Identify a benefit of applying statistical forecasting methods

Answer:

Speed of current = 5 mph

Step-by-step explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph

Answer:

[tex]x^2+x-1-\frac{6}{x+4}[/tex]

Step-by-step explanation:

Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]

a(x) = dividend

b(x) = divisor

q(x) = quotient

r(x) = remainder

Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]

We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]

So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]

Thus a(x) = dividend =  [tex]x^3+5x^2+3x-10 [/tex]

b(x) = divisor= [tex]x+4[/tex]

q(x) = quotient=[tex]x^2+x-1[/tex]

r(x) = remainder=-6

Substitute the value in the rational form.

[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]

Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is  [tex]x^2+x-1-\frac{6}{x+4}[/tex]

multiply 5.5 cm by 11.5 km

5.5 * 11.5 = 63.25

 rounded to nearest tenth = 63.3 km

he pays 29.59 a week

 multiply that by 52 weeks in a year

29.59 * 52 = 1538.68 a year

 Answer is A

Answer:

It's three. Look at 11 on the Y axis (computers) and count how many dots are at  11. There's a total of three computers based on the dots at 11.

Step-by-step explanation:

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

The number of offices that have 11 computers is 3.

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

We have,

Horizontal axes =  number of desks

Vertical axes = number of computers

Each dot in the scatter plot indicates offices.

Number of offices = 12 dots = 12

We need to find the number of dots that is with 11 computers.

We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.

Thus the number of offices that have 11 computers is 3.

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The equation of the line that passes through the point (-1,5) and has a slope of 3 in point-slope form is y = 3x + 8.

The subject of this question relates to Mathematics, specifically algebra and line equations. The line equation in point-slope form is given by y - y1 = m(x - x1). In this equation, (x1, y1) represents the point that the line passes through and m represents the slope of the line. In our case, we know that the line passes through the point (-1,5) and has a slope of 3.

By substituting these values into the point-slope formula, we get the following:y - 5 = 3(x - (-1)), or, after simplifying, y - 5 = 3x + 3. So, the equation of the line that passes through (-1,5) and has a slope of 3 is y = 3x + 8.

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I believe that the correct word here is correlation. Correlation is the term that we use when we want to say that something is strong related to the other. Correlation must be however differentiated from causality. Correlation is when two things occur at the same time. Causality is when one results in the occurrence of the other.

Correlation coefficient has a maximum value of 1 which indicates strong relationship.

For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.

Here's how to solve a similar problem based on the given examples:

Let the first train's speed be 50 mph and the second train's speed be 55 mph.

The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).

The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.

Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.

So, the second train will overtake the first train after 5 hours.

the answer to this question is B

Answer:

Option B. is correct.

Step-by-step explanation:

Tiana's checking account charges a $7.75 monthly service fee and $0.16 per check fee.

If Tiana writes 17 checks per month, her total charges =

0.16 × 17 = 2.72 + 7.75 = $10.47

Her total account charges $10.47 for 17 checks.

In the question it is asking that she should switch to a checking account that charges a $10.50 monthly service fee and no per check fee.

Answer : No, because her monthly fees are currently less than $10.50.

Answer:

The total cost of the monster truck = 29000 $

Step-by-step explanation:

Stan bought a monster truck for $2,000 down and payments of $450 a month for five years.

Initial payment = 2000 $

Monthly payment = 450 $

Number of years paid = 5

Number of months in 5 years = 12 x 5 = 60

Total amount paid = 2000 + 60 x 450 = 29000 $

The total cost of the monster truck = 29000 $

x-5>-2

x> -5+2

X>3

 Answer is: {x | x R, x > 3}

Answer: i did the test and i got B and i was right so its B

Step-by-step explanation:

Answer:

The graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

Step-by-step explanation:

Consider the provided graph.

it is not always possible to find maximum or minimum for the whole function, but locally it is.

To find the local maximum and minimum we need to choose an interval first.

Local maximum: f(c) ≥ f(x) for all x in the interval

Local minimum: f(c) ≤ f(x) for all x in the interval

For better understanding refer the figure 1

Now consider the provided graph:

The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.

Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.

Also the graph of the function has local maximum at (0,0) as at x = 0

The value of function f(x)≤f(c) for every x in the domain.

Hence, the graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.

We will get that the distance is 3.22

So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)

That distance is:

[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]

Now we want to minimize this, which is equivalent to minimize d^2, then we can define:

D = d^2

and write:

[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]

Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).

Remember that for a parabola like:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then for our parabola, the vertex will be at:

x = -(-44)/(2*10) = 44/20 = 2.2

Thus the minimum distance is given by:

[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]

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