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3 years ago

The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.

Mathematics

1 answer:

deff fn [24]3 years ago

7 0

Answer: (B) 3 times as fast

<u>Step-by-step explanation:</u>

rate of change is the "slope" between the given interval.

f(x) = 125(.9)ˣ

f(1) = 125(.9)¹

= 112.5

f(5) = 125(.9)⁵

= 73.8

$\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675$

********************

f(11) = 125(.9)¹¹

= 39.2

f(15) = 125(.9)¹⁵

= 25.7

$\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375$

********************

The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.

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In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1

svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$1)\, XY=XZ$ Given

$2) \text{ $ m\angle Y= m\angle Z$}$ Isosceles Triangle Theorem

$\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}$ Angle Addition

$\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}$ Given

$5) \text{ $m\angle XYQ=m\angle QYZ$}$ Definition of Bisector

$\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}$ Substitution

$7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}$ Angle Addition

$8)\text{ $ZP$ bisects $\angle XZY$}$ Given

$\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }$ Definition of Bisector

$\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}$ Substitution

$11)\text{ } 2m\angle QYZ=2m\angle PZY$ Substitution

$12)\text{ }m\angle QYZ=m\angle PZY$ Division Property of Equality

$13)\text{ } YZ=YZ$ Reflexive Property

$14)\text{ } \Delta YZP\cong\Delta ZYQ$ Angle-Side-Angle Congruence*

$15)\text{ } YQ=ZP$ CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0

3 years ago

Read 2 more answers

Lines LaTeX: CEC E and LaTeX: ADA D intersect at LaTeX: BB.

Goshia [24]

Answer:

✔️The measure of angle <CBA is equal to the measure of angle <DBE.

✔️The measure of angle CBD is equal to the measure of angle ABE.

✔️The sum of the measures of angles CBD and CBA is 180 degrees.

Step-by-step explanation:

Vertical angles are formed when two straight lines intersect each other at a certain point. The diagram given is a typical example. This, vertical opposite angles formed are said to be congruent, that is their measures are equal to each other.

The following statements are true of the given diagram:

✔️The measure of angle <CBA is equal to the measure of angle <DBE.

(<CBA and ,<DBE are vertically opposite angles)

✔️The measure of angle CBD is equal to the measure of angle ABE.

(They are both vertically opposite angles)

✔️The sum of the measures of angles CBD and CBA is 180 degrees.

(<CBA and <CBD are supplementary angles)

3 0

3 years ago

Convert 52 centimetres to millimeters.

Stells [14]

The answer is 520 millimeters

3 0

2 years ago

Read 2 more answers

Step 8: Does the direction of the graphed line correspond to the sign of the calculated slope?

slega [8]

3rd choice i think but i could be wrong i’m kinda dumb

4 0

3 years ago

Read 2 more answers

Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as th

deff fn [24]

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

$f_k=\frac{\mu^ke^-^\mu}{k!}$

a) Evaluating at k=3

$f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240$

b)Evaluating at k=0,1,2:

$f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498$

$f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494$

$f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240$

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

4 0

3 years ago