Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.
Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.
The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.
The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.
The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.
Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
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Evaluate the integral
-7x³
x³ +1
Note: Use an upper-case "C" for the constant of integration.
I
dx
The value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
We know that finding the area of the curve's undersurface is the process of integration. To do this, cover the area with as many tiny rectangles as possible, then add up their areas. The sum gets closer to a limit that corresponds to the area under a function's curve. Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral over the domain is finite with the given bounds, then the integration is definite.
Here, we have to determine the value of the given integral
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx[/tex].
So,
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx = 7 \int {\frac{1-x^{3}-1 }{x^{3}+1} } \, dx[/tex][tex]= 7 \int [{1-\frac{1 }{x^{3}+1} } ]\, dx =7\int \, dx - 7 \int {\frac{1 }{x^{3}+1} } \, dx[/tex] ...(1)
Now,
[tex]\frac{1}{x^{3} +1} = \frac{1}{(x+1)(x^{2} -x+1)}[/tex]
We can write
[tex]\frac{1}{(x+1)(x^{2} -x+1)}=\frac{A}{(x+1)} + \frac{Bx+C}{(x^{2} -x+1)}[/tex]
i.e. [tex]1 = A(x^{2} -x+1)+(Bx+C)(x+1)[/tex]
i.e. [tex]1 = Ax^{2} -Ax + A+Bx^{2} +Bx+Cx+C[/tex]
i.e. [tex]1=(A+B)x^{2} +(-A+B+C)x +(A+C)[/tex]
Comparing both sides, we get
[tex]A+B=0 \implies B = -A[/tex] ...(2)
[tex]-A+B+C = 0 \implies -A+(-A)+C=0 \implies -2A+C=0[/tex] ...(3)
[tex]A+C=1[/tex] ...(4)
Subtracting (3) from (4),
[tex]A+C+2A-C=1-0 \implies 3A=1 \implies A=\frac{1}{3}[/tex]
From (4), [tex]C= 1-\frac{1}{3} =\frac{3-1}{3} =\frac{2}{3}[/tex]
From (2), [tex]B =-\frac{1}{3}[/tex]
We get
[tex]\frac{1}{x^{3}+1 } =\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{3} \frac{x-2}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-4}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1-3}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{3}{6} \frac{1}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{1}{2} \frac{1}{x^{2} -x+1}[/tex]
Integrate both sides,
[tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \int \frac{1}{(x+1)} \, dx - \frac{1}{6} \int \frac{2x-1}{x^{2} -x+1}\, dx+\frac{1}{2} \int \frac{1}{x^{2} -x+1}\, dx[/tex]
i.e. [tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \ln(x+1) - \frac{1}{6} ln (x^{2} -x+1)+\frac{\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })[/tex]
From (1),
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex]
Therefore, the value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
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how do i work this on calculator
2x-10=8
Answer:
x = 9Step-by-step explanation:
2x-10=8
2x = 10 + 8
2x = 18
x = 18 : 2 =
x = 9
-----------------------
check
2 * 9 - 10 = 8 (remember PEMDAS)
18 - 10 = 8
8 = 8
the answer is good
For all a and b, what is the sum of (a-b)² and (a+b)²
Answer:
2a² + 2b²
Step-by-step explanation:
(a - b)² + (a + b)² ← expand both factors using FOIL
= a² - 2ab + b² + a² + 2ab + b² ← collect like terms
= 2a² + 2b²
Step-by-step explanation:
Expand both classic quadratics and combine like terms to find the sum:
(a−b)2+(a+b)2
what is the value of the rational expression below when is equal to 5?
15-(5)/5-10=10/-5=-2 hope it helps!
Find the value of x.
Answer:
7x-1 + 2x-1 =7 ..... given
9x-2 = 7
9x = 9
x = 1
Step-by-step explanation:
This is the answer of the above condition.
Please mark as BRAINLIEST and THANK ME.
Solve 8x + c = k for x.
A. x=8(k-c)
OB. x=
_k+c
8
O C. x = 8(k+c)
O D. x=
k-c
8
Answer: [tex]x=\frac{c-k}{8}[/tex]
Step-by-step explanation:
[tex]1) \text { } 8x+c=k \text{ (given)}\\\\2) \text { }8x=c-k \text{ (subtract } k \text{ from both sides)}\\\\3) \text { } \boxed{x=\frac{c-k}{8}} \text{ (divide both sides by 8)}[/tex]
Is the graph increasing, decreasing, or constant?
Answer:
jxdhjsssdddddsssssdd
Answer:
increasing
Step-by-step explanation:
look left to right, line goes up
I NEED HELP ON THESE 2 PROBLEMS. pls good anawers or bad rating and report
Answer:
1.a. skew
1.b. parallel
1.c. none of the above
1.d. perpendicular
1.e. parallel
1.f. skew
2.a. never
2.b. always
2.c. always
2.d. sometimes, sometimes, sometimes
Step-by-step explanation:
For these questions, it is critical to know the definitions of each of the terms.
DefinitionsPerpendicular: Two intersecting lines that form a right angle.Parallel: Two non-intersecting lines that are coplanar.Skew: Two non-intersecting lines that are not coplanar.Problem Breakdown
1.a. skew [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]
Point E is not on line AB. Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar. Point F is not in plane ABE. Since line EF and line AB do not intersect and are not coplanar, they are skew.
1.b. parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]
Line CD is parallel to line AB, and line AB is parallel to line EH. Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.
1.c. none of the above [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]
Line AC and line GA share point A, necessarily intersecting at A. Therefore, line AC and line GA cannot be parallel or skew.
Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle? If the figure is cube-shaped, as depicted, then no.
Note that each line segment AC, AG, and CG are all the diagonal of a cube face. A cube has equal edge lengths, so each of those diagonals would be equal. Thus, triangle ACG is an equilateral triangle.
All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle). So, lines AC and GA are not perpendicular. (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)
"none of the above"
1.d. perpendicular [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]
Line DG and line HG share point G, so they intersect. Both lines are the edges of a face, so they intersect at a right angle. Perpendicular
1.e. parallel [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]
Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face. They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.
1.f. skew [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]
Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar. Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.
2.a. Two lines on the top of a cube face are never skew
Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face. By definition, skew lines are not coplanar. Therefore, these can never be skew.
2.b. Two parallel lines are always coplanar.
If two lines are parallel, by definition of parallel lines, they are coplanar.
2.c. Two perpendicular lines are always coplanar
If two lines AB and CD are perpendicular, they form a right angle. To form a right angle, they must intersect at the right angle's vertex (point P).
Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P. Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines. Therefore, they must always be coplanar.
2.d. A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular
Consider each of the following cases:
Parallel: Consider line CD (top face), and line GF (right face). They are coplanar and don't intersect. By definition, parallel.Skew: Consider line AD (top face), and line GF (right face). They aren't coplanar and don't intersect. By definition, skew.Perpendicular: Consider line AD (top face), and line GD (right face). They do intersect at D, and form a right angle. By definition, perpendicular.None of the above: Consider line AC (top face), and line GC (right face). These lines intersect at C, but as discussed in part 1.c, they form a 60° angle, not a right angle. By definition, "none of the above".These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above. So, those two lines are neither "always", nor "never", one of those choices. Therefore, they are each "sometimes" one of them.
one interior angle of a polygon is a right angle and each of the other interior angles is 126°. Calculate the number of sides of the polygon
Answer:
There are 7 sides.
Step-by-step explanation:
Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.
S=(n−2)180
Since we are given that the two angles are right, the angles and each of the remaining angles is 144.
And Therefore, the sum is:
S=90
(n−2)144
(n−2)180
=90
+90
+(n−2)144
⇒(n−2)180
−(n−2)144
=180
⇒(n−2)(180
−144
)=180
⇒(n−2)(36
=180
⇒n−2=
36
180
⇒n−2=5
⇒n=5+2=7
Hence, the polygon has 7 sides.
The number of sides of the polygon such that one angle is the right angle will be 6.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In any closed polygon, the number of sides is equal to the number of interior angles.
Suppose the number of sides is n in the given polygon.
Sum of angles = 90° + 126° × (n - 1)
The sum of angles is given as, 180(n - 2)
90° + 126° × (n - 1) = 180(n - 2)
90 + 126n - 126 = 180n - 360
180n - 126n = 90 - 126 + 360
54n = 324
n = 6
Hence "The number of sides of the polygon such that one angle is the right angle will be 6".
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The table below shows the average SAT math scores from 1993-2002.
Year
SAT math scores
1993
503
1994
504
1995
506
1996
508
1997
511
1998
512
1999
511
2000
514
Using the data from the table determine if there is a linear trend between the year and the average SAT math scores and determine if there is an exact linear fit of the data. Describe the linear trend if there is one.
a.
Positive linear trend, an exact linear fit.
b.
Positive linear trend, not an exact linear fit.
c.
Negative linear trend, not an exact linear fit.
d.
Negative linear trend, an exact linear fit.
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).
How to calculate the average of the results?To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.
503 + 504 + 506 + 508 + 511 + 512 + 511 + 514 = 40694069 ÷ 8 = 508.6Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.
On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.
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Select the correct answer.
Choose the system of inequalities that best matches the graph below.
Answer:
Its A
Step-by-step explanation:
I said so
Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
Answer:
6.3 *30= 189; so 4 cotton swabs
What is the following answer to 2+2
Answer:
well the answer is 4 have a good day
Given m = -1/2 and the point (3, -6), which of the following is the point-slope form of the equation
Answer:
y + 6 = -1/2(x-3)
Step-by-step explanation:
let me know if you want an explanation
Select the correct statement about the function represented by the table. x y 1 34 2 41 3 48 4 55 5 62 A. It is a linear function because the difference y – x for each row is constant. B. It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values. C. It is an exponential function because the factor between each x- and y-value is constant. D. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values.
Answer:
sorry
Step-by-step explanation:
HELP STAT:
Graph the function F(x)= -sec (x/4) +3 on the interval [-2pi,6pi]
Answer:
Step-by-step explanation:
Please help !! I will give 20 points for correct answer !!!!
Ella wants to buy a home. The maximum loan she can get from the bank is $445,000
If Ella has $55,000 available to make a down payment, what is the highest valued home she can purchase?
Ella can buy a house worth $5 million
What is a Loan ?Loan is the amount of money borrowed from a bank or any other person , The amount has to be returned back with a Interest.
It is given that
The maximum loan Ella can get from the bank is $445,000
Ella has $55,000 available to make the down payment.
The highest value home that she can purchase is the sum of money she has and the maximum amount of money she can get from the bank.
It is given by
$445,000 + $55,000
$500,000
Therefore Ella can buy a house worth $5 million
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An electrical resistor is rated at 4500 ohms ± 3%. Express this tolerance in ohms and state the
actual range of resistance.
Answer:
Range = 4365-4635
Step-by-step explanation:
4500 * 3/100 = 135
4500 + 135 = 4635
4500 - 135 = 4365
Range = 4365-4635
The actual range of resistance is from 4365 ohms to 4635 ohms.
How to determine the tolerance in ohms and state the actual range of resistance.To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.
Tolerance in ohms = 3% of 4500 ohms
Tolerance in ohms = 0.03 * 4500
Tolerance in ohms = 135 ohms
The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:
Lower limit = Rated resistance - Tolerance
Lower limit = 4500 ohms - 135 ohms
Lower limit = 4365 ohms
Upper limit = Rated resistance + Tolerance
Upper limit = 4500 ohms + 135 ohms
Upper limit = 4635 ohms
So, the actual range of resistance is from 4365 ohms to 4635 ohms.
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Last year over 10,000 students took an entrance exam at a certain state university. Ivanna's score was at the 36th percentile. Aldo's score was at the 19th percentile.
Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Last year, over 10,000 students took an entrance exam at a certain state university.
Let the maximum score be 100.
Ivanna's score was at the 36th percentile, will be
⇒ [(10,000 – 36) / 10,000] x 100
⇒ 99.64
Aldo's score was at the 19th percentile, will be
⇒ [(10,000 – 19) / 10,000] x 100
⇒ 99.81
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Write a function rule for the table.
Days
1
2
3
4
Cost to Rent a Truck
29
47
65
83
Answer:
can you give upload the pictures
The assets (in billions of dollars) for a financial firm can be approximated by the function A(x)=318e^0.27x, where x=7 corresponds to the year 2007. Find the assets in each following years. A)2012 B) 2014 C) 2017
The value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively. A function assigns the values.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the assets (in billions of dollars) for a financial firm can be approximated by the function [tex]A(x)=318e^{0.27x}[/tex], where x=7 corresponds to the year 2007. Therefore, the assets value in the following years will be,
A.) 2012 - [tex]A(12)=318e^{0.27\times 12} = 8,119.72[/tex]
B.) 2014 - [tex]A(14)=318e^{0.27\times 14} = 13,933.5[/tex]
C.) 2012 - [tex]A(17)=318e^{0.27\times 17} = 31,321.23[/tex]
Hence, the value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively.
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Giving you the brainliest!
Answer:
The answer will be J
Step-by-step explanation:
Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.
Therefore the Answer Will Be J: 70,000 timed by 0.20.
Expert-Certifieder of Cousin.
There are 60 students studying Sciences (Biology, Chemistry or Physics). 7 students study Biology, Chemistry and Physics. 12 students study Biology and Chemistry. 15 students study Biology and Physics. 20 students study Chemistry and Physics. 35 students study Biology. 32 students study Physics. B Complete the Venn diagram. E P C There are 60 students studying Sciences ( Biology , Chemistry or Physics ) . 7 students study Biology , Chemistry and Physics . 12 students study Biology and Chemistry . 15 students study Biology and Physics . 20 students study Chemistry and Physics . 35 students study Biology . 32 students study Physics . B Complete the Venn diagram . E P C
Answer:
8 in the box.
Step-by-step explanation:
As, it is given that 35 students study Biology.
So, in Biology circle,
15+7+5+x=35
27+x=35
x=35-27
x=8
Which linear equation has a slope of 3 and a y-intercept of -2?
y = 3x + 2
y = 3x - 2
y = -2x + 3
y=-2x-3
Answer:
y = 3x - 2
Step-by-step explanation:
The number beside the x is the slope. The number at the end of the equation is the y-intercept.
All the answers are in this form:
y = mx + b
m is the slope.
b is the y-intercept.
With a 3 filled in for slope and -2 filled in for the y-intercept, you get:
y = 3x + -2
is the same as,
y = 3x - 2
Question 2
A) 800 cents
A laptop computer consumes about 40 watts of electricity per hour when operating. At $0.20 per kilowatt-hour, how much does.
laptop cost to operate for 10 hours?
B) 40 cents
200 cents
8 cents
19 OF 20 QUESTIONS REMAIN
Question 3
10 Point
10 Points
Answer: $80
Step-by-step explanation:
Given:
The laptop consumes 40 watts/hour
The operating cost is $0.20 per kilowatt - hour
So,
The cost for 1 hour of consumption = 40 * 0.20 = $8
The cost for 10 hours of consumption = $8 * 10 hours = $80
two variables x and y have corresponding values as shown in the table below. x=2,3,a and y=20,40,104 given that y varies directly as x power 2+1 find (a) value of k (b) value of a
The value of k is 4 and the value of a is 5
How to determine the value of k?The table of values is given as:
x=2,3,a
y=20,40,104
The variation is given as:
[tex]y\ \alpha\ x^2+1[/tex]
Express as an equation
y = k(x^2 + 1)
When x = 2, y = 20.
So, we have:
[tex]20 = k(2^2 + 1)[/tex]
Evaluate the sum
20 = 5k
Divide by 5
k = 4
Hence, the value of k is 4
How to determine the value of a?In (a), we have:
y = k(x^2 + 1)
Substitute 4 for k
y = 4(x^2 + 1)
When x = a, y = 104.
So, we have:
104 = 4(a^2 + 1)
Divide by 4
26 = a^2 + 1
Subtract 1 from both sides
a^2 = 25
Take the square root
a = 5
Hence, the value of a is 5
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The slope of the line below is 0.8. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side. Coordinates (-2,-3)
The equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope m = 0.8
The line passing through coordinates (-2,-3)
y = mx + c
y = 0.8x + c
Plug the point in the equation.
-3 = 0.8(-2) + c
c = -1.4
y = 0.8x - 1.4
Thus, the equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
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Which pair represents equivalent ratios?
A.2/3,95
B.5/8,15/21
C.3/12,6/18
D.4/10,12/30
Answer:
D
Step-by-step explanation:
We can test each pair making each ratio into its simplest form.
For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.
For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.
For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.
For D, 4/10=2/5, and 12/30=2/5. They are equivalent.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Let's see which ones are equivalent}\\\huge\textbf{to each other, shall we?}\\\\\\\huge\textbf{We will convert the given fractions to}\\\huge\textbf{decimals or make the fractions on the}\\\huge\textbf{right to easier to solve or comparing it}\\\huge\textbf{to the one on the left.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\mathsf{\dfrac{2}{3}, \dfrac{9}{15}}[/tex]
[tex]\mathsf{\dfrac{2}{3}}\\\\\mathsf{= 2\div3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{\dfrac{9}{15}}\\\\\mathsf{= \dfrac{9\div3}{15\div3}}\\\\\mathsf{= \dfrac{3}{5}}\\\\\\\\\mathsf{\dfrac{2}{3} \neq \dfrac{9}{15}}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\mathsf{\dfrac{5}{8}, \dfrac{15}{21}}[/tex]
[tex]\mathsf{\dfrac{5}{8}}\\\\\mathsf{= 5\div8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{\dfrac{15}{21}}\\\\\mathsf{= \dfrac{15\div3}{21\div3}}\\\\\mathsf{= \dfrac{5}{7}}\\\\\mathsf{\dfrac{5}{8}\neq \dfrac{15}{21}}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\mathsf{\dfrac{3}{12}.\dfrac{6}{18}}[/tex]
[tex]\mathsf{\dfrac{3}{12}}\\\\\mathsf{= 3 \div 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{\dfrac{6}{18}}\\\\\\\mathsf{= \dfrac{6\div3}{18\div3}}\\\\\\\mathsf{= \dfrac{2}{6}}\\\\\\\mathsf{= \dfrac{2\div2}{6\div2}}\\\\\\\mathsf{= \dfrac{1}{3}}\\\\\\\mathsf{\dfrac{3}{12}\neq \dfrac{6}{18}}[/tex]
[tex]\huge\textsf{Option D.}[/tex]
[tex]\mathsf{\dfrac{4}{10}, \dfrac{12}{30}}[/tex]
[tex]\mathsf{\dfrac{4}{10}}\\\\\mathsf{= 4\div10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{\dfrac{6}{18}}\\\\\mathsf{= \dfrac{12\div3}{30\div3}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4\div2}{10\div2}}\\\\\mathsf{= \dfrac{2}{5}}\\\\\mathsf{\dfrac{4}{10} = \dfrac{12}{20}}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. \dfrac{4}{10}, \dfrac{12}{30}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Select the correct answer.
A system of equations and its solution are given below.
System A
x + y = 8
4x - 6y = 2
Solution: (5,3)
Choose the correct option that explains what steps were followed to obtain the system of equations below.
System B
x + y = 8
10x = 50
Answer:
B will be the answer...
Step-by-step explanation:
The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.
To do that, we need to multiply the first equation by 5.
5 (-x − 2y = 7)
-5x − 10y = 35
Add to the second equation. Notice the x terms cancel out.
(-5x − 10y) + (5x − 6y) = 35 + (-3)
-16y = 32
Combining this new equation with the first equation from system A will get us system B.
-x − 2y = 7
-16y = 32
Answer:
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.
Step-by-step explanation:
exact answer
