Find the missing length?

The exponential function f with f(2) = 3 and a doubling time of 5 results in f(27) = 096.

To find f(27) given that f(2) = 3 and the doubling time is 5, we can use the general form of an exponential function: f(x) = a * (2^(x/d)), where a represents the initial value, x is the input value, and d is the doubling time.

Given that f(2) = 3, we can substitute these values into the exponential function equation: 3 = a * (2^(2/5)).

To find the value of a, we can solve the equation for a: a = 3 / (2^(2/5)).

Now, we can substitute a into the exponential function to find f(27): f(27) = (3 / (2^(2/5))) * (2^(27/5)) = 096.

Therefore, the value of f(27) is 096.

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Supporting answer:

In this problem, we are given an exponential function with an initial value of f(2) = 3 and a doubling time of 5. The doubling time represents the time it takes for the function to double its value. We can use the general form of an exponential function, f(x) = a * (2^(x/d)), to find the value of f(27).

Substituting the given values, we have 3 = a * (2^(2/5)). To solve for a, we divide both sides of the equation by (2^(2/5)): a = 3 / (2^(2/5)).

Now, we can substitute the value of a into the exponential function to find f(27). By plugging in x = 27, we get f(27) = (3 / (2^(2/5))) * (2^(27/5)). Evaluating this expression gives us f(27) = 096.

Therefore, the value of f(27) is 096, which is the answer.

In summary, the exponential function f with f(2) = 3 and a doubling time of 5 results in f(27) = 096.

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24 x ^2 + 54 x + 21,

if you would like me to explain how to do it, I can in the comments.

Answer:

x=-4

Step-by-step explanation:

h(x)=5(x^2+8x+16)-5*16+64=5(x+4)^2-16

vertex (-4,-16)

AOS (Axis of Symmetry) is a vertical line passing the vertex: x=-4

Answer:

2

Step-by-step explanation:

give me brainliest

Answer:

3/4

Step-by-step explanation:

9-6/-2 -(-6= 3/4

I hope this helps! :D

Answer:    m = ¾

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Answer:

The correct option is;

B. a. Whole number b. Irrational number

Step-by-step explanation:

The height, h of the equilateral triangle = 3·√2·s

The item by which equilateral triangle is made = 2-inch toothpicks

Therefore, we have;

The sides of the equilateral triangle = Comprises multiples of 2 inches

Therefore, the sides of the equilateral triangle is a whole number

The height of the triangle is the product of the side and (√3)/2

Therefore, the height of the triangle is an irrational number

The correct option is A. a. Whole number b. Irrational number.

A whole number are the positive counting numbers, 0, 1, 2, ..., while an integer includes negative numbers which is not possible for a real triangle.

wouldn't the angles be 92° and 88°?

Answer:

31 + 2x-67 + x = 360

Step-by-step explanation:

u can solve the equation im to lazy to do math rn

Answer:

Step-by-step explanation:

A) Using the formula for calculating simple interest. This is expressed as:

SI = PRT/100

P is the principal = 17,000

Rate = 5%

Time = 3years

SI = 17,000×5×3/100

SI = 170×5×3

SI = 170×15

SI = $2550

Hence the total amount that the shoe store will pay back to the bank is $2550.

B) To get the total amount plus loan to be paid, we will use the formula below;

Amount = Principal + Interest

Amount = $17000+$2550

Amount = $19550

Hence the total amount will be $19500

C Based on the calculation, the estimate was gotten by simply multiplying 15 by 17 to get $225 then multiply by 10 to get $2250 making it thousands of dollars.

The total loan amount was derived by simply adding the original amount borrowed with the interest charges by the bank

Answer:

c) How could you use estimation to determine if your answer is reasonable? Explain. (2 points)

Step-by-step explanation:

Based on the calculation, the estimate was gotten by multiplying 15 by 17 to get $225 then multiply by 10 to get $2250 making it thousands of dollars. The total loan amount was made by adding the original amount borrowed with the interest charges by the bank.

(I'm doing a math paper/docs on it and this is what i put).

The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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Answer:

13. you have to divide the numbers. hope this helps.

Answer:

18

Step-by-step explanation:

Just took the test

Answer:

D is the answer

Step-by-step explanation: Explanation:

The domain is the set of

x

-values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be

≥

0

.

Therefore we need all of the

x

-values that result in the value of

4

−

x

being

≥

0

.

4

−

x

≥

0

4

≥

x

x

≤

4

So all

x

-values

≤

4

will work in the equation. Now we right this in terms of all real numbers:

The Domain of

x

is all the real numbers expect when

x

>

4

(This produces a negative under the square root)

brainliest please

Answer:

Option 4.

Step-by-step explanation:

We know if under the square root is a negative, then it will become an imaginary number i.

We see that in order to make the square root negative, we would have to have a number smaller than 4.

√(x - 4)

√(4 - 4) = √0 = 0

√(3 - 4) = √-1 = i

Therefore, in order for f(x) to be real numbers, x ≥ 4, [4, ∞), or {x | x ≥ 4}

The units that could apply to the variable t representing the amount of time the workers have left to clean the windows are hours or minutes, not workers or buildings. None of the given Options.

The variable t represents the amount of time the workers have left to clean the windows. From the given information, it is stated that it takes a total of 12 hours to clean the windows of the office building, and on the first day, the workers were able to clean for 9 hours.

Therefore, the remaining time left to clean the windows can be expressed as 12 - 9 = 3 hours.

Based on this, we can determine the appropriate units for the variable t. Since t represents time, the units that apply to this variable should also be units of time. In this case, the units of time that could apply to the variable t are hours or minutes.

OA. workers is not an appropriate unit for the variable t because it represents the number of individuals performing the task, not the amount of time remaining.

B. buildings is also not an appropriate unit for the variable t because it represents the number of office buildings, which is unrelated to the amount of time left to clean the windows. None of the given Options is correct.

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Answer:

22.5° and 67.5°

Step-by-step explanation:

The sum of complementary angles equal 90°.

Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.

Thus, the following expression can be written to represent this case:

[tex] x + 3x = 90 [/tex]

Solve for x

[tex] 4x = 90 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{90}{4} [/tex]

[tex] x = 22.5 [/tex]

The measure of the complementary angles are:

x = 22.5°

3x = 3(22.5) = 67.5°

Answer:

-78,6

Step-by-step explanation:

Answer:-6,78

Step-by-step explanation:

So that would be D!

You are welcome :)

Answer:

65%

Step-by-step explanation:

uhhhhh

Answer:

(-7,5 ; -2,5)

Step-by-step explanation:

Midpoint : ((5+10)/2, (-7+2)/2) =

(-7,5 ; -2,5)

Answer:

(7.5, - 2.5 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (10, 2 ) and (x₂, y₂ ) = (5, - 7 ) , then

midpoint = ( [tex]\frac{10+5}{2}[/tex] , [tex]\frac{2-7}{2}[/tex] ) = ([tex]\frac{15}{2}[/tex] , [tex]\frac{-5}{2}[/tex] ) = (7.5, - 2.5 )

Answer:

3rd option

Step-by-step explanation:

Answer:

2≤z≤5 or 2<z<5

Step-by-step explanation:

B or D I'm not sure

Answer: I think a second 30° angle in the diagram is JGH. A congruent angle to JGH is JGF.

Step-by-step explanation:

Answer:

hey come have it with me

Step-by-step explanation:

Answer:

y = x/4 - 1/2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write equation

x = 4y + 2

Step 2: Subtract 2 on both sides

x - 2 = 4y

Step 3: Divide both sides by 4

x/4 - 1/2 = y

Answer:

[tex]y=\frac{1}{4} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To get slope-intercept form (y=mx+b), you have to solve this equation for y by using inverse operations. First, we can subtract by 2 on both sides to eliminate the +2 on the right side. This results in x-2=4y. To get y by itself, we can divide by 4 on both sides. This becomes (x-2)/4=y. To make this in slope-intercept form, we have to separate the terms into x/4 and -2/4. This is (x/4)+(-2/4)=y. We can reduce the second fraction to -1/2 and rewrite x/4 as 1/4x. The equation is y=1/4x-1/2.

Answer:

I peed my pants once laughing too much

Answer:

I do.... but I ain´t telling them because they are secrets lol

Step-by-step explanation:

To find the PDF (Probability Density Function) of the duration of the trip, we need to determine the distribution of the speed and calculate the corresponding duration.

Given that the speed of John Slow is uniformly distributed between 30 and 60 miles per hour, we have a continuous uniform distribution over this interval.

The duration of the trip can be calculated by dividing the distance (180 miles) by the speed (v) since speed = distance/time, rearranging the equation gives time = distance/speed.

Let's denote the duration of the trip as T. We can express T in terms of the speed (v) as follows:

T = 180 miles / v

To find the PDF of T, we need to determine the probability density function of v. Since v is uniformly distributed between 30 and 60 mph, its PDF is a constant over this interval.

The width of the interval is (60 - 30) = 30 mph, and since it is a uniform distribution, the height of the PDF is 1/30 mph^(-1) to ensure the total area under the PDF equals 1.

Therefore, the PDF of T is given by:

PDF(T) = PDF(v) * |dt/dv|

Since v = 180/T, we can differentiate this equation with respect to T to find |dt/dv|:

|dt/dv| = |-180/T²|

Substituting the PDF of v and |dt/dv| into the PDF of T:

PDF(T) = (1/30 mph^(-1)) * |-180/T²|

Simplifying further, we have:

PDF(T) = 6/T² mph^(-1)

Therefore, the PDF of the duration of the trip is 6/T² mph^(-1).

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Answer:

83.4

Step-by-step explanation:

(16.2x2) +1/2x8.5x12

32.4 +1/2x8.5x12

lets spilt this up

32.4+ (1/2x8.5x12)

32.4 + 51

83.4

Answer:

it's the letter "B" 83.4

Answer:

h

Step-by-step explanation:

Answer:

l0l its fun and b0ring tbh.

Step-by-step explanation:

I get t0 watch tv and play games a l0t, but i l0st like all my friends witch is sad.

Answer:

see explanation

Step-by-step explanation:

We require to create 2 equations with the repeating value placed after the decimal point.

let x = 2.1616...... → (1) Multiply both sides by 100

100x = 216.1616..... → (2)

Subtract (1) from (2) to eliminate the repeating decimal.

99x = 214 ( divide both sides by 99 )

x = [tex]\frac{214}{99}[/tex] = 2 [tex]\frac{16}{99}[/tex] as a mixed number

Thus

2.1616...... = [tex]\frac{214}{99}[/tex] = 2 [tex]\frac{16}{99}[/tex]

Answer:

10b

Step-by-step explanation:

The approximate real rate of interest is 4.86% and the exact real rate of interest is 4.98% is the correct naswer.

Real Rate of Interest: Real rate of interest is the actual interest earned or paid on an investment or loan, irrespective of the impact of inflation. It can be calculated by subtracting the rate of inflation from the nominal rate of interest. Therefore, the nominal rate of interest adjusted for inflation gives us the real rate of interest.

Approximate Real Rate of Interest: By using the formula Real rate = (1 + nominal rate) / (1 + inflation rate) - 1Real rate = (1 + 6.4%) / (1 + 1.5%) - 1

Real rate = 0.0486 or 4.86%

Thus, the approximate real rate of interest is 4.86%.

Exact Real Rate of Interest: The exact real rate of interest can be calculated using the Fisher effect formula that is: Real Rate = [(1+ nominal rate) / (1 + inflation rate)] - 1Real Rate = [(1 + 6.4%) / (1 + 1.5%)] - 1

Real Rate = 0.0498 or 4.98%

Thus, the exact real rate of interest is 4.98%.

In conclusion, the approximate real rate of interest is 4.86% and the exact real rate of interest is 4.98%.

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Answer:

-11

Step-by-step explanation:

Answer:

No the Answer is 24

Step-by-step explanation:

The number (x) in: "9 more than three times a number is 24" is what we are solving here. In other words, you are looking for a number (x) that if you multiply it by three (same as three times) and then add 9, you get 24.