Which of the statements describes a situation which models growth or decay by an equal factor over equal
intervals?
O
A. A water tank is filled at a rate of 2 gallons per minute.
B. A vine grows 6 inches every week.
o
C. A species of fly doubles its population every month during the summer.
D. A car increases its distance from a garage as it travels at a constant speed of 25 miles per hour.

Answers

Answer 1

Answer:

The statement that describes a situation that can be modeled as a growth or decay over equal interval is;

C. A species of fly doubles its population every month during the summer

Step-by-step explanation:

We have for exponential growth or decay, the following equation;

Exponential growth or decay;

[tex]y = a \cdot b^t[/tex]

Where;

a = The initial amount of the item

1 + r =  The rate of growth in percentage

b = The growth or decay factor

t = The time

For exponential decay, we have;

0 < b < 1

b = 1 - r

[tex]y = a \cdot(1 - r)^t[/tex]

For exponential growth, we have;

b > 1

b = 1 + r

[tex]y = a \cdot(1 + r)^t[/tex]

Therefore, given that the number of the fly population doubles every month, we have the growth rate, r as 100%, which is written as 100/100 = 1, to give;

[tex]y = a \cdot(1 + 1)^t = a \cdot(2)^t[/tex]

Which is expressed as an exponential growth by an equal factor of, r, over equal intervals of, t, time.


Related Questions

The gcf of 36 and 60

Answers

Answer:

the gcf is 12

Step-by-step explanation:

.............

Answer:

The gcf is 12!

A building casts a shadow 47 feet long. At the same time, a 38‐foot‐tall flagpole casts a shadow 9.4 feet long. What is the height of the building?

Answers

210 feet  To answer this question you need to know the ratio of shadow with the actual object. In this case, 42 feet flagpole cast 9.4 feet shadow. Then the ratio is:

42feet/9.4 feet= 4.468

That means the actual height is 4.468 times of shadow length. After that, you can multiply the ratio with the shadow to know the object actual size. It would be: 47 feet x 4.468=  210 feet.

Suppose f(x)=4x-2 and g(x)=-2x+1. Find the value of f(5)/g(-3)

Answers

Answer:

17/7 (2 3/7 or 2. 428571...)

Step-by-step explanation:

f(x) = 4x-2

Find f(5)

f(5) = 4(5)-3f(5) = 20-3f(5) = 17

g(x) = -2x+1

Find g(-3)

g(-3) = -2(-3)+1g(-3) = 6+1g(-3) = 7

Find f(5)/g(-3)

f(5)/g(-3)17/7 (2 3/7 or 2. 428571...)

The value of f(5)/g(-3) will be 18/7.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The value of the function are,

⇒ f (x) = 4x - 2 and

⇒ g(x) = -2x + 1

Now,

Since, The value of the function are,

⇒ f (x) = 4x - 2 and

⇒ g(x) = -2x + 1

Hence, We get;

⇒ f (5) = 4 × 5 - 2

          = 20 - 2

         = 18

And, g (- 3) = - 2 × - 3 + 1

⇒ g (-3) = 6 + 1

            = 7

Thus, The value of f(5)/g(-3) = 18/7

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A 24 foot long tree casts a shadow that is 9 feet long at the same time a nearby building casts a shadow of 45 feet long how tall is the building

Answers

Answer:

i think the answer you're looking for is 60

Step-by-step explanation:

24-9=15

45+15=60

gET RIGHT AND GET BRAINLIEsT

Answers

Answer:

68

Step-by-step explanation:

k=-34

absolute value makes k positive

34+34


A rain gutter is made from aluminum sheets that
28 cm wide. The first step in forming a rain gutter is to lift the edges of the aluminum sheet to form right angles, as show in in the illustration below. The cross-section
area formed by the raised edges affects the water flow. This cross-section area, A, can be represented by the function A = x(28-2x) where x
represents the height of the raised edges.
1. To the nearest centimetre, determine the height of the raised edge, x cm, which will maximize the
transverse area.

Answers

Answer:

               7 cm

Step-by-step explanation:

For any quadratic function f(x)=ax²+bx+c given in form f(x)=a(x-h)²+k, where:

h=-b/2a  and k=f(h) the point (h, k) is vertex of the function graph.

It means that k is maximum (if a<0) or minimum (if a>0) value of function and x=h is the x which will maximize function.

A(x) = x(28-2x) = 28x - 2x² = - 2x² + 28x ⇒ a = -2 , b = 28

h = -28/[2•(-2)] = 7

The coordinates of points A and B are A(4, -2) and B(12, 10). What are the coordinates of the point that is 1/4 of the way from A to B?

Answers

Answer:

Step-by-step explanation:

(4 + 12)/4 = 16/4 = 4

(-2 + 10)/2= 8/4 = 2

(4, 2) is 1/4 of the way from A to B

The coordinates of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).

What is an ordered double?

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

The coordinates of points A and B are A(4, -2) and B(12, 10)

The coordinates of the point that is 1/4 of the way from A to B

The above statement means that the line segment AB is divided in the ratio of 1:4 internally.

Using the section formula:

Let C be the new coordinate point:

C(x) = [1(12) + 4(4)]/(1+4)

C(x) = 28/5

C(y) = [1(10) + 4(-2)]/(1+4)

C(y) = 2/5

Thus, the coordinate of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).

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4(b+24)=(12b+8) pls help

Answers

Answer:

b=11

Step-by-step explanation:

4(b+24)=(12b+8)

4b+96=12b+8

-4. -4

96=8b+8

-8. -8

88=8b

88÷8=11

please help!! (click on pic)

Answers

Answer:

1/2x³y^6

Step-by-step explanation:

Roselyn is driving to visit her family, which lives 150 km away. Her average speed is 60 km/h. The cars tank has 20 L of fuel at the beginning of the drive, and its feel efficiency is 6 km/L. Fuel cost 0.60 dollars per liter what is the price for the amount of feel that Rosalyn will use for the entire drive?

Answers

Answer:

15

Step-by-step explanation:

It was very long

The price for the amount of fuel that Roselyn will use for the entire drive is $25

What is an Equation?

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, and quadratic equations.

Roselyn's family lives 150 km away.

Her average speed is 60km/h

The car tank has 20 L of fuel at the beginning of the the drive.

Fuel efficiency is 6km/ L.

The cost of the fuel is $0.60/L.

The total drive is 150km.

The 6km of distance requires 1 L of fuel

Then 150 km  of the distance requires

= 150 * 1 / 6

= 150/6

= $25.

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Cindy lost 47 pounds while on a diet. She now weighs 144 pounds. Write and solve an equation to find her initial weight.

Answers

Answer:

191

Step-by-step explanation:

47+144=191

Answer:

equation: 144+ 47= 191

Step-by-step explanation:

If Jamie is riding at 14 mph and cori is riding at 0.04km per minute, how far will each of yjem bike in two hours? 1 mile = 1.61 km use the equation D=V/T

Answers

Answer:

Jamie will have covered a distance of 45.08 km while Cori will be 4.8 km away

Step-by-step explanation:

Here, we want to know how far will each of both riders be in 2 hours time.

Jamie is riding 14 mph

This means the number of miles covered in two hours will be 14 mph * 2 = 28 miles

For comparison purposes, let’s convert this to kilometer.

Since 1 mile = 1.61 km, then 28 miles will be 28 * 1.61 km = 45.08 km

For Cori, he is riding at 0.04 km per minute

1 hour = 60 minutes

so 2 hours = 2 * 60 = 120 minutes

Since the speed is 0.04 km in a minute

Then the distance in 120 minutes will be 0.04 * 120 = 4.8 km

Answer:

The answer is B.

Step-by-step explanation:

0.40 km to miles 0.248548

Then 0.248548 x 120=2 hours

Find the root

X^3-125=0

Answers

Given Equation:

[tex] \huge {\sf {{x}^{3} - 125 = 0}} [/tex]

To Find:

The root of the equation.

Solution:

By adding 125 to both the sides, we get

[tex] \huge {\sf { {x}^{3} = 125}} [/tex]

Take cube to the RHS (Right Hand Side), we get

[tex] \huge {\sf { x = 5}}[/tex]

Answer: x = 5

The solution to the expression is x = 5.

We have,

Expression:

x³ - 125 = 0

This can be written as,

x³ = 125

Now,

Cube of 5:

5³ = 5 x 5 x 5 = 125

Now,

x³ = 5³

Cube cancels out on both sides.

x = 5

Thus,

The solution to the expression is x = 5.

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Points P, R, and S, are collinear such that R lies on PS. It is known that the ratio of
PR: RS = 1/3}. Find the location of coordinate R if P is located at (-2,-6) and is
located at (10,30).

Answers

Answer:

1,3

Step-by-step explanation:

Sorry if my English is bad

or if my answer is wrong but from my understanding,

as you can recognize from the photos, we need to understand what a collinear is. Collinear are points that are lying in the same straight line. Thus, we can transform the ratio to fractions which means 1 : 3 into 1/3

Hence, the coordinate R is 1/3 between P and S.

Therefore, to determine coordinate R, we must use the formula that is provided. P is (X1, Y1), S is (X2,Y2), M1 is 1 or the Numerator and M2 is 3 or The denominator.

16 PS 19
E question Help
Some friends played a board game. During the game, one unlucky player had to move back 9 spaces
7 turns in a row. Find a number to represent that player's movements for those 7 turns

Answers

Answer:

-63

Step-by-step explanation:

Because -9 x 7 = -63. If the signs are different then it will be negative. -9 x 7 = -63 is the same like 9 x 7 = 63. I hope this answer your question!

Can someone help me with this please :)

Answers

It 90 because u mult 10 x9

Answer:

47.25

Step-by-step explanation:

9 times 10.5=94.5/2=47.25

2xº
(8x - 10°
a. Solve for x
b. Find the measure of the angle on the right
c. Find the measure of the angle on the left

Answers

Step-by-step explanation:

2x + 7x - 10 = 180° because these rwo angles are supplementary

10x - 10 = 180°

10x = 190° divide both sides by 10

x = 19

measure of angle on the right:

8x - 10 ➡ 8 × 19 - 10 = 142°

measure of angle on the left:

2x ➡ 2 × 19 = 38°

Convert 6 7/20
into a decimal

Answers

Answer:

6.35

Explanation:

7 divided by 20 is 0.35+6= 6.35

find the value of f(3) for the function f(x)=-4(x+3) f(3)=

Answers

Answer:

-24

Step-by-step explanation:

Given function

f(x)= -4(x+3)

To find

f(3)=?

Solution

Substitute x with 3 in the equation to find f(3)

f(3) = -4(3+3) = -4*6 = -24

Can someone answer all these for me please

Answers

5^3 is 15 i hope this helps im sorry if it didnt
First section
1. 169
2. 64
3. 81
4. 125
5. 4
6. 216
7. 2304
8. 27
9. 49

Second section
1. 4
2. 3
3. 5
4. 9
5. 1
6. 2
7. 7
8. 6
9. 10

Third section
1. 24
2. 3
3. 15(squareroot sign) 5
4. 18 (squareroot sign) 6
5. 6 (squareroot sign) 2
6. 72 (squareroot sign) 3
7. 21 (squareroot sign) 7
8. 0
9. 81

What value does the 8 represent in the number 865,202 ?

Answers

The value of 8 is 800,000.

The value of each digit in a number is known as the place value.  The place value of 8 in the number 865,202 is 800,000.

What is the place value of a digit in a number?

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

How do identify the place value of a digit in a number?

The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths and so on

The tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10

The place value of 8 in the number 865,202 is 800,000.

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What’s the value of k?

Answers

Answer: k = 5°

Step-by-step explanation:

A triangle adds up to 180°. Therefore, the equation is 115 + (4k + 5) + (6k + 10) = 180.Remove the parenthesis and combine the like terms. 115 + 5 + 10 = 130 and 4k + 6k = 10k. The equation simplifies to 130 + 10k = 180.Subtract 130 on both sides. 10k = 50Divide by 10 on both sides. k = 5

Answer:

The value of k is 10°

Step-by-step explanation:

Assuming that straight line is 180°. First, you have to find the angle of ZYX by subtracting 115° from 180° :

∠ZYX = 180° - 115° = 65°

Given that total angles in a triangle is 180°. So you have to add up all the angles in the triangle in terms of k :

∠XZY + ∠ZYX + ∠ZXY = 180°

4k + 5 + 65 + 6k + 10 = 180

10k + 80 = 180

10k = 180 - 80

10k = 100

k = 100 ÷ 10

k = 10

This graph shows the number of miles a freight train travels over a period of time.
Freight Train Travel Rate
What is the slope of the line?
Use the number pad to enter your answer in the box

Answers

It issssssssssssssss 3/4 . X 3204

Which step can you use to solve the equation t - 8= -3?
O Add 8 to each side of the equation.
Subtract 8 from each side of the equation.
O Multiply each side of the equation by 8.
O Divide each side of the equation by 8.
Solve the equation t-8=
3.

Answers

You will need to add 8 to the other side of the equation to get t = -3 + 8

Sarah is playing a board game. Her score was -275 at the start of her turn. At the end of her turn, her score was -425. What was the change in Sarah's score (in points) from the start of her turn to the end?

Answers

Answer:

150 points

Step-by-step explanation:

Since they are asking for a change, first you need to subtract the greater number by the least number. So the equation now looks like -275 - (-425), solving this using integer skills will get you a answer of 150 points.

Answer: -150

Step-by-step explanation:

The change is obtained by subtracting the original term from the second term so you do -425 + 275 = -150, the change in Sarah’s score.

A rectangular lawn is 40 feet by 50 feet. How wide a uniform strip has been mowed around
the edge if 3/10 of the lawn has not yet been mowed?

Answers

Answer:

The width of the strip is 28 ft

Step-by-step explanation:

First lest us calculate the area of the rectangle

given that

length= 50ft

width= 40 ft

Area = length *width

Area=  50*40

Areaa= 2000 ft^2

given that 3/10 of the lawn is yet to be mowed

(3/10)*2000

0.3*2000= 600ft^2

Therefore the area that has been mowed is 2000-600= 1400 ft^2

1400 ft^2

since the direction of the mower is along the lenght of the lawn

area= lenght*width

1400= 50*width

width= 1400/50

width= 28 ft

szfdxgcvjhgfdshdxfjcgkvhlkgfgd

Answers

Answer: B

Step-by-step explanation:

-6.53, -6 1/4, 6.57, 6 3/4.

In expanded form, log(1,000a^3/b) is equivalent to...​

Answers

Answer:

Option (4)

Step-by-step explanation:

Given expression is,

[tex]\text{log}(\frac{1000a^3}{b})[/tex]

To solve this expression we will use the logarithmic properties.

[tex]\text{log}(\frac{1000a^3}{b})=\text{log}1000a^3-\text{log}(b)[/tex] [Since, [tex]\text{log}\frac{p}{q}=\text{log}p-\text{log}q[/tex]]

                 = log(1000) + log(a³) - log(b) [Since, log(pq) = log(p) + log(q)]

                 = 3 + 3log(a) - log(b)

                 = 3[1 + log(a)] - log(b)

Therefore, Option (4) will be the correct option.

Algebra KPL and LJPL are a linear pair, m_ KPL = 2x + 24, and mLJPL = 4x + 36. What are the measures of ZKPL and LJPL? (2x + 24) (4x + 36) к P

Answers

Answer:

64° = ∠KPL116° = ∠JPL

Step-by-step explanation:

The sum of the measures of a linear pair of angles is 180°.

  (2x+24) +(4x+36) = 180

  6x = 120 . . . . . . subtract 60, collect terms

  x = 20

  (2(20) +24)° = 64° = ∠KPL

  (4(20) +36)° = 116° = ∠JPL

500g:3kg.Give answer in lowest term​

Answers

Answer:

Step-by-step explanation:

First, you have to convert the units, since kilograms and grams aren't the same unit. 1000 grams=1 kilogram. Keep that in mind, and lets move on.

So, that means 3 kilograms=3,000 grams. Let's rewrite our ratio.

500g:3,000g

So now they're the same units, but it isn't simplified. This last parts easy. To simplify a ratio, find the number you can divided both number with. In this situation, that number is 500. 500 divided by 500= 1, and 3,000 divided by 500= 6.

Final Simplified Ratio: 1g:6g

Hope this helped :)

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