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3 years ago

Please help, what is the measurement of YZ?

Mathematics

2 answers:

VLD [36.1K]3 years ago

6 0

Answer:

24.4

Step-by-step explanation:

tan(16) = opposite/adjacent

tan(16) = 7/YZ

YZ = 7/tan(16)

YZ = 7/0.287

YZ = 24.39

YZ = 24.4

aliya0001 [1]3 years ago

3 0

Answer:24.39

Step-by-step explanation:

Let YZ be x

Tan x = opp/Adj

Tan 16 = 7/x

Cross multiply

x Tan 16 = 7

0.287x = 7

Divide both side by 0.287

x =24.39

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The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

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Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

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3 years ago

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3 years ago

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3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared

navik [9.2K]

The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

$\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end$

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

Learn more about limiting factor from here brainly.com/question/18415071.

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