To create a 4 quadrant chart in Microsoft Word, follow the 13 steps given below.
1. Open a new Word document and click on the Insert tab.
2. Select Chart from the Illustrations group.
3. Choose the type of chart you want to create from the drop-down menu.
4. Click on the Design tab and select the Chart Layout option.
5. Select the Four Quadrant Chart option under the Layout section.
6. Enter the data for each quadrant into the chart.
7. Click on the Format tab and select the Chart Elements option.
8. Select the axes you want to use for the four quadrants from the drop-down menu.
9. Enter the labels for the four quadrants in the Axis Labels section.
10. Select the desired formatting options for the chart.
11. Click the Insert button to insert the chart into the document.
12. Adjust the position and size of the chart as desired.
13. Click the Save button to save the document.
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Need help with this question. Please !!!!!
The required coordinates of point B are (2, 3) which is the correct answer would be option (C).
To find the coordinates of point B, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.
As per the question, we are given the coordinates of points A and O, which are (4, 5) and (3, 4), respectively.
We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AO.
Let the coordinates of B would be (x, y)
Substituting the coordinates of points A and O into the midpoint formula gives us :
3 = (x+4)/2 ; 4 = (y+5)/2
6 = x +4; 8 = y + 5
x = 2; y = 3
Therefore, the required coordinates of point B are (2, 3).
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How many angles are formed when 2 parallel line are split by a transversal?
When two parallel lines are cut by a transversal, eight angles are formed. Interior angles are supplementary to corresponding exterior angles and the sum of an interior and its corresponding exterior angle is 180 degrees.
Two parallel lines are cut by a transversal, eight angles are formed. Four of these angles are interior angles, which are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. The other four angles are exterior angles, which are the angles formed between the two lines and the transversal that lie outside the region bounded by the parallel lines. Interior angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior and exterior angles is important in geometry, as they can be used to prove the parallelism of lines.
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One of the solutions to the quadratic equation x - 12x – 45 = 0 is x = -3 Which statement is true? Select all that apply. (Check Screenshot)
Answer:
1st and 3rd 4th
graph of f(x) = x² - 12x-45 has an x-intercept at x = -3
-3 is a zero of the function f(x) = x²-12x- 45
x + 3 is a factor of x² - 12x-45
Steps:
other solution is (x - 15) or x = 15
x² - 12x-45
2 numbers that when multiplied give -45 & when added give -12 are -15 & 3
(x-15) (x+3)
"zero" is a fancy way for asking for the answer or root
imaginary number is i which is √-1 so
if you have √-9 = √9 * √-1 = 3i
if you have √-20 = √4 * √-1 * √5 = 2i√5
.
Circle A has center of (2, 3), and a radius of 5 and circle B has a center of (1, 4), and a radius of 10. What steps will help show that circle A is similar to circle B? (6 points) Group of answer choices
Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.
Pls help and explain
Answer:
$48/4 pizzas
Step-by-step explanation:
⭐ A ratio is a fraction that relates one variable to another.
⭐ A proportion is when you make two ratios equal to each other to solve for one of the variables.
We want to find what it costs for Mike to buy 4 pizzas. To achieve this, we must make a proportion.
The first ratio we are given is $12/1 pizza, which means that it costs $12 for 1 pizza.The ratio for Mike buying 4 pizzas is x/4 pizzas, where x is the cost of buying 4 pizzas.Set these two ratios equal to each other and solve for x. *remember: keep the numerators and denominators the same units.[tex]\frac{12}{1 pizza} = \frac{x}{4 pizzas}[/tex]Multiply both sides of the equal sign by 4 to isolate the variable x.[tex]\frac{12}{1 pizza} (4) = \frac{x}{4 pizzas} (4)[/tex][tex]48 = x[/tex]∴ It costs Mike $48 for 4 pizzas.Now we need to write the ratio of cost to pizzas for buying 4 pizzas.$48/4 pizzasWhat are the factors of 3x² 4x 4?
The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2) .
The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.
The quadratic expression is given as 3x² -4x -4 ;
it can be written as ⇒ 3x² -6x +2x -4 ,...by using split the middle term method .
⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .
⇒ (3x + 2)(x - 2)
Therefore , the factors are (3x + 2)(x - 2) .
The given question is incomplete , the complete question is
What are the factors of the quadratic equation 3x² -4x -4 ?
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17. एउटा वस्तुको अङ्कित मूल्यमा 20% छुट दिएपछि 13% भ्याट जोडेर रु. 18080 मा बिक्री गरियो भने उक्त वस्तुको अङ्कित मूल्य पत्ता लगाउनुहोस् । (Allowing 20% discount on the marked price of an article, the value of the article will be Rs. 18080 when a VAT of 13% is added, find its marked Ans: Rs. 20,000 price.)
Answer:
11111111111111111111
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (1, -2)
Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 1)² - 2
Also, from the graph, we have the point (0, 1)
This means that
a(0 - 1)² - 2 = 1
So, we have
a(1) = 3
Divide both sides by 1
a = 3
Substitute a = 3 in f(x) = a(x - 1)² - 2
f(x) = 3(x - 1)² - 2
Hence, the equation is f(x) = 3(x - 1)² - 2
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100 POINTS HELP PLEASE WILL GIVE BRAINLIEST
Answer:
D. Increase in assets
Step-by-step explanation:
The entry "Cash 750,000" is listed as a debit in the T-account because it is an increase in assets. In double-entry bookkeeping, a debit is used to record an increase in assets and a credit is used to record a decrease in assets. In this case, the business received cash in exchange for the airplane, which represents an increase in the business's assets. So the Cash account is debited and the Airplane account is credited.
For the polynomial function f(x) = x5-x4-9x3 + 9x2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.
A.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, cross
B.) x = -3, cross; x = 0, cross; x = 1, cross; x = 3, touch
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
D.) x = -3, cross; x = 0, cross; x = 1, touch; x = 3, touch
Answer:
C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross
Step-by-step explanation:
You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.
FactorsThe equation can be factored as ...
f(x) = x^2(x^3 -x^2 -9x +9)
The cubic can be factored as ...
x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)
and the quadratic factor can be factored as the difference of square. The complete factorization is then ...
f(x) = x^2(x -1)(x -3)(x +3)
ZerosThe zeros are the values of x that make the factors zero:
x = 0, multiplicity 2x = -3, multiplicity 1x = 1, multiplicity 1x = 3, multiplicity 1Touch/CrossWhen the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.
When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.
__
Additional comment
As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.
Write the equation of the line that passes through the points (-9,-9) and (−8,1).
Answer: slope= change in y-intercept and x-intercept
Step-by-step explanation:
1-9=-8
-8- -9=1
-8/1=-8
Does asymptote mean undefined?
The eccentricity of the conic section below is
A. Closer to 0 than 1
B. Closer to 1 then 0
The eccentricity of the conic section below is: A. closer to 0 than 1.
What is a conic section?In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.
In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:
Hyperbola: its eccentricity is greater than one (1).Parabola: its eccentricity is equal to one (1).Ellipse: its eccentricity is 0 < e < 1.Circle: its eccentricity is equal to zero (0).In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.
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Can two equilateral triangles always be congruent Is it true or false?
Suppose y varies directly proportional with "x" y=6 when x=8 Find y when x=10
Step-by-step explanation:
directly proportional means
y = kx
to find k we use the first given pair (8, 6) :
6 = k×8
k = 6/8 = 3/4
so, for x = 10
y = 3/4 × 10 = 30/4 = 7.5
A diver leaps from the edge of a diving platform into a pool below. The figure shows the initial position of the diver and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver's shoulders is given by xXt and the vertical distance from the water surface to her shoulders is given by t), where x(t) and yt) are measured in meters. Suppose that the diver's shoulders are 11.4 meters above the water when she makes her leap and that d0.8 and dar 3.6 9.8t for Os ts A, where A is the time that the diver's shoulders enter the water. image y0) Note: Figure not drawn to scale Question 1 (3 points) Find the maximum vertical distance from the water surface to the diver's shoulders. Question 2 (2 points) Find A, the time that the diver's shoulders enter the water Question 3 (2 points) Find the total distance traveled by the diver's shoulders from the time she leaps from the platform until the time her shoulders enter the water. Question 4 (2 points) Find the angle e. 0くθ 〈 π , between the path of the diver and the water at the instant the diver's shoulders enter the water.
A- The maximum vertical distance from the water surface to the diver’s
shoulders are 12.061 meters.
B- The time that the diver’s shoulders enter the water is 1.936 seconds.
C- The total distance traveled by the diver’s shoulders from the time
she leaps from the platform until the time her shoulders enter the water is 12.946 meters.
D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.
A-
[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]
The maximum vertical distance from the water surface to the diver’s
shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.
B-
[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]
when A= 1.936 seconds.
C-
[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]
At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]
D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]
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Rewrite the equation using completing the square.
Answer: 8*8=64
6*6*=216
64-216+21=0
Step-by-step explanation:
How do you find the inverse of two variables?
To find the inverse of a function you just have to switch the x and the y and then solve for y.
Inverse Function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.
The inverse function returns the original value for which a function gave the output.
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What are the 5 ways to prove triangles similar?
Five different ways to prove the given triangles are similar is given by :
SAS, SSS, ASA, AA, and RHS.
Five different ways to prove triangles are similar is given by:
1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.
2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle
3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.
4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.
5. RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.
Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.
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you walk 45 m at an angle of 25 degrees s of e. then you walk 30 m north. what is the angle of the resultant vector?
So the angle of the resultant vector is approximately 53.13 degrees.
To find the angle of the resultant vector, you can use trigonometry to break the two vectors into their x and y components and then use the arctangent function to find the angle.
First, let's find the x and y components of the first vector (the one that travels 45 meters at an angle of 25 degrees south of east). To do this, we can use the trigonometric functions sine and cosine. The x component is equal to the distance traveled (45 meters) times the cosine of the angle (25 degrees), and the y component is equal to the distance traveled times the sine of the angle.
In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.
Now let's find the x and y components of the second vector (the one that travels 30 meters north). The x component of this vector is 0 meters (since it doesn't move in the east-west direction), and the y component is 30 meters (since it travels 30 meters in the north direction).
To find the resultant vector, we can add the x components and y components of the two vectors. The x component of the resultant vector is 39.74 meters + 0 meters = 39.74 meters, and the y component of the resultant vector is 22.36 meters + 30 meters = 52.36 meters.
To find the angle of the resultant vector, we can use the arctangent function (also known as the inverse tangent function). The angle is equal to the arctangent of the y component divided by the x component.
In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.
So the angle of the resultant vector is approximately 53.13 degrees.
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Find the x and y components of the initial vector first (the one that travels 45 meters at an angle of 25 degrees south of east). The trigonometric functions sine and cosine can be used to do this. The y component is equal to the distance traveled times the sine of the angle, and the x component is equal to the distance traveled times the cosine of the angle, or 45 meters times the cosine of the angle, or 25 degrees.
In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.
The two vectors' x and y components can be added to determine the resultant vector. The resultant vector has two components: an x component of 39.74 meters plus 0 meters equals 39.74 meters, and a y component of 22.36 meters plus 30 meters equals 52.36 meters.
The arctangent function can be used to determine the angle of the resulting vector (also known as the inverse tangent function). The angle is determined by dividing the y component's arctangent by its x component.
In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.
So the angle of the resultant vector is approximately 53.13 degrees.
The area of a rectangle is 56.96 m²
If the length is 16, what is the width and perimeter?
Answer:
width is 3.56
Step-by-step explanation:
Area is = width x length
so Area/length
so 56.96/16=3.56
The width of the rectangle is 3.56 m and the perimeter is 39.12 m.
To find the width of the rectangle,
We need to use the formula for the area of a rectangle, which is:
Area = Length x Width
We know that the area of the rectangle is 56.96 m², and the length is 16 m. So,
We can substitute these values into the formula and solve for the width:
56.96 m² = 16 m x Width
Width = 56.96 m² / 16 m
Width = 3.56 m
Therefore, the width of the rectangle is 3.56 m.
To find the perimeter of the rectangle,
We need to use the formula:
Perimeter = 2 x Length + 2 x Width
We know that the length is 16 m and the width is 3.56 m,
So we can substitute these values into the formula and solve for the perimeter:
Perimeter = 2 x 16 m + 2 x 3.56 m
Perimeter = 32 m + 7.12 m
Perimeter = 39.12 m
Therefore, the perimeter of the rectangle is 39.12 m.
In conclusion, the width of the rectangle is 3.56 m and the perimeter is 39.12 m when the area is 56.96 m² and the length is 16 m.
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Which way is negative infinity?
Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".
Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.
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What is the solution to the system of equations y =- 5 3 y 1?
The solution to the system of equations y = -5x + 3 and y = 1 is x = 0.4 and y = 1.
Therefore, the answer is (0.4, 1).
To solve the system of equations :
y = -5x + 3 (1)
y = 1 (2)
In the given equation, coefficient of y is same in both equations. So subtracting equation (2) from equation (1) we get
y - y = -5x + 3 - 1
0 = -5x + 2
Adding 5x on both sides
0 + 5x = -5x + 2 + 5x
5x = 2
Dividing both sides by 5
x = 2/ 5
x = 0.4
--The question is incomplete, answering to the question below--
"What is the solution to the system of equations?
y = -5x + 3 and y = 1"
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The last step mentioned in building equations to solve real-world problems is to check your answer by substituting it into the original equation. Another way to check your answer is to use estimation and to make sure the answer is reasonable for the situation. In the problem above, are all of the solutions reasonable for the given situation? Why or why not?
Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
What is meant by linear equation ?There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.
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a cylinder whose height is 7cm and total surface area is 1936/7 . find radius
The radius of the cylinder 37cm.
How to find radius?The radius of a circle is the distance a circle's center from any point along its circumference. Usually, "R" or "r" is used to indicate it.Cylinder y's Curved Surface Area (CSA) Its other name is lateral surface area (LSA). The formula for the curved surface area (CSA) of a cylinder with base radius "r" and height "h" is: CSA of cylinder = 2rh sq. units.cylinder's entire surface area is equal to 2r(h+r).
total surface area = 1936 square cm
height=7 cm
radius is
therefore,
2πr(h+r)=1936
2πr(r+7)=1936
44(r+7)=1936
r+7 = 1936/44
r+7=44
r= 44-7 =37
r=37cm.
The radius of the cylinder 37cm.
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What is the nature of roots of 2x² 4x 3 0?
The given quadratic equation 2x²-4x+3=0 has no real roots.
The roots of the quadratic equation are real and equal if the discriminant equals zero, a, b, and c are real values and a≠0.
The roots of the quadratic equation are real and unequal if the discriminant is greater than zero, a, b, and c are real values, and a≠0.
The quadratic equation's roots are imaginary and unequal if the discriminant is less than zero, a, b, and c are real integers and a≠0.
2x²-4x+3=0
Comparing the equation with ax²+bx+c=0
We know that,
D = b²-4ac
= (-4)²-4(2)(3)
= 16- 24
= -8
Since D < 0
Hence, the given equation 2x²-4x+3=0 has no real roots.
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Describe what is happening in the graph below.
A. The function is steady, and then it increases
B. The function decreases sharply, and then it stays the same
C. The function increases a little, and then it decreases sharply
D. The function stays constant, and then it decreases sharply
(Picture of graph included)
D.
The line never increases, so we can cancel out A and C.
The line starts off straight, so it's not B.
So, the answer is D. since it starts off constant and then decreases sharply.
What is the mean of the following data set 4 8 11 12 13?
Answer:
9.6
Step-by-step explanation:
What is the mean of the following data set 4 8 11 12 13?
Mean: is the average of values so:
(4 + 8 + 11 + 12 + 13) / 5 = 9.6
what is the weekly average proportion of opposed feeling? group of answer choices 0.225 0.025 none of the above 0.125 0.200
The weekly average proportion of opposed feeling is 0.0375. (Option D)
A sample proportion is the proportion of individuals in a sample who have a particular characteristic of interest. It refers to the number of successes (success means that an individual possesses the characteristic of interest) of the sample divided by the sample size. According to the provided data, the number of successes in the sample size is 30 and the sample size is 100. Hence, the sample proportion is:
Sample proportion = 30/100 = 0.3
As the survey is conducted weekly for eight weeks, the average proportion of the samples is determined by sample proportion divided by number of weeks. Hence,
Average proportion = 0.3/8 = 0.0375
Note: The question is incomplete. The complete question probably is: A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey to be constructed of township residents. Each week, a sample of 100 residents are questioned on their feeling toward the project. The results to date are shown below. What is the weekly average proportion of opposed feeling? (3 pts.) a. 0.0250 b. 0.1250 c. 0.3000 d. 0.0375 e. None
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Hodor combines 3 quarts of a 5% sugar solution and 2 quarts of an 8% sugar solution. How many additional quarts of a 12% sugar solution must be added to make a 10% sugar solution?
Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons
The data of the sugar solutions are;
The volume of 5% sugar solution Kate has = 3 quarts
The volume of the 12% sugar solution = X
Let 'Y' represent the volume of the 8% sugar solution, we have;
The volume of the resultant solution, Z = X + Y + 3
The concentration of the resultant solution = 10%
0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)
Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;
X = (2·Y + 15)/2
When the volume of the 8% sugar solution, Y = 2 quartz, we have;
X = (2 × 2 + 15)/2 = 9.5 Quartz
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