MATHEMATICS COLLEGE

What is the slope of the line?

Answers

Answer 1

Answer:

Hi there!

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I believe your answer is:

m = (7/4)

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Here’s why:

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$\boxed{\text{The slope formula is rise over run.}}\n\nm=\frac{\text{Rise}}{\text{Run}}\n\nm=(y_2-y_1)/(x_2-x_1)\n-------------\n(x_1,y_1) \text{ and } (x_2,y_2) \text{ are two points that are on the line.}$

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The line passes through the points (3,4) and (-1, -3).

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$\boxed{\text{Calculating the Slope:}}\n\n\rightarrow m = (-3-4)/(-1-3)\n\n\rightarrow m=(-7)/(-4)\n\n\rightarrow m=\boxed{(7)/(4)}$

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Hope this helps you. I apologize if it’s incorrect.

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When designing and writting questions for a survey , which of the following are issues that you need to pay attention to?A. Wording of questions
B. Order of questions
C. Sensitive questions
D. All of the above

Answers

Answer:A

Step-by-step explanation:

A total of 600 advertisements were sold for a certain magazine. If 30 percent of the first 200 sold were in color, 20 percent of the next 300 sold were in color, and 90 percent of the last 100 sold were in color, what percent of the 600 advertisements were in color?

Answers

Answer:

%35 of them were in color

Step-by-step explanation:

Since 30 percent of the first 200 sold were in color, 200x30/100 = 60 of them were in color.

Since 20 percent of the next 300 sold were in color, 300x20/100 = 60 of them were in color.

Since 90 percent of the last 100 sold were in color, 100x90/100 = 90 of them were in color.

In total, 60 + 60 + 90 = 210 out of 600 were in color.

The percentage is: $(600)/(100)$ = $(210)/(x)$ → x = $(21000)/(600)$ = 35

Final answer:

To find the percentage of advertisements that were sold in color, divide the number of color ads by the total number of ads and multiply by 100. We get answer 35.

Explanation:

To find the percentage of advertisements that were sold in color, we need to find the number of color advertisements in each group and then calculate the percentage.

For the first 200 ads, 30% were in color, so the number of color ads is 0.3 * 200 = 60.
For the next 300 ads, 20% were in color, so the number of color ads is 0.2 * 300 = 60.
For the last 100 ads, 90% were in color, so the number of color ads is 0.9 * 100 = 90.

The total number of color ads is 60 + 60 + 90 = 210. To find the percentage, we divide 210 by 600 and multiply by 100.

So, the percentage of advertisements that were in color is 35%.

Learn more about Percentage Calculation here:

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What is the angle (relative to the horizontal) of a 4 in 4 roof? Is it possible to have a 7 in 4 foot? Explain.

Answers

If "y in x" means the rise is y for a run of x (both in the same units), then the tangent of the angle is y/x.

... angle for 4 in 4 roof: arctan(4/4) = 45°

Yes, it is possible to have a 7 in 4 roof.

... angle for 7 in 4 roof: arctan(7/4) = 60.3°

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As long as the run is non-zero, the rise can be anything you like.

Write an equation in slope-intercept form of the line that passes through thegiven point and is parallel to the graph of the given equation.

(-3, 12); y = -3x + 5

Answers

Answer: y = -3x + 3 or y = 3 - 3x

Step-by-step explanation:

First, we need to determine our slope. Thankfully for us, the slope of a line parallel to another is the same.

So our slope is -3.

Now, we need to find our y-intercept. To do that, we will use y = mx + b. y is the y-coordinate, m is the slope, x is the x-coordinate, and b is the y-intercept.

Plug in the numbers given.

12 = -3(-3) + b

Simplify.

12 = 9 + b

Subtract 9 from both sides.

12 - 9 = 9 - 9 + b

3 = b

Our y-intercept is 3.

Now, we just put everything together.

y = -3x + 3

The line parallel to y = -3x + 5 that passes through the point (-3, 12) is

y = -3x + 3 or y = 3 - 3x (both are the same just written differently)

$f(x) = {x}^(2) + 4x - 5$ ; >-2Find $\frac{d {f}^( - 1) }{dx}$ at x=16

Please show solving

Answers

The inverse function theorem says

$(\mathrm df^(-1))/(\mathrm dx)(16)=\frac1{(\mathrm df)/(\mathrm dx)(f^(-1)(16))}$

We have

$f(x)=x^2+4x-5$

defined on $x>-2$ , for which we get

$f^(-1)(x)=-2+√(x+9)$

and

$f^(-1)(16)=-2+√(16+9)=3$

The derivative of $f(x)$ is

$f'(x)=2x+4$

So we end up with

$(\mathrm df^(-1))/(\mathrm dx)(16)=\frac1{(\mathrm df)/(\mathrm dx)(3)}=\frac1{10}$

A local doctor’s office logged the number of patients seen in one day by the doctor for ten days. Find the means, median, range, and midrange of the patients seem in 10 days. 27 31 27 35 35 25 28 35 33 24

Answers

Answer:

Mean = 30, Median = 29.5, Range = 9 and Mid-range = 29.5.

Step-by-step explanation:

We are given that a local doctor’s office logged the number of patients seen in one day by the doctor for ten days.

Arranging the given data in ascending order we get;

24, 25, 27, 27, 28, 31, 33, 35, 35, 35.

(a) Mean is calculated by using the following formula;

Mean, $\bar X$ = $\frac{\text{Sum of all values}}{\text{Total number of observations}}$

= $(27+ 31+ 27+ 35+ 35+ 25+ 28+ 35+ 33+ 24)/(10)$

= $(300)/(10)$ = 30

So, the mean of the given data is 30.

(b) For calculating the median, we have to first have to observe that the number of observations (n) in the data is even or odd.

If n is odd, then the formula for calculating median is given by;

Median = $((n+1)/(2))^(th) \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{((n)/(2))^(th) \text{ obs.}+ ((n)/(2)+1)^(th) \text{ obs.} }{2}$

Here, the number of observations is even, i.e. n = 10.

So, Median = $\frac{((n)/(2))^(th) \text{ obs.}+ ((n)/(2)+1)^(th) \text{ obs.} }{2}$

= $\frac{((10)/(2))^(th) \text{ obs.}+ ((10)/(2)+1)^(th) \text{ obs.} }{2}$

= $\frac{(5)^(th) \text{ obs.}+ (6)^(th) \text{ obs.} }{2}$

= $(28+31)/(2)$

= $(59)/(2)$ = 29.5

So, the median of the data is 29.5.

(c) The range of the data is given by = Highest value - Lowest value

= 35 - 24 = 9

So, the range of the data is 9.

(d) Mid-range of the data is given by the following formula;

Mid-range = $\frac{\text{Highest value}+\text{Lowest value}}{2}$

= $(35+24)/(2)$ = 29.5

Final answer:

The mean of the patients seen in 10 days is 30, the median is 29.5, the range is 11, and the midrange is 29.5.

Explanation:

To find the mean, median, range, and midrange of the numbers, we first need to understand what these terms mean. The mean is the average, the median is the middle number in a sorted set, the range is the difference between the highest and lowest values, and the midrange is the average of the highest and lowest values.

First, let's sort the numbers: 24 25 27 27 28 31 33 35 35 35.

To calculate the mean, add all the numbers and divide by the count (10): (24+25+27+27+28+31+33+35+35+35)/10 = 30.

The median is the average of the two middle numbers (which are 28 and 31 in this case): (28 + 31) / 2 = 29.5.

The range is the highest number minus the lowest number: 35 - 24 = 11.

The midrange is the average of the highest and lowest values: (35 + 24) / 2 = 29.5.

Learn more about Mean, Median, Range

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