What could be the time of a place at 90-degree West longitude if the Greenwich Time is 12pm

Answer:

x = 4

Step-by-step explanation:

\(5^{9x} =25^{4x+2}\)

First you need to get a common base as your number.

\(5^{9x} =5^{2(4x+2)}\)

The second number changed because 5 squared is 25. Changing it to this form gives us the same base number of 5. Now we use the distributive property in the exponent.

\(5^{9x} =5^{8x+4}\)

Now we can use this statement:

\(A^{m} =A^{n}\) if \(m=n\)

Using this we solve:

9x = 8x+4

-8x  -8x

x = 4

Hope it helps!

As per Chebyshev's theorem, for any data set, at least (1 - 1/k^2) fraction of the data values will lie within k standard deviations of the mean, where k is any positive number greater than 1.

Using Chebyshev's theorem, we can determine the percentage of the population values between 51 and 91 for this question:

k = (91 - 71)/10 = 2

So, at least (1 - 1/2^2) = 75% of the population values will lie between 51 and 91.

However, as the population is assumed to be bell-shaped, we can use the empirical rule to get a more accurate estimate. According to the empirical rule, approximately 68% of the population values will lie within 1 standard deviation of the mean, 95% of the population values will lie within 2 standard deviations of the mean, and 99.7% of the population values will lie within 3 standard deviations of the mean.

The standard deviation of the population is the square root of the variance, which is 10 in this case.

So, we want to find the percentage of the population values that are between 51 and 91, which is 2 standard deviations away from the mean in either direction.

Using the empirical rule, approximately 95% of the population values will lie between (71 - 2(10)) = 51 and (71 + 2(10)) = 91.

Therefore, approximately 95% of the population values are between 51 and 91.

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Answer:

4x - y = 16

Step-by-step explanation:

y = 2(x – 3)2 - 4

When written in standard form, this will be the answer --->

4x - y = 16

Answer:

y = 2x² - 12x + 14

Step-by-step explanation:

The equation of a parabola in standard form is

y = ax² + bx + c ( a ≠ 0 )

Given

y = 2(x - 3)² - 4 ← expand (x - 3)² using FOIL

  = 2(x² - 6x + 9) - 4 ← distribute parenthesis

  = 2x² - 12x + 18 - 4

y  = 2x² - 12x + 14 ← in standard form

Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

Here,

The z-score which separates the top 10% of a normally distributed

population is 1.282.

Since z = (x-u)/sigma

1.282 = (40-38)/sigma

sigma = 2/1.282

sigma = 1/0.641 = 1561

The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer:

486cm^2

Step-by-step explanation:

Surface area of cube = (6a^2)

6×9×9=486.

Main AnswerIn the study by Hoynes (2012), the population that is of interest to the researchers are families who receive Supplemental Nutrition Assistance Program (SNAP) or more commonly known as food stamps. The study examines the impact of the policy-driven change in economic resources available in utero and during childhood on the economic health of individuals in adulthood.

The sample that the study examines are 60,782 families over the time period of 1968 to 2009, which is subsequent to the introduction of the Food Stamp Program in 1961. The data links family background in early childhood to adult health and economic outcomes.The characteristics of the population that are of interest to the researchers are the impact of a positive and policy-driven change in economic resources available in utero and during childhood on the economic health of individuals in adulthood. Specifically, the researchers looked at the long-term effect of access to food stamps in childhood on the incidence of metabolic syndrome (obesity, high blood pressure, and diabetes) and an increase in economic self-sufficiency for women.

Based on the study, the researchers concluded that access to food stamps in childhood leads to a significant reduction in the incidence of metabolic syndrome and, for women, an increase in economic self-sufficiency. Hence, the results suggest substantial internal and external benefits of SNAP.

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The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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Answer:

16

Step-by-step explanation:

PEMDAS

The given sequence defined by a1 = 1 and an+1 = 5 - 1/an is increasing, meaning each term is greater than the previous term. Additionally, all terms in the sequence are less than 5.

To prove that the sequence is increasing, we need to show that each term is greater than the previous term. We can do this by induction.

For the base case, a1 = 1.

Now, assuming an > an-1, let's consider an+1:

an+1 = 5 - 1/an

Since an > an-1, 1/an > 1/(an-1), and 5 - 1/an < 5 - 1/(an-1).

From the induction assumption, 5 - 1/(an-1) < 5 - 1/an-1.

Therefore, 5 - 1/an < 5 - 1/(an-1), which means an+1 > an. Hence, the sequence is increasing.

To prove that an < 5 for all n, we can also use induction.

For the base case, a1 = 1 < 5.

Assuming an < 5, let's consider an+1:

an+1 = 5 - 1/an

Since an < 5, 1/an > 1/5.

Therefore, 5 - 1/an < 5 - 1/5 = 4.8.

Hence, an+1 = 5 - 1/an < 4.8, which means an+1 < 5. Thus, an < 5 for all n.

Therefore, we have shown that the sequence defined by a1 = 1 and an+1 = 5 - 1/an is increasing, and all terms in the sequence are less than 5.

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Answer:

Number 1. Hope you can read that

Step-by-step explanation:

Answer:

8+6+4

Step-by-step explanation:

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

2/3

Step-by-step explanation:

Have a good day :)

Answer:

19-13=6+1=7-14=-7+4=-3

Step-by-step explanation:

Answer:

5 m/s^2

Step-by-step explanation:

Force = mass x acceleration

f = ma

We have the force of 10 N and the mass of 2 kg.

10 N = 2 kg a

divide by 2 on both sides to isolate the a

a = 5 m/s^2

Answer:

\(\boxed {\boxed {\sf a= 5 \ m/s^2}}\)

Step-by-step explanation:

The formula for force is:

\(F=m*a\)

If we rearrange the formula for acceleration (a) and divide both sides by m we get:

\(\frac{F}{m}=a\)

The net force is 10 Newtons. Let's convert the units to make the problem easier later on.

The mass is 2 kilograms.

\(F=10 \ kg*m/s^2\\m= 2 \ kg\)

Substitute the values into the formula.

\(\frac{10 \ kg*m/s^2}{2 \ kg} =a\)

Divide. Note the kilograms (kg) will cancel each other out (this is why we converted the units)

\(\frac{10 \ m/s^2}{2}=a\)

\(5 \ m/s^2=a\)

The acceleration of the box is 5 meters per second squared.

Using the Improved Euler Method with step size of h = 0.5, the estimated value of y(3) is 1.625 for the initial value problem.

An initial value problem is a type of differential equation problem that involves finding the solution of a differential equation under given initial conditions. It consists of a differential equation describing the rate of change of an unknown function and an initial condition giving the value of the function at a particular point.

The goal is to find a function that satisfies both the differential equation and the initial conditions. Solving initial value problems usually requires techniques such as separation of variables, integration of factors, and numerical techniques. A solution provides a mathematical representation of a function that satisfies specified conditions. 

(a) To estimate y(3) using the improved Euler method, start with the initial condition y(2) = 1. Compute the x, y, and f values ​​iteratively using a step size of h = 0.5. ( x, y) and incremental delta y.

Using the improved Euler formula, we get:

\(delta y = h * (f(x, y) + f(x + h, y + h * f(x, y))) / 2\)

The value can be calculated as:

\(× | y | f(x,y) | delta Y\\2.0 | 1.0 | 2(2) + 1 - 5(1) + 1 = 1 | 0.5 * (1 + 1 * (1 + 1)) / 2 = 0.75\\2.5 | 1.375 | 2(2.5) + 1 - 5(1.375) + 1 | 0.5 * (1.375 + 1 * (1.375 + 0.75)) / 2 = 0.875\\3.0 | ? | 2(3) + 1 - 5(y) + 1 | ?\)

To estimate y(3), we need to compute the delta y of the last row. Substituting the values ​​x = 2.5, y = 1.375, we get:

\(Delta y = 0.5 * (2(2.5) + 1 - 5(1.375) + 1 + 2(3) + 1 - 5(1.375 + 0.875) + 1) / 2\\delta y = 0.5 * (6.75 + 0.125 - 6.75 + 0.125) / 2\\\\delta y = 0.25\)

Finally, add the final delta y to the previous y value to find y(3) for the initial value problem.

y(3) = y(2.5) + delta y = 1.375 + 0.25 = 1.625. 

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To solve the system of equations using matrix inversion, we need to represent the system in matrix form. Let's define the coefficient matrix A and the vector of constants B as follows:

A = [[1, 3, 1],

[2, 2, 1],

[2, 3, 1]]

B = [[4],

[-1],

[3]]

Now, we can find the inverse of matrix A, denoted as A^(-1). Then, we can solve for the solution vector X by multiplying A^(-1) with B:

X = A^(-1) * B

b. In order to explain the process and significance of matrix inversion, let's consider the system of equations as a linear system. The coefficient matrix A represents the linear transformation applied to the variables x₁, x₂, and x₃, and the vector B represents the target values or constants on the right-hand side of the equations.

By finding the inverse of matrix A, we essentially obtain the inverse transformation that can undo the effect of the original transformation. In other words, we can obtain the solution vector X by multiplying the inverse matrix A^(-1) with B, which effectively "undoes" the transformation and reveals the values of the original variables.

The inverse of matrix A can be calculated using various methods such as Gaussian elimination or the adjugate formula. Once we have the inverse matrix, we can multiply it with the vector B to obtain the solution vector X, which represents the values of x₁, x₂, and x₃ that satisfy the system of equations.

Matrix inversion is particularly useful in solving systems of equations because it provides a direct and efficient method to find the solution vector without the need for iterative methods or extensive algebraic manipulations. However, it's important to note that not all matrices have an inverse, and in those cases, alternative methods such as Gaussian elimination or singular value decomposition may be employed to solve the system.

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The statements that is true about the similarity of the two triangles the option D

D. ΔMNO and ΔJKL are not similar triangles

Similar triangles are triangles which have proportional corresponding sides

The parameters in the question are;

The length of segment MN = 20

Length of segment NO = 12

Length of segment OM = 25

Measure of angle ∠O = 56°

Length of segment LJ =- 15

Length of segment JK = 12

Length of segment KL = 9

Measure of angle ∠L = 56°

Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included  angle between the two sides are congruent

The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL

However, the ratio of the sides  LK to ON and JL to MO are;

9/12 ≠ 15/25

Therefore, the triangles are not similar

The correct option is option D

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Answer:

the answer is the third one k > - 5

Answer/Step-by-step explanation:

 Step 1: Simplify both sides of the inequality.

\(\frac{1}{4}k+\frac{-3}{4}>-2\)

Step 2: Add 3/4 to both sides.

\(\frac{1}{4}k+\frac{-3}{4}+\frac{3}{4}>-2+\frac{3}{4}\)

\(\frac{1}{4}k>\frac{-5}{4}\)

Step 3: Multiply both sides by 4.

\(4*\frac{1}{4}k>4*\frac{-5}{4}\)

K > -5

 So according to this the value of k has to be greater than -5

You can check your answer by substituting the values in for k.

You can use a calculator..

\(\frac{-10-3}{4} >-2\)  

\(\frac{-7-3}{4} >-2\)

\(\frac{-1-3}{4} >-2\)

\(\frac{0-3}{4} >-2\)

Solve these and you will get your 2nd answer.

[RevyBreeze]

The probability P[X+Y>3] is approximately 0.82.

To find the probability P[X+Y>3], we need to determine the range of values for X and Y that satisfy the given condition. Since X and Y are independent and identically distributed uniform random variables in the interval (0, 5), their sum X+Y will follow a triangular distribution within the range (0, 10).

To visualize this, imagine a square with side length 5 units, representing the possible values for X and Y. The region where X+Y>3 corresponds to the area above the line X+Y=3 within this square.

The area of this triangular region can be calculated as the difference between the area of the entire square and the area of the right triangle below the line X+Y=3. The area of the square is 5 * 5 = 25 square units, and the area of the right triangle is (5 * 3) / 2 = 7.5 square units.

Therefore, the area of the region where X+Y>3 is 25 - 7.5 = 17.5 square units. To find the probability, we divide this area by the total area of the square, which gives us 17.5 / 25 = 0.7.

Hence, the probability P[X+Y>3] is approximately 0.7 or 70%.

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Answer:

175

Step-by-step explanation:

hey! so it's basically an "estimate" meaning that you can round all the measurements up to the nearest whole number. and since finding the prism's volume is l*h*w divided by 2, i did 7*5*10 and got 350. half of 350 is 175 which is the volume of the prism :)

Answer:

175

Step-by-step explanation:

the formula of triangular prism is

v = 1÷2( b×h×l)

base (b) =5.1cm

height( h) = 6.9

length ( l) = 9.9

v =1÷2 ( 5.1 × 6.9× 9.9 )

v = 174.19 cm^3

so th closest will be 175cm^3

Answer:whats the question  

Explanation:(pls dont report me as soon as u tell me the question i will edit my answer and answer correctly)

Answer:

It is because the is

Step-by-step explanation:  

Answer:

it will be 10.5 so he will take the bus

Step-by-step explanation:

Answer:

The inequality representing the situation is 0.5x + 3 < 10.

Use inverse operations and properties of inequality to solve.

Find that x < 14.

Carl lives 15 miles from home, so he will take a bus.

Step-by-step explanation:

Answer:

48 degrees

Step-by-step explanation:

x+132 should be equal to 180, property of a parallelogram (and same side interior angles)

180-132=48

Answer:

x = 48

Step-by-step explanation:

Consecutive angles in a parallelogram sum to 180° , so

x + 132 = 180 ( subtract 132 from both sides )

x = 48

Answer:

its 43

Step-by-step explanation:

i had a test with the same question, i promise its right :)

Use the formula V = P(1 - r)ᵗ, where V is the final value of the car, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the time in years. Substituting the given values, the value of the car after 9 years is approximately 10920.91 dollars.

To calculate the value of the car after 9 years, we can use the formula for exponential decay:

V = P(1 - r)ᵗ

where V is the final value of the car, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the time in years.

Substituting the given values, we get:

V = 22400(1 - 0.0675)⁹ ≈ 10920.91

Therefore, the value of the car after 9 years is approximately 10920.91 dollars.

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The answer choice which represents a function among the given answer choices is; Choice B.

According to the given task content; the table which represents a function among the given answer choice is to be identified.

Recall that a function can be defined as a relation in which case; each input value is assigned not more than one value.

By observation, only the answer choice B has a combination of input and output values in which case; each input value is assigned only one output value.

Hence, since a function is a relation which is characterized by assigning only one output value to each input value; the correct answer choice is; Choice B.

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To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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