{-4+8 x^{3}}{x} d x$ by algebraic manipulation. Assume $x>0$ when $\ln (x)$ appears. Use capital C for the free constant.
Answer: $\square$

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Problem 51552

Find the zeros of $m(x)=-5 x^{2}+50 x-135$

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Problem 51553

Wachstumsgeschwindigkeit und Wendepunkt beim logistischen Wachstum
7. Rechts sehen Sie den Graphen einer Funktion w, die näherungsweise den jährlichen Höhenzuwachs einer Fichte beschreibt. Die Fichte war zu Beobachtungsbeginn 1 m hoch, ihre maximale Höhe beträgt 50 m . a) Skizzieren Sie den Graphen der Funktion h, welche die Höhe $h(t)$ der Fichte zum Zeitpunkt t (in Jahren ab dem Beobachtungsbeginn) angibt. b) Welches Wachstumsmodell wird zugrunde gelegt? c) Nach 10 Jahren hat die Fichte eine Höhe von $4,20 \mathrm{~m}$ . Bestimmen Sie jeweils einen Funktionsterm für die Funktion h und die Funktion w.
8. Das Wachsen einer Fichte kann mit dem Modell logistischen Wachstums beschrieben werden. Für die Höhe h (t) (in Meter) in Abhängigkeit von der Zeit t (in Jahren) gilt: $h(t)=\frac{80}{1+39 e^{-0,1 t}}$ a) Ermitteln Sie ohne Verwendung eines CAS einen Term für die Wachstumsgeschwindigkeit. Stellen Sie diese auch grafisch dar. b) Bestimmen Sie, wann die Wachstumsgeschwindigkeit maximal ist. Dokumentieren Sie Ihren Lösungsweg. c) Interpretieren Sie das Ergebnis von Teilaufgabe b) am Graphen von h.

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Problem 51554

A TYT/Temel Matematik
13. Bir babanın yaşı, oğlunun yaşının 3 katıdır. Oğul, babasının bugünkü yaşına geldiğinde yaşlarının toplamı 72 olacaktır. Buna göre baba bugün kaç yaşındadır? A) 20 B) 25 C) 27 D) 35 E) 40

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Problem 51555

5. A number of classicists were asked to identify their favorite epic poets. The results are summarized below. 62 appreciate Homer 40 appreciate Virgil 2 appreciate Homer and Virgil and Gomer 5 appreciate Gomer 3 appreciate Virgil and Gomer 20 appreciate Homer and Virgil AZ appreciate Homer and neither of the other two terappreciate none of these three edic poets A. How many were surveyed? B. How many don't appreciate Gomer? C. How many appreciate Homer or Gomer? D. How many appreciate exactly one of the three epic poets?

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Problem 51556

1) $m$ and $n$ are integers and $\sqrt{m n}=10$ . Which of the (a) 25 (b) 52 following cannot be a value of $m+n$ ? (c) 101 (d) 50 2) The number of factors of a number $N=2^{3} \times 3^{2} \times 5^{3}$ is (a) 18 (b) 45 (c) 48 (d) 9

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Problem 51557

Let $f$ be a function. Below is the graph of its derivative, $f^{\prime}(x)$ . Find the critical points of $f(x)$ and label them as a local maximum, minimum, or neither. Separate multiple values with commas, if necessary. Enter DNE if no such value exist.
Graph of the Derivative, $\mathrm{f}^{\prime}(\mathrm{x})$ (You can click on a graph to enlarge it.) Local maxima: $x=$ $\square$ Local minima: $x=$ $\square$ Critical points that are neither: $x=$ $\square$

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Problem 51558

12. If the graph of $f(x)$ has a horizontal asymptote at $y=1$ and a vertical asymptote at $\boldsymbol{x}=-\mathbf{2}$ , then the horizontal \& vertical asymptotes of $g(x)=\boldsymbol{f}(\boldsymbol{x}-1)+5$ are A. $y=-2, x=1$ B. $y=-1, x=-2$ C. $y=5, x=-3$ D. $y=6, x=-1$

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Problem 51559

Let $f$ be a function. Below is the graph of its second derivative, $f^{\prime \prime}(x)$ . On what intervals is the original function $f(x)$ concave down? If necessary, enter multiple intervals using a union symbol using the math palette or by typing $U$ . Enter DNE if no such interval exist. (You can click on a graph to enlarge it.) Concave down: $\square$

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Problem 51560

2. Which one of these functions might have the given graph? A. $f(x)=-x(x-1)(x-2)$ B. $f(x)=x(x-1)(x-2)$ C. $f(x)=x^{2}(x-1)(x-2)$ D. $f(x)=-x^{2}(x-1)(x-2)$

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Problem 51561

10) Factors of $x^{4}+5 x^{2}+9$ are: (a) $\left(x^{2}+2 x+3\right)\left(x^{2}+3 x+3\right)$ (b) $\left(x^{2}-x+3\right)\left(x^{2}-x-3\right)$ (c) $\left(x^{2}-x-3\right)\left(x^{2}+x+3\right)$ (d) $\left(x^{2}-x+3\right)\left(x^{2}+x+3\right)$

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Problem 51562

$\frac{1}{4}=\frac{3}{\square}=\frac{\square}{20}$

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Problem 51563

Add or subtract. $\begin{array}{l} 7 \sqrt{50}-5 \sqrt{12}-4 \sqrt{18} \\ 7 \sqrt{50}-5 \sqrt{12}-4 \sqrt{18}= \end{array}$ $\square$ (Type an exact answer, using radicals as needed. Simplify your answer. Do not factor.)

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Problem 51564

Add or subtract. Assume that all variables represent positive real numbers. $\begin{array}{l} \sqrt[3]{189 x y^{3}}+3 \sqrt[3]{7 x y^{3}}+y \sqrt[3]{448 x} \\ \sqrt[3]{189 x y^{3}}+3 \sqrt[3]{7 x y^{3}}+y^{3} \sqrt{448 x}= \end{array}$ $\square$ (Type an exact answer, using radicals as needed. Simplify your answer.)

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Problem 51565

Part II: Solve the following problems ( 60 points) Problem 1. (20 points)
The Revenue Department of the Tax Administration employs certified public accountants (CPAs) to audit corporate tax returns and bookkeepers to audit individual tax returns. The CPA is paid $\$ 36,200$ per year, while the bookkeeper is paid $\$ 28,000$ per year. Based on the current staffing, a study shows that that MP of a CPA to audit corporate returns is $\$ 58,000$ of additional tax revenue per year. In contrast, the MP of a bookkeeper is $\$ 38,000$ of additional tax revenue per year. (A) If the Department's objective is to minimize the costs of tax collection, is the present mix of CPAs and bookleepers optimal (i.e. is the mix of them the cost-minimizing combination)? Explain your answer!

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Problem 51566

Add and subtract. Assume that all variables represent positive real numbers. $\begin{array}{l} -2 \sqrt[4]{x^{11}}+6 \sqrt[4]{16 x^{11}}-4 x^{2} \sqrt[4]{x^{3}} \\ -2 \sqrt[4]{x^{11}}+6 \sqrt[4]{16 x^{11}}-4 x^{2} \sqrt[4]{x^{3}}= \end{array}$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

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Problem 51567

Trigo problem
Rad mode Mode table write the function Start : according to the problem End: accorang to the proviem Step: $\frac{\text { period }}{4}=$
Question 2: (10 points: $2+4+2+2)$ Consider the function: $f(x)=-4 \cos \left(\frac{\pi}{2} x\right)+1 \quad$ for $-3<x \leq 6$ Find the fillowing: a) Amplitude
Periot $=$ b) Graph $f(x)$ c) The interval(s) where $f(x)$ is decenasing d) The range of $f(x)$

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Problem 51568

1. С помощью формулы Тейлора найдите рациональное приближения числа $\sqrt{26}$ с точностью 0.0001 (сделайте оценку погрешности).

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Problem 51569

(2) Isaac paid $\$ 2.75$ for 4 granola bars and 1 apple. Amelia paid $\$ 2.25$ for 2 granola bars and 3 apples. Find the cost of a granola bar and an apple.

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Problem 51570

10. If $\sin ^{2}\left(5 \theta-30^{\circ}\right)+\cos ^{2}\left(\theta+70^{\circ}\right)=1$ , then the acute angle $\theta$ is equal to: A. $5^{\circ}$ B. $10^{\circ}$ C. $20^{\circ}$ D. $25^{\circ}$

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Problem 51571

b) Find an acute angle $\theta$ in degree such that $\sin \left(3 \theta-4^{\circ}\right)=\cos \left(2 \theta-1^{\circ}\right)$

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Problem 51572

Perform the division. $\frac{9 x^{3} y^{3}-27 x y+x^{2} y^{2}}{9 x y}$

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Problem 51573

8. Solve each of the puzzle-problems below: (e) Euler, 1770 . Divide 100 into two summands such that one is divisible by 7 and the other by 11 .

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Problem 51574

7. (0-2) Podstawą prostopadłościanu jest kwadrat o boku x, a jego krawędź boczna jest o 2 krótsza od krawędzi podstawy. Wyznacz wielomian V opisujący objętość tego prostopadłościanu. Określ dziedzinę funkcji. 142-7

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Problem 51575

Determine whether this pair of lines is parallel, perpendicular, or neither. $\begin{array}{l} 2+9 x=3 y \\ 3 x+9 y=1 \end{array}$
Choose the correct answer below. A. These two lines are parallel. B. These two lines are neither parallel nor perpendicular. C. These two lines are perpendicular.

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Problem 51576

b) $2 x(3 x+2)\left(x^{2}+9\right)\left(x^{2}-25\right)=0$

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Problem 51577

Question two: Income statement for XYZ company at the end of Year 2021 follows. (15 points) \begin{tabular}{|l|c|c|c|c|} \hline \multicolumn{4}{|c|}{ XYZ } & \\ \hline \multicolumn{3}{|c|}{ Income Statement (Multiple-Step) } & & \\ \hline & $\mathbf{2 0 2 1}$ & $\mathbf{2 0 2 0}$ & \multicolumn{2}{c|}{ Vertical analysis } \\ \hline Net Sales & 105000 & 120000 & $\mathbf{2 0 2 1}$ & $\mathbf{2 0 2 0}$ \\ \hline Cost of Sales & $(60,000$ & $(72,000)$ & & \\ \hline Gross Profit & 45000 & 48000 & & \\ \hline Expenses: & & & & \\ \hline & 11,000 & 11,000 & & \\ \hline Salaries expenses & 3.000 & 2,500 & & \\ \hline Depreciation expenses & 1,500 & 500 & & \\ \hline Electricity expenses & 0 & 1,200 & & \\ \hline Advertising expenses & $\mathbf{1 4 , 5 0 0}$ & $\mathbf{1 5 , 2 0 0}$ & & \\ \hline Total expenses & 30,500 & 32,800 & & \\ \hline & & & & \\ \hline Net operation income & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline \end{tabular}
Instructions:
1. Complete the income statement, it should be noted that the rent income $\$ 1,200$ , loss on sales of car \$ 2,000. Income tax 10\%
2- Analyze the income statement vertically 3 - comment on the results.

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Problem 51578

$\begin{array}{l}\text { If } 142 n=47 \mathrm{ten} \\ \text { find } n \text {. }\end{array}$

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Problem 51579

Pflichtaufgabe 2: (8 Punkte) Gegeben sind die Geraden $g: g: \vec{x}=\left(\begin{array}{c}3 \\ -3 \\ 3\end{array}\right)+r \cdot\left(\begin{array}{c}3 \\ 0 \\ -1\end{array}\right)$ mit $r \in \mathbb{R}$ und $h: \vec{x}=\left(\begin{array}{c}3 \\ -3 \\ 3\end{array}\right)+s \cdot\left(\begin{array}{l}1 \\ 0 \\ 3\end{array}\right)$ mit $s \in \mathbb{R}$ . (1) Geben Sie die Koordinaten des Schnittpunkts von $g$ und $h$ an und zeigen Sie, dass $g$ und $h$ senkrecht zueinander verlaufen. (2) Die Ebene $E$ enthält die Geraden $g$ und $h$ . Prüfen Sie, ob der Punkt $P(7|-3| 5)$ in $E$ liegt.

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Problem 51580

$\lim _{x \rightarrow 0}(1+2 x)^{\frac{3}{2 x}}$

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Problem 51581

Discrete Mathematics (1)All sections Time left 0:06:05
Question 4 Answer sived Marked out of 1.0 F Flazquestion $\text { The } \sum_{i=3}^{10}(i+1)^{2}=$ FINISH ATTEMPT ... ourinnthation 1 2 3 $\square$ moh2023116 (1) moh2023116 (1) moh2023116 (1) moh2023116 moh2023116 (4) moh20231164 moh20231164
Finishattempt - 1) moh20231164 moh20231164 6 elearning.psut.edu,jo

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Problem 51582

13. The distribution of cholesterol levels in teenage boys is approximately normal with $\mu=170$ and $\sigma=$ 30. Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200. A) 0.3419 B) 0.2138 C) 0.8413 D) 0.1587

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Problem 51583

Problem 3.7. Nora spends part of her summer driving a combine during the wheat harvest. Assume she starts at the indicated posttton heading east at $10 \mathrm{ft} / \mathrm{sec}$ toward a circular wheat field of radtus 200 ft . The combine cuts a swath 20 feet wide and begins when the corner of the machine labeled "a" is 60 feet north and 60 feet west of the western-most edge of the field. (a) When does Nora's rig first start cutting the wheat? (b) When does Nora's rig first start cutting a swath 90 feet wide?

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Problem 51584

Factor the trinomial by grouping. $6 x^{2}-5 x-21$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $6 x^{2}-5 x-21=$ $\square$ (Factor completely.) B. The polynomial is prime.

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Problem 51585

Find the domain of the rational function. $f(x)=\frac{x}{3 x+9}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is $\{x \mid x$ is a real number and $x \neq$ $\square$ \}. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The domain is $\{x \mid x$ is a real number $\}$ .

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Problem 51586

Graph each system of inequalities. Shade the solution of each system. 1.) $\left\{\begin{array}{l}y \leq 2 x-1 \\ y>-x+3\end{array}\right.$ 2.) $\left\{\begin{array}{l}3 x-2 y<4 \\ -2 x-6 y<-12\end{array}\right.$ 3.) $\left\{\begin{array}{l}2 x+2 y \geq-6 \\ x+y \leq-1\end{array}\right.$

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Problem 51587

Subtract. Simplify the result if possible. $\frac{3 a}{a^{2}+4 a-32}-\frac{12}{a^{2}+4 a-32}$ $\frac{3 a}{a^{2}+4 a-32}-\frac{12}{a^{2}+4 a-32}=$ $\square$ (Simplify your answer.)

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Problem 51588

Simplify. If an expression does not represent a real number, state so. $\sqrt[4]{-81}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\sqrt[4]{-81}=$ $\square$ (Type an integer.) B. The root is not a real number.

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Problem 51589

Use the properties of exponents to simplify each expression. Write with positive exponents. $6^{\frac{3}{4}} \cdot 6^{\frac{1}{8}}$ $6^{\frac{3}{4}} \cdot 6^{\frac{1}{8}}=$ $\square$ (Simplify your answer. Type exponential notation with rational exponents.)

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Problem 51590

$8(x+2)+(x-7)(x+1)$

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Problem 51591

A. Write the expressions and answer to each question.
1. The original price of a calculator is $\$ 300$ . It is now sold at $\$ 270$ . What is the percentage discount? $\qquad$ $\qquad$
2. The original price of a jacket is $\$ 1000$ . John saved $\$ 240$ with the discount. What is the percentage discount? $\qquad$ $\qquad$
3. The original price of a pair of socks is $\$ 20$ and it is sold after a deduction of $\$ 5$ . What is the percentage discount? $\qquad$ $\qquad$

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Problem 51592

Aufgaben zur Linearen Algebra mit Schwerpunkt auf Schnittpunkten und Lagebeziehungen 1) a) Es wird die Gleichung einer Geraden durch die Punkte $A(4 ; 1 ; 3)$ und $B(5 ; 3 ; 5)$ gesucht. b) Liegt R(2; 3 ; -1 ) auf der Geraden aus a)? c) Wo schneidet die Geraden aus a) die $x-y$ -Ebene ( $E: z=0$ )? 2) Wie ist die Lage der Geraden g und h zueinander? a) $g: \vec{x}=\left(\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right)+s \cdot\left(\begin{array}{l} 1 \\ 1 \\ 2 \end{array}\right) \text { und } h: \vec{x}=\left(\begin{array}{l} 2 \\ 2 \\ 3 \end{array}\right)+t \cdot\left(\begin{array}{l} 2 \\ 2 \\ 4 \end{array}\right)$ b) $g: \vec{x}=\left(\begin{array}{c} 4 \\ 2 \\ -1 \end{array}\right)+s \cdot\left(\begin{array}{c} 2 \\ 1 \\ -1 \end{array}\right) \text { und } h: \vec{x}=\left(\begin{array}{l} 0 \\ 0 \\ 1 \end{array}\right)+t \cdot\left(\begin{array}{c} -2 \\ -1 \\ 1 \end{array}\right)$ c) $g: \vec{x}=\left(\begin{array}{c} 1 \\ 4 \\ -2 \end{array}\right)+s \cdot\left(\begin{array}{c} -1 \\ 1 \\ 4 \end{array}\right) \text { und } h: \vec{x}=\left(\begin{array}{c} -1 \\ 5 \\ 5 \end{array}\right)+t \cdot\left(\begin{array}{c} -1 \\ -2 \\ 3 \end{array}\right)$ 3) Wie muss a gewählt werden, damit sich $\mathrm{g}_{\mathrm{a}}: \overrightarrow{\mathrm{x}}=\left(\begin{array}{l}\mathrm{a} \\ 1 \\ 4\end{array}\right)+\mathrm{s} \cdot\left(\begin{array}{l}3 \\ 1 \\ 5\end{array}\right)$ und $\mathrm{h}: \overrightarrow{\mathrm{x}}=\left(\begin{array}{c}6 \\ 4 \\ 20\end{array}\right)+\mathrm{t} \cdot\left(\begin{array}{l}4 \\ 1 \\ 4\end{array}\right)$ AF III nittwinkel? scheiden, wo liegt der Schnittpunkt und wie groß ist der Schnittwinkel? 4) Es soll eine Ebene durch die Punkte $P(4 ; 0 ; 0), Q(2 ;-1 ; 0)$ und $R(1 ;-2 ;-1)$ gelegt werden. Wie lautet eine Gleichung dieser Ebene in Parameterform und wie in Koordinatenform? 5) Gegeben ist die Gleichung der Ebene $E:-x+y+2 z=4$ . a) No schneidet die Ebene die z-Achse? Basisan/g. b) $S(1 ; 1 ; r)$ soll in E liegen, wie muss $r$ gewählt werden? Hibue's: c) Es wird der Schnittpunkt von E mit der Geraden Enisgehe. $\mathrm{g}: \overrightarrow{\mathrm{x}}=\left(\begin{array}{c} 2 \\ 10 \\ 3 \end{array}\right)+\mathrm{t} \cdot\left(\begin{array}{c} -1 \\ 2 \\ 1 \end{array}\right)$ gesucht. tedinen.

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Problem 51593

Question 1 of 20 This quiz: 20 point(s) possible This question: 1 point(s) possible Submit q
Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $y^{2}=40 x$
The focus is $\square$ (Type an ordered pair.) The directrix is $\square$ (Type an equation.) Use the graphing tool to graph the parabola only.
Click to enlarge graph

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Problem 51594

A billion electrons are added to pith ball. Its charge is: (A) $-1.6 \times 10^{-10} \mathrm{C}$ (B) $-1.6 \times 10^{-12} \mathrm{C}$ (C) $-1.6 \times 10^{-10} \mathrm{C}$

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Problem 51595

On donne: $(a+b)^{4}=a^{4}+4 a^{2} b+6 a^{2} b^{2}+4 a b^{3}+b^{4}$ . On considère le polynôme $P$ défini par: $P(x)=(x+2)^{4}+x^{4}-82$ . 1) $a / M o n t r e r ~ q u e, ~ p o u r ~ t o u t ~ x ~ x ~ I R, ~ o n ~ a: ~ P ~(-2-x)=P(x)$ . b/ Vérifier que 1 est une racine de $P$ , puis trouver une autre racine de $P$ . 2) a) Montrer que: $P(x)=2 x^{4}+8 x^{2}+24 x^{2}+32 x-66$ . $b /$ Justifier que: $P(x)=\left(x^{2}+2 x-3\right) Q(x)$ , pour tout $x \in I R$ où $Q$ est un polynôme que l'on déterminera. c/ Résoudre dans IR linéquation : $P(x) \geq 0$ . 3) Soit $F(x)=\frac{P(x)}{x^{4}-11 x^{2}+18}$ a/ Déterminer le domaine de définition de $F$ puis simplifier $F(x)$ . $b /$ Résoudre dans IR rinéquation : $F(x) \geq 0$ .

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Problem 51596

On donne: $(a+b)^{4}=a^{4}+4 a^{2} b+6 a^{2} b^{2}+4 a b^{3}+b^{4}$ . On considère le polynôme $P$ défini par: $P(x)=(x+2)^{4}+x^{4}-82$ . 1) $a / M o n t r e r ~ q u e, ~ p o u r ~ t o u t ~ x ~ x ~ I R, ~ o n ~ a: ~ P ~(-2-x)=P(x)$ . b/ Vérifier que 1 est une racine de $P$ , puis trouver une autre racine de $P$ . 2) a) Montrer que: $P(x)=2 x^{4}+8 x^{2}+24 x^{2}+32 x-66$ . $b /$ Justifier que: $P(x)=\left(x^{2}+2 x-3\right) Q(x)$ , pour tout $x \in I R$ où $Q$ est un polynôme que l'on déterminera. c/ Résoudre dans IR linéquation : $P(x) \geq 0$ . 3) Soit $F(x)=\frac{P(x)}{x^{4}-11 x^{2}+18}$ a/ Déterminer le domaine de définition de $F$ puis simplifier $F(x)$ . $b /$ Résoudre dans IR rinéquation : $F(x) \geq 0$ .

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Problem 51597

2.2 Quadratische Funktionen
2 Das Angebot für ein Produkt auf einem polypolistischen Markt wird beschrieben durch die Funktion $p_{\mathrm{A}}$ mit $p_{\mathrm{A}}(x)=0,1 x^{2}+0,4 x+1,4$ und die Nachfrage durch die Funktion $p_{\mathrm{N}}$ mit $p_{\mathrm{N}}(x)=0,05 x^{2}-x+4$ bestimmt ( $p$ in GE/ME, $x$ in ME). a) Berechnen Sie das Marktgleichgewicht und den Umsatz mit dem Produkt im Marktgleichgewicht. b) Bestimmen Sie die Sättigungsmenge, den Höchstpreis und den Mindestangebotspreis für das Produkt auf diesem Markt. c) Geben Sie einen ökonomisch sinnvollen Definitionsbereich für die Angebots- und die Nachfragefunktion an. d) Erläutern Sie, welche Situation auf dem Markt bei einem Marktpreis von 2 GE/ME herrscht. Berechnen Sie, wie hoch jetzt der Umsatz mit dem Gut ist.

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Problem 51598

$5 x-30<x-4$

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Problem 51599

Exercícios Avançados: a) Simplifique $\log _{4}(16 x)+2 \log _{4}(y)$ . b) Reescreva $\log _{7}\left(\frac{x^{3}}{y}\right)$ como uma soma e subtração. c) Resolva: $\frac{\log _{2}(16)}{\log _{2}(4)}$ .

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Problem 51600

2 You need to find out how many $\qquad$ there are in $\qquad$ . 3 The scoop holds $\frac{1}{3}$ cup of batter. How many scoops are in 1 cup? $\qquad$ 4 Divide each of the 5 rectangles into sections to show your answer to problem 3. 5 How many scoops are in 5 cups? $\qquad$ $65 \div \frac{1}{3}=$ $\qquad$ 7 What multiplication equation will also solve this problem? $\qquad$

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Math

Problem 51501

12. 18x+12y=243x+2y=6\begin{array}{l} 18 x+12 y=24 \\ 3 x+2 y=6 \end{array}18x+12y=243x+2y=6​

Problem 51502

10. Find the quotient of the expression (−864.3)÷(−3)(-864.3) \div(-3)(−864.3)÷(−3)Type a response Show Your Work

Problem 51503

8 Prove that 1+cos⁡θ1−cos⁡θ≡(cosec⁡θ+cot⁡θ)2\frac{1+\cos \theta}{1-\cos \theta} \equiv(\operatorname{cosec} \theta+\cot \theta)^{2}1−cosθ1+cosθ​≡(cosecθ+cotθ)2

Problem 51504

Evaluate the integral. ∫−77edx\int_{-7}^{7} e d x∫−77​edx

Problem 51505

Convert the following equation to polar coordinates. y=4x2y=4 x^{2}y=4x2The polar form of y=4x2y=4 x^{2}y=4x2 is □\square□ (Type an exact answer.)

Problem 51506

Problem 51507

Solve the inequality: −2(x+2)<14-2(x+2)<14−2(x+2)<14 x<−5x<-5x<−5 x<−9x<-9x<−9 x>−5x>-5x>−5 x>−9x>-9x>−9

Problem 51508

Problem 51509

3. Construct Arguments Gene stated that finding 25%25 \%25% of a number is the same as dividing the number by 14\frac{1}{4}41​. Is Gene correct? Explain.

Problem 51510

Problem 51511

Problem 51512

Problem 51513

Problem 51514

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​, where h≠0h \neq 0h=0, for the function below. f(x)=xx+1f(x)=\frac{x}{x+1}f(x)=x+1x​Simplify your answer as much as possible. f(x+h)−f(x)h=\frac{f(x+h)-f(x)}{h}=hf(x+h)−f(x)​= □\square□

Problem 51515

Problem 51516

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) sec⁡(arcsin⁡(35))\sec \left(\arcsin \left(\frac{3}{5}\right)\right)sec(arcsin(53​))

Problem 51517

Find the value of the constant k\boldsymbol{k}k such that integral has the prescribec value: ∫143x+kxdx=8\int_{1}^{4} \frac{3 x+k}{\sqrt{x}} d x=8∫14​x​3x+k​dx=8

Problem 51518

Problem 51519

24. 求微分方程 y′′+4y′−12y=0y^{\prime \prime}+4 y^{\prime}-12 y=0y′′+4y′−12y=0 的通解.25. 计算不定积分 ∫xarctan⁡x dx\int x \arctan x \mathrm{~d} x∫xarctanx dx 。

Problem 51520

Problem 51521

Problem 51522

Solve this system of equations by using graphing. {y=12x+1y=−x−2\left\{\begin{array}{l} y=\frac{1}{2} x+1 \\ y=-x-2 \end{array}\right.{y=21​x+1y=−x−2​ ([?], □\square□ Enter

Problem 51523

How many real zeros does the following quadratic function have? y=5x2+2x+4y=5 x^{2}+2 x+4y=5x2+2x+4Use the Discriminant: b² - 4ac no real zeros two real zeros one real zero

Problem 51524

Problem 51525

Solve the equation. 3w2+2w−8+3w2+w−6=5w2+7w+12\frac{3}{w^{2}+2 w-8}+\frac{3}{w^{2}+w-6}=\frac{5}{w^{2}+7 w+12}w2+2w−83​+w2+w−63​=w2+7w+125​

Problem 51526

What is the present value of $3780\$ 3780$3780 due in nine months if simple interest rate is 5%5 \%5% ?The present value is $\$$ □\square□ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Problem 51527

Evaluate the expression for the given value of the variable. x−4+3 for x=68\sqrt{x-4}+3 \text { for } x=68x−4​+3 for x=68

Problem 51528

Graph the inequality 4x−5y>204 x-5 y>204x−5y>20.

Problem 51529

Find the sales tax. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Sales Tax } \\ \hline Selling Price & Rate of Sales Tax & Sales Tax \\ \hline$90.00\$ 90.00$90.00 & 5%5 \%5% & ??? \\ \hline \end{tabular}The sales tax is $\$$ □\square□

Problem 51530

Problem 51531

Problem 51532

Find the commission. \begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{ Earning Commission } \\ \hline Sales & Commision Rate & Commission \\ \hline$540\$ 540$540 & 7%7 \%7% & ??? \\ \hline \end{tabular}The commission is $□\$ \square$□.

Problem 51533

Simplify. Enter the result as a single logarithm with a coefficient of 1. log⁡7(6x6)−log⁡7(7x7)\log _{7}\left(6 x^{6}\right)-\log _{7}\left(7 x^{7}\right)log7​(6x6)−log7​(7x7) □\square□ Question Help: Video Message instructor Submit Question

Problem 51534

Problem 51535

Mental Math A typical tip in a restaurant is 15%15 \%15% of the total bill. If the bill is $140\$ 140$140, what would the typical tip be?The typical tip would be \ \square$

Problem 51536

Section 4.4 Score: 9.5/12 Answered: 10/12Question 3Simplify. Enter the result as a sing Next log⁡8(4x7)−log⁡8(5x4)=\begin{array}{l} \log _{8}\left(4 x^{7}\right)-\log _{8}\left(5 x^{4}\right) \\ = \end{array}log8​(4x7)−log8​(5x4)=​ Question Help: Video Message instructor

Problem 51537

Question 3Find the domain of y=log⁡(3+3x)y=\log (3+3 x)y=log(3+3x). The domain is: □\square□ Question Help: Video Message instructor Submit Question

Problem 51538

Question 4Write an equation for the transformed logarithm shown below, that passes through (2,0)(2,0)(2,0) and (1(1(1, f(x)=f(x)=f(x)= □\square□ Question Help: Video 1 Video 2 Video 3 Message instructor Submit Question

Problem 51539

Solve this system of equations by using elimination. {3x+5y=−2−x+2y=8([?]\begin{array}{c} \left\{\begin{array}{l} 3 x+5 y=-2 \\ -x+2 y=8 \end{array}\right. \\ ([?] \end{array}{3x+5y=−2−x+2y=8​([?]​ Enter

Problem 51540

Problem 51541

x−111=−21\sqrt{x-111}=-21x−111​=−21

Problem 51542

3. f(x)=x4−4x2f(x)=x^{4}-4 x^{2}f(x)=x4−4x2

Problem 51543

Problem 51544

Problem 51545

Problem 51546

Problem 51547

Problem 51548

Problem 51549

tan⁡45∘+tan⁡300∘1−tan⁡45∘tan⁡300∘\frac{\tan 45^{\circ}+\tan 300^{\circ}}{1-\tan 45^{\circ} \tan 300^{\circ}}1−tan45∘tan300∘tan45∘+tan300∘​

Problem 51550

Problem 51551

12. $\begin{array}{l} 18 x+12 y=24 \\ 3 x+2 y=6 \end{array}$

10. Find the quotient of the expression $(-864.3) \div(-3)$
Type a response Show Your Work

8 Prove that $\frac{1+\cos \theta}{1-\cos \theta} \equiv(\operatorname{cosec} \theta+\cot \theta)^{2}$

Evaluate the integral. $\int_{-7}^{7} e d x$

Convert the following equation to polar coordinates. $y=4 x^{2}$
The polar form of $y=4 x^{2}$ is $\square$ (Type an exact answer.)

Solve the inequality: $-2(x+2)<14$ $x<-5$ $x<-9$ $x>-5$ $x>-9$

3. Construct Arguments Gene stated that finding $25 \%$ of a number is the same as dividing the number by $\frac{1}{4}$ . Is Gene correct? Explain.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ , where $h \neq 0$ , for the function below. $f(x)=\frac{x}{x+1}$
Simplify your answer as much as possible. $\frac{f(x+h)-f(x)}{h}=$ $\square$

Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) $\sec \left(\arcsin \left(\frac{3}{5}\right)\right)$

Find the value of the constant $\boldsymbol{k}$ such that integral has the prescribec value: $\int_{1}^{4} \frac{3 x+k}{\sqrt{x}} d x=8$

24. 求微分方程 $y^{\prime \prime}+4 y^{\prime}-12 y=0$ 的通解.
25. 计算不定积分 $\int x \arctan x \mathrm{~d} x$ 。

Solve this system of equations by using graphing. $\left\{\begin{array}{l} y=\frac{1}{2} x+1 \\ y=-x-2 \end{array}\right.$ ([?], $\square$ Enter

How many real zeros does the following quadratic function have? $y=5 x^{2}+2 x+4$
Use the Discriminant: b² - 4ac no real zeros two real zeros one real zero

Solve the equation. $\frac{3}{w^{2}+2 w-8}+\frac{3}{w^{2}+w-6}=\frac{5}{w^{2}+7 w+12}$

What is the present value of $\$ 3780$ due in nine months if simple interest rate is $5 \%$ ?
The present value is $\$$ $\square$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Evaluate the expression for the given value of the variable. $\sqrt{x-4}+3 \text { for } x=68$

Graph the inequality $4 x-5 y>20$ .

Find the sales tax. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Sales Tax } \\ \hline Selling Price & Rate of Sales Tax & Sales Tax \\ \hline $\$ 90.00$ & $5 \%$ & $?$ \\ \hline \end{tabular}
The sales tax is $\$$ $\square$

Find the commission. \begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|c|}{ Earning Commission } \\ \hline Sales & Commision Rate & Commission \\ \hline $\$ 540$ & $7 \%$ & $?$ \\ \hline \end{tabular}
The commission is $\$ \square$ .

Simplify. Enter the result as a single logarithm with a coefficient of 1. $\log _{7}\left(6 x^{6}\right)-\log _{7}\left(7 x^{7}\right)$ $\square$ Question Help: Video Message instructor Submit Question

Mental Math A typical tip in a restaurant is $15 \%$ of the total bill. If the bill is $\$ 140$ , what would the typical tip be?
The typical tip would be \\square$

Section 4.4 Score: 9.5/12 Answered: 10/12
Question 3
Simplify. Enter the result as a sing Next $\begin{array}{l} \log _{8}\left(4 x^{7}\right)-\log _{8}\left(5 x^{4}\right) \\ = \end{array}$ Question Help: Video Message instructor

Question 3
Find the domain of $y=\log (3+3 x)$ . The domain is: $\square$ Question Help: Video Message instructor Submit Question

Question 4
Write an equation for the transformed logarithm shown below, that passes through $(2,0)$ and $(1$ , $f(x)=$ $\square$ Question Help: Video 1 Video 2 Video 3 Message instructor Submit Question

Solve this system of equations by using elimination. $\begin{array}{c} \left\{\begin{array}{l} 3 x+5 y=-2 \\ -x+2 y=8 \end{array}\right. \\ ([?] \end{array}$ Enter

$\sqrt{x-111}=-21$

3. $f(x)=x^{4}-4 x^{2}$

$\frac{\tan 45^{\circ}+\tan 300^{\circ}}{1-\tan 45^{\circ} \tan 300^{\circ}}$

This is similar to Section 4.5 Problem 6:
Determine the indefinite integral $\int \frac{-4+8 x^{3}}{x} d x$ by algebraic manipulation. Assume $x>0$ when $\ln (x)$ appears. Use capital C for the free constant.
Answer: $\square$

Find the zeros of $m(x)=-5 x^{2}+50 x-135$

A TYT/Temel Matematik
13. Bir babanın yaşı, oğlunun yaşının 3 katıdır. Oğul, babasının bugünkü yaşına geldiğinde yaşlarının toplamı 72 olacaktır. Buna göre baba bugün kaç yaşındadır? A) 20 B) 25 C) 27 D) 35 E) 40

1) $m$ and $n$ are integers and $\sqrt{m n}=10$ . Which of the (a) 25 (b) 52 following cannot be a value of $m+n$ ? (c) 101 (d) 50 2) The number of factors of a number $N=2^{3} \times 3^{2} \times 5^{3}$ is (a) 18 (b) 45 (c) 48 (d) 9

$\frac{1}{4}=\frac{3}{\square}=\frac{\square}{20}$

1. С помощью формулы Тейлора найдите рациональное приближения числа $\sqrt{26}$ с точностью 0.0001 (сделайте оценку погрешности).

(2) Isaac paid $\$ 2.75$ for 4 granola bars and 1 apple. Amelia paid $\$ 2.25$ for 2 granola bars and 3 apples. Find the cost of a granola bar and an apple.

b) Find an acute angle $\theta$ in degree such that $\sin \left(3 \theta-4^{\circ}\right)=\cos \left(2 \theta-1^{\circ}\right)$

Perform the division. $\frac{9 x^{3} y^{3}-27 x y+x^{2} y^{2}}{9 x y}$