Answer:
The average rate of change is 1.275
Step-by-step explanation:
The average rate of change of f(x) from x=a to x=b is given by:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The money Terry invested is modeled by the function [tex]f(x)=0.01(2)^x[/tex] where x represents number of days.
The average rate of change from day 2 to day 10 is given by:
[tex]\frac{f(10)-f(2)}{10-2}[/tex]
[tex]f(10)=0.01(2)^{10}=10.24[/tex]
[tex]f(2)=0.01(2)^{2}=0.04[/tex]
The average rate of change becomes:
[tex]\frac{10.24-0.04}{8}[/tex]
[tex]=\frac{10.2}{8}=1.275[/tex]
Answer:
The average rate of change is 1.275
Name the types of angles shown.
Check all that apply.
A. complementary angles
B. right angle
C. supplementary angles
D. straight angle
Answer:
C. supplementary angles
D. straight angle
The given angles ABD and DBC lies on a straight line. So they are straight angle.
We know that the sum of the straight angles is = 180 degrees. If the sum of two angles is 180 degrees, then they are also called supplementary angles.
It means the shown angles are also supplementary angles.
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Answer:
D and C
Step-by-step explanation:
The cost, y, of red apples can be represented by the equation y = 2x, where x
is the number of pounds of red apples.
The graph shows the cost of green apples.
Which type of apple costs more per pound?
Answer:
red apples
Step-by-step explanation:
cause for 1 pound, a red apple will cost 2 dollars, while for 1 pound, a green apple will cost less
Answer:
Red apples
Step-by-step explanation:
Since the cost of red apples is given by the equation y = 2x
where x = is number of pounds of red apples
Therefore clearly it can seen from the equation that the slope of this equation will be more steeper than the slope of the cost of the cost the green apples.
Now since the slope is more steep, therefore we can conclude that the red apples will cost more than the green apples for per pound of apples.
Thus, red apples will cost more per pound than green apples.
if a + b + C = -1 and x + y + z = -8, what is -8z -8x + 5a + 5c - 8y + 5b
Answer:
59
Step-by-step explanation:
a + b + C = -1
x + y + z = -8
We want 5a so multiply the first equation by 5
5(a + b + c) = -1*5
5a+5b+5c = -5
We want -8x so multiply the second equation by -8
-8(x + y + z) = -8*-8
-8x-8y-8x = 64
Add these equations together
5a+5b+5c = -5
-8x-8y-8x = 64
---------------------------
-8x -8y-8x+5a+5b+5c = 59
Rearrange the order
-8z -8x + 5a + 5c - 8y + 5b = 59
Answer:
59
Step-by-step explanation:
The first step here is to rewrite -8z -8x + 5a + 5c - 8y + 5b as
-8x - 8y - 8z + 5a + 5b + 5c.
This is the same as -8(x + y + z) + 5(a + b + c).
Subbing -8 for (x + y + z) and -1 for (a + b + c), we get -8(-8) - 5, or 59.
In triangle ABC, m∠ABC = (4x – 12)° and
m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he correct? Justify your answer.
Answer:
A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.
Step-by-step explanation:
x = 19,
Putting value of x to find m∠ABC and m∠ACB
m∠ABC = (4x – 12)°
m∠ABC = (4(19) – 12)°
m∠ABC = (76 – 12)°
m∠ABC = 64°
m∠ACB = (2(19) + 26)°
m∠ACB = (38 + 26)°
m∠ACB = 64°
now we know sum of angles of triangle is 180°. We can find the measure of third angle.
180 = 64+64 +x
x= 180 - 64 - 64
x = 52°
A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.
Sample Response: No, Yin is not correct. If
x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.
What did you include in your response? Check all that apply.
Yin is not correct.
The measure of the congruent base angles is 64°.
The measures of the angles in an equilateral triangle are 60°.
Which is the graph of the equation y-1=2/3(x-3)?
The graph of the given equation is the line that passes through (0,-1) and (3/2,0) and whose slope is m = 2/3 and this can be determined by using the slope-intercept form of the line.
Given :
Equation - [tex](y -1) = \dfrac{2}{3}(x-3)[/tex]
The following steps can be used to draw the graph of the given equation:
Step 1 - Write the given equation.
[tex](y -1) = \dfrac{2}{3}(x-3)[/tex]
Step 2 - Simplify the above equation.
[tex]y = \dfrac{2}{3}x - 2 + 1[/tex]
[tex]y = \dfrac{2}{3}x - 1[/tex]
Step 3 - Draw the graph of (y = x).
Step 4 - Find the y-intercept and the slope of the above equation.
c = -1
[tex]m = \dfrac{2}{3}[/tex]
Step 5 - So, the graph of the given equation is the line that passes through (0,-1) and (3/2,0) and whose slope is m = 2/3.
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The graph of the equation is a line that passes through the origin (0, 0) and has a slope of 2/3.
Explanation:The given equation is y - 1 = ⅓(x - 3). To graph this equation, we can start by rearranging it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y by adding 1 to both sides of the equation:
y = ⅓(x - 3) + 1
Now, simplify the expression on the right side:
y = ⅓x - 1 + 1
y = ⅓x
So, the equation y - 1 = ⅓(x - 3) represents a line with a slope of ⅓ and a y-intercept of 0. To graph this line, we can plot the y-intercept at (0, 0) and use the slope to draw the line.
The graph of this equation is a line that passes through the origin (0, 0) and has a slope of ⅓. Any point on this line can be represented as (x, ⅓x).
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f(x)=8x^2-2x+3
g(x)=12x^2+4x-3
What is h(x)=f(x)-g(x)?
A) h(x)=20x^2+2x
B) h(x)=-4x^2-6x
C) h(x)=-4x^2-6x+6
D) h(x)=-4x^2+2x
Answer:
-4x^2-6x+6
Step-by-step explanation:
We are asked to subtract g from f.
So the problem is:
[8x^2-2x+3]-[12x^2+4x-3]
So I'm going to distribute and write without [].
8x^2-2x+3-12x^2-4x+3
Now I'm going to pair up any like terms:
8x^2-12x^2-2x-4x+3+3
Simplifying:
-4x^2-6x+6
Answer: The correct option is
(C) [tex]h(x)=-4x^2-6x+6.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=8x^2-2x+3,~~~~~g(x)=12x^2+4x-3.[/tex]
We are to find the value of h(x) if h(x) = f(x) - g(x).
To find the value of h(x), we must subtract the expression of g(x) from the expression of f(x).
The value of h(x) can be calculated as follows :
[tex]h(x)\\\\=f(x)-g(x)\\\\=(8x^2-2x+3)-(12x^2+4x-3)\\\\=8x^2-2x+3-12x^2-4x+3\\\\=-4x^2-6x+6.[/tex]
Thus, the required value of h(x) is [tex]-4x^2-6x+6.[/tex]
Option (C) is CORRECT.
Solve for x: [.02(x-2)]=1
Answer:
x=1.04 i bet u thats right no joke hope i helped ;)
Step-by-step explanation:
What’s 18/20 simplified
Find the GCD (or HCF) of numerator and denominator
GCD of 18 and 20 is 2
Divide both the numerator and denominator by the GCD
18 ÷ 2
-----------
20 ÷ 2
Reduced fraction:
9
----
10
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{What's }\huge\dfrac{18}{20}\huge\text{ simplified?}[/tex]
[tex]\huge\text{Both terms have the GCF}[/tex] [tex]\huge\text{(Greatest Common Factor) of 2}[/tex]
[tex]\huge\text{So, divide both numbers by 2.}[/tex]
[tex]\huge\dfrac{18\div2}{20\div2}[/tex]
[tex]\huge\text{18}\huge\div\huge\text{2 = 9}[/tex]
[tex]\huge\text{9 is the numerator (top \#)}[/tex]
[tex]\huge\text{20}\huge\div\huge\text{2 = 10}[/tex] [tex]\huge\text{10 is the denominator (bottom \#)}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: }\huge\dfrac{9}{10}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
The blue segment below is a radius of O. What is the length of the diameter of the circle?
Answer:
B, 14.6 units.
Step-by-step explanation:
The answer is be because:
the diameter = radius times 2
radius= 7.3
diameter=7.3*2
=14.6
Therefore the answer is, B
Answer: B. 14.6 units
Step-by-step explanation: The diameter of a circle is two times the length of the radius. So multiply the radius by 2.
7.3 x 2 = 14.6
The diameter of the circle is 14.6 units.
Sarah received scores of 85, 92 and 78 on her first three exams of the grading
period. What is the lowest score Sarah can earn on the next exam for the exam
average to be at least a 87 for the grading period.
Answer:
92
Step-by-step explanation:
The total Score is 85 + 92 + 79 + x = 4 * 87
The total Score needed is 4 * 87 = 348
So to get that score we need to add the other scores up
256 + x
which equals the total of the 4 tests.
256 + x = 348
Subtract 256 from both sides.
256 - 256 + x = 348 - 256
x = 92 Pretty high, but doable.
How to convert 3.5 gallons into quarts. There are 4 quarts in 1 gallon.
Answer:
look at the picture attached
Which of these triangle appears not to be congruent to any others shown here? Check all that apply.
Answer: the actual answer is triangle b and triangle f
Triangle B and triangle F are not congruent with any other given triangles
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to find which of these triangle appears not to be congruent to any others shown ?Clearly we can see that triangle A and triangle E are congruent since they have the same shape and sizeAlso triangle C and triangle C are congruentSo we are left with triangle B and triangle F.
The size and shapes of these triangles does not matches with any other triangles.
So triangle B and triangle F are not congruent with any other given triangles.
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The appropriate translation of the phrase 11 more than 20 percent of a number is:
0.2n+11
True or false?
Answer: True
Step-by-step explanation: 20% can also be written as 0.2 and if you know the number then you would multiply it by 0.2, then if you needed to add 11 that is exactly how you would write that equation
If sinx= sqrt(3)/2, and 90° < x < 180°, what is cos(x/2)?
Answer:
cos 60° = 1/2
Step-by-step explanation:
* Lets explain how to solve the question
- If angle Ф lies in the first quadrant then sin Ф , cos Ф and tan Ф
are positive values
- The equivalent angle of angle Ф in the second quadrant is 180° - Ф
and sin Ф is positive but cos Ф and tan Ф are negative
- The equivalent angle of angle Ф in the third quadrant is 180° + Ф
and tan Ф is positive but cos Ф and sin Ф are negative
- The equivalent angle of angle Ф in the fourth quadrant is 360° - Ф
and cos Ф is positive but sin Ф and tan Ф are negative
* Lets solve the problem
∵ sin x = √3/2
∵ 90° < x < 180°
∴ ∠ x lies in the second quadrant
∴ m∠ x = 180° - Ф
- Let sin Ф = √3/2
∴ Ф = sin^-1 (√3/2)
∴ Ф = 60°
∵ x = 180° - Ф
∴ x = 180° - 60°
∴ x = 120°
- To find cos(x/2) divide 120° by 2
∵ cos (120°/2) = cos (60°)
∴ cos 60° = 1/2
The function f(x) = 3,267(1 + 0.02)* represents the amount of money in a savings account where x represents time in years. What does the 3,267 represent?
A.The amount of money in the savings account after one year
B.The amount of money added to the savings account each year
C .The initial amount of money placed in the savings account
D.The growth rate
Answer:
C .The initial amount of money placed in the savings account
Step-by-step explanation:
f(x) = 3,267(1 + 0.02)^x
This is in the form
y = a b^x
where a is the initial amount
b is the growth rate
x is the time
3267 is the initial amount
1.02 is the growth rate, so it grows by .02 or 2 percent
and x is the time
The function f(x) = 3,267(1 + 0.02)* represents the amount of money in a savings account where x represents time in years. What does the 3,267 represent?
Answer:
C .The initial amount of money placed in the savings account
I need to simplify for the question
Answer:
[tex]\tt x^2+3xy+4y^2[/tex]
Step-by-step explanation:
[tex]\tt(x-2y)^2+7xy\\\\=x^2-4xy+4y^2+7xy\\\\=x^2+3xy+4y^2[/tex]
Answer:
[tex] x^2 + 3xy + 4y^2 [/tex]
Step-by-step explanation:
[tex] (x - 2y)^2 + 7xy = [/tex]
[tex] = (x - 2y)(x - 2y) + 7xy [/tex]
[tex] = x^2 -2xy - 2xy + 4y^2 + 7xy [/tex]
[tex] = x^2 + 3xy + 4y^2 [/tex]
what is a reasonable estimate for the problem? 3 3/4 x -2/5
Answer:
You can not break that down any further if x does not equal anything and the equation is not equal to anything.
Step-by-step explanation:
What is the following simplified product? Assume x>/= 0
Answer: second option.
Step-by-step explanation:
We know that:
[tex]\sqrt[n]{a^n}=a[/tex]
[tex](a^m)(a^n)=a^{(m+n)[/tex]
Then we can simplify the radicals:
[tex]2\sqrt{8x^3}(3\sqrt{10x^4}-x\sqrt{5x^2})=(2\sqrt{2^2*2*x^2*x})(3\sqrt{10x^4}-x\sqrt{5x^2})=\\\\=2*2*x\sqrt{2x}=3x^2\sqrt{10}-x*x\sqrt{5}\\\\=4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})[/tex]
Since:
[tex](a\sqrt[n]{x})*(b\sqrt[n]{y})=ab\sqrt[n]{xy}[/tex]
We can apply Distributive property:
[tex]4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})\\\\12x^3\sqrt{20x}-4x^3\sqrt{10x}[/tex]
Simplifying:
[tex]12x^3*2\sqrt{5x}-4x^3\sqrt{10x}\\\\24x^3\sqrt{5x}-4x^3\sqrt{10x}[/tex]
Answer:
B
Step-by-step explanation:
edg2021
Try this trick out on a friend. Tell your friend to place a dime in one hand and a penny in the other hand. Explain that you can determine which hand is holding the penny.
Here’s how to do it:
a. Ask the friend to multiply the value of the coin in his or her RIGHT hand by 4, 6, or 8 and then to multiply the value of the coin in his or her LEFT hand by 3, 5, or 7.
b. Now ask the friend to add the two results together and tell you the total.
c. If the total is EVEN, the penny is in the RIGHT hand. If the total is ODD, the penny is in the left hand.
The math trick described allows you to figure out which hand a friend is holding a penny in by having them multiply the value of the coins in their hands by specific numbers, adding the results, and determining whether the total is even or odd.
Explanation:The subject at hand pertains to a mathematical trick used to determine in which writing a friend is holding a penny. To execute the scheme, follow the procedure:
Ask your friend to multiply the coin's value in their right hand by 4, 6, or 8. Then, instruct them to bear the coin's weight in their left hand by 3, 5, or 7.Next, ask them to add the two results and the total.the penny is in the friend's right hand if the total is even. If the sum is odd, the penny is in their left hand. Here's why: When a dime (10 cents) is multiplied by any integer, the result will be an even number. But a penny (1 cent) multiplied by any number will keep its parity (odd or even). So, if the total sum is weird, the left-hand number, odd, must have been contributed by the penny.Learn more about math tricks here:
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A. y-2=2(x-3)
B. y-3=2(x-2)
C. y-10=2(x-1)
D. y-1=2(x-10)
Answer:
C. y-10=2(x-1)
Step-by-step explanation:
We have two points on the line, we can find the slope
m = (y2-y1)/(x2-x1)
= (10-2)/(1--3)
= 8/(1+3)
=8/4
=2
The slope is 2
We can use point slope form using the point (1,10)
y-y1 = m(x-x1)
y-10 = 2(x-1)
Answer:
C. y - 10 = 2(x - 1)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, 2) and (1, 10). Substitute:
[tex]m=\dfrac{10-2}{1-(-3)}=\dfrac{8}{4}=2[/tex]
Using the point (-3, 2):
[tex]y-2=2(x-(-3))\\\\y-2=2(x+3)[/tex]
Using the point (1, 10):
[tex]y-10=2(x-1)[/tex]
a researcher wishes to estimate the proportion of adults who have high speed internet access. what size sample should be obtained if she wishes the estimate to be within 0.04 with 90% confidence if she uses a previous estimate of 0.54
Answer:
421
Step-by-step explanation:
Margin of error = E = 0.04
Confidence Level = 90%
z value associated with this confidence level = z = 1.645
Previous estimate of population proportion = p = 0.54
q = 1 - p = 1 - 0.54 = 0.46
The formula of Margin of Error for population proportion is:
[tex]E=z\sqrt{\frac{pq}{n}}[/tex]
Here, n is the sample size.
Re-arranging the equation for n and using the values we get:
[tex]n=(\frac{z}{E})^{2} \times pq\\\\ n = (\frac{1.645}{0.04})^{2} \times 0.54 \times 0.46\\\\ n = 421[/tex]
Thus the minimum sample size required to estimate the proportion of adults who have high speed internet access is 421
Cassie is travelling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 of gas and paid $19.08. and, at her third stop, she put in 6.6 gallons and paid $20.39, the second part
if the gas station that cassie stopped, at last, lowers their price 6%, what will be their new price per gallon?
The last gas station she stopped at she got 6.6 gallons and paid $20.39
If they lower the price by 6%, that means she would pay 94% of the original amount ( 100% - 6% = 94%)
Multiply the amount she paid by 94%:
20.39 x 0.94 = 19.17
She would pay $19.17 total.
Now divide that by the number of gallons bought:
19.17 / 6.6 = $2.90 per gallon ( Rounded to the nearest cent).
which number has the lesser value 5.13 or5.099
Answer: 5.099
Step-by-step explanation:
technically, 5.099 is 5.10
10 is bigger than 13 so
5.13 > 5.10
/5×+4/ =/×+9/ solve for x
Answer:
[tex]\large\boxed{x=\dfrac{5}{4}\ \vee\ x=-\dfrac{13}{6}}[/tex]
Step-by-step explanation:
[tex]|5x+4|=|x+9|\iff5x+4=x+9\ or\ 5x+4=-(x+9)\\\\5x+4=x+9\qquad\text{subtract 4 from both sides}\\5x=x+5\qquad\text{subtract x from both sides}\\4x=5\qquad\text{divide both sides by 4}\\x=\dfrac{5}{4}\\\\5x+4=-(x+9)\\5x+4=-x-9\qquad\text{subtract 4 from both sides}\\5x=-x-13\qquad\text{add x to both sides}\\6x=-13\qquad\text{divide both sides by 6}\\x=-\dfrac{13}{6}[/tex]
Chicago to Memphis is 527.4 miles Memphis to New Orleans is 393.8. How far is Chicago to new movie orleans
The total distance from Chicago to New Orleans is calculated by adding the distances from Chicago to Memphis and then from Memphis to New Orleans, which totals to 921.2 miles.
Explanation:In order to calculate the total distance from Chicago to New Orleans, we simply need to add the given distances. The distance from Chicago to Memphis is 527.4 miles and from Memphis to New Orleans is 393.8 miles. Hence, the total distance from Chicago to New Orleans would be 527.4 miles + 393.8 miles = 921.2 miles. So, the total travel distance from Chicago to New Orleans is 921.2 miles.
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What are the solutions of the equation 4x2 + 3x = 24 – x? –3, 2, or 4 –3 or 2 –2, 3, or 4 –2 or 3
Answer:
x = -3 or x = 2Step-by-step explanation:
[tex]4x^2+3x=24-x\qquad\text{subtract 24 from both sides}\\\\4x^2+3x-24=-x\qquad\text{add}\ x\ \text{to both sides}\\\\4x^2+4x-24=0\qquad\text{divide both sides by 4}\\\\x^2+x-6=0\\\\x^2+3x-2x-6=0\\\\x(x+3)-2(x+3)=0\\\\(x+3)(x-2)=0\iff x+3=0\ \vee\ x-2=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2[/tex]
The given equation, 4·x² + 3·x = 24 - x, can be simplified and factorized
to give the solution as; -3, 2
Which methods are use to find the solution of the equation?The solution to the given equation, 4·x² + 3·x = 24 - x, is the point of
intersection of the parabola, 4·x² + 3·x, and the line, 24 - x
The solution is therefore, found as follows;
4·x² + 3·x = 24 - x
4·x² + 3·x - (24 - x) = 0
4·x² + 4·x - 24 = 0
Dividing by 4, gives;
4·(x² + x - 6) = 0
x² + x - 6 = 0 ÷ 4 = 0
x² + x - 6 = 0Factorizing, the above quadratic equation, we have;
(x + 3) × (x - 2) = 0
x = -3, or x = 2The solution of the equation is therefore;
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How do u do this please help!!
Answer:
C. 3 gal. 3 qt. 1 pt.Step-by-step explanation:
1 gallon = 4 quarts
5 gallons 2 quarts 1 pint = 4 gallons 6 quarts 1 pint
(5 gallons 2 quarts 1 pint) - (1 gallon 3 quarts)
= (4 gallons 6 quarts 1 pint) - (1 gallon 3 quarts)
= 3 gallons 3 quarts 1 pint
Which is the completely factored form of 4x3 + 10x2 – 6x?
Answer:
2x(x + 3)(2x - 1)
Step-by-step explanation:
Given
4x³ + 10x² - 6x ( factor out 2x from each term )
= 2x(2x² + 5x - 3)
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 5
The factors are + 6 and - 1
Use these factors to split the x- term
2x² + 6x - x - 3 ( factor the first/second and third/fourth terms )
2x(x + 3) - 1(x + 3) ← factor out (x + 3) from each term
(x + 3)(2x - 1), hence
2x² + 5x - 3 = (x + 3)(2x - 1)
Hence
4x³ + 10x² - 6x = 2x(x + 3)(2x - 1)
Answer:
B
Step-by-step explanation:
What is the slope of the line containing (6, -7) and (5, -9)?
A) 1
B) -2.
C) 2
D) 16
Answer: C
Step-by-step explanation:
y2-y1/x2-x1
-9+7/5-6 = 2
Which choice below is a boxplot for the following distribution?
58, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 14
A. Boxplot A
B. Boxplot B
C. Boxplot C
D. Boxplot D
E. Boxplot E
Answer:
Boxplot A
Step-by-step explanation:
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
58, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 14.
We will write in ascending order:
14 ,22 ,24 ,26 ,28,30 ,32 ,34, 36 ,38, 40, 42 ,44 ,46 ,48,50,58.
Since there are 17 terms in the above data.
So, Median would be 36.
As box plot shows the middle point of the data i.e. median.
In box plot A it shows the correct median at the middle i.e. 50% of the scores.
Hence, option 'A' is correct.