two trains leave stations 560 miles apart at the same time and travel toward each other. one train travels at 95 miles per hour while the other travels at 105 miles per hour. how long will it take for the two trains to meet?

Answer:1.66 and .1 if you multiply 1/2 and 1/5

And add everything

Step-by-step explanation:

The sum of the given series, which alternates between multiplying by 1/2 and 1/5 to obtain successive terms, is 1.2.

To find the sum of the series, we can analyze the pattern of the terms. The series starts with 1, followed by 1/2, then 1/10, and so on. We can observe that each term is obtained by alternately multiplying the previous term by 1/2 and 1/5.

If we consider the terms as separate subsequences, we can see that the first subsequence is 1, 1/10, 1/100, and so on, which forms a geometric series with a common ratio of 1/10. The sum of this subsequence can be calculated using the formula for the sum of an infinite geometric series: S1 = a / (1 - r), where a is the first term and r is the common ratio. Plugging in the values, we get S1 = 1 / (1 - 1/10) = 1 / (9/10) = 10/9.

Similarly, the second subsequence is 1/2, 1/20, 1/200, and so on, which also forms a geometric series with a common ratio of 1/10. Again, applying the formula, we find S2 = (1/2) / (1 - 1/10) = (1/2) / (9/10) = 5/9.

Now, to find the sum of the entire series, we add the sums of the two subsequences: S = S1 + S2 = 10/9 + 5/9 = 15/9 = 1.666... = 1.2.

Therefore, the sum of the given series is 1.2.

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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

The expected number of cards Henry needs to turn up to get the third ace is 31.8

Given: We need to find what is the expected number of cards Harry needs to turn up to get the third ace and Harry has a standard deck of 52 cards.

Now, we know there are 4 ace cards. Let’s consider the ace cards and non-ace cards separately.

There are (52-4) = 48 non-ace cards.

Let us consider that the non-ace cards will be cut by an ace card.

So, there are 5 possible ways in which the ace cards can cut the division, provided

We are having an equal number of non-ace cards in between the appearance of each ace card which means the setup is symmetric among the non-ace cards.

So let us name the spaces between ace cards as s1, s2, s3, s4, and s5.

Therefore, the position of the third ace card is equal to s1 + s2 + s3 + 3.

The expected value of this position is E[s1 + s2 + s3 + 3].

By linearity of expectation, E[s1 + s2 + s3 + s4] is E[s1] + E[s2] + E[s3] + 3.

As the setup is symmetric between the five places, E[s1] = E[s2] = E[s3] = E[s4] = E[s5]

And since E[s1 + s2 + s3 + s4 + s5] = E[s1] + E[s2] + E[s3] + E[s4] + E[s5] = 48

Therefore, E[s1] = E[s2] = E[s3] = E[s4] = E[s5] = 48 / 5

The expected value of position is E[s1] + E[s2] + E[s3] + 3

   = 48 / 5 + 48 / 5 + 48 / 5 + 3

   = 3 * 48 / 5 + 3

   = 31.8

Hence, the expected number of cards Henry needs to turn up to get the third ace is 31.8

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To determine the proportion of respondents who felt vulnerable to identity theft, we can use a confidence interval with a specified confidence level. Let's assume we want a 95% confidence level. Here's how we can calculate it:

1. Gather the data: Determine the total number of respondents in the poll and the number of respondents who answered "yes" to feeling vulnerable to identity theft.

2. Calculate the proportion: Divide the number of "yes" responses by the total number of respondents to find the proportion of respondents who felt vulnerable to identity theft.

3. Determine the critical value: For a 95% confidence level, the critical value is approximately 1.96. This value can be obtained from a standard normal distribution table or a statistical software.

4. Calculate the standard error: Multiply the proportion by the square root of (1 minus the proportion), and then divide it by the square root of the total number of respondents.

5. Calculate the margin of error: Multiply the critical value by the standard error.

6. Calculate the confidence interval: Subtract the margin of error from the proportion to obtain the lower bound of the confidence interval. Add the margin of error to the proportion to obtain the upper bound of the confidence interval.

By using a confidence level, we are estimating a range within which the true proportion of respondents who feel vulnerable to identity theft lies. A 95% confidence level means that if we were to repeat this poll many times, we would expect the true proportion to fall within our calculated confidence interval 95% of the time.

Based on the data from the research institute poll, we can use a confidence level to estimate the proportion of respondents who felt vulnerable to identity theft. This will provide a range within which the true proportion is likely to fall.

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The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

Step-by-step explanation:

Answer:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation =

Step-by-step explanation:

Thats the best i can find.

Answer:

Your answer is correct and you showed all the necessary steps to find the circumference and the number of times the tire would have to rotate to travel one mile. Well done!

Answer:

84/90

Step-by-step explanation:

Let 0.9333....... be x.

10x = 9.3333....... & 100x = 93.33333.......

So,

=> 100x - 10x = 93.33333...... - 9.333333.....

=> 90x = 84

=> x = 84/90

Answer:

14/15

Step-by-step explanation:

Let x = 0.9333...

Multiply this by 100:

100x = 93.333...

Multiply the first one by 10, as well:

10x = 9.333...

We now have:

100x = 93.333...

10x = 9.333...

Since the right of the decimal point for both numbers includes this repeating 3 part, we can simply subtract the two equations and cancel out the 3s:

100x - 10x = 93.333... - 9.333...

90x = 84

Divide by 90:

x = 84/90 = 14/15

The answer is thus 14/15.

~ an aesthetics lover

Answer: 1 ticket = 70 cents.

Step-by-step explanation:

If you get 20 tickets for 14.00, then we have to divide 14 by 20.

14 ÷ 20 = 0.7, or 70 cents. Because of this, each ticket will cost 70 cents.

the probability of the event that  a sample of 5 cans will have a meaningful amount of at least 12.13 oz is 0.0078

We are provided with the information that cans of coke are filled in the account of having normal distribution, with the provided means which is  12.00 oz and the standard deviation of 0.12 oz and the sample size is

n= 5.

let X be the sample mean, so the probability will be :

P(X\(\geq\) 12.13) = 1- P(X<12.13)

               =1-  P(X-(μ/(σ/\(\sqrt{n}\))) < (12.13 -12.00)/(0.12/\(\sqrt{5}\)))

            = 1- P(z<2.42)

            = 1-0.9922

           =0.0078

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Cans of regular Coke are labeled as containing 12 oz. Statistics students weighted the content of 5 randomly chosen cans, and found the mean weight to be 12.13. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.13 oz.

We can find the equation of any line passing through a given point and parallel or perpendicular to a given line by finding the slope of the given line and using slope-intercept form.

Given, the line passing through a given point and parallel and perpendicular to a given line

we have to find the equation of the lines

Let l1 be a line passing through a point (p , q) and parallel to a line l2.

suppose the equation of the line l2 be,

y = mx + c

the line l2 has slope m

Now to find the equation of the line l1,

(y - q)/(x - p) = m

On cross-multiplying, we get

y - q = m(x - p)

y = mx - pm + q

So, the equation of the line l1 be,

y = mx + (q - pm)

Similarly, we can find the equation of any line passing through a point and parallel to a given line.

Hence, we can find the equation of any line with the slope.

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We have demonstrated the definition of an isosceles triangle.

What is an isosceles triangle?

An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.

The isosceles triangle has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.

The given diagram shows an isosceles triangle.

Hence, we have demonstrated the definition of an isosceles triangle.

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Answer:

2:3

Step-by-step explanation:

2 : 3

divide both numbers by 14

Answer:

Your answer will be (-5,7).

Step-by-step explanation:

Answer:

(-7,5)

Step-by-step explanation:

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

11

Step-by-step explanation:

Answer:11

Step-by-step explanation:

because you have to create the equation and solve

The percentage difference if Jasmine had $120,000 last year and this year she has $50,000 is 41.6%.

As it is clear from the term per cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

The last year value = $120000,

The new value of this year = $50000,

Calculate the percentage by the following formula,

Percentage difference = The new value of this year / The last year's value ×100

Substitute value

Percentage difference = 50000 / 120000 × 100

Percentage difference = 41.6%

Therefore, the percentage difference if Jasmine had $120,000 last year and this year she has $50,000 is 41.6%.

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a) To find the extreme points and determine if they are minimum or maximum, we need to take the derivative of the function and set it equal to zero.

a) f(x) = x^2 + x - 6

Taking the derivative:

f'(x) = 2x + 1

Setting it equal to zero and solving for x:

2x + 1 = 0

2x = -1

x = -1/2

To determine if it is a minimum or maximum, we can examine the concavity of the function. Since the coefficient of x^2 is positive (1), the function opens upward and the critical point at x = -1/2 is a minimum.

b) f(x) = x^3 + x^2

Taking the derivative:

f'(x) = 3x^2 + 2x

Setting it equal to zero and solving for x:

3x^2 + 2x = 0

x(3x + 2) = 0

This gives two critical points:

x = 0 and x = -2/3

To determine if they are minimum or maximum, we need to examine the concavity of the function. Since the coefficient of x^3 is positive (1), the function opens upward. The critical point at x = 0 is a minimum, while the critical point at x = -2/3 is a maximum.

b) Graphical method:

To solve the problem graphically, we will draw a graph representing the constraints and find the feasible area. Then we will identify the corner point feasible solutions (CPFS) and determine if there is an optimal solution.

a) Maximize subject to:

x1 + x2

2x1 + 5x2 <= 5

x1 + x2 <= 5

3x1 + x2 <= 15

x1, x2 >= 0

b) Minimize subject to:

x1 + x2

-x1 + x2 <= 5

x2 <= 3

3x1 + x2 >= 7

x1, x2 >= 0

Unfortunately, the given optimization problems are incomplete as there are no objective functions specified. Without an objective function, it is not possible to determine an optimal solution or solve the problem graphically.

Please provide the objective function for the optimization problems so that we can proceed with the graphical solution and find the optimal solution, if any.

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a) The extreme point for the function f(x) = x² + x - 6 is a minimum point.

b) The extreme point for the function f(x) = x³ + x² is neither a minimum nor a maximum point.

Step 1: For the function f(x) = x² + x - 6, to find the extreme points, we can take the derivative of the function and set it equal to zero. By solving for x, we can identify the x-coordinate of the extreme point. Taking the second derivative can help determine if it is a minimum or maximum point. In this case, the extreme point is a minimum because the second derivative is positive.

Step 2: For the function f(x) = x³ + x², finding the extreme points follows the same process. However, after taking the derivative and solving for x, we find that there are no critical points. Without any critical points, there are no extreme points, meaning there are no minimum or maximum points for this function.

In summary, for the function f(x) = x² + x - 6, the extreme point is a minimum, while for the function f(x) = x³ + x², there are no extreme points.

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Answer:

207

Step-by-step explanation:

Lucy I appreciate that virtual Gift you gave me so that is why this is my gift

Answer:

Michael would make $207 for 9 hours of work.

Step-by-step explanation:

To know how much money Michael earns every hour, we need to divide $299 by 13.

299 ÷ 13 = 23

Therefore, Michael earns $23 an hour.

In order to figure out how much money Michael earns in 9 hours, we need to multiply the hourly amount, or $23, by 9.

23 x 9 = 207

Therefore, Michael would make $207 for 9 hours of work.

Hope this helps! :D

Answer:

Step-by-step explanation:

Superfiber ⇒ 5 grams  ⇒ x cups

Fiber Oats  ⇒ 4 grams ⇒ y cups

The required inequality is:

Answer:

its (A) 5x+4y≥30

Step-by-step explanation:

Answer:

Surface area of the figure = 1000 in²

Step-by-step explanation:

From the figure attached,

Two rectangular prisms A and B have been shown with the dimensions.

Surface area of a rectangular prism = 2(length + width) × height

Surface area of prism A = 2(9 + 10) × 20

                                        = 760 in²

Surface area of prism B = 2(15 + 10) × 8

                                        = 16×25

                                        = 400 in²

But one surface of prism B along the width and the same area of prism A are hidden.

Area of the hidden surfaces = 2(10 × 8)

                                               = 160 in²

Total surface area of the figure = 760 + 400 - 160

                                                    = 1000 in²

Answer:

516

Step-by-step explanation:

to solve this equation, multiply both sides by 4

a/4 * 4 = 129 * 4

a = 516

Answer:

a= 516

Step-by-step explanation:

a= 129*4

4*129 = 516

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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The plane EFG  in the rectangular prism is parallel to plane ABC.

In this question, we have been given the rectangular prism ABCDEFGH

We need to find the plane which is parallel to plane ABC.

We can observe that in given rectangular prism,

plane ABH is parallel to the plane CDF

plane BCE is parallel to the plane AGF

plane EFG is parallel to plane ABC.

Therefore, the plane EFG  in the rectangular prism is parallel to plane ABC.

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Answer:

x is the number of successes

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

There is a 17.18% probability that a randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}\)

In which

x is the number of successes

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

In this problem we have that:

A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:

\(P=\dfrac{525}{561}=0.9358\)

Assume that we want to find the probability that a randomly selected region had exactly two hits.

This is P(X = 2).

\(P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}\)

\(P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718\)

There is a 17.18% probability that a randomly selected region had exactly two hits.

Answer:

y=-2

Step-by-step explanation:

because it's parallel --> a=-2

therefore we have y=-2x+b

the line goes through the point (3,-6) --> (-2).3+b=-6 --> b=0