Mathematics Middle School

which of the following are examples of exponential decay? select all that apply.

a) the population of Florida is increasing by 43% each year
b) the pesticide DDT has a half-life of 15 years
c)march madness has 64 teams in the bracket. each round, half of the teams are eliminated
d)after an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours
e) a tree frog population doubles every three weeks

Answers

Answer 1
B, C and D are exponential decay.

Half-lives are given by exponential function, and since they are decreasing, it is decay.
With the teams being eliminated, this is decay.
Bacteria can be represented by exponential functions, and it is decreasing.

Related Questions

the perimeter of a triangle is 75 cm. The triangle is isosles now, but if its base were lenghthened by 2 cm and each leg were shortened by 7 cm, it would be equilateral. find the length of the base of the original triangle

Answers

(-14)+2=(-12)

75-12=63

63/3=21

21-2=19     BASE=19

21+7=28  EACH LEG=28

28+28+19=75

new triangle 21+21+21

19+2=21

28-7=21

Final answer:

To find the original base length of the isosceles triangle, we set up equations based on the given perimeter and the condition for the triangle turning into an equilateral triangle after changes to its sides. Solving these equations, we find that the original base length is 19 cm.

Explanation:

The student is asking about solving a problem related to the perimeter of an isosceles triangle and finding the original base length given certain conditions that would turn it into an equilateral triangle.

In the original isosceles triangle, we'll denote the equal sides as 'a' and the base as 'b'. Since the perimeter is the sum of all sides, we have:

a + a + b = 75 cm

When altered, the base becomes 'b + 2 cm' and the equal sides become 'a - 7 cm'. To form an equilateral triangle, all sides must be equal:

b + 2 = a - 7

Simplifying gives us two equations:

2a + b = 75b + 2 = a - 7

Rearranging the second equation we get a = b + 9. Substituting 'a' in the first equation we get:

2(b + 9) + b = 75

Which simplifies to:

3b + 18 = 75
b = 19 cm

Therefore, the length of the base of the original isosceles triangle is 19 cm.

What is (x-5)1/2+5=2

Answers

For this case we have the following expression:
 (x-5) 1/2 + 5 = 2
 Rewriting correctly we have:
 (x-5) ^ (1/2) + 5 = 2
 Clearing x we have:
 (x-5) ^ (1/2) = 2-5
 (x-5) ^ (1/2) = -3
 (x-5) = root (-3)
 x = 5 + i * root (3)
 Answer:
 The value of x is given by:
 x = 5 + i * root (3)

A sided cube labeled 1-6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one statement.
Probability the same, Probability is smaller. Probability is larger. There's not enough information

Answers

Probability is smaller.

Answer:

Probability is smaller.

Step-by-step explanation:

Donna wants to draw a right triangle. She wants the hypotenuse to be 1.5 inches long and one of the legs to be 1.2 inches long. Enter the length that she must use for the second leg to form a right triangle.

Answers

We will use the pythagorean theorem to answer this problem. a^2+b^2=c^2, where a and b are the legs of the right triangle, while c is the hypotenuse.
Since the measurements for one of the legs and the hypotenuse are already given, this leaves out only with one unknown, which we may say the "a" leg.

Substituting the given values, we have a^2 + (1.2)^2 = (1.5)^2. Simplying the exponents, we have a^2+1.44 sq.inches = 2.25 sq.inches. Now, isolating the unknown, a^2 = 2.25 - 1.44 sq.inches. Further, we have a^2 = 0.81 sq.inches. Therefore, a = √0.81 sq.inches or a = 0.9 inch.

Evaluate square root of 24 - x when x = 6 . Write the answer in simplified radical form.?

Answers

So, first we input 6
24 - 6 = 18
So we now need to find the square root of 18
If you're allowed to use a calculator, the square root is 4.242

But if you don't, let's get as close as we can:
√(9 * 2)
Because the square root of 9 is 3:
3 * √2

QUESTION 1:
The probability that an event will occur is 15%. Which of these best describes the likelihood of the event occurring?

A: Likely
B: Certain
C: Unlikely
D: Impossible

QUESTION 2:
The probability that an event will occur is 1/8 . Which of these best describes the likelihood of the event occurring?

A: Likely
B: Certain
C: Unlikely
D: Impossible

Thanks :)

Answers

1. Unlikely
2. Unlikely
They are both unlikely.  Certain would be 100%, likely would be anywhere above 50%, AND unlikely would be under 50%
Can I have Brainliest, please?Thanks!!

please help ...... ............

Answers

A because for the x values it is always the opposite side and for the y values it is correct. It is also because of the direction of the axes.

Will mark as Brainliest.

Michaela drops a ball vertically from a height of 80 feet. The peak height after each bounce is half the previous height. How far does the ball travel from the time she drops it until it reaches the peak height after the 5th bounce?

155 ft

230 ft

232.5 ft

312.5 ft

Answers

It will reach (C) 232.5 ft.

Sally is making sun tea. Every hour the concentration of the tea doubles. If it takes 6 hours for the tea to be ready how long would it take the tea to reach half of the final concentration?

Answers

i think is 3 because if the concentration every hour the tea doubles then it take 

It is given Sally is making sun tea. Every hour the concentration of the tea doubles.Let the concentration of tea  at start is  nil.Then after  first hour concentration will be 2.After third hour concentration will be double of 2 that is 4.After fourth concentration will be 4(2)=8.After fifth hour concentration will be 8(2)=16.After sixth hour concentration will be 16(2)=32.

It is given:it takes 6 hours for the tea to be ready.WE need to find  how long would it take the tea to reach half of the final concentration.Half of final concentration is 32÷2=16.

Concentration of 16 is after fifth hour.

A class of 24 students was asked to identify a team sport in which they have participated. Their responses are shown in the line plot.

ty <3

Answers

a) There are a total of 28 votes on the chart.

b) The number of students polled is 24.

c) One or more students must have participated in more than 1 sport, that would explain why there was a higher number of sport participation than students.

a) The total responses recorded from the line plot is n = 28 responses

b) The number of students polled = 24 students

c) The fact that there were more responses than students polled suggests that one or more students engaged in more than one sport.

What is a line plot ?

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the line plot be represented as A

Now , the total number of students in the class = 24 students

So , the total number of polls = 24 students

The total number of responses recorded from the points on the line plot is give by

The number of responses for football = 4

The number of responses for soccer = 8

The number of responses for baseball = 7

The number of responses for basketball = 5

The number of responses for football = 4

The total number of responses recorded from the points on the line plot is n = 28

Given that there were more replies than students asked, it is likely that some students participated in several sports.

Hence , the line plot is solved

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Find three consecutive integers such that three times the sum of the first two is eight more than 5 times the third.

Answers

Consecutive integers are numbers one after the other on the number one (ie. 1,2,3,4,5 or 203,204,205).

times= multiplication
sum= addition
more than= addition
is= equal sign

x= first integer
x+2= second integer
x+3= third integer

3(x + (x + 2))= 5(x + 3) + 8
add inside parentheses

3(2x + 2)= 5(x + 3) + 8
multiply 3 and 5 by their parentheses

(3*2x) + (3*2)= (5*x) + (5*3) + 8
multiply in parentheses

6x + 6= 5x + 15 + 8

6x + 6= 5x + 23
subtract 5x from both sides

x + 6= 23
subtract 6 from both sides

x= 17 first integer

x + 1= 17 + 1= 18 second integer

x + 2= 17 + 2= 19 third integer


CHECK:
3(x + (x + 2))= 5(x + 3) + 8
3(17 + (17 + 2))= 5(17 + 3) + 8
3(17 + 19)= 5(20) + 8
3(36)= 100 + 8
108= 108


ANSWER: The three consecutive integers are 17, 18 and 19.

Hope this helps! :)

Need help with 2 3 4 5 6

Answers

Answer:

all answers are shown and pictured

the denominator of a certain number was 147 greater than its numerator. What was the denominator of this fraction, if after the fraction was reduced it became 5/12

Answers

Let [tex]x[/tex] be the denominator of the number. Since we know that the denominator of the number was 147 greater than its numerator, the denominator of the number was [tex]x+147[/tex], so our number was [tex] \frac{x}{x+147} [/tex]. We also know that after the fraction was reduced it became 5/12, so we can equate both fractions and solve for [tex]x[/tex]:
[tex] \frac{x}{x+147} = \frac{5}{12} [/tex]
[tex]12x=5(x+147)[/tex]
[tex]12x=5x+735[/tex]
[tex]7x=735[/tex]
[tex]x= \frac{735}{7} [/tex]
[tex]x=105[/tex]

Now we can replace 105 in our original fraction to get our number:
[tex] \frac{x}{x+147} [/tex]
[tex] \frac{105}{105+147} = \frac{105}{252} [/tex]

We can conclude that the original number was [tex]\frac{105}{252} [/tex]

1. Suppose the population of deer in a region was 3500 in the year of 2000 since when the population has grown by 3.5% annually what will the approximate population be in the year of 2020 y equals 8 x b x where a is the starting amount B is the growth rate increasing add to 1 and X is time.
2.
The population of New Haven was 148220 in 2004 since when the population has been decreasing at an annual rate of 2.9% if the rate of the decline continues what will the population be in the year 2015

Answers

number 1 the answer to that one should be 6964

To calculate future population growth, we use a formula incorporating the initial population, annual growth rate, and number of years. For growth, we add one to the growth rate and raise it to the power of elapsed years, then multiply by the initial population. For decline, we subtract the rate from one and then do similar exponentiation and multiplication.

Calculating Future Population Growth

To calculate the future population of deer given a starting population and a constant annual growth rate, we use the formula y = a(1+b)^x, where 'a' is the starting amount, 'b' is the growth rate, and 'x' is the number of years elapsed. For the deer population, from 2000 to 2020, there are 20 years of growth at 3.5% annually. Using a=3500, b=0.035, and x=20, the calculation is as follows:

Convert the percentage to a decimal: 3.5% becomes 0.035.

Add 1 to the growth rate: 1 + 0.035 = 1.035.

Raise this sum to the power of 20: (1.035)^20.

Multiply the result by the initial population: 3500 * (1.035)^20.

For the New Haven population, which is decreasing at 2.9% annually from 2004 to 2015 (11 years), the steps are similar. However, we subtract the percentage decline from 1 instead since the population is decreasing.

Convert the percentage to a decimal: 2.9% becomes 0.029.

Subtract this from 1: 1 - 0.029 = 0.971.

Raise this to the power of 11: (0.971)^11.

Multiply the result by the initial population of New Haven: 148220 * (0.971)^11.

After performing these calculations, we will get the estimated populations for both the deer and New Haven in the specified years.

Look at the model below and write an expression to match.

Answers

Since these appear to be algebra tiles, an expression for this would be 2x+6.

The rectangular blocks are x and the squares are 1 unit.  There are 2 x's, or 2x, and 6 units; 2x+6.

simplify this expression 3x^2 y^2/24x

Answers

For this case we have the following expression:
 3x ^ 2 y ^ 2 / 24x
 Rewriting we have:
 (3/24) (x ^ 2 y ^ 2 / x)
 Simplifying we have:
 (1/8) (xy ^ 2)
 Answer:
 The simplified expression for this case is given by:
 (1/8) (xy ^ 2)
The answer would be  (1/8) (xy ^ 2).
Equation: 
3x ^ 2 y ^ 2 / 24x

 =(3/24) (x ^ 2 y ^ 2 / x)
SO simplify it is
= (1/8) (xy ^ 2)

 The simplified expression for this case is given by:
 (1/8) (xy ^ 2)

a jewelry store buys 24 necklaces for $300. the store wants to make a profit of $540. assuming it sells all 24 necklaces, how much should the store charge for each necklace?

Answers

If its meaning making a profit after the $300 then:
540+300=840
840/24= 33.60
They would charge $33.60 per necklace.

If you were meaning a profit of $540 total then:
540/24=22.5
They would charge $22.50 per necklace.

Answer:

i agree with the other person

Step-by-step explanation:

What’s the ratio decimal of
2:3
3:7
3:6
3:8
2:5
3:7
2:4

Answers

To find the ratio decimal form, write each ratio as it's corresponding fraction, then divide. Simplify fractions, if possible.


2:3= 2/3= 0.6666666= 0.67 rounded

3:7= 3/7= 0.42857= 0.43 rounded

3:6= 3/6= 1/2= 0.5

3:8= 3/8= 0.375

2:5= 2/5= 0.4

3:7= 3/7= 0.42857= 0.43 rounded

2:4= 2/4= 1/2= 0.5


Hope this helps! :)

sixty eight is one fourth of what number

Answers

You would have to multiply by the reciprocal so 68 times 4 is 272. Therefore, one forth of 272 is 68. 
the answer is 272. 

68 times 4 equals 272. 
or if you did 272 divided by 4 you would get 68. 

The perimeter of a rectangle is dependent on the length of each of its sides. Suppose the base of a rectangle is two more than its height. Complete an input/output table for at least three pairs of inputs and outputs. Make sure to use values that make sense within the context of this situation.

Answers

let
x---------> length of the base of a rectangle 
y--------->height of the base of a rectangle 

we know that
perimeter of a rectangle=2*[x+y]
and
x=y+2------> y=x-2


step 1
inputs
x=3
x=5
x=10

step 2
find the outputs

for x=3
y=x-2----> y=3-2-----> y=1
perimeter=2*[3+1]-----> 8

for x=5
y=x-2----> y=5-2-----> y=3
perimeter=2*[5+3]-----> 16

for x=10
y=x-2----> y=10-2-----> y=8
perimeter=2*[10+8]----->36

see the attached table

l To finance a bridge costing $94,500, the state contributed twice as much as the county and the county contributed twice as much as the city. How much did each contribute?

Answers

The city contributes $13,500, the county contributes $27,000, and the state contributes $54,000.

Let x = the amount the city contributes.
The county contributes twice this amount, or 2x.
The state contributes twice as much as the county, or 2(2x)=4x.

Together, they all contribute 94500:
x+2x+4x=94500

Combining like terms,
7x = 94500

Divide both sides by 7:
7x/7 = 94500/7
x=13500

The city contributes 13500.
The county contributes 2(13500) = 27000.
The state contributes 2(27000) = 54000.

The length of a rectangle is 5/2 units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?

Answers

Answer:
perimeter = 6w + 5 units

Explanation:
Perimeter of a rectangle can be calculated as follows:
Perimeter = 2(width + length)

We are given that:
width = w units
length is 5/2 units greater than twice the width. This means that:
length = 2w + 5/2

Now, substitute in the above equation to get the expression for the perimeter as follows:
Perimeter = 2(width + length)
Perimeter = 2(w + 2w + 5/2)
Perimeter = 2(3w + 5/2)
Perimeter = 2(3w) + 2(5/2)
Perimeter = 6w + 5

Hope this helps :)

Answer:

D: 6w + 5

Step-by-step explanation:

The perimeter of a rectangle can be calculated as follows:

Perimeter = 2(width + length)

We are given that:

width = w units

length is 5/2 units greater than twice the width. This means that:

length = 2w + 5/2

Now, substitute in the above equation to get the expression for the perimeter as follows:

Perimeter = 2(width + length)

Perimeter = 2(w + 2w + 5/2)

Perimeter = 2(3w + 5/2)

Perimeter = 2(3w) + 2(5/2)

Perimeter = 6w + 5

u=1-3v/vt-w make t the subject

Answers

Final answer:

By isolating terms involving 't' and solving for 't', we manage to rearrange the provided equation to get t = (1-u+w)/(3v^2).

Explanation:

To rearrange the provided equation u=1-3v/vt-w with t as the subject, we can follow these steps:

Start by isolating terms involving t to one side, i.e., bring all other terms to the opposite side. We get: vt = (1-u+w)/3v.The next step is to solve for t by dividing both sides of the equation by v. Hence, the final rearranged equation is: t = (1-u+w)/(3v2).

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In a circle,which ratio is equivalent to pi?

Answers

It is approximately equal to 3.14159. It can be simplified to 3.14
22/7 is the correct answer, hope this helps!:)

Please help on the fraction question

Answers

Im pretty sure the answer is 10. Hope this helped.

10 4/5 is the answer

Factor the quadratic expression Completely; -8x^2-15x+2

Answers

Answer:
(x + 2)(-8x + 1) or,
(-8x + 1)(x + 2)

Explanation:
To factor quadratic equations in the form ax² + bx + c that cannot be factored in your head, the first step is to find factors for the product of coefficient a and constant c whose sum equates to coefficient b. This may sound confusing, but it is easier in practice.

So, we find the product of -8 and 2 which is -16.
Now we list the factors of -16. I like to list them as factor pairs. These are:
1, -16, 2, -8, 4, -4, 8, -2, 16, -1

Next, we examine which combination of factor pairs has a sum of -15. These are -16 and 1. To check: -16 + 1 = -15

Then, we place these values as coefficients into the original equation as substitutes for -15x and find factor out the greatest common factor (GCF) of the equation terms:
-8x² - 16x + x + 2
(-8x² - 16x) + (x + 2)

The GCF between -8x² and -16x is -8x. The GCF between x and 2 is 1.
-8x(x + 2) + 1(x + 2)

If these binomials within the parenthesis match, then you have found the factors. The binomial within the parenthesis is one factor and the GCFs outside of each binomial are is the other factor. Thus, the factors of the original quadratic expression are:
(-8x + 1)(x + 2)

To check these factors for accuracy, we can use the FOIL method to expand the expression, combine like terms, and observe if it matches the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing which terms of each binomial are multiplied together.
Firsts: -8x(x) = -8x²
Outsides: -8x(2) = -16x
Insides: 1(x) = x
Lasts: 1(2) = 2

In an equation: -8x² - 16x + x + 2 → -8x² - 15x + 2
This is the original equation, therefore (-8x + 1)(x + 2) are accurate factors.

Need help on #16 ASAP

Answers

Look at the picture.

c. ΔABC to ΔA"B"C" using translation (x, y) → (x - 2; y - 8)

A stop sign has 8 equal sides. If each side is 11 inches in length, what is the perimeter of the stop sign?

Answers

The perimeter of the stop sign would be 88

On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?

Answers

Hi,
First we need to find 3.75/0.25, then multiply that with 1(same number),since 0.25 inch =1 mile
3.75/0.25=15
That means length=15 miles
Find width in the same way.
2.25/0.25=9
Width=9 miles
a=l*b
a=15*9
a=135 sq. miles
Hope this helps you.

Answer:

135 Square Miles

Step-by-step explanation:

On a map, 0.25 inches represents 1 mile. What is the area of a rectangle on the map that is 3.75 inches long and 2.25 inches wide?

270 square miles

135 square miles

48 square miles

24 square miles

Odyssey



A factory machine produces 5/10 kilograms of chocolate every 1/6 minutes.
At what rate does the machine produce chocolate?
A. 1/3 kg/min
B. 2/5 kg/min
C. 3 kg/min
D. 6 kg/min

Answers

The answer is C, 3 kg/min
:) Have a nice day and maybe consider grading this answer brainliest? <3
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