Function

Problem 2601

Solve the equation $2(x+1) \neq 4x!$ for values of $x$ .

See Solution

Problem 2602

Find the value of $d$ if the minimum of $f(x) = \cos x + d$ is -6.

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Problem 2603

Find the primary trigonometric ratios for $\theta = 2$ radians at the point $(-9,4)$ on the circle's circumference.

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Problem 2604

Identify the transformations of the function $y=3 \cos [5 x+90]+1$ .

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Problem 2605

Find the height $h$ of a passenger on a Ferris wheel (radius $10 \mathrm{~m}$ , revolution time $48 \mathrm{~s}$ ) at time $t$ .

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Problem 2606

Differentiate the function $\frac{5 x^{2}-5}{2 x}$ .

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Problem 2607

Differentiate the function $F(x)=\frac{\ln x}{3 x^{2}}-\frac{e^{-9 x}}{\ln x^{2}}$ .

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Problem 2608

Find the second derivative $H^{\prime \prime}(x)$ of the function $H(x)=x e^{x}$ .

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Problem 2609

Find the derivative $g^{\prime}(x)$ for the function $g(x)=\frac{x^{2}}{1+x}+\frac{e^{x}}{1+x^{2}}$ .

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Problem 2610

Let $f(\theta_{0}, \theta_{1})$ be a smooth function. Which statements about gradient descent minimizing $f$ are true?

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Problem 2611

A chemist studies how carbon atoms in hydrocarbons affect energy release during combustion. Estimate $\theta_{0}$ and $\theta_{1}$ for $y = \theta_{0} + \theta_{1} x$ . Options: $\theta_{0}=-569.6, \theta_{1}=530.9$ ; $\theta_{0}=-1780.0, \theta_{1}=530.9$ ; $\theta_{0}=-569.6, \theta_{1}=-530.9$ ; $\theta_{0}=-1780.0, \theta_{1}=-530.9$ .

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Problem 2612

Graph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

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Problem 2613

In a linear regression with $J(\theta_{0}, \theta_{1})=0$ , which statements are true? Check all that apply:
1. We can perfectly predict $y$ for unseen examples.
2. This requires $\theta_{0}=0$ and $\theta_{1}=0$ so $h_{\theta}(x)=0$ .
3. It's impossible for $J(\theta_{0}, \theta_{1})=0$ to exist.
4. For $\theta_{0}$ and $\theta_{1}$ satisfying $J(\theta_{0}, \theta_{1})=0$ , $h_{\theta}(x^{(i)})=y^{(i)}$ for all training examples.

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Problem 2614

Check if the function $f(x)$ is continuous at $x=-3$ where $f(x)=\begin{cases} 6+x^{2}, & x \geq-3 \\ 4-3 x, & x<-3 \end{cases}$ .

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Problem 2615

Motosikal memecut $2.5 \mathrm{~km/j}$ . Jika laju awal $20 \mathrm{~km/j}$ , cari laju selepas 0.25 minit.

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Problem 2616

An ice sphere melts at $2 \pi$ m³/hr. Find the surface area decrease rate when radius is 5 m. Options: (A) $\frac{4 \pi}{5}$ (B) $40 \pi$ (C) $80 \pi^{2}$ (D) $100 \pi$

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Problem 2617

Calculate $(-4) \cos \left(\frac{2 \pi}{3}\right)$ .

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Problem 2618

Solve: Isqrt[3]{x+28} - Isqrt[3]{x-28} = 2. Find x.

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Problem 2619

已知 $y=(m^{2}+2 m)x^{2}+m^{-1}$ ，求： (1) $m$ 取何值使 $y$ 为 $x$ 的正比例函数？ (2) $m$ 取何值使 $y$ 为 $x$ 的二次函数？ (3) $m$ 取何值使 $y$ 为 $x$ 的反比例函数？

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Problem 2620

Find the derivative of the function $\frac{e^{x}}{2^{e^{x}}}$ with respect to $x$ .

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Problem 2621

Transpose the following equations to make the letter in brackets the subject: 1) $k=s+n t$ (s) 2) $x=a b c$ (c) 3) $x=s t$ (s) 4) $c=q t+p$ (p) 5) $y=m x+c$ (m) 6) $A=hw+2$ (w) 7) $AB=CD$ (D) 8) $\frac{dk}{3}=c$ (k)

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Problem 2622

Arjun needs a \$350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayments, approx. \$2160.

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Problem 2623

Arjun needs a \ $350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayment of about$ 2160$.

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Problem 2624

Solve for $\alpha$ in the following equations: a. $2 \cdot \cos \alpha - 1 = 0$ b. $\alpha \sqrt{2} - 4 \sin \alpha = 0$ c. $\alpha \sin^2 \alpha - 3 \sin \alpha + 1 = 0$ d. $\sqrt{3} \cot^2 \alpha - (\sqrt{3} + 1) \cot \alpha + 1 = 0$ with $0^{\circ} \leq \alpha \leq 150^{\circ}$ .

See Solution

Problem 2625

Given the function $r(x)=-\frac{2}{3} x+4$ , find:
1. $r(-6)$
2. $r\left(\frac{1}{2}\right)$
3. Solve for $x$ when $r(x)=-4$ .

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Problem 2626

Elfira's $6\%$ bond at RMI,OOO has a yield to maturity of $7\%$ . Calculate the change in bond value. 5 marks

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Problem 2627

Find $d(5.5)$ for the function $d(x)=-2\left|x^{2}-3.6\right|$ .

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Problem 2628

Michael bought 5,000 shares at RM1.50 and sold 2,000 call options at RM0.20 with a strike of RM2.20. If the stock rises to RM3, what is his profit?

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Problem 2629

An investor estimates JDX Bhd's sales at RMI 50M with 10M shares, 15% profit, and 40% payout. Find the estimated net earnings.

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Problem 2630

An investor estimates JDX Bhd's sales at RM 50M, with a 15% profit and 40% dividend payout. Compute net earnings, dividends, stock price, and holding return.

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Problem 2631

Smith bought 3,000 shares of ABX at RM0.20, sold 1,000 call options at RM0.20 with a strike price of RM2. If the stock rises to RM3, how much profit does he make when the options are exercised?

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Problem 2632

Smith bought 3,000 shares at RM0.20 and sold 1,000 call options at RM0.20 each. What is his profit if the stock hits RM3?

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Problem 2633

Smith bought 3,000 shares of ABX at RM0.20 and sold 1,000 call options at RM0.20.
i) What is Smith's profit if the stock rises to RM3 and the options are exercised?
ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

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Problem 2634

Find the Macaulay duration of a RM1,000 bond with a $5\%$ coupon, maturing in 4 years, priced at RM965.35 and YTM $6.0\%$ .

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Problem 2635

Smith bought 3,000 shares of $\mathrm{ABX}$ at RM0.20 and sold 1,000 call options at RM0.20.
i) What is Smith's profit if the stock rises to RM3 and the options are exercised?
ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

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Problem 2636

Calculate yield to call for a bond with an 8% coupon, 10 years to maturity, par RM1,000, price RM1,071, callable at RM1,020 after 5 years.

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Problem 2637

Simplify the expression: $w=\bar{x}(x+y)+\bar{z}+z y$ , where $\bar{x}$ and $\bar{z}$ are operations on $x$ and $z$ .

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Problem 2638

What is the derivative of $\cos x$ with respect to $x$ ?

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Problem 2639

If $n=1$ is a solution to $n + 2 = \sqrt{a - n}$ , what is the value of the constant $a$ ?

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Problem 2640

Find the value of $x$ where the function $f(x)$ reaches its minimum. Options: A) -5 B) -3 C) -2 D) 3

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Problem 2641

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and test for significance at 0.05.
2. For CPI and subway fare, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

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Problem 2642

Find $y=f(-1)$ and $y=f(21)$ using the provided table of values for $x$ and $y$ .

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Problem 2643

Find $h(7)$ for the function $h(v)=4v+2$ .

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Problem 2644

Calculate the current yield, yield to call, and yield to maturity for a RM1000 bond with 8% coupon, 15 years maturity, and market price RM1150.

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Problem 2645

Chloe sells tortillas at a fair. Expenses: R500 rent + R5 per tortilla. Income: R15 per tortilla. Calculate break-even and profit for 240 sold.

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Problem 2646

A ball's height is given by $h(t)=9+128 t-16 t^{2}$ .
a. Find $h(1)$ and explain it. b. Find $h(4)$ . c. Determine when the ball stops climbing.

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Problem 2647

Calculate the monthly bill using the formula $f(W)=0.866 W+18.35$ for $W=8000$ and $W=4500$ kWh.

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Problem 2648

Amina Chua owns 100 shares of Nestlo at RM35 each. If she writes a call option at RM55 with a RM2 premium, answer:
i) How does she profit if the price drops to RM45? ii) What's her total profit selling at RM45? iii) What profit/loss if the call option is exercised?

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Problem 2649

Simplify the expression using reduction formulas:
$\frac{\cos 120^{\circ} \cdot \cos 210^{\circ} \cdot \tan 315^{\circ}}{\cos 330^{\circ}}$
without a calculator. Show all steps.

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Problem 2650

Una persona quiere tener $\$ 27000,00$ en 10 años. ¿Cuánto ahorrar mensualmente a una tasa del $14\%$ anual?

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Problem 2651

Encuentra el precio de contado de una computadora con enganche de \$ 5,600 y pago de \$ 10,000 a 3 meses, con interés del 14\% mensual.

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Problem 2652

Calcular el monto acumulado de pagos semestrales de \$ 650,00 a un fondo del 14\% anual, capitalización trimestral, 4 años.

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Problem 2653

Un auto parte del reposo y a los 5 s tiene una velocidad de $90 \mathrm{~km/h}$ . Calcula: a) aceleración, b) espacio recorrido, c) velocidad a los $11 \mathrm{~s}$ .

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Problem 2654

Una persona quiere tener $\$ 27000,00$ en 10 años. ¿Cuánto debe ahorrar cada mes a una tasa del $14\%$ anual?

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Problem 2655

¿Cuánto paga semestralmente un agricultor que prestó \$ 85500 a 4 años con tasa del 14\% anual y pagos semestrales?

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Problem 2656

The function $C(t)=25.50 t-16.75$ gives the cost for concert tickets.
1. Calculate $C(4)$ .
2. Explain what $C(4)$ means.
3. Is $C(6.5)$ reasonable in this context?

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Problem 2657

Un motociclista parte del reposo y recorre $2200 \mathrm{~km}$ en $10 \mathrm{~s}$ . ¿Cuánto tiempo necesita para llegar a $400 \mathrm{~km/h}$ ?

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Problem 2658

Find $T(1)$ from the graph, explain its meaning, and determine when the temperature reaches $70^{\circ} \mathrm{F}$ .

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Problem 2659

Un móvil parte del reposo con aceleración de $81.440 \mathrm{~km} / \mathrm{h}^{2}$ . Calcula: a) Velocidad a los 10 s. b) Distancia a los 32 s. c) Gráfica de velocidad vs. tiempo.

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Problem 2660

Un auto acelera a $30 \mathrm{~m} / \mathrm{s}^{2}$ por 2 minutos. a) ¿Cuántos km recorrió en ese tiempo? b) ¿Qué distancia a las 2 horas?

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Problem 2661

Un motociclista parte del reposo y recorre 2200 km en 10 s. ¿Cuánto tiempo necesita para alcanzar 400 km/h?

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Problem 2662

Un móvil parte del reposo con aceleración de $81.440 \mathrm{~km/h}$ . Calcula: a) Velocidad a los 10s. b) Distancia a los 32s.

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Problem 2663

Find the integral of $\sec^{2} \theta$ with respect to $\theta$ .

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Problem 2664

A biker rides distances: 12, 24, 36, 48 miles in 1, 2, 3, 4 hours. Model with $f(x)=12x$ . What transformation if teammate leaves 1 hour later?

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Problem 2665

Find the integral of $7^{x}$ with respect to $x$ .

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Problem 2666

Given the home prices in thousands of dollars and their availability, explain $n(0)=0$ , find $n(320)$ , and interpret it.

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Problem 2667

$f$ is an odd, continuous, periodic function with period 2. If $g(x) = \int_{0}^{1} f(t) dt$ , then find properties of $g(x)$ .

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Problem 2668

Find the min and max of $\tau=x^{2}+y^{3}-3 x+2124$ given $x=0$ , $y=0$ , and $x+y=3$ .

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Problem 2669

Dua pelajar dipilih dari kelas Amal (lelaki $x$ , perempuan 2) dan kelas Bestari (lelaki 2, perempuan 6). Cari $x$ jika P(different gender) = $\frac{7}{12}$ .

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Problem 2670

The temperature rises 1.5°C per hour. After 10 hours, it's 40°C. What is the model for temperature $\mathrm{y}$ after $\mathrm{x}$ hours?

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Problem 2671

Evaluate the function $b(t)=4 t^{3}-t^{2}$ at $t=-2$ . What is $b(-2)$ ?

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Problem 2672

Evaluate the function $a(c)=2c-4$ at $c=4$ . What is $a(4)$ ?

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Problem 2673

Evaluate the function $f(x)=-2x+5$ at $x=-4$ . What is $f(-4)$ ?

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Problem 2674

Evaluate the function $f(x) = x^{3} - 6x$ at $x = -3$ . What is $f(-3)$ ?

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Problem 2675

Evaluate the function $d(t)=\frac{5}{6} t+4$ for $t=12$ .

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Problem 2676

Identify a key property of the linear parent function: A. Curved line B. Slope = 0 C. In quadrants I & III D. Passes through origin.

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Problem 2677

Find the value of $\operatorname{arccot}(-1)$ .

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Problem 2678

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 2679

Find the change in demand when price drops from \ $2.25 to \$1, given$ x=\frac{1000}{\sqrt{p}+1}$.

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Problem 2680

A company sells $Q(x) = 60x - x^2$ units after spending $\$x$ thousand on ads. Find $Q(7)$ and $Q'(7)$ , and interpret.

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Problem 2681

Encuentra dos números naturales en la relación 5:2, donde el cuadrado del mayor más el cubo del menor sea 441. Suma los números.

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Problem 2682

Mohan wants \ $30000 in 10 years. How much to deposit bi-weekly at$ 7.8\%$ interest compounded bi-weekly?

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Problem 2683

What is the current price of a car with a \$3000 down payment and 60 monthly payments of \$280 at a 12% interest rate?

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Problem 2684

Two companies produce phones. Company A starts at 600 and increases by 300 weekly. Company B starts at 500 and increases by $15\%$ weekly. Find: a) Phones produced in week 15 b) Total production in 15 weeks

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Problem 2685

```latex \begin{tabular}{|c|c|} \hline x & g(x) \\ \hline 6 & \square \\ \hline 8 & 8 \\ \hline 10 & 10 \\ \hline \end{tabular}
The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.
Dialogue Transcript:
Hello! It looks like you have a table with some values for a function $g(x)$ , but there is a missing value where $x = 6$ . Could you please provide more context or specify what you need help with? For example, are there any additional equations or information given in the problem that would help in finding $g(6)$ ? Let me know so I can assist you further! Yes Great! Could you please provide the additional information or context for the problem? This will help me understand how to proceed with solving it. What the g (x) for 6 To find $g(6)$ , we need some additional information or a rule about how $g(x)$ is determined.
For example, is there a pattern or a formula given for $g(x)$ that applies to the other values in the table? If you have any additional equations or relationships related to $g(x)$ , please share them.
Once I have that information, I can assist you in finding $g(6)$ . 6,8,10 ```

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Problem 2686

School-Semeste...
Given the function below, determine the following. $f(x)=-3 x^{2}+5$ (24) Find $f(-x)$ .
Education iteboard) racker

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Problem 2687

$\begin{array}{|c|c|} \hline x & f(x) \\ \hline 4 & \square \\ \hline 6 & 4 \\ \hline 8 & 10 \\ \hline \end{array}$
Determine the value of $f(x)$ for $x = 4$ given the table above. The known values are $f(6) = 4$ and $f(8) = 10$ . Identify any pattern or rule that can be used to find the missing value at $x = 4$ .

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Problem 2688

A board game involves tossing a fair, regular die (with $1,2,3,4,5$ , and 6 dots on the faces) and moving the number of spaces indicated by the number of dots. If the die is tossed many times, what is the expected value of the number of spaces to be moved? (Round your answer to one decimal place if applicable.) expected Value: $\square$
What does that mean in context? This means that with a large number of tosses, the average number of spaces moved is 3.5 . This means that the most likely dice roll will be about 3.5 . This means the number of spaces moved the next time the die is rolled will probably be around 3.5 . The average number of spaces moved is 3.5 .

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Problem 2689

Given the function below, determine the following. $f(x)=-4 x^{2}+4 x$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 2690

Consider the following polynomial function. $f(x)=(x+1)^{2}(x-3)^{5}(x-2)$
Step 3 of 3 : Find the zero(s) at which $f^{\prime \prime}$ flattens out". Express the zero(s) as ordered pair(s).
Answer
Select the number of zero(s) at which $f$ "flattens out".
Selecting an option will display any text boxes needed to complete your answer. none 1 2 3 4

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Problem 2691

Given the function below, determine the following. $f(x)=-5 x^{2}-8 x-2$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-n f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 2692

24. Find the domain of the following rational function. $H(x)=\frac{-8 x^{2}}{(x-5)(x+4)}$

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Problem 2693

Given the function below, determine the following. $f(x)=-5 x^{2}$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 2694

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm . If the area of printed material on the poster is fixed at $1,536 \mathrm{~cm}^{2}$ , find the dimensions (in cm ) of the poster with the smallest area.

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Problem 2695

Siven the function below, determine the following. $f(x)=4 x^{3}-5 x$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 2696

Given the following functions, find the indicated values. $f(x)=8-6 x$ (a) $f(-7)$ (b) $f(0)$ (c) $f(8)$ (a) $f(-7)=$

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Problem 2697

Given $f(x)=2 x-3$ , describe how the graph of $g$ compares with the graph of $f$ . $g(x)=2(4 x)-3$ A. The graph of $g(x)$ is translated $\square$ unit(s) to the left compared to the graph of $f(x)$ . B. $g(x)$ has a scale factor of $\square$ compared to $f(x)$ . Because it scales the horizontal direction, the graph is compressed horizonta C. The graph of $g(x)$ is translated $\square$ unit(s) up compared to graph of $\mathrm{f}(\mathrm{x})$ . D. $g(x)$ has a scale factor of $\square$ compared to $f(x)$ . Because it scales the horizontal direction, the graph is stretched horizontally. E. The graph of $g(x)$ is translated $\square$ unit(s) down compared to graph of $f(x)$ . F. $g(x)$ has a scale factor of $\square$ compared to $f(x)$ . Because it scales the vertical direction, the graph is stretched vertically.

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Problem 2698

Given the function below, determine the following. $f(x)=-4 x^{2}+10$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 2699

Question Watch Video Show Examples
The table below shows Fawzia's earnings on the job. \begin{tabular}{|c|c|} \hline Time (hours) & Earnings (dollars) \\ \hline 5 & $\$ 134.50$ \\ \hline 11 & $\$ 295.90$ \\ \hline 18 & $\$ 484.20$ \\ \hline \end{tabular}
What is Fawzia's rate of pay, in dollars per hour?
Answer Attempt 1 out of 20 \\square$ per hour Submit Answer

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Problem 2700

Which table was created using the equation $y=5 x-3$ ?
A \begin{tabular}{|c|c|} \hline Input $(x)$ & Output $(y)$ \\ \hline 3 & 12 \\ \hline 4 & 17 \\ \hline 5 & 32 \\ \hline 6 & 37 \\ \hline 7 & 42 \\ \hline 8 & 47 \\ \hline \end{tabular}
C \begin{tabular}{|c|c|} \hline Input (x) & Output $(y)$ \\ \hline 3 & 50 \\ \hline 4 & 51 \\ \hline 5 & 53 \\ \hline 6 & 55 \\ \hline 7 & 56 \\ \hline 8 & 57 \\ \hline \end{tabular}
B \begin{tabular}{|c|c|} \hline Input $(x)$ & Output $(y)$ \\ \hline 3 & 12 \\ \hline 4 & 17 \\ \hline 5 & 22 \\ \hline 6 & 27 \\ \hline 7 & 32 \\ \hline 8 & 37 \\ \hline \end{tabular}
D

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Function

Problem 2601

Solve the equation 2(x+1)≠4x!2(x+1) \neq 4x!2(x+1)=4x! for values of xxx.

Problem 2602

Find the value of ddd if the minimum of f(x)=cos⁡x+df(x) = \cos x + df(x)=cosx+d is -6.

Problem 2603

Find the primary trigonometric ratios for θ=2\theta = 2θ=2 radians at the point (−9,4)(-9,4)(−9,4) on the circle's circumference.

Problem 2604

Identify the transformations of the function y=3cos⁡[5x+90]+1y=3 \cos [5 x+90]+1y=3cos[5x+90]+1.

Problem 2605

Find the height hhh of a passenger on a Ferris wheel (radius 10 m10 \mathrm{~m}10 m, revolution time 48 s48 \mathrm{~s}48 s) at time ttt.

Problem 2606

Differentiate the function 5x2−52x\frac{5 x^{2}-5}{2 x}2x5x2−5​.

Problem 2607

Differentiate the function F(x)=ln⁡x3x2−e−9xln⁡x2F(x)=\frac{\ln x}{3 x^{2}}-\frac{e^{-9 x}}{\ln x^{2}}F(x)=3x2lnx​−lnx2e−9x​.

Problem 2608

Find the second derivative H′′(x)H^{\prime \prime}(x)H′′(x) of the function H(x)=xexH(x)=x e^{x}H(x)=xex.

Problem 2609

Find the derivative g′(x)g^{\prime}(x)g′(x) for the function g(x)=x21+x+ex1+x2g(x)=\frac{x^{2}}{1+x}+\frac{e^{x}}{1+x^{2}}g(x)=1+xx2​+1+x2ex​.

Problem 2610

Let f(θ0,θ1)f(\theta_{0}, \theta_{1})f(θ0​,θ1​) be a smooth function. Which statements about gradient descent minimizing fff are true?

Problem 2611

Problem 2612

Graph the piecewise function: f(x)={4for x≤−1x+3for −1<x<42x−2for x≥4 f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases} f(x)=⎩⎨⎧​4x+32x−2​for x≤−1for −1<x<4for x≥4​

Problem 2613

Problem 2614

Check if the function f(x)f(x)f(x) is continuous at x=−3x=-3x=−3 where f(x)={6+x2,x≥−34−3x,x<−3f(x)=\begin{cases} 6+x^{2}, & x \geq-3 \\ 4-3 x, & x<-3 \end{cases}f(x)={6+x2,4−3x,​x≥−3x<−3​.

Problem 2615

Motosikal memecut 2.5 km/j2.5 \mathrm{~km/j}2.5 km/j. Jika laju awal 20 km/j20 \mathrm{~km/j}20 km/j, cari laju selepas 0.25 minit.

Problem 2616

An ice sphere melts at 2π2 \pi2π m³/hr. Find the surface area decrease rate when radius is 5 m. Options: (A) 4π5\frac{4 \pi}{5}54π​ (B) 40π40 \pi40π (C) 80π280 \pi^{2}80π2 (D) 100π100 \pi100π

Problem 2617

Calculate (−4)cos⁡(2π3)(-4) \cos \left(\frac{2 \pi}{3}\right)(−4)cos(32π​).

Problem 2618

Solve: Isqrt[3]{x+28} - Isqrt[3]{x-28} = 2. Find x.

Problem 2619

已知 y=(m2+2m)x2+m−1y=(m^{2}+2 m)x^{2}+m^{-1}y=(m2+2m)x2+m−1，求： (1) mmm 取何值使 yyy 为 xxx 的正比例函数？ (2) mmm 取何值使 yyy 为 xxx 的二次函数？ (3) mmm 取何值使 yyy 为 xxx 的反比例函数？

Problem 2620

Find the derivative of the function ex2ex\frac{e^{x}}{2^{e^{x}}}2exex​ with respect to xxx.

Problem 2621

Transpose the following equations to make the letter in brackets the subject: 1) k=s+ntk=s+n tk=s+nt (s) 2) x=abcx=a b cx=abc (c) 3) x=stx=s tx=st (s) 4) c=qt+pc=q t+pc=qt+p (p) 5) y=mx+cy=m x+cy=mx+c (m) 6) A=hw+2A=hw+2A=hw+2 (w) 7) AB=CDAB=CDAB=CD (D) 8) dk3=c\frac{dk}{3}=c3dk​=c (k)

Problem 2622

Arjun needs a \$350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayments, approx. \$2160.

Problem 2623

Arjun needs a \350,000loanfor20yearsat4.2%interest,compoundedmonthly.Findhismonthlyrepaymentofabout350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayment of about 350,000loanfor20yearsat4.2%interest,compoundedmonthly.Findhismonthlyrepaymentofabout2160$.

Problem 2624

Problem 2625

Given the function r(x)=−23x+4r(x)=-\frac{2}{3} x+4r(x)=−32​x+4, find: 1. r(−6)r(-6)r(−6) 2. r(12)r\left(\frac{1}{2}\right)r(21​) 3. Solve for xxx when r(x)=−4r(x)=-4r(x)=−4.

Problem 2626

Elfira's 6%6\%6% bond at RMI,OOO has a yield to maturity of 7%7\%7%. Calculate the change in bond value. 5 marks

Problem 2627

Find d(5.5)d(5.5)d(5.5) for the function d(x)=−2∣x2−3.6∣d(x)=-2\left|x^{2}-3.6\right|d(x)=−2∣∣​x2−3.6∣∣​.

Problem 2628

Michael bought 5,000 shares at RM1.50 and sold 2,000 call options at RM0.20 with a strike of RM2.20. If the stock rises to RM3, what is his profit?

Problem 2629

An investor estimates JDX Bhd's sales at RMI 50M with 10M shares, 15% profit, and 40% payout. Find the estimated net earnings.

Problem 2630

An investor estimates JDX Bhd's sales at RM 50M, with a 15% profit and 40% dividend payout. Compute net earnings, dividends, stock price, and holding return.

Problem 2631

Smith bought 3,000 shares of ABX at RM0.20, sold 1,000 call options at RM0.20 with a strike price of RM2. If the stock rises to RM3, how much profit does he make when the options are exercised?

Problem 2632

Smith bought 3,000 shares at RM0.20 and sold 1,000 call options at RM0.20 each. What is his profit if the stock hits RM3?

Problem 2633

Smith bought 3,000 shares of ABX at RM0.20 and sold 1,000 call options at RM0.20. i) What is Smith's profit if the stock rises to RM3 and the options are exercised? ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

Problem 2634

Find the Macaulay duration of a RM1,000 bond with a 5%5\%5% coupon, maturing in 4 years, priced at RM965.35 and YTM 6.0%6.0\%6.0%.

Problem 2635

Smith bought 3,000 shares of ABX\mathrm{ABX}ABX at RM0.20 and sold 1,000 call options at RM0.20. i) What is Smith's profit if the stock rises to RM3 and the options are exercised? ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

Problem 2636

Calculate yield to call for a bond with an 8% coupon, 10 years to maturity, par RM1,000, price RM1,071, callable at RM1,020 after 5 years.

Problem 2637

Simplify the expression: w=xˉ(x+y)+zˉ+zyw=\bar{x}(x+y)+\bar{z}+z yw=xˉ(x+y)+zˉ+zy, where xˉ\bar{x}xˉ and zˉ\bar{z}zˉ are operations on xxx and zzz.

Problem 2638

What is the derivative of cos⁡x\cos xcosx with respect to xxx?

Problem 2639

If n=1n=1n=1 is a solution to n+2=a−nn + 2 = \sqrt{a - n}n+2=a−n​, what is the value of the constant aaa?

Problem 2640

Find the value of xxx where the function f(x)f(x)f(x) reaches its minimum. Options: A) -5 B) -3 C) -2 D) 3

Problem 2641

1. Given commuter and parking space data, find the correlation coefficient, critical values for rrr, and test for significance at 0.05. 2. For CPI and subway fare, find the regression equation with CPI as xxx and predict fare for CPI = 182.5.

Solve the equation $2(x+1) \neq 4x!$ for values of $x$ .

Find the value of $d$ if the minimum of $f(x) = \cos x + d$ is -6.

Find the primary trigonometric ratios for $\theta = 2$ radians at the point $(-9,4)$ on the circle's circumference.

Identify the transformations of the function $y=3 \cos [5 x+90]+1$ .

Find the height $h$ of a passenger on a Ferris wheel (radius $10 \mathrm{~m}$ , revolution time $48 \mathrm{~s}$ ) at time $t$ .

Differentiate the function $\frac{5 x^{2}-5}{2 x}$ .

Differentiate the function $F(x)=\frac{\ln x}{3 x^{2}}-\frac{e^{-9 x}}{\ln x^{2}}$ .

Find the second derivative $H^{\prime \prime}(x)$ of the function $H(x)=x e^{x}$ .

Find the derivative $g^{\prime}(x)$ for the function $g(x)=\frac{x^{2}}{1+x}+\frac{e^{x}}{1+x^{2}}$ .

Let $f(\theta_{0}, \theta_{1})$ be a smooth function. Which statements about gradient descent minimizing $f$ are true?

Graph the piecewise function: $f(x) = \begin{cases} 4 & \text{for } x \leq -1 \\ x + 3 & \text{for } -1 < x < 4 \\ 2x - 2 & \text{for } x \geq 4 \end{cases}$

Check if the function $f(x)$ is continuous at $x=-3$ where $f(x)=\begin{cases} 6+x^{2}, & x \geq-3 \\ 4-3 x, & x<-3 \end{cases}$ .

Motosikal memecut $2.5 \mathrm{~km/j}$ . Jika laju awal $20 \mathrm{~km/j}$ , cari laju selepas 0.25 minit.

An ice sphere melts at $2 \pi$ m³/hr. Find the surface area decrease rate when radius is 5 m. Options: (A) $\frac{4 \pi}{5}$ (B) $40 \pi$ (C) $80 \pi^{2}$ (D) $100 \pi$

Calculate $(-4) \cos \left(\frac{2 \pi}{3}\right)$ .

已知 $y=(m^{2}+2 m)x^{2}+m^{-1}$ ，求： (1) $m$ 取何值使 $y$ 为 $x$ 的正比例函数？ (2) $m$ 取何值使 $y$ 为 $x$ 的二次函数？ (3) $m$ 取何值使 $y$ 为 $x$ 的反比例函数？

Find the derivative of the function $\frac{e^{x}}{2^{e^{x}}}$ with respect to $x$ .

Transpose the following equations to make the letter in brackets the subject: 1) $k=s+n t$ (s) 2) $x=a b c$ (c) 3) $x=s t$ (s) 4) $c=q t+p$ (p) 5) $y=m x+c$ (m) 6) $A=hw+2$ (w) 7) $AB=CD$ (D) 8) $\frac{dk}{3}=c$ (k)

Arjun needs a \ $350,000 loan for 20 years at 4.2\% interest, compounded monthly. Find his monthly repayment of about$ 2160$.

Given the function $r(x)=-\frac{2}{3} x+4$ , find:
1. $r(-6)$
2. $r\left(\frac{1}{2}\right)$
3. Solve for $x$ when $r(x)=-4$ .

Elfira's $6\%$ bond at RMI,OOO has a yield to maturity of $7\%$ . Calculate the change in bond value. 5 marks

Find $d(5.5)$ for the function $d(x)=-2\left|x^{2}-3.6\right|$ .

Smith bought 3,000 shares of ABX at RM0.20 and sold 1,000 call options at RM0.20.
i) What is Smith's profit if the stock rises to RM3 and the options are exercised?
ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

Find the Macaulay duration of a RM1,000 bond with a $5\%$ coupon, maturing in 4 years, priced at RM965.35 and YTM $6.0\%$ .

Smith bought 3,000 shares of $\mathrm{ABX}$ at RM0.20 and sold 1,000 call options at RM0.20.
i) What is Smith's profit if the stock rises to RM3 and the options are exercised?
ii) If the stock rises to RM1.80, should the options buyer exercise? Explain.

Simplify the expression: $w=\bar{x}(x+y)+\bar{z}+z y$ , where $\bar{x}$ and $\bar{z}$ are operations on $x$ and $z$ .

What is the derivative of $\cos x$ with respect to $x$ ?

If $n=1$ is a solution to $n + 2 = \sqrt{a - n}$ , what is the value of the constant $a$ ?

Find the value of $x$ where the function $f(x)$ reaches its minimum. Options: A) -5 B) -3 C) -2 D) 3

1. Given commuter and parking space data, find the correlation coefficient, critical values for $r$ , and test for significance at 0.05.
2. For CPI and subway fare, find the regression equation with CPI as $x$ and predict fare for CPI = 182.5.

Find $y=f(-1)$ and $y=f(21)$ using the provided table of values for $x$ and $y$ .

Find $h(7)$ for the function $h(v)=4v+2$ .

A ball's height is given by $h(t)=9+128 t-16 t^{2}$ .
a. Find $h(1)$ and explain it. b. Find $h(4)$ . c. Determine when the ball stops climbing.

Calculate the monthly bill using the formula $f(W)=0.866 W+18.35$ for $W=8000$ and $W=4500$ kWh.

Amina Chua owns 100 shares of Nestlo at RM35 each. If she writes a call option at RM55 with a RM2 premium, answer:
i) How does she profit if the price drops to RM45? ii) What's her total profit selling at RM45? iii) What profit/loss if the call option is exercised?

Simplify the expression using reduction formulas:
$\frac{\cos 120^{\circ} \cdot \cos 210^{\circ} \cdot \tan 315^{\circ}}{\cos 330^{\circ}}$
without a calculator. Show all steps.

Una persona quiere tener $\$ 27000,00$ en 10 años. ¿Cuánto ahorrar mensualmente a una tasa del $14\%$ anual?

Un auto parte del reposo y a los 5 s tiene una velocidad de $90 \mathrm{~km/h}$ . Calcula: a) aceleración, b) espacio recorrido, c) velocidad a los $11 \mathrm{~s}$ .

Una persona quiere tener $\$ 27000,00$ en 10 años. ¿Cuánto debe ahorrar cada mes a una tasa del $14\%$ anual?

The function $C(t)=25.50 t-16.75$ gives the cost for concert tickets.
1. Calculate $C(4)$ .
2. Explain what $C(4)$ means.
3. Is $C(6.5)$ reasonable in this context?

Un motociclista parte del reposo y recorre $2200 \mathrm{~km}$ en $10 \mathrm{~s}$ . ¿Cuánto tiempo necesita para llegar a $400 \mathrm{~km/h}$ ?

Find $T(1)$ from the graph, explain its meaning, and determine when the temperature reaches $70^{\circ} \mathrm{F}$ .

Un móvil parte del reposo con aceleración de $81.440 \mathrm{~km} / \mathrm{h}^{2}$ . Calcula: a) Velocidad a los 10 s. b) Distancia a los 32 s. c) Gráfica de velocidad vs. tiempo.

Un auto acelera a $30 \mathrm{~m} / \mathrm{s}^{2}$ por 2 minutos. a) ¿Cuántos km recorrió en ese tiempo? b) ¿Qué distancia a las 2 horas?

Un móvil parte del reposo con aceleración de $81.440 \mathrm{~km/h}$ . Calcula: a) Velocidad a los 10s. b) Distancia a los 32s.

Find the integral of $\sec^{2} \theta$ with respect to $\theta$ .

A biker rides distances: 12, 24, 36, 48 miles in 1, 2, 3, 4 hours. Model with $f(x)=12x$ . What transformation if teammate leaves 1 hour later?

Find the integral of $7^{x}$ with respect to $x$ .

Given the home prices in thousands of dollars and their availability, explain $n(0)=0$ , find $n(320)$ , and interpret it.

$f$ is an odd, continuous, periodic function with period 2. If $g(x) = \int_{0}^{1} f(t) dt$ , then find properties of $g(x)$ .

Find the min and max of $\tau=x^{2}+y^{3}-3 x+2124$ given $x=0$ , $y=0$ , and $x+y=3$ .

Dua pelajar dipilih dari kelas Amal (lelaki $x$ , perempuan 2) dan kelas Bestari (lelaki 2, perempuan 6). Cari $x$ jika P(different gender) = $\frac{7}{12}$ .

The temperature rises 1.5°C per hour. After 10 hours, it's 40°C. What is the model for temperature $\mathrm{y}$ after $\mathrm{x}$ hours?

Evaluate the function $b(t)=4 t^{3}-t^{2}$ at $t=-2$ . What is $b(-2)$ ?

Evaluate the function $a(c)=2c-4$ at $c=4$ . What is $a(4)$ ?

Evaluate the function $f(x)=-2x+5$ at $x=-4$ . What is $f(-4)$ ?

Evaluate the function $f(x) = x^{3} - 6x$ at $x = -3$ . What is $f(-3)$ ?