A trip to St. Louis from Atlanta will take 7¾ hours. Assuming you're two-thirds of the way there, how much longer, in hours, will the trip take?

The simplified form of the expression (8h + 7) - (7h + 6) is h + 1. We subtract this by using the distributive law.

An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.) that represents a mathematical quantity or value. Expressions can be simple, consisting of just a single number or variable, or they can be complex, involving multiple numbers, variables, and operations.

The distributive law, also known as the distributive property or distributive property of multiplication over addition, is a fundamental property of arithmetic and algebra that allows the distribution of a multiplication operation over an addition or subtraction operation.

The distributive law states that for any three numbers a, b, and c:

a × (b + c) = (a × b) + (a × c)

According to the given information:

To subtract (8h + 7) - (7h + 6), we can use the distributive property of multiplication over addition to simplify the expression.

(8h + 7) - (7h + 6)

= 8h + 7 - 7h - 6 (Applying the distributive property)

Now, we can combine like terms by adding or subtracting coefficients of the same variable:

= (8h - 7h) + (7 - 6) (Grouping-like terms)

= h + 1 (Simplifying)

So, the simplified form of the expression (8h + 7) - (7h + 6) is h + 1.

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The composite function g(h(8)) when evaluated is 94.

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

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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Answer:

Y= (x+4)(x+4)-21

Step-by-step explanation:

If you are factoring It out:

Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21

Let me know if it is incorrect!

-a friendly 8th grader

Answer: 100 times

Step-by-step explanation:

The cube is numbered 1 to 6. That is, 1, 2, 3, 4, 5, 6. That means there are 6 possible outcomes for each toss. But there are 2 outcomes we want, 5 and 6 (greater than 4).

So, for each toss, there is a probability of 2/6 = 1/3 that this will occur.

With 300 tosses, we can say that this will probably happen 300 times. This means that it will happen

1/3 * 300 times = 100 times.

Therefore, we can predict we will get a 5 or 6 about 100 times.

The total cost of sending 97 text messages is $9.70

A unit cost is defined as the total expenditure incurred by a specific company to produce, store, and sell one unit of a specific product or service. Unit costs are also synonymous with cost of goods sold (COGS). This accounting measure also involves all of the fixed and variable costs associated with the production of a good or service.

Now, we are told that It cost Chile 17.70$ to send 177 text messages. Thus:

Unit cost of message = 17.70/177 = $0.1 per message

Thus:

Cost of 97 text messages = 97 * 0.1 = $9.7

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The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

A linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

given the slope m = -3/5 and y intercept b = 6, we can write the equation as;

y = (-3/5)x + 6

y = -3x/5 + 6.

Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

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Therefore, it takes four days for the rain gauge to be free of water. The answer is option D, day 7.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation usually contains one or more variables, which are symbols that represent unknown or varying quantities. The values of the variables that satisfy the equation are called the solutions of the equation.

Here,

Let's start by finding out how much water is left in the gauge after one day of evaporation and addition. If the rain gauge had 10 inches of water at the start of the week, then after one day:

4 inches of water would have evaporated, leaving 10 - 4 = 6 inches of water.

2 more inches of rain would have fallen, bringing the total to 6 + 2 = 8 inches of water.

So after one day, the rain gauge has 8 inches of water.

Now we need to repeat this process until there is no water left in the gauge.

After the second day:

4 more inches of water would have evaporated, leaving 8 - 4 = 4 inches of water.

2 more inches of rain would have fallen, bringing the total to 4 + 2 = 6 inches of water.

After the third day:

4 more inches of water would have evaporated, leaving 6 - 4 = 2 inches of water.

2 more inches of rain would have fallen, bringing the total to 2 + 2 = 4 inches of water.

After the fourth day:

4 more inches of water would have evaporated, leaving 4 - 4 = 0 inches of water.

2 more inches of rain would have fallen, but it would not have filled the gauge since it was already empty.

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Answer:

(1/256)

Step-by-step explanation:

[tex](\frac{1}{4})^{4} = \frac{1^{4} }{4^{4} } = \frac{1}{256}[/tex]

Using laws of exponents I distributed the exponent to the fraction and solved.

Answer:

Step-by-step:

1.The probability of picking a brown ball can be calculated as:

Probability of picking a brown ball = Number of brown balls / Total number of balls

Number of brown balls = 25

Total number of balls = 13 + 25 = 38

Probability of picking a brown ball = 25/38

Probability of picking a brown ball is approximately 0.658 or 65.8%

Therefore, the probability of Jaide picking a brown ball from the jar is approximately 0.658 or 65.8%.

2.There are four kings in a pack of 52 cards (one king for each suit). Therefore, the probability of drawing a king from a pack of 52 cards can be calculated as:

Probability of drawing a king = Number of kings / Total number of cards

Number of kings = 4

Total number of cards = 52

Probability of drawing a king = 4/52

Probability of drawing a king is approximately 0.077 or 7.7%

Therefore, the probability of getting a king when drawing a card at random from a pack of 52 cards is approximately 0.077 or 7.7%.

Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.

In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.

To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:

Linearity: The relationship between the dependent variable and the independent variables must be linear.

Independence: The observations must be independent of each other.

Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.

Normality: The residuals should be normally distributed.

No multicollinearity: The independent variables should not be highly correlated with each other.

If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.

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The true statement is that An integer programming solution can be better than the linear programming solution to the same problem. So, option(b) is right one.

In integer linear programming is harder than linear programming, because the branch-and–bound method requires many iterations of the simplex method, integer programming problems, So, option(a) is false one.

Hence, required answer is option(b).

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Complete question :

which of the following statements is true? group of answer choices

a) in general, it is no more difficult to solve an integer programming model than a linear programming one.

b) an integer programming solution is better than the linear programming solution to the same problem rounding does not necessarily.

c) provide feasible solutions and feasible solutions from rounding are not necessarily optimal.

d) all of these answers

In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.

In 2011, the total number of cars produced in the world was 59.9 million.

In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.

Let us say in 2016 the total number of cars produced in the world was N million.

Therefore, by expressing the given problem in a linear equation we get,

Total number produced in 2016, N = 59.9 + (21% of 59.9 )     in millions

⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex]     ( in millions )

= 59.9 + 12.579    ( in millions )

= 72.479  ( in millions )

= 72 millions ( rounded to the nearest whole number)

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Answer: The hypotheses of this test are:

Null hypothesis: The average weight of the product on the line is equal to the specified value of 16 ounces.

Alternative hypothesis: The average weight of the product on the line is different from the specified value of 16 ounces.

Step-by-step explanation:

The situation that represents a proportional relationship is " Renting a movie for $5 per day"

Proportional relationships are relationships between two variables where their ratios are equivalent.

For example, A student reads 5 novels per 2days is a statement that shows the relationship between the Novels read and the number of days. This means that 10 novels will be read in 4 days.

In general a proportion relationship should obey,

change in y/ change in x= constant. The constant is the slope.

Therefore the statement that best explain a proportional relationship is " Renting a movie for $5 per day"

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To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms

2. Use the given information

3. Determine when the object is stopped

4. Calculate the distance traveled

Identify the terms:

For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:

Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:

To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.

Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:

Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.

We can use the equation s = ut + 0.5at²,

where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.

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The square root of the number 23 is 5 after using the division method the answer is 25.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 23 which is a real number and positive number.

As we know we can find the square root of a positive numbers only, the square root of a negative number cannot exist

The square root of the number 23 = [tex]\sqrt{23}[/tex]

The sign √ is a radical sign.

After using the division method:

[tex]\sqrt{23} = 4.7958[/tex]

After reducing the number up to two decimal places:

[tex]= 4.79[/tex]

Rounding the above number to the whole:

[tex]= 4.79 \thickapprox 5[/tex]

[tex]5\times5 = 25[/tex]

Thus, the square root of the number 23 is 5 after using the division method the answer is 25.

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The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

In mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.

To translate the triangle by a vector (x, y), we use the following transformation matrix:

|1 0 x|

|0 1 y|

|0 0 1|

For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:

|1 0 -2|

|0 1 4 |

|0 0 1 |

To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:

| -1 | | 1 0 -2 | | -3 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

| 0 | | 1 0 -2 | | -2 |

| -4 | -> | 0 1 4 | = | 0 |

| 1 | | 0 0 1 | | 1 |

| 3 | | 1 0 -2 | | 1 |

| 3 | -> | 0 1 4 | = | 7 |

| 1 | | 0 0 1 | | 1 |

So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:

|-3 -2 1 |

| 7 0 7 |

| 1 1 1 |

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The area of the circle rounded of to the nearest tenth having radius 9 inches is 254.3 square inches.

Hence option d is the correct answer.

The radius of a circle is, say r = 9 inches

The formula of calculating area of a circle is,

Area = πr² (square units)

= π(9)² square inches

= 81π square inches

Let us take π= 3.14 (approximated up to two decimal places).

Thus, area of the circle = 81(3.14) square inches = 254.34 square inches

Rounding of a number is a process of approximating the original number to some decimal points resulting the original number to shorten up for more explicit representation.

Rounding of a number to its nearest tenth gives the original number to round of to one decimal place.

Here Area =  254.34 square inches is rounded of to the nearest tenth is 254.3 square  inches, since the digit after the first decimal place of the original number is lesser than 5 then we round down the number by decreasing the previous place value digit by 1.

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Answer:

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds

The area of the irregular polygon is equal to 30.5 square units.

In this problem we find the representation of an irregular pentagon, that is, a polygon of five sides of different length. Whose area can be found by adding the areas of rectangles and triangles:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the irregular polygon:

A = 0.5 · 1 · 4 + 0.5 · 3 · 2 + 2 · 4 + 0.5 · 3 · 2 + 3 · 4 + 0.5 · 5 · 1

A = 2 + 3 + 8 + 3 + 12 + 2.5

A = 30.5

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Her current checking account balance is $2,641.50.

To find Carrington's current checking account balance, we need to add up all the deposits and subtract all the withdrawals from her starting balance.

Starting balance = $800

Deposits = $2,800

Withdrawals = $310 + $88 + $35.50 + $150 + $375 = $958.50

Therefore, Carrington's current checking account balance is:

$800 + $2,800 - $958.50 = $2,641.50

Her current checking account balance is $2,641.50.

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The height of the cone is approximately 1.5 cm.

Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.

The volume of the cone is given as:

V = (1/3)πr²h

Rearranging the equation to isolate h we get:

3V = πr²h

h = (3V)/(πr²)

Now, for  volume

of 48 cm³ and a base with a radius of 4 cm we have:

h = (3(48))/(π(4)²)

h ≈ 1.5 cm

Hence, the height of the cone is approximately 1.5 cm.

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The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.

We can use the formula for the surface area of a cone:

Surface Area = πr² + πr√(r² + h²)

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:

Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)

Surface Area = π(20.25) + π(4.5)√(436.25)

Surface Area = 353.43 millimeters²

Therefore, the surface area of the cone is approximately 353.43 square millimeters.

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Answer: 22,050.

Step-by-step explanation: The number of individuals who went on Summer Visit B is given within the moment push of lattice S as 150.

The fetched per individual for Summer Tour B is given within the moment push of matrix T as $145.

Hence, the whole income created from Summer Visit B is:

150 individuals × $145 per individual = $21,750

The area of the shaded region is 192 m².

We have,

(g)

The shaded region.

= Area of the rectangle - Area of the triangle

So,

Length = 16 m

Width = 18 m

Area of the rectangle.

= 16 x 18

= 288 m²

And,

Base² + 16² = 20²

Base² = 400 - 256

Base = √144 = 12

So,

Area of the triangle.

= 1/2 x base x height

= 1/2 x 12 x 16

= 96

Now,

The shaded region.

= Area of the rectangle - Area of the triangle

= 288 - 96

= 192 m²

Thus,

The area of the shaded region is 192 m².

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Answer:

[tex]y = {1.5}^{x} [/tex]

[tex] ln(y) = ln( {1.5}^{x} ) [/tex]

[tex] ln(y) = x ln(1.5) [/tex]

[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]

[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]

Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.

To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.

1 liter = 1000 milliliters

Therefore, Ann drinks 1000 milliliters of water in total for the day.

To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.

1000 milliliters / 8 hours = 125 milliliters per hour

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Answer:

"I think of a number, take away 1 and multiply the result by 3" can be written algebraically as:

3(x - 1)

where x is the unknown number that is being thought of.

We subtract 1 from x because the problem asks to "take away 1", and then we multiply the result by 3 because the problem asks to "multiply the result by 3".

So the expression 3(x - 1) represents the result of thinking of a number, taking away 1, and multiplying the result by 3.

Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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