All categories

3 years ago

Question number 7 Give a reasonable domain and range for the function in this context

Mathematics

1 answer:

alina1380 [7]3 years ago

3 0

Answer: D: [0, ∞)

R: [0, ∞)

Step-by-step explanation:

f(x) = 1.5x

x is the number of bottles

f(x) is the cost

Domain is the x-values. The least amount of bottles you can buy is 0 and the most you can buy is infinite (technically you can only buy the amount you can afford and the amount the store has to sell but for mathematical purposes you can buy an infinite amount)

So, the domain (D) is x = 0 to ∞ → D: [0, ∞)

Range is the y-values. The least and most amounts are based on the domain. Since the smallest x-value is 0, input that value into the equation to solve for f(x). Similarly, input the greatest x-value to solve for f(x).

f(x) = 1.5(0)

= 0

f(x) = 1.5(∞)

= ∞

So, the range (R) is f(x) = 0 to ∞ → R: [0, ∞)

You might be interested in

What is the mean, variance, and standard deviation of the values? Round to the nearest tenth. 1,9,4,12,13,13

tankabanditka [31]

To compute the mean, you simply have to sum all the elments in the data set and the divide the sum by the number of elements:

$M = \frac{1+4+9+12+13+13}{6} = \frac{52}{6} = 8.6$

To compute the variance, we first need to compute the distance of each element from the mean. To do so, we build a "parallel" dataset, given by the difference of every value and the mean:

$D' = 1-8.6,9-8.6,4-8.6,12-8.6,13-8.6,13-8.6$

$D' = -7.6, 0.4, -4.6, 3.4, 4.4, 4.4$

Now we need those difference squared:

$(D')^2 = 57.76, 0.16, 21.16, 11.56, 19.36, 19.36$

The variance is the mean of this new vector, so

$\sigma^2 = \frac{57.76+ 0.16+ 21.16+ 11.56+ 19.36+ 19.36}{6} = \frac{129.36}{6} = 21.6$

Finally, the standard deviation is simply the square root of the variance, so you have

$\sigma = \sqrt{21.6} = 4.6$

8 0

3 years ago

The sides of two regular octagons are 3 in. And 6 in. respectively. Find the ratio of their perimeters and their areas

photoshop1234 [79]

The ratio of their perimeters is $\frac{1}{2}$ and the ratio of their areas is $\frac{1}{4}$

Step-by-step explanation:

A regular n-side polygon has

n equal sides
n equal angles
The measure of each interior angle = $\frac{(n-2).180}{n}$
Its perimeter = n × a, where a is the length of its side

V.I.Note: all regular polygons have same number of sides are similar, because their interior angles are equal in measures and their sides are proportion

∵ There are to regular octagons

- Regular octagon has 8 equal sides and 8 equal angles

∴ The two octagon are similar

∵ Their sides are 3 inches and 6 inches

∴ The constant ratio between their sides = $\frac{3}{6}$

- Divide the two terms of the ratio by 3 to simplify it

∴ The constant ratio between their sides = $\frac{1}{2}$

In similar figures the ratio between their perimeters is equal to the constant ratio between their sides, and the ratio between their areas is equal to square the constant ratio between their sides

∵ The two octagons are similar

∵ The constant ratio between their sides = $\frac{1}{2}$

∵ The ratio between their perimeters = the constant ratio between

their sides

∴ The ratio between their perimeters = $\frac{1}{2}$

∵ The ratio between their areas = (constant ratio)²

∴ The ratio between their areas = $(\frac{1}{2})^{2}=\frac{1}{4}$