Which sign makes the statement true?

16
1
16

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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Answer:

The expression is repeated multiplication form is 5.

The expression as power is 9.

Step-by-step explanation:

Answer:

The expression as powers is 5^9

Answer:

Mrs. Habib will have 22.25 feet of border left after she puts border around the board.

Step-by-step explanation:

You must find the perimeter of the board and subtract it from the amount of border she has to find how much she will have left after she uses it. The formula for perimeter is \(P=2(l+w)\), where \(l=\) the length of the board, and \(w=\) the width of the board. You will add those together and multiply them by 2 because there are 4 sides to a rectangle. That means this equation will look like:

\(P=2(8.25+3.75)\)

Now you can just solve for the perimeter.

\(P=2(12)\)

\(P=24\)

The perimeter is 24 feet. That means it will take 24 feet of border to cover her board. In order to find out how much she'll have left over, just subtract 24 from the total amount of border she has.

\(46.25-24=22.25\)

Therefore Mrs. Habib will have 22.25 feet of border left over after she covers the bulletin board.

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer:

35.97

Step-by-step explanation:

113 divided by pie (3.14)

Hexadecimal and binary are two numbering systems that are commonly used in computing. Binary is a base-2 numbering system, which means it uses only two digits, 0 and 1, to represent all numbers. Hexadecimal, on the other hand, is a base-16 numbering system, which means it uses 16 digits, from 0 to 9 and A to F, to represent numbers.

One hexadecimal digit can represent 16 different values, while one binary digit can represent only two values (0 or 1). This means that one hexadecimal digit can represent 16 times as many values as one binary digit.

To understand this better, let's consider an example. The binary number 1111 is equivalent to the hexadecimal number F. In binary, 1111 can represent only one value, which is 15 in decimal. However, in hexadecimal, the digit F can represent 16 different values, from 0 to 15 in decimal.

Therefore, using hexadecimal notation can be more efficient and compact than using binary notation, especially when dealing with large numbers. In addition, hexadecimal is often used in computing to represent memory addresses, color codes, and other values that need to be represented in a compact and easily readable format.

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Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Three consecutive even integers can be written with difference of two.

The even integers are defined as the numbers that are completely divisible by two. The complete division means that the result of division will be zero. The even integers are always present after a gap of one number in between.

This means that there is a difference of two numbers between integers. Firstly of all, the first even number is two. Following it four. There is a gap of number that is three. Hence, to find the consecutive even integers, add number two to the number.

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The exponential form of the equation -5 = log₁ 3,125 can be found by using the definition of logarithms, which states that logₐ b = c if and only if aᶜ = b.

In this case, we want to solve for the base and exponent, so we can rewrite the equation as:

10⁻⁵ = 3,125

To get rid of the negative exponent, we can take the reciprocal of both sides:

10⁵ = 1 / 3,125

Then we can simplify by finding a common factor of 3 and 10:

10⁵ = 1 / (5⁵ * 2⁵)

Finally, we can write the exponential form as:

(2 * 5)⁵ = 3⁻⁵

So the exponential form of the equation -5 = log₁ 3,125 is 2⁵ * 5⁵ = 1 / 3⁵.

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Answer:

-10

Step-by-step explanation:

We can figure out that the number line is by four.

How?

There is one line between 10 and 2. Sooo:

10 - 2 = 8

8 / 2 = 4

If we check it (10 - 4 - 4 = 2) it checks out!

Using this information we can figure out what the blue dot is.

2 (given) - 4 (incriments of number line) - 4 - 4 = - 10

There is our answer, -10!

Answer:

I Know it is B trust me

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The volume of the solid generated by revolving the shaded region about the y-axis is 12π(√3 - 1) cubic units.

We have,

We can use the disk method to find the volume of the solid generated by revolving the shaded region about the y-axis.

The volume of each disk is π(radius)^2(height), where the radius is the distance from the y-axis to the curve and the height is the thickness of the disk.

The distance from the y-axis to the curve at y is given by x = 6 tan ((π/3)y). Therefore, the radius of each disk is 6 tan ((π/3)y).

The thickness of each disk is dy.

Thus, the volume of the solid is given by:

V = \(\int\limits^1_0\) π(6 tan((π/3)y))² dy

Simplifying, we get:

V = 36π \(\int\limits^1_0\) tan²((π/3)y) dy

Using the identity tan²θ + 1 = sec²θ, we have:

V = 36π \(\int\limits^1_0\) (sec²((π/3)y) - 1) dy

= 36π (tan(π/3) - 1)

= 12π (√3 - 1)

Therefore,

The volume of the solid generated by revolving the shaded region about the y-axis is 12π(√3 - 1) cubic units.

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Answer with Step-by-step explanation:

The time a vehicle is left parked is not a function of the cost of parking because the two variables are not directly related. The cost of parking in this situation depends on how long a vehicle is parked, while the opposite is not true.

This is because the cost of parking is based on an hourly rate, and the maximum cost is capped at $12. So, regardless of how long a car is parked, the maximum cost will always be $12. For example, a car parked for 1 hour will cost $3, a car parked for 4 hours will cost $12, and a car parked for 6 hours will still only cost $12.

On the other hand, the amount of time a car is parked is not limited by the parking cost. A driver may choose to park their car for any length of time within the maximum limit of the parking lot. So, the amount of time parked is not dependent on the cost but rather on the driver's choice and parking lot regulations.

As a result, there is no direct correlation between the length of time a car is parked and the cost of parking, and the length of time a car is parked is not a function of the cost of parking.

Answer:

B. 3.14(24^2)(2.5)

Step-by-step explanation:

24 is the radius and 2.5 is the height. plug it into 3.14*r^2*h

Answer:

x = 0

Step-by-step explanation:

a line perpendicular to x axis has always the same x

x = 0

Answer:

1. a = 5, b = 8

2. d = 2

Step-by-step explanation:

1. The sum of two adjacent angles of a parallelogram is 180 degrees

Hence,

\(14a-5+115 = 180 \\14a = 180 -110\\a = 70/14\\a = 5\)

Like wise

\(8b+1+115 = 180 \\8b = 180 -116\\8b = 64\\b = 8\)

2.

The two intersecting diagonals cut each other into equal half

\(5d + 1 = 3d + 5\\2d = 4\\d = 2\)

Answer:

Bacteria A has diameter size of 1 micrometer = 1 × 10⁻⁶ m

a) B is 1× 10⁻³ size of A:

b) 1 nanometer = 1 × 10⁻⁹ m

Answer:

25%

Step-by-step explanation:

The Average Sample Range in a Sample Range Chart, used for monitoring process variability, is always an integer. The given statement is true.

What is a sample range chart?

A sample range chart is a type of control chart that is used to track the variability of process data that has been collected in subgroups.

The sample range is defined as the difference between the highest and lowest values in the subgroup.

This chart is used to monitor the variability of a process over time.

When we consider a sample range chart, the average sample range is calculated by adding up all the sample ranges and then dividing the total by the number of subgroups.

The average range is an estimator of the process variation or the standard deviation.

Since the sample range is an integer, and the average range is calculated by taking the mean of the sample ranges, the value of the average sample range need must be an integer.

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Step-by-step explanation:

can't you see it ?

the goal is always to get the variable on one side, and everything else on the other side.

1. step : add 1 to both sides to get rid of the free constant "-1" on the side of the variable.

2. step : multiply both sides by -2 to get rid of the "-1/2" factor that binds 5x and -8 into one term.

3. step : add 8 to both sides to get rid of the now free constant "-8" on the side of the variable.

4. step : divide both sides by 5 to finally have only the variable on the left side giving us the solution of the equation.

remember, we always have to do every change on both sides of the equation to keep the original balance and information of the equation.

Answer:

Add 1 to both sides.

Multiply both sides by -2.

Add 8 to both sides.

Divide both sides by 5.

Step-by-step explanation:

Step 1

\(-\dfrac{1}{2}(5x-8)-1=6\quad \quad \textsf{Write the equation.}\)

Step 2

\(-\dfrac{1}{2}(5x-8)=7 \quad \quad \textsf{Add 1 to both sides.}\)

This is called the Addition Property of Equality.  When the same number is added to both sides of an equation, the two sides remain equal.

\(\implies -\dfrac{1}{2}(5x-8)-1+1=6+1\)

\(\implies -\dfrac{1}{2}(5x-8)=7\)

Step 3

\(5x-8=-14 \quad \quad \textsf{Multiply both sides by -2.}\)

This is called the Multiplication Property of Equality.  When both sides of an equation are multiplied by the same number, the two sides remain equal.

\(\implies -2 \cdot -\dfrac{1}{2}(5x-8)=-2 \cdot 7\)

\(\implies 5x-8=-14\)

Step 4

\(5x=-6 \quad \quad \textsf{Add 8 to both sides.}\)

This is called the Addition Property of Equality.  When the same number is added to both sides of an equation, the two sides remain equal.

\(\implies 5x-8+8=-14+8\)

\(\implies 5x=-6\)

Step 5

\(x=-\dfrac{6}{5} \quad \quad \textsf{Divide both sides by 5.}\)

This is called the Division Property of Equality.  When both sides of an equation are divided by the same number, the two sides remain equal.

\(\implies \dfrac{5x}{5}=\dfrac{-6}{5}\)

\(\implies x=\dfrac{-6}{5}\)

Conclusion

\(\begin{aligned}-\dfrac{1}{2}(5x-8)-1 & =6 & \quad \quad& \textsf{Write the equation.}\\\\-\dfrac{1}{2}(5x-8) & =7 & & \boxed{\textsf{Add 1 to both sides.}}\\\\5x-8 & =-14 & & \boxed{\textsf{Multiply both sides by -2.}}\\\\5x & =-6 & & \boxed{\textsf{Add 8 to both sides.}}\\\\x & =-\dfrac{6}{5} & & \boxed{\textsf{Divide both sides by 5.}}\\\end{aligned}\)

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Given: The probability is 0.35 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In nine traffic fatalities. We need to find the probability that the number, Y, which isa. exactly three,b. at least three, at most three,between two and four, inclusive.

The distribution is binomial as there are a fixed number of trials, each of which results in success or failure. And also we have only two outcomes for each trial.Solution:a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is:

\(P(Y = 3) = {9 \choose 3}(0.35)^3(1-0.35)^{9-3}\)\(P(Y = 3) = 0.3004\)

b. At least three fatalities:

\(P(Y \geq 3) = \sum_{i=3}^9 {9 \choose i}(0.35)^i(1-0.35)^{9-i}\)\(P(Y \geq 3) = 0.5945\)

At most three fatalities:

\(P(Y \leq 3) = \sum_{i=0}^3 {9 \choose i}(0.35)^i(1-0.35)^{9-i}\)\(P(Y \leq 3) = 0.1628\)

Between two and four, inclusive:

\(P(2 \leq Y \leq 4) = \sum_{i=2}^4 {9 \choose i}(0.35)^i(1-0.35)^{9-i}\)\(P(2 \leq Y \leq 4) = 0.4352\)c.

The mean of the random variable Y is:

\(\mu = np = (9)(0.35) = 3.15\)

Interpretation: The average number of fatalities caused by intoxicated or alcohol-impaired driver or nonoccupant in 9 traffic fatalities is 3.15.d. The standard deviation of the random variable Y is:

\(\sigma = \sqrt{np(1-p)}\)\(\sigma = \sqrt{(9)(0.35)(0.65)} = 1.3299\)

Therefore, CE + a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is 0.3004. The probability that at least three fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is 0.5945. The probability that at most three fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is 0.1628. The probability that between two and four fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is 0.4352.

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The ratio of the lengths of corresponding sides in triangles ABC and RST is determined by comparing the lengths of their corresponding sides.

In order to determine the ratio of the lengths of corresponding sides in triangles ABC and RST, we need the specific lengths of the sides in both triangles. Without that information, we cannot provide a definitive ratio.

However, in general, the ratio of corresponding sides in similar triangles remains constant. If triangles ABC and RST are similar triangles, then the ratio of any corresponding side lengths in these triangles will be the same. This means that if, for example, the length of side AB in triangle ABC is twice the length of side RS in triangle RST, then the ratio of AB to RS is 2:1. Similarly, the ratio of the lengths of other corresponding sides can be determined by comparing their lengths.

Without additional information about the lengths of sides in triangles ABC and RST, we cannot provide a specific ratio. It is essential to have the specific lengths of corresponding sides in both triangles to determine the ratio accurately.

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Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:

Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.

Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.

Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.

Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.

Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.

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Answer:

use a standard digital bathroom scale.

Step-by-step explanation:

Answer:

Step-by-step explanation:

20 oz walnuts = 20/25 = 0.8 ounces of walnuts per bag. / bag

11.2 oz of almonds = 11.2 / 25 = 0.448 ounces of almonds / bag

28.3 oz of cashews = 28.3 / 25 = 1.132 oz of cashews / bag

Step-by-step explanation:

x=20

x aris is stright .right?

Answer:

16xy

Step-by-step explanation:

Multiply both together to get 16xy.

The value of x in the polygon is 30

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

Exterior angles = x, 2x, 4x, 5x, 8x, and 10x.

The sum of exterior angles of a polygon is 360

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

x + 2x + 4x + 5x + 8x + 10x = 360

Evaluate the like terms

30x = 360

So, we have

x = 12

Hence, the value of x is 12

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The required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11.\

A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.

According to given question we have

In the analysis of the given options, the most likely answer to this question is A rewards customer earns 2 free ounces of yogurt because total amount paid for 10 ounces and 12 ounces is the same.

Also 9 dollars spent at 20 ounces.

Therefore, the required statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt is earns 2 free ounces.

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Answer:

A

Step-by-step explanation:

A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.