For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.
a. n = 400,p =10
b. n =50,p = 10
c. n =20,p =5
d. n =20, p= 3
Answers
a. n(1-p) is less than 10, the sample size is not large enough to use the methods of this chapter.
b. n(1-p) is less than 10, the sample size is not large enough to use the methods of this chapter.
c. both np and n(1-p) are less than 10, the sample size is not large enough to use the methods of this chapter.
d. Both np and n(1-p) are greater than or equal to 10, so the sample size is large enough to use the methods of this chapter.
According to the guidelines of this chapter, the sample size is considered large enough when the following conditions are met:
The sample size n is large enough to ensure that both np and n(1-p) are greater than or equal to 10.
The sample is drawn randomly from the population of interest.
The observations in the sample are independent of each other.
Using these guidelines, we can determine if the sample size in each part is large enough:
a. n = 400, p = 10
np = 40010 = 4000 and n(1-p) = 400(1-10) = -3600. Since n(1-p) is less than 10, the sample size is not large enough to use the methods of this chapter.
b. n = 50, p = 10
np = 5010 = 500 and n(1-p) = 50(1-10) = -450. Since n(1-p) is less than 10, the sample size is not large enough to use the methods of this chapter.
c. n = 20, p = 5
np = 205 = 100 and n(1-p) = 20(1-5) = 60. Since both np and n(1-p) are less than 10, the sample size is not large enough to use the methods of this chapter.
d. n = 20, p = 3
np = 203 = 60 and n(1-p) = 20(1-3) = 40. Both np and n(1-p) are greater than or equal to 10, so the sample size is large enough to use the methods of this chapter.
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Related Questions
Hannah has a bag containing 6 yellow, 7
black, 8 green, 15 blue, and 9 white marbles
that are all the same size and shape. What
is the probability of randomly choosing a
blue marble on the first pick, NOT replacing
it, and then randomly choosing a white
marble on the second plek?
Answers
The probability of randomly selecting a blue marble on the first pick is 15/45 since there are a total of 45 marbles and 15 of them are blue. After the blue marble is not replaced, there are now 44 marbles remaining and 9 of them are white. Therefore, the probability of selecting a white marble on the second pick is 9/44. To find the probability of both events occurring, we multiply the probabilities together: (15/45) x (9/44) = 0.045 or 4.5%. Thus, there is a 4.5% chance of randomly selecting a blue marble on the first pick and a white marble on the second pick without replacing the blue marble.
Probability is the measure of the likelihood of an event occurring, and it is expressed as a fraction or percentage. To calculate the probability of selecting a blue marble on the first pick, we divide the number of blue marbles by the total number of marbles. The same process is used to calculate the probability of selecting a white marble on the second pick. However, since the blue marble is not replaced, the number of marbles decreases by one, and the probability of selecting a white marble changes accordingly.
In conclusion, the probability of randomly selecting a blue marble on the first pick and a white marble on the second pick without replacing the blue marble is 4.5%. This means that out of every 100 times that the experiment is repeated, we would expect to get a blue marble on the first pick and a white marble on the second pick approximately 4-5 times.
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To prepare for a bake-off, Lee used 640 grams of flour each day for 4 weeks. How many kilograms did Lee use in those 4 weeks?
Answers
4weeks = 28 days
So 28 x 640 = 17920
1000grams = 1kg
17920 divide 1000 =17.92
Lee uses 17.92kg in those 4weeks
what are the coordinates of the image of vertex after a reflection of r x-axias (x,y)
Answers
The coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
To get the coordinates of a point reflected on the x - axis, some important rules be considered here:
1. The x - coordinate of the reflected point is the same as the x - coordinate of the original point.
2. The y - coordinate of reflected point has opposite sign of y-coordinate of original point.
Example:
(1,9) when reflected on the x - axis it will be (1,-9).
Therefore the coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
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Hi can you please help me
Answers
The probability that student chosen at random is 16 years is 0.28.
How to find the probability of the student chosen?The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is 16 years can be found as follows:
Therefore,
probability = number of favourable outcome to age / total number of possible outcome
Hence,
probability that student chosen at random is 16 years = 420 / 150
probability that student chosen at random is 16 years = 0.28
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TRUE / FALSE.
In the C-Chart, the value of \( \mathrm{C} \)-bar must be an integer.
Answers
In the C-Chart, the value of the C-bar, representing the average count of nonconformities per unit, does not have to be an integer. So, the statement 'In the C-Chart, the value of C-bar must be an integer' is false.
In the C-Chart (also known as the Count Chart), the value of C-bar does not necessarily have to be an integer.
C-bar represents the average count of nonconformities per unit. It can be a decimal value, especially when dealing with continuous data or when the sample size is large.
The C-Chart is a statistical process control chart used to monitor the count of nonconformities in a process. It helps to determine if the process is in control or if there are any unusual patterns or trends in the nonconformity counts. The C-bar value is typically calculated as the total number of nonconformities divided by the number of units or observations.
So, the value of the C-bar in the C-Chart can be a decimal or fractional value, not necessarily an integer.
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The radius of a circle is 4 meters. What is the circle's circumference?
r=4m
Use 3.14 for pie
Answers
This value is approximate because pi = 3.14 is approximate
===========================================================
Work Shown:
r = 4 = radius
pi = 3.14 approximately
C = circumference
C = 2*pi*r
C = 2*3.14*4
C = 25.12
The circumference is approximately 25.12 meters.
Side note: The circumference is the same as the perimeter of a circle.
HELP!PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answers
Answer:
180
Step-by-step explanation:
Answer:
504
Step-by-step explanation:
first you would multiply 6 * 15 * 4 for the bases. then you multiply 6 *12*2 for the ends. that leaves you with 360 and 144. you add those two together to get 504
41x41= i need some bad help
Answers
Answer:
1681
Step-by-step explanation:
41 × 41 = 1681
hope this helps
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.Tell whether each statement is True or False.
Answers
Answer:
a. True, because they are corresponding angles.
b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.
c. True, because they are corresponding angles.
d. True, becuase they are two angles that add up to 180 degrees.
e. True, because they are both interior angles on opposite sides of the transversal.
Answer:
a. True.
b. False.
c. True.
d. True.
e. True.
Step-by-step explanation:
a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.
b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.
c. This statement is true because angles 5 and 1 correspond to each other.
d. This statement is true because angles 7 and 8 form a straight line.
e. This statement is true because they are interior angles that are alternate.
Hope this helps!
The product of two irrational number is always __-
Answers
Answer:
\(irrational \: or \: rational \\ for \: exmple \sqrt{2} \times \sqrt{2} = 2 \\ thnk \: you\)
Consider y' = 1 – 2t + 3y, y(0) = 0.5. Find approximate values of the solution at t= 0.1, 0.2, 0.3. (a) Use Euler's method with h = 0.1
Answers
Find the surface area of this cone please help
Answers
The calculated value of the surface area of the cone is 36π
Calculating the surface area of the cone
From the question, we have the following parameters that can be used in our computation:
Radius, r = 4 meters
Slant height, l = 5 meters
using the above as a guide, we have the following:
SA = πr(r + l)
Substitute the known values in the above equation, so, we have the following representation
SA = π * 4 * (4 + 5)
Evaluate
SA = 36π
Hence, the surface area of the cone is 36π
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Pls Reply before tommorrow
1. A bathtub is being filled at a rate of 2.5 gallons per minute. The bathtub will
hold 20 gallons of water.
a. How long will it take to fill the bathtub?
b. Is the relationship described linear, inverse, exponential, or neither? Write
an equation relating the variables.
2. Suppose a single bacterium lands on one of your teeth and starts reproducing
by a factor of 4 every hour.
a. After how many hours will there be at least 1,000,000 bacteria in the new
colony?
b. Is the relationship described linear, inverse, exponential, or neither? Write
an equation relating the variables.
Answers
1.
a.
It will take 8 minutes to fill the bathtub.
b.
The relationship described is linear.
The equation is 20 = 2.5t + 0.
2.
a.
It will take approximately 4.807 hours to have at least 1,000,000 bacteria in the new colony.
b.
The relationship described is exponential,
The equation is Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)
We have,
1.
a.
To fill the bathtub, we need 20 gallons of water.
The rate at which the water is being filled is 2.5 gallons per minute.
Using the formula:
time = amount/rate
we get:
time = 20/2.5 = 8 minutes
b.
The relationship described is linear.
The equation relating the variables can be written as:
amount of water = rate x time + initial amount
where the rate is 2.5 gallons per minute, the initial amount is 0 gallons, and the amount of water is 20 gallons.
So, the equation is:
20 = 2.5t + 0
where t is the time in minutes.
2.
a.
The relationship described is exponential.
The equation relating the variables can be written as:
number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)
where the initial number of bacteria is 1, the reproduction factor is 4, and we need to find the time it takes to reach 1,000,000 bacteria.
So, we have:
1,000,000 = 1 x 4^(time/hour)
Taking the logarithm of both sides, we get:
log(1,000,000) = log(4^(time/hour))
6 = (time/hour) x log(4)
time/hour = 6/log(4)
time = (6/log(4)) x hour
time ≈ 4.807 hours
b.
The relationship described is exponential, and the equation relating the variables is:
Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)
where the initial number of bacteria is 1, the reproduction factor is 4, and t is the time in hours.
Thus,
1.
a.
It will take 8 minutes to fill the bathtub.
b.
The relationship described is linear.
The equation is 20 = 2.5t + 0.
2.
a.
It will take approximately 4.807 hours to have at least 1,000,000 bacteria in the new colony.
b.
The relationship described is exponential,
The equation is Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)
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For the equation f(x) = -3x7 + 2x- 1, identify the vertex, line of symmetry, and y intercept
Answers
The vertex of the equation is (0, -1), the line of symmetry is x = 0 and the y-intercept is (0,-1).
For the equation f(x) = \(-3x^7\) + 2x - 1, the vertex is the highest or lowest point on the parabola and it can be found by completing the square method.
To find the line of symmetry, we can set the function equal to zero and solve for x. The x-coordinate of the vertex is the same as the line of symmetry.
The y-intercept is the point at which the parabola crosses the y-axis, and it can be found by setting x equal to zero and solving for y.
The vertex of the parabola:
The equation is in form f(x) = a\((x-h)^2\) + k, where a is -3, h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. In this case, h = 0 and k = -1.So the vertex is (0, -1)The line of symmetry:
We can set the function equal to zero and solve for x:\(-3x^7\) + 2x - 1 = 0The x value that makes the equation equal to zero is x = 0So the line of symmetry is x = 0The y-intercept:
We can set x equal to zero and solve for y: f(0) = \(-3(0)^7\) + 2(0) - 1 = -1So the y-intercept is (0, -1)To learn more about vertex, line of symmetry, and intercept at
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An elevator travles 310 feet in 10 seconds. at that speed, how far can this elevaor travles in 12 seconds? explain your reasoning.
Answers
Explanation:
We can do cross multiplying through ratios:
310 feet / 10 secs = x feet / 12 secs
10x = 310 * 12
10x = 3720
x = 372 feet
OR
Divide 310 feet and 10 secs to get 31 feet in 1 sec
Multiply 31 ft and 1 sec to get 372 ft in 12 secs
the area of a square poster is 31 square inches. find the length of one side of the poster. Explain
Answers
Answer:
5.57
Step-by-step explanation:
In order to find the are of a square you would use the equation a². However, since you are finding the length of one side and its a square, you use the equation \(\sqrt{a}\). The area of this square is 31 sq in., so you would replace a with 31. The equation then becomes \(\sqrt{31}\). When out into a calculator, the answer is 5.567764... which rounded up to the nearest hundreth is 5.57.
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
Answers
The correct format of the question is
At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. \(P = 400 ( 1.2 )^ t\) Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?
(A) 291
(B) 691
(C) 1040
(D) 1440
Answer:
The increase in the population at the end of 2009 is 291 people
Step-by-step explanation:
We are given the equation as \(P = 400 ( 1.2 )^ t\)
where
P = No of People
t= No of Years
it is given that in the year 2006 the population is 400
this will only happen when we take t= 0
so for
Year value of t
2006- t = 0
2007- t = 1
2008- t = 2
2009 t = 3
No of people in 2009 will be
\(P = 400(1.2)^3\)
= 400*1.728
P = 691.2
Since the equation represents no of people so it can't be in decimals, Therefore the population will be 691
Increase = P(2009) - P(2006)
= 691 - 400
= 291
The increase in the population at the end of 2009 is 291 people.
What is the actual net income for the month? What, if any, changes would have improved the budget for the month? a. The actual net income for the month is -$30. No changes to the budget are necessary. b. The actual net income for the month is $30. No changes to the budget are necessary. c. The actual net income for the month is $30. More money could have been spent on food. d. The actual net income for the month is -$30. Less money could have been spent on food.
Answers
Answer:
The correct answer is D
Step-by-step explanation:
Answer: choice D
Step-by-step explanation:
Trust me I did this test and got a 100
The table lists the values of two parameters, x and y, of an experiment. What is the approximate value of y for x=4?
Answers
Answer:
y = 16
Step-by-step explanation:
From the pattern in the table we can see that x to the power of two results in y (2.5 x 2.5 = 6.25, 9.4 x 9.4 = 88.36, etc.) This means that 4 x 4 = 16, which is the value of y.
Answer:
16
Step-by-step explanation:
Plato/Edmentum
what is the moment of intertia of an average bike wheel
Answers
The moment of inertia is a measure of an object's resistance to rotational motion and is important for determining the stability and handling of a bicycle.
The moment of inertia of an average bike wheel can be determined by calculating the mass and distribution of the wheel's components, including the rim, spokes, and hub.
A larger moment of inertia means the wheel will be more resistant to changes in rotational velocity, making the bike more stable. On the other hand, a smaller moment of inertia allows for easier acceleration and maneuvering, but may result in a less stable ride.
The moment of inertia of a bike wheel is affected by its size, material, and overall design.
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Identify the pieces of the cytoplasmic membrane correctly. drag the appropriate labels to their respective targets.
Answers
The cytoplasmic membrane consists of phospholipids, proteins, and other molecules.
The cytoplasmic membrane, also known as the plasma membrane, is a vital component of cells in both prokaryotes and eukaryotes. It surrounds the cell, separating its internal contents from the external environment. The main structural component of the cytoplasmic membrane is phospholipids. These phospholipids form a lipid bilayer, with hydrophilic (water-loving) heads facing outward and hydrophobic (water-fearing) tails facing inward. This lipid bilayer provides a barrier that controls the movement of substances in and out of the cell.
In addition to phospholipids, the cytoplasmic membrane contains proteins. These proteins are embedded within the lipid bilayer and have various functions. Some proteins act as transporters, facilitating the movement of molecules across the membrane. Others serve as receptors, allowing the cell to detect and respond to signals from the environment. Enzymes involved in cellular metabolism can also be found in the cytoplasmic membrane. Additionally, the cytoplasmic membrane may contain other molecules such as cholesterol, which helps maintain the fluidity and stability of the membrane.
Overall, the cytoplasmic membrane is a complex structure composed of phospholipids, proteins, and other molecules. It plays a crucial role in maintaining the integrity of the cell and regulating the exchange of substances with the external environment.
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2) Write the equation of the plane containing the points (3, 2, 1), (1, 2,-2) and (2,0,1) (Hint: you need to start with a vector perpendicular to this plane) (+5)
Answers
The equation of the plane containing the points (3, 2, 1), (1, 2, -2), and (2, 0, 1) is -6x + 6y - 4z = -10.
To find the equation of the plane containing the points (3, 2, 1), (1, 2, -2), and (2, 0, 1), we can start by finding two vectors that lie in the plane. We can then use the cross product of these two vectors to find a normal vector to the plane, which will help us determine the equation. Here's how to do it step by step:
Step 1: Find the vectors lying in the plane.
Let's choose two vectors from the given points:
Vector AB = B - A = (1, 2, -2) - (3, 2, 1) = (-2, 0, -3)
Vector AC = C - A = (2, 0, 1) - (3, 2, 1) = (-1, -2, 0)
Step 2: Find the cross product of the two vectors.
To find a normal vector to the plane, we can take the cross-product of AB and AC:
Normal vector N = AB × AC
= (-2, 0, -3) × (-1, -2, 0)
= (-6, 6, -4)
Step 3: Write the equation of the plane using the normal vector and one of the given points.
Using the point A (3, 2, 1) and the normal vector N (-6, 6, -4), we can write the equation of the plane in the form Ax + By + Cz = D:
-6x + 6y - 4z = D
To find the value of D, we substitute the coordinates of point A into the equation:
-6(3) + 6(2) - 4(1) = D
D = -18 + 12 - 4
D = -10
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What is the value of y in the equation 2(3y + 4 + 2) = 196 − 16?
Answers
step by step explanation:
6y+8+4=180
8+4=12
180-12=168
168 divided by 6 is 28
so y=28
hope this helps
Answer:
y=28
Step-by-step explanation:
Can someone help me with this please?
Answers
Answer:
skater: 12.5 meters in 1 second
cheetah: 26 meters in 1 second
Step-by-step explanation:
To find meters in 1 second (meters per second) divide meters by seconds.
skater: (500 m)/(40 s) = 12.5 m/s . . . . . 12.5 meters in 1 second
cheetah: (260 m)/(10 s) = 26 m/s . . . . . 26 meters in 1 second
What is the perimeter of the following rectangle?
Answers
Answer:
C
Step-by-step explanation:
\(x^2 +8+x^2+8+x^2+6x-3+x^2+6x-3\)
\(x^2+x^2+x^2+x^2=4x^2\)
\(6x+6x=12x\)
\(8+8-3-3=10\)
Ans: \(4x^2+12x+10\)
suppose the 99% confidence interval for the mean sat scores of applicants at a business college is given by [1,692, 1,842]. this confidence interval uses the sample mean and the sample standard deviation based on 25 observations. what are the sample mean and the sample standard deviation used when computing the interval?
Answers
The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.
Here, the two boundaries are 1692 and 1842.
Mean = (1692+1842) /2 = 1767
Here the degree of freedom, df = (n-1) = 25-1 =24
Margin of error = (1842-1692)/2 = 75
Confidence level = 99%
From the t table, value of T with confidence level 99% and df= 24 is 2.80
The equation for margin of error is M = Ts/√n
M= 75 , T= 2.80, n =25
75 = (2.80 × s) / √25
75 = 2.80s/ 5
s = (75×5)/2.80 = 133.928 = 133.93
So the sample mean is 1767 and the standard deviation is 133.93.
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Given that a = (- 8) b = 2 c = 7 and d = 11 , solve for x, y, z, and w.
[[x + y, z], [z - x, w - y]] =
[[a, b], [c, d]]
What is the value of w?
(Only type a number, nothing else)
Answers
Answer:
24
Step-by-step explanation:
Okay, let's solve this step-by-step:
1) We are given: a = -8, b = 2, c = 7, d = 11
2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]
3) Matching up the elements in the matrices:
x + y = a = -8 (1)
z = b = 2 (2)
z - x = c = 7 (3)
w - y = d = 11 (4)
4) Solving the equations:
From (1): x + y = -8 => x = -8 - y
Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y
Substitute (2) into the above: 2 = 15 + y => y = 13
Substitute y = 13 into (1): -8 - 13 = -21 = x
Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24
Therefore, the values are:
x = -21
y = 13
z = 15
w = 24
So the final value of w is:
w = 24
You decide to take a hot air balloon ride and remember to take binoculars to look around while you are airborne. As the balloon rises, you use a GPS to determine your height in meters, h, and the distance in kilometers, d, to the farthest object that you can see. The table below shows the two measurements.
Height in meters 15 30 45 60 75 90 105
Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table.
Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round answer to the nearest whole number
Answers
Answer:
Step-by-step explanation:
Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.
Gauge Readings ( pounds per square inch )
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Pressure readings ( pounds per inch) answers:
Answers
The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.
Given readings:
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Expressed as rational numbers with a common denominator:
25 psi = 25/1
13 psi = 13/1
6.3 psi = 63/10
7.8 psi = 78/10
1.9 psi = 19/10
2 psi = 2/1
7.8 psi = 78/10
Now, let's order these rational numbers from least to greatest:
1.9 psi = 19/10
6.3 psi = 63/10
7.8 psi = 78/10
7.8 psi = 78/10
13 psi = 13/1
25 psi = 25/1
2 psi = 2/1
Ordered from least to greatest:
19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1
Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
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Kellogg increases the length of their rectangular Pop-Tarts by 10% and decreases thewidth by 10%. By what percent willthe area of their Pop-Tarts change?ANo changeB1% decreaseс21% increaseD19% decrease
Answers
Let the initial length and width Kellogg's rectangular Pop-Tarts be represented as l and b
The area of the initial rectangular Pop-Tarts will be
\(\begin{gathered} A_{rec\tan gle}=length\text{ }\times width \\ A_{i\text{nitial}}=l\times b \end{gathered}\)If the new length is increased 10% of the initial length, then the new length L will be
\(undefined\)