Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below.

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

Step-by-step explanation:

x-5>-2

x> -5+2

X>3

 Answer is: {x | x R, x > 3}

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).

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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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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In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.

In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.

For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.

In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.

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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:

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 $

      Simplified form of the given logarithmic expression ln(4500) will be         ln(4500) = 3ln(5) + 2ln(6)

Given logarithmic expression in the question is,

We have to convert this expression in terms of ln(5) and ln(6).

Since, Factored form of 4500 = 5×5×5×6×6

                                                  = 5³×6²

Therefore, ln(4500) = ln(5³×6²)

                                 = ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]

                                 = 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]

   Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.

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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.

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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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.

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]