Answer:
• First city: $5,500
,• Second city: $6,000
Explanation:
• Let the hotel charge before tax in the first city = x
,• Let the hotel charge before tax in the second city = y
The hotel charge before tax in the second city was $500 higher than in the first.
[tex]y=x+500\cdots(1)[/tex]The tax in the first city was 8.5%, and the tax in the second city was 7.5%.
The total hotel tax paid for the two cities was $917.50.
[tex]\begin{gathered} (8.5\%\text{ of x\rparen+\lparen7.5\% of y\rparen=917.50} \\ 0.085x+0.075y=917.50\cdots(2) \end{gathered}[/tex]The problem gives rise to the system of linear equations below:
[tex]\begin{gathered} y=x+500\cdots(1) \\ 0.085x+0.075y=917.50\operatorname{\cdots}(2) \end{gathered}[/tex]The system is then solved for x and y.
Substitute equation (1) into equation (2):
[tex]\begin{gathered} 0.085x+0.075y=917.50\operatorname{\cdots}(2) \\ 0.085x+0.075(x+500)=917.50 \\ 0.085x+0.075x+37.50=917.50 \\ 0.16x=917.50-37.50 \\ 0.16x=880 \\ \text{ Divide both sides by 0.16} \\ \frac{0.16x}{0.16}=\frac{880}{0.16} \\ x=\$5500 \end{gathered}[/tex]Finally, solve for y:
[tex]\begin{gathered} y=x+500 \\ =5500+500 \\ =\$6,000 \end{gathered}[/tex]The hotel charge before tax in each city was:
• First city: $5,500
,• Second city: $6,000
Problem 1. P (0 < Z< 1.06) = Problem 2. P (0 < z < ∞) =Problem 3. (-∞ < z < 0) =
As given by the question
There are given that the probability
[tex]P(0Now,According to the cumulative probability,
The value of the probability, P(0Hence, the correct option is C.
In ALMN, the measure of ZN=90°, LM = 68 feet, and MN = 38 feet. Find themeasure of ZL to the nearest tenth of a degree.
The sine of an angle(in a right triangle) is given by the the ratio of the opposite side with the hypotenuse, so the sine of (xº) is given by:
[tex]\frac{38}{68}=\sin (x^o)[/tex]Using the arcsin(x) function we can find the measure of the angle:
[tex]\begin{gathered} \sin ^{-1}(\frac{38}{68})=x^o=33.9744759503\ldots \\ \Rightarrow x^o\approx34^o \end{gathered}[/tex]A battery is charged. The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed. 100* 90 80 70 50 Capacity (% charged) 40 30 20 10+ 25 5 30 15, 20 10
Answer:
(a) 2% per minute
Step-by-step explanation:
Given a graph that shows a battery charging from 40% to 100% in 30 minutes, you want to know the charging rate in % per minute.
SlopeThe slope (rate of change) is the ratio of "rise" to "run" for the line on the graph. Here, the line rises 60% from 40% to 100% when the run is 0 minutes to 30 minutes.
The ratio is ...
(60%)/(30 minutes) = 2%/minute
The battery charges at the rate of 2% per minute.
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Find the area of the triangle below. Be sure to include the correct unit in your answer. 16yd 6yd 10yd
Consider the figure.
From the triangle ABD, we have,
[tex]BD=\sqrt[]{16^2-6^2}=14.83[/tex]Therefore,
[tex]BC=14.83-10=4.83[/tex]From the traingle ABC, we have,
[tex]AC=\sqrt[]{4.83^2+6^2}=7.7[/tex]Thus, the area of the traingle is,
[tex]\frac{1}{2}\times7.7\times10=38.5[/tex]Question 8 Ella has $6.11 and purchases snacks for $3.28. How much money does she have left over after buying her snacks? T Question Help: Message instructor Check Answer a 07
Given:
Total money that Ella has : $6.11
The money she spent on snacks is $3.28.
The objective is to find how much money does she left over after buying her snacks, so,
Money she is left with= total money - money spent on snacks.
[tex]\begin{gathered} \text{Money she is left with= \$6.11-\$3.28} \\ =2.83 \end{gathered}[/tex]Therefore, Ella is left with $2.83 after buying her snacks.
Which figure below is the image of the given figure translated 5 units to the left and down 2 units?
Solution:
Given a graph with triangle ABC;
The coordinates of ABC are
[tex]\begin{gathered} A(-1,1) \\ B(1,4) \\ C(3,-2) \end{gathered}[/tex]If the image is translated 5 units to the left, that means, subtracting 5 from the x coordinates of ABC
[tex]\begin{gathered} A(-1-5,1)\Rightarrow A(-6,1) \\ B(1-5,4)\Rightarrow B(-4,4) \\ C(3-5,-2)\Rightarrow(-2,-2) \end{gathered}[/tex]Then, the image is translated 2 units down, i.e. subtracting 2 units from the y coordinates of the ABC
[tex]\begin{gathered} A(-6,1-2)\Rightarrow A(-6,-1) \\ B(-4,4-2)\Rightarrow B(-4,2) \\ C(-2,-2-2)\Rightarrow C(-2,-4) \end{gathered}[/tex]The coordinates are
[tex]\begin{gathered} A(-6,-1) \\ B(-4,2) \\ C(-2,-4) \end{gathered}[/tex]Hence, the figure is
Help please been trying to figure these out and I want to learn
Given:
Two binomials are given.
[tex](2A+3B)(2A-3B)[/tex]Required:
Find the product of the binomials.
Explanation:
The given binomials are:
[tex](2A+3B)(2A-3B)[/tex]Use the following identity
[tex](a+b)(a-b)=a^2-b^2[/tex][tex]\begin{gathered} (2A+3B)(2A-3B)=(2A)^2-(3B)^2 \\ (2A+3B)(2A-3B)=4A^2-9B^2 \end{gathered}[/tex]This matches with option D.
Final Answer:
Option D is the correct answer.
What is the perimeter of a square if the hight is 5x and the length is 4x+7
Given data:
The given height of the square is h=5x.
The given lenght of the square is l=4x+7.
In square all dimensions are equal.
5x=4+7
x=7
The
You have decided to purchase a home that has an asking price of $159,900. You wish to put a down payment is the percent equivalent to the date you were born on (for example I was born on the 29th of the month so I would have a 29% down payment). Explain how you would determine the amount that you would be financed for your mortgage. (The amount financed is the is the amount of the asking price that would be left after the down payment is paid.) Your explanation should include the mathematical support.
You have decided to purchase a home at $159,900.
I was born on the 28th so I choose to put a 28% down payment.
The amount I would be financed for my mortgage would be 100 - 28 = 72% of $159,900.
This can be simplified as;
[tex]\begin{gathered} =\frac{72}{100}\times159900 \\ =\text{ \$115128} \end{gathered}[/tex]Therefore, the amount that I would be financed for my mortgage is $115,128
Last question choose from the correct choice A,BC, or D
Given the function
[tex]R(x)=\frac{7x+7}{6x+12}[/tex]we have to determine the behavior of the graph on either sides of the vertical asymptotes. if one exists.
Remember that vertical asymptotes occur when in a rational function, that is a function of the form
[tex]R(x)=\frac{f(x)}{g(x)}[/tex]The denominator, g(x), becomes 0.
In our case, the denominator of the rational function is
[tex]g(x)=6x+12[/tex]therefore
[tex]6x+12=0\text{ }\Rightarrow\text{ }x=-2[/tex]we conclude that there is a vertical asymptote at x=-2.
Now we will determine the behavior on both sides of the asymptote
One possible approach to discover this behavior is to pick up close to x=-2 values on both sides and evaluate it to determine the sign. Let us take
[tex]x=-2.01\text{ and }x=-1.99[/tex]Evaluation the first one
[tex]R(-2.01)=\frac{7(-2.01)+7}{6(-2.01)+12}=117.83[/tex]since the result is big and positive we conclude that on the left side of the asymptote the function approach to + infinity.
Now we will evaluate on the other side to determine the sign
[tex]R(-1.99)=\frac{7(-1.99)+7}{6(-1.99)+12}=-115.5[/tex]Therefore, the on the right the function approach to - infinity as the numbers approach to x=-2
Looking at the options we see that the correct option is the option c).
Write a equation in slope intercept form using the following informationslope: 1 y- intercept : (0,-1)
Need help solving this math class work I don’t understand it
Given:
[tex]\frac{2+i}{1-2i}[/tex][tex]\frac{2+i}{1-2i}=\frac{2+i}{1-2i}\times\frac{1+2i}{1+2i}[/tex][tex]\frac{2+i}{1-2i}=\frac{2+4i+i-2}{1+4}[/tex][tex]\frac{2+i}{1-2i}=\frac{5i}{5}[/tex][tex]\frac{2+i}{1-2i}=i[/tex]If angle d=130 and angle c=60, what is angle a?
The sum of all internal angles of a triangle is 180°, therefore
[tex]a+b+c=180[/tex]Also, we know that
[tex]b+d=180[/tex]We have the value of d then we can find b using the second equation
[tex]\begin{gathered} b+130=180 \\ \\ b=180-130 \\ \\ b=50 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} a+50+60=180 \\ \\ a=180-50-60 \\ \\ a=180-110 \\ \\ a=70 \end{gathered}[/tex]The value of a is 70°
rewrite the equation below in slope intercept form ( y = mx + b)-4y + 2y = 12
The slope intercept form : y = mx + b
The given equation : -4x + 2y = 12
to write the equation in the slope intercept form, Simplify the equation for y
[tex]\begin{gathered} -4x\text{ + 2y =12} \\ \text{Add 4x on both side} \\ 4x-4x+2y=12+4x \\ 2y=12\text{ +4x} \\ \text{Divide both side by 2} \\ \frac{2y}{2}=\frac{12}{2}+\frac{4x}{2} \\ y=6+2x \\ y=2x+6 \end{gathered}[/tex]The slope intercept form is y = 2x + 6
Answer : y = 2x + 6
The crackers in a box have three shapes. Max randomly choose one cracker at a time 40 times, returning the cracker to the box each time.Crackers (Shape/frequency)Oval: 18Rectangle: 14Star: 8Find the experimental probability of choosing a cracker that is not star-shaped.
Can you see my message now?
Alright, give me one moment to read the exercise, please.
I'll type the explanation now. I'll bold the explanation so that you can tell it appart from my messages.
There are 3 shapes of crackers in the box, oval, rectangular and star. Max took one cracker at a time, 40 times, recorded its shape and put it back in the box.
To calculate the experimental probability of getting each shape, you have to divide the number of times he got that determined shape (frequency of the cracker shape) by the total number of times he repeated the experiment.
So for the oval crackers, the probability will be:
[tex]P(oval)=\frac{\text{frequency}}{\text{Total}}=\frac{18}{40}=0.45[/tex]For the rectangular crackers the probability will be
[tex]P(rec\tan gular)=\frac{\text{frequency}}{\text{Total}}=\frac{14}{40}=0.35[/tex]For the star-shaped crackers the probability will be:
[tex]P(star)=\frac{\text{frequency}}{\text{Total}}=\frac{8}{40}=0.20[/tex]Now you have to determine the probability of the event "NOT star shaped" this occurs when you get either rectangular or oval shaped crackers. This event is complementary to the event "Star shaped" and you can calculate it as:
[tex]\begin{gathered} P(Star^c)=1-P(Star) \\ P(Star^c)=1-0.20 \\ P(Star^c)=0.80 \end{gathered}[/tex]You have to express it as a percentage so multiply the result by 100
[tex]0.80\cdot100=80[/tex]The experimental probability of not geting a star shaped cracker is 80%
Done!
Tell me if you have any doubts regarding the explanation.
5. A science museum opened its butterfly exhibit in January 1996 with an initial population of 30 butterflies. The population doubles in size every 6 months. Which value of x, the number of doubling cycles, should be used to determine the number of butterflies in the exhibit in January 2000?C. 32A 4B. 8D. 64
Given that
A science museum opened its butterfly exhibit in January 1996 with an initial population of 30 butterflies. The population doubles in size every 6 months. And we need to find the number of doubling cycles till January 2000.
Explanation -
To find the doubling rate we will divide the initial population by the time in which it is getting doubled.
So, the initial population is 30 and the time is 6 months.
The doubling rate will be = 30/6 = 5
So the value of x will be
[tex]x=2^5=32[/tex]So the correct option is C.
And the final answer is 32.
< Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many minutes have passed, m, when Tank A contains 151 liters How many minutes have passed, m, when Tank A contains 191.5 liters How many minutes have passed,y, when Tank A contains x liters
we get that the equation that models this situation is:
[tex]L=9m+124[/tex]where L is the number of liters and m the minutes. So we have that
[tex]151=124+9m\rightarrow m=\frac{151-124}{9}=3[/tex]so after 3 minutes the tank jas 151 liters
[tex]191.5=124+9m\rightarrow m=\frac{191.5-124}{9}=7.5[/tex]so after 7.5m the tanks has 191.5 liters
and for the last one we get
[tex]x=9y+124\rightarrow y=\frac{x-124}{9}[/tex]Use Law of Cosines to solve for this problem. Round your answer to the nearest TENTH.
We can find the distance from the basket to malachi (BC) using the law of cosines. Therefore:
[tex]\begin{gathered} BC=\sqrt{AB^2+AC^2-2(AB)(AC)cos(A)} \\ BC=\sqrt{24^2+26^2-2(24)(26)cos(34)} \\ BC\approx14.7ft \end{gathered}[/tex]Answer:
The distance between the basket and Malachi is 14.7 ft
need help asappppppp
Cross Product of Vectors. definition and example
Cross product is the method you use to multiply two vectors.
General formulas of a cross product (axb):
[tex]\begin{gathered} a(a_x,a_y,a_z) \\ b(b_x,b_y,b_z) \\ \\ a\times b=c \\ \\ c_x=a_yb_z-a_zb_y \\ c_y=a_zb_x-a_xb_z \\ c_z=a_xb_y-a_yb_x \\ \\ c(c_x,c_y,c_z) \end{gathered}[/tex]Example:
Multiply the next vectors:
a(5,2,-3)
b(-1,-4,7)
[tex]\begin{gathered} a\times b=c \\ \\ c_x=2*7-(-3)*(-4) \\ c_x=14-12 \\ c_x=2 \\ \\ c_y=(-3)*(-1)-5*7 \\ c_y=3-35 \\ c_y=-32 \\ \\ c_z=5*(-4)-2*(-1) \\ c_z=-20+2 \\ c_z=-18 \\ \\ a\times b=(2,-32,-18) \end{gathered}[/tex]find the missing measure in the triangle with the given angle measures.100°, x°, 40°a. 40b.90c.220d.30
For this exercise you need to remember that, by definition, the sum of the interior angles of any triangle is 180 degrees.
In this case, you know the following interior angles of the triangle given in the exercise:
[tex]\begin{gathered} 100\degree \\ 40\degree \end{gathered}[/tex]Then, based on the explained above, you can set up the following equation:
[tex]40\degree+100\degree+x=180\degree[/tex]Finally, you must solve for the variable "x" in order to find the measure of the missing angle of the triangle. You get that this is:
[tex]\begin{gathered} 140\degree+x=180\degree \\ x=180\degree-140\degree \\ x=40\degree \end{gathered}[/tex]The answer is: Option a.
1.3b Practice Your teacher has limited times you may check yo this item i Determine whether the equation 2(h+1) = 5h – 7 has one solution, no solution, or infinitely many solutions. The equation has If the equation has a solution, enter it below. If the equation has no solution or infinitely many solutions, leave the solution field blank. h= 201 PREV 1 2 3 4 5 6 NEXT > Check ? Help
1) Let's check that by solving it
2(h+1) = 5h – 7 Distribute the factor
2h +2 = 5h -7 Subtract 2 from both sides
2h -5h = -7 -2 Combine like terms
-3h= -9
3h=9 Divide both sides by 3
h=3
This equation has one solution. h=3
2. 8.EE.1.4 At a given time, Saturn was 9.1 x 108 miles from the Sun and Earth was 9.3 X 107 miles from the Sun. By what distance is one planet closer to the Sun than the other planet? A. 2 x 101 B. 2 x 105 C. 8.17 x 107 D. 8.17 x 108
The planet Saturn from the Sun was:
[tex]9.1\times10^8[/tex]The Earth miles from the Sun is:
[tex]9.3\times10^7[/tex]The difference between them is:
[tex]\begin{gathered} (9.1\times10^8)\text{ -(9.3}\times10^7) \\ (91\times10^7)\text{ - (9.3}\times10^7) \\ \text{Factor out 10}^7,\text{ we get} \\ (91-9.3)10^7 \\ 81.7\times10^7 \\ 8.17\times10^1\times10^7 \\ 8.17\times10^{1+7} \\ 8.17\times10^8\text{ miles} \end{gathered}[/tex]Thus, the correct answer is option D
Please help I’m failing math and my quarter ends Friday
y-intercept (0, -7) and x-intercept (5,0)
1) To find the y-intercept, let's rewrite that equation into the slope-intercept form to better do it:
2/5x -2/7y =2 Add 2/7y to both sides
-2/7y = 2 -2/5x Multiply the whole equation by 7 to get rid of the fraction x
-2y = 14 -14/7x Divide by -2
y = -7 +x
y= x -7
So the y-intercept is at y=-7
2) To find the x-intercept, let's plug into that y=0
2/5x -2/7y =2
2/5x -2/7(0) = 2
2/5x = 2
x= 2 : 2/5
x = 2 x 5/2
x= 5
3) Hence, the answer is y-intercept (0, -7) and x-intercept (5,0)
Jonah and Mike are playing a game with a fair number cube withfaces numbered 1 to 6 and a spinner with the numbers 3,2 6, 4, 6,4, 3, 2. In order for Jonah to advance to the next level, he must rollan even number on cube and spin an even number on the spinner.What is Jonah's chance of advancing?Your answer needs to bewritten as a % and do not round your answer.
Answer:
[tex]\begin{gathered} P(A\text{ and B)=}\frac{3}{8} \\ P(A\text{ and B)= 37.5\%} \end{gathered}[/tex]Step-by-step explanation:
The probability of an event is represented by the following equation;
[tex]P(A)=\frac{\text{ Number of favorable outcomes}}{\text{ Total number of possible outcomes}}[/tex]Then, he must roll an even number on the cube and spin an even number on the spinner.
The probability of two independent events happening is given as:
[tex]P(A\text{ and B)=}P(A)\cdot P(B)[/tex]Hence, Jonah's chance of advancing is:
[tex]\begin{gathered} P(A\text{ and B)=}\frac{3}{6}\cdot\frac{6}{8} \\ P(A\text{ and B)=}\frac{18}{48} \\ P(A\text{ and B)=}\frac{3}{8} \end{gathered}[/tex]i was having internet issues with my last tutor:( how do you graph y= 2/3x -7?
Explanation:
To graph the equation y = 2/3x - 7, we need to identify two points on the line.
So, to find the points, we will give a specific value to the variable x, and then we will calculate the value of y.
Therefore:
If x = 3 then:
y = (2/3)x - 7
y = (2/3)*3 - 7
y = 2 - 7
y = -5
If x = 6 then:
y = (2/3)x - 7
y = (2/3)*6 - 7
y = 4 - 7
y = -3
Now, we have the points (3, -5) and (6, -3). So, we can graph the equation as:
julia is going to invest $860 in an account and leave it for 8 years. assuming the interest rate is compounded continuously, What interest rate To the nearest Hundresth of a percent Would be required in order for julia To end up with $1190?
Find the equation (in terms of x ) of the line through the points (-4,5) and (2,1)y=
Given:
There are given that the two points are:
[tex](-4,5)\text{ and }(2,1)[/tex]Explanation:
To find the equation, first, we need to find the slope of the line from the given points.
So,
From the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=-4,y_1=5,x_2=2,y_2=1[/tex]Then,
Put all the values into the above formula:
So,
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-5}{2+4} \\ m=-\frac{4}{6} \\ m=-\frac{2}{3} \end{gathered}[/tex]Now,
From the formula of point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Then,
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-5=-\frac{2}{3}(x-(-4)) \\ y-5=-\frac{2}{3}(x+4) \\ 3y-15=-2(x+4) \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3y-15=-2(x+4) \\ 3y-15=-2x-8 \\ 3y-15+2x+8=0 \\ 3y+2x-7=0 \\ 3y=-2x+7 \\ y=-\frac{2}{3}x+\frac{7}{3} \end{gathered}[/tex]Final answer:
Hence, the equation of line is shown below:
[tex]y=-\frac{2}{3}x+\frac{7}{3}[/tex]a particular plant root grows 1.5 inches per month how many centimeters is in the plant root growing per month 1 in equals 2.54 cm
Answer:
3.81 centimeters per month
Explanation:
We know that 1 inch is equal to 2.54 centimeters, so to convert 1.5 inches per month to centimeters per month we will use the proportion 2.54 cm / 1 in.
Therefore, 1.5 inches per month is equal to:
[tex]1.5\text{ in per month }\times\frac{2.54\text{ cm}}{1\text{ in}}=3.81\text{ cm per month}[/tex]So, the plant root grows 3.81 centimeters per month
One figure is a rotation image of the other One figure is a translation image of the other Neither figure is a translation or rotation image of the other
Given:
Two figures are congruent.
Required:
We need to find the correct statement.
Explanation:
One figure is rotated and we get the image.
One figure is a rotation image of the other
We know that rotation transformation preserved the sides.
Final answer:
One figure is a rotation image of the other