Zoologists have been carefully observing an
endangered species in the foothills. They have
noticed that the population, P, of the animal in the
foothills has increased by 3% each year. Their
observations indicated that 500 of the animals
were initially in their study.
Which rule can be used to estimate the
population of the endangered animal over time?

Answer:

y = 12 [tex](2.9)^{x}[/tex]

Step-by-step explanation:

The standard form of the exponential function is

y = a [tex](b)^{x}[/tex]

Find a and b by substituting ordered pairs from the table into the equation

Using (0, 12 ), then

12 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ), so

a = 12, then

y = 12 [tex]b^{x}[/tex]

Using (1, 34.8 ) , then

34.8 = 12 [tex]b^{1}[/tex] ( divide both sides by 12 )

b = 2.9

Thus exponential function is

y = 12 [tex](2.9)^{x}[/tex]

Answer:

y=1 x=9

Step-by-step explanation:

-4(9y) + y = -35

-36y+y=-35

-35y= -35

y=1

To check-

-4(9) + 1 = -35

-36 + 1 =-35

Answer:

45% of the mangoes are bad.

Step-by-step explanation:

Given that:

Number of mangoes in basket = 40

Number of good mangoes = 22

Number of bad mangoes = Total mangoes - Good mangoes

Number of bad mangoes = 40-22

Number of bad mangoes = 18

Percent of bad mangoes = [tex]\frac{bad\ mangoes}{total\ mangoes}*100[/tex]

Percent of bad mangoes = [tex]\frac{18}{40}*100[/tex]

Percent of bad mangoes = 0.45*100 = 45%

Hence,

45% of the mangoes are bad.

Answer:

Yes.

Step-by-step explanation:

It is given that, A sponge can filter 8 liters of water in 10 hours or 12 liters in 15 hours.

8 L = 10 h

1 h = [tex]\dfrac{10}{8}[/tex] = 1.25 h

or

12 L = 15 h

1 h = [tex]\dfrac{15}{12}[/tex] = 1.25 h

Hence, this relationship is proportional.

Answer: Slope= 0.833/2.000= 0.417

​

Step-by-step explanation:

Answer:

x=12/5y+24/5

Step-by-step explanation:

5x-12y=24

add 12y to both sides

problem comes down to 5x=12y+24

divide everything by 5

Answer:

Step-by-step explanation:

1 foot = 12 inches

12 inches/ 48 inches = 1/4 foot

or  1 foot/4 feet = 1/4 foot

Answer:

33 days

Step-by-step explanation:

15 + 18 = 33

Answer:

C

Step-by-step explanation:

amd merry Christmas to you too

Answer:

its C.

Step-by-step explanation:

Answer:

24.3

Step-by-step explanation:

its really hard to explain but trust me

Answer:

The tree would be 27.6

Step by Step:

I took the height of the mailbox (6 ft) and its shadow (5.4) and subtracted that and got 0.6. Then I took 0.6 and added it to the shadow of the tree (27 ft) and got the answer 27.6.

Answer:

∠m = 84º

Step-by-step explanation:

48 + 48 + x = 180

96 + x = 180

x = 84º

hope this helped!

Answer:

∠m = 84º

Step-by-step explanation:

Answer:

There are 10 boys and 6 girls in the class

Step-by-step explanation:

The given parameters are;

The number of boys = The number of girls + 4

The number of students in the class = 16

Let x represent the number of girls in the class and let y represent the number of boys in the class

Therefore;

y = x + 4...(1)

x + y = 16...(2)

Making y the subject of equation (2) gives;

y = 16 - x

Equating the values of y from equation (1) and equation (2) gives;

x + 4 = 16 - x

Which gives;

2·x = 16 - 4 = 12

x = 12/2 = 6

x = 6

The number of girls = x = 6

From equation (1), we have;

y = x + 4 = 6 + 4 = 10

y = 10

The number of boys = y = 10.

Answer:

D

Step-by-step explanation:

Answer:

3 < x < 7

Step-by-step explanation:

From the diagram; |AB| = |AC|

The length AB is calculated as;

[tex]Sin\ 52^o = \frac{|BD|}{|AB|} \\\\|AB| = \frac{|BD|}{Sin\ 52^o} \\\\|AB| = \frac{12}{Sin\ 52^o} \\\\|AB| =15.228 \ m[/tex]

The length CD is calculated as;

[tex]Sin \ 31^o = \frac{|CD|}{|AC|} \\\\|CD| = |AC| \ \times \ Sin \ 31^o \\\\|CD| = 15.228 \ \times \ 0.515\\\\|CD| = 7.84[/tex]

|CD| = 2x - 6

2x - 6  = 7.84

2x = 7.84 + 6

2x = 13.84

x = 13.84 / 2

x = 6.92

x ≅ 7

Thus, 3 < x < 7

Answer:

the answers are bolded below!

Step-by-step explanation:

1. y-y1=m(x-x1)

line one- 14-4/6-1 = 10/5 = 2

so....     y-1=2(x-4)

simplified     y=2x-7

line two- -2-23/1-6 = -25/5 = -5

so.....      y-6=-5(x-23)

simplified         y=-5x+121

b- they will intersect 1 time at (18.2,29.5)

2. No, it the system has infinitely many solutions, then the lines would be on top of each other. But since there are only two solutions, then your answer would not be infinitely many solutions.

3. y=-2x+1. This would not intersect with y=-2x+3 because they are parallel. the slopes are the same so they will each travel at the same rate but they have different y intercepts.

4. y=-2x+7 ------> x=-1/2y-7/2

y=-3(-1/2y+7/2)+8  -----> y=5

y=-2x+7 --->   5=-2x+7  ----> x=1

one solution at (1,5) because f graphed, the lines would only intersect once.

b- x=5

3x-y=5   --->   3(5)-y=5   --->   y=10

one solution at (5,10) because f graphed, the lines would only intersect once.

c- no solutions because if it were to be graphed, the lines would not intersect at all.

d- no solutions because if it were to be graphed, the lines would not intersect at all.

e- no solutions because if it were to be graphed, the lines would not intersect at all.

i am in algebra two so you can trust my answer. If you need more help lmk in the comments. Happy holidays and stay safe!

Answer:

y = 2x - 12 or A

Step-by-step explanation:

6x - 3y = 36                        Subtract 6x from both sides.

-3y = 36 - 6x                       Divide by - 3

-3y/-3 = 36/-3 - 6x/-3

y = -12 + 2x

The answer is A

Answer:

Step-by-step explanation:

12:18

can both be divided by 6

answer is 2:3

Answer:

6:9

Step-by-step explanation:

that's the simplest form

Answer:

There would be 1080 bacteria in the culture.

Step-by-step explanation:

Initial number of bacteria = 40

Given that

culture of bacteria triples by the end of each hour

Number of bacteria after 1 hour = 40*3 (multiplying initial number of bacteria by 3)

Number of bacteria after 1 hour = 120

number of bacteria after 2 hours = 3*Number of bacteria after 1 hour = 3*120

number of bacteria after 2 hours =360

number of bacteria after 3 hours = 3*Number of bacteria after 2 hour = 3*360 = 1080

Thus,

there would be 1080 bacteria in the culture.

Answer:

1080 bacteria

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

c x-110

Step-by-step explanation:

if im wrong im so sorry

Answer:

1. 3 inches per hour

2.72 miles per hour

Answer:

1. 3 2. 72

Step-by-step explanation:

For number 1 and 2 you have todivide them

Answer: (0,8)

Step-by-step explanation:

Convert to slope intercept form

-y+8=2x

-y=2x-8

y=-2x+8

Therefore 8 would be the y intercept

Answer:

56

Step-by-step explanation:

8 = 2³ and 32 = 2⁵, so

√(8) = √(2²•2) = 2√(2)

√(32) = √(2⁴•2) = 2²√(2) = 4√(2)

Then

1/√(2) + 3/√(8) + 6/√(32)

= 1/√(2) + 3/(2√(2)) + 6/(4√(2))

= 4/(4√(2)) + 6/(4√(2)) + 6/(4√(2))

= 16/(4√(2))

= 4/√(2)

Optional step: Rationalize the denominator by multiply this by √(2)/√(2) to get

4/√(2) • √(2)/√(2) = (4√(2))/2 = 2√(2)

which you can also write as √(8).

Answer:

A

Step-by-step explanation:

b is the range

9514 1404 393

Answer:

  D.  Multiply the top equation by 3 and the bottom equation by 4.​

Step-by-step explanation:

If you're using subtraction, you want the coefficients of one of the variables to be the same in both equations. If the variable you choose is x, then you need to multiply the top equation by the coefficient of x in the bottom equation (3), and the bottom equation by the coefficient of x in the to equation (4). Doing this will make both x-coefficients equal to 3×4 = 12. In short, ...

  Multiply the top equation by 3 and the bottom equation by 4.​

Answer:

The answer is Q

Step-by-step explanation:

√10= 3.16

Answer:

To answer your question use the code ICE on here to get your answer works every time for me hope this helps

Answer:

[tex]{:}\longrightarrow\tt f (x)=6 (1-x)[/tex]

[tex]{:}\longrightarrow\tt f (-7)=6 (1-(-7))[/tex]

[tex]{:}\longrightarrow\tt f (-7)=6 (1+7)[/tex]

[tex]{:}\longrightarrow\tt f (-7)=6(8)[/tex]

[tex]{:}\longrightarrow\tt f (-7)=48 [/tex]

[tex]\therefore\sf f (-7)=48 [/tex]

Answer:

:⟶f(x)=6(1−x)

{:}\longrightarrow\tt f (-7)=6 (1-(-7)):⟶f(−7)=6(1−(−7))

{:}\longrightarrow\tt f (-7)=6 (1+7):⟶f(−7)=6(1+7)

{:}\longrightarrow\tt f (-7)=6(8):⟶f(−7)=6(8)

{:}\longrightarrow\tt f (-7)=48:⟶f(−7)=48

\therefore\sf f (-7)=48∴f(−7)=48

Answer:

C

Step-by-step explanation:

To find the volume of a cube, raise the value of one side to the third power. 2.5 centimeters to the third power is 15.625, which can also be expressed as the fraction 125/8

Answer: choice C

Step-by-step explanation:

Since V = s^3

And side length = 2.5

V = (2.5)^3

V = 15.625

V = 125/8 cm^3

Answer:

x = 0

Step-by-step explanation:

If one were to fold this figure in half over the line x = 0, then one would end up with a single figure, with no overhang. Hence x = 0 is the line of symmetry. Note; x = 0, can also be called the y-axis.

Answer:

Option D) x = 0

Step-by-step explanation:

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object. Here we see that the object's Axis of symmetry is the line x =0

The line x = 0,1,2,3,4,5,..... and so on are all vertical lines and

The line y=0,1,2,3,4,5,..... and so on are all horizontal lines

In this this case the line x = 0 is the Axis of symmetry which divides the object in two equal halves.