A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was5%, and the tax in the second city was 6%. The total hotel tax paid for the two cities was $552.50. How much was the hotel charge in each city before tax?Note that the ALEKS graphing calculator can be used to make computations easier.
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SOLUTION
Let us represent the hotel charge with different variables x and y:
Let the hotel charge before tax in the first city be x
Let the hotel charge before tax in the second city be y
Now, let us represent the word problem in equation form:
First, we were told that the charge before tax in the second city is $500 more than the charge before tax in the first city, this can be represented thus:
[tex]y=x+500\ldots\text{.eqn 1}[/tex]Going forward in the question, we were told the tax for the first city (x) is 5%(0.05), and the tax for the second city is 6%(0.06). The total tax from both cities is $552.5, this expression can be written mathematically as:
[tex]0.05x+0.06y=552.5\ldots\ldots\text{eqn 2}[/tex]Now, by solving equation 1 and equation 2 simultaneously, we will obtain the hotel charge in each city before tax. (that is the value of x and y).
[tex]\begin{gathered} y=x+500 \\ 0.05x+0.06y=552.5 \\ \end{gathered}[/tex]Using, the substitution method of solving simultaneous equation, we will solve further:
[tex]\begin{gathered} \text{substitute equation 1 into equation 2} \\ 0.05x+0.06(x+500)=552.5 \\ 0.05x+0.06x+30=552.5 \\ 0.11x+30=552.5 \end{gathered}[/tex][tex]\begin{gathered} 0.11x=552.5-30 \\ 0.11x=522.5 \\ x=\frac{522.5}{0.11} \\ x=4750 \end{gathered}[/tex]The hotel charge before tax in the first city is $4750.
Now, substitute the value of x into equation 1 to get the value of y (hotel charge before tax in the second city)
[tex]\begin{gathered} y=x+500 \\ x=4750 \\ y=4750+500 \\ y=5250 \end{gathered}[/tex]The hotel charge before tax in the second city is $5250.
Related Questions
Which of the following is equal to - 7/4w expressed as a linear combination of vectors, if W= -1/2i- 3/2j?
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Therefore, the scalar multiplication of vector -7/4 w is given by
[tex]-\frac{7}{4}w=-\frac{7}{4}(-\frac{1}{2}i-\frac{3}{2}j)[/tex][tex]=\frac{7}{8}i+\frac{21}{8}j[/tex]Hence, the linear combination is 7/8 i + 21/8 j
Use four rectangles to estimate the area between the graph of the function f(x) = Ty and the taxis on the interval 12, 6) using the left endpointsof the subintervals as the sample points. Write the exact answer, Do not round,
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To find the area using four rectangles, we will use the following equation:
[tex]Area\approx A_1_{}+A_2+A_3+A_4[/tex][tex]Area\approx f(x_1)\Delta x+f(x_2)\Delta x+f(x_3)\Delta x+f(x_4)\Delta x[/tex][tex]Area\approx f(3)\Delta x+f(4)\Delta x+f(5)\Delta x+f(6)\Delta x[/tex][tex]Area\approx(\frac{6}{7(3)})(1)+(\frac{6}{7(4)})(1)+(\frac{6}{7(5)})(1)+(\frac{6}{7(6)})(1)[/tex][tex]Area\approx\frac{57}{70}[/tex](-1,2) and (3,32)
For each of the following, find the formula for an exponential function that passes through the two points given.
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The required exponential function f(x) = (4)(2)ˣ which is passes through the two points (-1,2) and (3,32).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Let the formula for an exponential function would be as
⇒ f(x) = abˣ
The exponential function passes through the two points (-1,2) and (3,32).
f(-1) = 2
f(3) = 32
2 = ab⁻¹
2b = a
32 = ab³
Substitute the value of a = 2b in the above equation,
32 = 2b×b³
32 = 2b⁴
b⁴ = 16
b⁴ = 2⁴
b = 2
Substitute the value of b = 2 in the equation a = 2b,
So a = 2×2 = 4
⇒ f(x) = (4)(2)ˣ
Therefore, the required exponential function f(x) = (4)(2)ˣ
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O GRAPHS AND FUNCTIONSGraphing a piecewise-defined function: Problem type 1
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Answer:
Explanation:
To get the plot of h(x), we just plot the given values of y at the given values of x.
For example, we are told that between x = -3.5 and -2.5, h(x) = -3. Therefore, the plot gives
The hollow circle tells us that the value x = -3.5 itself is not included. The solid circle tells us that x = -.2.5 is included. All this comes from the fact that the interval given is -3.5 < x ≤ -2.5.
Using the same method for other entries on the graph, we get our desired plot.
Write an inequality for the graph shown below. Use x for your variable. + -11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 X
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according to the graph, inequality is:
[tex]x\ge3[/tex]A flower bed is in the shape of a rectangle. It measures7 yd long and 4 yd wide. Chris wants to use mulch tocover the flower bed. The mulch is sold by the squarefoot. Use the facts to find the area of the flower bed insquare feet.2ftX 5?Conversion facts for length1 foot (ft)1 yard (yd)1 yard (yd)===12 inches (in)3 feet (ft)36 inches (in) i need help with this math problem.
Answers
Answer
252 ft²
Step-by-step explanation
1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 7 yd is:
[tex]\begin{gathered} 7\text{ yd =}7\text{ yd}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ \text{ Simplifying the units:} \\ 7\text{ yd =}\frac{7\cdot3}{1}\text{ ft} \\ 7\text{ yd }=21\text{ ft} \end{gathered}[/tex]Similarly, the equivalence of 4 yards is:
[tex]\begin{gathered} 4\text{ yd }=4\text{ yd}{}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ 4\text{ yd }=4\cdot3\text{ ft} \\ 4\text{ yd}=12\text{ ft} \end{gathered}[/tex]Therefore, the length of the bed is 21 ft and the width is 12 ft.
Finally, the area of the bed (a rectangle) is calculated as follows:
[tex]\begin{gathered} A=legnth\cdot width \\ A=21\cdot12 \\ A=252\text{ ft}^2 \end{gathered}[/tex]Picture explains it all
Answers
Reason
The question gave you a 90 degree angle.
We know the straight angle would be 180 degrees.
So the second half is another 90 degrees.
Half of that (45) added to 90 = 135 degrees.
Picture attached shows it’s at 45 degrees on the second half or you can assume it’s half of 90.
Mr Gregory drives a furniture delivery truck 4 days each week the table below shows the driving record for 1 week find the difference in meters between the distance Mr Gregory traveled on Wednesday and Thursday
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ANSWER:
6150 meters
STEP-BY-STEP EXPLANATION:
To calculate the difference between the two days we must calculate the subtraction of the values corresponding to the days Wednesday and Thursday.
[tex]80.75\text{ km}-74.6\text{ km}=6.15\text{ km}[/tex]Now, we convert this value in kilometers to meters, knowing that 1 kilometer is equal to 1000 meters:
[tex]6.15\text{ km}\cdot\frac{1000\text{ m}}{1\text{ km}}=6150\text{ m}[/tex]will send image. select the expression. that is not equivalent to 10 + 10p
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We have that
[tex]\begin{gathered} 5(10\text{ + p +p) = 5(10 + 2p)} \\ =\text{ 50 + 10p }\ne\text{ 10 + 10 p} \end{gathered}[/tex]So the answer is the first one.
Karen wants to buy a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 4%, charged as simpleInterest. They lend her $8000 for 6 years. She makes no payments except the one at the end of that time.Answer the following questions. If necessary, refer to the list of financial formulas.х5?(a) How much total interest will Karen have to pay?s0(b) What will the total repayment amount be (including Interest)?s[]
Answers
Answer:
a) $1,920
b) $9,920
Explanation:
Step 1. Gather all of the information.
The amount borrowed will be the principal or starting amount P:
[tex]P=8,000[/tex]The interest rate will be r:
[tex]r=4\text{ percent}[/tex]We will need the interest rate in decimal form, for that, divide the percentage amount by 100:
[tex]\begin{gathered} r=\frac{4}{100} \\ \downarrow \\ r=0.04 \end{gathered}[/tex]And the time of the loan is 6 years, this will be the value of t:
[tex]t=6[/tex]Step 2. To solve part a, we use the following formula to calculate the interest:
[tex]I=p\times r\times t[/tex]Substituting all of the known values:
[tex]I=8,000\times0.04\times6[/tex]The result is:
[tex]I=1,920[/tex]The total interest that Karen will have to pay is $1,920.
Step 3. To solve part b, we need to find the total repayment amount.
To find this, we add the interest and the principal amount:
[tex]T=P+I[/tex]Where T represents the total amount.
Substituting P and I:
[tex]\begin{gathered} T=8,000+1,920 \\ \downarrow \\ T=9,920 \end{gathered}[/tex]The total amount she will have to repay is $9,920.
Answer:
a) $1,920
b) $9,920
I need help solving an optimization math problem please :)
Answers
Answer:
Explanation:
Let the side opposite the river = x
Let the adjacent side to the river = y
Harper just lit a new candle and then let it burn all the way down to nothing. The length of the candle remaining unburned, in inches, can be modeled by the equation L=15-1.5t,L=15−1.5t, where tt represents the number of hours since the candle was lit. What is the slope of the equation and what is its interpretation in the context of the problem?
Answers
From the information given, the slope (m) of the equation is -1.5. This means that there is an inverse relationship between the Lenght of the Candle and the number of hours. Where, the longer the number of hours, the smaller the length of the candle. See further explanation below.
What is a slope?The slope of a line is its steepness as it goes from LEFT to RIGHT. The slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always fixed (it never changes) regardless of whatever two locations on the line are chosen.
When dealing with a linear relationship, the question is usually represented in this format:
y = mx + b; where
m = slope and
b= y-intercept (or constant)
From the case above, the equation shows the relationship between time (t) the candle spends burning and the length of the candle (l).
Logically, we can infer that there will be a negative relationship between the two but first lets us determine the slope.
Restating the equation in intercept format, we have:
L = 15 - 1.5t................................1; in intercept format the slope we have
L = -1.5t + 15 ...........................2.
Where L [tex]\sim[/tex] y; m [tex]\sim[/tex] -1.5 and t [tex]\sim[/tex] x; and b [tex]\sim[/tex] 15
Hence we can state that the m (slope) = -1.5 and that if plotted on a graph, the line crosses the y-axis at y = 15 where x = 0.
Also, if L (that is y) is set to zero, then the total time taken for ALL the candles to burn is 10 hours.
See attached graph as proof.
The logical interpretation above is hence confirmed that there is an inverse relationship between x and y. This means that the longer the time, the shorter the length of the candle.
This also means that the length of the candle cannot be or is not longer than 15.
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The slope of the equation is -3/2 describing the rate at which the length of the candle is decreasing.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0.
We know slope is the rate of change of the y-axis with respect to the x-axis
also, rise over run which is (y₂ - y₁)/(x₂ - x₁).
The burning equation of the candle is represented by L = 15 - 1.5t.
Where L = length of the candle and any point of time and t = time in hours.
Now, we'll need two points from this equation to obtain the slope.
At, t = 2, L = 12. and at t = 4, L = 9.
So, the two points are (2, 12) and (4, 9).
∴ Slope(m) = (9 - 12)/(4 - 2).
Slope(m) = -3/2.
The slope of this equation describes the rate at which the height of the candle is changing.
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5. a) Look at the number grid below. Shade the Multiples of 4, 1 2 3 4 5 6 7 00 8 9 10 11 12 13 14 15 16 17 17 18 19 20
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We need to find the multiples of 4 using the next given set:
The multiples of 4 are given by
4*1 =4
4*2 = 8
4*3= 12
4*4=16
4 *5 =20
Then:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20.
Solve Each System by Elimination:-12x-2y=30-4x+y=-5
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We solve as follows:
-12x - 2y = 30
2(-4x + y = -5)
---------------------
-12x -2y = 30
-8x + 2y = -10
--------------------
-20x = 20 => x = -1
Now we replace the value of x in one of the original equations to solve for y, that is:
-4(-1) + y = -5 => 4 + y = -5 => y = -9
So, the solution is the point (-1, -9).
9) Professor Elderman has given the same multiple-choice final exam in his Principles ofMicroeconomics class for many years. After examining his records from the past 10 years, hefinds that the scores have a mean of 76 and a standard deviation of 12.Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What isthe probability that he will have to deliver on his promise?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
score:
mean = 76
standard deviation = 12
Step 02:
probability:
normal distribution:
normal distribution diagram:
mean + 1 standard deviation = 76 + 12 = 88
probability (class average score is above 80):
p (score > 80) = 34% + 13.5% + 2.4% + 0.1% = 50% = 0.5
The answer is:
p (score > 80) = 50% = 0.5
As I am completely brand new to this subject/branch of mathematics, please explain thoroughly, step by step on how to complete this This is a practice from my ACT prep guide take your time, as there is no rush *Ignore the last answer option
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Remember that
The difference of squares is of the form
[tex](a+b)(a-b)=a^2-b^2[/tex]In this problem we have
[tex](3x-4y^2)(3x+4y^2)[/tex]so
a=3x
b=4y^2
therefore
Apply the difference of squares
[tex](3x-4y^2)(3x+4y^2)=(3x)^2-(4y^2)^2=9x^2-16y^4[/tex]please helpppppp i dont get it
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The subtraction of the mixed fractions and presenting the result in simplest form gives;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]
What is are mixed fractions?A mixed fraction is one that has both a quotient part as a whole number, the remainder, as the numerator of the fraction part, and the divisor as the denominator of the fraction part.
The equation involves the subtraction of mixed fractions, which are expressed as follows;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} } = [/tex]
To subtract the mixed fractions, the mixed fraction can first be rearranged into improper fractions as follows;
[tex] \displaystyle{ \frac{5 \times 9 + 2}{5} - \frac{5 \times 4 + 4}{5} = \frac{47}{5} + \frac{24}{5} }[/tex]
[tex] \displaystyle{ \frac{47}{5} + \frac{24}{5} = \frac{71}{5} }[/tex]
The result of the addition of the improper fraction which is also an improper fraction can be rearranged into partial fractions again as follows;
71 = 5 × 14 + 1
Which gives;
[tex] \displaystyle{ \frac{71}{5} = 14 \frac{1}{5} }[/tex]
Therefore;
[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]
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Which of the following tests should be administered to see if an experimental medicine lowers blood pressure among hypertensive patients? A. two-tailed test OB. right-tailed test OC. alternative test OD. left-tailed test
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We have to select the appropiate test to see if an experimental medicine lowers blood pressure among hypertensive patients.
In this case, we want to test if the mean for the blood pressure after the treatment is significantly lower than the blood pressure mean without treatment.
Then, for the blood pressure to be significantly different it has to be to the left of a critical value.
Then, it is a left-tailed test.
Answer:
9×2=2×9 what is the property of this problem?
Answers
The property involved is called "commutative property of product"
SInce we are flipping the oerder of the factors and arrive at the same result.
The "flipping is called "commuting" in Math terms.
Solve the problem15) 21 and 22 are supplementary angles. What are the measures to the nearest hundredth) of the two angles?5x - 92I
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∠1 is 31.5°
∠2 is 148.5°.
Given:
∠1 = x
∠2 = 5x-9
The measure of ∠1 and ∠2 are supplementary angles.
First, the value of x can be calculated as,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=\frac{189}{6} \\ x=31.5 \\ x=\angle1 \end{gathered}[/tex]Substitute the value of x in ∠2.
[tex]\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}[/tex]Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.
Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $6 and a drink for $4. How much would it cost if they bought 5 bags of popcorn and 7 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?Total cost, 5 bags of popcorn, and 7 drinks: Total cost, p bags of popcorn and d drinks:
Answers
a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,
[tex]\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}[/tex]Therefore, the answer to the first question is $58.
b) Substitute 5 for p and 7 for d in the expression above; therefore,
[tex]T=6p+4d[/tex]The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.
Two train leave stations 210 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other traves a 70miles per hout. How long will it take for the two trains to meet?___ hours Do not do any rounding
Answers
SOLUTION
At the same time t,
Train 1 would have covered a distance of 80t, since distance = average speed x time.
Train 2 would have covered a distance of 70t.
Now both added should give 210 miles
That is 80t + 70t = 210
150t = 210
t = 210/150
t = 1.4 hours
You want to hang a picture on your wall the wall is 20 feet long you want to have at least 3 feet on both sides of the painting for plans to be placed right a quality showing the possible lanes of you being mean
Answers
We can consider
x = length of the painting
20 ft wall long
we want at least 3 ft per side so the total available length is 20-6= 14
x must be shorter than 14
inequality
x< 20-2(3)
x<14
En un depósito había 127 bolsas de harina  cada una de 60 kg se sacaron ocho camiones de 12 bolsas cada uno cuantos kilogramos de harina quedaron en el depósito 
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Based on the number of bags of flour that were taken by the trucks and the number that were in the warehouse, the amount of kilograms left in the warehouse is 1,860 kg
How to find the number of kilograms?First, find the number of bags that were taken by the trucks by the formula:
= Number of trucks x Number of bags per truck
= 8 x 12
= 96 bags
This means that the number of bags left are:
= 127 bags - 96 bags taken
= 31 bags left
The number of kilograms of flour left is:
= Number of bags left x Number of kilograms per bag
= 31 x 60
= 1,860 kg
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Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark ( 1 ) for the fraction bar.
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Consider that the coordinates of the mid-point of a line segment is given by the formula,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]The given diagram represents the line segment between the points (-3,4) and (-6,-1).
So the corresponding mid-point is given by,
[tex]\begin{gathered} x=\frac{-3+(-6)}{2}=\frac{-9}{2} \\ y=\frac{4+(-1)}{2}=\frac{3}{2} \end{gathered}[/tex]Thus, the mid-point of the given line segment is ( -9/2 , 3/2 ) .
Which statement is equivalent to ~p? p: Even numbers are divisible by 2.
Answers
The statement ~p is "Even numbers are not divisible by 2."
Given statement:-
p: Even numbers are divisible by 2.
We have to find ~p for the statement p.
We know that ~p means negation of p.
Hence, we will negate the statement by adding "not" in the statement.
Hence, the statement will become,
Even numbers are not divisible by 2.
Negation of a statement
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written ~P or -P.
It is interpreted intuitively as being true when P is false, and false when P is true.
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Which describes the product when two fractions greater than 0 and less than 1 are multiplied?
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When you multiply two numbers, one of them greater than 0 and the other one lower than 1. The result is a number that is lower than the first one, that is, a number lower than the number greate than 0.
estimate 794 divided by 18=?
Answers
Answer:
C 40
Step-by-step explanation:
794 is about 800
18 is about 20
800/20=40
Evaluate the logarithmLog 6 1/36
Answers
Answer:
-2
Explanation:
By properties of logarithms, the logarithm of a fraction is equal to the difference of logarithms, so
[tex]\log _6(\frac{1}{36})=\log _61-\log _636[/tex]Now, log₆(1) = 0 and log₆36 = 2, so
[tex]\begin{gathered} \log _6(\frac{1}{36})=0-2 \\ \log _6(\frac{1}{36})=-2 \end{gathered}[/tex]Therefore, the answer is -2
In the diagram below, DE is parallel to yy. What is the value of x? 110° A. 90 0 B. 120 O C. 110 O D. 70
Answers
Angle shown x is corresponding angle to 110 degree angle shown (from property of transversal cutting a pair of parallel lines).
hence
x = 110