Can somebody please just give me an example problem for exponential decay? I will give brainliest, thanks!

Answer: because the mean is 48

Step-by-step explanation:

the average (mean) is 48 so therefore its reasonable that half scored under half scored higher

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

We are given that the scores are normally distributed.

The mean of the data is 573.

The standard deviation of this data is 72.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

So,

We can write,

μ = 573

σ = 72

Then, the given expression is,

( μ - 3σ < x < μ +3σ ) = 99.7%

So,

μ - 3σ = 573 - 3*72

μ - 3σ = 573-216

μ - 3σ = 357

μ +3σ = 573 + 3*72

μ + 3σ = 573+216

μ + 3σ = 789

Hence, the mean is halfway between these two integers are = 357 and 789

Empirical rule states that for a normally distributed data that

about 68% data lies between μ + 1σ that is one standard deviation from mean.

about 95% data lies between μ + 2σ that is one standard deviation from mean.

about 99.7% data lies between μ + 3σ that is one standard deviation from mean.

Therefore,

The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between  that is it will lie in the range.

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Answer:

36 minutes

Step-by-step explanation:

Depth of the fjord = 1308 m

Rate at which the submersible dives = 35 meters/minute

Distance to the bottom of the fjord should be 48 m

Distance the submersible has to go underwater is \(1308-48=1260\ \text{m}\)

Time is found by dividing the distance the submersible has to go underwater by rate at which the submersible dives

\(\dfrac{1263}{35}=36\ \text{minutes}\)

The time taken by the submersible to dive the required distance is 36 minutes.

Answer:/11-5/9×14/11

Step-by-step explanation:

-4/5+1/4÷3

Answer:

Final Amount = $1,112.72 (Approx.)

Step-by-step explanation:

Given:

Amount deposit = $940

Rate = 8.8%

Time = 2 year

Find:

Final Amount

Computation:

Final Amount = P[1+r]ⁿ

Final Amount = 940[1+8.8%]²

Final Amount = $1,112.72 (Approx.)

Answer:

AB= A. (50)^1/2

BC= B. (65)^1/2

AC= D. (145)^1/2

<ABC≈ 105

a) An equation that could be used to solve for W, the number of weeks it would take Jim to go from running 7 miles to running 3 miles is;

N = 7 + (W - 1)0.5

B) W = 9 weeks

C) The number of weeks it would take Jim to go from running 7 miles to running 3 miles is; 9 weeks.

Number of miles that Jim ran today = 7 miles

Now, the general formula for arithmetic progression is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

Since it is 7 miles this week, then a = 7

Since she wants to reduce by 1/2 or 0.5 miles weekly, then d = -0.5

Thus for miles to be 3 miles, we have;

7 + (n - 1)0.5 = 3

7 - 0.5n + 0.5 = 3

4.5 = 0.5n

n = 4.5/0.5

n = 9 weeks

The number of weeks it took to go from running 7 miles to running 3 miles is; 9 weeks.

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The terminal side of the angle -240 lies in the third quadrant when drawn in the standard position.

In the standard position, an angle is drawn with its initial side along the positive x-axis and its vertex at the origin. The terminal side of the angle is the side that rotates from the initial side.

The angle -240 starts from the positive x-axis (initial side), rotates clockwise for 240 degrees, and ends up in the third quadrant. Since one full revolution or circle is 360 degrees, a rotation of 240 degrees in the clockwise direction goes beyond the negative x-axis and into the third quadrant.

The third quadrant is characterized by negative x-coordinates and negative y-coordinates. In this quadrant, both the x and y values are negative. Therefore, when the angle -240 is drawn in the standard position, its terminal side lies in the third quadrant.

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Given:

The length of the sofa is 6'3''.

We need to convert the foot into inches.

Multiply both sides by 6, we get

The length of the sofa is

The scale of the plan is

Multiply by 75/12 on both sides, we get

Hence the length of the sofa on the plan is

(a)The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident  is approximately 0.522.

(c) The probability that at least one adult is very confident is   approximately 0.478.  

What is the probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults, given the proportion of very confident individuals?

The probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults depends on the proportion of very confident individuals. By calculating the probability of all four adults being very confident (a), none of the four adults being very confident (b), and at least one of the four adults being very confident (c), we can determine the likelihood of these scenarios occurring based on the given information.

To solve this problem, we can use the concept of probability and combinations.

(a)Given that there are 150 out of 1000 U.S. adults who are very confident, the probability of selecting one adult who is very confident is:

P(very confident) = 150/1000

= 0.15

Since the sampling is done without replacement, after each selection, the sample size decreases by 1. Therefore, for the second selection, the probability becomes 149/999, for the third selection, it becomes 148/998, and for the fourth selection, it becomes 147/997.

To find the probability that all four adults are very confident, we multiply these probabilities together:

P(all four adults are very confident) = (0.15) * (149/999) * (148/998) * (147/997)

≈ 0.0056

(b) The probability of selecting one adult who is not very confident (opposite of very confident) is:

P(not very confident) = 1 - P(very confident)

= 1 - 0.15

= 0.85

Since we are selecting four adults at random without replacement, the probability of none of them being very confident can be calculated as:

P(none very confident) = P(not very confident) * P(not very confident) * P(not very confident) * P(not very confident)

= (0.85)* (0.85) * (0.85) * (0.85)

≈ 0.522

(c) The probability of at least one adult being very confident is the complement of none of them being very confident:

P(at least one very confident) = 1 - P(none very confident)

= 1 - 0.522

= 0.478

Therefore,

(a) The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident is approximately 0.522.

(c) The probability that at least one adult is very confident is approximately 0.478.  

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Answer:

a) Option A is correct.

b) Option B is correct.

Step-by-step explanation:

\(a) \: \: 5 \times a \\ = 5a\)

\(b) \: \: b \times b \\ = {b}^{2} \)

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer: We see that 26 people must lie, and 2 of them passed making the fraction 2/80 doesn't work, then we see 7 people of the 54 failed the test, meaning another 7/80 which the sum equals 9/80. And since the percentage rate from 80 to 100 is 1.25, we multiply 9 and 1.25, to receive that the fail percent was 11.25, so the percent that was accurate was 88.75%. It is pretty confusing, but in time it will make sense.

Hope this helps.

To determine the Annual Percentage Rate (APR) based on a monthly interest rate, you can use the following formula:

APR = (1 + monthly interest rate)^12 - 1

In this case, the monthly interest rate is 0.5% or 0.005 (decimal form). Plugging it into the formula, we have:

APR = (1 + 0.005)^12 - 1

Calculating this expression:

APR = (1.005)^12 - 1

APR = 1.061678 - 1

APR ≈ 0.061678 or 6.17% (rounded to two decimal places)

Therefore, the bank would quote an APR of approximately 6.17% for this account.

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Answer:

A, C, D, B

Step-by-step explanation:

In a cross-country race with 30 runners, there are 4,060 different groups that can finish in the top 3 positions.

Use the concept of combination defined as:

Combinations are made by choosing elements from a collection of options without regard to their sequence.

Contrary to permutations, which are concerned with putting those things/objects in a certain sequence.

Given that,

There are 30 runners in a cross-country race.

The objective is to determine the number of different groups of runners that can finish in the top 3 positions.

To determine the number of different groups of runners that can finish in the top 3 positions:

Use combinations instead of permutations.

In this case:

Calculate the number of different groups,

Use the combination formula:

\(^nC_r = \frac{n!} { (r!(n - r)!)}\)

Here

we have 30 runners and want to select 3 for the top 3 positions.

Put the values into this formula:

\(^{30}C_3 = \frac{30!}{ (3!(30 - 3)!)}\)

Simplifying this expression, we get:

\(^{30}C_3 = \frac{30!}{ (3! \times 27!)}\)

Calculate the value:

\(^{30}C_3 = 4060\)

Hence,

There are 4,060 different groups of runners that can finish in the top 3 positions.

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In order to describe how f(x) increases and grows over different intervals, you'll need to analyze the given graph and determine whether the function exhibits exponential growth or decay. Then, you can discuss the behavior of the function in the context of the intervals on the x-axis.

From x=0 to x=2, f(x) increases from 6 to 10, with a growth rate of 2.

From x=2 to x=4, f(x) increases from 10 to 14, with a growth rate of 2.

From x=4 to x=5, f(x) increases from 14 to 18, with a growth rate of 4.

Overall, f(x) shows exponential growth, with a constant growth rate of 2 except for the last interval where the growth rate is 4.
Based on the provided information, it seems that there is a missing graph. However, I can still help you understand how an exponential function, f(x), increases and grows over different intervals.

An exponential function typically has the form f(x) = ab^x, where a and b are constants, and b > 0. The growth of f(x) depends on the value of b:

1. If b > 1, the function increases as x increases. This is called exponential growth.
2. If 0 < b < 1, the function decreases as x increases. This is called exponential decay.

So, in order to describe how f(x) increases and grows over different intervals, you'll need to analyze the given graph and determine whether the function exhibits exponential growth or decay. Then, you can discuss the behavior of the function in the context of the intervals on the x-axis.

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Answer:

279.987

this is da answer

Step-by-step explanation:

There are 280.035 lbs in 127 kilograms. The answer is obtained by applying the unit conversion.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.

Now,

we have been given 127 kilograms which are to be converted into pounds and to be represented in lbs.

We know that 1 kilogram = 2.205 lbs (approx)

Therefore,

⇒127 kilograms = 127 * 2.205

⇒127 kilograms = 280.035 lbs

Hence,

          There are 280.035 lbs in 127 kilograms.

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Answer: I think it’s 1/6

Step-by-step explanation:

Answer:

480 in

Step-by-step explanation:

Rectangular Prism Formula :

V=whl

Which,

W = Width

H = Height

L = Length

Solve:

Given that:

Length = 8 in

Width = 10 in

Height = 6 in

Since the formula is:

V = whl

Then,

V = 8 × 10 × 6

V = 80 × 6

V = 480 in

Kavinsky

The final answer is the sum of the number of possibilities for each case:

Total possibilities = Sum[(10 * 9 * (36)^n) * (nC4) * (36)^(n-4) * (36C3) * (nC3) * (36)^(n-3)] for all valid values of n.

To find the number of valid strings that satisfy the given properties, we can break down the problem into several cases and count the possibilities for each case.

Case 1: The first and last symbols are distinct digits.

There are 10 choices for the first digit (0-9) and 9 choices for the last digit (since it cannot be the same as the first digit). The middle characters can be any combination of letters and digits. Since there are no restrictions on the middle characters, we have a total of (36)^n possibilities, where n is the number of middle characters.

Case 2: Precisely four symbols in the string are the letter 'a'.

There are (nC4) ways to choose the positions of the four 'a' characters in the string, where n is the number of total characters in the string. For each arrangement of 'a's, the remaining characters can be any combination of letters and digits, which gives us (36)^(n-4) possibilities.

Case 3: Precisely three characters are elements of the set, and these characters are all distinct.

There are (36C3) ways to choose three distinct characters from the set of 36 (26 lowercase letters + 10 decimal digits). Once the three characters are chosen, they can be arranged in (nC3) positions in the string, where n is the total number of characters. The remaining characters can be any combination of letters and digits, which gives us (36)^(n-3) possibilities.

To find the total number of valid strings, we need to consider all possible combinations of these cases. Therefore, the final answer is the sum of the number of possibilities for each case:

Total possibilities = Sum[(10 * 9 * (36)^n) * (nC4) * (36)^(n-4) * (36C3) * (nC3) * (36)^(n-3)] for all valid values of n.

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Answer:

You are correct!!

It would be (-infinity, infinity) :)

Answer:

200mm^2 is the area of shadded region

It is meaningful to compute the probability that a continuous random variable is greater than or equal to a number, less than or equal to a number, or between two numbers.

In probability theory, a continuous random variable is a variable that can take on any value within a certain range or interval.

As a result, the probability that a continuous random variable takes on a specific value is zero, since there are infinitely many possible values the variable can take on.

Therefore, it is not meaningful to compute the probability that a continuous random variable is exactly equal to a number.

However, it is meaningful to compute the probability that a continuous random variable is greater than or equal to a number, less than or equal to a number, or between two numbers.

These probabilities can be calculated using the cumulative distribution function (CDF) of the random variable. The CDF gives the probability that a random variable takes on a value less than or equal to a certain value, which can be used to compute probabilities for ranges of values.

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Let us set up some variables:

Now let us set up some equations based on the facts:

Equations:

   L = 4W     -- equation 1

   2L + 2W = 80 -- equation 2

   Plug the value of L from equation 1 into equation 2

    2(4W) + 2W = 80

     8W + 2W = 80

        10W = 80

           W = 8 -- equation 3

   Plug the value of W from equation 3 into equation 1:

    L = 4W = 4 * 8 = 32

Therefore the length is 32 and the width is 8.

Hope that helps!

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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There are 834 positive integers not exceeding 1000 that are not divisible by either 8 or 12.

To find the number of positive integers not exceeding 1000 that are not divisible by either 8 or 12, we can use the principle of inclusion-exclusion. First, let's find the number of positive integers not exceeding 1000 that are divisible by 8. The largest multiple of 8 that does not exceed 1000 is 992 (8 * 124). So, there are 124 positive integers not exceeding 1000 that are divisible by 8. Next, let's find the number of positive integers not exceeding 1000 that are divisible by 12. The largest multiple of 12 that does not exceed 1000 is 996 (12 * 83). So, there are 83 positive integers not exceeding 1000 that are divisible by 12.

However, we have counted some numbers twice—those that are divisible by both 8 and 12. To correct for this, we need to find the number of positive integers not exceeding 1000 that are divisible by both 8 and 12 (i.e., divisible by their least common multiple, which is 24). The largest multiple of 24 that does not exceed 1000 is 984 (24 * 41). So, there are 41 positive integers not exceeding 1000 that are divisible by both 8 and 12.

Now, we can apply the principle of inclusion-exclusion to find the number of positive integers not exceeding 1000 that are not divisible by either 8 or 12: Total number of positive integers not exceeding 1000 = Total number of positive integers - Number of positive integers divisible by 8 or 12 + Number of positive integers divisible by both 8 and 12. Total number of positive integers not exceeding 1000 = 1000 - 124 - 83 + 41

= 834. Therefore, there are 834 positive integers not exceeding 1000 that are not divisible by either 8 or 12.

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Answer: 10/12 0r 5/6

Step-by-step explanation: