A fair dice i rolled once, what i the probability of getting a factor of 4 or a multiple of 3
Lets Recall the formula of Probability, where we know that;
P = Favourable outcomes / possible outcome
Given that , after rolling a die once we get the chances of probability
So , the total possible outcomes are 6 because are only 6 highest outcome possible
The factors of 4 are the numbers 1 , 2 and 4 which means its 3 outcomes
And the multiple of 3 are the numbers 3 and 6 which means it has 2 outcome
So, the chances of the outcome on the dice are = 1,2,3,4,6
Thus,
Probability = (1,2,4,3,6) / 6
There are 5 favourable outcomes on the numerator ,
Thus,
P=5/6
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Find the 200th term in the sequence below.
a₁ = 8
d=12
The 200th term in the sequence is 2,396.
To find the 200th term in the sequence we have the formula:
an=a1+(n-1)d --------(1)
Given that values of a1 and d are 8,12
"a1" is called the first value of the sequence.
"d" is called the difference between two numbers.
Assume that n is 200 because we have to find the 200th term.
Now, we will substitute all the values in the above equation(1)
an=a1+(n-1)d
a200=8+(200-1)12
a200=8+(199)12
a200=8+2,388
a200=2,398.
So, the 200th term in the sequence is:2,398
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Please help me solve!!
The percentage of population between 130 and 102 is 68%.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Given that the mean is 116 and the standard deviation is 14. Therefore, the approximate population between the given range of 102 to 130 is,
P(102 ≤ X ≤ 130) = P(X ≤ 130) - P(102 ≤ X)
[tex]= P(z \leq \dfrac{130-116}{14})- P(z \leq \dfrac{102-116}{14})[/tex]
= P(z ≤ 1) - P(z ≤ -1)
= 0.8413 - 0.1587
= 0.6826
Hence, the percentage is 68%.
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To gather information about the elk population, scientists marked 30 elk. Later, they flew over the area and counted 150 elk, 18 of which
were marked.
To the nearest whole number, what is the best estimate of the elk population?
O 198
O 200
O250
O 280
Answer:
250
Step-by-step explanation:
We can approximate that the scientists counted [tex]\frac{18}{30}=\frac{3}{5}[/tex] of the elk.
So, the best estimate of the elk population is [tex]150(5/3)=250[/tex].
Answer:1,250
Step-by-step explanation:
Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.
Create two unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game.
The equation that that model the number of 2-point shots, x, and the number of 3-point shots, y is x + y = 21, 2x + 3y = 38
How to represent situation with an equation?Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.
The unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game is as follows:
where
x = number of 2-points shoty = number of 3-points shotTherefore, the equation that represent the situation is as follows:
x + y = 21
2x + 3y = 38
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Simplify 6(4x-3)-9x
Answer:
(24x-18)-9x
hope this helps, tell me if you need to simplify it further
1. Let Triangle ABC be congrent to Triangle DEF. Find m< E.
the value of m< E is-----------------.
The value of m∠E is 120°
Define Congruent angles
Congruent angles are two or more angles that are identical to one another.Congruent angles can be acute, obtuse, exterior, or interior angles.Given,
The Δ ABC be congruent to Δ DEF.
Since, the triangles are congruent, B and E are automatically congruent, since they are corresponding angles.
First let's find the value of y,
To find y, equate the measure of y like this
95 + y = 6y - 30
95 + 30 = 6y - y
125 = 5y
y = 25
Now, substitute the value of y in ∠E
∠E = 6y - 30
∠E = 6* 25 - 30
∠E = 120°
Hence, the value of m∠E is 120°
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A pair of shoes is priced at $35.99 but is on sale for 20% off. What is the sale price of the shoes?
Answer:
The shoes are on sale for $28.79
Step-by-step explanation:
First, you find the 20% of 35.99 which is 7.198.
Then, i rounded that number to 7.20.
Then do $35.99 - 7.20.
Your final answer is $28.79!
Hope this helps and good luck!
What is m∠B?
There is a seven sided polygon ABCDEFG in which the measure of angle BCD is 148 degrees, the measure of angle DEF is 142 degrees, the measure of angle EFG is 130 degrees, the measure of angle FGA is 129 degrees, and the measure of angle GAB is 120 degrees. Angle CDE is a right angle.
A. 51°
B. 129°
C. 134°
D. 141°
The measure of angle B is 141 degrees
Given,
In the question:
There is a seven sided polygon ABCDEFG
The measure of angle BCD is 148 degrees,
The measure of angle DEF is 142 degrees,
The measure of angle EFG is 130 degrees,
The measure of angle FGA is 129 degrees,
and the measure of angle GAB is 120 degrees.
Angle CDE is a right angle.
To find the m∠B.
Now, According to the question:
The sum of angles in a polygon adds up to 180(n - 2), where n is the number of sides of the polygon
The angles are given as:
∠BCD = 148
∠DEF = 142
∠EFG = 130
∠FGA = 129
∠GAB = 120
∠CDE = 90
So, the measure of angle B is calculated using:
∠B + 148 + 142 + 130 + 129 + 120 + 90 = 180(n - 2)
∠B + 759 = 180(n - 2)
The value of n is 7
∠B + 759 = 180(7 - 2)
∠B + 759 = 180 x 5
∠B = 900 - 759
∠B = 141
Hence, the measure of angle B is 141 degrees
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Sofia bought a package of 20 bottles of water. Each bottle contains w ounces. Write an
expression that shows the total number of ounces.
Answer:
20w
Step-by-step explanation:
If you have 20 bottles, and each contains w ounces, we can use the following example to solve.
If there were 4oz per bottle,
20 * 4 = 80
80oz
We have w oz per bottle,
20 * w = ?
20w
The distance traveled at speed s for time t is st. Keith rode on a train traveling at 60 miles per hour for 2.5 hours.
How far did the train travel?
Answer:
150 miles
Step-by-step explanation:
60*2.5=150
A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 645 mi/h, how far is she from her starting position?
Answer:
Below
Step-by-step explanation:
Break into components
1.5 + 2 cos 10 = 3.4696 hr for the 'x' components
2 sin 10 = .347296 hr the 'y' component
Use Pythag theorem to find hrs from start
sqrt (3.4696^2 + .347296^2 ) = 3.478295 hr
3.478295 hr * 645 mi/hr = 2243.5 mi from start position
someone help me please
Answer:
Step-by-step explanation:
The first step is combining like terms 3000 and 3000. The next step is to use the distributive property of equality. After that, combining like terms is the next step, and the last step will be the division property of equality to get the final answer.
hope this helps!! :3
20. A pair of standard dice are rolled. What is
the probability that at least one die is a 5,
given that the sum of the numbers on the
dice is at least 8?
The probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The outcomes when the sum dice is 8 are
S = { (2,6), (3,5), (4,4), (5,3) , (6,2)}
Total outcomes = 5
Number of outcomes when there is at least one die is a 5,
given that the sum of the numbers on the dice is at least 8 = 2
Probability = (Number of possible outcomes)/(Total number of outcomes)
So, the probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5
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If ABC is an equilateral triangle, then the mA =60
A. If the mA = 60, then ABC is an equilateral triangle.
B. If ABC is not an equilateral triangle, then the mA does not equal 60.
C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Answer is C!
The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Equilateral triangle:An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also called an equiangular triangle since each of its angles has a value of 60 degrees.
The equal angle in an Equilateral triangle = 60°
Here we have 3 options
A. If the mA = 60, then ABC is an equilateral triangle.
B. If ABC is not an equilateral triangle, then the mA does not equal 60.
C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Here we need to justify which of the given point will be true in the case of Equilateral Triangles.
Given
Option A: If the mA = 60, then ABC is an equilateral triangle.
With the measurement of A = 60°, here we can't conclude that ABC is an equilateral triangle because there is a possibility that the remaining angles are not equal to 60°
Option B: If ABC is not an equilateral triangle, then the mA does not equal 60.
Any type of triangle can have an angle that is equal to 60° so the given statement is wrong.
Option C. If the mA does not equal 60, then ABC is not an equilateral triangle.
As we know each angle of an equilateral triangle is 60°, So it is true that If the mA does not equal 60, then ABC is not an equilateral triangle.
Therefore,
The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.
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The graphs of f of x is equal to 2 times x over the quantity x plus 4 end quantity and g(x) = −log3(x + 3) + 1 have which of the following features in common?
x-Intercept
Vertical asymptote
Range
End behavior
The x-intercept of both the functions is 0. Therefore, option A is the correct answer.
The given functions are f(x)=2x/(x+4) and g(x)= -log3(x+3)+1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
For f(x)=2x/(x+4)
Vertical Asymptotes: x=-4
Horizontal Asymptotes: y=2
No Oblique Asymptotes
For g(x)= -log3(x+3)+1
An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (0,0)
y-intercept(s): (0,0)
The x-intercept of both the functions is 0. Therefore, option A is the correct answer.
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Data can be modeled by a cubic function when the Response area set of finite differences are Response area and Response area
Yes Data can be modeled by a cubic function
Using finite differences to determine the degree of the polynomial function that fits the data, you know when a set of data could be modeled by a cubic function if you obtain a third difference that is nonzero and constant.
The entities that contain the measures and dimensions make up the relational graph that is the Cube data model. The term "cubes" for entities in Cube was adopted from OLAP cubes. They are essentially data tables with a semantic meta layer that describes the measures, dimensions, and connections between the cubes.
The basic primitives of dimensions and measurements are the basis on which Cube operates. These primitives can be combined to create metrics by the user.
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consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
what is perimeter ?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.
calculation
In order to construct a hog pen, I have 800 feet of fencing.
Assume that "l" represents the rectangle's length and "w" its width.
One of your properties borders a river that I own.
I can secure my property with fencing on its three sides.
because of this, the fencing's necessary perimeter p = l + 2w
The fencing's perimeter is now equal to
⇒ l + 2w = 800
= l = 800 - 2w
now the rectangle's area = A = lw
Therefore, A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]
By diffusing the area equation, we can figure out the rectangle's greatest area.
Therefore, A' = 800 - 4w
Again, A" = -4
The rectangle has the largest area since the second order differentiation is constant negative.
Put simply, we obtain: A' = 0 , A' = 800- 4w
⇒800- 4w = 0
⇒ 4 w = 800
⇒ w = 200
So the rectangle has a 200-foot width.
The rectangle's length is currently:
l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
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to compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.
Given,
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.
Now, According to the question:
Let's know:
The Degrees of Freedom:
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.
Hence, To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.
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A snail is moving away from a rock.
The equation represents the relationship between the distance, , in inches that the snail is from the rock and time, , in minutes.
How many minutes does it take for the snail to reach a distance of inches from the rock?
The amount of minute to reach a distance of 9 inches from the rock is 3 minutes
How to determine the amount of minute to reach the given distance?The complete question is added at the end of this solution
From the question, we have the equation to be
d = 3t
A distance of 9 inches from the rock means that
d = 9
So, we have
3t = 9
Divide both sides by 3
t = 3
Hence, the amount of time is 3 minutes
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Complete question
The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.
How many minutes does it take for the snail to reach a distance of 9 inches from the rock?
Colleen and Kara were ordering at Mc D's. Colleen ordered 4
hamburgers and 2 fries, paying $11. Kara ordered 4 hamburgers and 4
fries. She paid $14. What is the cost of one hamburger and what is the
cost of one order of fries?
Express Colleen's Order in terms of H and F.
1.
Express Kara's Order in terms of H and F.
Solve for H and F using the elimination method.
Answer: Fries = $1.50 Hamburger = $2
Step-by-step explanation:
so since the first person payed 11 for 4 burgers and 2 fries and the second person got 2 more fries than the first person and spent 14 and there is a 3 dollar difference which 3 divided by 2 is 1.5 which means that the fires a 1 dollar and 50 cents. so 3 dollars subtracted from 11 equals 8 and 8 divided by 4 is 2 dollars leaving you with hamburgers being 2 dollars and fries being 1 dollar and 50 cents
Find EDED if AC=9x+1AC=9x+1 and BD=13x-11BD=13x−11 and ABCDABCD is a rectangle.
Rectangles are plane figures with common length of opposite sides. Thus the required value of ED is 14 units.
A rectangle is a family of quadrilateral which has two equal opposite sides, with two adjacent sides at right angle to each other. Some properties of a rectangle are:
opposite sides have equal length two adjacent sides are at right angle to each otherthe two diagonals are equalFrom rectangle ABCD, it can be deduced that:
AB = DC
AD = BC
AC = BD
So that;
9x + 1 = 13x - 11
11 + 1 = 13x - 9x
12 = 4x
x = [tex]\frac{12}{4}[/tex]
= 3
Therefore, we have;
BD = 13x - 11
= 13(3) - 11
BD = 39 - 11
= 28
But ED = [tex]\frac{BD}{2}[/tex]
So that;
ED = [tex]\frac{28}{2}[/tex]
= 14
ED = 14 units
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function rule to find f(72)
Answer:
-10
Step-by-step explanation:
When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.
find the 12th term of the geometric sequence
5,-25,125....
The 12th term of the geometric sequence is a₁₂ = -244140625.
Define Geometric Progression
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is,
aₙ = a₁ · rⁿ⁻¹.
The geometric sequence,
5, -25, 125 ....
from here,we know
a₁ = 5
Calculate the ratios of all the adjacent terms ,
r = aₙ₊₁ / aₙ
r = -25/5 = -5
r = 125/-25 = -5
We know, the formula for geometric sequence is
aₙ = a₁ · rⁿ⁻¹
Where, a₁ = initial term
r = common ratio
Now, we need to find 12th term so for that n = 12
Now, plug in the values
aₙ = a₁ · rⁿ⁻¹
a₁₂ = 5 * (-5) ¹²⁻¹
= 5 * -5¹¹
After calculation we get,
a₁₂ = -244140625
Hence, the 12th term of the geometric sequence is a₁₂ = -244140625.
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Which graphs of ordered pairs represent functions? there's one more graph to so if all of those are wrong then its the one I could not get a image of
Ordered pairs of graphs III and IV represents a function.
How do you find out if a set of ordered pairs is a function or not?
For a set of ordered pairs to be a function, there must not be any two points that have the same first elements.
This means that, the x-coordinates must not repeat for any two given points.
According to the given question:
Graph I - Clearly x coordinate repeats for the ordered pairs (-8, 12) and (-8, -8). Therefore ordered pairs of Graph I does not represents a function.
Graph II - Clearly x coordinate repeats for the ordered pairs (9, 2) and (9, -10). Also for (18,4) and (18, -14) Therefore ordered pairs of Graph II does not represents a function.
Graph III - Every ordered pair of this graph is unique hence the ordered pairs of the graph III represents a function.
Graph IV - Every ordered pair of this graph is unique hence the ordered pairs of the graph IV represents a function.
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What is the measure of ∠Y 40° 80° 90° 100°?(please help me)
The measure of <Y: 40⁰,80⁰90⁰100⁰ are the complementary angles and their supplementary angles respectively which are 50⁰,10⁰,0⁰ and 70⁰ respectively
How to calculate measurement of angles?The measure of angles is defined as the complementary or or supplementary angle of the given angle.
Complementary angles add up to 90⁰
supplementary angles add up to 180⁰
The given angles are: 40⁰, 80⁰, 90⁰ and 100⁰
The measure of 40⁰
x+40=90⁰
x=90-40
x=50⁰
The measure of 80⁰ is
x+80=90
x=90-80
x=10⁰
The measure of 90⁰ is
x+90=90
x=90-90
x=0⁰
The measure of 100⁰ is
x+100=180
Since 100⁰ is an obtuse angle
x=180-100
x=80⁰
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The school is 3.64 miles from Tonya's house and 1.27 miles from Jamal's house. How much farther from school is Tonya's house than Jamal's house? Complete the explanation on how you can use a quick picture to solve the problem.
Answer: Tonya's house is 2.37 miles farther from the school than Jamal's house.
Step-by-step explanation: To solve this problem using a quick picture, we can draw a line segment to represent the distance from the school to Tonya's house, and another line segment to represent the distance from the school to Jamal's house. We can then use a ruler to measure the length of each line segment and subtract the length of the line segment representing the distance to Jamal's house from the length of the line segment representing the distance to Tonya's house.
For example, if we draw a line segment that is 3.64 inches long to represent the distance from the school to Tonya's house and a line segment that is 1.27 inches long to represent the distance from the school to Jamal's house, then we can use a ruler to measure the lengths of the line segments and find that the line segment representing the distance to Tonya's house is 3.64 - 1.27 = 2.37 inches longer than the line segment representing the distance to Jamal's house. This means that Tonya's house is 2.37 miles farther from the school than Jamal's house.
LMNO is a parallelogram. If PN=7x-13PN=7x−13 and LP=8x-19LP=8x−19, find LPLP. Round to the nearest tenth, if necessary.
A parallelogram is a type of quadrilateral which has opposite sides to be equal. So that the value of LP required is 26 units.
Generally, all four sided shapes or figures can be classified as quadrilateral. Some of these examples are; cube, square, rectangle, rhombus, trapezoid, parallelogram etc.
A parallelogram is a form of shape which has four sides with two opposite sides to have equal length.
From the parallelogram LMNO, it can be deduced that;
LP = PN
So that;
8x - 19 = 7x - 13
8x - 7x = -13 + 19
x = 6
Thus,
LP = 8x - 19
LP = 8(6) - 19
LP = 48 - 19
LP = 29
Therefore, the value of LP is 26 units.
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how can you graph point with rational coordinates on a coordinate plane
Answer:
Locate the given point in the coordinate plane: for example; (−9,4)
Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.
Here, the given point (−9,4) is located in the coordinate plane. It will be located on the top left side of the coordinate plane if you drew it out.
Step-by-step explanation:
1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.
2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.
3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis
4. Here, you mark the point of intersection and mark it as \ ((-9, 4).\)
The management of a division National Motor Corporation that produces compact and subcompact cars has estimated that the quantity demanded of their compact models is 1400 units/week if the price of oil increases at a higher than normal rate, whereas the quantity demanded of their subcompact models is 2600 units/week under similar conditions. However, the quantity demanded of their compact models and subcompact models is 3500 units and 2300 units/week, respectively, if the price of oil increases at a normal rate. Determine the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week. (Round your answers to the nearest percent.)
The percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.
What is meant by percentage?The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian term per cento, which means "for a hundred," gradually shrank to become the sign for "percent," which is now used globally. It eventually vanished entirely. The word "per" was frequently shortened to "p."
Given,
If the oil price increases at a higher than normal state,
Demand for the compact cars=1400
Demand for the sub-compact cars=2600
If the oil price increases at a normal rate,
Demand for the compact cars=3500
Demand for the sub-compact cars=2300
Assuming that the probability of price increases at higher than the normal rate is 50% and at a normal rate is 50%.
Then,
Demand for compact cars=50%(1400)+50%(3500)
=(50/100)×1400+(50/100)×3500
=700+1750
=2450
Demand for the sub-compact cars=50%(2600)+50%(2300)
=(50/100)×2600+(50/100)×2300
=1300+1150
=2450
Therefore, the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.
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