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satela [25.4K]
2 years ago
5

A population of beavers decreases exponentially at a rate of 7.5% per year. What is the equivalent monthly rate to the nearest h

undredth of a percent?
0.65%

0.81%

0.91%

2.37%
Mathematics
2 answers:
Elena-2011 [213]2 years ago
8 0
Hey there,

Your correct answer will be A.)0.65 because when you do 7.2 divided by 12 because of the year, and it will get you 0.65

~Jurgen
Fiesta28 [93]2 years ago
3 0

Answer:

0.63%


Step-by-step explanation:

If 7.5% decrease in 1 year (12 months), then the percentage decrease per month will be 7.5% divided by 12.

\frac{7.5}{12}=0.625 percent per month


Rounded to the nearest hundredth, 0.625% is equal to 0.63%


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Answer: There are 3 strips that can be cut from the roll of ribbon.

Step-by-step explanation:

since we have given that

Length of a ribbon is given by

7\frac{1}{2}\ ft\\\\=\frac{15}{2}\ ft

Length of pieces of ribbon cut into strips is given by

2\frac{1}{2}\ ft\\\\=\frac{5}{2}\ ft

So, we need to find the number of strips that can be cut is given by

\text{ Number of strips }=\frac{\text{Length of roll}}{\text{ Length of strip}}\\\\=\frac{\frac{15}{2}}{\frac{5}{2}}\\\\=\frac{15\times 2}{2\times 5}\\\\=\frac{15}{5}\\\\=3

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2 years ago
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Which statements are true regarding triangle LMN? Check all that apply.
dimaraw [331]

Answer:

NM = x

LM = x\sqrt{2}

tan (45) = 1

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

                                        LM^{2} =LN^{2} +NM^{2}

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

                                        sin (\theta) = \frac{opposite}{hypotenuse}

                                        cos (\theta) = \frac{adjacent}{hypotenuse}

                                    tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}

Step 3: Verifying all the possible answers

A: Since, LN = x and using tan (45) =1

we can calculate

                                              tan (\theta)= \frac{opposite}{adjacent}

                                           tan (45)= \frac{NM}{x} =1

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to x\sqrt{2\\}.

C: Using Pythagoras Theorem

                                        LM^{2} =LN^{2} +NM^{2}

                                           LM^{2} =x^{2} +x^{2}

                                              LM^{2} =2x^{2}

                                         LM = \sqrt{2x^{2}} = x\sqrt{2}

It can also be proved using trigonometric relation

                                           cos (45) = \frac{x}{LM}

                                            LM = \frac{x}{cos (45)}

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Therefore

                                            LM = x\sqrt{2}

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

                                              tan (\theta)= \frac{opposite}{adjacent}

                                           tan (45)= \frac{x}{x} =1

Therefore, tan (45) = 1  and not equal to \frac{\sqrt{2} }{2}

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