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postnew [5]
3 years ago
8

The sale price of an item is four-fifths the original price of the item, x.

Mathematics
2 answers:
hammer [34]3 years ago
7 0

Answer:

B. Multiplying by \frac{4}{5} is the same as multiplying by 80%.

Step-by-step explanation:

Let x be the original price of item.

We have been given that the sale price of an item is four-fifths the original price of the item.

Let us find the sale price of item.

\text{Sale price}=\frac{4}{5}x

\text{Sale price}=0.8x

Let us convert 0.8 into percentage by multiplying by 100%.

\text{Sale price}=(0.8)(100\%)x

\text{Sale price}=(80\%)x

Therefore, the sale price of the item could be figured out by  \frac{4}{5}x and 0.8x because Multiplying by \frac{4}{5} is the same as multiplying by 80%.

MrRissso [65]3 years ago
4 0

B. Multiplying by 45 is the same as multiplying by 80%.


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a) The probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average is 0.3085.

b) The probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average is 0.3085.

c) The probability of sampling at random a fish that has a size between the two values is 0.383.

d) The 25th and 75 percentiles of fish size for the population using the normal distribution table is 5.69 and 5.87 respectively.

e) The probability that the average calculated will be less than the value is 0.3707.

Step-by-step explanation:

For the given data set mean (\mu) = 5.75913

Standard deviation (\sigma) = 0.172229

Variance (\sigma2) = 0.0296

Here we get is

a)

P(x < \mu - \sigma/2) = p(x < 5.673) \\\\          = 0.3085

b)

P(x < \mu + \sigma/2) = p(x < 5.845) \\\\= 0.3085

c)

P(\mu - \sigma/2 < x < \mu + \sigma/2) = p(5.673 < x < 5.845) \\\\= 0.383

d)

25th percentile:-

= 25*[(n+1)/100]th term \\\\= 5.69

75the percentile:-

= 75*[(n+1)/100]th term\\\\ = 5.87

e)  

p(x < \mu - \sigma/3) = p(x < 5.7017) \\\\= 0.3707

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3 years ago
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3 years ago
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Step-by-step explanation:

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3 years ago
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vitfil [10]

This article is about the math term. For other uses, see Slope (disambiguation).

For the grade (incline or gradient or pitch or slope) of any physical feature, see Grade (slope).

Slope: {\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}{\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.[1] Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844)[2] who wrote the equation of a straight line as "y = mx + b" and it can also be found in Todhunter (1888)[3] who wrote it as "y = mx + c".[4]

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.

A line is increasing if it goes up from left to right. The slope is positive, i.e. {\displaystyle m>0}m>0.

A line is decreasing if it goes down from left to right. The slope is negative, i.e. {\displaystyle m<0}m<0.

If a line is horizontal the slope is zero. This is a constant function.

If a line is vertical the slope is undefined (see below).

The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words, the rise is (y2 − y1) = Δy. For relatively short distances, where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x2 − x1) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.

In mathematical language, the slope m of the line is

{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}m=\frac{y_2-y_1}{x_2-x_1}.

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of incline θ by the tangent function

{\displaystyle m=\tan(\theta )}m = \tan (\theta)

Thus, a 45° rising line has a slope of +1 and a 45° falling line has a slope of −1.

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