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Advocard [28]
3 years ago
13

Find the domain and range of the equation:b(x)=|x-3|​

Mathematics
1 answer:
zzz [600]3 years ago
4 0

Domain: Set of all real numbers.

The domain in interval notation is (-infinity, infinity)

The reason why the domain is the set of all real numbers is because we can pick any number we want for x, without having to worry about division by zero errors or taking the square root of negative values. There are no restrictions for x.

==========================================================

Range: Set of all non-negative numbers.

As an inequality, you would write y \ge 0 (y is greater than or equal to 0)

In interval notation, the range is written as [0, infinity)

The absolute value result cannot be negative. The smallest y = |x| can get is y = 0. This applies to y = |x-3| as well. The use of square brackets tells the reader "include y = 0 as part of the range". You always use curved parenthesis for infinity because you can never actually reach infinity.

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A zoologist is studying four very closely related feline species. She wishes to compare their gestation periods. An observationa
diamong [38]

Answer:

p_v= 0.01

Since the significance level is 0.05 we see that pv so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different, NOT to conclude that the all the means are different.

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

Solution to the problem

The hypothesis for this case are:

Null hypothesis: \mu_{A}=\mu_{B}=\mu_{C}= \mu_D

Alternative hypothesis: Not all the means are equal \mu_{i}\neq \mu_{j}, i,j=A,B,C,D

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have p=4 groups and on each group from j=1,\dots,p we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2  

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2  

And we have this property  

SST=SS_{between}+SS_{within}  

And in order to test this hypothesis we need to ue an F statistic and for this case the p value calculated is

p_v= 0.01

Since the significance level is 0.05 we see that pv so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different NOT to conclude that the all the means are different.

8 0
3 years ago
A kayaker travels x miles per hour downstream for 4 hours. On the 6-hour return trip, the kayaker travels 2 mile per hour slower
Stolb23 [73]

                              time       *      rate          =       distance

Downstream           4           *       x              =          4(x)

Upstream                6           *     x - 2           =        6(x - 2)

distance downstream = distance upstream:

                              4(x) = 6(x - 2)

                               4x  = 6x - 12

                              -2x  =   -12

                                 x   =    6

Distance Upstream: 4x   = 4(6)   = 24

Distance Upstream: 6(x - 2)  = 6(6 - 2)   = 6(4)   = 24

Total distance traveled is Upstream + Downstream = 24 + 24 = 48

Answer: 48 miles

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Answer:

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Step-by-step explanation:

x/47=82.8/92

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2 years ago
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