Browse Equation problems Studdy Solved!

Problem 13301

1) assume that you bought a stock for $\$ 50$ . If you sold the stock for $\$ 60$ and you got $\$ 2$ divider What was your annual return?

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Problem 13302

Write the standard form of the equation of the circle with the given center and radius. Center $(-7,2), r=5$

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Problem 13303

You go to the doctor and he gives you 15 milligrams of radioactive dye. After 12 minutes, 8 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
You will spend $\square$ minutes at the doctor's office.

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Problem 13304

$5-4$ Standardized Test Prep
Point-Slope Form Multiple Choice For Exercises 1-5, choose the correct letter.
1. Which equation is equivalent to $y-6=-12(x+4)$ ? A. $y=-6 x-48$ C. $y=-12 x-42$ B. $y=6 x-48$ D. $y=-12 x-54$
2. Which point is located on the line represented by the equation $y+4=-5(x-3) ?$ F. $(-4,-5)$ G. $(-5,-4)$ H. $(3,-4)$ I. $(-3,4)$
3. Which equation represents the line that passes through the points $(6,-3)$ and $(-4,-9)$ ? A. $y+4=-\frac{3}{5}(x+9)$ C. $y-3=\frac{3}{5}(x+6)$ B. $y+4=\frac{5}{3}(x+9)$ D. $y+3=\frac{3}{5}(x-6)$
4. Which equation represents the line shown in the graph? F. $y=-3 x-2$ G. $y=3 x+2$ H. $y+4=-3(x-2)$ l. $y+8=-3(x-2)$
5. The population of a city increases by 4000 people each year. In 2025 , the population is projected to be 450,000 people. What is an equation that gives the city's population $p$ (in thousands of people) $x$ years after 2010? A. $p=4 x+450$ C. $p-15=4(x-450)$ B. $p-450=4(x-15)$ D. $p=4 x+15$
Short Response
6. The table shows the cost of a large cheese pizza with additional toppings on it. a. What is an equation in point-slope form that represents the relationship between the number of toppings and the cost of the pizza? \begin{tabular}{|c|c|} \hline Toppings & Cost (\$) \\ \hline 2 & 10.50 \\ \hline 3 & 11.75 \\ \hline 5 & 14.25 \\ \hline \end{tabular} b. What is the graph of the equation?

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Problem 13305

$5=\frac{5(4 n-1)}{3}$

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Problem 13306

ALEKS - Danlette Tah - Learn New Chrom Gmail VouTube Google Docs Login More Section - Resu... Confldence intervals and Hypothesis Testing Danlette Computing and comparing confidence intervals for a population... Espanol
You are looking at a population and are interested in the proportion $p$ that has a certaln characteristic. Unknown to you, this population proportion is $p=0.85$ . You have taken a random sample of size $n=115$ from the population and found that the proportion of the sample that has the characteristic is $\widehat{p}=0.84$ . Your sample is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the $75 \%$ and $90 \%$ confidence intervals for the population proportion. Use 1.150 for the critical value for the $75 \%$ confidence interval, and use 1.645 for the critical value for the $90 \%$ confidence interval. (If necessary, consult a list of formulas.) - Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with two decimal places. - For the points ( $*$ and $\bullet$ ), enter the population proportion, 0.85 . ? 凅 ■ 回 (4) (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size $n=115$ from the same population. Notice that the confidence intervals for these samoles are drawn automaticallv, Then complete parts (c) and ( $d$ ) below the table. Explanation Check

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Problem 13307

Imagine you need to purchase a laptop bag for your 14 -inch laptop. The only problem is you don't have your laptop with you, and it sure would be frustrating to buy a bag only to realize that your laptop doesn't quite fit.
You recall laptop computers are measured according to the diagonals of their screens, and you remember your 14 -inch laptop has a screen that is 8 inches tall. How wide is the screen?
Exact Answer (written as a simpified radical): $\square$ in.
Approximate (decimal) Answer: $\square$ in. Give your approximate answer accurate to 2 decimal places.

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Problem 13308

Solve the equation. * $5 x-6=29$ $x=3$ $x=5$ $x=7$ $x=9$

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Problem 13309

Solve. $\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}$

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Problem 13310

Find the missing side.
Round to the nearest tent

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Problem 13311

Solve the equation. * $3 x+8=2$ $x=-4$ $x=-2$ $x=2$ $x=4$

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Problem 13312

Find the missing side.

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Problem 13313

Tammy's take-home pay is $\$ 800$ a month. $7 \%$ of her take-home pay is spent on her cell phone bill. How much is Tammy's monthly cell phone bill? A. $\$ 109$ B. $\$ 69.99$ C. \ $56 D.$ \ $76$

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Problem 13314

A cylinder with a movable piston contains gas at a temperature of $24.3^{\circ} \mathrm{C}$ , a volume of $2.09 \mathrm{~m}^{3}$ , and an absolute pressure of 13700 Pa .
What will be its final temperature if the gas is compressed to $0.34 \mathrm{~m}^{3}$ and the absolute pressure increases to 63350 Pa ?
Answer in units of ${ }^{\circ} \mathrm{C}$ .

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Problem 13315

Find the center of the ellipse defined by the equation $\frac{(x+1)^{2}}{9}+\frac{(y+3)^{2}}{16}=1$ . If necessary, round to the nearest tenth.
Answer Attempt 1 out of 2
Center: $\square$ , $\square$

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Problem 13316

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

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Problem 13317

Solve for $X$ in the equation, where $\left.\begin{array}{c} A=\left[\begin{array}{rrr} -2 & 3 & 1 \\ -5 & 0 & 2 \end{array}\right] \text { and } B=\left[\begin{array}{rrr} 0 & 4 & -2 \\ 3 & 0 & 3 \end{array}\right] . \\ 4 B=-2 X-2 A \\ X=\square \square \\ \square \end{array}\right] \Rightarrow$ ■

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Problem 13318

Type the correct answer in the box. Round your answer to the nearest integer.
A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of $5^{\circ}$ .
The vertical height that the train climbed is approximately $\square$ feet.

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Problem 13319

15. Solve the equation in the real number system. $x^{4}-2 x^{3}+6 x^{2}-18 x-27=0$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ ß. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type each answer only once.) B. The solution set is $\varnothing$ .

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Problem 13320

WeBWorK 5 - Topics 10 - 12: Problem 12 (1 point)
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent". $\int_{2}^{\infty} \frac{8}{(x+5)^{3 / 2}} d x=$ $\square$
Preview My Answers Submit Answers
You have attempted this problem 0 times.

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Problem 13321

Solve for $w$ . $(w+2)^{2}=2 w^{2}+11 w+16$
If there is more than one solution, separate them with commas.

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Problem 13322

4) Aşağıda verilen daire grafiği bir giyim mağazasında satılan 240 adet ơrünün dağılımını, sâtun grafiği ise eld len gelirin ürün çeșidine göre dağılımını gơstermektedir.
Graflk: Satilan Ürün Adetleri Graflk: Satılan Ūründen Elde Edilen Gelir
Yukarida verllen bllgllere göre mağazadan blr adet gōmlek ve pantolon alan blr kIṣl kaç Iira ōdemlṣ A) 100 B) 150 C) 200 D) $250^{\circ}$ 6. IHRACAT RAKAMLARI

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Problem 13323

lem 2.3 Jamar's class painted 50 square feet of a mural using 4 cans 0 paint.
On the previous screen, you said that Jamar's class could paint 12.5 square feet per can of paint and use 0.08 cans per square foot of the mural.
They want to paint a total of 310 square feet.
How many cans of paint will they need?

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Problem 13324

Fill in the blank so that the resulting statement is true. If $\log _{7}(x+5)=4$ , then $\qquad$ $=x+5$ .
If $\log _{7}(x+5)=4$ , then $\square$ $=x+5$ .

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Problem 13325

Fill in the blank so that the resulting statement is true. If $\log _{7}(x+5)=4$ , then $\qquad$ $=x+5$ .
If $\log _{7}(x+5)=4$ , then $\square$ $=x+5$ . $\square$

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Problem 13326

An artiot is hired to create an art display for the interior of a city building. The deplay is to span a total width of 11.5 yd. The artist decides to cover this space with equally sized portraits placed side-by-side in a horizontal line with no gaps. Each portrat has a width of 46 in. How many portraits will be used in the display?
First fill in the blanks on the left side of the equation using three of the ratios shomn. Then write your anewer on the right side of the equation.

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Problem 13327

Solve the following equation for $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ . $4 \cos 2 \theta=1$

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Problem 13328

At the grocery store, Abdullah purchased 3 pounds of mac and cheese for $\$ 7.50$ .
What does mac and cheese cost per pound? $\square$ How much mac and cheese does he get per dollar? $\qquad$ $\qquad$ $\square$
How much mac and cheese could Abdullah buy for $\$ 20$ ? $\square$ Submit

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Problem 13329

An 80.0 kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is: a. At rest b. Moving upward at a constant speed of $5.00 \mathrm{~m} / \mathrm{s}$ c. Moving downward at a constant speed of $5.00 \mathrm{~m} / \mathrm{s}$ d. Moving with an upward acceleration of $3.00 \mathrm{~m} / \mathrm{s} / \mathrm{s}$ e. Moving with a downward acceleration of $4.00 \mathrm{~m} / \mathrm{s} / \mathrm{s}$

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Problem 13330

Question 2 of 6
Austin received an invoice for $\$ 5,000$ that had payment terms of $\$ 4 / 15$ $n / 30$ . He made a partial payment of $\$ 2,500$ during the discount period. a. Calculate the amount credited. $\square$ Round to the nearest cent b. Calculate the balance on the invoice after the partial payment was made. $\square$ Round to the nearest cent

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Problem 13331

Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the $\log _{4}(x+11)-\log _{4}(x-4)=2$
Rewrite the given equation without logarithms. Do not solve for $x$ . $\frac{x+11}{x-4}=16$
Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to cor A. The solution set is $\square$ (Simplify your answer. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. There is no solution.

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Problem 13332

Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give the exact $\ln (x-5)+\ln (x+2)=\ln (x-14)$
Rewrite the given equation without logarithms. Do not solve for $x$ . $(x-5)(x+2)=x-14$
Solve the equation to find the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3. (Simplify your answer. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. There is no solution.

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Problem 13333

Han offe one test score with the score earned here. Please state what reak таке ноте тest 2) Solve the following equation for m. y = mx + b

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Problem 13334

A computer assembly firm purchases computer parts at $\$ 245$ per computer. The operating expenses are $28 \%$ on cost and rate of markup is $50 \%$ on cost. a. What is the selling price of each computer? $\square$ Round to the nearest cent b. What is the operating profit per computer? $\square$ Round to the nearest cent

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Problem 13335

3. In 2017 Rickard Rakell scored 26 goals after playing the first 53 games for the Anaheim Ducks. If the NHL season is 82 games long, and his scoring rate stayed consistent, how many goals can you expect Rakell to have scored by the end of the season?
4. In the year 2000 , there were approximately 500 million computers in use and it was projected that the amount of computers would increase at a rate of $10 \%$ each year. Based on this model, how many computers were in use in the year 2005? Round to the nearest millions of computers.

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Problem 13336

Solve. $|4 x-7|=8$

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Problem 13337

Carlton holds undeveloped land for investment. His adjusted basis in the land is $\$ 114,600$ , and the FMV is $\$ 191,000$ . On November 1 . 2023, he exchanges this land for land owned by his son, who is 31 years old. The appraised value of his son's land is $\$ 184,000$ with a basis of $\$ 170,000$ .
Required: a. Calculate Carlton's realized and recognized gain or loss from the exchange with his son and on Carlton's subsequent sale of the land to a real estate agent on July 19, 2024, for \$231,500. b1. Calculate Carlton's realized and recognized gain or loss from the exchange with his son if Carlton does not sell the land received from his son, but his son sells the land received from Carlton on July 19, 2024. b2. Calculate Carlton's basis for the land on November 1, 2023, and July 19, 2024 if Carlton does not sell the land received from his son, but his son sells the land received from Carlton on July 19, 2024. c. What could Carlton do to avoid any recognition of gain associated with the first exchange prior to his sale of the land?
Complete this question by entering your answers in the tabs below. \begin{tabular}{|l|l|l|l|} \hline $\operatorname{Req} A$ & Req B1 & Req B2 & Req C \\ \hline \end{tabular}
Calculate Carlton's realized and recognized gain or loss from the exchange with his son and on Carlton's subsequent sale of the land to a real estate agent on July 19, 2024, for \$231,500. Note: If no gain or loss is recognized, select "No gain or loss. \begin{tabular}{|l|l|l|} \hline \\ \hline & Amount \\ \hline \end{tabular}

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Problem 13338

Complète le tableau suivant. \begin{tabular}{|c|l|l|l|l|} \hline Équation & Foyer(s) & Sommet(s) & Centre & \begin{tabular}{c} Équation des asymptotes \\ ou de la directrice \end{tabular} \\ \hline $\frac{(x+2)^{2}}{16}+\frac{(y+1)^{2}}{25}=1$ & & $(-2,-1)$ & & \\ \hline $(x-3)^{2}=8(y+4)$ & & $(3,-4)$ & & \\ \hline $\frac{x^{2}}{36}-\frac{(y-4)^{2}}{64}=1$ & & $(0,2)$ & & \\ \hline \end{tabular}

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Problem 13339

$2(3 x+5)=10+4(2 x-3)$
Use the keypad to enter the answer in the box. $x=$

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Problem 13340

$2 x+12=4$

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Problem 13341

What is the basis of the new property in each of the following situations? What is the recognized gain or loss? Required: a. Rental house with an adjusted basis of $\$ 121,500$ exchanged for a personal-use river cottage with an FMV of $\$ 155,750$ . b. General Motors common stock with an adjusted basis of $\$ 26,000$ exchanged for Quaker Oats common stock with an FMV of \ $19,000. c. Land and building with an adjusted basis of$ \ $27,350$ used as a furniture repair shop exchanged for land and a building with an FMV of $\$ 57,900$ used as a car dealership. d. An office building with an adjusted basis of $\$ 23,800$ exchanged for a heavy-duty truck with an FMV of $\$ 29,950$ . Both properties are held for 100\% business purposes. e. A residential rental property held for investment with an adjusted basis of $\$ 265,150$ exchanged for a warehouse to be held for investment with an FMV of \$214,000. Note: For all requirements, if no gain or loss is recognized, select "No gain or loss". \begin{tabular}{|l|l|l|} \hline & & Amount \\ \hline a. & Basis of the new property & \\ \hline a. & & \\ \hline b. & Basis of the new property & \\ \hline b. & & \\ \hline c. & Basis of the new property & \\ \hline c. & & \\ \hline d. & Basis of the new property & \\ \hline d. & \\ \hline e. & Basis of the new property & \\ \hline e. & & \\ \hline \end{tabular}

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Problem 13342

11) 0.7515 moles of nitrogen gas and 0.1135 moles of methane gas are placed in a 171.6 ml container at $20.8^{\circ} \mathrm{C}$ . What is the partial pressure (atm) of nitrogen gas? A) 1.14 B) 0.473 C) 16.0 D) 106 E) 226

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Problem 13343

2) Prove the following identities $\operatorname{arcos}(\pi+\theta)=2 \cos ^{2} \theta-1$

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Problem 13344

Cheese production in a country is currently growing at a rate of $4 \%$ per year. The equation $y=8.3(1.04)^{x}$ models the cheese production in the country from 2003 to 2009. In this equation, $y$ is the amount of cheese produced, in billions of pounds, and x represents the number of years after 2003. a. Estimate the total cheese production in the country in 2007. b. Assuming this equation continues to be valid in the future, use the equation to predict the total amount of cheese produced in the country in 2016. a. The total cheese production in the country in 2007 was about 9.7 billions of pounds. (Round to the nearest tenth as needed.) b. The total cheese production in the country in 2016 will be about $\square$ billions of pounds. (Round to the nearest tenth as needed.)

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Problem 13345

Lewis owns 200 shares of stock in Modlin Corporation. His adjusted basis for the stock is $\$ 185,250$ . On December 15,2023, he sells the stock for $\$ 173,500$ . He purchases 200 shares of Modlin Corporation stock on January 8, 2024, for \$173,500.
Required: a. What are Lewis's realized and recognized gain or loss on the sale? b. What is Lewis's adjusted basis for the 200 shares purchased on January 8, 2024? c. How would your answers in parts (a) and (b) change if he purchased only 100 shares for \$107,800 in January? Note: For all requirements, if no gain or loss is recognized, select "No gain or loss". \begin{tabular}{|l|l|l|} \hline & & Amount \\ \hline a. & & \\ \hline a. & & \\ \hline b. & Adjusted basis of shares & \\ \hline c. & & \\ \hline c. & & \\ \hline c. & Adjusted basis of shares & \\ \hline \end{tabular}

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Problem 13346

A 2.00 L container is filled with $\mathrm{Ar}(\mathrm{g})$ at 752 mmHg and $35^{\circ} \mathrm{C}$ . A 0.728 g sample of $\mathrm{C}_{6} \mathrm{H}_{6}$ vapor is then added. a) What is the total pressure in the container? (b) What is the partial pressure of Ar and of $\mathrm{C}_{6} \mathrm{H}_{6}$ ?

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Problem 13347

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{-3 y}=5$

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Problem 13348

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{y-3}=9$

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Problem 13349

Select the correct answer.
What value of $x$ satisfies $\cot \left(90^{\circ}-x\right)=-\frac{\sqrt{3}}{3} ?$ A. $120^{\circ}$ B. $240^{\circ}$ C. $210^{\circ}$ D. $150^{\circ}$

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Problem 13350

If: $13 \operatorname{Sin}\left(90^{\circ}-\theta\right)-5=0$ then: $\cos \theta=\ldots \ldots \ldots$ (a) $\frac{12}{13}$ (b) $-\frac{12}{13}$ (c) $-\frac{5}{13}$ (d) $\frac{5}{13}$
بقية الأسنلة فى الصفحة التالية

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Problem 13351

(9) If : $\cos \frac{20^{\circ}+\theta}{2}=\sin \frac{40^{\circ}+\theta}{2}, 0^{\circ}<\theta<90^{\circ}$ then $\theta=$ $\qquad$ (a) $60^{\circ}$ (b) $45^{\circ}$ (c) $30^{\circ}$ (d) $20^{\circ}$ (10) If the ratio between areas of two similar triangles equals $9: 25$ and the pe the smaller triangle is 60 cm then the perimeter of the greater triangle equals (a) 60 (b) 80 (c) 100 (d) 120

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Problem 13352

Avery and Collin were trying to challenge each other with equations for sequences. Avery was looking at an explicit equation that Collin wrote. $t(n)=4.5 n-8$ a. Write the first 4 terms for the sequence. b. What would Avery do to write the $15^{\text {th }}$ term of this sequence? c. Write a recursive equation for this sequence.

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Problem 13353

Given that $I_{0}=10^{-12}$ watts/meter ${ }^{2}$ , what is the intensity of a sound for which the decibel level of the sound measures 99 ? Round off your answer to three decimal places.
Answer How to enter your answer (opens in new window) Keyboard Sh $\square$ watts/meter ${ }^{2}$

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Problem 13354

11 What is the perimeter of an equilateral triangle with a height of 6 feet? \begin{tabular}{|c|c|c|c|} \hline a & $2 \sqrt{3}$ & b & $6 \sqrt{3}$ \\ \hline c & $12 \sqrt{3}$ & d & $4 \sqrt{3}$ \\ \hline \end{tabular}

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Problem 13355

Date: Name: $\qquad$ $\qquad$ RECOGNIZING STRUCTURE TO SOLVE TWO STEP EQUATIONS N-GEN MATH ${ }^{\text {(8) }} 7$ HOMEWORK
Fluency
1. Which of the following is the solution to: $5(x+7)=50$ ? (1) $x=1$ (3) $x=3$ (2) $x=8$ (4) $x=11$
2. Which value below solves the equation: $\frac{n-6}{2}=4$ ? (1) $n=10$ (3) $n=8$ (2) $n=14$ (4) $n=7$
3. Solve each of the following equations in two different ways: (1) by reversing the order of operations and (2) by using the distributive property to simplify the left-hand side. (a) $5(x+3)=45$
Method (1) Method (2) (b) $3(n-7)=27$
Method (1) Method (2) N-Gen Matis 7, Unit 6-Linear Equations and Inequalties - Lesson 5 eMATHinstruction, RED HooK, NY 12571, 02020

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Problem 13356

2 Дервен өнцегтийн өнцгүүд 1:5:2:4 харыцатай бол өнцег тус бүрийн хэмжәэг ar.

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Problem 13357

7. The largest interval in which a solution of the IVP $y^{\prime}+(\ln t) y=\tan t, \quad y\left(\frac{\pi}{4}\right)=1$ is certain to exist is (a) $\left(0, \frac{\pi}{2}\right)$ (b) $(0, \pi)$ (c) $(0,1)$ . (d) $(1, \infty)$

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Problem 13358

4 Хоёр машины нэг нь нөгөөгөөс 20\%-оор их хурдтай бол машинуудын хурдны харьцааг олоорой. Хэрэв нэг машин нь 60 км/ц хурдтай бол нөгөө машин ямар хурдтай байх вэ?

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Problem 13359

2. The integral $\int \sin (x) \sin (3 x) d x$ can be solved by trigonometric identity: a. $\frac{\sin (-2 x)+\sin (4 x)}{2}$ b. $\frac{\cos (2 x)-\cos (4 x)}{2}$ c. $\frac{\sin (-2 x)-\sin (4 x)}{2}$ d. None

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Problem 13360

TICE TEST
21 Mark for Review
In the $x y$ -plane, line $\ell$ passes through the point $(0,0)$ and is parallel to the line represented by the equation $y=8 x+2$ . If line $\ell$ also passes through the point $(3, d)$ , what is the value of $d$ ? $\square$
Answer Preview: $\square$ Show Keypad

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Problem 13361

mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=685494365\&questionld=1\&flushed=false\&cld=8051021\&back=DoAssignments.aspx?view=h... Finish update ne MATH 1414 College Algebra - Oct. 15 through Dec. 13, 2024 Anthony Reyes Homework: 10.1 Homework Question 2, 10.1.3 HW Score: 6.25\%, 1 of 16 points Save estion list
Question 1
Question 2
Question 3
Question 4
Question 5
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Question 7
Graph the ellipse and locate the foci. $\frac{x^{2}}{25}+\frac{y^{2}}{64}=1$
Choose the correct graph below. A. B. c. D.

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Problem 13362

minules.
1. Peter. Tom, and Carl simultancously shoot at a target. Peter hits the target with a probability of $1 / 2$ . Tho with a probability of $2 / 3$ , and Carl with a probability of $3 / 4$ . a) Assume that only one of them hit the target. What is the probability that it was Carl? b) What is the most likely number of hits on the larget? Determine the expected vilue of the uumber hits.

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Problem 13363

(40) صحة اعتّاد صاحب المصنع من عدمه عند مستوى الدلالة الإجابة:

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Problem 13364

EXERCICE 2 (04 points) Un jeune agriculteur décide de pratiquer de la culture sous serre dans son champ. A cet effet, il choisit dans son plan de représentation un repère orthonormal $(O ; \vec{u}, \vec{v})$ . Il place dans ce repère deux points $A$ et $B$ dont les affixes respectives $z_{A}$ et $z_{B}$ sont des racines du polynôme $P$ défini par: $P(z)=2 z^{3}-3(1+i) z^{2}+4 i z+1-i, \text { où } z \in C .$
Son objectif est de pratiquer sa culture sous serre dans l'ensemble ( $E$ ) des points $M$ de son plan de représentation tels que $\|\overrightarrow{M A}+\overrightarrow{M B}+2 \overrightarrow{M O}\| \leq 2$ , qui contient un point du segment $[A B]$ . 1) Vérifier que 1 et $i$ sont des racines de $P$ . 2) Déterminer le polynôme $g$ tel que $P(z)=(z-1)(z-i) g(z)$ . 3) Résoudre dans $\mathbb{C}$ l'équation $P(z)=0$ . (0,5 pt) (0,5 pt) (0,5 pt) 4) On pose $z_{A}=1, z_{B}=i$ et $z_{C}=\frac{1}{2}+\frac{1}{2} i$ . a) Placer les points $A, B$ et $C$ d'affixes respectives $z_{A}, z_{B}$ et $z_{C}$ dans le repère orthonormal $(O ; \vec{u}, \vec{v})$ en choisissant comme unite graphique 4 cm . ( $0,75 \mathrm{pt}$ ) b) Démontrer que $C$ est le milieu de $[A B]$ , puis que $C$ appartient à l'ensemble $(E)$ ., ( $0,5 \mathrm{pt}$ ) c) Déterminer l'affixe $z_{G}$ du point $G$ barycentre du système $\{(A, 1) ;(B, 1) ;(0,2)\}$ , puis placer $G$ . ( $0,5 \mathrm{pt}$ ) 5) Déterminer puis construire l'ensemble ( $E$ ) des points $M$ du plan tels que $\|\overrightarrow{M A}+\overrightarrow{M B}+2 \overrightarrow{M O}\| \leq 2$ ( $0,5 \mathrm{pt}$ ) 6) Le jeune agriculteur atteindra-t-il son objectif? ( $0,25 \mathrm{pt}$ )

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Problem 13365

16. The Euler differential equation $x^{2} y^{\prime \prime}+5 x y^{\prime}+3 y=0, \quad y(1)=1, \quad y^{\prime}(1)=0$ has a solution (a) $y(t)=-\frac{1}{2} x^{-3}+\frac{3}{2} x^{-1}$ (b) $y(t)=x^{-1} \ln x$ (c) $y(t)=x^{-3}(1+2 \ln x)$ (d) $y(t)=x^{-3}+2 \ln x$

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Problem 13366

47 Em relação a um referencial ortonormado Oxy considera a circunferência de centro em $A(0,3)$ e que passa em $B(3,-1)$ . 47.1. Seja $r$ a reta que é tangente à circunferência no ponto $B$ . Representa a reta $r$ por uma equação na forma reduzida. 47.2. Considera o conjunto dos pontos $P(x, y)$ que satisfazem a condição $\overrightarrow{A B} \cdot \overrightarrow{B P}=0$ . Representa essa condição por uma equação e resolve-a em ordem a $y$ . 140

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Problem 13367

Write the following equation in its equivalent logarithmic form. $\sqrt[3]{64}=4$
The equation in logarithmic form is $\square$ (Type an equation.)

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Problem 13368

Q3. A car of mass 800 kg is travelling along a straight horizontal road. A constant retarding force of FN reduces the speed of the car from $18 \mathrm{~ms}^{\wedge}-1$ to $12 \mathrm{~ms}^{\wedge}-1$ in 2.4 s . Calculate: (a) the value of $F$
Answer: $\square$

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Problem 13369

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

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Problem 13370

2. A store is to be built within a rectangular lot. The lot measures 70 m by 45 m . A lawn of uniform width, equal to the area of the store, must surround the store and be within the boundaries of the lot. How wide is the strip of lawn, to the nearest tenth? ( 6 marks)

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Problem 13371

10. $11 k+2=24$

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Problem 13372

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

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Problem 13373

Q1: For some event $A$ with $P(A)=0.1$ then $P(A \mid \Omega)+P(\phi \mid \Omega)+P(\Omega \mid A)=$ A) 0.1 B) 1.2 C) 2.3 D) 1.1 E) None
Q2: Let $X$ be a random variable with $E(X)=1$ and $E\left(X^{10}+X\right)=2$ Then $E\left(X^{10}\right)=$ A) 0 B) 1 C) 2 D) 3 E) None
Q3: For $x>0$ we have $u(x)+3 \delta(y)=$ A) 1 B) 2 C) 3 D) 4 E) None
Q4: For $R_{X Y}=\{(0,0),(1,1)\}$ , if $f(0,0)=0.2$ and $f(1,1)=0.8$ . Then $E(X Y)=$ A) 1 B) 0.2 C) 0.8 D) 0.7 E) None
Q5: For some disjoint events $A, B$ with $P(A)=0.2$ and $P(B)=0.4$ , we have $P(A \cup B)=$ A) 0.2 B) 0.3 C) 0.4 D) 0.6 E) None
Q6: If $P(A)=0.2$ and $P(\bar{A} \cap B)=P(\bar{B} \cap A)$ , then $P(B)=$ A) 0.1 B) 0.2 C) 0.4 D) 0.6 E) None
Q7: $\int_{-\infty}^{\infty} x^{3} \delta(x+1) d x=$ A) -1 B) 8 C) -8 D) 1 E) None

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Problem 13374

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS:

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Problem 13375

(12) Let $y_{1}$ and $y_{2}$ be two solutions of the DE $t^{2} y^{\prime \prime}-t(t+1) y^{\prime}+y=0, \quad t>0 .$
If $W\left(y_{1}, y_{2}\right)(2)=2 \mathrm{e}^{2}$ , then $W\left(y_{1}, y_{2}\right)(-1)=$ (a) -e (b) $\mathrm{e}^{-1}$ (c) $e^{2}$ (d) $-\mathrm{e}^{-1}$ (e) $e$

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Problem 13376

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: $\qquad$

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Problem 13377

4. Solve the equation $\sin (8 x)=\sin (7 x) \cos (x)$ for $x \in(0, \pi)$ .
ANS:

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Problem 13378

5. If a savings account offers a nominal interest rate of $3 \%$ per year, compounded every four months, then how many years will it take for a deposit to double in value?
ANS:

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Problem 13379

$(-4)+(-5)=-9$

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Problem 13380

Consider the line with the equation: $y=x+10$ Give the equation of the line parallel to Line 1 which passes through $(8,6)$ : $\square$ Give the equation of the line perpendicular to Line 1 which passes through $(8,6)$ : $\square$

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Problem 13381

ANS: $x \in(1,5) \cup 18 ;+$
3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS: $N=10$

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Problem 13382

Leah Hernandez-Matute 8 of 12 Next
Your Favorite Mistake It takes 20 tomato slices to make 2 of Ivan's pizzas.
Two students made a mistake when making 6 pizzas.
Select your favorite mistake.
Ivan (120 slices) Jada (24 slices)
What advice would you give to Ivan?
Jada: 24 slices

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Problem 13383

A multiple choice quiz has three questions, each with five answer choices. Only one of the choices is correct. You have no idea what the anwer is to any question and have to guess each answer.
2 Numeric 1 point What is the probability of answering the first question correctly?
Type your answer...
3 Numeric 2 points What is the probability of answering the first two questions correctly?
Type your answer...
4 Numeric 2 points What i the probability of answering all three questions correctly? Type your answer...

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Problem 13384

Jack is a banker who enjoys having fun with friends after work. The team will usually meet at a beer bar joint to drink and eat kebab. Jack will usually eat 5 sticks of pork kebab and drink three jugs ( 750 ml is volume of the jug) of beer. His caloric needs for the day is 1800 Calories as a young man.
Analysis of the kebab shows each contains 5 grams fat.
Calculate the \% fat contribution of the fat from the kebab to his daly energy needs.
If 100 g of beer contains 43 Cal , and assuming a jug of 750 mls is equivalent to 750 g . Calculate total energy he consumed while with friends.

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Problem 13385

Q15: For $X \sim B(n, p)$ we have $\operatorname{Var}(X)=0.8 E(X)$ . Find $p$

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Problem 13386

8. a) A stationer buys 1 dozen of pens at Rs 20 each and sells them at Rs 25 each. (ii) Find the cost price and selling price of 1 dozen of pens. (ii) How much profit does he make in 1 dozen of pens. (iii) Express his profit into profit percent. (iv) If he had given Re 1 discount in each pen, what would be his profit percent? b) A grocer purchased 5 dozen of eggs at Rs 12 each. 10 eggs were broken and he sold the remaining eggs at Rs 14 each. (i) Find the cost price of total number of eggs and the selling price of the remaining number of eggs. (ii) Calculate his profit or loss and express it in percent. (iii) If non of the eggs were broken, how much profit or loss percent would he make? c) A fruit seller sold 50 kg of oranges at the rate of Rs 80 per kg and gained Rs 800. (i) Find the selling price of 50 kg of oranges. (ii) At what rate of price did he buy the oranges? (iii) Calculate his profit percent.
1 kg d) A vegetable seller purchased 1 quintal of potatoes at Rs 35 per kg and sold at a loss of Rs $\mathbf{3 5 0}$ . Find: (i) the rate of selling price (ii) Loss percent.

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Problem 13387

12. Numa experiência, Acontecimento é um subconjunto do espaço amostral. Diz-se que um Acontecimento é elementar se é constituído por... A um único resultado. C todos os elementos. B mais do que um resultado. D nenhum elemento.
13. Quantos elementos terá o espaço amostral de uma experiência que consiste em lançar três dados de cores diferentes e registar os resultados obtidos nas faces superiores? A 124 (B) 216
C 432 D 648
14. A probabilidade de ganhar uma bicicleta numa rifa de 100 bilhetes da qual você comprou 4 é...
A $\frac{1}{100}$ B $\frac{1}{50}$ (C) $\frac{1}{25}$
D $\frac{1}{10}$
15. Qual é a probabilidade de obter pelo menos uma cara no lançamento de três moedas?
A $\frac{7}{8}$ B $\frac{5}{8}$ C $\frac{3}{8}$ (D) $\frac{1}{8}$
16. Uma sucessão de termo geral $\boldsymbol{a}_{\boldsymbol{n}}$ é estritamente crescente se para $\forall \boldsymbol{n} \in \mathbb{N}$ ... (A) $a_{n+1}>a_{n}$
B $a_{n+1}<a_{n}$ C $a_{n+1} \leq a_{n}$ D $a_{n+1} \geq a_{n}$
17. Qual é o termo geral de uma progressão geométrica cuja razão é 2 e $u_{2}=3$ ?
A $u_{n}=3 \cdot 2^{n-1}$ B $u_{n}=2 \cdot 3^{n-1}$ (C) $u_{n}=3 \cdot 2^{n-2}$
D $u_{n}=2 \cdot 3^{n-2}$
18. Quais são os primeiros seis termos da sucessão $u_{n}=2 n-1$ ?
A $\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}$ ... C $0,2,4,6,8,10,12 \ldots$ B $-1,1,3,5,7,9, \ldots$ (D) $1,3,5,7,9,11 \ldots$
19. Numa sucessão de termo geral $a_{n}=\frac{2 n^{2}+5}{5}$ , o décimo termo é...
A 40 (B) 41
C 42 D 43
20. Qual é $4^{\circ}$ termo de uma Progressão Geométrica, cujo primeiro termo é -4 e a razão é 2 ?
A - 128 B -64 (C) -32
D -16

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Problem 13388

Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field $F=6 x i-2 y j$ . Take the domains of integration in each case to be the disk $R: x^{2}+y^{2} \leq a^{2}$ and its bounding circle $C$ : $r=(a \cos t) i+(a \sin t) j, 0 \leq t \leq 2 \pi$ . i Click here for the two forms of Green's Theorem.
The flux is $\square$ (Type an exact answer, using $\pi$ as needed.)

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Problem 13389

Graph the line $y=1$ .

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Problem 13390

Calculator
Solve for $x$ in this figure. Enter your answer in the box. $x=$

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Problem 13391

EXERCICE 12 Soit le polynôme complexe $\mathrm{P}(\mathrm{z})$ de la variable complexe z $P(z)=z^{3}-(7+9 i) z^{2}+(39 i-14) z+50$
1-Montrer que l'équation $\mathrm{P}(\mathrm{z})=0$ admet une racine $\mathrm{z}_{0}$ imaginaire pure. 2- Résoudre l'équation $\mathrm{P}(\mathrm{z})=0$ . On notera $\mathrm{z}_{1}$ la racine non imaginaire pur ayant la plus petite partie réelle et $\mathrm{z}_{2}$ la troisième. 3-Dans le plan affine euclidien rapporté au repère ( $\mathrm{o}, \mathrm{i}, \mathrm{j}$ ) orthonormé on considère les points $\mathrm{A}, \mathrm{B}$ , et C d'affixes respectives $\mathrm{z}_{0} ; \mathrm{z}_{1} ; \mathrm{z}_{2}$ . Déterminer et construire l'ensemble des points M du plan tels que : $\mathrm{MA}^{2}-\mathrm{MB}^{2}+\mathrm{MC}^{2}=4$ .

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Problem 13392

For the triangle shown below, use your calculator to solve for the missing sides and angles. $\theta=$ $\square$ degrees $f=$ $\square$ $e=$ $\square$ Round your answers to two decimal places. Question Help: Video 1 Video 2

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Problem 13393

8. 11. The conductance of a wire is $2,5 \mathrm{~S}$ . Another wire of the same material and at the same temperature has a diameter one-forth as great and the length twice as great. Find the conductance of the second wire. Ans. $78,1 \mathrm{mS}$ .

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Problem 13394

14. 17. Find the temperature coefficient of resistance of iron at $20^{\circ} \mathrm{C}$ , if iron has an inferred zero resistance temperature $-162^{\circ} \mathrm{C}$ ? Ans $0,00551 /{ }^{\circ} \mathrm{C}-$

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Problem 13395

Graph each equation. 5) $y=x^{2}-2 x-3$
Identify the $\min / \max$ value of each. Th

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Problem 13396

Problem 8. An e.m.f. of 250 V is connected across a resistance and the current flowing through the resistance is 4 A . What is the power developed? Ans. 1 kW.

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Problem 13397

Exercice 8 : 1) Annoter le schéma suivant 2) Au de la synthèse de l'eau on mélange $60 \mathrm{~cm}^{3}$ de dioxygène et de dihydrogène. Après passage d'une étincelle électrique il reste $15 \mathrm{~cm}^{3}$ de dioxygène dans l'eudiomètre a) Quel est le volume de gaz disparu ? b) Quel est le volume dioxygène disparu? c) Quel est le volume dihydrogène disparu?
Exercice 9: Une salle de théâtre à la forme d'un cône dont le diamètre est de 10 m et de hauteur 7 m 1) Calcule le volume d'air dans la salle de théâtre ( $V=\pi r^{2} h$ ) 2) Calcule les volumes des gaz majoritaires dans cette salle (le volume de dioxygène et diazote)

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Problem 13398

3. Find the missing measures.

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Problem 13399

6. $\angle 1$ and $\angle 2$ form a linear pair. If $m \angle 1=(5 x+9)^{\circ}$ and $m \angle 2=(3 x+11)^{\circ}$ , find the measure of each angle.

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Problem 13400

31. The sum of two numbers is 37 . One number is 5 more than the other. Find the numbers.

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Equation

Problem 13301

1) assume that you bought a stock for $50\$ 50$50. If you sold the stock for $60\$ 60$60 and you got $2\$ 2$2 divider What was your annual return?

Problem 13302

Write the standard form of the equation of the circle with the given center and radius. Center (−7,2),r=5(-7,2), r=5(−7,2),r=5

Problem 13303

Problem 13304

Problem 13305

5=5(4n−1)35=\frac{5(4 n-1)}{3}5=35(4n−1)​

Problem 13306

Problem 13307

Problem 13308

Solve the equation. * 5x−6=295 x-6=295x−6=29 x=3x=3x=3 x=5x=5x=5 x=7x=7x=7 x=9x=9x=9

Problem 13309

Solve. 5.4=−t7.5t=\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}5.4t​=−7.5t​=​

Problem 13310

Find the missing side.Round to the nearest tent

Problem 13311

Solve the equation. * 3x+8=23 x+8=23x+8=2 x=−4x=-4x=−4 x=−2x=-2x=−2 x=2x=2x=2 x=4x=4x=4

Problem 13312

Find the missing side.

Problem 13313

Tammy's take-home pay is $800\$ 800$800 a month. 7%7 \%7% of her take-home pay is spent on her cell phone bill. How much is Tammy's monthly cell phone bill? A. $109\$ 109$109 B. $69.99\$ 69.99$69.99 C. \56D.56 D. 56D.\76 7676

Problem 13314

Problem 13315

Find the center of the ellipse defined by the equation (x+1)29+(y+3)216=1\frac{(x+1)^{2}}{9}+\frac{(y+3)^{2}}{16}=19(x+1)2​+16(y+3)2​=1. If necessary, round to the nearest tenth.Answer Attempt 1 out of 2Center: □\square□ , □\square□

Problem 13316

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. x=x=x= Question Help: Video

Problem 13317

Problem 13318

Type the correct answer in the box. Round your answer to the nearest integer.A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of 5∘5^{\circ}5∘.The vertical height that the train climbed is approximately □\square□ feet.

Problem 13319

Problem 13320

Problem 13321

Solve for www. (w+2)2=2w2+11w+16(w+2)^{2}=2 w^{2}+11 w+16(w+2)2=2w2+11w+16If there is more than one solution, separate them with commas.

Problem 13322

Problem 13323

Problem 13324

Fill in the blank so that the resulting statement is true. If log⁡7(x+5)=4\log _{7}(x+5)=4log7​(x+5)=4, then \qquad =x+5=x+5=x+5.If log⁡7(x+5)=4\log _{7}(x+5)=4log7​(x+5)=4, then □\square□ =x+5=x+5=x+5.

Problem 13325

Fill in the blank so that the resulting statement is true. If log⁡7(x+5)=4\log _{7}(x+5)=4log7​(x+5)=4, then \qquad =x+5=x+5=x+5.If log⁡7(x+5)=4\log _{7}(x+5)=4log7​(x+5)=4, then □\square□ =x+5=x+5=x+5. □\square□

Problem 13326

Problem 13327

Solve the following equation for θ\thetaθ in the interval [0∘,360∘)\left[0^{\circ}, 360^{\circ}\right)[0∘,360∘). 4cos⁡2θ=14 \cos 2 \theta=14cos2θ=1

Problem 13328

Problem 13329

Problem 13330

Problem 13331

Problem 13332

Problem 13333

Han offe one test score with the score earned here. Please state what reak таке ноте тest 2) Solve the following equation for m. y = mx + b

Problem 13334

Problem 13335

Problem 13336

Solve. ∣4x−7∣=8|4 x-7|=8∣4x−7∣=8

Problem 13337

Problem 13338

Problem 13339

2(3x+5)=10+4(2x−3)2(3 x+5)=10+4(2 x-3)2(3x+5)=10+4(2x−3)Use the keypad to enter the answer in the box. x=x=x=

Problem 13340

2x+12=42 x+12=42x+12=4

Problem 13341

Problem 13342

11) 0.7515 moles of nitrogen gas and 0.1135 moles of methane gas are placed in a 171.6 ml container at 20.8∘C20.8^{\circ} \mathrm{C}20.8∘C. What is the partial pressure (atm) of nitrogen gas? A) 1.14 B) 0.473 C) 16.0 D) 106 E) 226

Problem 13343

2) Prove the following identities arcos⁡(π+θ)=2cos⁡2θ−1\operatorname{arcos}(\pi+\theta)=2 \cos ^{2} \theta-1arcos(π+θ)=2cos2θ−1

Problem 13344

Problem 13345

Problem 13346

Problem 13347

Solve for yyy in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. e−3y=5e^{-3 y}=5e−3y=5

Problem 13348

Solve for yyy in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. ey−3=9e^{y-3}=9ey−3=9

Problem 13349

Select the correct answer.What value of xxx satisfies cot⁡(90∘−x)=−33?\cot \left(90^{\circ}-x\right)=-\frac{\sqrt{3}}{3} ?cot(90∘−x)=−33​​? A. 120∘120^{\circ}120∘ B. 240∘240^{\circ}240∘ C. 210∘210^{\circ}210∘ D. 150∘150^{\circ}150∘

Problem 13350

Problem 13351

Problem 13352

Problem 13353

Problem 13354

1) assume that you bought a stock for $\$ 50$ . If you sold the stock for $\$ 60$ and you got $\$ 2$ divider What was your annual return?

Write the standard form of the equation of the circle with the given center and radius. Center $(-7,2), r=5$

$5=\frac{5(4 n-1)}{3}$

Solve the equation. * $5 x-6=29$ $x=3$ $x=5$ $x=7$ $x=9$

Solve. $\begin{aligned} 5.4 & =-\frac{t}{7.5} \\ t & = \end{aligned}$

Find the missing side.
Round to the nearest tent

Solve the equation. * $3 x+8=2$ $x=-4$ $x=-2$ $x=2$ $x=4$

Tammy's take-home pay is $\$ 800$ a month. $7 \%$ of her take-home pay is spent on her cell phone bill. How much is Tammy's monthly cell phone bill? A. $\$ 109$ B. $\$ 69.99$ C. \ $56 D.$ \ $76$

Find the center of the ellipse defined by the equation $\frac{(x+1)^{2}}{9}+\frac{(y+3)^{2}}{16}=1$ . If necessary, round to the nearest tenth.
Answer Attempt 1 out of 2
Center: $\square$ , $\square$

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

Type the correct answer in the box. Round your answer to the nearest integer.
A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of $5^{\circ}$ .
The vertical height that the train climbed is approximately $\square$ feet.

Solve for $w$ . $(w+2)^{2}=2 w^{2}+11 w+16$
If there is more than one solution, separate them with commas.

Fill in the blank so that the resulting statement is true. If $\log _{7}(x+5)=4$ , then $\qquad$ $=x+5$ .
If $\log _{7}(x+5)=4$ , then $\square$ $=x+5$ .

Fill in the blank so that the resulting statement is true. If $\log _{7}(x+5)=4$ , then $\qquad$ $=x+5$ .
If $\log _{7}(x+5)=4$ , then $\square$ $=x+5$ . $\square$

Solve the following equation for $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ . $4 \cos 2 \theta=1$

Solve. $|4 x-7|=8$

$2(3 x+5)=10+4(2 x-3)$
Use the keypad to enter the answer in the box. $x=$

$2 x+12=4$

11) 0.7515 moles of nitrogen gas and 0.1135 moles of methane gas are placed in a 171.6 ml container at $20.8^{\circ} \mathrm{C}$ . What is the partial pressure (atm) of nitrogen gas? A) 1.14 B) 0.473 C) 16.0 D) 106 E) 226

2) Prove the following identities $\operatorname{arcos}(\pi+\theta)=2 \cos ^{2} \theta-1$

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{-3 y}=5$

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{y-3}=9$

Select the correct answer.
What value of $x$ satisfies $\cot \left(90^{\circ}-x\right)=-\frac{\sqrt{3}}{3} ?$ A. $120^{\circ}$ B. $240^{\circ}$ C. $210^{\circ}$ D. $150^{\circ}$

11 What is the perimeter of an equilateral triangle with a height of 6 feet? \begin{tabular}{|c|c|c|c|} \hline a & $2 \sqrt{3}$ & b & $6 \sqrt{3}$ \\ \hline c & $12 \sqrt{3}$ & d & $4 \sqrt{3}$ \\ \hline \end{tabular}

Write the following equation in its equivalent logarithmic form. $\sqrt[3]{64}=4$
The equation in logarithmic form is $\square$ (Type an equation.)

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

10. $11 k+2=24$

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS: