Solve for X. Round to the nearest tenth, if necessary.

The dimensions of the rectangular pen that maximize the area are a shorter side of 100 ft and a longer side of 200 ft along the river.

To maximize the area of the rectangular pen using 400 ft of fencing, with a river on one side of the property, we need to determine the optimal dimensions. Let's denote the length of the pen along the river as 'x' and the width perpendicular to the river as 'y'.

Since the river is on one side, we only need to use the fencing for the other three sides. The total fencing length is 400 ft, so the equation representing the fencing is:

x + 2y = 400

We need to find the maximum area of the pen, which is given by the product of its length and width, i.e., A = xy.

First, we need to express 'x' in terms of 'y' using the fencing equation. From the equation, we get:

x = 400 - 2y

Now, substitute this expression for 'x' in the area equation:

A(y) = (400 - 2y)y = 400y - 2y²

To find the maximum area, we need to find the critical points of this equation by taking the derivative with respect to 'y' and setting it to zero:

dA/dy = 400 - 4y = 0

Solve for 'y':

4y = 400
y = 100 ft

Now, find 'x' using the expression we derived earlier:

x = 400 - 2y
x = 400 - 2(100)
x = 400 - 200
x = 200 ft

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Answer:

17.5 feet

Step-by-step explanation:

The picnic are shortest side is 5 units long on the scale drawing

Since each unit on the scale drawing is 1 inch, the shortest side length on the drawing is 5 inches

Each inch on the drawing corresponds to an actual size of 3.5 feet

Therefore 5 inches corresponds to 5 x 3.5ft = 17.5 feet

Therefore the actual length of the shortest side of the picnic area is 17.5 feet

Answer: 9 x 10^4

Step-by-step explanation:

9 ten thousands in standard form is written like this: 90,000

To convert this into scientific notation, we simply count how many spaces we want to move the decimal point.

So far, our number looks like this with a decimal point: 90000.0

To make this number equal to 9, we have to move the decimal point 4 spaces to the left.

The 4 then becomes our exponent.

So now we have 9 by itself, and all we do is multiply it by 10 with an exponent of 4, to show you are multiplying 10 four times.

Therefore, 9 ten thousands written in scientific notation is 9 x 10^4

The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).

The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.

To calculate the 95% confidence interval for the population mean, we use the formula:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).

Plugging in the values, we get:

CI = 15 ± 1.96*(3/√350)

Simplifying, we get:

CI = 15 ± 0.29

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Based on the cost and revenue function, if they want to make a profit, the range of pulp in tons per day that they should produce is between 152.6 and 152.8 tons per day.

To find the range of pulp in tons per day that will generate profit, we need to set the profit function equal to zero and solve for x. The profit function P(x) is given by:

P(x) = R(x) - C(x)

Substituting the given revenue and cost functions, we get:

P(x) = -3x^2 + 1000x - 400

Setting P(x) = 0, we can solve for x using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Plugging in the values from our profit function, we get:

x = [-(1000) ± sqrt((1000)^2 - 4(-3)(-400))] / 2(-3)

Simplifying, we get:

x = [1000 ± sqrt(1000000 + 4800)] / 6

x = [1000 ± sqrt(1004800)] / 6

x ≈ 152.7 or x ≈ 55.6

Since we're looking for the range of pulp in tons per day that will generate profit, we only want the positive solution, which is approximately 152.7 tons per day. Therefore, the company should produce between 152.6 and 152.8 tons per day to generate profit, rounded to the nearest tenth of a ton.

Note: The question is incomplete. The complete question probably is: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x^2 - 250x + 525 and R(x) = -3x^2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit.

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The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)

The refrigerator energy usage per day in BTU is 12283.704 BTU

The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.

The duration the refrigerator fan runs per hour = 30 minutes

The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts

The amount of energy the refrigerator uses per hour = 150 watt-hour

1 kWh = 3412.14 BTU

Therefore;

The amount of energy in BTU the refrigerator uses per day = 12283.704 BTU

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The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.

In order to calculate the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.

First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:

d = √(h² + p²)

d = √(179² + 16.5²)

d = 180.14 ft

Next, we can use the tangent function to find the angle of deviation (θ):

tan(θ) = p/h

tan(θ) = 16.5/179

θ = tan⁻¹(16.5/179)

θ ≈ 5.31 degrees

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Answer:

60%

Step-by-step explanation:

Take 96 and divide it by 160.

(easier if done on a calculator.)

For example: Find A/B as a percentage: take "A" and divide it by "B"

The expression (2x-3)(2x-3) is equal to (2x-3)^2.

To expand the expression (2x-3)(2x-3), we can use the FOIL method (which stands for First, Outer, Inner, Last).

Multiplying the first terms of each binomial, we get 2x times 2x, which is 4x^2.

Multiplying the outer terms, we get -3 times 2x, which is -6x.

Multiplying the inner terms, we get -3 times 2x again, which is also -6x.

Multiplying the last terms of each binomial, we get -3 times -3, which is 9.

Combining like terms, we get 4x^2 - 12x + 9.

Therefore, (2x-3)(2x-3) is equal to (2x-3)^2, which is equivalent to 4x^2 - 12x + 9.

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Answer:

see explanation

Step-by-step explanation:

the arc BX is equal to the measure of the central angle BCX

the measure of the inscribed angle BNX is half the measure of its intercepted arc BX

a) To find the volume of the region A bounded by the sphere x^2 + y^2 + z^2 = 12 and the paraboloid z = x^2 + y^2, we can use cylindrical coordinates.

In cylindrical coordinates, the equations of the surfaces become:Sphere: ρ^2 + z^2 = 12Paraboloid: z = ρ^2The region A is bounded by the sphere and the paraboloid, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to √(12 - z^2), the limits for φ are 0 to 2π, and the limits for z are 0 to 4. So the triple integral for the volume of region A in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to √(12 - z^2), φ: 0 to 2π, and z: 0 to 4.b) To find the volume of the region B in the first octant bounded by the surfaces z = x^2 and x^2 + y^2 + z = 1, we can again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:z = ρ^2 (since we are in the first octant where x and y are non-negative)z = 1 - ρ^2The limits for ρ are 0 to 1, and the limits for φ are 0 to π/2. So the triple integral for the volume of region B in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 1, φ: 0 to π/2, and z: ρ^2 to 1 - ρ^2.c) To find the volume of the region C inside both spheres x^2 + y^2 + (z - 2)^2 = 16 and x^2 + y^2 + 2 = 16, we can once again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:Sphere 1: ρ^2 + (z - 2)^2 = 16Sphere 2: ρ^2 = 12The region C is bounded by both spheres, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to 2√3, the limits for φ are 0 to 2π, and the limits for z are 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2). So the triple integral for the volume of region C in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 2√3, φ: 0 to 2π, and z: 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2).

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Answer:

Step-by-step explanation:

The original image is the the black one.  The dilated image is blue.  It got bigger.  So it is an enlargment.

Each side got bigger by times 2

So the dilation is 2

Answer:

f(2) = 2

Step-by-step explanation:

We are given
f(x) = x² - 7x + 4

To find f(2), just plug in 2 wherever you see an x and simplify

f(2) = 3 · 2² - 7 · 2 + 4

= 3 · 4 - 7 · 2 + 4

= 12 - 14 + 4

= 2

In the given binary operation, a and b are two numbers, and the operation is defined as a * b = a - 2b.

Binary operations are mathematical operations that take two operands and produce a single result. In this problem, we are given a binary operation "*". The operation is defined such that for any two numbers a and b, a * b = a - 2b.

We are then asked to evaluate 5 * 2 using this operation. To do so, we substitute a = 5 and b = 2 into the expression a * b = a - 2b:

5 * 2 = 5 - 2(2)

Simplifying the right-hand side of the equation, we get:

5 * 2 = 5 - 4

5 * 2 = 1

Therefore, 5 * 2 equals 1 when the binary operation is defined as a * b = a - 2b.

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2X (2² + sin 3) can be simplified as 8X + 2X sin 3

To solve the expression, we will first have to compute the values inside the parentheses and then apply the given operations. so we Calculate the values inside the parentheses by multiplying across the bracket:

2² is equal to 4, and sin 3 is a trigonometric function that returns the sine of the angle 3

Therefore, the expression 2X (2² + sin 3) simplifies to:

2X (4 + sin 3)

or

8X + 2X sin 3

where X is an unknown variable and sin 3 is a trigonometric function

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Answer:

Solution

verified

Verified by Toppr

I=∫e

2x

sin3xdx

I=sin3x∫e

2x

dx−∫(

dx

d

​

sin3x∫e

2x

dx)dx

I=sin3x

2

e

2x

​

−∫

2

3

​

cos3xe

2x

dx

I=sin3x

2

e

2x

​

−

2

3

​

∫cos3x∫e

2x

dx−∫(

dx

d

​

cos3x∫e

2x

dx)dx

I=sin3x

2

e

2x

​

−

2

3

​

[

2

cos3xe

2x

​

−∫(−sin3x

2

e

2x

​

)dx]

I=

2

sin3xe

2x

​

−

4

3

​

cos3xe

2x

−

4

3

​

∫sin3xe

2x

dx

I=

2

sin3xe

2x

​

−

4

3

​

cos3xe

2x

−

4

3

​

I

I+

4

3

​

I=

2

sin3xe

2x

​

−

4

3

​

cos3xe

2x

4

7I

​

=

4

2e

2x

sin3x−3cos3xe

2x

​

I=

7

e

2x

​

(2sin3x−3cos3x)

∴∫e

2x

sin3dx=

7

e

2x

​

(2sin3x−3cos3x)

Solve any question of Integrals with:-

Patterns of problems

Patterns of problems

>

Solve :∫e xe e xe e e x

dx

Medium

View solution>Solve:-∫ a 2b 2(a 2 −b 2) 2

Step-by-step explanation:

pls brain

The value of the scale factor for the similar figures is 1/2

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

The similar figures

The corresponsing sides of the similar figures are

Original = 8

New = 4

Using the above as a guide, we have the following:

Scale factor = New /Original

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

Scale factor = 4/8

Evaluate

Scale factor = 1/2

Hence, the scale factor for the similar figures is 1/2

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The correct statement is given as follows:

The function g(t) reveals the market value of the house increases by 3.6% each year.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter b for this problem is given as follows:

b = 1.036.

As the parameter b has an absolute value greater than 1, the function is increasing, with a rate given as follows:

1.036 - 1 = 0.036 = 3.6% a year.

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Using statistics, we can calculate the following percentages:

A. The percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is approximately 49.38%.

B. The percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is approximately 89.15%.

C. The percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is approximately 22.53%.

D. The percentage of workers who receive wages less than Birr 11.00 is approximately 1.22%.

E. The percentage of workers who receive wages more than Birr 12.95 is approximately 0.47%.

These percentages are obtained by calculating the areas under the normal distribution curve using z-scores and the standard normal distribution table.

We are given that the daily wages in a particular industry are normally distributed with a mean of Birr 11.90 and a standard deviation of Birr 0.40.

A. To find the percentage of workers who receive wages between Birr 10.90 and Birr 11.90, we need to calculate the z-scores for both values and use the standard normal distribution table.

z1 = (10.90 - 11.90) / 0.40 = -2.50

z2 = (11.90 - 11.90) / 0.40 = 0

From the standard normal distribution table, the area to the left of z = -2.50 is 0.0062, and the area to the left of z = 0 is 0.5000. Therefore, the percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is:

0.5000 - 0.0062 = 0.4938, or approximately 49.38%.

B. To find the percentage of workers who receive wages between Birr 10.80 and Birr 12.40, we need to calculate the z-scores for both values.

z1 = (10.80 - 11.90) / 0.40 = -2.75

z2 = (12.40 - 11.90) / 0.40 = 1.25

From the standard normal distribution table, the area to the left of z = -2.75 is 0.0029, and the area to the left of z = 1.25 is 0.8944.

Therefore, the percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is:

0.8944 - 0.0029 = 0.8915, or approximately 89.15%.

C. To find the percentage of workers who receive wages between Birr 12.20 and Birr 13.10, we need to calculate the z-scores for both values.

z1 = (12.20 - 11.90) / 0.40 = 0.75

z2 = (13.10 - 11.90) / 0.40 = 3.00

From the standard normal distribution table, the area to the left of z = 0.75 is 0.7734, and the area to the left of z = 3.00 is 0.9987. Therefore, the percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is:

0.9987 - 0.7734 = 0.2253, or approximately 22.53%.

D. To find the percentage of workers who receive wages less than Birr 11.00, we need to calculate the z-score for this value.

z = (11.00 - 11.90) / 0.40 = -2.25

From the standard normal distribution table, the area to the left of z = -2.25 is 0.0122. Therefore, the percentage of workers who receive wages less than Birr 11.00 is approximately:

0.0122, or approximately 1.22%.

E. To find the percentage of workers who receive wages more than Birr 12.95, we need to calculate the z-score for this value.

z = (12.95 - 11.90) / 0.40 = 2.63

From the standard normal distribution table, the area to the left of z = 2.

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_______________________________

_______________________________

Answer:

Therefore, the product of 23.5 and 2.3 is 54.05.

Step-by-step explanation:

To determine the product of 23.5 and 2.3, we can use the following steps:

Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).

   23.5

 x 2.3

 -----

Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.

   23.5

 x 2.3

 -----

    71

Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.

   23.5

 x 2.3

 -----

    71

   470

Add the two partial products together.

   23.5

 x 2.3

 -----

    71

   470

 -----

   54.05

Therefore, the product of 23.5 and 2.3 is 54.05.

The particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

To find when the particle is at rest, we need to find the values of t where the velocity of the particle is zero.

The velocity function is obtained by taking the derivative of the position function: v(t) = x'(t) = x²(t) - 5x(t) + 6

Setting v(t) = 0, we get a quadratic equation in x(t): x²(t) - 5x(t) + 6 = 0. Factoring the quadratic, we get: (x(t) - 2)(x(t) - 3) = 0

Therefore, x(t) = 2 or x(t) = 3. We now need to check which values of t correspond to these values of x(t).

At x(t) = 2, we get: v(t) = x²(t) - 5x(t) + 6 = 4 - 10 + 6 = 0. Thus, the particle is at rest at t = 2. At x(t) = 3, we get: v(t) = x²(t) - 5x(t) + 6 = 9 - 15 + 6 = 0

Thus, the particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

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The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.

In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is

(0.064 + (-0.014))/2 = 0.050/2

= 0.025

Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

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The solution of the graphs of the equations is; )(6, 3 2/3)

A system of equation consists of two or more equations that share the same variables.

The solution of a system of equations obtained graphically can be obtained from the point of intersection of the lines of the graph of the equations

Taking the axis as the lowermost and  leftmost white lines, we get;

The points on the function f are (0, 1), and (9, 5)

The slope is; (5 - 1)/(9 - 0) = 4/9

The y-intercept is; (0, 1)

The equation is; y = (4/9)·x + 1

The equation of the line g is; x = 6

Therefore, the point of intersection is; y = (4/9)×6 + 1 = 8/3 + 1 = 11/3 = 3 2/3

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The total weight of the cards inside the box is approximately 217.6 oz.

Each deck of cards weighs 3.4 oz, and there are 64 decks of cards in the box. Therefore, the total weight of the cards inside the box is 3.4 oz/deck x 64 decks = 217.6 oz. As the answer needs to be rounded to the nearest ounce, we round 217.6 to the nearest ounce, which gives us 218 oz.

However, the question asks for the weight of the cards, which is only accurate to one decimal place. Therefore, we round 217.6 to one decimal place, which gives us 217.6 oz. Hence, the total weight of the cards inside the box is approximately 217.6 oz.

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The advertisement generates the maximum rate of growth of car sales on the first day.

The rate of growth of sales is given by the derivative of N(t) with respect to time t:

dN/dt = 72t

To find the day when the maximum rate of growth of sales occurs, we need to find the value of t that maximizes this expression.

Setting dN/dt = 0, we get:

72t = 0

t = 0

However, since we are interested in finding the day when the maximum rate of growth of sales occurs, we need to consider the second derivative of N(t):

d2N/dt2 = 72

Since this is a positive constant, it tells us that N(t) is a convex function and has a minimum value at t = 0. Therefore, the maximum rate of growth of sales occurs on the day when t = 0, which corresponds to the first day of the advertisement.

Answer: 1. on day 12

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The value of x for the circle is,

⇒ x = 13.2

We have to given that;

In circle Y,

m arc WX = 142°

m ∠WZX = (8x - 35)°

Since, angle WZX is half the measure of arc WX,

Hence, We get;

⇒ (8x - 35)° = 142 / 2

⇒ 8x - 35 = 71

⇒ 8x = 35 + 71

⇒ 8x = 106

⇒ x = 13.2

Thus, The value of x for the circle is,

⇒ x = 13.2

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Answer:

3/y

Step-by-step explanation:

15x÷5xy

15x/5xy....you will cancel x by x and simplify by 5(GCF)

3/y ...... it is the simplify form of the given equetion.

Answer: The given polynomial is -2x³.

a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:

-2x³

b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.

c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.

Step-by-step explanation:

We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.

We can start by listing all the factors of 288:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.

For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.

We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).

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The surface area of the right rectangular prism is 880 cm².

Given Top and bottom measurements of the rectangular prism = 15 cm and 11 cm

The front and back measurements of the rectangular prism = 11cm and 11cm

The two sides measurements of the rectangular prism = 11 cm and 14 cm

To find the surface area of the rectangular prism, we have to substitute the above values in the below equation,

Surface area = (top*bottom) + (front*back) + (sides)

Surface area = (15 cm * 11 cm) + (11 cm * 11 cm) + (11 cm * 14 cm)

Surface area = 330 cm² + 242 cm²  + 308 cm²  

Surface area = 880cm²

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