Amtrak's annual passenger revenue for the years 1985 - 1995 is modeled approximately by the formulaR = -60|x- 11| +962where R is the annual revenue in millions of dollars and x is the number of years after 1980. In what year was the passenger revenue $722 million?In the years ____ and ___, the passenger revenue was $722 million.
Answers
ANSWER
1987 and 1995
EXPLANATION
The revenue is modeled by:
[tex]R=-60|x-11|+962[/tex]To find the years that the revenue was $722 million, we have to solve for x when R is 722.
That is:
[tex]\begin{gathered} 722=-60|x-11|+962 \\ \Rightarrow722-962=-60|x-11| \\ -240=-60|x-11| \\ \Rightarrow|x-11|=\frac{-240}{-60} \\ |x-11|=4 \end{gathered}[/tex]We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.
That is:
[tex]\begin{gathered} x-11=4 \\ x-11=-4 \end{gathered}[/tex]Solve for x in both:
[tex]\begin{gathered} x=11+4 \\ \Rightarrow x=15 \\ x=11-4 \\ \Rightarrow x=7 \end{gathered}[/tex]That is to say 7 and 15 years after 1980.
Therefore, in the years 1987 and 1995, the revenue was $722 million.
Related Questions
What is the inverse function of y = (x-4)^2+2
Answers
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
Answers
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
| 5-6x | -12 = 0Solve the absolute. equation for 2 values of x
Answers
Given
[tex]|5-6x|-12=0[/tex]To solve this equation for both possible values of x, you have to separate it into two calculations.
1) One will be for the case that the values inside the absolute term are multiplied by "+1":
[tex]\begin{gathered} 1\cdot(5-6x)-12=0 \\ 5-6x-12=0 \\ -6x+5-12=0 \\ -6x-7=0 \\ -6x=7 \\ -\frac{6x}{-6}=\frac{7}{-6} \\ x=-\frac{7}{6} \end{gathered}[/tex]The first value of x is -7/6
2) The second will be the case that the absolute values are negative, that is as if they are multiplied by -1
[tex]\begin{gathered} (-1)(5-6x)-12=0 \\ -5+6x-12=0 \\ 6x-5-12=0 \\ 6x-17=0 \\ 6x=17 \\ \frac{6x}{6}=\frac{17}{6} \\ x=\frac{17}{6} \end{gathered}[/tex]The second value of x is 17/6
So for this absolute equation, the possible values of x are -7/6 and 17/6
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
Answers
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
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prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
Answers
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
the sum of the angle measures of a polygon with n sides is given find n1440
Answers
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answers
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.
14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Answers
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
Answers
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
Answers
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
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Answer parts a through E for the function shown below
Answers
Solution
We are given the function
[tex]f(x)=x^3+4x^2-x-4[/tex]First, Let us do the simplification or factorization
[tex]\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}[/tex](a).
The coefficient of x^3 is positive
(b).
So basically, we set f(x) = 0 to get the x - intercepts
[tex]\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}[/tex]The x - intercepts are
[tex]x=1, -1, -4[/tex]The graph of f(x) is also given below
I will send u a picture of my equation
Answers
Answer:
where is the picture????
-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Answers
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answers
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
Answers
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Answers
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
Answers
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.can anyone help me? solve using system of linear equations using elimination x – y - 3z = 4 2x + 3y – 3z = -2 x + 3y – 2z = -4
Answers
The solution is x = 2, y = -2 and z =0
How to solve the system of equations?The system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Start by eliminating y
To do that, we subtract (2) from (3)
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
This gives
-x + z = -2
Make x the subject in the above equation
x = z + 2
Substitute x = z + 2 in (1) and (2)
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Solve the equations
-2z - y = 2
-z + 3y = -6
Multiply -z + 3y = -6 by 2
-2z + 6y = -12
Start by eliminating z
Subtract -2z + 6y = -12 from -2z - y = 2
7y = -14
Evaluate
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the values of the variables are x = 2, y = -2 and z =0
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Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
Answers
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
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solve for missing variable: 11y-36=63
Answers
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. Which probabilities correctly completethis probability distribution for the 50 pieces of fruit, in the order listed?
Answers
Given:
Total number of pieces = 50
So, the probabilities are:
Apples
[tex]P(apples)=\frac{8}{50}=0.16[/tex]Bananas
[tex]P(bananas)=\frac{10}{50}=0.2[/tex]Lemons
[tex]P(lemons)=\frac{5}{50}=0.1[/tex]Oranges
[tex]P(oranges)=\frac{15}{50}=0.3[/tex]Pears
[tex]P(pears)=\frac{12}{50}=0.24[/tex]Answer: A.
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Answers
Pls someone help me! Giving brainless
Answers
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
Factor by grouping:y^3-5y^2+3y-15
Answers
we have the expression
y^3-5y^2+3y-15
Grouping terms
(y^3-5y^2)+(3y-15)
factor y^2
y^2(y-5)+(3y-15)
factor 3
y^2(y-5)+3(y-5)
factor (y-5)
(y-5)[y^2+3]An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )
Answers
Let be "x" the number of gallons of gas that can be treated with a 16-ounce bottle of alcohol.
According to the information given in the exercise, 3 ounces of isopropyl alcohol should be mixed with 14 gallons of gas.
Then, you can set up the following proportion:
[tex]\frac{14}{3}=\frac{x}{16}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (16)(\frac{14}{3})=x \\ \\ \frac{224}{3}=x \\ \\ x\approx74.67 \end{gathered}[/tex]Therefore, the answer is:
[tex]\approx74.67\text{ }gallons[/tex]Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answers
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answers
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
Answers
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmFirst try was incorrect Fill in the blank. Constant: a number that is next to a variable.
Answers
A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
Answers
True.
Since it is strictly greater