using equations : two sum of two is 15.3 times the smaller number is 5 more the larger number.. Calculate the 2 numbers (hint : Let the smaller number be x)

Answer: He walked 2.76 more miles.

Step-by-step explanation: In this problem, we would subtract James' miles from Richard's miles to get the answer.

15.74 miles - 12.98 miles = 2.76 miles.

Therefore, Richard walked 2.76 more miles than James.

Without knowing the total cost of the wallpaper or the dimensions of the rectangular prism, it is not possible to determine the cost of the wallpaper per square foot.

To calculate the cost per square foot, we would need to know the total cost of the wallpaper and the total area covered by the wallpaper. Since we do not have this information, we cannot determine the cost per square foot.

In summary, the cost of the wallpaper per square foot cannot be determined without knowing the total cost of the wallpaper and the dimensions of the rectangular prism that Lamar built.

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Answer:

Step-by-step explanation:

b

The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

We have to given that;

To find the set of side lengths can be used to construct a triangle.

Now, We know that;

The sum of two side of a triangle is always greater than third side.

Hence, We can check all options as;

⇒ 3, 4, 9

Since, 3 + 4 = 7 < 9

Hence, It does not form a triangle.

⇒ 3, 5, 7

Since, 3 + 5 = 8 > 7

Hence, It form a triangle.

⇒ 3,5, 8

Since, 3 + 5 = 8 = 8

Hence, It does not form a triangle.

⇒ 2, 6, 8

Since, 2 + 6 = 8 = 8

Hence, It does not form a triangle.

Thus, The value of set of side lengths can be used to construct a triangle are,

⇒ 3, 5, 7

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The height of the 1-cup measuring cylinder with a radius of 2 inches is approximately 1.1508 inches.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

We know that 1 cup is equal to 14.4375 in^3. So, we can set up an equation:

14.4375 = π(2)^2h

Simplifying, we get:

14.4375 = 4πh

Dividing by 4π, we get:

h = 14.4375 / (4π) ≈ 1.1508 inches

Therefore, the height of the 1-cup measuring cylinder with a radius of 2 inches is approximately 1.1508 inches.

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Answer:

4x-6

Step-by-step explanation:

when it ask for less than, we are subtracting. subtract 6 from 4x and you have your expression.

have a great day and thx for your inquiry :)

In a net of a solid, the number of faces meeting at each vertex can be determined by examining the net and counting the number of lines that meet at each vertex. Each line corresponds to an edge of a face, so the number of lines meeting at a vertex is equal to the number of faces meeting at that vertex.

For example, if we consider a cube net, we can see that three faces meet at each vertex. Therefore, a cube has three faces meeting at each vertex.

Similarly, for other solids, we can count the number of faces meeting at each vertex by examining the net. For example, for a regular tetrahedron, four faces meet at each vertex; for a regular octahedron, four faces meet at each vertex; for a regular dodecahedron, three faces meet at each vertex; and for a regular icosahedron, five faces meet at each vertex.

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Answer:

Step-by-step explanation:

step 1 : finding the area of a floor using trapezius area formula

A= [tex]\frac{(10+14)*6}{2} = \frac{24*6}{2} =72 m^{2} \\[/tex]

step 2 : the problem said 1 litre of paint convers an area of 2.5 m^2, so let's calculate how many liters of paint are needed to paint the floor

[tex]\frac{72 m^2}{2.5 m^2} = 28.8 litre\\[/tex]

so we need 28.8 litre to paint the floor

step 3 : Each tin is 5 litre of paint so let's calculate how many tins do we need

n=[tex]\frac{28.8}{5} = 5.76 \\[/tex]

we can't by 5.76 tins so it's 6 tins

step 4 : Each tin costs 21.99 and now we calculate how much 6 tins cost for us

cost = 6 × 21.99 = 131.94

step 5 : Gary has a budget of 150 and the total cost is 131.94. So, Gary has enough money to buy all the paint he needs.

There seems to be an error in the problem statement or some information is missing.

Let's represent the amount of juice the pitcher holds when it's full by x.

According to the problem, the pitcher is initially half empty, which means it is filled with x/2 amount of juice.

After 1/2 cup of juice is added, the pitcher becomes full, which means it is now filled with x amount of juice.

So, the amount of juice added to the pitcher is (x - x/2) + 1/2 = x/2 + 1/2.

Since this amount is equal to 1/2, we can write the equation:

x/2 + 1/2 = 1/2

Solving for x, we get:

x/2 = 0

Multiplying both sides by 2, we get:

x = 0

This means that the pitcher does not hold any juice when it's full, which is not a valid answer.

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The arrival time will be 1:45 pm (13:45) on the day after the departure day.

To see why, we can add the travel time of 25 hours and 25 minutes to the departure time of 12:20 pm.

First, we convert 25 minutes to hours by dividing by 60:

25 minutes ÷ 60 minutes/hour = 0.42 hours

Then, we add the 25 hours and 0.42 hours to the departure time:

12:20 pm + 25 hours + 0.42 hours = 1:45 pm

So the train will arrive in Alice Springs at 1:45 pm on the day after it departs from Adelaide.

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The values of T(0) = e(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), r''(t) = 8e^(2t) + 8e^(-2t).

We are given that r(t) = e^(2t), e^(-2t), te^(2t). To find T(0), we need to evaluate the unit tangent vector T(t) at t=0. The formula for the unit tangent vector is T(t) = r'(t)/|r'(t)|, where |r'(t)| is the magnitude of r'(t).

r'(t) = 2e^(2t) - 2e^(-2t), so r'(0) = 2 - 2 = 0.

Thus, T(0) = r'(0)/|r'(0)| = 0/|0|, which is undefined.

However, since r'(0) = 0, we can use the normal vector instead to find the direction of the tangent line at t=0.

The normal vector N(0) is given by N(t) = T'(t)/|T'(t)|. To find T'(t), we differentiate r'(t) with respect to t:

r''(t) = 4e^(2t) + 4e^(-2t)

So, r''(0) = 4 + 4 = 8. Thus, T'(0) = r''(0)/|r'(0)| = 8/0, which is undefined.

To find r'(t), we can differentiate r(t) using the product rule:

r'(t) = 2e^(2t), -2e^(-2t), 2te^(2t) + e^(2t)

To find r''(t), we can differentiate r'(t):

r''(t) = 4e^(2t), 4e^(-2t), 4te^(2t) + 4e^(2t)

Thus, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

Therefore, T(0) = e^(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

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The expected time until the device first hits zero starting from state m is E[T_m] = m * (1 + E[T_{m-1}])/2

The expected time until the zero-seeking device hits zero starting from state m can be found using the principle of conditional expectation. Let T_m be the time until the device first hits zero starting from state m. We have T_0 = 0 since the device is already at zero. For m > 0, we can condition on the next state of the device at time n+1. Since the device is uniformly distributed over the states 0,1,...,m-1 at time n+1, the expected time until the device hits zero starting from the next state is T_{m-1}. Therefore, we have:

E[T_m] = 1 + (1/m) * [T_0 + T_1 + ... + T_{m-1}]

Using the principle of linearity of expectation and the fact that T_0 = 0, we can simplify this to:

E[T_m] = 1 + (1/m) * (T_1 + T_2 + ... + T_{m-1})

We can continue this process recursively to get:

E[T_m] = 1 + (1/m) * (1 + E[T_{m-1}] + 1 + E[T_{m-2}] + ... + 1 + E[T_1])

Simplifying this expression, we get:

E[T_m] = m * (1 + E[T_{m-1}])/2

Using this recursive formula and the base case E[T_0] = 0, we can calculate E[T_m] for any value of m. This simplified model for an algorithm that seeks a maximum over a finite set of points provides useful insight into the expected behavior of such algorithms.

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The functions y = 8•2ˣ and y = 8•2ˣ are equivalent using the laws of exponents

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

y=2*+³ and y=8•2*

Express properly

So, we have

y = 2ˣ ⁺ ³ and y=8•2ˣ

When the first function expression is expanded, we have

y = 2ˣ * 2³ and y=8•2ˣ

Evaluate the exponent

y = 2ˣ * 8 and y=8•2ˣ

So, we have

y = 8•2ˣ and y = 8•2ˣ

hence, the functions are equivalent using the laws of exponents

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Answer:

If two secant segments intersect outside a circle, then the product of one secant segment with its external portion equals the product of the other secant segment with its external portion.

x^2 = 2(6)

x^2 = 12, so x = 2√3 = 3.5

The cost to put a fence along the borders of the flower patch is $19.27

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

Cost = $2.89 for a 27-inches section

Next, we calculate the perimeter of the patch by adding the side lengths

So, we have

Perimeter = 2 ft 3 in + 2 ft + 2 yd + 25 in + 3 ft 5 in

Evaluate

Perimeter = 15 feet 9 inches

Convert to inches

Perimeter = 180 inches + 9 inches

So, we have

Perimeter = 189 inches

Next, we have

Cost = 180 * 2.89/27

Evaluate

Cost = $19.27

Hence, the cost is $19.27

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The average rate of change in the time it takes sound to travel 1 kilometer is 2.995 seconds.

Given that, the time t(in seconds) it takes for sound to travel 1 kilometer can be modeled by t=1000/(0.6T+331), where T is the air temperature (in degree Celsius)

1) Given that, you hear the thunder 2.9 seconds later.

Here, 2.9=1000/(0.6T+331)

2.9(0.6T+331)=1000

1.74T+959.9=1000

1.74T=1000-959.9

1.74T=40.1

T=40.1/1.74

T=23.045° Celsius

2) Here, T=0° Celsius and T=10° Celsius

2.9=1000/(0.6T+331)

t=1000/(0.6×0+331)

t=1000/331

t=3.02 seconds

Where, T=10

t=1000/(0.6×10+331)

t=1000/337

t=2.97

So, average time = (3.02+2.97)/2

= 2.995 seconds

Therefore, the average rate of change in the time it takes sound to travel 1 kilometer is 2.995 seconds.

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The surface area of the sphere is 1133.54cm² and sinθ  = 5/13, cosθ = 12/13 and tan θ = 5/12 respectively.

The surface area of a sphere is defined as the region covered by its outer surface in three-dimensional space.  A Sphere is a three-dimensional solid having a round shape, just like a circle. The formula of total surface area of a sphere in terms of pi (π) is given by:

S.A = 4πr²

In the given question;

radius = diameter / 2

radius = 19 / 2

radius = 9.5cm

The surface area = 4 * 3.14 * 9.5²

S.A = 1133.54cm²

17.

To find the value of sinθ, cosθ and tanθ, we need to apply trigonometric ratio;

sinθ = opposite / hypothenuse

hypothenuse = ?

Using Pythagorean theorem;

x² = 5² + 12²

x = 13

sinθ = 5/13

cosθ = 12/13

tan θ = 5/12

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The coefficient of x² in the expansion of (3x - 1)5  IS: D) -90.

Make use of  the binomial theorem formula to find the coefficient of x².

(a + b)ⁿ = Σ[n choose k] [tex]a^(n-k) * b^k[/tex]

Where:

a represent 3x

b represent -1

n represent  5

k represent 0, 1, 2, 3, 4, 5

n choose k represents  binomial coefficient,

So,

(3x - 1)⁵ = Σ[5 choose k] [tex](3x)^(5-k) * (-1)^k[/tex]

= (3x)⁵ - 5(3x)⁴ + 10(3x)³ - 10(3x)² + 5(3x) - 1

Thus:

-10(3x)².

-10*3²

= -90

Therefore the coefficient of x² is option D.

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False, An algorithm is a step-by-step procedure or set of instructions for solving a problem or performing a specific task.

It is not limited to calculating the time it takes to solve a problem, but rather it provides a systematic approach to reach the desired solution. Algorithms can be designed to solve a wide range of problems, from simple mathematical calculations to complex computer programming tasks.

Their efficiency can be measured in terms of time and space complexity, which helps in determining the performance of the algorithm. However, the primary purpose of an logarithmic  is to provide a clear and effective method for solving problems, not merely calculating the time it takes to solve them.

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If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

If you invest $3000 in an account that pays simple interest of 4% for 30 years, the amount of money you'll have at the end of 30 years can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
In this case, Principal = $3000, Rate = 4%, and Time = 30 years
Interest = 3000 x 0.04 x 30 = $3600
Therefore, the total amount of money you'll have at the end of 30 years will be the sum of the principal and interest:
Total Amount = Principal + Interest = $3000 + $3600 = $6600
It's important to note that the interest earned in a simple interest account does not compound over time, meaning you earn the same fixed interest rate each year. If you were to invest in an account that compounds interest annually or even monthly, the total amount of money you'll have at the end of 30 years would be significantly higher.

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This option represents a correct sequence of steps in the conventional research model, starting with forming a hypothesis, then designing the research, followed by collecting data, and finally analyzing the data.

The correct sequence of steps in the "conventional" research model is D) Hypothesis formation, research design, data collection, data analysis. The first step is to form a hypothesis or a tentative explanation for the phenomenon being studied. The next step is to design the research study to test the hypothesis. This includes selecting the sample, determining the variables to measure, and deciding on the research methods.

Once the research design is finalized, data collection can begin. This involves gathering data using various techniques such as surveys, interviews, or experiments. Finally, data analysis is performed to examine the data and determine if the results support or refute the hypothesis.
Your answer: D) Hypothesis formation, research design, data collection, data analysis

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Thus,  the vector perpendicular to [4, -2, -3] can be represented as [2]s + [-2]t.

The statement about the vectors being perpendicular if x + y = 0 is incorrect.

Two vectors are called perpendicular if their dot product is 0, not their sum.

To find a vector perpendicular to [4, -2, -3], you can use the cross product, which is calculated as follows:

Let the perpendicular vector be [a, b, c] = [u]s + [v]t. We need to find the values of a, b, and c such that the dot product of [4, -2, -3] and [a, b, c] is 0:
4a - 2b - 3c = 0

Since you're looking for an answer in the form of [ ]s + [ ]t, we can represent the perpendicular vector as:
[a, b, c] = [u]s + [v]t

An example of a perpendicular vector to [4, -2, -3] is [2, -2, 4]. We can write this as:
[2, -2, 4] = [2]s + [-2]t

This means the vector perpendicular to [4, -2, -3] can be represented as [2]s + [-2]t.

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(a) The probability that you drive to school in less than 50 minutes is [tex]\int_{0}^{50} f(t) dt[/tex].

(b) The probability that it takes you more than a quarter of an hour to get to school is [tex]\int_{15}^{\infty} f(t) dt[/tex].

(a) The probability that you drive to school in less than 50 minutes can be expressed as the integral of the probability density function f(t) over the interval from 0 to 50 minutes. This is represented as:
[tex]\int_{0}^{50} f(t) dt[/tex]

(b) The probability that it takes you more than a quarter of an hour (15 minutes) to get to school can be expressed as the integral of the probability density function f(t) over the interval from 15 minutes to infinity.

This is represented as:
[tex]\int_{15}^{\infty} f(t) dt[/tex]

Remember that these integrals represent the probabilities we're looking for, and we would need to actually evaluate them with the specific probability density function f(t) to obtain numerical values.

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The correct answer is option A - True. An array is a data structure in programming that allows you to store a collection of values of the same data type in a single variable.

Each value is assigned an index number, starting from 0, which represents its position in the array.  Arrays are useful in programming because they allow you to store and manipulate multiple values using a single variable. This can help simplify code and make it more efficient.

For example, if you wanted to store the grades of 10 students in a program, you could create an array of 10 elements and assign each grade to a specific index in the array.  In addition to storing data, arrays can also be used to perform calculations and manipulate data.

For example, you could use a loop to iterate through an array and calculate the average of all the values stored in the array. Overall, arrays are a powerful tool in programming that can help you organize and manipulate data.

By thinking of an array as a collection of variables contained within a single variable, you can better understand how arrays work and how to use them effectively in your programs.

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The probabilities are P(a golf ball then a basketball) is 0.0451, P(a football then a baseball) is 8.33%, P(basketball, then not a football) is 0.0864 and  P(two baseballs) is 0.15.

For the first probability, we want to find the probability of drawing a golf ball first and a basketball second. There are a total of 25 balls in the bag, so the probability of drawing a golf ball first is 3/25. After drawing a golf ball, there are 22 balls left in the bag, including 3 basketballs.

Therefore, the probability of drawing a basketball second is 7/22. Since we want both events to occur, we multiply the probabilities together to get:

P(a golf ball then a basketball) = 3/23 * 7/22 ≈ 0.0451

For the second probability, we want to find the probability of drawing a football first and a baseball second. There are a total of 25 balls in the bag, so the probability of drawing a football first is 5/25.

After drawing a football, there are 24 balls left in the bag, including 10 baseballs. Therefore, the probability of drawing a baseball second is 10/24. Since we want both events to occur, we multiply the probabilities together to get,

P(a football then a baseball) = 5/25 * 10/24

= 1/12

= 0.0833

In percentage it will be 8.33%.

For the third probability, we want to find the probability of drawing a basketball first and then any ball that is not a football. There are a total of 25 balls in the bag, so the probability of drawing a basketball first is 3/25.

After drawing a basketball, there are 24 balls left in the bag, including 5 footballs. Therefore, the probability of not drawing a football second is (24-5)/24 = 19/24. Since we want both events to occur, we multiply the probabilities together to get,

P(basketball, then not a football) = (3/25) * (1 - 5/24)

= 0.0864

For the fourth probability, we want to find the probability of drawing two baseballs. There are 10 baseballs in the bag, so the probability of drawing a baseball first is 10/25. After drawing a baseball, there are 9 baseballs left in the bag out of a total of 24 balls.

Therefore, the probability of drawing another baseball second is 9/24. Since we want both events to occur, we multiply the probabilities together to get:

P(two baseballs) = 10/25 * 9/24

= 3/20

= 0.15

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In Fechner's Law, as one variable increases arithmetically, the other variable increases geometrically.

In Fechner's Law, as one variable increases arithmetically, the other variable increases: b. geometrically.

Fechner found in his research that different people have different sensitivities to certain stimuli. For example, the ability to see differences in light can affect the quality of a person's vision. It has also been noted that people are sensitive to changes in stimuli due to emotional impact. He used this to create another version of Weber's law, which he called die Maß formel, or "measurement formula." Fechner's law states that the force of thought is proportional to the logarithm of the force.

If the intensity of the stimulus is tripled (eg 3×1), the sensitivity doubles from its original value (eg 1+1).

If the intensity of the stimulus is tripled again (eg 3×3×1), the corresponding sensitivity will be three times its original value (eg 1+1+1).

So, for the stimulus intensity to double, the perceived intensity only increases.

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To compare the likelihoods of two candidates winning their elections when they are running in different elections, it is important to collect relevant data such as historical voting patterns, demographic information, campaign funding, candidate popularity, and election-specific factors.

1. This data will allow for a comprehensive analysis that considers various factors influencing the outcomes of elections and enables a fair comparison between the candidates.

2. When comparing the likelihoods of two candidates winning their elections in different contexts, several types of data should be collected and analyzed. Firstly, historical voting patterns and trends in the respective regions where the elections are taking place are essential. This data can provide insights into the voting behavior of the electorate and help identify any consistent patterns or shifts in support for particular candidates or parties.

3. Demographic information is another crucial factor. Understanding the composition of the electorate in terms of age, gender, ethnicity, socioeconomic status, and other relevant factors can provide valuable insights into the candidate's potential support base and help gauge the likelihood of their success.

4. Campaign funding is an important indicator of a candidate's resources and support. Analyzing the financial contributions and expenditures of each candidate can provide insights into their campaign strategies, level of organization, and potential impact on the electorate.

5. Candidate popularity and public opinion data are also crucial. Collecting and analyzing polling data, surveys, and public sentiment from reputable sources can help assess the candidates' popularity, public perception, and the overall sentiment towards their campaigns.

6. Lastly, it is important to consider election-specific factors. Each election may have unique circumstances such as political climate, incumbent advantage, key issues, or local dynamics that can significantly influence the outcome. Gathering information on these specific factors and their potential impact on the candidates' chances of winning is important for a comprehensive analysis.

7. By collecting and analyzing this diverse range of data, one can make a more informed comparison of the likelihoods of two candidates winning their elections, even when they are running in different contexts. It is important to note that while data analysis provides valuable insights, election outcomes can still be influenced by unforeseen events, changing circumstances, and individual voter decisions.

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Answer: 4.5

Step-by-step explanation: We can find the answer to this using toa (Tanjent). We’d start with tan(75)= 17/x. From here we’d multiply both sides by x to get xtan(75) = 17. Now we’d just have to divide both sides by tan(75) to get 4.5.