Find the volume of a solid that results when the region enclosed by y= sqrt(x), y=0, and x=9 is revolved about the line x=9.
Answers
The volume of the solid that results when the region enclosed by y= sqrt(x), y=0, and x=9 is revolved about the line x=9 is 243π.
The solid that results when the region enclosed by y= sqrt(x), y=0, and x=9 is revolved about the line x=9 is called the solid of revolution. It is a geometric shape that is generated by rotating a region of a plane about a fixed line lying in the same plane.What is the formula to calculate the volume of a solid of revolution?The formula to calculate the volume of a solid of revolution is given as follows:$$V = \int_{a}^{b} \pi r^{2} \,dx $$Where a and b are the limits of integration, r is the radius, and x is the variable of integration.Now, let us calculate the volume of the solid that is formed by rotating the region enclosed by y= sqrt(x), y=0, and x=9 about the line x=9.Step 1: Sketch the given regionThe given region is the area between the curves y=0, y=sqrt(x), and x=9. The following is the sketch of the region.Step 2: Find the radius of the solid of revolutionThe radius of the solid of revolution is the distance between the axis of rotation and a point on the curve. In this case, the axis of rotation is x=9, and the curve is y= sqrt(x). Therefore, the radius of the solid of revolution is given by:r = 9 - xStep 3: Find the limits of integrationThe limits of integration are the x-coordinates of the intersection points of the curves y= sqrt(x), y=0, and x=9. The intersection points are (0,0) and (9,3). Therefore, the limits of integration are a=0 and b=9.Step 4: Calculate the volume of the solidNow, we can substitute the values of r, a, and b in the formula for the volume of a solid of revolution.$$V = \int_{a}^{b} \pi r^{2} \,dx $$$$V = \int_{0}^{9} \pi (9 - x)^{2} \,dx $$$$V = \pi \int_{0}^{9} (81 - 18x + x^{2}) \,dx $$$$V = \pi \left[81x - 9x^{2} + \frac{x^{3}}{3}\right]_{0}^{9} $$$$V = \pi (729 - 729 + 243) $$$$V = \boxed{243\pi}$$
Therefore, the volume of the solid that results when the region enclosed by y= sqrt(x), y=0, and x=9 is revolved about the line x=9 is 243π.
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Related Questions
How many students answered exactly two questions incorrectly
Answers
Step-by-step explanation:
you didn't post the questions yk?!
A roller coaster’s height is given by the equation h = –.067t2 7t 50, where t represents the time in seconds. how long will it take riders to pass over the hill and reach ground level? hint: set h = 0. 13.40 seconds 50.07 seconds 52.24 seconds 111.19 seconds
Answers
The time it take riders to pass over the hill and reach ground level is 111.19 seconds .
Given :
the roller coaster's height expressed by the equation below;
h = -0.067t^2 + 7t + 50
where
t is the time in seconds
The driver will hit the ground at the point where h = 0
Substitute
-0.067t^2 + 7t + 50 = 0
Multiply through by -1
0.067t^2 - 7t +-50 = 0
Factorize :
On factorizing, the positive value of "t" is 111.19 seconds
Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds
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Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm
Answers
Answer: 28cm²
Step-by-step explanation: To calculate the area of the trapezium, we can use the formula:
Area = (1/2) x (sum of parallel sides) x (height)
In this case, the two parallel sides are 6 cm and 8 cm, and the height is 4 cm.
Plugging in the values, we get:
Area = (1/2) x (6 cm + 8 cm) x 4 cm
Area = (1/2) x 14 cm x 4 cm
Area = 28 cm²
the mean per capita consumption of milk per year is 126 liters with a standard deviation of 24 liters. if a sample of 100 people is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 5.91 liters? round your answer to four decimal places.
Answers
The probability shows sample mean differ from the true mean by less than 5.91 liters is equal to 0.9864.
Standard deviation = 24 liters
sample size = 100
The standard error of the mean is,
Standard error = σ / √(n)
where σ is the population standard deviation, n is the sample size.
Substituting the given values, we get,
Standard error
= 24 / √(100)
= 2.4
Probability that the sample mean would differ from the true mean by less than 5.91 liters, standardize the difference using the standard error,
z = (X - μ) / (SE)
where X is the sample mean,
μ is the true population mean,
and SE is the standard error of the mean.
Substituting the given values, we get,
z = (5.91) / 2.4
= 2.4625
Probability corresponding to this z-score,
Use a standard normal distribution attached table
The probability of the sample mean differing from the true mean by less than 5.91 liters is the probability of getting a z-score between -2.4625 and 2.4625.
This can be found by taking the difference between the cumulative probabilities corresponding to these two z-scores.
Using a standard normal distribution attached table ,
Probability of getting a z-score less than -2.4625 is 0.0068,
Probability of getting a z-score less than 2.4625 is 0.9932.
Probability of getting a z-score between -2.4625 and 2.4625 is
0.9932 - 0.0068 = 0.9864 (Rounding to four decimal places)
Therefore, the probability that the sample mean would differ from the true mean by less than 5.91 liters is 0.9864.
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Determine wheater rolles theorom can be applied
f (x)=x^2−2x−3
On closed intervals [−1, 3] if rolles theorom can be applied find all values of C in open interval (−1,3) such that f'’ (c)=0
Answers
Rolle's Theorem can be applied to the function f(x) = x^2 - 2x - 3 on the closed interval [-1, 3].
Rolle's Theorem states that if a function f(x) is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in the open interval (a, b) such that f'(c) = 0.
In this case, the function f(x) = x^2 - 2x - 3 is a polynomial, which is continuous and differentiable for all values of x. The closed interval [-1, 3] satisfies the conditions of Rolle's Theorem since f(a) = f(-1) = (-1)^2 - 2(-1) - 3 = 0 and f(b) = f(3) = 3^2 - 2(3) - 3 = 0.
Therefore, since the function f(x) satisfies the conditions of Rolle's Theorem on the closed interval [-1, 3], there exists at least one point c in the open interval (-1, 3) such that f'(c) = 0.
To find the values of c, we need to find the derivative of f(x) and solve for f''(c) = 0. Taking the derivative of f(x), we have:
f'(x) = 2x - 2.
To find the value(s) of c in the open interval (-1, 3) where f''(c) = 0, we need to find the second derivative of f(x) and solve for f''(c) = 0.
Differentiating f'(x), we have:
f''(x) = 2.
The second derivative of f(x) is a constant function, f''(x) = 2, which is equal to 0 for no value of x. Therefore, there are no values of c in the open interval (-1, 3) such that f''(c) = 0.
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Please Help!!!!!! Will give brainliest
Answers
Answer:
55
Step-by-step explanation:
whyeyeyeyeuwu2u2727277e3
The table below shows the the total cost of admittance for a basketball game,y, for x students
Answers
Answer:
The 2nd one
Step-by-step explanation:
What are the answers to the following?
Convert the following to decimals: Round to the nearest thousandth place.
1) 90% 2) 30%
3) 115.9% 4) 9%
5) 7%
Convert the following to percent: Round to the nearest tenth of the percent.
6) 0.452 7) 0.006
8) 0.002 9) 0.05
10) 4.78
Answers
Answer:
1) .90 2) .30 3) .116 4).9 5).7
6)50% 7) 0.6% 8)0.2% 9) 10% 10)480%
Step-by-step explanation:
Find an expression which represents the difference when (10x-6y)(10x−6y) is subtracted from (7x-4y) in simplest terms.
Answers
Answer:-3x+2y
Step-by-step explanation:
The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find GE.
Answers
GE = 89 feet when using the definition of a rectangle's diagonals.
Explain the term rectangle's diagonals?A rectangle is split into two equal right triangles by a diagonal. A rectangle's diagonals are all the same length.The sides of a rectangle.Two of the diagonals in a rectangle are congruent, meaning they are equivalent to one another.A rectangle's diagonals cut each other down into equal segments.The rectangle room's diagonals are as follows:
DF and GE
So,
DF = GE
DH = 1/2(DF)
Put
44.5 = 1/2(DF)
DF = 2(44.5)
DF = 89
Thus,
DF = GE = 89
GE = 89 ft.
Therefore, GE = 89 feet when using the definition of a rectangle's diagonals.
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question the random variable x is exponentially distributed, where x represents the time it takes for a whale watcher to spot a whale. if x has an average value of 45 minutes, what is the probability that x is less than 45 minutes? round the final answer to three decimal places.
Answers
0.368 .
The probability that a random variable x is exponentially distributed and less than 45 minutes,
given that the average value is 45 minutes, is 0.368.
This can be calculated by taking the negative of the natural logarithm of 1/2 (i.e. -ln(0.5)) and dividing it by the average value of 45 minutes.
The result, -ln(0.5)/45, equals 0.368, rounded to three decimal places.
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Select the correct answer. how might an architect use geometry in their work? to determine the best materials for a structure to decide how many electrical outlets to install to decide how much to charge for their design to design the floorplan of a structure
Answers
An architect uses geometry to charge for their design to design the floorplan of a sructure.
Architects use geometry to help them design buildings and structures. Mathematics can help architects express design images and to analyze as well as calculate possible structural problems.
The shapes and sizes used in the architect’s design are often possible due to mathematical principles.
An example of this would be the Pythagorean Theorem. Architects are required to know college level algebra, trigonometry, probability and statistics, linear programming, calculus I and calculus II. They are also required to obtain a professional degree, gather work experience in an internship setting and pass the Architect registration exam for licensing purposes.
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Answer:
to design the floorplan of a structure
Step-by-step explanation:
Geometry describes the properties and arrangement of shapes in space. Designing the floor plan of a structure would involve the arrangement of shapes in a defined space.
Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5
Answers
Step-by-step explanation:
Let's make the number we're finding to be \(a\). So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be \(\frac{a}{4} +12\\\). It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be \(\frac{a}{3} -5\\\). Since they are the same, we have the equation below.
\(\frac{a}{4} +12 = \frac{a}{3} -5\\\)
All we have to do now is to find \(a\).
\(\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204\)
Answer:Our number must be \(204\). I think
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Combine like terms to simplify the expression. 5 x + 4 + 2 x + 5
Answers
Answer:
\( \huge{ \boxed{ \bold{ \text{7x + 9}}}}\)
Step-by-step explanation:
\( \text{5x + 4 + 2x + 5}\)
\( \text{Combine \: like \: terms} : \)
\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)
\( ➝ \: \text{5x + 2x + 4 + 5}\)
➝ \( \text{ 7x + 4 + 5}\)
\( \text{Add \: the \: numbers : 4 \: and \: 5}\)
\( ➝ \: \text{7x + 9}\)
\( \text{Hope \: I \: helped}\)!
\( \text{Best \: regards}\)!
~\( \mathfrak{TheAnimeGirl}\)
Answer:
7x + 9
Step-by-step explanation:
Combine like terms, means put the ones that have something in common together; in this case they are the terms with an 'x' value, and a regular numeric value.
5x+2x = 7x
5+4 = 9
therefore:
7x+9
At a school assembly, there are 150 students. If the students are to be dismissed in groups of 10, how many groups will be made?
Answers
Answer:
15 groups would be made.
Explanation:
150 divided by 10 = 15
consider the curve y=x^-2 on the interval -4 -1/2, recall that two given points
Answers
The curve y = x^(-2) represents a hyperbola that is symmetric about the y-axis. Let's examine the two given points on the curve, (-4, 1/16) and (-1/2, 4), within the interval -4 to -1/2.
The point (-4, 1/16) means that when x is -4, y (or f(x)) is 1/16. This indicates that at x = -4, the corresponding y-value is 1/16. Similarly, the point (-1/2, 4) signifies that when x is -1/2, y is 4.
By plotting these two points on a graph, we can visualize the curve and its behavior within the given interval.
The point (-4, 1/16) is located in the fourth quadrant, close to the x-axis. The point (-1/2, 4) is in the second quadrant, closer to the y-axis. Since the curve y = x^(-2) is symmetric about the y-axis, we can infer that it extends further into the first and third quadrants.
As x approaches -4 from the interval (-4, -1/2), the values of y decrease rapidly. As x approaches -1/2, y approaches positive infinity. This behavior is consistent with the shape of the hyperbola y = x^(-2), where y becomes increasingly large as x approaches zero.
It's worth noting that the given interval (-4, -1/2) does not include x = 0, as x^(-2) is undefined at x = 0 due to division by zero. Therefore, we do not have information about the behavior of the curve at x = 0 within this interval.
To summarize, the given points (-4, 1/16) and (-1/2, 4) lie on the curve y = x^(-2) within the interval -4 to -1/2. Plotting these points reveals the shape and behavior of the hyperbola, showing a rapid decrease in y as x approaches -4 and an increase in y as x approaches -1/2.
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Consider the curve y=x^-2 on the interval -4 -1/2, recall that the two given points on the curve y = x^(-2) on the interval -4 to -1/2 are (-4, 1/16) and (-1/2, 4).
Write an equation in slope-intercept form for the line with slope 3/5 and -intercept -6. Then graph the line.
Answers
The equation in slope-intercept form for the line with slope 3/5 and -intercept -6 is,
⇒ y = 3/5x - 6
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The slope of line is, 3/5
And, y - intercept is, - 6
Now, We know that;
The slope - intercept form of the line is,
⇒ y = mx + b
Where, 'm' is slope and 'b' is y - intercept.
Hence, The equation in slope-intercept form for the line with slope 3/5 and y-intercept -6 is,
⇒ y = 3/5x - 6
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What is the relationship between <4 and <15? *
Answers
The Least Common Factor of 4 and 15 is 1. The factors of 4 are 1, 2 and 4, and the factors of 15 are 1, 3, 5 and 15. Hence, 1 is the Least Common Factor of 4 and 15.
What's meant by Factor?A factor is a number that fully divides another number.
To put it another way, if adding two whole figures results in a product, also the figures we're adding are factors of the product because the product is separable by them.
Factor simply translates to" doer" in Latin. therefore, a" factor" in English is a" actor,"" element," or" element" in a situation or number.
Success can depend on charm, and having a terrible constitution can affect from inadequate exercise.
Variable factors are those whose employment varies in proportion to affair; further are employed when product rises and smaller when product falls.
Labor, energy, and raw accoutrements employed directly in product are exemplifications of typical variable rudiments.
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Solve for b
a) 2b x 3 = 6 c) 6 + 7b = 41
b) 32 - 3b = 2 d) 100/ 5b = 2
Answers
a) The solution for b in the equation 2b × 3 = 6 is b = 1.
b) The solution for b in the equation 32 - 3b = 2 is b = 10.
c) The solution for b in the equation 6 + 7b = 41 is b = 5.
d) The solution for b in the equation 100/5b = 2 is b = 10.
a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.
2b × 3 = 6
(2b × 3) / 2 = 6 / 2
3b = 3
b = 3/3
b = 1
Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.
c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.
6 + 7b - 6 = 41 - 6
7b = 35
b = 35/7
b = 5
Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.
b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.
32 - 3b - 32 = 2 - 32
-3b = -30
b = (-30)/(-3)
b = 10
Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.
d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.
(100/5b) × 5b = 2 × 5b
100 = 10b
b = 100/10
b = 10.
Therefore, the solution for b in the equation 100/5b = 2 is b = 10.
In summary, the solutions for b in the given equations are:
a) b = 1
c) b = 5
b) b = 10
d) b = 10
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The area of an 19-cm-wide rectangle is 437 cm. What is its length?
Answers
The area of a rectangle is equal to:
\(\text{Area = Width }\cdot\text{ length}\)In this case, we know that the area is equal to 437 cm^2 and the width is 19 cm, so we can replace the values and get:
\(437cm^2=(19\operatorname{cm})\cdot(length)\)So, we can solve for length dividing both sides by 19 cm as:
\(\begin{gathered} \frac{437cm^2}{19\text{ cm}}=\frac{(19\operatorname{cm})}{19\operatorname{cm}}\cdot(length) \\ 23\text{ cm = length} \end{gathered}\)Therefore, the length of the rectangle is 23 cm
Answer: 23 cm
The length of a rectangle is 23 cm.
To find the length of a rectangle, we will use the formula of the area of a rectangle,
Area = L × B
Where,
L = length
B = breadth
Given in the question,
Area = 473 cm
breadth = 19 cm
length =?
Now, we will put values in the above formula,
Area = L × B
437 = L × 19
L = 437/19
L = 23 cm
Therefore, the length of a rectangle is 23 cm.
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An ice machine produces ice cubes that are inch on each side.
What is the volume, in cubic inches, of one ice cube produced by this
ice machine?
Answers
The volume of an ice cube produced by this machine is of:
Volume ice cube = 1 inch³
What is a volume?A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.
If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:
Volume cube = side x side x side
Volume cube = side³
side = 1 inch
Volume ice cube = 1 inch³
As the side is 1 the volume and area will be 1 but with corresponding unit
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Please help me and tysm i’m advance!!
Answers
Answer:
\(r = \sqrt{\frac{3V}{'pi'h}}\)
replace the 'pi' in that equation to the symbol pi, π
Step-by-step explanation:
his figure is made from part of a circle and part of a square.
Answers
Answer:
What?
Step-by-step explanation:
A researcher wants to set up a regression equation where Y is a function X. Evaluate the researcher’s options given the following scenarios: (3)
i. Y is I(0); X is I(0)
ii. Y is I(2); X is I(0)
iii. Y is I(1); X is I(1); and the error term is I(0).
Answers
The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.
In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.
In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.
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ABC Game store sells new games, n, for $19 and used games, u, for $9. The store earned $7500 in revenue last month. The store sold 4 times as many used games as new games. Write a system of equations that represents this scenario.
Answers
Answer:
19n+9u=7500 and 4u-n
Step-by-step explanation:
help me plz i asked this question too much
Answers
Answer:
24 cookies in each bag
Step-by-step explanation:
36 cookies X 8 bags = 288 cookies
240 cookies / 20 cookies = 12 bags
288 cookies / 12 bags = 24 cookies
What is the largest decimal value that can be represented in:
2 bits
5 bits
7 bits
15 bits
1 byte
2 bytes
4 bytes
Answers
The largest decimal value that can be represented in
a. 2 bits is 3;
b. in 5 bits is 31;
c. in 7 bits is 127;
d. in 15 bits is 32767;
e. in 1 byte is 255;
f. in 2 bytes is 65535 and
g. in 4 bytes is 4294967295.Bits
The smallest unit of measurement used to describe data storage is known as a bit. Bits are used to represent information in binary format. Binary values have two possible values: 0 and 1, and each digit is called a bit. A byte is made up of eight bits. The largest decimal number that can be represented in 2 bits is 11 (3).In five bits, the largest decimal value that can be represented is 11111 (31). In seven bits, the largest decimal value that can be represented is 1111111 (127).In 15 bits, the largest decimal value that can be represented is 111111111111111 (32767). In one byte, the largest decimal value that can be represented is 11111111 (255).In two bytes, the largest decimal value that can be represented is 1111111111111111 (65535). In 4 bytes, the largest decimal value that can be represented is 11111111111111111111111111111111 (4294967295).
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A five-question multiple-choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers and 1’s representing correct answers, to answer the following question: What is the probability of correctly guessing at random exactly two correct answers? Round your answer to the nearest whole number. 5% 25% 55% 75%
Answers
In a random guessing exercise, there is a 25% probability of taking precisely two right answers.
What is experimental probability?The number of times an event happened during the experiment as a percentage of all the times the experiment was run is known as the experimental probability of that event occurring.
The experiment's location, timing, participants, conditions, and use of a standardized process are all decided by the researcher. Each independent variable group receives a random distribution of participants.
From the table, the ones that have two numbers of 1's are referred to as correct answers. Thus, counting them in the question is:
01010, 10001, 11000, 01001, 00011
Thus, out of 20 alternative responses, 5 are likely to be correct.
Thus;
The probability of correctly guessing at random exactly two correct answers is given by
5/20
= 25%
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The complete question is:
A five-question multiple-choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers and 1’s representing correct answers, to answer the following question: What is the probability of correctly guessing at random exactly two correct answers? Round your answer to the nearest whole number. 5% 25% 55% 75%
If 9(x-9) = -11, then x= ?
A. - 92/9
B. -20/9
C. - 11/9
D. -2/9
E. 70/9
Answers
A poll estimates that 47% of likely voters are in favor of additional restrictions on teenage drivers. The poll has a margin of error of plus or minus 5%. Write and solve an absolute-value equation to find the minimum and maximum percent of voters that actually support the restrictions.
Answers
Answer:
5
Step-by-step explanation: