Answer:
[tex]e = \frac{bd}{v - bc} [/tex]
Step-by-step explanation:
[tex] \frac{v}{b } - c = \frac{d}{e } [/tex]
[tex] = > multiply \: bothsides \: by \: e[/tex]
[tex] = > \frac{v}{b} \times e - c \times e = \frac{d}{e} \times e[/tex]
[tex] \frac{ve}{b} - ce = d[/tex]
[tex] = > multiply \: both \: sides \: by \: b[/tex]
[tex] \frac{ve}{b} \times b - ce \times b = bd[/tex]
[tex] = > ve - bce = bd[/tex]
[tex] = > e(v - bc) = bd[/tex]
[tex] = > divide \: both \: sides \: by \: (v - bc)[/tex]
[tex] = > e = \frac{bd}{v - bc } [/tex]
Find the slope Y intercept in the equation for the data in the table and in the graph
Answer:
slope 6
y intercept 4
y = 6x + 4
Step-by-step explanation:
The slope is the change in y over the change in x.
Look at he two points (0,4) and (1,10)
The y started at 4 and went up to 10. That is a distance of 6.
AT the same time, the x changes from 0 tp 1 (0,4) (1,10). That is a distance of 1.
6/1 = 6
The y intercept is where the line crosses the y axis. It crosses at (0,4). 4 is the y intercept
y = mx + b Put the slope is for m and the y intercept for b
y = 6x + 4
Use the following function rule to find f(11).
f(x)=12|x+8|
f(11)=____
Answer:
f(11) = 228
Step-by-step explanation:
Which equation represents the volume of the box
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
What is volume?The volume of any object is the capacity. How much it can hold.
What is the formula of volume?The formula of volume is a product of length, breadth and height.
Volume = L × B × H
Given:
The perimeter of the square base of side s plus height h = 250cm
as per the given question,
The perimeter of the square base of side s plus height h = 250cm
2( s + s ) + h = 250
2 (2s) + h = 250
4s + h = 250
We can express h in the terms of s as,
h= 250 - 4s
Volume = length X breadth X height
Volume = s × s × h
V = s² × h
V = s² × (250 - 4s)
V = 250s² - 4s³
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
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AB of rhombus ABCD passes through the point (6, 6) and is perpendicular to the graph of y=3/4x-11. CD is parallel to AB and passes through the point (-6, 10). Select the equation in slope-intercept form of the line that includes CD.
A. y=4/3x+2
B. y=-4/3x+2
C. y=-3/4x+2
D. y=3/4x+2
Answer: [tex]y=-\frac{4}{3}x+2[/tex]
Step-by-step explanation:
The slope of [tex]AB[/tex] is [tex]-4/3[/tex]. Thus, the slope of [tex]CD[/tex] is also [tex]-4/3[/tex].
Thus, the equation of [tex]CD[/tex] can be found as follows:
[tex]y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2[/tex]
Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c · ·d. b. The critical points of f' (x) are same as the critical points of f(x) c. The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. d. All of the statements are false. e. Every local maximum a global maximum
The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.
What is a critical value of a function?The critical value is the value of x for which the double derivative of the function f(x) becomes zero.
When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either
a maxima or a minima.
Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.
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Teri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long will it take for Teri's account to earn $5000?
It will take 54 days for Teri's account to earn an amount of $5000.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
It is given by formula
A = [tex]p*e^{r*t}[/tex]
where:
A is final amount
p is principal amount
r is rate of interest and
t, is time period
Given: A= $5000, p=$1500, r=2.25% = 0.0225
To find: time period to get compounded amount
5000=1500×[tex]e^{0.0225*t}[/tex]
[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]
0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])
t = 53.5099 ≈ 54 days
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determine the sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000
The total of all multiples of either the first or second integer from the previous issue that are below 1000 will be 233168.
What is multiples of integer?Manifold is the fundamental definition of multiplicity. A multiple in mathematics refers to the outcome of multiplying two numbers together. In mathematics, multiples are the results of multiplying an integer by a given number. A number that is produced by multiplying a given integer by a natural number is referred to as a multiple of that number. The factors of 20, for instance, are 1, 2, 4, 5, 10, and 20. The multiples of 20 include, for instance, 20, 40, 60, 80, 100, etc.
Here,
The statement of the problem is to sum the multiples of 3 and 5 below 1000, not up to and equal 1000.
The equation is attached in image,
166833+99500−33165=233168
The sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000 will be 233168.
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Simplify (m^6n)^3.
mn^21
m^9n^3
m^18n
m^18n^3
After solving the given expression, the value obtained is [tex](m^1^8^n)[/tex]. Hence, option C is correct.
What is Simplification?To streamline a phrase, one must use many techniques to make it shorter and simpler. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.
Minimize a fraction to its simplest form to make it simpler. A fraction is said to be in its simplest form if both its numerator and denominator only include the integer.
As per the given information in the question,
The expression is,
[tex](m^6^n)^3[/tex]
= [tex](m^1^8^n)[/tex]
Therefore, option C is correct.
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Solve for a
2x-2=-3x+13
X =
To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:
2x - 2 + 3x + 2 = -3x + 13 + 3x + 2
5x = -3x + 15
8x = 15
Dividing both sides by 8, we get:
x = 15/8
= 1.875
Therefore, the value of x is approximately 1.875.
The value of x in equation 2x-2= -3x+13 is 3
To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:
2x+3x=13+2
5x=15
Now divide both side with 5 then, we get:
5x/5=15/5
x=3
Therefore, the value of x is 3
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Simplify and state the restrictions on the domain:
The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x ≠ 1, 2.
Explain domain of the function?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
According to question:We have,
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]
[tex]\frac{(x-1)^{2}}{x-2}[/tex]
For domain, Function should have solution should not be not defined.
For this, denominator must not equal to zero
Then, x -2 ≠ 0, x - 1 ≠ 0
x ≠ 2, x ≠ 1
Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x ≠ 1,2 is correct.
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Answer:
(b) (x -1)²/(x -2), x ≠ -3, 1, 2
Step-by-step explanation:
You want to know the domain restrictions and the simplified form of ...
[tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]
SimplifyWe can "invert and multiply", then cancel the common factor from numerator and denominator.
[tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]
DomainThe values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.
The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.
Here is a summary of what you get at the restricted values:
-3: (0)(-4)/-5 ÷ 0/-4 . . . . division by 01: (4)(0)/-1 ÷ 4/0 . . . . . . . divisor undefined2: (5)(1)/0 ÷ 5/1 . . . . . . . division by 0The simplified form with restrictions is ...
[tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]
The Christmas lights on the tree and the lights on the porch blink at a consistent rate. The tree lights blink every 4 seconds which the porch lights blink every 6 seconds after how many second will they blink together
Answer:
The tree lights and the porch lights will blink together every 12 seconds.
Step-by-step explanation:
In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
What is barometric air pressure?In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.
In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.
Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.
F(x) is the pressure in inches of mercury
It is given pressure 28 inches of mercury
Put F(x) equal to 28
F(x) = 0.48㏑(x+2) +27
28 = 0.48㏑(x+2) + 27
28-27= 0.48㏑(x+2)
1= 0.48㏑(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= [tex]e^{\frac{25}{12} }[/tex]
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
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Sketch a cone with diameter of 16 feet and height of 10 feet, then find the volume. If needed, round to the nearest hundredth.
The volume is 2679.46ft^3.
What is volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
We know that
The volume of the cone is equal to
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
where
r is the radius of the circular base of the cone [tex]$\mathrm{h}$[/tex] is the height of the cone
we have
[tex]$$\begin{aligned}& r=16 f t \\& h=10 f \mathrm{t}\end{aligned}$$[/tex]
assume
[tex]\pi=3.14[/tex]
substitute the values
[tex]$$\begin{aligned}& V=\frac{1}{3}(3.14)(16)^2(10) \\& V=2679.46 f t^3\end{aligned}$$[/tex]
The drawing in the attached figure
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opinions: y= -3x + 5, y = - 1/5x + 3, y= 1/3x + 1/5, y=1/3x + 5, y= 3x + 1/5
The required matches for the given equation of line are explain below.
Explain general equation of line.The general equation of a straight line is y = mx + c, where m is the inclination, and y = c is the worth where the line cuts the y-hub. This number c is known as the block on the y-pivot. The condition of a straight line with slope m and block c on the y-hub is y = mx + c.
According to question:We will find the graph, by using general form of equation
y = -3x + 5
Its y-intercept is 5,and angle is negative,So graph(3) is matches
similarly,
y = - 1/5x + 3
Its y-intercept is 3,So graph(1) is matches
y=1/3x + 5
Its y-intercept is 5,and angle is Positive,So graph(4) is matches
y= 3x + 1/5
Its y-intercept is 1/5,and angle is more than one,So graph(2) is matches
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The pattern below has been created by placing toothpicks together a) Find an expression for the total number of toothpicks in any set up b) How many toothpicks should there be in the 45th set up? Show your work.
For 45th set up 140 toothpicks are required.
What is Arithmetic Progression?A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.
given:
For First Figure, 8 toothpicks are used
For Second Figure, 11 toothpicks are used
For Third Figure, 14 toothpicks are used
So, we get the series 8, 11, 14, ...
Now, for n= 45
Using Arithmetic Progression
[tex]a_{45} = a+ (45- 1) d[/tex]
= 8 + 44(3)
= 140
Hence, for 45th set up 140 toothpicks are required.
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How much simple interest is made on an investment of $800 for 7 years at 6%
Answer:
$1,136
Step-by-step explanation:
The simple interest equation is A = P(1 + rt)The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 274 people entered the park, and the admission fees collected totaled 836.00 dollars. How many adults were admitted?
a. 209
b.170
c.104
Therefore in this question the solution of particular equation is 108 children and 175 adults in the amusement park on that particular day.
What is Equation ?When two expressions' values are set to be equal by a mathematical statement, that statement is known as an equation. To put it another way, it is a mathematical expression that means "this is equivalent to that." An equal sign, a mathematical expression, and a mathematical expression can all be seen on the left side of the symbol. The right ride of the equation frequently contains zero.
Let's first configure our system by giving x and y meaningful definitions. Let x be the total number of kids and y be the total number of adults.
Children cost $1.50, while adults cost $4.00. The number of kids, x, is multiplied by 1.5 to determine how much money a group of kids will cost. The 1.5x symbol stands for this. We will use 4y for adults, who must pay $4 to enter. On the specified day, $862 in total revenue was earned. We must add 1.5x and 4y to get at this sum.
1.5x + 4y = 862 equation required
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 283
System of equations:
1.5x + 4y = 862
x + y = 283
Thus,
x + y = 283
y = 283 - x
Substitute y = 283 - x
862=1.5x + 4 (283 - x)
1.5x + 1132 - 4x = 862
1132 - 2.5x = 862
-2.5x = -270
x = 108
Substitute x =108 back into y = 283 - x
y = 283 - 108 = 175
Therefore there were 108 children and 175 adults in the amusement park on that particular day.
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hi!! if someone could help me out and find the answer for number 17 i would appreciate it sm:) 100 points im just trying to get some of my work done by tomorrow
Answer: y=−2x+16
Step-by-step explanation:
[tex]\frac{1}{10} +\frac{7}{10}[/tex]
Answer given in the screenshot below. ↓
Force An 8.0-pound weight is lying on a sit up bench at the gym. If the bench is
inclined at an angle of 15°, there are three forces acting on the weight, as shown
in Figure 12. Find the magnitude of N and the magnitude of F.
Answer: 7
Step-by-step explanation: 7+2
Which is a strict inequality?
A. y>4
B. y≤4x+2
C. y≥x
D. y=−8x+3
The option that is a strict inequality is A. y>4
How can you tell if an inequality is strict?It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.
In conclusion, the correct option is A.
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Old Faithful in Yellowstone National Park has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. What is the probability that a randomly selected sample of 35 time intervals between eruptions has a mean longer than 95 minutes?
The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.
How to solve for the probability of a ramdom sample?mean of x = 85 minutes
σ = 21.25 minutes
x ~ N(σ², μ)
p(x < 95)
1-p(x≤95)
1 - p(z≤0.47)
Using the z table here
1-0.6808 = 0.3192
Probability of x > 95 = 0.3192
b. n = 20
from central limit theorem
1 - p (z < 2.1045)
1-0.99826 = 0.0174
1 - p (z < 2.58)
1-0.9951
= 0.0049
. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.
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A pre-paid phone company charges $17.75 as a monthly access fee and $0.13 per minute of calling time.
What will the monthly cost be if you make 176 minutes of calls this month?
Answer:
$40.63
Step-by-step explanation:
If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:
17.75 + (0.13 × 176) = total price
We need to figure out how much 0.13 multiplied by 176 is.
0.13 × 176 = 22.88
Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.
22.88 + 17.75 = 40.63
The monthly cost will be $40.63.
An interior designer is designing a room. Her options include 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures. How many
different room designs can be created from these options?
Answer
The total number of different room designs is 1296.
What is the fundamental principle of counting?According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.
Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.
As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3
= 1296
Hence, the total number of different room designs is 1296.
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Substitutions this equation
8x-y=-6
2x-3y=4
Sue and her brother wanted to buy 25 pieces of candy for their family's stockings. They chose to buy Kit Kats and Skittles. After shopping they spent $ 20.70. Skittles
cost 80 cents each and kit kats cost 90 cents each. How many of each candy did they get at the store? Let s-skittles and k=kit kats.
Which systems of equations represents this situation?
Answer:
18 Skittles and 7 Kit Kats
Linear system of equations in two variables
Step-by-step explanation:
We a linear system of two equations which can be solved simultaneously
Total pieces of candy equation
s + k = 25 [1]
Total cost equation
0.8s + 0.9k = 20.70 [2]
Multiply [1] by 0.80
0.80s + 0.80k = 20 [3]
Subtract [3] from [2]
0.80s + 0.90k = 20.70
[tex]-[/tex]
0.80s + 0.80k = 20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k = 0.70
k = 0.70/0.10 = 7
In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]
Answer: 18 Skittles and 7 Kit Kats
10. You are ordering shirts for the math club at your school. Short-sleeved shirts cost $ 8 each. Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts. The equation 8 x+20 y=200 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts. Graph the equation. Interpret the intercepts.
x-intercept:_____
y-intercept:_____
The x - intercept is (25, 0) and the y - intercept is (0, 10).
What is intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put y = 0 and work out x to find the x-intercept.
Set x = 0 and work out y to find the y-intercept.
Given: You are ordering shirts for the math club at your school.
Short-sleeved shirts cost $ 8 each.
Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.
The equation 8 x+20 y=200 models the total cost,
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
To find the x - intercept plug y = 0 in the above equation.
⇒ 8x + 20(0) = 200
8x = 200
x = 25
So, the point becomes, (25, 0).
To find y - intercept plug x = 0 in the above equation.
⇒ 8(0) + 20y = 200
20y = 200
y = 10
So the point becomes, (0, 10).
Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).
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PLEASE HELPED I"M TIMED I WILL GIVE BRAINLIST
Answer:
Below
Step-by-step explanation:
Angle 2 or angle HFE
Vertex is F
GF and FE are the sides of angle 1
The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a
local office building is 3:11. If a car in the lot is selected at random to get
the reserved parking space nearest the building, find the probability the car
selected is a hybrid. Express your answer as a simplified fraction.
The probability of getting a Hybrid car = 3/14
Probability:The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.
The formula for the probability of an event is given by
P(E) = No of favorable outcomes/ total number of outcomes
Here we have
The ratio of hybrid cars to gasoline-powered cars is 3:11
Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]
Then total number of cars = 3x + 11x = 14x
From the given data,
Total number of cars = 280
=> 14x = 280
=> x = 20
Number of Hybrid cars, 3x = 3(20) = 60
Here we select a car from a random experiment
Number of outcome = 280
Number of outcomes that we get Hybrid car = 60
Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]
= [tex]\frac{6}{28}[/tex] = [tex]\frac{3}{14}[/tex]
Therefore,
The probability of getting a Hybrid car = 3/14
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Complete question:
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.