Francis went on a business trip to Minneapolis, Minnesota, and stayed at a hotel for one night at a rate of $150, plus tax. The state of Minnesota has a general sales tax rate of 6.875%, and the city of Minneapolis has a general sales tax rate of 0.5%. In addition, Hennepin County, where Minneapolis is located, has a 0.25% sales tax for transit improvement and a 0.15% sales tax to finance a baseball stadium. Not only that, but there is an additional lodging tax in Minneapolis of 3%. Help Francis determine his total bill at the hotel. Round all your answers to the nearest cent.
How much money was Francis charged by the state of Minnesota at its general sales tax rate?
How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
How much money was Francis charged by Hennepin County for transit improvement?
How much money was Francis charged by Hennepin County to help finance a baseball stadium?
part 1How much money was Francis charged by the state of Minnesota at its general sales tax rate?
we have that
the sales tax rate is 6.875%
6.875%=6.875/100=0.06875
Multiply by $150
150(0.06875)=$10.31
part 2How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
the sales tax rate is 0.5%
0.5=0.5/100=0.005
Multiply by $150
150(0.005)=$0.75
part 3How much money was Francis charged by Hennepin County for transit improvement?
sales tax is 0.25%
0.25/100=0.0025
150(0.0025)=$0.38
part 4How much money was Francis charged by Hennepin County to help finance a baseball stadium?
the sales tax is 0.15%
0.15/100=0.0015
150(0.0015)=$0.23
part 5additional lodging tax in Minneapolis of 3%
3/100=0.03
150(0.03)=$4.5
part 6
the total bill is equal to
150+10.31+0.75+0.38+0.23+4.5=$166.17
the total bill is $166.1721 pointUse the given information to complete the proof of the following theorem.If a quadrilateral is a parallelogram, then its opposite sides are congruent.By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.angle-side-angleCorresponding parts of congruent triangles are congruent.side-angle-sideOpposite sides of a parallelogram are congruent.
The Solution:
Required:
To prove that opposite sides are congruent in a parallelogram.
Step 1:
Draw a parallelogram.
Step 2:
[tex]DB\cong DB\text{ \lparen Reason: Reflexive property\rparen}[/tex]Step 3:
[tex]AB\parallel CD\text{ and BC }\parallel AD\text{ \lparen Reason: Definition of a parallelogram\rparen}[/tex]Step 4:
[tex]\angle1\cong\angle4\text{ and }\angle2\cong\angle3\text{ \lparen Reason: Alternative angles are equal.\rparen}[/tex]Step 5:
[tex]\angle ABD\cong\angle CDB\text{ \lparen Reason: Angle-Side-Angle \lparen ASA\rparen Theorem\rparen}[/tex]Step 6:
[tex]undefined[/tex]You must do this one by hand. No desmos!!! Find the solution to the following system of equations:
The equations are given
[tex]\begin{gathered} -5x+y=-5\ldots\ldots\ldots\ldots1 \\ -4x+2y=2\ldots\ldots\ldots\ldots\ldots\text{.}.2 \end{gathered}[/tex]ExplanationTo determine the coordinates of x and y by elimination method.
Divide equation 2 by 2.
[tex]\begin{gathered} -\frac{4x}{2}+\frac{2y}{2}=\frac{2}{2} \\ -2x+y=1\ldots\ldots\ldots\ldots..3 \end{gathered}[/tex]Now subtract equation 1 by 3,
[tex]\begin{gathered} (-5x+y+5)-(-2x+y-1)=0 \\ -5x+y+5+2x-y+1=0 \\ -3x+6=0 \\ x=2 \end{gathered}[/tex]Substitute the value of x in the equation 1.
[tex]\begin{gathered} -5\times2+y=-5 \\ -10+y=-5 \\ y=5 \end{gathered}[/tex]AnswerThe solution of the system of equations is [tex](2,5)[/tex]The correct option is A.
TyR Match the name of each figure on the left with the best description on the right. a quadrilateral with rectangle one set of parallel sides a quadrilateral with four congruent sides trapezoid a quadrilateral with two pairs of parallel sides square a quadrilateral with four right angles rhombus a quadrilateral with four right angles and four congruent sides parallelogram
Parallelogram---->a quadrilateral with two pairs of parallel sides
Square----> a quadrilateral with four right angles and four congruent sides
Rectangle----> a quadrilateral with four right angles
Trapezoid----> . a quadrilateral with one set of parallel sides
Rhombus-----> a quadrilateral with four congruent sides
Answer: here
Step-by-step explanation:
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What is the value of x? R 2x+880 Q 78° 8x-940 X+790 s T
We have here that all of these angles must sum 360 degrees since we have here a circle. Then, we have that:
[tex]2x+88+8x-94+x+79+78=360[/tex]Now, to solve this equation, we need to group and sum the like terms:
[tex]2x+8x+x+88-94+79+78=360_{}[/tex][tex]11x-6+157=360\Rightarrow11x+151=360[/tex]To isolate 11x, we need now to subtract 151 to both sides of the equation:
[tex]11x+151-151=360-151\Rightarrow11x=209[/tex]Divide both sides of the equation by 11:
[tex]\frac{11x}{11}=\frac{209}{11}\Rightarrow x=19[/tex]We can check this solution if we substitute the value x = 19 in the original equation (after the simplification process):
[tex]11x+151=360\Rightarrow11\cdot(19)+151=360\Rightarrow209+151=360\Rightarrow360=360[/tex]Since the last result is TRUE, then the value for x = 19 is the correct solution.
In summary, the value for x = 19.
the life expectancy of a circulating coin is 30 years. the life expectancy of a circulating dollar bill is only 1/20 as long. find the life expectancy of circulating paper money. Life expectancy= how many years ( type a whole number or a mixed number simplify your answer)
Given
the life expectancy of a circulating coin is 30 years
the life expectancy of a circulating dollar bill is only 1/20 as long.
Procedure
c=life expectancy of a circulating coin
p= life expectancy of circulating paper money
[tex]p=\frac{1}{20}\cdot c[/tex][tex]\begin{gathered} p=\frac{1}{20}\cdot30 \\ p=\frac{30}{20} \\ p=1.5 \end{gathered}[/tex]The answer is: life expectancy of a dollar bill = 1.5 years
Solve the following system of equations by graphing and state whether the system is dependent, independent, or consistent. 1/2x + 3/4y = 12x - 3y = 4
We have to solve the following system of equations:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ 2x-3y=4 \end{gathered}[/tex]We have to graph the equations and, as they are written in standard form, we are going to calculate the intercepts for both.
We will write the equations in slope-intercept form.
For the first equation we have:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ \frac{3}{4}y=-\frac{1}{2}x+1 \\ y=\frac{4}{3}(-\frac{1}{2}x+1) \\ y=-\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]For the second equation we have:
[tex]\begin{gathered} 2x-3y=4 \\ 2x-4=3y \\ y=\frac{1}{3}(2x-4) \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Both slopes are different, what means that the lines are not parallel and will intersect, so we already know that the system is independent.
Using the slopes and the y-intercepts, we can graph the equations as:
The solution to the system is the intersection point which is (2,0).
Answer:
The system is independent and its solution is (x,y) = (2,0)
Decide if the following biconditionalstatement is true or false:Two angles are congruent if and only ifthey are vertical angles.TrueFalse
Answer:
False
Explanation:
A biconditional statement is true if both conditionals are true.
• The statement: Two angles are congruent if they are vertical angles is ,True,.
,• The Statement: Two angles are congruent only if they are vertical angles is ,False,.
Therefore, the biconditional statement is false.
please help I will give a good review.... can you help me with these two questions
When a system of equations has infinite solutions, you'll end up with a statements that's true no matter what. For example, 6=6. Or when the graphs of the equations are the same exact line.
Then:
3x+4y=12 and
6x+8y=24 divided by 2: 3x+4y=12. That means they are the same exact line, so it has infinite solutions.
[tex]\begin{gathered} 3(2x+y)=24 \\ 6x+3y=24 \\ y=-6x+24\text{ dividing by 3} \\ y=-2x+8 \end{gathered}[/tex]The answer would be the first one and the third one.
Solve Equation: 12(x-2.3)= 15.6 Help
To solve for x you can first divide by 12 into both sides of the equation, like this
[tex]\begin{gathered} \frac{12\mleft(x-2.3\mright)}{12}=\frac{15.6}{12} \\ x-2.3=1.3 \end{gathered}[/tex]Now, you can add 2.3 from both sides of the equation
[tex]\begin{gathered} x-2.3+2.3=1.3+2.3 \\ x=3.6 \end{gathered}[/tex]Therefore, the value of x that satisfies the equation is
[tex]x=3.6[/tex]Finally, to check that this value satisfies the given equation, just plug x = 3.6 into the equation and see that a true proposition is reached. So, you have
[tex]\begin{gathered} 12\mleft(x-2.3\mright)=15.6 \\ \text{ Replace x = 3.6} \\ 12(3.6-2.3)=15.6 \\ 12(1.3)=15.6 \\ 15.6=15.6 \\ \text{ True proposition} \end{gathered}[/tex]what are the solutions of the equation 2x ^ 2 equals 18 use a group of related function whose group answers the question
The given expression is :
[tex]2x^2=18[/tex]Simplify the equation for x :
[tex]2x^2=18[/tex]Divide both side by 2 :
[tex]\begin{gathered} \frac{2x^2}{2}=\frac{18}{2} \\ x^2=9 \end{gathered}[/tex]taking square root on both side :
[tex]\begin{gathered} x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}[/tex]Answer :
Determine the perimeter of kite NITE below where EB = 40 feet and BI = BN= 9. Round your answer to the nearest hundredth necessary.BE
From the basic knowledge of pythagoras thorem,
EH
X ^2 = 40^2 + 9^2 = 1`600 + 81 = 1681
X = square root of 1681
= ET = EH = X = 41 feet
NI
y ^ 2 = 9 ^2 + 9^2 = 81 + 81 = 162
y = square root of 162
NI = T I = y = 12.72 feet
The perimeter of the Kite = EN + ET + NI + TI = 41 + 41 + 12. 72 + 12. 72 = 107.44 feet
what is the slope of the line below?Show your work.
To be able to determine the slope, let's identify at least two points that pass through the graph and use it in the following formula:
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let,
Point A: x1, y1 = -4, -4
Point B: x2, y2 = 4, -4
We get,
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{-4\text{ - (-4)}}{4\text{ - (-4)}}[/tex][tex]\text{ = }\frac{-4\text{ + 4}}{4\text{ + 4}}[/tex][tex]\text{ = }\frac{0}{8}\text{ = 0}[/tex][tex]\text{ Slope (m) = 0}[/tex]Therefore, the slope of the line is 0.
Fill in missing terms. Simplify any fractions. 3(t+1)=3T+1= Divide both sides by 3T= Subtract 1 from both sides
Given:
The equation is given as,
[tex]3(t+1)=3[/tex]The objective is to complete the missing terms.
Explanation:
In the first step, dividing both sides by 3,
[tex]\begin{gathered} \frac{3(t+1)}{3}=\frac{3}{3} \\ t+1=1 \end{gathered}[/tex]In the next step, subtract 1 from both sides.
[tex]\begin{gathered} (t+1)-1=1-1 \\ t=0 \end{gathered}[/tex]Hence, the result of first box is 1 and the second box is 0.
The equation yˆ=−0.37x^2+6.15x+52.3 approximates the average temperature in October in degrees Fahrenheit at an agricultural community x hours after 5 a.m.What is the best estimate for the average temperature in October at 9 a.m.?64°F67°F71°F78°F
So we have the equation:
[tex]y=-0.37x^2+6.15x+52.3[/tex]Where x represents the hours passed after 5 am and y represents the temperature in degrees Fahrenheit. We are being asked about the temperature at 9 am so we need to express 9 am in terms of hours passed after 5 am. Since there's a difference of 4 hours between this two times then we must use x=4 and the result of substituting x by 4 in the former equation will give us the temperature we are looking for:
[tex]y_{(4)}=-0.37\cdot4^2+6.15\cdot4+52.3=70.98[/tex]So the temperature in october at 9 am is 70.98°F so the best approximation would be option C, 71°F.
List every way possible to prove that two triangles are congruent (ASA, SSS, etc.,), including a sketch of each scenario, with the proper marks to show congruence.
Given
triangles
Find
List every way possible to prove that two triangles are congruent
Explanation
1) SSS congruence (Side - side - side)
when all corresponding sides of the two triangles are equal.
then ,
[tex]\Delta ABC\cong\Delta PQR[/tex]b) SAS congruence (Side - Angle - Side)
when two sides and one angle are equal.
then ,
[tex]\Delta ABC\cong\Delta PQR[/tex]c) ASA congruence (Angle - side - angle)
when two angles and one side are equal
[tex]\Delta ABC\cong\Delta PQR[/tex]d) RHS (right - hypotenuse - side)
in two right triangles when hypotenuse and one side are equal.
then ,
[tex]\Delta ABC\cong\Delta DEF[/tex]Final Answer
Hence , there are four possible ways to prove the triangles are congruent.
What form is the following number in standard form or scientific notation? 0.0000000008
A scientist uses the equation shown below to predict the future population of a species. In the equation, y represents the estimated population and t represents the number of years.
1200
Explanation:y represents the estimated population
t represents the number of years.
The equation that predicts the population after t years is given as:
[tex]y=150\times4^t[/tex]Substitute t = 3/2 into the equation
[tex]\begin{gathered} y=150\times4^{\frac{3}{2}} \\ y=150\times2^{2(\frac{3}{2})} \\ y=150\times2^3 \\ y=150\times8 \\ y=1200 \end{gathered}[/tex]The closest valuie to the value of y is 1200
Solve the inequality and graph the solution on the line provided. -2 + 6x > 34 Л ^ < OT Inequality Notation: Number Line: 8 12 6 2 10 -8 -2 0 4 -6 -12 -10 -4 Click and drag to plot line. Submit Answer at
The inequality to solve is:
[tex]-2+6x>34[/tex]We can take the numbers to one side and variables to one and solve for x. Shown below:
[tex]\begin{gathered} -2+6x>34 \\ 6x>34+2 \\ 6x>36 \\ x>\frac{36}{6} \\ x>6 \end{gathered}[/tex]This is the solution
x > 6Graphing this on a number line would look something like this:Note: the open circle in '6' means the number six isn't included.
Erika needs a test average of 85 or higher to make the honor roll. • There are four tests in the term. • Her first three test grades were 78, 80, and 88. Which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll?
Answer:
[tex]x\ge94[/tex]Explanation:
Average test score is expressed using the formula;
Average = Sum of the grades/Total number of test
Let x be the grade of the fourth test.
If Erika needs a test average of 85 or higher to make the honor roll, this can be expressed as;
[tex]\frac{78+80+88+x}{4}\ge85[/tex]Cross multiply
[tex]\begin{gathered} 78\text{ + 80 + 88 +x }\ge4\cdot85 \\ 246\text{ + x}\ge340 \end{gathered}[/tex]Subtract 246 from both sides
[tex]\begin{gathered} 246\text{ + x-246}\ge340-246 \\ x\ge94 \end{gathered}[/tex]Hence the inequality that could be used to find what she needs to score on her fourth test, in order to make the honor roll is
[tex]x\ge94[/tex]I need help with this practice problem solving My attempted answer is in the pic, though I am not sure if I am correct or not
Solution
To convert from polar coordinate to rectangular coordinate,
[tex]\begin{gathered} (r,\theta)\to(r\cdot\cos \theta,r\cdot\sin \theta) \\ \\ \Rightarrow(3\sqrt[]{5},-\frac{\pi}{8})\to(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8})) \\ \\ \Rightarrow(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8}))=(6.20,-2.57) \end{gathered}[/tex]I need to find the exact area of the sector.
Help! Solve the equation and show all work. Use Quadratic Formula
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} \text{where a = 1, b = -6, c = 34} \\ x\text{ = }\frac{-(-6)\text{ }\pm\sqrt[]{(-6)^2-4(1)(34)}}{2(1)} \\ x\text{ = }\frac{6\text{ }\pm\sqrt[]{36-132}}{2} \\ x\text{ = }\frac{6\pm\sqrt[]{-96}}{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = = }\frac{6\pm\sqrt[]{-1\times96}}{2} \\ In\text{ }comple\text{ }xnumber,-1=i^2 \\ x\text{ = = }\frac{6\pm\sqrt[]{i^2\times16\times6}}{2} \\ x\text{ = }\frac{6\pm4\text{ i }\sqrt[]{6}}{2}\text{ } \\ x\text{ = }\frac{2(3\pm2\text{ i }\sqrt[]{6})}{2}\text{ } \\ x\text{ = }3\pm2\text{ i }\sqrt[]{6} \end{gathered}[/tex][tex]x\text{ = }3+2\text{ i }\sqrt[]{6}\text{ or x = }3-2\text{ i }\sqrt[]{6}[/tex]Represent the following expressions as a power of the number a (a≠0): (a^5*a/a^-3)^-1
PLS HELP
We can simplify the given expression:
((a⁵*a)/(a⁻³) )⁻¹
To get:
a⁻⁹
How to simplify the expression?There are some properties we need to use:
xᵃ*xᵇ = xᵃ⁺ᵇ(xᵃ)ᵇ = xᵃ*ᵇx⁻ᵃ = 1/xᵃOur expression is:
((a⁵*a)/(a⁻³) )⁻¹
First we can simplify the numerator:
a⁵*a = a⁵⁺¹ = a⁶
((a⁶)/(a⁻³) )⁻¹
Using the third property we can also rewrite the denominator:
(1/a⁻³) = a³
Replacing that we get:
((a⁶)/(a⁻³) )⁻¹ = ((a⁶)*a³ )⁻¹ = (a⁶⁺³)⁻¹ = a⁻⁹
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I need help solving the linear system I need to create an ordered pair
To create the ordered pairs you need to pic any value of x and look what the corresponding value fo y is.
For the point where both linear dunctions cross each other the value in the x-axis is x= 2 and the value in the y-axis is y=7
how do I find a unit rate for graphs
Unit rate of graph can be calculated by finding the slope of the graph or by dividing it's change in 'y' to the change in 'x' .
Generally, for linear graph unit rate can be calculated by finding it's slope but for curve graph it can be done by dividing it's change in 'y' to the change in 'x'.
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X^2+15x+24y+10 what is the constant expression
The constant term in the given expression is 10.
The given polynomial is x²+15x+24y+10.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
Constants are considered as algebraic expressions which only involve numbers.
In the given algebraic expression x²+15x+24y+10, the constant term is 10.
Hence, the constant term in the given expression is 10.
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Angela has 3 gallons of milk. How many quarts of milk does she have?- word problem
Angela has 12 quartz of milk
Explanations:Note:
1 gallon = 4 quartz
3 gallons of milk = (3 x 4) quartz
3 gallons of milk = 12 quartz of milk
Therefore, Angela has 12 quarz of milk
Find the midpoint for G(9, 7) , H(10, -7)
we have G(9, 7) , H(10, -7)
The formula to calculate the midpoint between two points is equal to
[tex]m(\frac{x1+x2}{2},\frac{y1+y2}{2}_{})[/tex]substitute the given coordinates
[tex]m(\frac{9+10}{2},\frac{7-7}{2}_{})[/tex][tex]m(9.5,0_{})[/tex]Let's Practice!1.Consider the following functions.f(x) = 3x2 + x + 2g(x) = 4x2 + 2(3x – 4)h(x) = 5(x2 - 1)a.lFind f(x) - g(x).b. Find g(x) - h(x).
To find the functions we need to remember that
[tex](f-g)(x)=f(x)-g(x)[/tex]Then
[tex]\begin{gathered} (f-g)(x)=(3x^2+x+2)-(4x^2+2(3x-4)) \\ =3x^2+x+2-(4x^2+6x-8) \\ =3x^2+x+2-4x^2-6x+8 \\ =-x^2-5x+10 \end{gathered}[/tex]Therefore
[tex]f(x)-g(x)=-x^2-5x+10[/tex]Similarly
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =4x^2+2(3x-4)-(5(x^2-1)) \\ =4x^2+6x-8-(5x^2-5) \\ =4x^2+6x-8-5x^2+5 \\ =-x^2+6x-3 \end{gathered}[/tex]therefore
[tex]g(x)-h(x)=-x^2+6x-3[/tex]What is next in sequence 2 and 1/4, 2 and 3/4, 3 and 1/4 come in 3 and 3/4,
Given:
[tex]2\frac{1}{4},2\frac{3}{4},3\frac{1}{4},3\frac{3}{4},.......[/tex]Required:
To find the next term in the given sequence.
Explanation:
Clearly the given sequence is in arithmetic.
Therefore,
[tex]a_5=a+(n-1)d[/tex]Here,
[tex]\begin{gathered} a=2\frac{1}{4} \\ =\frac{9}{4} \\ \\ n=5 \\ \\ d=2\frac{3}{4}-2\frac{1}{4} \\ =\frac{11}{4}-\frac{9}{4} \\ =\frac{2}{4} \end{gathered}[/tex][tex]\begin{gathered} a_5=\frac{9}{4}+(5-1)\frac{2}{4} \\ \\ =\frac{9}{4}+2 \\ \\ =\frac{17}{4} \\ \\ =4\frac{1}{4} \end{gathered}[/tex]Final Answer:
The next term in the sequence is 4 1/4.