what if question is a passenger train travels at a speed of 72 km/h a man on the passenger train observes a goods train travelling at the speed of 54km/h in the opposite direction. if the goods train passes him in 8secs, find the length of the goods train whats the answer and method for it

The pieces of wood needed to construct the sandbox is 12542.28 cubic inches

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

The pentagonal prism

The pieces of wood needed to construct the sandbox is the volume, and this is calculated as

Volume = 1/4√[5(5+2√5)]a²h

Where

a = side length = 27 inches

h = height = 10 inches

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

Volume = 1/4 * √[5(5+2√5)] * 27² * 10

Evaluate

Volume = 12542.28

Hence, the pieces of wood needed to construct the sandbox is 12542.28 cubic inches

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For the question "Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x....". the best explanation of the accuracy of Geraldine’s statements and her conclusion is: The conclusion is incorrect because the range is limited to the set of integers. Option D. This is further explained below.

Generally, The formula f(x) = ax is the definition of an exponential function. In this formula, the input variable x appears in the form of an exponent. The exponential curve is dependent not only on the exponential function but also on the value that is used for x.

In conclusion, In response to the question "Geraldine is tasked with explaining the restrictions on the range of an exponential equation by making use of the function f(x) = 2x...." The most plausible justification for the correctness of Geraldine's claims and her conclusion is as follows: The conclusion is fallacious due to the fact that the range is restricted to the set of integers. option D.

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Complete Question

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements:

1. As x increases infinitely, the y-values are continually doubled for each single increase in x.2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.

She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion?

Statement 1 is incorrect because the y-values are increased by 2, not doubled.

Statement 2 is incorrect because the y-values are doubled, not halved.

The conclusion is incorrect because the range is limited to the set of integers.

The conclusion is incorrect because the range is limited to the set of positive real numbers.

Answer:

D

Step-by-step explanation:

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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The perimeter of the isosceles triangle is 74.8 inches

To calculate the perimeter of a triangle, we simply add the lengths of the sides given. The basic formula used to calculate the perimeter of a triangle is:

Perimeter = Sum of three sides

But in this case, we need to find the length of all sides

Using Pythagoras theorem;

x² = 24² + 11²

x = √697

x = 26.4

The length of the hypothenuse is 26.4 in and since it's an isosceles triangle, it has it two sides equal to each other.

But the base of the triangle = 2 * 11 = 22in

The perimeter of the triangle = 26.4 + 26.4 + 22 = 74.8 in

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Answer:

9m+6

have a good day! <3

Answer: 25.5ft

Step-by-step explanation:

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Teresa needs to buy two new tires for her mountain bike.

With a budget of $120, she will likely spend within $25 of that amount.

To help her find the best deal, Teresa should first research what type of mountain bike tire she needs. She can look at the bike's current tires to determine the size, or she can look up the bike model and size online. She should then research prices at a variety of local bike shops and online retailers to compare costs.

Once she finds the best price, Teresa should look for discounts and coupon codes that she can use to reduce the cost of her tires. She should also make sure she is aware of any extra costs, such as shipping and taxes.

With some research and savvy shopping, Teresa should be able to find two mountain bike tires that fit within her budget of $120 and that will keep her bike running smoothly.

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Answer:

31.42cm

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

reduce the index of the radical and exponent with 2 , the absoulute value of any expression is always positive or zero and all together it ends up to 5/6 .

v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.

Let's start with understanding what the kernel of a linear transformation is. The kernel, also known as the null space, is the set of all vectors that get mapped to the zero vector by the transformation.
In this case, the kernel is the line spanned by the vector ⎡ ⎣ −1 1 2 ⎤ ⎦. This means that any vector on this line will get mapped to the zero vector by the linear transformation we're looking for.
One example of a linear transformation that has this kernel is the projection onto the plane orthogonal to ⎡ ⎣ −1 1 2 ⎤ ⎦. This transformation takes any vector in R^3 and projects it onto the plane that is perpendicular to the given vector.
To see why this works, let's call our given vector v = ⎡ ⎣ −1 1 2 ⎤ ⎦. We can find a basis for the plane orthogonal to v by finding the orthogonal complement of v. This is the set of all vectors w in R^3 that satisfy the equation v^T w = 0.
If we solve this equation, we get the set of all vectors of the form ⎡ ⎣ a -a/2 b ⎤ ⎦, where a and b are any real numbers. This is a basis for the plane orthogonal to v.
Now, we can define our linear transformation T as follows: T(x) = x - proj_v(x), where proj_v(x) is the projection of x onto the plane orthogonal to v.
Since proj_v(x) is in the plane orthogonal to v, it is also orthogonal to v. This means that v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.

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Answer:

60

Step-by-step explanation:

Given: 1/2a + 2/3b =50

(Since b is equal to 30 we will automatically replace b with 30)

Step 1: Simplify both sides of the equation.

1/2a+20=50

Step 2: Subtract 20 from both sides.

1/2a=50-20

1/2a=30

Step 3: Multiply both sides by 2.

2(1/2a) 2(30)

a=60

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

a = 15

Step-by-step explanation:

1/2(a) + (2/3 x 30) = 50

2/3 x 30 = 20

1/2(a) + 20 = 50

Rearrange > 20 to -20

-20 + 50 = 30

1/2(a) = 30

Rearrange 1/2 to 2

2 > 30/2

30/2 = 15

a = 15

Hope this helps, and please let me know if it is correct or isn't.

Have a nice day

Answer:

Hi there! 60x60=3600

Step-by-step explanation:

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The linear programming problem can be formulated as follows:

Maximize: P = 25x + 40y (profit function)

Subject to:

90x + 160y ≤ 600,000 (manufacturing cost constraint)

x + y ≤ 2,400 (demand constraint)

x, y ≥ 0 (non-negativity constraint)

Maximize: P = 25x + 40y (profit function) - This objective function represents the total profit, which is the sum of the profits from selling model A (25x) and model B (40y).

Subject to: 90x + 160y ≤ 600,000 (manufacturing cost constraint) - This constraint ensures that the total cost of manufacturing model A and model B does not exceed $600,000.

Subject to: x + y ≤ 2,400 (demand constraint) - This constraint ensures that the total number of portable printers produced (model A + model B) does not exceed 2,400 units, which represents the total demand.

Subject to: x, y ≥ 0 (non-negativity constraint) - This constraint ensures that the number of units produced for each model cannot be negative; they must be non-negative values.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The exponential function passing through the points (-2, 2500) and (2, 4) is: f(x) = 12500*(4/2500)^(x/4)

An exponential function has the form of f(x) = a*b^x, where "a" is the initial value, "b" is the base, and "x" is the independent variable.

Using the given points, we can set up a system of two equations to solve for "a" and "b":

Dividing the second equation by the first equation gives:

4/2500 = b^2/b^(-2)

Simplifying:

4/2500 = b^4

Taking the fourth root of both sides:

b = (4/2500)^(1/4)

Substituting back into either equation to solve for "a":

Therefore, the exponential function passing through the points (-2, 2500) and (2, 4) is: f(x) = 12500*(4/2500)^(x/4)

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The triangle with three acute angles and three congruent sides is classified as an equilateral acute triangle by it's sides and angles.

An equilateral triangle is a triangle in which all the side lengths have the same measure.

Consequently, all the angle measures on the triangle will be equal, and the measure will be of:

180/3 = 60º.

(as the sum of the internal angles of a triangle is of 180º).

As the larger angle measures is less than 90º, the angle is an acute triangle.

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Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

\(\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6\)

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

m a t h w a y

Step-by-step explanation:

Answer: their bank balance would be

- 64.49

Step-by-step explanation:

They have 100 in savings and 121.50 in their bank account. It means that the total amount that they have to buy the freezer is

100 + 121.5 = 221.5

The cost of the freezer is 285.99. If they buy the freezer, the amount that would be left in their bank account or the bank balance would be

221.5 - 285.99 = - 64.49

The negative value is due to the face that they the cost of the freezer is higher than what they have in total.

Answer:

C is the answer

Step-by-step explanation:

Answer:

Its the third bubble

Step-by-step explanation:

Hope I helped you.

Answer:

(4,2)

Step-by-step explanation:

hope this answerss

The 2-, 10-, and 100-year peak floods for a normal distribution are 5500 cfs.

Given a mean and standard deviation of 3,500 and 2,000 cfs, respectively, the 2-, 10-, and 100-year peak floods for a normal distribution can be found as follows:

Formula used in finding the peak flood is as follows:

Q_T= Q_m + K_T

σ

Where Q_T is the flow for a given period,

Q_m is the mean flow, K_T is the coefficient of skewness, and σ is the standard deviation of the flows.

For a normal distribution, K_T= frac{\text{duration of period in years}-1}{2}\times\frac{\text{duration of period in years}+1}{2}

Substitute the mean and standard deviation to the formula above:

When the period of interest is 2 years, the coefficient of skewness is calculated below:

[{{K}_{T}}=\frac{\text{(2-1)(2+1)}}{2}=1\]

Also, K_{T} is 1 for the 10-year and 100-year flood.

When these values are computed, we get the following values:

Q_{2}=3500+1(2000)=5500 \text{ cfs}

Q_{10}=3500+1(2000)=5500 \text{ cfs}

Q_{100}=3500+1(2000)=5500 \text{ cfs}

Therefore, the 2-, 10-, and 100-year peak floods for a normal distribution are 5500 cfs.

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Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.

explanation: like 57 * Y =142500

what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped

The probability of red is 0.1724, given the following table.

The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.

The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.

The probability of Red can be calculated using the formula;

P(Red) = (Frequency of Red) / (Total Frequency)

Using the values provided in the table

,P(Red) = 15/87P(Red) = 0.1724

Hence, the probability of red is 0.1724.

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The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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