The area of triangle JKL is given as follows:
D. 24 units².
How to obtain the area of a triangle?The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:
A = 0.5bh.
Considering segment JK as the base, it's length is given as follows:
b = 2 - (-2) = 4 units.
The midpoint of the base has the coordinates given as follows:
x = (-2 + 2)/2 = 0.y = (4 + 4)/2 = 4.The height is the distance between the midpoint of the base and the remaining vertex, hence between (0,4) and (0, -2), thus:
h = 4 - (-2) = 6 units.
Then the area of the triangle is obtained as follows:
A = 4 x 6
A = 24 units².
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What is the product of 55 and 10\sqrt{72}10
72
in simplest radical form?
The prοduct οf 5 and 10√72 is 300√2
What is The square rοοt οf a number?The square rοοt οf a number is a value that, when multiplied by itself, gives the οriginal number. It is denοted by the symbοl √, and the number under the symbοl is called the radicand.
Fοr example, the square rοοt οf 25 is 5, because 5 multiplied by itself equals 25. This can be written as √25 = 5
Here we have
5 and 10√72
As we knοw 72 = 36 × 2
10√72 = 10 [ √(36 × 2) ]
= 10 [√(6 × 6 × 2) ]
= 10 (6) √2
= 60 √2
Hence, the prοduct οf 5 and 10√72 can be calculated as fοllοws
=> 5 × 60√2 = 300√2
Therefοre,
The prοduct οf 5 and 10√72 is 300√2
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Yall PLease help with this one.
Answer:
i think 4<6
Step-by-step explanation:
Answer:
=
Step-by-step explanation:
5j543nn al
12) The diameter of a bracelet is 17.8 cm.
Work out its circumference.
Round your answer to an appropriate degree of accuracy.
PLEASE SHOW WORK!!!!!!!!!
1) The equal expressions are I and III
2) The value of the expression is 3 41/80
What is an absolute value expression?An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.
The absolute value of a number x is denoted by |x| and is defined as follows:
|x| = x, if x is positive or zero
|x| = -x, if x is negative
Since -/x/ = -x then this are the equal expressions.
[tex]a^2/a + 1 + a + 1/a^2[/tex]
Then;
[tex]4^2/4 + 1 + 4 +1/4^2[/tex]
16/5 + 5/16
= 3 41/80
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cory and quentin went bowling on friday night corey has his own bowling shoes but quentin had to rent his at the alley shoes rent for a flat fee of $4 plus $2 per hour the equation y=2x+4 describes the cost of renting the shoes if quentin only had $11 how many hours can he rent the bowling shoes.
Therefore , the solution of the given problem of equation comes out to be he can hire the shoes for three hours with his meagre $11 budget.
Equation : What is it?Complex algorithms frequently employ a variable term to guarantee congruence with the two opposing assertions. Equations, which are academic expressions, are used to demonstrate the equality of different academic figures. In this instance, the normalise method provides b + 6 rather than merely expression separating 12 into two pieces for using the data from y + 6.
Here,
To begin, we can construct an expression to symbolise the circumstance:
=> y = 2x + 4
where x represents the number of hours that Quentin rents the shoes for and y represents the overall cost of the rental.
We can put y equal to 11 because we know that Quentin only has $11 to spend:
=> 11 = 2x + 4
We can now determine x:
=> 2x = 11 - 4
=> 2x = 7
=> x = 7/2
Quentin can therefore spend $11 to hire the shoes for 3.5 hours (7/2 hours).
He would have to pay either $10 or $12 to hire the shoes for either three or four hours. He can hire the shoes for three hours with his meagre $11 budget.
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What are the domain and range for the function f(x)=2x?
The domain and range for the function f(x) = 2x include the following:
Domain = (-∞, ∞).
Range = (-∞, ∞).
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or {x|x ∈ R}.
Range = {-∞, ∞} or {y|y ∈ R}.
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Please I need help with quiz corrections should be easy if you are good at geometry!!
A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees.
What is a right angle triangle?Right triangles have some unique properties that make them useful in various applications, such as in geometry and trigonometry. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We know that;
Tan 45 = 14/x
x = 14
Sin 45 = 14/y
y = 20
Again;
Tan 60 = 16√3/x
x = 16√3 * 1/√3
x = 16
Sin 60 = 16√3/y
y = 16√3 ^ 2/√3
y = 32
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Find the slope of the line that contains the points (10, 0) and (-20, -18)
The slope of the line that contains the points (10, 0) and (-20, -18) is: slope = (change in y)/(change in x) = 3/5.
The slope of a line is the measure of its steepness, and it's found by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. In this case, the slope of the line that passes through the points (10, 0) and (-20, -18) can be calculated as follows:
slope = (change in y-coordinates) / (change in x-coordinates)
slope = (-18 - 0) / (-20 - 10)
slope = -18 / -30
slope = 3/5
Therefore, the slope of the line is 3/5.
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Is enough information given to prove that GHF =KHJ using the SAS Congruence Theorem? yes no If yes, complete the two-column proof. If no, complete only the last line with an explanation of why no
No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle.
No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle. To use the SAS Congruence Theorem to prove that GHF =KHJ, it would be necessary to have information about the lengths of the corresponding sides and the measure of the included angle in each triangle. Without this information, it is not possible to prove that GHF =KHJ using the SAS Congruence Theorem. To prove that GHF =KHJ using this theorem, it would be necessary to show that the two sides GK and KH are congruent, the two sides HF and HJ are congruent, and the included angle GHF is congruent to the included angle KHJ.
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Mrs.kenimer had a chocolate bar that weighed 1/2 lb.At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound.How much chocolate did mrs kenimer eat at recess?
Mrs. kenimer had a chocolate bar that weighed 1/2 lb. At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound. Mrs. kenimer ate 3/8 lb of the chocolate bar.
What do you mean by pound(lb)?The British imperial and American cοnventiοnal methοds οf measurement bοth use the pοund as a unit οf mass. The internatiοnal avοirdupοis pοund, which is fοrmally defined as precisely 0.45359237 kilοgrammes and is split intο 16 avοirdupοis οunces, is the term that is currently mοst frequently used. The avοirdupοis pοund's wοrldwide standard sign is lb.
Given,
Mrs.kenimer had a chocolate bar that weighed 1/2 lb or 0.5lb
At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound or 0.25 of a pound.
Remaining weight of the chocolate bar= ½* ¼ = 1/8 lb
She ate= (1- ¼)= ¾ or 0.75 of a pound
So she ate= ½ * ¾ = 3/8 lb of the chocolate.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
12 units
Step-by-step explanation:
Help me plsssssssssssssssssssss
Answer:
157°
Step-by-step explanation:
We can see that the angle here is an alternate angle, this means it is an opposite angle that has the same value as each other.
Knowing this, we can see that if the angles are alternated the missing angle should be 157 as well.
Hope this helps have a lovely day! :)
Use the equation to find the awnser
Using the trend line equation, we can find that the record was set in the year 2005.
What is a scatter plot?Data is shown visually in a scatter plot.
The coordinate axes are used in a straightforward scatter plot to plot the points according to their values.
Now in the given question,
The scatter plot equation is:
y = - 0.14x + 12.5
Now we know that y = 11.8 seconds.
So,
11.8 = -0.14x + 12.5
⇒ 0.14x = 12.5 - 11.8
⇒ x = 0.7/0.14
⇒ x = 5
Therefore, the year when the record was set is 2000+5 = 2005.
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In a sequence of numbers, a4=12, a5=14, a6=16, a7=18, and a8=20.
Which equation can be used to find the nth term of the sequence, an?
an=2n+12
an=3n+12
an=3n
an=2n+4
The correct equation to find the nth term of the given sequence is an=2n+12, which can be demonstrated by calculating the 4th to 8th terms and verifying that they match the given values.
The formula an=2n+12 can be used to find the nth term of the sequence. This formula states that the nth term is equal to twice the value of n (2n) plus 12 (2n + 12). To demonstrate, for the 4th term of the sequence (a4), we can use the formula and calculate a4 = 2(4) + 12 = 20, which is equal to the given value of a4 = 12. Similarly, we can calculate the other values of the sequence using the same formula: a5 = 2(5) + 12 = 22 (which is equal to the given value of a5 = 14), a6 = 2(6) + 12 = 24 (which is equal to the given value of a6 = 16), a7 = 2(7) + 12 = 26 (which is equal to the given value of a7 = 18), and a8 = 2(8) + 12 = 28 (which is equal to the given value of a8 = 20). Therefore, we can conclude that an=2n+12 is the correct equation to find the nth term of the sequence.
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The equations of four lines are given. Identify which lines are parallel.
Line 1:
y = 8x - 3
Line 2: y-6=(x-4)
Line 3:
Line 4:
y = 3x + 4
1
x - 3y = -4
O All four lines are parallel.
O Lines 3 and 4 are parallel.
O Lines 1 and 3 are parallel.
O Lines 2 and 3 are parallel.
►
For the given equations, using slope formula option B: Lines 3 and 4 are parallel, is the correct option.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The four different equations are given.
To identify parallel lines, we need to compare their slopes.
If two lines have the same slope, they are parallel.
Line 1 is in slope-intercept form (y = mx + b) where the slope is m = 8.
Line 2 is in point-slope form (y - y1 = m(x - x1)) where the slope is m = 1/8.
Line 3 is in slope-intercept form where the slope is m = 3.
Line 4 is in slope-intercept form where the slope is m = 1/3.
Comparing the slopes, we see that -
Lines 1 and 2 have different slopes, so they are not parallel.
Lines 1 and 3 have different slopes, so they are not parallel.
Lines 1 and 4 have different slopes, so they are not parallel.
Lines 2 and 3 have different slopes, so they are not parallel.
Lines 2 and 4 have different slopes, so they are not parallel.
Lines 3 and 4 have the same slope (m = 3), so they are parallel.
Therefore, lines 3 and 4 are parallel.
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What is the most specific category this shape can be sorted into?
A Venn diagram titled Triangles. Inside the diagram are circles, there is one labeled Scalene and one labeled Isosceles. Inside the Isosceles circle is another circle labeled Equilateral. Below the diagram is a triangle with a single tick mark on each side.
Equilateral
Isosceles
Scalene
Triangle
Therefore, the most specific category this shape can be sorted into is "Triangle."
What would you say about a triangle?3 sides, 3 angles, and 3 vertices make up a closed triangle. It has only two dimensions. Triangles are a part of polygons as well.
The most specific category this shape can be sorted into is "Triangle."
In the given Venn diagram, the category "Triangle" represents the overall group of all types of triangles, which includes "Equilateral," "Isosceles," and "Scalene" triangles.
The triangle with a single tick mark on each side may represent any type of triangle that is not necessarily equilateral, isosceles, or scalene, but it is still a triangle.
Therefore, the most specific category this shape can be sorted into is "Triangle."
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Allison needs 13 inches of cloth for a sewing project, but the fabric store only sells the cloth by the centimeter. Since 1 inch is the same as 2. 54 centimeters, how much cloth will Allison buy in centimeters?
If Allison needs 13 inches of cloth for sewing project, then Allison will need to buy 33.02 centimeter of cloth.
The length of cloth that Allison needs to buy is = 13 inches ,
The conversion factor is ⇒ 1inch = 2.54 centimeter,
Allison needs 13 inches of cloth, and we know that 1 inch is the same as 2.54 centimeters.
So, to convert 13 inches to centimeters we multiply it by the conversion factor of 2.54 centimeters per inch,
Which is written as;
⇒ (13 inches) × (2.54 centimeters per inch)
⇒ 33.02 centimeters
Therefore, Allison needs to buy 33.02 centimeters of cloth for her sewing project.
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The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Writ an equation and solve to determine the cost of the system with the printer.
Express sin A as a fraction in simplest terms.
Answer:
7/25
Step-by-step explanation:
Sin = [tex]\frac{opposite}{Hypotenuse}[/tex]
Hypotenuse = 50
Adjacent = 48
Pythagorean Theorem: a² + b² = c²
48² + b² = 50²
2304 + b² = 2500
b² = 196
b = 14
Opposite = 14
Sin A = 14/50 = 7/25
In circle V V, V W = 3 VW=3 and m ∠ W V X = 9 0 ∘ ∠WVX=90 ∘ . Find the length of ⌢ WX ⌢ . Express your answer as a fraction times π π.
The length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π
What is Circle ?
In geometry, a circle is a two-dimensional shape consisting of all the points that are equidistant from a given point, called the center. The distance from the center to any point on the circle is called the radius of the circle.
From the given information, we know that V, W, and X are points on a circle with center V, and that VW = WX = 3. We also know that ∠WVX = 90°.
Since WX is a diameter of the circle, it has length equal to twice the radius of the circle. Let r be the radius of the circle, then we have:
VW + WX = 2r
3 + 3 = 2r
r = 3
So the radius of the circle is 3. Since WX is a diameter, its length is 2r = 6. Therefore, the length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π
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the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 4 years, how long will it take to triple? (round your answer to one decimal place.) 4.8 incorrect: your answer is incorrect. yr how long will it take to quadruple? (round your answer to one decimal place.)
The population will take around 6.9 years to triple and 9.2 years to quadruple.
Let P(t) be the population at time t. According to the problem, the rate of increase of the population is proportional to the population itself, which means: dP/dt = kP
where k is the proportionality constant. This is a separable differential equation that can be solved by separating the variables and integrating both sides:
∫ dP/P = ∫ k dt
ln|P| = kt + C
where C is the constant of integration. Applying the initial condition that the population doubles in 4 years, we get:
ln|2p0| = k(4) + C
ln|p0| + ln|2| = 4k + C
ln|p0| + ln|2| - 4k = C
Substituting C into the previous equation and using it for the new population level, we get:
ln|3p0| = kt + ln|p0| + ln|2| - 4k
ln|3p0|/|p0| = kt - 4k + ln|2|
ln|3/2| = (k/ln2)t - 4k/ln2
ln|3/2|/(k/ln2) = t - 4/ln2
t = ln|3/2|/(k/ln2) + 4/ln2
Therefore, it will take approximately 6.9 years for the population to triple and 9.2 years to quadruple.
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It’s the average distance to the ____ also measures how far is the data spread apart in the population.
*
It’s the average distance to the Mean also measures how far is the data spread apart in the population.
What is Population?
In statistics, a population refers to the entire group or set of individuals, objects, or events that share a common characteristic or feature. The population can be any size, from a small group of people to an entire country or even the whole world.
In order to make statistical inferences about a population, it is often not practical or feasible to study the entire population. Instead, researchers typically take a sample from the population, which is a smaller subset of the population, and use the sample data to make predictions or draw conclusions about the population as a whole.
The average distance to the mean (or average) also measures how far the data is spread apart in the population.
This is commonly known as the standard deviation, which is a measure of the amount of variation or dispersion in a set of data values. A larger standard deviation indicates a greater amount of variability or spread in the data, while a smaller standard deviation indicates that the data points are closer to the mean.
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The answer to the question please
Answer:
2/9
Step-by-step explanation:
Answer:2/9
Step-by-step explanation:
Look at this table:
Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data.
x y
–
1 1
0 3
1 9
2 27
3 81
We may state with confidence that the exponential function y = [tex]3(3^{x} )[/tex]models the provided data because both of these values agree with the data.
How is exponential function determined?
Since the output values (y) increase by a factor of three every time the input value (x) increases by one, the data demonstrate exponential growth. As a result, we can use an exponential function of the form y = a(b)x to represent this data.
We can utilise the first two data points to determine the values of a and b.
With y = 3 and x = 0, we get:
3 = [tex]a(b^{0} )[/tex]
3 = a
With x=1 and y=9, we get:
9 = [tex]a(b^{x} )[/tex]
b = 3
Hence, y = [tex]3(3^{x} )[/tex] is the exponential function that represents the data.
We may substitute the other input values and compare them to the appropriate output values to validate this model:
If x = 2, then y = [tex]3(3^{2} )[/tex] = 27.
If x = 3, then y = [tex]3(3^{3} )[/tex] = 81.
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point) Use the quadratic formula to solve thequadratic equation2x²−3x−5=0Solutions (separate by commas): x=
The solution to the quadratic equation 2x²−3x−5=0 are x=5/2 or x=-1/2
The quadratic formula can be used to solve the quadratic equation 2x²−3x−5=0. Here’s how to do it:
First, identify the coefficients of the equation. In this case, a=2, b=-3, and c=-5.
Next, plug these values into the quadratic formula: x = (-b ± √(b²-4ac)) / 2a,Substitute the values in the equation: x = (-(-3) ± √((-3)²-4(2)(-5))) / 2(2)
Simplify the equation to get:x = (3 ± √(9+40)) / 4,
x = (3 ± √49) / 4
x = (3 + 7) / 4 or x = (3 - 7) / 4
x = 5/2 or x = -1/2
In summary, the quadratic formula can be used to solve quadratic equations with ease. It is important to know the values of the coefficients of the equation and substitute them into the quadratic formula. The formula will simplify the equation and give the solutions.
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work out the value of 7a - 7b
when a-b=5
Answer:
35
Step-by-step explanation:
Simplification :
7(a-b) as 7 is common
as we know a-b is 5 ,
7 * 5 = 35 in the answer.
Please mark me as the brainliest TQ!
Answer: 35
Step-by-step explanation:
7a - 7b
= 7(a-b)
= 7(5)
= 35
Write the following as a radical expression.
7^{\frac{7}{8}}
Answer: $\sqrt[8]{7^7}$
Step-by-step explanation:
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Line segment RS passes through R(−3, 1) and S(4,3). Find the point P on line segment RS such that the ratio of RP to SP is 5 to 4. Is there more than one possibility? If so, solve for the new coordinates.
In this case, the coordinates of point P are ( __ , __ )
[A. ) Yes there is B. ) No, there isn't ] ______ more than one possibility with coordinates of point P ( __, __ )
"Yes, there is." The coordinates of point P are either (11/4, 63) or (73/52, 36), depending on the chosen value of x.
We can use the distance formula to find the distance between R and P, and between P and S:
Distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values, we get:
RP = √((x - (-3))² + (y - 1)²)
SP = √((x - 4)² + (y - 3)²)
Now, we can set up an equation based on the given ratio of RP to SP:
RP/SP = 5/4
We can substitute the expressions we just derived for RP and SP into this equation:
√((x - (-3))² + (y - 1)²) / √((x - 4)² + (y - 3)²) = 5/4
Squaring both sides of the equation to eliminate the square roots, we get:
((x - (-3))² + (y - 1)²) / ((x - 4)² + (y - 3)²) = 25/16
Expanding the squares and simplifying, we get:
41x² - 146x - 191y² + 1210y + 2900 = 0
For simplicity, let's solve for y:
y = (73x + 2900)/191
Now we can substitute this expression for y into one of the original equations:
RP = √((x - (-3))² + ((73x + 2900)/191 - 1)²)
Simplifying this expression, we get:
RP = √(1049x² - 12212x + 36010)/191
We want RP to be 5x units long, so we can set up the equation:
√(1049x² - 12212x + 36010)/191 = 5x
Squaring both sides, we get:
Expanding the square and simplifying, we get:
1044x² - 12212x + 36010 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1044, b = -12212, and c = 36010. Plugging in these values, we get:
x = (-(-12212) ± √((-12212)² - 4(1044)(36010))) / 2(1044) x = (12212 ± √(5924688)) / 2088 x = (12212 ± 3864) / 2088
This gives us two possible values for x:
x = 11/4 or x = 73/52
Now we can substitute each value of x back into the expression we derived for y:
y = (73x + 2900)/191
For x = 11/4, we get:
y = (73(11/4) + 2900)/191 = 63
So one possible set of coordinates for P is (11/4, 63).
For x = 73/52, we get:
y = (73(73/52) + 2900)/191 = 36
So another possible set of coordinates for P is (73/52, 36).
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ella has 0.5 lb of suger how much water should she add to make the following concentrations tell ella how much syrup she will have in each case
From the given concentrations of the solution, She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.
Concentration is equal to [ (mass of sugar)/(mass of solution) ] × 100
1) 20% concentration
sugar mass equals 0.5 pounds
concentration = 0.5 lbs × 100 / mass of solution = mass of sugar * 100
The solution weighs 2.5 pounds.
Sugar and solution combined equal 2.5 pounds, hence 2.5 pounds minus 0.5 pounds equals 2.0 pounds of water.
She needs to add 2.0 pounds of water to get 2.5 pounds of syrup.
2) 25% concentration
adhere to the same process.
Solution mass = 0.5 lbs × 100 / 25 =
Solution weight is 2.0 lbs.
water weighs 2.0 lbs minus 0.5 lbs, or 1.5 lbs.
She needs to add 1.5 pounds of water to get 2.0 pounds of syrup.
3) Repeat the process
Concentration = 0.5 lbs × 100 / 1.5, where mass of solution = mass of sugar × 100
solution weight is 33.33 pounds.
water's mass is 32.83 pounds after subtracting 0.5 pounds.
She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.
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Complete question -
Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 20%, 25% and 1.5% syrup?
A _______ is an educated guess based on patterns in data figures
A. deductive
B. inductive
C. postulate
D. conjecture
E. counter example
F. converse
Answer:
B. inductive
Step-by-step explanation:
An inductive reasoning process involves making a generalization based on specific observations. In the case of the given question, the statement is: "A _______ is an educated guess based on patterns in data figures."
To use inductive reasoning to find the answer, we can follow these steps:
Look for patterns in the data figures. Identify the commonalities between different examples of educated guesses.
Based on these patterns, make an initial generalization about what the blank might be. For example, if we notice that all educated guesses involve making a prediction based on previous observations, we might guess that the missing word is "conjecture."
Test the generalization by looking at additional examples. Do these examples fit the pattern we identified earlier? If so, our initial guess might be correct. If not, we might need to revise our generalization or consider other options.
Continue testing and refining the generalization until we feel confident that it accurately describes the relationship between the given words.
In this case, using inductive reasoning, we can make an educated guess that the missing word is "conjecture," as it fits the pattern of being an educated guess based on patterns in data figures.