Which type of parent function does the equation f(x) = 1 represent?

A. Reciprocal

B. Square root

C. Absolute value

D. Cube root

The answer is B.

In order to get the answer, you replace the letter n to 5 and workout the problems to see which one is true.

B is the answer because n + 3 = 8

5 + 3 = 8

Answer:

B

Step-by-step explanation:

n+3 =

5+3=

The equations which satisfy (6, -3) are: y = -5x + 27 and y = 2x - 15 (Option C and D)

To know which equation will result in (6, -3), we shall determine the value of y in each equation since we know that x = 6. Details below:

For A

y = -3x + 6

y = -3(6) + 6

y = -18 + 6

y = 12

For B

y = 2x - 9

y = 2(6) - 9

y = 12 - 9

y = 3

For C

y = -5x + 27

y = -5(6) + 27

y = -30 + 27

y = -3

For D

y = 2x - 15

y = 2(6) - 15

y = 12 - 15

y = -3

For E

y = -4x + 27

y = -4(6) + 27

y = -24 + 27

y = 3

From the above, the equation that satisfy (6, -3) are:

Thus, the correct answer to the question is Option C and D

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Answer:

The answer to your problem is, A. 10

Step-by-step explanation:

So first add up all the total number of ‘ X ‘

Which is:

4 + 3 + 2 + 1 = 10

Technically 10 is our answer.

Thus the answer to your problem is, A. 10

Not a 100% sure

Answer:

5, 8, 8, 8, 8, 9, 9, 9, 10, 10

The median of this data set is 8.5, so the correct answer is B.

Step-by-step explanation:

Since there are 10 observations, we are looking for the number halfway between the two middle observations (observations #5 and #6) when the data are arranged in order. Here, observation #5 is 8, and observation #6 is 9, so the median of this data set is (8 + 9)/2 = 8.5. B is the correct answer.

The p-value for the hypothesis test is 0.0314.

To find the p-value for this hypothesis test, we can use a t-test since the population standard deviation is unknown.

The test statistic is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

In this case, we have:

x = 424

μ = 400

s = 83

n = 53

So the test statistic is:

t = (424 - 400) / (83 / √53) ≈ 2.2071

To find the p-value, we need to compare this test statistic to the t-distribution with n-1 degrees of freedom (df = 52, in this case). Using a t-distribution table or calculator, we find that the probability of getting a t-value as extreme or more extreme than 2.2071 (in either direction) is approximately 0.0157.

Since this is a two-tailed test (Ha: u ≠ 400), we need to double this probability to get the p-value:

p-value = 2 * 0.0157 ≈ 0.0314

Therefore, the p-value for the hypothesis test is approximately 0.0314 (rounded to 4 decimal places).

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Answer: 720

Step-by-step explanation:

there are 6 letters in "choice"

and they must be permuted into 6 word letters:

6P6 = 720 distinct possibilities

The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:

S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)

We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:

|an+1| = 0.49((n+1)^2)

So we need to find the smallest value of n such that:

|an+1| < 10^-6

0.49((n+1)^2) < 10^-6

(n+1)^2 < (10^-6)/0.49

n+1 < sqrt((10^-6)/0.49)

n < sqrt((10^-6)/0.49) - 1

n < 11.75

Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

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We have shown that f(x) = f(0) for all x ∈ (-1,1).

Since f is continuous at 0, we have:

lim x → 0 f(x) = f(0)

Since f(x) = f(x³) for all x ∈ (-1,1), we can substitute x = x³ and get:

f(x) = f(x³) = f(x⁹) = f(x²⁷) = ...

Since |x| < 1, we have x² < |x| < 1, and thus:

lim x² → 0 f(x²) = f(0)

Therefore, we can apply the limit of the sequence of nested intervals to obtain:

f(x) = f(x³) = f(x⁹) = f(x²⁷) = ... = lim n → ∞ f(x^(3ⁿ)) = lim y → 0 f(y) = f(0)

where we have made the substitution y = x^(3ⁿ), which implies that x = y^(1/(3ⁿ)) → 0 as n → ∞.

Thus, we have shown that f(x) = f(0) for all x ∈ (-1,1).

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The equation of the plane tangent to the surfacer=3u2i+(5u−v2)j+3v2kr=3u2i+(5u−v2)j+3v2kat the point P that is P(12,9,3).z(x,y)=z(x,y)= 90x + 1296y + 810z = 14218.

To find the equation of the plane tangent to the surface at point P(12, 9, 3), we first need to find the partial derivatives of the surface with respect to u and v:

∂r/∂u = 6ui + 5j

∂r/∂v = -2vj + 6vk

Next, we can evaluate these partial derivatives at the point P(12, 9, 3) to get:

∂r/∂u = 6(12)i + 5j = 72i + 5j

∂r/∂v = -2(9)j + 6(3)k = -18j + 18k

Using these partial derivatives, we can find the normal vector to the tangent plane at point P by taking their cross product:

n = (∂r/∂u) x (∂r/∂v) = (72i + 5j) x (-18j + 18k)

= -90i - 1296j - 90k

Since the tangent plane passes through point P, its equation can be written in the form:

-90(x - 12) - 1296(y - 9) - 90(z - 3) = 0

Simplifying this equation gives:

-90x + 12960 - 1296y - 810z + 1458 = 0

or

90x + 1296y + 810z = 14218

Therefore, the equation of the plane tangent to the surface at point P is 90x + 1296y + 810z = 14218.

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The distance that the plane has flown, c, is 1,683 ft.

The distance of the plane is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height attained by the plane is the opposite side, while the hypothenuse is the distance travelled by the plane.

sin (12) = h/c

c = h/sin(12)

c = (350 ft ) / sin(12)

c = 1683.4 ft ≈1,683 ft

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The shape of the distributive is such that; it is skewed to the right. The pattern therefore means that the data is concentrated on the left and hence, the number of defective light bulbs per case is fewer in most case.

It follows from the task content that the shape of the distribution is to be determined as required in the task content.

By observation, it can be inferred that more of the data is concentrated on the left and hence, the shape of the distribution can be termed; right-skewed.

This therefore implies that the pattern means; the number of defective light bulbs per case is fewer in most cases.

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The measures of angle B is derived as 75° to the nearest degree using the cosine rules.

The cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Using the cosine rule:

2² = 5² + (√45)² - 2(5)(√45)cosB

4 = 25 + 45 - 250cosB

4 = 70 - 250cosB

250cosB = 70 - 4 {collect like terms}

250cosB = 66

B = cos⁻¹(66/250) {cross multiplication}

B = 74. 6925°

Therefore, the measures of angle B is derived as 75° to the nearest degree using the cosine rules.

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The circle relation C defined on the set of real numbers is not reflexive and transitive but it is symmetric.

(a) C is not reflexive. To be reflexive, for every real number, xCx must hold true, meaning [tex]x^{2} + x^{2}[/tex]= 1. This is false. For example, let x=0. In this case, [tex]x^{2} + x^{2}[/tex] = 0, which does not equal 1. Therefore, C is not reflexive.

(b) C is symmetric.  If xCy then yCx, for all real numbers x and y. If we see the definition of C, this means that if [tex]x^{2} + y^{2}[/tex] = 1, then [tex]y^{2} + x^{2}[/tex] = 1. This is true due to the commutative property of addition ([tex]x^{2} + y^{2} = y^{2} + x^{2}[/tex] for all real numbers x and y). Thus, C is symmetric.

(c) C is not transitive. To be transitive, if xCy and yCz, then xCz must hold true for all real numbers x, y, and z. This means that if [tex]x^{2} + y^{2}[/tex] = 1 and [tex]y^{2} + z^{2}[/tex] = 1, then [tex]x^{2} + z^{2}[/tex]must equal 1. This is not always true. Let's take an example (x, y, z) = (1, 0, -1). Then [tex]x^{2} + y^{2}[/tex] = 1, [tex]y^{2} + z^{2}[/tex]= 1, but [tex]x^{2} + z^{2}[/tex] = 2, not 1. Thus, C is not transitive.

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The bush is 26.4 inches tall after 2 weeks. This means it has grown by 14.4 inches since it was first planted and the percentage increase is 120%

To calculate the height of the bush after 2 weeks, we can use the following formula:

New height = initial height + (percent increase/100) * initial height

In this case, the initial height of the bush is 12 inches, and the percent increase is 120%. Plugging in these values, we get:

New height = 12 + (120/100) * 12

New height = 12 + 14.4

New height = 26.4 inches

Therefore, the bush is 26.4 inches tall after 2 weeks. This means it has grown by 14.4 inches since it was first planted.

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B. An odd number of data values will always have one middle value is true.

D. An even number of data values will always have two middle numbers is also true.

In an odd set of data, there will always be one exact middle number. But in an even set of data, there will be two middle numbers, and they will be the two numbers closest to the center.

So if the middle of {1, 2, 3, 4, 5} is 3 and the middle of {1, 2, 3, 4} is 2 and 3, the correct statements will be;

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The equation for total cost is The Total cost = (10s + 5m + 8l + 0.5n)  

First, we can  calculate  the total cost plus the both the shipping and the handling charge:

The Small shirts is  10 x $5.00 = $50.00

Medium shirts is  5 x $7.50 = $37.50

Large shirts is 8 x $12.00 = $96.

Lets add  three amounts plus also the  shipping and  the handling charge to the over all total cost:

The Total cost  is  (10 x $5.00) + (5 x $7.50) + (8 x $12.00) + (23 x $0.50)

Total cost = 195.00

Therefore, the equation of  total cost is

The Total cost = (10s + 5m + 8l + 0.5n)  s, m, and l refer to the  prices of small, medium, and large shirts, respectively,  n is the total number of shirts.

let now substitute the  values of s, m, l, and n.

The Total cost = 10 x 5.00 + 5 x 7.50 + 8 x 12.00 + 23 x 0.50)  in  dollars

Therefore, the Total cost = $195.00

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Answer:

I assume that "Rud" is a typo and you mean "Sin" instead.

To find the derivative of Sin(x^2) - Cos(x), we need to use the chain rule and the derivative of the trigonometric functions.

The derivative of Sin(x^2) is:

d/dx [Sin(x^2)] = Cos(x^2) * d/dx [x^2] = 2x * Cos(x^2)

The derivative of -Cos(x) is:

d/dx [-Cos(x)] = Sin(x)

Therefore, the derivative of the function Sin(x^2) - Cos(x) is:

2x * Cos(x^2) + Sin(x)

So the answer is option (b) -2xcos(x^2) + sin(x).

The answer is option (b): -2xcos(x^2).

Assuming that "Rud-cost" is a typo and the function is meant to be "Rudin-cost", which is a function defined as:

Rudin-cost(x) = cos(x^2)

To find the derivative of Rudin-cost(x), we can use the chain rule and the power rule for differentiation. Specifically, if we let u = x^2, then we have:

Rudin-cost(x) = cos(u)

Using the chain rule, we get:

Rudin-cost'(x) = -sin(u) * u'

where u' is the derivative of u with respect to x, which is:

u' = d/dx(x^2) = 2x

Substituting this back into the expression for Rudin-cost'(x), we get:

Rudin-cost'(x) = -sin(x^2) * 2x

Therefore, the answer is option (b): -2xcos(x^2).

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Rotter Partners is planning a major investment, and to ensure that the investment is profitable, it is essential to understand the expected profit from the investment. The probability distribution of profits from similar investments indicates that the expected profit (mx) can be calculated as the weighted average of profits, where the weights are the probabilities associated with each profit level.

Based on the given probability distribution, the expected profit (mx) can be calculated as follows:

mx = (1 x 0.1) + (1.5 x 0.2) + (2 x 0.4) + (4 x 0.2) + (10 x 0.1)
mx = 0.1 + 0.3 + 0.8 + 0.8 + 1
mx = 2.7

Therefore, the expected profit from the investment is $2.7 million. This estimate is valuable to Rotter Partners as it can help them make informed decisions about the investment. If the expected profit is lower than the cost of the investment, then the investment may not be worthwhile. On the other hand, if the expected profit is higher than the cost of the investment, then the investment is likely to be profitable. In any case, the expected profit is a useful metric for assessing the potential success of the investment.

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The given figure is a right triangular prism, with 2 parallel and congruent triangular faces and 3 rectangular faces.

The triangular faces have sides 13 ft, 13ft and 24 ft and the height of 5 ft.

Two of the rectangular faces are 13 ft x 30 ft and the remaining face is 24 ft x 30 ft.

Surface area is the sum of areas of all 5 faces.

Area formula for triangle is A = bh/2 and for rectangle is A = ab.

Let's verify the steps of calculation.

Step 1

This is right

Step 2

This is wrong

Step 3

This is right

Step 4

Correction in step 2, it should be 720 but not 1440.

Correction in last step, the sum:

The simplified value of the expression is 12km³.

We have,

[tex]12k^2m^8 \div 4km^5[/tex]

This can be written as:

[tex]\frac{12k^2m^8}{ 4km^5}[/tex]

Canceling common expression.

= 12km³

Thus,

The simplified value of the expression is 12km³.

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The measure of angle arc CD is 45⁰.

The measure of angle arc VW is 133⁰.

The measure of angle subtended by the arc CD is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠AEB = ¹/₂( AB - CD)

26 = = ¹/₂(97 - CD)

2 x 26 = 97 - CD

52 = 97 - CD

CD = 97 - 52

CD = 45⁰

m∠VYX = ¹/₂( VW - VX)

37 = ¹/₂( VW - 59)

2 x 37 = VW - 59

74 = VW - 59

VW = 74 + 59

VW = 133⁰

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The calculated value of the expression when a = 3 and b = -2 is 1

The expression is given as

(StartFraction 3 a Superscript negative 2 Baseline b Superscript 6 Baseline Over 2 a Superscript negative 1 Baseline b Superscript 5 Baseline EndFraction) squared

Mathematically, this can be expressed as

(3a^-2b^6/2a^-1b^5)^2

The values of a and b are given as

a =3 and b = -2

substitute the known values in the above equation, so, we have the following representation

(3(3)^-2(-2)^6/2(3)^-1(-2)^5)^2

Evaluate

So, we have

1

Hence, the solution is 1

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Answer: might be the 2nd one

Step-by-step explanation:

The difference in the account balances is $138,435.93.

We have,

We can solve this problem by using the formula for the future value of an annuity:

[tex]FV = PMT \times [(1 + r)^n - 1] / r[/tex]

where FV is the future value of the annuity, PMT is the yearly contribution, r is the annual interest rate, and n is the number of years.

Using the given information, we can find the future value of the annuity if the person starts at age 35:

FV1

= $5,000 x [(1 + 0.065)^30 - 1] / 0.065

= $431,874.32

Now we can find the future value of the annuity if the person starts at age 40:

FV2 = $5,000 x [(1 + 0.065)^25 - 1] / 0.065

= $293,438.39

The difference in the account balances is:

FV1 - FV2

= $431,874.32 - $293,438.39

= $138,435.93

Therefore,

The difference in the account balances is $138,435.93.

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Answer: you would have a 75% chance

The margin of error for a 80% confidence interval for the population mean is  57.82 square feet.

The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. To find the margin of error for a 80% confidence interval, we need to use the formula:

Margin of error = z*(σ/√n)

where z is the z-score corresponding to the level of confidence (80% corresponds to z=1.282), σ is the population standard deviation (given as 137), and n is the sample size (given as 19).

Plugging in the values, we get:

Margin of error = 1.282*(137/√19) = 57.82

Therefore, the margin of error for a 80% confidence interval is 57.82 square feet.

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We then use the condition that b is unique to obtain a restriction on the values of a. Solving this restriction, we find that a can take any value except a = 2/3.

Let the given quadratic equation be denoted by f(x) = x^2 + 2bx + (a-b) = 0. Since f(x) has only one real solution, its discriminant must be zero: b^2 = a-b. Rearranging this equation, we get a = b^2 + b.

Substituting this expression for a into the equation for f(x), we obtain:

f(x) = x^2 + 2bx + (b^2 + b - b) = x^2 + 2bx + b^2.

This is a quadratic equation in b with discriminant 4x^2 - 4b^2 = 4(x+b)(x-b). For f(x) to have a unique real solution, this discriminant must be zero, which implies that x = -b. Substituting this value into f(x), we get:

f(-b) = (-b)^2 + 2b(-b) + b^2 = b^2 - 2b^2 + b^2 = 0.

Therefore, -b is a root of f(x), and since f(x) is a quadratic, this means that f(x) is divisible by (x+b). Thus we have:

f(x) = (x+b)(x+(a-b)/b) = (x+b)(x+b+1).

Since b is unique, this implies that (a-b)/b = b+1, or equivalently, a = b^2 + 2b.

Finally, we need to find the values of a for which b is unique. Suppose there are two distinct values of b that satisfy the condition above. Then, their difference satisfies:

(b_1)^2 + 2b_1 - (b_2)^2 - 2b_2 = 0,

which factors as (b_1 - b_2)(b_1 + b_2 + 2) = 0. Since b_1 and b_2 are distinct, the only possibility is that b_1 = -b_2 - 2.

Substituting this into the expression for a, we get:

a = (b_1)^2 + 2b_1 = (-b_2 - 2)^2 - 2(b_2 + 2) = b_2^2 + 2b_2 - 4.

Therefore, a - b_2^2 - 2b_2 + 4 = 0, or equivalently, (a-2)/3 = (b_2+1)^2, which implies that a-2 is a perfect square multiple of 3. Since b_2 can be any real number, this restriction on a is necessary and sufficient.

In summary, the value of a for which the given quadratic equation has a unique real solution is a = b^2 + 2b, where b is any real number except b = -1/2. Equivalently, a can take any value except a = 2/3.

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1. What is the probability a randomly selected bag will have a positive test? Give your answer to four decimal places is 0.1032

2. Given a randomly selected bag has a positive test, what is the probability it actually contains a large amount of liquid is 0.3780

3. Given a randomly selected bag has a positive test, what is the probability it does not contain a large amount of liquid is  0.6219

Let's characterize the taking after occasions:

A: The pack contains huge sums of fluid.

B: The test is positive.

We are given the taking after probabilities:

P(A) = 0.04

P(B | A) = 0.98

P(B | not A) = 0.07

1. To discover the likelihood of a positive test, we are able to utilize the law of adding up to likelihood:

P(B) = P(B | A) P(A) + P(B | not A) P(not A)

= 0.98 * 0.04 + 0.07 * 0.96

= 0.1032

So the likelihood of a haphazardly chosen pack having a positive test is 0.1032 (adjusted to four decimal places).

2. To discover the likelihood that a sack really contains large amounts of fluid given a positive test, we are able to utilize Bayes' hypothesis:

P(A | B) = P(B | A) P(A) / P(B)

= 0.98 * 0.04 / 0.1032

= 0.3780

So the likelihood that a pack really contains expansive sums of fluid given a positive test is 0.3780 (adjusted to four decimal places).

3. To discover the likelihood that a sack does not contain expansive sums of fluid given a positive test, ready to utilize Bayes' hypothesis again:

P(not A | B) = P(B | not A) P(not A) / P(B)

= 0.07 * 0.96 / 0.1032

= 0.6219

So the likelihood that a pack does not contain expansive sums of fluid given a positive test is 0.6219 (adjusted to four decimal places). 

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If A is an m x n matrix, and let B be an n xp matrix such that AB = 0, then rank A + rank B ≤ n

To start, we can use the fact that for any matrix A, rank A + dim Nul A = n, where n is the number of columns in A. This is a result of the rank-nullity theorem.

Now, let's consider the subspaces associated with A and B. The column space of A, Col A, is a subspace of R^m, and the null space of A, Nul A, is a subspace of R^n. Similarly, the column space of B, Col B, is a subspace of R^n, and the null space of B, Nul B, is a subspace of R^p.

We want to show that rank A + rank B ≤ n, so let's consider the dimensions of the subspaces. We know that dim Col A = rank A and dim Col B = rank B. We also know that AB = 0, which means that every column of B is in the null space of A, Nul A. In other words, Col B is a subset of Nul A.

Using the fact that dim Col B + dim Nul B = n, we can write:

rank B + dim Nul B = n - dim Col B

Since Col B is a subset of Nul A, we know that dim Nul A ≥ dim Col B. Therefore:

dim Nul B ≥ dim Nul A

Substituting this inequality into the previous equation, we get:

rank B + dim Nul B ≥ rank B + dim Nul A = n - dim Col A

Finally, we can use the fact that rank A + dim Nul A = n to substitute for dim Nul A:

rank B + dim Nul B ≥ n - rank A

Adding rank A to both sides, we get:

rank A + rank B + dim Nul B ≥ n

But we know that dim Nul B ≥ 0, so:

rank A + rank B ≤ n

Therefore, we have shown that rank A + rank B ≤ n, as desired.

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Answer:

Please mark me the brainliest

Step-by-step explanation:

To solve the equation (6 – 2x)(3 – 2x)x = 40, we can start by simplifying the left-hand side:

(6 – 2x)(3 – 2x)x = 40

(18x – 12x^2 – 6x + 4x^2)x = 40

(2x^3 – 8x^2 + 18x)x = 40

2x^4 – 8x^3 + 18x^2 = 40

2x^4 – 8x^3 + 18x^2 – 40 = 0

We can try to factor this equation by grouping terms:

2x^4 – 8x^3 + 18x^2 – 40 = 0

2(x^4 – 4x^3 + 9x^2 – 20) = 0

2((x^2 – 2x + 1)(x^2 – 2x – 20)) = 0

2(x – 1)^2(x – 5)(x + 4) = 0

Therefore, the real solutions of the equation are x = 1 (with multiplicity 2), x = 5, and x = -4.

Now, to answer the question, we need to determine whether it is possible to cut squares with sides of 3/2 in. to make a box. We can use the value of x = 3/2 to find the dimensions of the box:

length = 6 – 2x = 6 – 2(3/2) = 3 in.

width = 3 – 2x = 3 – 2(3/2) = 0 in.

height = x = 3/2 in.

Since the width is 0, it is not possible to cut squares with sides of 3/2 in. to make a box. Therefore, the correct answer is:

No. It is not possible to cut squares of this size.