We can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.
What is Line point postulate ?
The line-point postulate, also known as the incidence postulate, is a fundamental axiom in geometry that states that for any two points in a plane, there exists exactly one line that contains both points.
In other words, the line-point postulate asserts that a line can be uniquely determined by two distinct points that lie on it. This is one of the most basic and intuitive principles in geometry, and it is essential for building a foundation for more advanced concepts such as angles, triangles, circles, and more.
The Line-Point Postulate states that a line can be uniquely determined by any two distinct points on the line. In this diagram, we can see an example of this postulate in action.
For instance, we can say that line $q$ passes through points $J$ and $K$, so according to the Line-Point Postulate, this is enough information to uniquely determine the line $q$. Similarly,
Therefore, we can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.
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Solve the inequality 9> n-2
Answer:
n < 11
Step-by-step explanation:
We must solve for n, first we will rearrange the inequality
n - 2 < 9
n < 9 + 2
n < 11
Answer:
n < 11
Step-by-step explanation:
9feet to3 3/8inches ratio
Answer:
32 : 1
Step-by-step explanation:
dimensions of the parts of the ratio must be in the same units
convert 9 feet to inches
1 foot = 12 inches
then
9 feet = 9 × 12 = 108 inches
then ratio
9 feet : 3 [tex]\frac{3}{8}[/tex] inches
= 108 inches : 3 [tex]\frac{3}{8}[/tex] inches ( change mixed number to improper fraction )
= 108 : [tex]\frac{27}{8}[/tex] ( multiply both parts by 8 to clear the fraction )
= 864 : 27 ( divide both parts by 27 )
= 32 : 1
What is the tax on a $40 purchase if sales tax is 5%?
Answer:
Before Tax Price: $40.00
Sale Tax: 5.00% or $2.00
After Tax Price: $42.00
Step-by-step explanation:
Answer:
42 dollars
Step-by-step explanation:
When doing tax problems, we need to memorize the formula of:
price + tax • price = price with sales tax.
This formula works because you have the initial percentage of the cost, with the added tax, which gives the extra value--then added together it gives the sales cost price.
So let's plug our numbers in
40 + (0.05 or 5%) • 40 = price with sales tax
40 + 2 = price with sales tax
42 = price with sales tax
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Unit 5 Day 4 - Exit Ticket 5.3 - Dividing Polynomials
Perform the operation shown below.
Hint: Shift 6 for exponents and put remainders in (),
Ex. 2x^2+(4/x+2)
(x3+10x2+13x+36)÷(x+9)
We can state that the polynomial [tex]x^3 + 10x^2 + 13x + 36[/tex] is
factored by (x + 9).
the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as
[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]
What are polynomials?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
Poly (which means "many") and Nominal (which means "terms") are the two terms that make up polynomials. An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable)
From the question:
We use the long division method to divide polynomials.
[tex]x^2 + 9x + 4[/tex]
_____________________________
[tex]x + 9 | x^3 + 10x^2 + 13x + 36 - (x^3 + 9x^2)[/tex]
_________________
[tex]x^2 + 13x - (x^2 + 9x)[/tex]
___________
[tex]4x + 36 - (4x + 36)[/tex]
__________
0
the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as
[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]
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Find the length of the third side. If necessary, write in simplest radical form.
The length of the third side is 9.
Describe Right Angled Triangle?A right-angled triangle is a triangle in which one of its angles is a right angle, meaning it measures exactly 90 degrees (π/2 radians). The other two angles are acute angles, meaning they measure less than 90 degrees.
In a right-angled triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called the legs. The leg opposite to an acute angle is called the opposite side, and the leg adjacent to that angle is called the adjacent side.
The Pythagorean theorem is a fundamental concept in right-angled triangles. It states that the sum of the squares of the lengths of the legs of a right-angled triangle is equal to the square of the length of its hypotenuse. This theorem is often used to calculate the length of one side of a right-angled triangle when the lengths of the other two sides are known.
Let's call the missing side of the right triangle "x". We can use the Pythagorean theorem to solve for x, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
So, we have:
x² + 7² = (√130)²
Simplifying:
x² + 49 = 130
x² = 81
Taking the square root of both sides, we get:
x = 9
Therefore, the length of the third side is 9.
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Answer:
The length of the third side of the given right triangle is 9 units.
Step-by-step explanation:
We can use Pythagoras Theorem to find the length of the third side of the given right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
[tex]a = 7[/tex][tex]c = \sqrt{130}[/tex]Substitute these values into the formula and solve for the third side, b:
[tex]\implies 7^2+b^2=\left(\sqrt{130}\right)^2[/tex]
[tex]\implies 49+b^2=130[/tex]
[tex]\implies 49+b^2-49=130-49[/tex]
[tex]\implies b^2=81[/tex]
[tex]\implies \sqrt{b^2}=\sqrt{81}[/tex]
[tex]\implies b=9[/tex]
Therefore, the length of the third side of the given right triangle is 9 units.
evaluate the trigonometric function.
In response to the query, we have that The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.
what is Pythagorean theorem?The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.
This trigonometric identity is valid for all theta values. Because it is connected to the geometry-related Pythagorean theorem, it is known as the Pythagorean identity.
According to Pythagorean theory,
[tex]Cos(theta)^2 + Sin(theta^)2 = 1[/tex]
So, you can easily include that value into the equation and simplify it if you need to assess sin(theta) + cos(theta) for a certain value of theta:
[tex]Cos(theta)2 + Sin(theta)2 = 1\\Sin(2) + Cos(30)\\If theta = 30, then 2(30) = 1.\\(1/2)\\c^2 + (√3/2)\\c^2 = 1 \s1/4 + 3/4 = 1 \s1 = 1[/tex]
The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.
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Which of the diagrams below represents the contrapositive of the statement
"If it is a square, then it is a quadrilateral"?
not quadrilateral
not square
Figure A
OA. Figure A
OB. Figure B
not square
not
quadrilateral
Figure B
Figure B is the correct option which represents the the contrapositive of the statement "If it is a square, then it is a quadrilateral".
What is a contrapositive statement ?
A contrapositive statement is a statement formed by negating both the hypothesis and the conclusion of the original statement, and then switching them and negating the entire statement.
In other words, if the original statement is of the form "If A, then B", then the contrapositive statement is of the form "If not B, then not A". The contrapositive statement is logically equivalent to the original statement, which means that if the original statement is true, then the contrapositive statement is also true, and if the original statement is false, then the contrapositive statement is also false.
Finding the contrapositive statement -
We are given "if it is a square,then it is a quadrilateral ".
To determine the contrapositive of a conditional statement, we must switch the hypothesis and the conclusion and negate both.
The original statement is "If it is a square, then it is a quadrilateral." The hypothesis is "it is a square," and the conclusion is "it is a quadrilateral."
Contrapositive of our given statement is -
"if it is not a square,then it is not a quadrilateral "
Therefore, figure B is correct option.
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Find the value of each expression for a=1/3 b=9 c=5
Answer: Provide the picture if you have one or write out the whole problem
Step-by-step explanation:
You would like to retire 25 years from now and have a retirement fund from which you can draw an income of $50,000 per year – forever! How can you do it? Assume a constant APR of 7%. (What balance do you need to earn $50,000 from interest? How can you get to that balance?)
We need a retirement fund balance of $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To generate an income of $50,000 per year forever, we need to create a retirement fund that can generate this income through interest and not deplete the principal amount.
We can use the following formula to calculate the required balance in the retirement fund:
Balance = Annual income / Annual interest rate
The annual income we need is $50,000, and the annual interest rate is 7%, so we can calculate the required balance as:
Balance = $50,000 / 0.07
= $714,285.71
Therefore, we need a retirement fund balance of $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.
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A right triangle has side lengths 5, 12, and 13 as shown below.
Use these lengths to find tanB, sin B, and cos B.
In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side, the sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Using the side lengths given in the problem, we can identify that angle B is the acute angle opposite the side with length 5.
So, we have:
tanB = opposite/adjacent = 12/5
sinB = opposite/hypotenuse = 12/13
cosB = adjacent/hypotenuse = 5/13
Therefore, the values of the trigonometric functions for angle B in this right triangle are:
tanB = 12/5
sinB = 12/13
cosB = 5/13
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 20 feet. Container B has a diameter of 36 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
no websites or links
After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.
What is the volume?The volume refers to the amount of space in a container.
The volume of a container can be determined using the following formula: πr²h, where:
π = pi = 22/7r = radius = diameter/2h = height.Container A:Diameter = 26 feet
Height = 20 feet
The volume of water in Container A = πr²h
r = radius = diameter/2
= 20/2 = 10 feet
Volume = 22/7 x 10 x 10 x 20
= 22/7 x 100 x 20
=6,285.7
= 6,286 feet³
Container B:Diameter = 36 feet
Height = 19 feet
Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.
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Question Completion:After the pumping of Container A's water into Container B, what is the volume of water in Container B?
4 Y 3 5 Z What is the value of the tan ratio for the refernce angle of X? 3/4 5/4 3/5 4/5
The tangent of angle Z is given as follows:
tan(Z) = length of opposite side/length of adjacent side.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.Hence the tangent for angle Z is given by the ratio between the length of the opposite side to angle Z and the length of the adjacent side to angle Z.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the tangent of angle Z is presented.
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The peaches are priced at three for $2. How much does one dozen cost? Write an equivalent ratio to find the answer. Show your work.
Answer:
12:8
Step-by-step explanation:
3:2
12:x
12÷3=4
2×4=8
12:8
7. A standard dartboard has a radius of 170 mm and is split into 20 equal sections. What is the arc length of a single section on a dartboard rounded to the nearest millimeter?
The arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.
What is equations ?
In mathematics, an equation is a statement that two expressions are equal. It typically involves one or more variables that can take on different values, and the goal is often to solve for the value(s) of the variable(s) that make the equation true.
According to given conditions :The total circumference of the dartboard is given by:
C = 2πr
where r is the radius of the dartboard.
Substituting the given values, we get:
C = 2π(170 mm)
C = 1068.18 mm
Dividing the circumference by the number of sections, we get the arc length of a single section:
Arc length = C/20
Arc length = 1068.18 mm/20
Arc length ≈ 53.41 mm
Rounding this to the nearest millimeter, we get:
Arc length ≈ 53 mm
Therefore, the arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.
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A construction company is building a retaining wall. It has a 12-inch piece of stone and then
bricks are stacked on top. Each brick measures 1.5 inches in height and the entire wall must
be at least 60 inches tall. How many rows of bricks will the retaining wall have?
The retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The wall needs to be at least 60 inches tall, and we already have a 12-inch piece of stone, so we need to stack enough rows of bricks to reach a height of:
60 inches - 12 inches = 48 inches
Each row of bricks adds 1.5 inches to the height
we can divide the remaining height of 48 inches by the height of each row:
48/1.5 = 32 rows
Therefore, the retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.
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Evaluate the function for the given value. g(x) = 7x + 6
Answer:
g(2) = 20
Step-by-step explanation:
g(x) = 7x + 6 g(2)
g(2) = 7(2) + 6
g(2) = 14 + 6
g(2) = 20
So, the answer is g(2) = 20
2x-y=-22
y=7x+67
Help me it might be simple but I need an explanation
The solution to the system of linear equations,
2x - y = - 22 and - 7x + y = 67 is x = - 9 and y = 4.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
Given, Two linear equations 2x - y = 22 and y = 7x + 67 in two variable 'x' and 'y'.
Arranging the equation in a similar pattern we have,
2x - y = - 22 and - 7x + y = 67.
Now, Adding these two equations +y and -y will cancel out,
So, We have - 5x = 45.
x = - 9, and 2(-9) - y = - 22 ⇒ y = 4.
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In a survey of 3,100 people who owned a certain type of car, 1,705 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
55.0% of the people surveyed were satisfied with the car.
What is percentage, how to solve it?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages is (Value/Total value) x 100.
If two values are presented to us, we must determine the percentage difference between them.
Given that, 1,705 said they would buy that type of car again.
Thus, to find people who were satisfied with the car:
Percentage = (Number of satisfied people / Total number of people) x 100%
Percentage = (1,705 / 3,100) x 100% = 55.0%
Hence, 55.0% of the people surveyed were satisfied with the car.
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You might need:
A circle has a circumference of 113.04 units.
I
Calculator
What is the diameter of the circle?
Use 3.14 for π and enter your answer as a decimal.
units
Answer:
36 Units
Step-by-step explanation:
The circumference (C) of a circle is related to its diameter (d) by the formula:
C = πd
We can rearrange this formula to solve for the diameter:
d = C / π
In this case, the circumference of the circle is C = 113.04 units and π is approximately 3.14. Substituting these values into the formula, we get:
d = 113.04 units / 3.14
d ≈ 36 units (rounded to the nearest unit)
Therefore, the diameter of the circle is approximately 36 units.
Answer:36 units
Step-by-step explanation:
How many solutions does the system of linear equations graphed below have?
A. No solution
B. 1 solution
B. Infinitely Many Solutions
If ∑X = 4,390 and n= 4, what is M?
O a. 1,097.5
O b. 17,560
O c. need more information
O d. .0100
The mean of the data is 1097.5
What is mean value?A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers. For example, with the data set: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
Mean = summation of item /number of items
summation of item = 4390
number of items = 4
therefore mean = 4390/4
= 1,097.5
therefore the mean if the data is 1,097.5
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What is the surface area of the triangular prism?
5 ft
5 ft
4 ft
[Not drawn to scale]
O 60 square feet
O 72 square feet
O82 square feet
3 ft
The surface area of the triangular prism is 72 ft squared.
How to find the surface area of a triangular prism?The surface area of a triangular prism can be found as follows:
Therefore,
surface area of a triangular prism = bh + l(s₁ + s₂ + s₃)
Hence,
b = 4 ft
h = 3 ft
l = 5 ft
s₁ = 4 ft
s₂ = 3 ft
s₃ = 5 ft
Therefore,
surface area of a triangular prism = 4 × 3 + 5(4 + 3 + 5)
surface area of a triangular prism = 12 + 5(12)
surface area of a triangular prism = 12 + 60
surface area of a triangular prism = 72 ft²
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Please help!!! see image below!!
Answer:
onomatopoeia
Step-by-step explanation:
Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.
a. 6.767
b. 0
c. 2.922
d. -2
The x-coordinate at which F(x) = G(x) is 0.667. By graphing the functions, the answer has been discovered.
What does graphing a function mean?Making a graph of the pertinent function is the first step in graphing a function. The function equation will be satisfied by a curve if it reflects the function at that location.
According to the given information:We are given two functions as f(x) = log (2x) and g(x) = 3x - 2
The graph of the given functions has been plotted and attached below.
In the graph, the red line represents the log function i.e. f(x) and the blue line represents the linear function i.e. g(x).
From the graph, we can observe that the two functions meet at two points which are (0.667, 0) and (0, -2).
Hence, the x value where F(x) = G(x) is 0.667.
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1.The angles above are examples of___________ angles. (SUPPLEMENTARY OR COMPLEMENTARY)
The value of the missing angle is _____
75
105
90
15
please please help
Therefore , the solution of the given problem of angle comes out to be x = 15° option d is correct.
What does an angle mean?In Euclidean geometry, an angle is a shape made up of two rays, or circular sides, that split at the wall's apex and the wall's apex, which is located at the centre. Two rays can combine at their points to create an angle. Another result of two things interacting is an angle. Dihedral angles are what they are called. Two line beams can be arranged at their edges in a number of ways to form a curve through two dimensions.
Here,
Given :
It is an right angle or we can say 90° angle.
So,
In order to find the value of x :
We can,
=> x + 75 = 90
=> x =90 -75
=> x = 15°
Therefore , the solution of the given problem of angle comes out to be x = 15° option d is correct.
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The youth center has installed a swimming pool on level ground. The pool is a right circular cylinder with a diameter of 24 feet and a height of 6 feet. To the nearest cubic foot, what is the volume of water that will be in the pool when it is filled with?
Rounding to the nearest cubic foot, the volume of water that will be in the pool when it is filled is approximately 2713 feet³.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The first step is to find the radius of the cylinder.
Since the diameter is given as 24 feet, the radius is half of the diameter or 12 feet.
Next, we can use the formula for the volume of a cylinder -
V = πr²h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get -
V = π(12)²(6)
= π(144)(6)
= 2712.96
≈ 2713 cubic feet
Therefore, the volume value is obtained as 2713 cubic feet.
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The length of a wall in a computer classroom is 15 metres. How many computer desks can be placed side-by-side along the wall if the desk has a length of 70cm and a breadth of 40cm
There will be 21 computer workstations that may be arranged side by side along the wall.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number of computer desks that can be placed side-by-side along the wall is calculated as,
⇒ (15 x 100) / 70
⇒ 1500 / 70
⇒ 21.42
There will be 21 computer workstations that may be arranged side by side along the wall.
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what is the diameter of a circle with a circumference of 132ft ? Use 22/7 for pie
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
Given that the circumference is 132ft and π is 22/7, we can write:
132 = (22/7)d
To solve for d, we can multiply both sides by 7/22:
132 × 7/22 = d
Simplifying the left side:
42 = d
Therefore, the diameter of the circle is 42 feet.
Answer:
D = 42
Step-by-step explanation:
Formula to find Diameter = [tex]\frac{C}{\pi }[/tex]
D = 132 ÷ [tex]\frac{22}{7}[/tex]
[tex]D = \frac{132}{1}[/tex] × [tex]\frac{7}{22}[/tex]
132 divide 22 = 6
D = 6 × 7
D = 42
the rectangle repersents the base of a right rectangular prism. The height of the prism is 6 inches. What is the volume of this prism
Given- The rectangle that represents the base of right rectangular prism
To find - The volume of the prism.
Explanation- we know that the volume of the right rectangular prism is product of area of rectangle and the height
Area of rectangle is [tex](lb)[/tex]
length (l) = 4.2
breadth = 3
area = 4.2×3=12.6
Volume of prism = 12.6 × height =12.6×6=75.6
Hence the volume of the prism is 75.6 in^3
Final answer - The correct option is D.
A sales director for an educational curriculum company shares information about reading proficiency with several regional school districts to inform them of new policies and assist in sales of a new product.
What region and grade should the sales director target as most likely to want a new reading product based on low reading scores and trending?
West region, 8th grade
Northeast region, 8th grade
West region, 4th grade
Northeast region, 12th grade
According to the information, it can be inferred that the region and grade that the sales director should target to offer a new reading product based on low reading scores is West region, 4th grade.
How to select the right conclusion?To select the correct conclusion we must carefully look at the graphs and identify in which regions and grades the reading score rates are low. Based on this information, we can infer that the region and grade with the lowest rates in this area is West region, 4th grade.
Due to the above, the sales manager should focus his sales strategy on new products in this population because there is a high probability that they will buy the products to improve the rates they have.
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