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First 700 kWh or less a 0.06S0/k Wh Over 700 k Wh : 0.0530/k Wh73. State income tax: Table 5 shows slale ineome tax rales for married couples filing joimt return in...

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First 700 kWh or less a 0.06S0/k Wh Over 700 k Wh : 0.0530/k Wh73. State income tax: Table 5 shows slale ineome tax rales for married couples filing joimt return in Louisiana. Wrile a piecewise delinition dor T(a) , the tax due On a taxable income of A dollars (B) Graph T(+)_ Find the tax due 0n a taxable income of $55,000. Of SHO,OOO.Table 5 Louisiana State Income Tax Married filing jointly or qualified surviving spouse: Over But not over Tax due is SO S25,000 29 of taxable income S25,000 SIOO,

First 700 kWh or less a 0.06S0/k Wh Over 700 k Wh : 0.0530/k Wh 73. State income tax: Table 5 shows slale ineome tax rales for married couples filing joimt return in Louisiana. Wrile a piecewise delinition dor T(a) , the tax due On a taxable income of A dollars (B) Graph T(+)_ Find the tax due 0n a taxable income of $55,000. Of SHO,OOO. Table 5 Louisiana State Income Tax Married filing jointly or qualified surviving spouse: Over But not over Tax due is SO S25,000 29 of taxable income S25,000 SIOO,O00 SS00 plus 4% of excess over $25,000 S100,000 S3,500 plus 6% of excess over Sioo,000 78



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A power company charges one household $\$ 0.12$ per kilowatt-hour $(\mathrm{kWh})$ and $\$ 14.89$ in monthly taxes.
a. Write a formula for the monthly charge $C$ for this household if it uses $k$ kilowatt-hour. b. Compute the monthly charge if the household uses $1200 \mathrm{kWh}$

Hello. Everyone in this problem it is given in are also different. Appliances are used. We are giving it. Get it? He get above it. 1.5 over. He did us for three over. Birdie four 100 for electric lamp. That is quite full clue. What? Electric lamp used foot, six hours party. All right. Three crew aboard electric school used for one. Quite pull over. Blurting Miss Milius however, convention in our hoses Glove What for? But our daily okay, Him course stop Electricity is why was you know $5 butter global over that in the first part We have to calculate what's stopping at the city of it. God stop course for electricity of it over a month off 30 days and in second. But we have to fight the mass of the port us and it produced 7000 You know salario energy. But Katie, I'm every since you up Power plant is 35%. No, we start solving it first we saw the first part the first part Total energy consumed in a month in a month we will cooperate, Include whatever on it is to find us father into okay in tow number of bits. That is 30 no b but into David Plus we do into NATO 33 in Tokyo. A trick plus before in two people 2 30 Now we are going to substitute the value we want is given. But when it grew, what time is three others? We do it quite fully. Group work and time is six hours G is three book robot and time is one point foot people. It is Google over and time it's But the more off dates back is 30 in a month. So this will be in clover cover when you solve it. Total contention off energy will be for 20 killer, but over 4 20 Robot over. No, we will estimate the cost off. Will course. Stop electricity of it. It's gonna be number off. No, but our that is for 20 and go Stop. But you know what? Over 10 fight. So it will be in dollar 44 point. What doughnut? What? This is the answer off first park. Now we have to solve for second part in second part. We have to calculate possible record required in a month, and Anderson Energy specifications is and already produced by the port. It's give it seven closing low calorie park egy. So we will convert it and to do so, do you one calorie is four point Do do so this will be you will perk aging Then you simplify you will get But I didn't save it I can't do the power six doing marketing Total energy require in a month be a major total energy required in a bun to be happy major for 20 No, but over this could be converted into do and Buddy Global Our is 3.6 into tend to give our six doing every sensi off The power plant is 35% If you dont believe output brother output energy You bet Goodbye and put energy cross Multiply it now if we substitute seven be required output energy to be for 20 into 3.6 and tend to devour six f decencies 35% the 3500 And if MPD off required then peuple energy releases on simplify Marsa Purple required is in 200 beauty This is the under part. This problem Thank you

Possibility. Read Option and sealed production is 50% reduction Siriporn one fight off carded carbon dioxide usage, which can be given by he's electricity. Gonzi um March Bradby amount are year. Thus alternative free are used. My son died by a mound bar Gavin This is a model for gathering as well. So that will come out of the 0.15 times 14,000 kiddo. What our far year. My spite by 1.54 following mass. But you know what? Our thus 900 gather for a year. Dives 26 point for bound mass part of gather in so Catholic In this we have to aboard 15 times 45,000 3 20 Katie off carbon dioxide. But year it was 67 6 800 found mass off that would excite bon year

We'll start by calculating the consumption. Each appliance starting with, uh, heater. I have 1.8 kilowatt and two hours per day. So this gives me 3.6 kilowatt. Our birthday. Next. The balls. I have four bulbs. Uh, you're going at 0.1 kilowatt and they're going for six hours a day. Give me a total of 2.4. You know what? Over per day? The Stoke and Zooms three. Cuba. What kind of runs? One hour every day. This gives three kilowatt hour pretty and miss. A lean use is to have a lot of power. That's perfect. So adding all those up we use 11 kilowatt hour per day aunt and a 30 day month with electricity costing zero point ones. Your $5 particular white power ones. You're dollars per cure our 30 these a month and I consume 11 Q a lot over her bay. These cancel it with these canceled and this gives me 34 65 dollars a month. Now the next part asks how much? What does it ask? How much coal must be bird by 35% efficient power plan to provide the yearly needs of this household. So first, since you're only operating at 35% efficiency, you're only effectively producing 7500 times 75000.35 which is 26 25 Europe. Callie's perk You ground. And if you convert this to Cuba, what power you have? 3.0 by Q. Our heard kilo ground and annually the household consumes Levin Kilowatt cover, and there are 3 65 days in a year, which gives me, Oh, 4000 and 15. He will want our per year. And finally, we can calculate how much cool that we need by basically doing 4015 divided by three planes. Your if I and this gives me 1000 316 the grounds are cool, so that's how much is needed to

You know, everyone is josh right, they were going to answer. Right. This question right here, that's what we have here is actually a tax schedule, right? It's an example for Kansas state. All right. And this is for those who would be filing or for those who are married and they will be filing um jointly. So the procedure is not too difficult. I just need to determine how much is the taxable income for a particular uh married couple? And from there we need to figure out which category they will fall under. All right, so we have category one, right? We're in the taxable income is above $0, but it does not exceed $30,000, so it's exactly $30,000.00. It's according to the The rule. Okay, so whatever the taxable income is just a 3.5 of that one. Okay. Now what if the combined um taxable income goes beyond $30,000, but It does not go beyond $60,000? That of course allows the couple to fall under the degree to. All right. We're in the tax jew right. For the couple would be $1000.1000 $50 and then 6.25% of that. Which is above $30,000. All right. Okay. All right. Now what if the couple's combined taxable income is above $60,000. Okay. So if it's above $60,000, then they fall under the category Treat we're in Their tax would be 2900 $25 plus 6.56 point 45% of the excess amount over $60,000. All right. Okay. Okay. So something here All right. We're going to do here is we're going to try to figure out All right, a piecewise function that would represent this um tax table. Okay. All right. So we're going to call that tax function um T All right. The effects. Okay. Now I think with the effects is that it actually we actually think we we'll probably put this further down. Okay. I think we need um Yeah. Okay. The city of X would be in three categories three categories. Because one we have a payment which is between zero and 30,000. Right? zero and 30,000 dollars. Right? And then we have a second category where in the amount is 30,000 is above 30,000, but smaller Or equal to 60,000. And then finally, All right, category three We're in we have the tax of the combined taxable income being higher then 60,000. All right, Okay. So now it's time to generate um Right. Piecewise parts. Alright. Uh Are the parts of this piece wise function? So, what's up with category one? So, according to Category one, If the taxable income is between zero and 30,000, all we have to do is just a 3.5% of the taxable income. Okay. So therefore For Category one, within this taxable income range, all we have to do Is take 3.5 off the taxable income. Huh? So we just have this one 0.0 35 times X. Alright, that would be the formula. Or that would be the part of the piecewise function for that particular part of the main. Okay. Now what about the category 2? Alright. How is that different? Okay, so according to Um category too. Right. If the taxable income is above 30,000 but Less than or equal to 60,000, then the tax should be 1,015 Plus 6.25% access of 30,000. All right. So that means in category two, Right. The married couple is supposed to pay $1,050 already. Then whatever is above 30,000. Right? They are supposed to pay. Oops. Let's raise this one. I think I'll need more space here. All right. They need to pay 6.25 of that. Yeah. Alright. Oops. Okay. Maybe we'll also need to arrest the one below. All right. If you know if the one bill um If if this one is like a particular trend. Okay, let's raise the stoop. All right. We'll bring it back later. Maybe. Maybe this space is enough X higher than 60,000. Okay. Right. So notice the difference between the first part And the second part because in the second part we know that we have to add 1051st. Right? And then whatever is in excess of 30,000. So in excess we need to subtract it from 30,000. Whatever is over. We need to multiply that with Um 6.25%. All right. Now, it's a very good at three. All right. It says here. All right. If the taxable income is above 60,000, then the couple must pay 2,925 And 6.45% of excess over 60,000. So this would be 2,925. And then the excess Right? For 60,000. Okay. It's going to be all right. Help. We're going to take 645 of that. Yeah. All right. And there we have it. This would be the piecewise function now, Right. For the tax schedule, right of married couples filing jointly, right at the state of Kansas. All right. So the next part is we're going to be graphing This one. All right. Okay. So, the graph this one. Alright. We're gonna go here to our graphing calculator. Clear this too. Right here. Okay. So we're going to call the function as tax. Alright. But this would be the first part. So, I'm going to call it one. All right. The first part of the peace. All right. You have to adjust also be um All right. The X value. Alright, because it ranges from zero all the way to past 60,000. So, maybe let's go with above uh 70,000. Let's make this. Let's just go with zero. Okay. All right. So there we go for the Y value. Okay. So I think we should start off with zero. All right. And then the amount is All right. So Protect your three. They need to pay at least 2,925. So maybe 4000 dollars of facts might be good enough. We'll definitely see if the graph, you know, extends further than this one. Let's just take it um 6000 I guess, you know, just to be sure. Okay. So here we go. So for the first part, right, for the first part for category one, it says you just need to take 3.5% off he taxable income. But this one it has to be constrained from zero. Right? All the way to Turkey outside. Right? So notice it cuts here. So therefore for a couple whose taxable income is 30,000, they need to pay whoa, $1,000. A $1,050. All right. Okay. Great. And this $1,050 is great because if you remember in category two mhm Minimum that they need to pay is actually $1,050. All right, okay. Now, for this one we need to get that right. Which is access of 30,000 and that access in 30,000. We need to multiply that with Yeah, 6.25 percent. All right. So this was a higher tax rate. The one before in category one is only 3.5% but this one is 6.25%. So, you can notice the blue part here is actually steeper than the red one. But of course we're going to constrain this Because according to mean, this is only acceptable from 30,000. Yeah. All right. All the way up to 60,000. All right. It also gets cut off. There we go. All right, Okay. So the highest um uh the highest tax that a married couple filing jointly. Right, if there are taxable income is 60,000 is actually 2,925. Which is of course, again very important because that is that is the initial amount. All right. We are going to be coming off from the 3rd category $2,925. Right? And for this one right? We need to get that which is in excess of 60,000. It's one of the green line over there. Mhm. Okay. But we only need to get um 6.45% of that. Okay, so notice is actually very very Um steep. It's almost as steep as the blue line because of the same tax rate. The blue line category two is 6.25%. The green one is 6.45%. But remember we have to right, we have to show that this has to be more done. £60 up. Okay. Right here. Yeah. Okay. 2025 for the blue line. But for the Green Line Alright, starts from 60,000 and then, you know, it keeps going up. So this would be how the graph would look like. Alright, for our tax schedule. All right. It's all connected. Okay, now we have another question. Right? So what if what if we have a couple whose Combined taxable income is 40,000? How much how much tax would they pay? It is actually good because we have the graphic and actually check there. How much would they be paying? All right. At 40,000. Okay. So to be to figure out how much they would be paying at 40,000, all we have to do Is to substitute 40,000 okay, onto our tax function. Now 40,000 Actually belongs to category two. Okay. So therefore what we're going to do is we're going to substitute This value of X on two. The second part of the piecewise function. So this would be 1050 plus X is now 40,000 minus 30,000. And then whatever the access is, we have to multiply that With 6.25 percent. Alright. So now we're going to compute for that using our calculator. All right. So, we have a 1050. Right? The base amount then we're going to At the access right? In 30,000. Mhm. All right. But we're only going to take 6.25% of that. All right. Uh The answer here would be the tax Right? That the couple would need to pay if their taxable income is 40,000. That goes as 1600 and 75. Yeah. All right. So, let's check. All right. Let's check in our graph whether All right. This would be the correct value. Right? As I mentioned, 40,000 is within category too. So let's just go to category two books. 40,000 is right here. Yeah. There we go. At 40,000. It is indeed, 1600 n 75. All right. So, our graphical model actually is correct. Okay, one more. What if what if the couple uh earns more than 60,000 or the taxable income is higher than $60,000. Let's say it's 70,000. All right. So, how much tax would be paid. Okay. So at 70,000. Alright, they now belong in category three. So this would be Yeah. The part of the function that we would use to evaluate the value of this month. So this would be 2925 plus 70,000 -60000. So that we can get how much is in excess of 60,000 in. Yeah. Yet only six points 45% of that one. Alright, so back to our calculator. I'm gonna clear this one. Okay, so we have 2,925. Right? Then we're going to add okay, we need to get the access. Alright, from 60,000, then we're going to Take 6.45% of that. All right. That gives us 3570. Oh. Mhm. All right. I think in our graph we go all the way to 70 there because you can see it is indeed 3517. All right. So, I hope Oh, this problem is clear. All right. And I hope if you keep enjoying learning math.


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