Find two positive real numbers who's product is a maximum and whose sum is 156.

Answers

Answer 1

Let the two positive real numbers be x and y.
The sum of two numbers is 156, so we can write:

x+ y = 156
or
y = 156 - x

The product of two numbers = xy
Using the value of y in previous equation we can write:

Product = x(156 - x) = - x² + 156x

The above equation is a quadratic equation and results in a parabola. The maximum value of parabola with negative coefficient of x² lies at its vertex.

The x component of vertex will be = [tex] \frac{-b}{2a} [/tex]
Here b is the coefficient of x term, and a is the coefficient of x² term.
So,
a = -1
b = 156
Using the values in the formula we get the x component of vertex x = [tex] \frac{-156}{-2}=78 [/tex]

So x = 78
and

y = 156 - x = 156 - 78 = 78

Thus, the two numbers whose sum is 156 and which result in maximum product are 78, 78

Answer 2

Final answer:

To maximize the product of two numbers with a fixed sum of 156, we set up an equation for the product, differentiate, and find that the maximum product is obtained when both numbers are 78.

Explanation:

To find two positive real numbers whose product is a maximum and whose sum is 156, we need to use the concept of optimization in calculus. This involves taking the derivative of the function representing the product of the two numbers and setting it equal to zero to find the critical points. Since the sum of the numbers is fixed at 156, we can express one number in terms of the other, for example, x and 156 - x. The product of these two numbers is x(156 - x). To find the maximum product, we differentiate this function with respect to x:

[tex]\frac{d}{dx} [x(156 - x)] = 156 - 2x[/tex]

Setting this derivative equal to zero gives us 156 - 2x = 0, solving for x we find-

x = 78.

This gives us the two numbers as 78 and 78, because the sum must be 156 and the other number would be 156 - 78. To confirm that this gives a maximum, we would test the second derivative or use the first derivative test. However, by symmetry, when the sum of two numbers is fixed, their product is maximized when the two numbers are equal. In this case, both numbers are 78.

Related Questions

A right triangle has legs that are 15 feet and 25 feet long.

What is the length of the hypotenuse?

Answers

15^2 + 25^2 = X62

225 + 625 = x^2

850 = x^2

x = 5sqrt(34)

if you need it as a decimal = 29.1547

Answer: The length of the hypotenuse is 5√34 units.

Step-by-step explanation: Given that a right-angled triangle has legs of length 15 ft and 25 ft.

We are to find the length of the hypotenuse.

As shown in the attached figure, AB and BC are the legs of the right-angled triangle ABC. AC is the hypotenuse of the triangle.

Also, AB = 15 ft and BC = 25 ft.

From Pythagoras theorem, we have

[tex]AC^2=AB^2+BC^2\\\\\Rightarrow AC^2=(15)^2+(25)^2\\\\\Rightarrow AC^2=225+625\\\\\Rightarrow AC^2=850\\\\\Rightarrow AC=\sqrt{850}\\\\\Rightarrow AC=5\sqrt{34}.[/tex]

Thus, the length of the hypotenuse is 5√34 units.

solve the right triangle shown in the figure BC = 1.6in< A=48.8 C =90

Answers

Drawing a diagram to represent the information you've given, the only angle we are missing is B. We can find that by subtracting the two we're given from 180:
180 - 90 - 48.8 = 41.2
m∠B = 41.2°.
We can use the angles and the one side we're given to find the remaining sides. Since we do not know the length of the hypotenuse, AB, we cannot use sine or cosine. We must use tangent (the ratio for tangent is opposite/adjacent):
[tex]\tan 41.2 = \frac{x}{1.6}[/tex]
Multiply both sides by 1.6:
[tex]1.6 \tan 41.2 = x \\ 3.67 = x[/tex]
This is the length of side AC, which is opposite to angle B.
To find the length of AB we can use the Pythagorean Theorem:
[tex](1.6)^2+(3.67)^2=c^2 \\ 2.56+13.4689=c^2 \\ 16.0289=c^2 \\ \sqrt{16.0289} = \sqrt{c^2} \\ 4=c[/tex]
The length of side AC, the hypotenuse, is 4 inches.

I think your answer is A

Jacqueline's piggy bank contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?

Answers

20 quarters and 2 dimes!! (Take a look at my question if possible!?)

Select the problems which show the correct answers. (1.12 x 105) (6.06 x 105) Answer: 6.79 x 1010 (2 x 101)(3.0 x 101) Answer: 6.0 x 101 (2.775 x 10−4) (4.775 x 104) Answer: 1.325 x 100 5 8.14 x 102 Answer: 6.14 x 10−3

Answers

Answer:

[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]

[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]

Step-by-step explanation:

To solve this problem we must solve all 4 operations.

For the first one we have:

[tex](1.12 x 10^5) (6.06 x 10^5)[/tex]

When we have multiplication of powers of equal base (10) the same base is placed and the exponents are added

So:

[tex]1.12 * 6.06 x 10^{5+5} = 6.787 x 10^{10}\\[/tex]

Therefore the answer to this question is correct.

For the second question we have:

[tex](2 x 10^1) (3.0 x 10^1)[/tex]

Then following the same procedure as in the previous question we have:

[tex]2 * 3.0 x 10 ^ {1 + 1} = 6 x 10 ^ 2\\[/tex]

Then the answer shown in the statement is not correct, because 10 must be squared, product of the sum of its exponents (1 + 1)

For the third question we have:

[tex](2,775 x 10^{-4}) (4,775 x 10^4)\\2.775 * 4.775 x 10 ^{(- 4) +4} = 13.251 x10 ^ 0\\[/tex]

Then it is verified that the answer for this operation is no correct

[tex]13.25\neq 1.325[/tex]

Finally, for the fourth question we have:

[tex]\frac{5}{(8.14 x 10 ^ 2)}\\[/tex]

This we can write it as:

[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2}\\[/tex]

In division of powers of equal base (10 in this case) the same base is placed and the exponents are subtracted:

[tex]\frac{0.5}{8.14 x 10 ^ {1-2}} = 0.0614 x 10 ^ {-1} = 6.14 * 10 ^ {-3}\\[/tex]

Finally, the problems that show correct answers are:

[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]

[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]

The sum of the roots of the equation 1/2x^2-5/4x-3=0

Answers

The equation is 1/2x² -5/4x -3=0
Multiplying all the terms by 4 to remove fractions
2x²-5x-12=0
we can use factorization method;
product = -24
sum = -5
numbers= -8 and 3
Threfore; 2x²-8x+3x-12 =0
2x(x-4) +3(x-4) =0
= (2x+3)(x-4) =0
thus 2x +3= 0 or x-4 =0
therefore; x = -3/2 and x =4
Thus the sum of the roots will be (-3/2 +4) = 2.5

Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 Which polynomial represents the standard form of the original polynomial?
a.x^3/2 – 2x^5 + x/4 + 1
b.–2x^5 + x^3/2 + x/4 + 1
c. –2x^5 + x/4 + x^3/2 + 1
d. 1 – 2x^5 + x^3/2 + x/4

Answers

Answer:

b. –2x^5 + x^3/2 + x/4 + 1

Step-by-step explanation:

In the given expression, the degrees of the terms, in the order given, are ...

1, 5, 3, 0

When the terms are properly arranged in standard form, they will be ...

5, 3, 1, 0 . . . . descending order

The standard form of this expression is ...

-2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B

Answer: b.–2x^5 + x^3/2 + x/4 + 1

Step-by-step explanation:

can someone answer this?

Answers

For x.
All the right triangles are similar, so
.. hypotenuse/(short side) = x/6 = 6/(x -9)
Multiplying by the product of denominators gives
.. x(x -9) = 36
Two factors of 36 that differ by 9 are 12 and 3, so we have
.. x = 12

For y, we can use the Pythagorean theorem.
y^2 +6^2 = 12^2
y^2 = 144 -36 = 108
y = √108 = √(36*3)
y = 6√3

30 POINTS!!! WILL MARK BRAINLIEST! : )

1. Name the property the equation illustrates.

8 x 1/8 = 1

A) Multiplication Property of –1

B) Inverse Property of Addition

C) Inverse Property of Multiplication

D) Identity Property of Division

2. Name the property the equation illustrates.

–5 + (8 + 10) = (–5 + 8) + 10

A) Multiplication Property of –1

B) Inverse Property of Addition

C) Inverse Property of Multiplication

D) Identity Property of Division

3. Name the property the equation illustrates.

-4 x -1/4 = 1

A) Multiplication Property of –1

B) Inverse Property of Addition

C) Inverse Property of Multiplication

D) Identity Property of Division

4. Name the property the equation illustrates.

(ab)3 = a(b3)

A) Multiplication Property of –1

B) Inverse Property of Addition

C) Inverse Property of Multiplication

D) Identity Property of Division

Answers

1. C) Inverse Property of Multiplication
2. B) Inverse Property of Addition
3. C) Inverse Property of Multiplication
4. Your answer is not listed (The answer is Associative Property of Multiplication)

Answer:

1. C) Inverse Property of Multiplication

2. None of these. The answer is Associative property of Addition

3. C) Inverse Property of Multiplication

4. None of these. The answer is Associative property of Multiplication

Step-by-step explanation:

Given a number a , the inverse property of multiplication states that

a * 1/a = 1

and 1/a is called the multiplicative inverse of a.

So 8 * 1/8 = 1 features the inverse property of multiplication where a = 8.

Given three numbers a,b,c , the associative property of addition states that a + (b + c) = (a + b) + c

In this case, a = -5, b = 8 and c = 10

-4 x -1/4 = 1 features the inverse property of multiplication where a = -4.

Given three numbers a,b,c , the associative property of multiplication states that (a * b) * c = a * (b * c)

In this case, a = a, b = b and c = 3

Write an expression for the following situation and solve it. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students.

Answers

Hi!
1/4 of 20 pencils are 5 pencils.
Since he gave away 4 pencils,
Total = 5 + 4 = 9
Mr. Simms use and give away total 9 pencils.

Factor the quadratic equations W^2-W-12

Answers

Given
W^2-W-12 = w^2+bW+c
b=-1,
c=-12
We look for m, n so that m+n=b=-1, m*n=c=-12, where m,n are integer factors of -12.

Now enumerate all possibilities for m*n=12
m n m*n m+n
1 -12 -12 -11
2 -6 -12 -4
3 -4 -12 -1 ....... so m*n=-12, m+n=-1
The factorization is then
W^2-W-12=(W+3)(W-4)

For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}

Answers

we have a geometric sequence----------- > {-4, 12, -36, ...}

the formula is a(r)^(n-1)

a------------- >a is the first term------------ > -4
r--------------- > is the common ratio------- > 12/(-4)=(-36/12)=-3
n--------------- > is the number of terms

The fifth term is -4[(-3)^(5-1)]=-4[(81]=-324

the answer is -324

First you need to identify the common ratio:

r = [tex] t_{n+1} / t_{n} [/tex]

where r is the common ratio
[tex] t_{n} [/tex] is any term in the sequence
[tex] t_{n} [/tex] is the term preceding [tex] t_{n} [/tex]

In your case the common ratio will be
12/-4 = -3
The recursive formula of a geometric sequence is:

An = [tex] A_{n-1} [/tex] x r
Where : An is the nth term
[tex] A_{n-1} [/tex] is the erm preceding the nth term
r = common ratio

For this case it is:
An = [tex] A_{n-1} [/tex] x -3

Now let us use this formula to find the 5th term:

[tex] A_{5} [/tex] = [tex] A_{5-1}[/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4}[/tex] x -3

Since you do not know the 4th term, you can use that by using our reclusive formula:

[tex] A_{4} [/tex] = [tex] A_{4-1} [/tex] x -3
[tex] A_{4} [/tex] = [tex] A_{3} [/tex] x -3
[tex] A_{4} [/tex] = [tex] -36 [/tex] x -3
[tex] A_{4} [/tex] = [tex] 108 [/tex]

Now that you know your fourth term, you can use the same formula:

[tex] A_{5} [/tex] = [tex] A_{5-1} [/tex] x -3
[tex] A_{5} [/tex] = [tex] A_{4} [/tex] x -3
[tex] A_{5} [/tex] = [tex] 108 [/tex] x -3
[tex] A_{5} [/tex] = [tex] -324 [/tex]

7. What is the angle measure that is vertical to an 83° angle?

Answers

vertical angles are the same so it would be 83 degrees

Write and solve an equation to find the value of each variable

Answers

check the picture below.

as you can see in the picture, the "near arc" is x°, and the "far arc", is the leftover from subtracting the arc of 120° and x°, therefore then

[tex]\bf 44=\cfrac{\stackrel{far~arc}{(360-x-120)~~-~~\stackrel{near~arc}{x}}}{2}\implies 88=240-2x \\\\\\ 2x=152\implies x=\cfrac{152}{2}\implies x=76[/tex]

Eric borrowed $1,800 for 9 months at 13.5% simple interest under an
add-on plan. What was his monthly payment?
a. $15.63
b. $220.25
c. $187.50
d. $1,982.25

ANSWER IS NOT C

Answers

The only sensible answer (from a test-taking point of view) is selection B.

You know the monthly repayment of $1800 over 9 months will be at least $200 per month. Since the interest is about 10% of the loan amount (3/4 of 13.5%), the amount added on for interest will be on the order of $20 per month.

If you work out the math, you find the payment is exactly $220.25 (selection B). You don't need to do that to make a sensible choice.

_____
Payment = ($1800 + 9/12*0.135*1800)/9 = $220.25.

helpppppppppppppppppppppp

Answers

Correct Answer:
Second Option

Solution:
A geometric series converges when the value of its common ratio is between -1 and 1. Else the series will diverge. So we find the common ratio for each of the given options, the series with common ratio between -1 and 1 will be converging series.

For first option, common ratio = 1/3 divided by 1/9 = 3
Common ratio is not between -1 and 1, so this series is diverging.

For second option, common ratio = 1/2 divided by 1 = 1/2
Since the common ratio is between -1 and 1, this series is converging.

For third option, common ratio = -4
This series is also diverging.

For Fourth option, common ratio = 2
This series is also diverging.

What is 4 equal parts

Answers

A square has 4 equal parts

It means that you have four parts of something, and they are all identical in every aspect that matters.

Suppose there are 7 dimes, and someone gives you 4 of them. Each dime they gave you represents a part of the whole amount of dimes, and each of those dimes is equal to the others in size, weight, color, value. They are 4 equal parts of the whole amount of dimes. (The four equal parts don't have to add up to the whole--except when we say the whole is divided into 4 equal parts.)

Usually, we talk about equal parts when we are dividing something into shares. If we have a pizza that four people want to share in such a way that each person gets as much as possible without any fighting, it would usually be divided into four equal parts. Each share would be the same as the others in every aspect that matters. Each of those parts would be 1/4 of the pizza. The "4" in that fraction tells you the number of equal parts. The "1" tells you the number of those parts any one person gets in this scenario.

_____
Each of the words in that phrase "4 equal parts" has its usual dictionary meaning.

Which answer represents the series in sigma notation?

Answers

[tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.

What is sigma notation?

The symbol Σ (sigma) is generally used to denote a sum of multiple terms. This symbol is generally accompanied by an index that varies to encompass all terms that must be considered in the sum.

Given is a series (-7 + (-2) + 3 + 8 + 13), we need to define it in sigma notation,

Therefore,

For j = 1 up to j = 5

j = 1

(5j - 12) = (5(1) - 12) = 5 - 12 = - 7

j = 2

(5j - 12) = (5(2) - 12) = 10 - 12 = - 2

j = 3

(5j - 12) = (5(3) - 12) = 15 - 12 = 3

j = 4

(5j - 12) = (5(4) - 12) = 20 - 12 = 8

j = 5

(5j - 12) = (5(5) - 12) = 25 - 12 = 13

This gives us the given series,

(-7 + (-2) + 3 + 8 + 13)

Hence, [tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.

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Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. How many more jumps (j) do they need to match the record? Show your work!

Answers

For this case what we must do first is to obtain the total amount that both have accumulated.
We have then:
Lindsay has gotten 14 jumps in a row and Lorraine has gotten 13:
14 + 13 = 27
Then, we must find the remaining amount:
j = 48-27
j = 21
Answer:
they need 21 more jumps to match the record

find the inverse of y=x2-10x

Answers

this is pretty hard but here is your answer

y = x^2 - 10x + 25 - 25

y = (x-5)^2 - 25

y+25 = (x-5)^2

x-5 = +/-sqrt(y+25)

And you get TWO inverses:

x = 5 + sqrt(y+25), for x>=5

x = 5 - sqrt(y+25), for x<=5

Answer:

[tex]y=5\pm \sqrt{(25+x)}[/tex]

Step-by-step explanation:

We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].

We know that to find inverse, we interchange x and y values and then solve for y.

After interchanging x and y values, we will get:

[tex]x=y^2-10y[/tex]

Switch sides:

[tex]y^2-10y=x[/tex]

[tex]y^2-10y-x=x-x[/tex]

[tex]y^2-10y-x=0[/tex]

Now, we will use quadratic formula to solve for y.

[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]

[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]

[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]

[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]

[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]

[tex]y=5\pm \sqrt{(25+x)}[/tex]

Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].

What is the total number of rectangles and triangles used for the net of this solid?

a. 3
b. 4
c. 5
d. 6

Answers

Final answer:

The total number of rectangles and triangles used for the net of this solid is 4.

Explanation:

To find the total number of rectangles and triangles used for the net of a solid, we need to examine the shape of the solid. If the given solid has 4 faces, like a regular tetrahedron or a pyramid, then it will have 3 triangles and 1 rectangle. Hence, the total number of rectangles and triangles used for the net of this solid is 4, so the answer is option b.

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how would I solve for x?

Answers

The Answer is Height: hb = 12.923

Acute scalene triangle.Sides: a = 15 b = 13 c = 14

Area: T = 84
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 67.38° = 67°22'49″ = 1.176 rad
Angle ∠ B = β = 53.13° = 53°7'48″ = 0.927 rad
Angle ∠ C = γ = 59.49° = 59°29'23″ = 1.038 rad

Height: ha = 11.2
Height: hb = 12.923 <- Answer
Height: hc = 12

Median: ma = 11.236
Median: mb = 12.971
Median: mc = 12.166

Inradius: r = 4
Circumradius: R = 8.125

Vertex coordinates: A[14; 0] B[0; 0] C[9; 12]
Centroid: CG[7.667; 4]
Coordinates of the circumcenter: U[7; 4.125]

A sidewalk forms the diagonal of a square park. The sidewalk is 30 meters long. To the nearest tenth of a meter, how long are the sides of the park ?

Answers

We can use the Pythagorean Theorem (A² + B² = C²) to solve for the lengths of the sides. We know that the diagonal, C, is 30 meters long, so C² = 900 meters. We know that since the park is square, A² + B² = 2A² = 2B²

900 = 2A²

A^2 = 450

Taking the square root of 450, we find that the lengths of A and B are roughly 21.2 meters.

Sidewalk is the diagonal of the square shaped park.
Length of the Diagonal l = 30 m
Formula for the length of the diagonal of a square l = square root of 2 x s; s being the side.
Therefore square root of 2 x s = 30 => s = 30 / square root of 2 = 30 / 1.414 Side of the Square s = 21.21 m

In the two triangles below, all angles equal 60 degrees and ab = ef. are the two triangles congruent?

Answers

yes the two triangles are congruent

The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. Which segments appear to be equal in length? Check all that apply. XP = YP for an acute triangle XP = ZP for an acute triangle YP = ZP for an obtuse triangle ZP = XP for a right triangle XP = YP for an obtuse triangle

Answers

The answers are-

XP=YP for an acute triangle

YP=ZP for an obtuse triangle

XP=YP For an obtuse triangle

XP=YP for an acute triangle
YP=ZP for an obtuse triangle
XP=YP for an obtuse triangle
this is right

Someone pleaser help me !

Answers

Elizabeth's contribution would be expected to be
.. $80,000 * 4/(3 +4) = 45,714.29

The closest answer is the 4th selection, but it doesn't really agree with the conditions of the problem statement.

_____
If Steve invests the balance after Elizabeth contributes 45,600, the ratio of their contributions will be 43:57, about 0.7544, not 3:4 = 0.7500.

Ginny has a sheet of plywood that is 4 feet by 8 feet. She wants to saw the plywood into pieces 1 foot high and 2 feet long for signs. How many signs can she make with the sheet of plywood?

Answers

the answer is 16 signs.

Answer: 16 signs

Step-by-step explanation: i not saying this cause the other person said it i am saying it because i tookthe question

A.)ii. and iii.
B.)ii.
C.)i.
D.)i. and iv.

Answers

The answer is B) ii

The notation "p --> q" means "if p, then q". For example

p = it rains
q = the grass gets wet

So instead of writing out "if it rains, then the grass gets wet" we can write "p --> q" or "if p, then q". The former notation is preferred in a math class like this.

So when is the overall statement p --> q false? Well only if p is true leads to q being false. Why is that? It's because p must lead to q being true. The statement strongly implies this. If it rained and the grass didn't get wet, then the original "if...then" statement would be a lie, which is how I think of a logical false statement.

If it didn't rain (p = false), then the original "if...then" statement is irrelevant. It only applies if p were true. If p is false, then the conditional statement is known to be vacuously true. So this why cases iii and iv are true.

The expression below is the factorization of what trinomial?

(2x + 7)(4x - 3)

A. 8x2 + 22x + 4
B. 8x2 + 28x - 21
C. 8x2 + 28x + 4
D. 8x2 + 22x - 21

Answers

(2x + 7)(4x -3)
= (2x)(4x) + (2x)(-3) + (7)(4x) + (7)(-3)
= 8x^2 - 6x + 28x - 21
= 8x^2 + 22x - 21 (Answer D)

If f is differentiable at x = c, then f is continuous at x = c.

True
False

Answers

Answer:

This is true!

Step-by-step explanation:

P.S: keep in mind that the opposite is not true! If f is continuous at x = c, then f is NOT differentiable at x = c.

:)))

If f is differentiable at x = c, then f is continuous at x = c is not true.

What is differentiable?

Any point inside the range of a function's purview has a derivative, making it a computable function of one real variable. In these other phrases, each interior site in the domain of an invertible method's graph does indeed have a non-vertical line segment.

F is NOT differentiable at x = c if it is continuous at x = c.

When working with units, this quality is highly helpful since, if a curve is discrete, we automatically infer that it is indeed continuous.

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The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 5 7.5 15 7.5 11 13.8 6.4
HS 16 0 9.5 14.5 5 13 . 10.7 5.3
Which of the choices below best describes how to measure the spread of this data? (Hint: Use the minimum and maximum values to check for outliers.) (2 points) A:Both spreads are best described with the IQR.
B:Both spreads are best described with the standard deviation.
C:The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D:The college spread is best described by the standard deviation. The high school spread is best described by the IQR.

Answers

Answer:

Option A is correct

Step-by-step explanation:

Given is a table which shows data from a survey about the amount of time students spend doing homework each week.

College HS

High 50 16

Low 5 0

Q1 7.5 9.5

Q3 15 14.5

IQR 7.5 5

Median 11 13

Mean 13.8 10.7

Std dev 6.4 5.3

1.5IQR 11.25 7.5

Q1-1.5IQR -9.38 -12

Q3+1.5IQR 37.5 29.5

WE find that there is only one outlier in college with 50 as high.

Except that all others are well within IQR range. Hence outliers are minimum

So option A is right.

Final answer:

To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.

Explanation:

To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.

When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.

Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.

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