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1 year ago

Pythagorean Theorem with Known Legs

Mathematics

1 answer:

7nadin3 [17]1 year ago

3 0

$c {}^{2} = 7 {}^{2} + 9 {}^{2} \\ c {}^{2} = 49 + 81 \\ c {}^{2} = 130 \\ c = \sqrt{130}$

<h2>Answer</h2>

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Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate

salantis [7]

The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t

We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.

We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.

8 0

3 years ago

Read 2 more answers

Is triangle ABC similar to triangle DEF? why or why not.

Lana71 [14]

Answer:

Step-by-step explanation:

Two triangles are congruent if they have the same three sides in proportion and they have exactly the same angles.

If the angles are different, the triangles are not similar.

3 0

3 years ago

In many fast food restaurants, there is a strong correlation between a menu item's fat content (measured in grams) and its calor

Kruka [31]

Answer:

1. The slope of the least-squares regressin line is 11.364

2. The intercept of the least-squares regression line is 204.343

3. The residual corresponding to this observation is -10 calories

Step-by-step explanation:

1. In order to calculate the slope of the least-squares regressin line we would have to use the following formula:

slope of the least-squares regressin line=r*sy/sx

Therefore, slope=0.979*324.90/27.99

slope=11.364

2. In order to calculate the intercept of the least-squares regression line we would have to use the following formula:

intercept of the least-squares regression line=ybar - slope*xbar

intercept=662.88 - 11.364*40.35

intercept=204.343

3. In order to calculate the the residual corresponding to this observation we would have to use the following formula:

residual = observed y - predicted y

predicted y=11.364*x + 204.343

if the x value is 7, therefore predicted y=11.364*107 + 204.343

predicted y=1,420

Therefore, residual=1410 calories - 1420 calories

residual=-10 calories

8 0

3 years ago

Olce Question<br> What type of notation uses these brackets {}?<br> A. Interval<br> B. Set

Sergio [31]

Answer:

Interval?

Step-by-step explanation:

5 0

2 years ago

Determine the expression you can substitute for y in to solve the system below.

FromTheMoon [43]

Answer:

Step-by-step explanation:

given are the two following linear equations:

f(x) = y = 1 + .5x

f(x) = y = 11 - 2x

Graph the first equation by finding two data points. By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

If x = 0, then f(0) = 1 + .5(0) = 1

If y = 0, then f(x) = 0 = 1 + .5x

-.5x = 1

x = -2

The resulting data points are (0,1) and (-2,0)

Graph the second equation by finding two data points. By setting first x and then y equal to zero it is possible to find the y intercept on the vertical axis and the x intercept on the horizontal axis.

If x = 0, then f(0) = 11 - 2(0) = 11

If y = 0, then f(x) = 0 = 11 - 2x

2x = 11

x = 5.5

The resulting data points are (0,11) and (5.5,0)

At the point of intersection of the two equations x and y have the same values. From the graph these values can be read as x = 4 and y = 3.

6 0

3 years ago