Answer: 15 miles
<u>Step-by-step explanation:</u>
2/3 of the way is 30 miles
Let x represent the total distance to grandmother's house, then
Since the total distance is 45 and they have already driven 30 miles, there is 15 miles to go
4. The data set DDT (MASS) contains independent measurements of the pesticide DDT on kale. Make a histogram and a boxplot of the
data. From these, estimate the mean and standard deviation. Check your answers with the appropriate functions.
1 answer:
Answer:
Step-by-step explanation:
Rcode:
library(MASS)
data(DDT,package="MASS")
head(DDT)
colnames(DDT)
print(DDT)
boxplot(DDT)
hist(DDT,main="Histogram for DDT")
fivenum(DDT)
dim(DDT)
outlier_values <- boxplot.stats(DDT)$out # outlier values.
boxplot(DDT, main="DDT", boxwex=0.1)
mtext(paste("Outliers: ", paste(outlier_values, collapse=", ")), cex=0.6)
mean(DDT)
sd(DDT)
Output: * see attachment below*
From Histogram the mean is at the peak
it lies in between 3and 3.5
Form Boxplot we found one outlier and it is 4.64
Fivenum summary is
2.790 3.075 3.220 3.360 4.640
min=2.790
Q1=3.075
Q2=3.220
Q3=3.360
max=4.640
From boxplot the center line is median which cuts the box into 2 equal halves
Distribution is symmetrical
Follows normal distribution.
Mean=3.328
Standard deviation=0.4371531
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So,
Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.
Answer:
the answer is g=2
Step-by-step explanation:
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The distance between an arbitrary point on the surface and the origin is
Recall that for differentiable functions
and 
, the composition 
attains extrema at the same points that does, so we can consider an augmented distance function
The Lagrangian would then be
We have partial derivatives
Set each partial derivative to 0 and solve the system to find the critical points.
From the second equation it follows that either
or 
. In the first case we arrive at a contradiction (I'll leave establishing that to you). If , then we have
This means
so that the points on the surface closest to the origin are
.
Recall that for differentiable functions
The Lagrangian would then be
We have partial derivatives
Set each partial derivative to 0 and solve the system to find the critical points.
From the second equation it follows that either
This means
so that the points on the surface closest to the origin are