Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varics due to weather conditions and other factors. The daily water level has a distribution that is is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake the water level in the lake will be at least 90 feet? CA 0.29 (B) 0.31 (C) 0.34 (D) 0.37 (E) 0.50

Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

Given that,

The new Malthusians worry that ______ of the population will lead to a scarcity of food.

We have to fill the blank.

We know that,

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth.

The formula for the exponential growth is

V=S×(1+R\()^{T}\)

The starting value, S, of an initial starting point subject to exponential growth can be multiplied by the sum of one plus the interest rate, R, raised to the power of T, or the number of periods that have passed, to get the current value, V.

Therefore, Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

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Answer:−\(5x_{2}\) −5x−2 o

Step-by-step explanation:

Answer: 10/3 every hour

Step-by-step explanation:

The rate the water level is rising is 3 feet and 4 inches per hour.

The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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Using the normal distribution, the project completion time with a 75% certainty is of 42 weeks.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(\mu = 40, \sigma = \sqrt{9} = 3\)

The project completion time with a 75% certainty is the 75th percentile, which is X when Z = 0.675, hence:

\(Z = \frac{X - \mu}{\sigma}\)

0.675 = (X - 40)/3

X - 40 = 3 x 0.675

X = 42.

The project completion time with a 75% certainty is of 42 weeks.

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Answer:

A) 36 inches

36 Incheon is the correct answer

Answer:

D.) 64pi in.³

Step-by-step explanation:

I got it right in quiz, trust me.

I hope this helps! ^^

The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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The answer to this question is 150 adults. This is calculated by subtracting the number of boys and girls from the total number of people in the museum, 250.

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people is equal to 100 girls. 3/10 of 250 people is equal to 75 boys. When these two numbers are subtracted from the total number of people in the museum, 250, the answer is 150 adults.

To work out the number of adults in the museum, it is important to first identify the fractions and convert them into decimals. For example, to convert 2/5 into a decimal, 2 is divided by 5, which gives an answer of 0.4. This process should be repeated for the other fractions given in this problem.

Once the fractions are converted into decimals, the next step is to multiply the decimals by the total number of people in the museum, 250. For example, 0.4 multiplied by 250 is equal to 100 girls.

Finally, the numbers of boys and girls should be subtracted from the total number of people in the museum, 250. This gives an answer of 150 adults.

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By subtracting the number of boys and girls from the total number of people in the museum, we get the number of adults that is 75.

What is subtracting?

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people = 100 girls.

3/10 of 250 people =75 boys.

When these two numbers are subtracted from the total number of people in the museum, that is

250-(100+75)= 75 adults

Thus, the number of adults among the 250 people in a museum are 75.

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The approximate length of line segment KL is 3.2 unit . The correct answer is C.

Line segment of KL kan be calculate as follows:

JL = 2.7 units

JK = 4.7 units

∠L = 150°

Using Law of sines,

sinL = sin K = sin J

L         K          J

sin 105° x 2.7  = sin K

    4.7

0.5548 = sin K

sin⁻¹ (0.5548) = K

33.7° = K

Using "Sum of a triangle's internal angles is supplementary" now

∠J +∠K+∠L = 180°

∠J + 33.7° + 105°= 180°

∠J = 41.3°

Then using law of cines we can get

sinL = sin K = sin J

L         K          J

sin105° = sin 41.3°

4.7             J

J of line KL = 3.211

line KL is 3.2 unit

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Answer:

sorry I can't understand the answer sorry

The sum of the first 40 terms of the geometric sequence is:

22,114,662.64

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The sum of the first n terms of a sequence is:

\(S_n = \frac{a_1(1 - q^n)}{1 - q}\)

For this problem, the parameters are:

a1 = 1, q = 1.5, n = 40.

Hence the sum is:

\(S_{40} = \frac{1 - 1.5^{40}}{1 - 1.5} = 22,114,662.64\)

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Monte Carlo and Historical simulation are widely used tools for risk measurement, generating random inputs based on probability distribution functions. Proper probability distributions are crucial for risk analysis, while statistics aids in risk management by obtaining probabilities and assessing results.

a) Monte Carlo and Historical simulation are the most extensively used tools for measuring risk. The significant difference between these two tools lies in their inputs. Monte Carlo simulation is based on generating random inputs based on a set of probability distribution functions. While Historical simulation, on the other hand, simulates based on the prior actual data inputs.\

b) In risk analysis, the right choice of probability distribution that explains the risk factor's values is of paramount importance as it can give rise to critical decision making and management of financial risks. Probability distributions such as the Normal distribution are used when modeling the return of an asset, or its log-returns. Normal distribution in financial modeling is essential because it best describes the distribution of price movements of liquid and high-frequency assets. Nonetheless, selecting the wrong distribution can lead to wrong decisions, which can be quite catastrophic for the organization.

c) Statistics are used in Risk Management to assist in decision-making by helping to obtain the probabilities of potential risks and assessing the results. Statistics can provide valuable insights and an objective evaluation of risks and help us quantify risks by considering the variability and uncertainty in all situations. With statistics, risks can be easily identified and properly evaluated, and it assists in making better decisions.

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Answer:

8

Step-by-step explanation:

6(6) - 20 - 32(1/4)

36 - 20 - 8

8

The value of k that satisfies the condition |A| = 1 is k = 1/3.

To find the value(s) of k for which the determinant of matrix A equals 1, we set up the equation:

|A| = 1

Using the given matrix:

|k 2|

|0 3|

The determinant of a 2x2 matrix is calculated as the product of the diagonal elements minus the product of the off-diagonal elements:

|A| = (k * 3) - (2 * 0)

Simplifying the equation, we have:

|A| = 3k - 0 = 3k

We set 3k equal to 1:

3k = 1

Dividing both sides by 3, we find:

k = 1/3

Therefore, the value of k for which the determinant of matrix A is equal to 1 is k = 1/3.

Explanation:

The determinant of a matrix is a scalar value that provides information about the matrix's properties. In this case, we are given a 2x2 matrix A and need to find the value of k for which the determinant equals 1.

We apply the formula for the determinant of a 2x2 matrix and set it equal to 1. By expanding the determinant expression and simplifying, we obtain the equation 3k = 1.

To isolate k, we divide both sides of the equation by 3, resulting in k = 1/3.

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Answer:

The distance of two points  = 6 √2 = 8.4852

Step-by-step explanation:

Explanation:-

From the graph

Given points are  A ( 4,2) and B ( -2 , -4)  

The distance formula

       = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

( x₁ , y₁ ) = ( 4,2 )   and (x₂ , y₂) = ( -2 , -4)

The distance formula

       = \(\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

     =\(\sqrt{(-2 -(4))^{2} + (-4 - (2))^{2} }\)

  =   \(\sqrt{36+36} = \sqrt{72} = 6\sqrt{2}\)

Final answer:-

The distance of two points  = 6 √2 = 8.4852

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

9. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c) and P(d)=P(e)=P(f)=0.1, find P(a).

Since P(a), P(b), and P(c) are equal, we can let P(a) = P(b) = P(c) = x.

Then, we know that P(d) = P(e) = P(f) = 0.1.

The total probability of the sample space S is equal to 1. So, we can write the equation:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

Substituting the given values, we get:
3x + 0.1 + 0.1 + 0.1 = 1
3x + 0.3 = 1
3x = 1 - 0.3
3x = 0.7

Dividing both sides by 3, we find:
x = 0.7/3
So, P(a) = 0.233.

10. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c), P(d)=P(e)=P(f), and P(d)=2P(a), find P(a).

Let P(a) = P(b) = P(c) = x. And let P(d) = P(e) = P(f) = y.

We also know that P(d) = 2P(a).

Using the equation for the total probability:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

We can substitute the given values:
3x + 3y = 1
We also know that P(d) = 2P(a):
y = 2x

Substituting this into the previous equation:
3x + 3(2x) = 1
3x + 6x = 1
9x = 1

Dividing both sides by 9, we find:
x = 1/9
So, P(a) = P(b) = P(c) = 1/9.

11. If E and F are two disjoint events in S with P(E)=0.2 and P(F)=0.4, find P(E∪F), P(Ec), and P(E∩F).

Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.2 + 0.4 = 0.6

The complement of E, Ec, is the event that consists of all outcomes in S that are not in E.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Ec) = 1 - P(E) = 1 - 0.2 = 0.8

Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

12. It is not possible for E and F to be two disjoint events in S with P(E)=0.5 and P(F)=0.7 because the sum of their probabilities would exceed 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for two events with probabilities that add up to more than 1 to be disjoint.

13. If E and F are two disjoint events in S with P(E)=0.4 and P(F)=0.3, find P(E∪F), P(Fc), P(E∩F), P((E∪F)c), and P((E∩F)c).
Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.4 + 0.3 = 0.7

The complement of F, Fc, is the event that consists of all outcomes in S that are not in F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Fc) = 1 - P(F)

= 1 - 0.3

= 0.7
Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

The complement of the union of two events, (E∪F)c, is the event that consists of all outcomes in S that are not in the union of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:

P((E∪F)c) = 1 - P(E∪F) = 1 - 0.7 = 0.3
The complement of the intersection of two events, (E∩F)c, is the event that consists of all outcomes in S that are not in the intersection of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P((E∩F)c) = 1 - P(E∩F) = 1 - 0 = 1

14. It is not possible for S={a,b,c} with P(a)=0.3, P(b)=0.4, and P(c)=0.5 because the sum of their probabilities exceeds 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

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The given triangle is a right triangle

The coordinates are given as:

D (0,n), E(m,n), F(m,0)

The length is calculated using:

\(l=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\)

So, we have:

\(DE=\sqrt{(0-m)^2 + (n-n)^2} = m\)

\(DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2\)

\(EF=\sqrt{(m-m)^2 + (n-0)^2} = n\)

The slope is calculated using:

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

So, we have:

\(DE = \frac{n -n}{0- m} = 0\)

\(DF = \frac{n -0}{0- m} = -\frac nm\)

\(EF = \frac{n -0}{m- m} = \mathbf{unde fined}\)

This is calculated using

\(m = 0.5 * (x_1 + x_2, y_1 + y_2)\)

So, we have:

\(DE = 0.5 * (0 + m, n+ n)=(0.5m, n)\)

\(DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)\)

\(EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)\)

In (a), we have:

Lengths

\(DE= m\)

\(DF = \sqrt{m^2 + n^2\)

\(EF= n\)

Slope

\(DE = 0\)

\(DF = -\frac nm\)

\(EF = \mathbf{unde fined}\)

The sides are not equal.

However, the 0 and the undefined slope implies that the triangle is a right triangle because the sides are perpendicular

It should be noted that the triangle cannot be graphed because the coordinates are not numeric

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The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Answer:

So Y, which represents height, goes down depending on how far you are in time, which is X.

The slope of the graph represents the elevator's descent speed, calculated as 12 feet per second based on the points (1, 838) and (2, 826).

The Slope of the line in the graph represents the rate of change of height with respect to time, or the speed of the elevator's descent.

In this case, the slope can be calculated using the formula: slope = (change in height) / (change in time). We know that the elevator's height changes from 838 feet at 1 second to 826 feet at 2 seconds,

So, the change in height is : 838 - 826 = 12 feet, and the change in time is 2 - 1 = 1 second.

Therefore, the slope is 12 feet/second, this indicates that the elevator is descending at a speed of 12 feet per second.

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Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

Answer:

B.less than 90 degrees

Step-by-step explanation:

Obtuse angle is greater than 90°

Since the sum of all 3 angles= 180°

The sum of other 2 angles less than  180°-90°= 90°

Answer:

Alright

100 * 4 = 400

1000 - 400 = 600

600/4 = 150

They can buy 150 baseballs

Inequality: 1000 ≥ (100*(# of baseballs))+(4*(# of bats))

Step-by-step explanation:

Answer:

340 balls

with the remaining of $2

Step-by-step explanation:

Answer:

\(\color{indigo}\rule{1pt}{1000000pt}\)

The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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Answer:

the pages read =265 more pages=147hedidnotread so pages he read =265

The minimum dimensions to minimize the amount of material is 15.87 x 15.87 x 15.87 inch.

We need to know about the minimum function to solve this problem. The minimum function can be defined as the minimum value of the variable. It can be calculated by the derivative of the function. The minimum function can be written as

f'(s) = 0

where f'(s) is the derivative function

From the question above, the given parameter is

V = 4000 inch³

The cubic volume can be written as

s² x h = 4000

where s is the length of the base area and h is the height of the box.

the minimum value of the  box refer to its surface area, hence

f(s) = 4sh + 2s²

f'(s) = 4h + 4s

4h + 4s = 0

h = s

It means that the length of the base area and the height must have the same dimension. The minimum volume should have a cube shape

V = s³

s³ = 4000

s = 15.87 inch

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