The casino manager anticipates that, during the next week, 25000 bets of the same type ($1 bet on red color) will be placed at all the (American) roulette tables. Assume independence for the corresponding roulette spins, and that the Central Limit Theorem provides an accurate approximation to the distribution of the casino’s total profit from the 25000 bets. What is the probability that the casino’s total profit will exceed $1000?

The area of the shaded region is,

(3) 100.28 sq. unit

(4) 72 sq.m

(5) 49.09  sq.m

What is the area?

The area of an object is the amount of room it occupies in two dimensions. It is the calculation of how many unit squares entirely encircle the area of a closed figure.

The accepted measure of area is the square unit, which is frequently expressed as square inches, square feet, etc. Most shapes and objects have edges and angles.

(3)

To calculate the area of the semi-circle having a radius of 3 cm,

[tex]A_1=\frac{1}{2} \pi r^2\\A_1=\frac{1}{2} \pi(3)^2\\A_1=14.14 \ \ sq. \ cm[/tex]

To calculate the area of the rectangle having a width of 12 cm and a height of 6 cm,

[tex]A_2=l*w\\A_2=12*6\\A_2=72 \ sq.cm[/tex]

To calculate the area of the semi-circle having a radius of 3 cm,

[tex]A_3=\frac{1}{2} \pi (3)^2\\A_3=14.14[/tex]

The shaded region's size was calculated using

[tex]A=A_1+A_2+A_3\\A=14.14+72+14.14\\A=100.28 \ \ sq.cm[/tex]

(4)

To calculate the area of the rectangle having a width of 13 m and a height of 8 m,

[tex]A_1=l*w\\A_1=13*8\\A_1=104 \ sq.m[/tex]

To calculate the area of an unshaded triangle,

[tex]A_2=\frac{1}{2} *b*h\\A_2=\frac{1}{2} *8*8\\\\A_2=32 \ sq.m[/tex]

The shaded region's size is thus,

[tex]A=A_1-A_2\\A=104-32\\A=72 \ sq.m[/tex]

(5)

The shaded region's size was calculated using

[tex]A=Area \ of \ circle-Area \ of \ square\\A=\pi (6)^2-(8)^2\\A=36\pi -64\\A=49.09 \ sq.m[/tex]

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{257}}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ (\sqrt{257})^2= (x)^2 + (15)^2\implies 257=x^2 + 225 \\\\\\ 32=x^2\implies \sqrt{32}=x\implies 4\sqrt{2}=x\implies 5.66\approx x[/tex]

Answer:

The answer is A: 2500 pi

Step-by-step explanation:

To find the volume of a cylinder use the formula:

π[tex]r^{2}h[/tex]

So we know that the diameter is 10, so radius must be 10/2 or 5.

Now we square 5 to get 25.

Multiply 25 times height which is 100.

So 25 x 100 is equal to 2500

Now multiply the pi or just let it stay like that

The answer is 2500π.

Hope this helps!

(i) The domain of f(x) is all real numbers, since there are no restrictions on the input variable x.

(ii) We have:

f(x) = x^4 - 2x^3

f'(x) = 4x^3 - 6x^2

f''(x) = 12x^2 - 12x

(iii) To find the critical points, we need to solve the equation f'(x) = 0:

4x^3 - 6x^2 = 0

2x^2(2x - 3) = 0

x = 0 or x = 3/2

So the critical points are (0,0) and (3/2, -27/16).

(iv) To determine where f(x) is increasing or decreasing, we need to examine the sign of f'(x) on different intervals. We can make a sign chart for f'(x):

| x | -∞ | 0 | 3/2 | +∞ |

|---------|--------|-------|-------|--------|

| f'(x) | - | 0 | + | + |

From the sign chart, we see that f(x) is decreasing on the interval (-∞, 0) and increasing on the interval (0, 3/2) and (3/2, +∞).

(v) To find the relative extrema, we need to examine the sign of f'(x) around the critical points. We can make a table:

| x | 0- | 0+ | 3/2- | 3/2+ |

|---------|-------|-------|-------|-------|

| f'(x) | - | + | - | + |

| f(x) | 0 | 0 | -27/16| -27/16|

From this table, we see that f(x) has a relative minimum of -27/16 at x = 3/2, and no relative maximum or minimum at x = 0.

(vi) To find the intervals where f(x) is concave up or concave down, we need to examine the sign of f''(x) on different intervals.

We can make a sign chart for f''(x):

| x | -∞ | 0 | 1 | +∞ |

|---------|--------|-------|------|--------|

| f''(x) | + | - | + | + |

From the sign chart, we see that f(x) is concave down on the interval (-∞, 0) and concave up on the intervals (0, 3/2) and (3/2, +∞).

(vii) To find the points of inflection, we need to solve the equation f''(x) = 0:

12x^2 - 12x = 0

12x(x - 1) = 0

x = 0 or x = 1

So the points of inflection are (0,0) and (1, -1).

(viii) To sketch the graph of f(x), we can use the information we have gathered so far.

At x = 0, f(x) has a relative minimum of 0 and is concave down. At x = 3/2, f(x) has a relative minimum of -27/16 and is concave up. The point (1, -1) is a point of inflection.

Based on this information, we can sketch a graph of f(x) that looks like this:

```

|

|

|

|

|

|

|

--------o------------o-------

0 3/2 x-axis

```

The graph is a "U" shape that opens upward, with a relative minimum at (3/2, -27/16) and a point of inflection at (1, -1).

Answer:

165.5

Step-by-step explanation:

Because you have to add them together and then divide

Answer: 4

Step-by-step explanation:  8x11=88.

352=88x

x=352/88

x=4

Check:

11x8x4=352

The 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is (62.49,69.51). So, the Lower and Upper end point are 62.49, 69.51 respectively.

We have a survey of 53 randomly selected homeowners. So,

Sample size, n = 53

Mean spend of home maintenance, μ

= $66 per month

Standard deviations, σ = $ 11 per month

We have to determine the Lower and Upper end point or bound of confidence interval. First we calculate the Z score for 98% of confidence interval. The level of significance, α = 0.02 and α/2 = 0.01, so using distribution table [tex]z_{ \frac{\alpha}{2}} = 2.326[/tex]

Now, Margin of error , [tex]MOE = z_{\frac{\alpha}{2}} ( \frac{\sigma }{\sqrt{}n}) [/tex]

[tex] = 2.326 ( \frac{11}{ \sqrt{}53 })[/tex]

=> E = 3.51

At 98% confidence interval estimate of the population mean is, [tex]\bar x - E < \mu < \bar x + E[/tex]

[tex]66 - 3.51 < \mu < 66 + 3.51[/tex]

=> 62.49 < μ < 69.51

Therefore, Lower end point or bound

= 62.49 and Upper end point or bound

= 69.51.

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The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y2 + 17xy³ = (2x²)xy + (8x)xy + (17xy²) = (2x2)xy + (8x)xy + (17xy²).

An expressiοn in mathematics is a set οf digits, symbοls, and οperatοrs that depicts a quantity οr a relatiοnship between twο quantities. Expressiοns can be straightfοrward, using a single number οr variable, οr cοmplicated, including a variety οf phrases and prοcedures. Expressiοns include things like "3 + 5" and "2x - 4", fοr instance.

The first phrase is straightfοrward and represents the additiοn οf twο numbers, whereas the secοnd expressiοn is mοre intricate and includes a variable, multiplicatiοn, and subtractiοn.

As the expressiοns yοu prοvided lack an equal sign and hence are nοt equatiοns, it is unclear what yοu mean when yοu say that yοu are "sοlving" the prοblem.

Hοwever if yοu wish tο cοmbine οr simplify these expressiοns, yοu can utilize the factοring apprοach.

We can factοr it οut because xy is a cοmmοn factοr thrοughοut the expressiοns:

8x²y² = (8x)xy, while 17xy³ = (17)xy²

We can nοw see that each expressiοn's remaining factοrs are (2x²), (8x), and (17), respectively.

Since these factοrs dο nοt share any cοmmοn factοrs, further simplificatiοn is nοt pοssible. In terms οf the cοmmοn factοr xy.

The cοndensed οr cοmbined fοrm is thus: 2x³y + 8x²y² + 17xy³ = (2x²)xy + (8x)xy + (17xy2) = (2x²)xy + (8x)xy + (17xy2).

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Complete Question

Write this expression  2x³y, 8x²y², 17xy³  in combined form

Step-by-step explanation:

N = 50 000   and  N = 1000 * 2^t

so

50 000 = 1000 2^t      divide both sides of the equation by 1000

50 = 2^t      LOG both sides

log 50 = t log 2

log 50 / log 2 = t = 5.64 hours

Using binomial probability and cumulative distribution function, the probability of having 24 heads is 0.000022

This problem can be solved using the binomial distribution. Let X be the number of heads that occur in 27 tosses of the fair coin. Then X follows a binomial distribution with parameters n = 27 and p = 0.5.

We want to find the probability that at most 24 heads occur, which is equivalent to finding the probability that X is less than or equal to 24. We can use the cumulative distribution function (CDF) of the binomial distribution to calculate this probability:

[tex]P(X \leq 24) = \sum_{k=0}^{24} {27 \choose k} (0.5)^{27}[/tex]

We can use a calculator or software to evaluate this sum, or we can use the complement rule to find the probability of the complement event (i.e., 25 or more heads) and subtract from 1:

[tex]P(X \leq 24) = 1 - P(X \geq 25) = 1 - \sum_{k=25}^{27} {27 \choose k} (0.5)^{27}[/tex]

Using a calculator or software, we find that the probability is approximately 0.000022, which corresponds to answer choice (a).

Therefore, the answer is (a) 0.000022.

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Answer:

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a simple fraction. Therefore 0.6263646 is irrational.

Answer: 625.528.618,26

Step-by-step explanation: The answer will be in the pictures

For function f(t) = 1.25^t, it is an exponential growth.

The percent rate of change per unit t is found by taking the derivative of the function:

f'(t) = ln(1.25) * 1.25^t ≈ 9.2%

Since f'(t) is positive, the function represents exponential growth.

For function g(t)=5^-t:

The percent rate of change per unit t is found by taking the derivative of the function:

g'(t) = -ln(5) * 5^-t ≈ -13.9%

Since g'(t) is negative, the function represents exponential decay.

For function h(t) = 1.20(t/11):

The percent rate of change per unit t is found by taking the derivative of the function:

h'(t) = 1.20/11 ≈ 10.9%

Since h'(t) is positive, the function represents exponential growth.

For function k(t) = 0.63t:

The percent rate of change per unit t is found by taking the derivative of the function:

k'(t) = 0.63 ≈ 63.0%

Since k'(t) is positive, the function represents exponential growth.

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After answering the provided question, we can conclude that Therefore, circle the length of the minor arc AB is approximately 50.9 cm.

A circle appears to be an a double component that is defined as the collection of all points in a jet that are equidistant out from hub. A circle is typically depicted with a capital "O" for the centre and a bottom end "r" for the radius, which represents the distance from where it started to any point on the circle. The formula 2r gives the girth (the distance from the center of the circle), where (pi) seems to be a proportionality steady roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which is the quantity of space inside the circle. To calculate the length of the minor arc AB, we need to first find the central angle that it subtends.

C = 2πr

r = C/(2π)

r = 65/(2π) ≈ 10.34 cm

angle = (arc length / radius) x (180/π)

ADB = 360° - AOB

ADB = 360° - 72° = 288°

angle ADB = (arc length AB / 10.34) x (180/π) = 288°

arc length AB = (288° x 10.34 cm x π) / 180 ≈ 50.9 cm

Therefore, the length of the minor arc AB is approximately 50.9 cm.

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[tex]\tan(68^o )=\cfrac{\stackrel{opposite}{AC}}{\underset{adjacent}{7}}\implies 7\tan(68^o)=AC\implies 17.3\approx AC[/tex]

Make sure your calculator is in Degree mode, as opposed to Gradians or Radians mode.

Quick Clarification:

if your put in your calculator tan(68) in Radians mode, your calculator assumes you meant 68 radians, if in Gradians mode, your calculator assumes you meant 68 Gradians, now, if you have it on Degree mode, your calculator thinks you meant tan(68°).

All trigonometric calculations depend on the mode used, since a circle can be divided in many ways and thus different modes mean, different angles, 68 Radians are extremely different than 68°.

Answer:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Step-by-step explanation:

All of these work. I hope this helps! Pls give brainliest!

Answer:

Your answer would be  

x/3<12

Answer:

9 x 17 is greater than 9 x 15

Step-by-step explanation:

You can tell without finding the product because 17 is greater than 15, and the higher the number you multiply by, the larger the solution will be. I hope this helped :)

I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

Let's assume that the width of the rectangular poster is "x".

According to the problem, the length is 8 more inches than half the width, which can be expressed as:

length = (1/2)x + 8

The area of the poster is given as 40 square inches, so we can write the equation:

Area = length × width

Substituting the values of length and width in terms of "x", we get:

40 = ((1/2)x + 8) × x

Simplifying the equation:

40 = (x^2)/2 + 8x

Multiplying both sides by 2 to eliminate the fraction:

80 = x^2 + 16x

Rearranging the equation in standard quadratic form:

x^2 + 16x - 80 = 0

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 16, and c = -80

x = (-16 ± sqrt(16^2 - 4(1)(-80))) / 2(1)

x = (-16 ± sqrt(736)) / 2

x = (-16 ± 8sqrt(9)) / 2

We can discard the negative solution since width cannot be negative:

x = (-16 + 24) / 2

x = 4

So, the width of the poster is 4 inches.

Using the equation for length:

length = (1/2)x + 8

length = (1/2)(4) + 8

length = 2 + 8

length = 10

Therefore, the dimensions of the poster are 10 inches by 4 inches.

Let us assume that the variables:

d = distance

t = time (in seconds)

~

The question assumes that the horse will move 15 meters every second. Therefore:

d = 15t

IF:

t (time) = 1 seconds, then:

d = 15(1)

d = 15

IF:

t (time) = 2 seconds, then:

d = 15(2)

d = 30

IF:

t (time) = 5 seconds, then:

d = 15(5)

d = 75

~

As you can see, the graphed numbers are much more larger than the numbers that you have already written, and so it is best to change the numbers. Generally the y-axis is used for time (in this case, seconds), whlie the x-axis is used for distance (in this case, meters).

~

For any rectangle ABCD the statement;

1. ∠A ≅ ∠D is always true

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true

A rectangle is a quadrilateral that has two pairs of parallel and congruent opposite sides and four right angles (90 degree angles). A rectangle is a special case of a parallelogram.

1. ∠A ≅ ∠D

The above statement is always true for rectangles. In Euclidean geometry, by the definition of a rectangle, the four interior angles are right angles, which means m∠A = m∠B = m∠C = m∠D = 90°, therefore; ∠A ≅ ∠B ≅ ∠C ≅ ∠D.

The statement; ∠A ≅ ∠D, according to the above expression and the transitive property of congruence, is always true.

Please find attached the drawing of the rectangle, created with MS Word that can be used to illustrate the congruence of the angles with the angle marks indicating perpendicular sides, forming 90° angles, which indicates that the angles are congruent.

   A_____[tex]{}[/tex]_____B

    |            [tex]{}[/tex]          |

    |           [tex]{}[/tex]           |

    |          [tex]{}[/tex]            |

    |          [tex]{}[/tex]            |

    |           [tex]{}[/tex]           |

    |____[tex]{}[/tex]______|

    D                     [tex]{}[/tex] C

2. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]

The above statement is sometimes true for rectangles. The definition of a rectangle indicates that the two pairs of opposite sides are congruent. In particular, [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are congruent, aa well as sides [tex]\overline{BC}[/tex] and [tex]\overline{AD}[/tex] are also congruent. The sides [tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are congruent if or when the rectangle is a square, therefore, the statement [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is sometimes true.

Please find attached the drawings created with MS Word which illustrates when [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] and when [tex]\overline{BC}[/tex] [tex]\ncong[/tex] [tex]\overline{CD}[/tex]

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Answer:a=9  b=27.5  c=41.25

Step-by-step explanation:

the internet

Using calculus, we can find the functions of the inverse functions as follows:

a. f(x) = x/5.

b. f(x) = ∛ 2x

c. f(x) = x - 10

d. f(x) = 2x/3 - 17

One of the most crucial areas of mathematics that addresses ongoing change is known as calculus. Calculus is primarily built on the two ideas of derivatives and integrals. A function's integral measures the area under its curve, whereas a function's derivative measures its rate of change.

Whereas the integral adds together a function's discrete values over a range of values, the derivative explains the function at a particular point.

Here in the question,

The inverse of the functions is:

f(x) = x/5.

f(x) = ∛ 2x

f(x) = x - 10

f(x) = 2x/3 - 17

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The values of Mean = 6.3 and Median = 6

A dot plot is a type of data visualization that displays data points as dots on a number line. Each dot represents a single data point and is placed at the corresponding value on the number line.

Here, each dot corresponds to a particular value in the data set, below diagram.

Mean: The mean is calculated by dividing the total value of all the data sets by the total number of data sets.

You can figure out the total as follows:

0 (1) = 0            4 (3) = 12             5(8) = 40          6(3) = 18

7(1) = 7              8(5) = 40             9(2) = 18           10 (3) = 30

Sum = 0+12+40+18+7+40+18+30 = 165

Number of data set = 26

⇒Mean = 165/26

             = 6.346 ≈ 6.3               (nearest tenth place)

⇒Median: The center value in the data collection is known as the median. Since there are 26 data points total, the middle value is located between data points 13 and 14. The median value will be determined by averaging the 13th and 14th data points.

So, the 13th and 14th values both are 6.

Therefore, median = {6+6} ÷ 2 = 12/2 = 6

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Complete Question-

The appropriate trend lines for the scatter plot include the following: B. scatter plot B.

In Mathematics and Statistics, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably infer and logically deduce that scatter plot B represent the line of best fit (trend line) because it is in a linear pattern, with equal number of data points on both sides of the line.

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Answer: 4 cans of tuna

Step-by-step explanation:

5 1/2 x 4 = 22

Answer:

To find which tuna is a better deal, divide the cost by the number of ounces of tuna you are getting to get the cost per ounce.

$0.90/5  = $0.18 per ounce

$2.40/12 = $0.20 per ounce

Since the 5-ounce can of tuna has a cheaper unit rate price, meaning you are getting a better value, makes this the best option. I hope this was helpful and have a great day! :)

Step-by-step explanation:

The fraction of the production run that was defective is 2/25.

What is the fraction?

A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities. It is expressed as one integer divided by another integer, with a horizontal line separating the two numbers. The number above the line is called the numerator and the number below the line is called the denominator.

The fraction of a production run that was defective is 0.08. This can be written as a fraction with a numerator of 0.08 and a denominator of 1:

0.08/1

To express this fraction with a denominator other than 1, we can multiply both the numerator and denominator by the same number, without changing the value of the fraction. For example, we can multiply by 100 to get:

(0.08/1) * (100/100) = 8/100

Simplifying this fraction gives:

8/100 = 2/25

Therefore, the fraction of the production run that was defective is 2/25.

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We need to add 6 mL of the 14% solution to the 8 mL of the 7% solution to obtain a 10% medication solution.

An equation is a mathematical statement that indicates that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to describe relationships between different variables, to solve problems, and to make predictions.

Let's call the number of milliliters of the 14% solution we need to add "x".

First, let's figure out how much medication is in the 8 mL of the 7% solution. Since the solution is 7%, we know that 7% of the solution is medication. We can convert that to milliliters by multiplying by the total volume of the solution:

0.07 x 8 mL = 0.56 mL of medication in the 7% solution

Next, let's figure out how much medication we want in the final solution. We want a 10% solution, so we want 10% of the total volume to be medication. We can write that as:

0.10 (x + 8 mL) = 0.1x + 0.8 mL

Now we can set up an equation based on the amount of medication in the 14% solution we add and the amount of medication in the final solution:

0.14x + 0.56 mL = 0.1x + 0.8 mL

Simplifying the equation, we get:

0.04x = 0.24 mL

Dividing both sides by 0.04, we get:

x = 6 mL

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The inequality that has the solutions represented by the graph?

2x - 5 > 3

The solution of the inequality represented by the graph is x > 4

The solution of the given inequalities are:

5 - x > 4;

solution: x < 1

2x + 1 ≥ 9;

solution: x ≥ 4

2x - 5 > 3

solution: x > 4

6x - 7 > 5

solution: x > 3

2. Considering the inequality statement given:

n ≤ 3: This is a solution.

If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number less than 3, the inequality will still hold.

3 ≥ n: This is also a solution.

If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number greater than 3, the inequality will still hold.

n ≤ 8: This is a solution.

If we substitute n with 8, we get 5 + 2(8) ≤ 11, which simplifies to 21 ≤ 11, which is false. But if we substitute n with any number less than or equal to 8, the inequality will still hold.

3 ≥ n: This is the same as the second representation, so it is also a solution.

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Complete question:

Which inequality has solutions represented by the graph?

5 - x > 4

2x + 1 ≥ 9

2x - 5 > 3

6x - 7 > 5

Consider the inequality Five plus two times a number n is less than or equal to eleven. Indicate whether each representation is or is not a solution.

n ≤ 3

3 ≥ n

n ≤ 8

3 ≥ n

There are 2,000 pounds in one ton. Therefore, to convert 25 tons to pounds, we can multiply 25 by 2,000:

25 tons x 2,000 pounds/ton = 50,000 pounds

So there are 50,000 pounds in 25 tons.