Find the slope of the line passing through the points (-3,7) AND (2,-6)
2 answers:
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Answer:
In the long run cost of the refrigerator g(x) will be cheaper.
Step-by-step explanation:
The average annual cost for owning two different refrigerators for x years is given by two functions
f(x) =
=
and g(x) =
=
If we equate these functions f(x) and g(x), value of x (time in years) will be the time by which the cost of the refrigerators will be equal.
At x = 1 year
f(1) = 850 + 62 = $912
g(1) = 1004 + 51 = $1055
So initially f(x) will be cheaper.
For f(x) = g(x)
=
x =
Now f(15) = 56.67 + 62 = $118.67
and g(x) = 66.93 + 51 = $117.93
So g(x) will be cheaper than f(x) after 14 years.
This tells below 14 years f(x) will be less g(x) but after 14 years cost g(x) will be cheaper than f(x).
Answer:
Step-by-step explanation:
Hello!
The objective is to estimate the population mean of the lung-capacity index (FEV1) the forced volume (in ml) of air that is exhaled in 1 second of children that came from households where coal is used for coal or heating or both. The researcher claims that the use of coal has a negative impact (reduces) on the mean FEV1.
a.
A sample of 512 children that came from households where coal is uses was taken, they obtained a sample mean of X[bar]= 1429ml and a standard deviation of S= 327ml
The study variable is X: the forced volume (in ml) of air that is exhaled in 1 second of a child that lives in a household where coal is used.
There is no information about the distribution of the variable, but the sample size is large enough to be valid to apply the Central Limit Theorem and approximate the distribution of the sample mean to normal:
X[bar]≈N(μ;δ²/n)
Using this approximation you can estimate the population mean using an approximate Z and 1 - α: 0.95:
X[bar] ± * (S/√n)
[1426 ± 1.965 * (327/√512)]
[1397.60; 1454.40]ml
Using a confidence level of 95% you'd expect that the interval [1397.60; 1454.40] contains the true average of the lung-capacity index of Chinese children that live in households where coal is used for cooking, hearing or both.
b.
Now using a value of S= 330 and a CI of 95% you need to calculate the sample size required to get an interval amplitude of 50ml
To calculate the sample size given a determined confidence level and amplitude the best is to use the semiamplitude or margin of error (d) of the interval.
The semiamplitude is half of the amplitude. The general structure of a confidence level for the mean is "point estimate" ± "margin fo error"
Then the formula for the margin of error is:
d= * (S/√n)
If a= 50ml then d= 50/2=25ml
(d* )= (S/√n)
√n*(d* )= S
n= [S/(d* )]²
n= [330/(25*1.965)]²
n= 37.29 ≅ 38
You need to take a sample of 38 childre.
I hope it helps!
The reflection of BC over I is shown below.
<h3>What is reflection?</h3>- A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3).
- A figure's mirror image in the axis or plane of reflection is its image by reflection.
See the attached figure for a better explanation:
1. By the unique line postulate, you can draw only one line segment: BC
- Since only one line can be drawn between two distinct points.
2. Using the definition of reflection, reflect BC over l.
- To find the line segment which reflects BC over l, we will use the definition of reflection.
3. By the definition of reflection, C is the image of itself and A is the image of B.
- Definition of reflection says the figure about a line is transformed to form the mirror image.
- Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.
4. Since reflections preserve length, AC = BC
- In Reflection the figure is transformed to form a mirror image.
- Hence the length will be preserved in case of reflection.
Therefore, the reflection of BC over I is shown.
Know more about reflection here:
#SPJ4
The question you are looking for is here:
C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.
