Gracie Shay wants to buy a new Hummer in five years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now at a rate of 6% compounded semiannually, she:
Multiple Choice
Will miss her goal by about $10,893.
Will miss her goal by about $11,680.
Will miss her goal by about $11,833.

Kinetic energy of Usain is 4700kg-m²/s².

Kinetic energy of Usain's brother is 18800kg-m²/s².

If we double the mass kinetic energy get doubled.

What is kinetic energy ?

Kinetic energy of an object is the energy that it possess due to its motion.

It is calculated as  [tex]\frac{1}{2}mv^{2}[/tex] where m is mass and v is velocity.

In Usain's case m = 94kg and v = 10m/s.

So, kinetic energy = 4700kg-m²/s².

In Usain's brother case mass is same but velocity is doubled.

So, kinetic energy = 18800kg-m²/s².

From the formula we can see ,

if mass is doubled then kinetic energy get doubled.

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The area of the rectangle, in square meters, is 7.56 meters².

Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.

Given;

a rectangle has a length of 42 centimeters,

and a width of 18 centimeters.

To find the area of the rectangle:

We multiply the length of the rectangle by the width of the rectangle.

Use formula,

The area of the rectangle = length x width

Substitute the value of length and width

The area of the rectangle = 42 x 18

The area of the rectangle = 756 cm².

To change centimeter to meter:

We have the rate of change,

1 centimeter = 0.01 meter

756 centimeters = 0.01 x 756 meters

756 centimeters = 7.56 meters

Therefore, the area of the rectangle = 7.56 meters².

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He will spend 5 minutes bicycling at 11mph and 40 minutes bicycling at 15mph.

From the information, the person is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph

This will be illustrated as:

x + y = 45 ..... i

6x + 9.25y = 400 ..... ii

From equation i, x = 45 - y ..... iii

x = number of minutes cycling at 11mph

y = number of minutes cycling at 15mph

Put equation iii into ii

6x + 9.25y = 400

6(45 - y) + 9.25y = 400

270 - 6y + 9.25y = 400

3.25y = 130

Divide

y = 40

Since x + y = 45.

x = 45 - 50

x = 5

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Answer:

-36

Step-by-step explanation:

-3[tex]a^{2}[/tex]b  Substitute -2 for a and 3 for b

-3[tex](-2)^{2}[/tex](3)

-3(4)(3)

-36

Answer:

= -36

Step-by-step explanation:

-3a²b

if:

a = -2

b = 3

Then:

= -3*-2²*3

= -3(-2*-2) * 3

= -3*4*3

= -36

The new interval for mu becomes narrower, If the number of observations stays the same, but the confidence is reduced to 90%.

The population mean 95% confidence interval is calculated to be between 65.32 and 73.54. The confidence interval for mu will get narrower if the range is trimmed to 90%. This is because the margin of error has decreased. The mean's potential values would be reduced as a result.

The probability that the confidence interval contains the actual population mean is known as the confidence level. You would anticipate that the true value would fall within these ranges 95% of the time if the study were to be repeated and the range computed each time. The more confident you may be that the interval contains the true mean, the greater the confidence level.

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The condition which is must be true for the given triangle ABC is m∠A = m∠C. Option 2 is correct. If AB = AC, then the triangle is said to be an isosceles triangle.

A triangle is said to be an isosceles triangle if it has two equal sides and two equal angles in measurement.

The angles in an isosceles triangle are acute. That means they are less than 90° each. So, their sum results in a total of 180°.

Given a triangle, ABC has AB = BC.

So, that means the given triangle is isosceles.

As we know, in an isosceles triangle, two angles are formed between one of the similar sides with the odd side being equal.

I.e., m∠A = m∠C

So, option 2 is correct.

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Answer:

$29,000

Step-by-step explanation:

To calculate the cost of merchandise sold, you can use the following formula:

Cost of Merchandise Sold = Sales - (Beginning Inventory + Purchases - Purchase Discounts - Ending Inventory)

Plugging in the values from the data provided, the cost of merchandise sold would be:

Cost of Merchandise Sold = $50,000 - ($6,000 + $20,000 - $1,000 - $4,000)

Cost of Merchandise Sold = $50,000 - $21,000

Cost of Merchandise Sold = $29,000

So, the cost of merchandise sold would be $29,000.

The quadrilateral is a parallelogram if and only if it has two pairs of parallel sides

What is parallelogram?

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

A parallelogram is a quadrilateral with two pairs of parallel sides.

As we know,

The quadrilateral can be defined as the four-sided polygon in geometry having four edges and four corners.

The quadrilateral, has:

Two pairs of congruent sides.

It has one pair of opposite congruent angles.

The diagonals of a kite are perpendicular.

One diagonal is bisected.

The top and bottom angles are bisected but does not have congruent diagonals.

A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.

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Answer:

3.35

Step-by-step explanation:

38.86=11.6x

x=3.35

The equation y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second.

i) Direction of wave propagation is negative x-axis.

ii) The wave speed is 1.25m/s.

iii)The maximum displacement from the mean position (i.e., the amplitude of the wave) is 0.16 m.

iv)The wave pulse is symmetric.

We compare the given wave equation from the standard wave equation. On comparing, direction and wave speed is found out. The Remaining two parts are found by maxima concept and changing x by −x at t=0 to get a wave is symmetric.

Moving pulse is given by

⇒y(x,t)=0.8[(4x+5t)2+5]

Comparing (4x+5t) with (ax+bt) then we get,

⇒a=4 and b=5 ⋯⋯⋯(1)

(i) When coefficients of x and t are positive then the wave pulse is moving negative x-direction. So, given an equation with coefficients a = 4 and b= 5 are positive. Therefore, the direction of the given equation will be negative x axis.

(ii) After getting the coefficient a and b, we can calculate the speed by determining the value of b/a. And we have value of a =4 and b =5 from the equation (1) .Then speed of the wave will be

=> b/a=5/4

=> speed of the wave =1.25m/s

(iii) To get the maximum displacement from the mean position we put (4x+5t)=0. As the denominator is minimum, the fraction will be maximum. Therefore displacement will be

=> y=0.85, putting the (4x+5t) is equal to zero.

After simplify we get,

=> y=0.16 m

Hence maximum displacement is 0.16m from the mean position,

(iv) We replace x by −x and also put t= 0 in the given equation. If the equation does not change, replacing the x by −x, it will be symmetric otherwise not.

Putting t=0 in the given equation y(x,t) we get,

=> y=0.8(4x)2+5

Now replace x by −x on the above equation we get, y=0.8(4x)2+5

there will not be any change. Therefore, the given equation is symmetric.

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Complete question:

If y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second. Find

(i) Direction of wave propagation.

(ii) The wave speed.

(iii) The maximum displacement from the mean position (i.e., the amplitude of the wave)

(iv) Whether the wave pulse is symmetric or not.

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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The ratio of tablespoons of raspberries to tablespoons of sugar should be considered as the 8 to 6.

What is ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

Calculation of the ratio:

Since Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 8 tablespoons of raspberries.

So here the ration be like

= 8 raspberries tablespoons to 6 tablespoons of sugar

= 8 to 6

hence, the second option is correct.

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The length of the hypotenuse of the triangle is √181 cm

Pythagoras theorem states that in the right -angled triangle , the square of the hypotenuse side is equal to the sum of the square of other two sides.

Hypotenuse it the longest side , as it is opposite to the angle 90°

Pythagoras theorem formula :

Let a be the base

b be the perpendicular and c is hypotenuse

So, according to the Pythagoras

c² = a² + b²

According to the question,

We have to find the length of hypotenuse

Given that base = 10

Perpendicular = 9

Let Hypotenuse = x

Using above theorem

=> x² = (10)² + (9)²

=> 100 + 81 = x²

=> c = √181

The length of hypotenuse is √181

I've answered the question in general as the question is incomplete

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we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.

The Empirical Rule (or 3 sigma rule) states that for a normal distribution (bell shaped distribution) 68% of the data falls within one standard deviation (μ ± σ), 95% percent within two standard deviations (μ ± 2σ), and 99.7% within three standard deviations from the mean (μ ± 3σ).

Given that the mean (μ) = $2200, standard deviation (σ) = $400

a) The percentage of data within one standard deviation = μ ± σ = (2200 ± 400) = (1800, 2600)

Hence 68% of the land are between ​$1800 and ​$2600.

Number of farms = 68% × number of sample = 0.68 × 80 = 54.4 ≈ 54 farms

Hence we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.

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The probability that a man who developed diabetes is very active is 0.0625.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

You want P(a/d) where a means active, d means diabetic. Then Bayer's rule gives

P(a/d)=P(d/a)p(a)/P(d)

We know P(d)=202/5990.

P(a)=1/4 and P(d/a) we need to figure out.

But

P(d)=1/4P(d/a)+3/4p(d/s)=1/4P(d/a)+3/4∗5P(d/a)

P(D&A)/P(A) = 1/5*P(D&A')/P(A')

I am given P(A) = 1/4, so this can be reduced to

P(D&A)/(1/4) = 1/5*P(D&A')/(3/4) 15*P(D&A) = P(D&A')

The probability I am interested in is P(A|D) = P(D&A)/P(D) = P(D&A)/(P(D&A) + P(D&A')) = P(D&A)/(P(D&A) + 15*P(D&A)) = 1/16

Hence ,The probability that a man who developed diabetes is very active is 0.0625.

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The area of the rhombus is 42 square units, and the correct answer is C.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

We have given that side of the rhombus is 7 units and height is 6 units.

To find the area of rhombus:

Remember that a rhombus is any quadrilateral that has four equal sides.

As a rhombus is also a parallelogram.

Formula to calculate area of rhombus using base and height;

Area of the rhombus = base x height

We have base = 7 units

And height = 6 units.

Substituting the values to the formula,

Area of the rhombus = 7 x 6

Area of the rhombus = 42 unit squared.

Therefore, the area is 42 square units.

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The given point estimators are unbiased and estimator b₁  is more efficient than b₂.

A statistic used to precisely estimate a population parameter is called an "unbiased estimator." An estimator's expected value must match the population parameter's value to be considered unbiased. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator tends if this difference is not zero.

a) To show whether the given point estimators are unbiased, first, find whether the expected value of the given estimators is equal to the population parameter μ.

[tex]\begin{aligned}E(b_1) &= E(0.10X_1 + 0.20X_2 + 0.40X_3 + 0.30X_4)\\&=0.10E(X_1) + 0.20E(X_2) + 0.40E(X_3) +0.30E(X_4)\\&=0.10\mu+0.20\mu+0.40\mu+0.30\mu\\&=\mu\\E(b_2) &= E(0.25X_1 + 0.25X_2 + 0.30X_3 + 0.20X_4)\\&=0.25E(X_1) + 0.25E(X_2) + 0.30E(X_3) +0.20E(X_4)\\& = 0.25\mu + 0.25\mu + 0.30\mu + 0.20\mu\\&=\mu \end{aligned}[/tex]

Therefore, both estimators are found to be unbiased.

b) To show which estimator is more efficient, first, find the two-point estimators' variance.

[tex]\begin{aligned}V ar(b_1)&= Var(0.10X_1+0.20X_2+0.40X_3+0.30X_4)\\&= 0.10^2V ar(X_1)+0.20^2Var(X_2)+0.40^2Var(X_3)+0.30^2Var(X_4)\\&= 0.10^2\sigma^2+ 0.20^2\sigma^2+ 0.40^2\sigma^2 + 0.30^2\sigma^2\\&=0.3\sigma^2\\Var(b_2)&= Var(0.25X_1+0.25X_2+0.30X_3+0.20X_4)\\&= 0.25^2Var(X_1)+0.25^2Var(X_2)+0.30^2Var(X_3)+0.20^2Var(X_4)\\&= 0.25^2\sigma^2 + 0.25^2\sigma^2 + 0.30^2\sigma^2 + 0.20^2\sigma^2\\&= 0.255\sigma^2\end{aligned}[/tex]

From this, we can say that Var(b₁) > Var(b₂). Therefore, b₁ is more efficient.

The complete question is -

Let X₁, X₂, X₃, and X₄ be a random sample of observations from a population with mean μ and variance σ². Consider the following two-point estimators:

b₁ = 0.10X₁ + 0.20X₂ + 0.40X₃ + 0.30X₄, and

b₂ = 0.25X₁ + 0.25X₂ + 0.30X₃ + 0.20X₄

(a) Show that both estimators are unbiased.

(b) Which estimator is more efficient, b₁ or b₂? Explain in detail.

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Internal validity refers to the accuracy of the evaluation in attributing the changes identified to the program and not to other factors, such as demographic differences between the participants and the control group.

To ensure internal validity, one must compare the participants and the control groups on demographic characteristics in order to show that the differences found in the evaluation are due to program differences and not to demographic differences. This is done by conducting a statistical comparison of the two groups and calculating the probability that any differences found between them are due to the program and not to some other factor. This is done by computing the probability that the two groups are the same, given the observed mean differences, and then evaluating the results to determine if the differences are statistically significant. For example, if the two groups have different means, the probability of them being the same is calculated, and if this probability is low, then the difference is likely to be due to the program and not to some other factor. This type of statistical analysis speaks to the internal validity of the evaluation.  

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The probability of passing if the minimum passing grade is 50 %. P(pass) is 0.000035 .

Given :

A quiz consists of 20 multiple - choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers .

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Binomial problem with n = 20 and p = 1/6 , q = 5/6

50 % of 20  = 10

P ( x = 10 ) = C ( 20 , 10 ) ( 1/6 )^10 ( 5/6 )^10

= 184756 * ( 1/6 )^10 ( 5/6 )^10

= 0.000035

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Answer:

  x = (π/2 +2nπ) ± π/3

Step-by-step explanation:

You want the solutions to the radical equation involving sin(x).

  [tex]\sqrt{\sin^2{x}-4\sin{x}+4}+\sqrt{\sin^2{x}+4\sin{x}+4}=\sqrt{\sin^2{x}+7\sin{x}+12.25}\\\\\sqrt{(\sin{x}-2)^2}+\sqrt{(\sin{x}+2)^2}=\sqrt{(\sin{x}+3.5)^2}\\\\|\sin{x}-2|+|\sin{x}+2|=|\sin{x}+3.5|\\\\(2-\sin{x})+(\sin{x}+2)=\sin{x}+3.5\\\\0.5=\sin{x}[/tex]

The values of x that make this true are ...

  x = {π/6, 5π/6} +2πn . . . . . for any integer n

__

Additional comments

  √(x²) = |x|

  sin(x) -2 is always less than zero, so its absolute value is 2-sin(x).

The attachment shows the equation written so the x-intercepts give the desired solutions.

The real number solution set for the trigonometric equation is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

We know that sin²x - 4sinx + 4 = (sinx - 2)².

Also, sin²x + 4sinx + 4 = (sinx + 2)².

Also, sin²x + 7sinx + 12.25 = (sinx + 3.5)².

So, substituting these into the equation, we have that

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

√(sinx - 2)² + √(sinx + 2)² = √(sinx + 3.5)²

|sinx - 2| + |sinx + 2| = |sinx + 3.5|

(2 - sinx) + (sinx + 2) = (sinx + 3.5)

2 - sinx + sinx + 2 = sinx + 3.5

Colecting like terms, we have that

-sinx + sinx + 2 + 2 = sinx + 3.5

0 + 4 = sinx + 3.5

4 = sinx + 3.5

Subtracting 3.5 from both sides, we have that

sinx = 4 - 3.5

sinx = 0.5

Taking inverse sin, we have that

x = sin⁻¹(0.5)

x = π/6 or 5π/6

So, the real number solution set is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

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The quadratic parent function is f(x) = x^2. (Option A)

In mathematics, family of functions refers to a group of functions that have the same degree or form. The examples of families of functions include linear functions, quadratic functions, square root functions, and absolute value functions. A parent function refers to the simplest function of a family of functions that preserves the definition of the entire family where the graph does not experience any transformations. The parent function of a quadratic equation is f(x) = x^2, whose graph has a vertex at the origin and experiences no vertical stretch or shrink. The other three options would be translated or transformed, hence are not the parent function of the quadratic equation.

Note: The question is incomplete. The complete question probably is: Which of these is the quadratic parent function? A. f(x) = x^2 B. f(x) = x^2 + 3 C. f(x) = x^2 – 5 D. f(x) = –4x^2

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Answer:

B which I assume to be a typo where you had meant 3/4

Answer:

B. [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

We need to find the HCF of 18 and 24 to simplify it into its lowest terms.

The HCF of 18 and 24 is 6, therefore we need to divide 6 on both sides to simplify it into its lowest terms.

Hence, [tex]\frac{18}{24}=\frac{3}{4}[/tex]

I would appreciate it if you mark my answer as brainliest.

The perimeter of smaller circle is 78.5 ft

What is area?

Area is that the amount that expresses the extent of a vicinity on the plane or on a semicircular surface. space|the world|the realm} of a plane region or plane area refers to the world of a form or planate plate, whereas area refers to the world of associate degree open surface or the boundary of a three-dimensional object.

Main Body:

A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25 ft and Garden B has a diameter of 45 ft.

outline the smaller garden means circumference of the circle.

Perimeter of circle is 2πr.

diameter = 25 ft

radius = 25/2 = 12.5 ft

Radius = 2π *12.5

            = 25 π

            = 25*3.14

            = 78.5 ft

Hence the perimeter of circle is 78.5 ft

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The value of the variable x in the circle is 18 units

From the question, we have the following parameters that can be used in our computation:

Diameter = (2x - 4) units

Radius = 16 units

These parameters can be expressed as

d = 2x - 4

r = 16

Start by calculating the radius of the circle

So, we have the following representation

Radius = Diameter/2

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

16 = (2x - 4)/2

Evaluate the quotients in the above equation

16= x - 2

Add 2 to both sides of the equation

x = 16 + 2

Evaluate the like terms

x = 18

Hence, the variable x is 18 units

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The chi-square test for independence compares the two variables within a sample set to one another, instead of comparing the single observed variable into the theoretical population.

The chi-square takes a statistical look in order to compare the found consequences of the with that of the familiar outcomes. The main goal of this test is to take a statistical view in order to make a distinction between the observed records and the expected facts, is due to the risk present, or if it's miles because of courting the variables that you are studying.

A chi-square test is used to measure the degree of variation between the frequencies which are determined and the expected frequencies according to the hard and fast rules of variables and occasions. Chi-rectangular is used to measure the differences of the nominal variables.

The term, 'independence' refers to the individual's own freedom of doing things, without being affected by other's opinions. As and when, a small child grows up to an adult, he/she tends to make their own decisions and selections. This is one of the example of independence. Realizing the importance of independence is crucial as the people of the nation are its most important assets. The way in which the founders of India has reunited the country into a single state, the same, if followed in USA, this would relieve the country from the chains of caste, sex, religion and exploitation.

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Answer:

200 cupcakes

Step-by-step explanation:

Let "x" be the total number of cupcakes sold at the bakery.

We know that 26 cupcakes represents 13% of the total number of cupcakes sold, so:

26 cupcakes = 13/100 * x

Solving for x, we get:

x = 26 / (13/100)

Simplifying the fraction, we get:

x = 2600 / 13

Dividing 2600 by 13 gives us 200, so:

x = 200

Therefore, the bakery sold a total of 200 cupcakes on that day.

The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5

From the question, we have the following parameters that can be used in our computation:

The quadratic inequality is:

x^2-5<0

Express properly

x² - 5 < 0

Add 5 to both sides of the inequality

x² < 5

Take the square root of both sides

x < ±√5

Expand the inequality expression

- √5 < x < √5

Hence, the solution is - √5 < x < √5

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The formula of the volume of the rectangular prism is,

V = l * w * h

The formula of the surface area of the rectangular prism is,

A = 2(lw + wh + lh)

the surface area of a box is 72 sq.ft.

For a rectangular prism with length(l), width(w) and height(h),

The formula of the volume of the rectangular prism is,

V = l * w * h

The formula of the surface area of the rectangular prism is,

A = 2(lw + wh + lh)

For a rectangular box with a length of 6 ft a width of 3 ft and a height of 2 ft,

here, l = 6 ft, w = 3 ft and h = 2 ft

using the formula for the surface area of a rectangular prism, the surface area of box would be,

A = 2(lw + wh + lh)

A = 2(6 * 3 + 3 * 2 + 6 * 2)

A = 2(18 + 6 + 12)

A = 2(36)

A = 72 sq.ft.

Therefore, the surface area of a box is 72 sq.ft.

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The value of x after simplification is 6/5.

What is an equation?

A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, in French, an equation is defined as having one or even more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values for the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables that the equation must be solved, and the unknown variable values that satisfy this same equality are known as the equation's solutions.

Main Body:

according to the given equation,

5x = 6

to solve it , divide by 5 on both sides,

5x *1/5  = 6*1/5

x = 6/5

Hence the value of x after simplification is 6/5.

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