Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. The sample of 2100 bacteria selected from this population reach the size of 2249 bacteria in two and a half hours. Find the hourly growth rate parameter.This is a continuous exponential growth model.Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.

Answers

Answer 1

In this problem, we have a continuous exponential growth model

so

the equation is of the form

[tex]y=a(e)^{kt}[/tex]

where

a is the initial value ------> a=2,100

y is the number of bacteria

x ----> number of hours

so

[tex]y=2,100(e)^{kt}[/tex]

For x=2.5 hours, y=2,249 bacteria

substitute

[tex]2,249=2,100(e)^{(2.5k)}[/tex]

solve for k

apply ln both sides

[tex]\ln (\frac{2,249}{2,100})=2.5k\cdot\ln (e)[/tex]

k=0.0274

convert to percentage

k=2.74%

Related Questions

Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest

Answers

Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

[tex]P=\frac{A\mleft(\frac{r}{n}\mright)}{\mleft[\mleft(1+\frac{r}{n}\mright)^{nt}-1\mright]}[/tex]

Given:

• The Financial Goal, A= $35,000

,

• Rate = 7.5% = 0.075

,

• Number of compounding period = 12 (Monthly)

,

• Time, t = 3 years

Substitute into the given formula:

[tex]\begin{gathered} P=\frac{35000\mleft(\frac{0.075}{12}\mright)}{\mleft[\mleft(1+\frac{0.075}{12}\mright)^{12\times3}-1\mright]} \\ P\approx\$870 \end{gathered}[/tex]

The monthly payment is $870.

[tex]\begin{gathered} \text{Total deposit}=870\times36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}[/tex]

Option D is correct.

help please ill give brainlest !!

Answers

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37

Write the expression as a monomial in standard form. -0.01a^4*(-10a^5)^3

Answers

The monomial -0.01a^4*(-10a^5)^3 as a single expression is 10a^19

How to rewrite the expression?

The expression is given as

-0.01a^4*(-10a^5)^3

Evaluate the expression in the bracket

So, we have the following equation

-0.01a^4*(-10a^5)^3 = -0.01a^4 * (-1000a^15)

Next, we remove the bracket

So, we have the following equation

-0.01a^4*(-10a^5)^3 = 0.01a^4 * 1000a^15

Evaluate the products in the above equation

So, we have

-0.01a^4*(-10a^5)^3 = 10a^19

Hence, the equivalent expression is 10a^19

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The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?

There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.

Answers

Answer:

A) there are no outliers in this distribution.

Answer:

Step-by-step explanation:

Answer there are no outlier

Translate this sentence into an equation.68 is the product of Diane's score and 4.Use the variable d to represent Diane's score.

Answers

68 = Diane's score x 4

Equation

68= 4d

___________________

Can you see the updates?

_________________

Diane's score

4d= 68

d= 17

A way to write a fraction as an equivalent fraction that contains no common factors is _________ form.

Answers

Answer:

simplest form.

Step-by-step explanation:

Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.

Answers

Answer:

The equation of the line is;

[tex]y=-2x+3[/tex]

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the values of the slope and coordinates;

[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]

Therefore, the equation of the line is;

[tex]y=-2x+3[/tex]

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

Evaluate the given expression.
10 C4 4C2
a.
1,260
C.
1,275
b.
1,278
d.
1,270

Answers

The value of an expression using combinations  ¹⁰C₄ ⁴C₂ is 1260.

What is the combination?The combination is a mathematical method for counting the number of potential configurations in a set of elements when the order of the selection is irrelevant.

The formula for finding the combination of any given expression is given:

ⁿCr =(n!)/(r!(n*r)!)

So,

¹⁰C₄ ⁴C₂¹⁰C₄ = 10! /(4!(10-4)!)¹⁰C₄ = 10! /(4!)*6!¹⁰C₄ = (10*9*8*7*6*5*4*3*2*1)/(4*3*2*1*6*5*4*3*2*1)¹⁰C₄ = 210

Then,

4C2 = 4! /(2!(4-2)!)4C2 = 4*3*2*1) /(2*1*2*1)4C2  = 6¹⁰C₄ ⁴C₂ = 210*6 ¹⁰C₄ ⁴C₂ =1260

Therefore, the value of an expression using combinations  ¹⁰C₄ ⁴C₂ is 1260.

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I need help with these asap

1) What is the equation of the line through the points (1,1), (5,4), (9,7), and (13,10)

A) y = 4/3 x + 1/3
B) y = 4/3 x - 1/3
C) y = 3/4 x + 1/4
D) y = 3/4 x - 1/4

2) Image

Answers

1st question (the image):

y= -5/4x + 3/2

how to solve:

y=mx+b

b: where the line meets the y axis

3/2 is 1.5 which matches up perfectly with the graph

m: the direction of the slope

If you look where the line matches with a point and you go down -5 and go right 4 it matches up and thats why m = -5/4

2nd question (the text):

C) y = 3/4 x + 1/4

how to solve

draw a graph (up above)

y:mx+b

to find m: rise/run

find the first point (1,1) you have to go 3 points up and 4 points right to get to the next point

(5,4) and thats why m=3/4

b: where the link hits the y axis compare the answers and the graph and find the most resonable one... which is 1/4

Anjelah took a hike.She finished in 2 hours and 47 minutes.If she started at 10:15 A.M.,what time did she finish?

Answers

Anjelah finished at 1:02 P.M. if she started at 10:15 A.M. and she took 2 hours and 47 minutes to complete it.

According to the question,

We have the following information:

Anjelah finished in 2 hours and 47 minutes.

She started at 10:15 A.M.

Now, we know that there are 60 minutes in an hour (more to know: there are 60 seconds in a minute).

So, we will add 2 hours to 10:15 A.M.:

10:15 + 2:00

12:15 P.M.

(Note that the digits before the colon gives us time in hours and the digits after the colon gives us minutes.)

Now, we will add 47 minutes to it:

12:15 + 0:47

(Now, we know that only 45 minutes can be added to 15 minutes because then it will make an hour. So, 2 more minutes will be added to the next hour.)

So, we have the following expression:

1:02 P.M.

Hence, the time when Anjelah will finish is 1:02 P.M.

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What is the volume of the diagram below? ​

Answers

Answer: 11 units^2

Step-by-step explanation: count the blocks

I understand the answer to simplifying it, i want a mathematical expression of the method of simplifying to know how to show my work

Answers

Answer:

This is how I would approach it

Step-by-step explanation:

The sides of an equilibrium triangle are 9.4cm,correct to the nearest milimetre. Work out the upper bound of the perimeter of this triangle.​

Answers

The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

What are the upper and lower bounds of an approximation?

The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.

The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.

The sides of an equilateral triangle are 9.4 cm

The perimeter of an equilateral triangle = 3 × length of the side

The perimeter of an equilateral triangle = 3 × 9.4

The perimeter of an equilateral triangle = 28.2 cm

Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

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Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buya new car, and is considering opening up a retirement account. He has a disposable income of$300/month, what would you recommend he do with this money? Why?

Answers

Problem

Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?

Solution

For this case the best option would be put the $45000 in a bank with a compound interest

And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things

What is x in this equation
2(x-7)=-4

Answers

x = 5

2x - 14 = -4

2x = -10

x = 5

Answer: 5

Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets.  Then because I did this I had to do the opposite to the other side. -4÷2

Then I just filled in the gaps 5-7=-2

3. a sociologist wishes to estimate the percentage of u.s. citizens living in poverty. what sample size should be obtained if she wishes the estimate to be within 2% points (the error) with 99% confidence if she uses the year 2000 estimate of 11.8% poverty obtained from the census?

Answers

The sample size is 1727 points for given data . Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population .

In this question we want to find the sample size and so let's, look at the formula that is given by, the value at over 2, divided by a margin of error, whole squared times p into 1 minus p.

N= ( Z ₐ / E)² p (1-p)

In this case , Z --> Z-Score

E --> error value

P --> estimated proportion or if given standard deviations

Given that, estimate error is 2% that is margin (E) = 2% = 2/100 =0.02

Now, what we have is our confidence level and our made error, so our estimate has been given us 2 percent or confidence level is 99 percent. Now, let's get our Z values, so we use alpha(a) to find out. For alpha value 1 minus 0.99 , we get 0.01. now we are going to be 0.01 divide by 2 and get 0.005 . So, the corresponding value of Z ₀.₀₀₅ is 2.576 . The only value of p is 11.8% (year 2000 estimate ) of what is required for getting an answer

= 118/1000= 0.118

Finally, we put all these values into formula of sample size , i.e.,

N= ( 2.576 / 0.02)² (0.118 )(1- 0.118) = 1726.56 1727

Our sample size is , 1727 point.

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Meow meow please help me

Answers

Answer:

area of trapezium → 1/2 × Sum of parallel sides × Distance between them.

Area → 15in² {given}

B1 → 4in

B2 → 6in

15 = 1/2 × ( 4+6 ) × h

h = 15 × 2 ÷ 10

h = 3in

I hope it's helpful

Answer:

i wouldd but likee

Step-by-step explanation:

i didnt pay a single second of attention in math

Venus has a mean distance from the sun of 67,240,000 miles while mars has a mean distance from the sun of 4,213,000,000 miles. how much farther is mars from the sun than venus? a. 4,145,760,000 miles b. 4,146,260,000 miles c. 4,245,760,000 miles d. 4,280,240,000 miles

Answers

The Mean distance is 4,145,760,000  miles

The correct option is (a)

Given,

The mean distance from Venus to the sun is 67,240,000 miles.

The mean distance from Mars to the sun is 4,213,000,000 miles.

Now, According to the question

Subtract the distance of Mars to the sun from Venus to the sun :

Let's Calculate the mean distance:

= 4,213,000,000 - 67,240,000

= 4,145,760,000 miles

Hence, The Mean distance is 4,145,760,000 miles.

The correct option is (a)

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There are 4,000 books in the town's library. of these, 2600 are fiction. write a percent equation that you can use to find the percentage of books that are fiction. then solve your equation.

Answers

The percent equation is = 2600/ 4000 × 100/1

The percentage of books that are fiction is 65%

What is percentage?

Percentage can be described as the ratio, quotient or number that is being expressed as a fraction of 100.

It is also described as the given part or amount in every hundred.

It is expressed as a fraction with 100 as the denominator of the fraction

It is represented with the symbol "%".

Given the information ;

Total number = 4000 books

Fiction books = 2600

The percentage is represented as;

= 2600/ 4000 × 100/1

Find the ratio

= 0. 65 × 100/1

Multiply through

= 65%

Hence,  the value is 65%

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Complete the following statement. Round your answer to the nearest percent
% of $700 = $1,400

Answers

Answer:

50

Step-by-step explanation:

Solution for 700 is what percent of 1400:

700:1400*100 =

(700*100):1400 =

70000:1400 = 50

Now we have: 700 is what percent of 1400 = 50

at an ice cream store with five flavors of ice cream (peppermint, hoarhound, chocolate malt, gingerbread, and squirrel), ice cream scoops are stored inside the ice cream containers. what is the smallest number of ice cream scoops that would need to be in use so that two of the scoops would have to be stored in the same flavor ice cream container? how many ice cream scoops must be in use if 3 of them have to be stored in the same flavor ice cream container?

Answers

ANSWER: 10 ICE-CREAM SCOOPS

There are 5 icecream flavors

For each we need 2 scoops so = 2*5 = 10 scoops

therefore ther must be 10 icecream scoops in use for five flavors.

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What is the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3? Responses y−1=3(x+2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y−2=3(x+1) y minus 2 equals 3 open parenthesis x plus 1 close parenthesis y+1=3(x−2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y+2=3(x−1)

Answers

The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5

We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3

The point slope form of a equation of a line is

y - y₁ = m(x - x₁)

y - (-2) = 3 (x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.

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I need to know what system of inequalities is graphed below

Answers

SOLUTION:

For inequalities, the solution to is usually where the two regions meet.

The graphs here are:

[tex]\begin{gathered} x-3y\leq6\text{ (thick lines)} \\ \text{Here, checks the graph testing points (3,-1) and (0,-2)} \\ 2x\text{ }+\text{ y }>2.\text{ (broken lines)} \\ \text{Here, the checks the graph testing points (}0,2)\text{ and (1,0)} \end{gathered}[/tex]

Final answer:

The final answer here is Option (B)

Ruth is a costume designer for the local children's theater company. Yesterday, she sewed 1 female costume and 5 male costumes, which used 52 yards of fabric. Today, she sewed 5 female costumes and 2 male costumes, which used a total of 76 yards. How many yards of fabric does each type of costume require? yards of fabric, and every male costume requires Each female costume requires yards.

Answers

Given:

Yesterday:

1 female and 5 male = 52 yards

Today:

5 female and 2 male = 76 yards

Let's find the number of yards of fabric each type of costume requires.

Let F represent the number if yards for each female customer use.

Let M represent the number of yards each male customer uses.

From this situation, we have the system of equations:

1F + 5M = 52

5F + 2M = 76

Now, let's solve the system of equations simultaneously using substitution method.

Rewrite equation 1 for F:

F = 52 - 5M

Substitute 52 - 5M for F in equation 2:

[tex]\begin{gathered} 5F+2M=76 \\ \\ 5(52-5M)+2M=76 \\ \\ 5(52)+5(-5M)+2M=76 \\ \\ 260-25M+2M=76 \\ \\ 260-23M=76 \end{gathered}[/tex]

Subtract 260 from both sides:

[tex]\begin{gathered} 260-260-23M=76-260 \\ \\ -23M=-184 \end{gathered}[/tex]

Divide both sides by -23:

[tex]\begin{gathered} \frac{-23M}{-23}=\frac{-184}{-23} \\ \\ M=8 \end{gathered}[/tex]

Substitute 8 for M in either of the equations:

F = 52 - 5M

F = 52 - 5(8)

F = 52 - 40

F = 12

Therefore, we have the solution:

F = 12, M = 8

Each male customer requires 8 yards while each female customer requires 12 yards.

ANSWER:

• Male customer = 8 yards

,

• Female customer = 12 yards

Please solve with an explanation

Answers

Answer:

10.8

Step-by-step explanation:

Hello!

Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.

We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

a and b are lengthsc is the hypotenuse

Solve for PQ[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 9^2 = PQ^2[/tex][tex]36 + 81 = PQ^2[/tex][tex]117 = PQ^2[/tex][tex]\sqrt117 = PQ\\[/tex]10.8 = PQ

The length of PQ is 10.8.

3y=x-6 in standard form

Answers

Answer: x-3y=6

Step-by-step explanation:

so first subtract x to get -x+3y = -6 because standford is ax+by = c

and then multiply by -1 since x has to be positive

x-3y = 6 That is your answer

Line m passes through points (9, 9) and (6, 1). Line n passes through points (10, 7) and (1, 15). Are line m and line n parallel or perpendicular?

Answers

Answer:

Step-by-step explanation:

Slopes of parallel lines are the same. ( [tex]m_{1}[/tex] = [tex]m_{2}[/tex] )

Slopes of two perpendicular lines are opposite reciprocals. ( [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1 )

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

~~~~~~~~~~~~~

(9, 9)

(6, 1)

[tex]m_{m}[/tex] = [tex]\frac{1-9}{6-9}[/tex] = [tex]\frac{8}{3}[/tex]

(10, 7)

(1, 15)

[tex]m_{n}[/tex] = [tex]\frac{15-7}{1-10}[/tex] = - [tex]\frac{8}{9}[/tex]

Lines m and n neither parallel, nor perpendicular.

What is the distance between 3 and 15?

Answers

The most appropriate choice for distance between numbers will be given by -

Distance between 3 and 15 is 12 units

What is distance between two numbers?

At first it is important to know about number line.

A pictorial representation of real numbers has been done along a horizontal straight line. That horizontal straight line is called number line. On a number line, all the integers has been placed at equal distance apart. In between integers, fractions, decimal numbers, rational numbers and irrational numbers can be marked. Number line can be used for addition or subtraction.

Distance between two numbers indicates how far one number is situated from other number on the number line.

Here,

Distance between 3 and 15 = 15 - 3

                                              = 12 units

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10. Which of the following is equivalent to thisexpression?72.7-4Tutor

Answers

To answer this question we need to remember that:

[tex]a^ma^n=a^{m+n}[/tex]

then:

[tex]\begin{gathered} 7^2\cdot7^{-4}=7^{2-4} \\ =7^{-2} \end{gathered}[/tex]

now we need to remember that:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

hence:

[tex]7^{-2}=\frac{1}{7^2}[/tex]

Therefore:

[tex]7^{-4}\cdot7^2=\frac{1}{7^2}[/tex]

and the asnwer is A.

5.What is the area of the triangle?Include the unit of measurein your answer.:::::

Answers

Answer: Area = 126 square inches

Explanation:

The formula for calculating the area of a triangle is expressed as

Area = 1/2 x base x height

From the information in the diagram,

base = 18

height = 14

Thus,

Area = 1/2 x 18 x 14

Area = 1/2 x 252 = 252/2

Area = 126 square inches

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The following lists consists of ionic compounds EXCEPTbarium hydroxide, zinc carbonate, ammonium sulfatecalcium chloride, carbon disulfide, magnesium nitratesodium sulfate, copper(II) oxide, potassium nitridealuminium sulfide, sodium sulfite, calcium fluoride jeff was in a fatal accident in which he died almost instantly due to a nervous system injury that interfered with essential life functions such as heartbeat and respiration. which part of jeff's nervous system is most like to have been injured? Felicia wants to make dessert and she would like to make a thick and creamy pudding. In order to achieve a thick texture, she is planning to use a cooking method that will allow the water to slowly be absorbed into the starch, resulting in a thick pudding. What method is Felicia most likely planning to use?caramelizationgelatinizationfreeze dryingbaking assume that a u.s. firm can invest funds for one year in the united states at 12 percent or invest funds in mexico at 14 percent. the spot rate of the peso is $.10 while the one-year forward rate of the peso is $.10. if u.s. firms attempt to use covered interest arbitrage, what forces should occur? group of answer choices which answer below describes what i am doing in the incident response process: what specifically happened? what was the entry point? what local computers/networks were affected? what remote computers/networks were affected? personnel interviews on scene response initial evaluation incident reporting key success factors are group of answer choices important characteristics of a company or its product that lead to success in an industry. similar to generic strategies. examples of defensive strategies. the economic characteristics of countries that lead to success. What is the largest possible electronegativity difference for a bond to be covalent?A.0.5B.1.7C.0.0D.1.0 0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here Classify CH3CH2NH2 as astrong base or a weak base.Strong BaseWeak Base Find the distance between the points (10, 1) and (9, -4) using the distance formula. Round to the hundredths place.A: 3.16B: 5.00C: 3.00D: 5.10Please explain. Alberto is saving money to buy a pair of shoes that cost $50 he has already saved $32 he still needs to save D dollars explain how to solve your equation to find how much money Alberto needs to save how much more does he need to save f(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x) at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high? (hint: the formula for the volume of a cone is v Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. a. 87 ft b. 74 ft c. 65 ft d. 63 ft What is -5/7 times (-1/6) PLEASE HELP!!Write an equation of a quadratic function with the given properties: f(3)=f(-5)=0; f(-6)=-36 you have just won the lottery! you can either receive $6,500 a year for 20 years or $100,000 as a lump sum payment today. what is the interest rate on the annuity option? Which graph represents 2x + 3y < 6?Choose 1 answer: Solve 5x + 25 = 0Ox= -5x = -5 and x = 5Ox=5No Real Solutions sean is performing barbell squats with the intent of building up his quadriceps muscles. to make the quadriceps perform more work and increase the efficiency of the exercise, he should: