For a continuous probablity distribution, 0 ≤ x ≤ 15. What is P(x > 15)

Answer:

calculator says 19.625

Answer:

19.625

Step-by-step explanation:

1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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Answer: C

You are looking for a shape that mirrors the question. If you mirror the question, your answer will be option C.

I hope you have a great day and take mental health breaks!

The correct reflection of the given shape is shown in option (c).

Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.

The given image shows the shape which is faced toward east direction, when we place a mirror in front of the shape, the reflection of the image changes in west direction.

Option (c) shows the exact reflection of the given shape.

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To find the least-squares solution x* of the system, we need to solve the equation Ax = b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. x₁ = -6 and x₂ = 1.

The given system can be written as:

[1 0]   [x₁]   [-6]

[0 1] * [x₂] = [ 1]

[0 0]   [x₃]   [-3]

Since the third row of the coefficient matrix is all zeros, it does not contribute to the equation. Therefore, we can ignore it for the purpose of finding the least-squares solution.

The reduced system becomes:

[1 0]   [x₁]   [-6]

[0 1] * [x₂] = [ 1]

This simplified system is already in the form of Ax = b, where A is the 2x2 identity matrix and b is the given vector. So the least-squares solution x* is simply equal to the vector b.

Therefore, the least-squares solution x* is:

x* = [-6]

      [ 1]

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Answer:

x = 76

Step-by-step explanation:

PQ is a tangent to the circle at Q , thus the angle between the tangent and the radius is 90°

The sum of the 3 angles in the triangle = 180°, thus

x = 180° - (90 + 14)° = 180 - 104 = 76

In the language of modular arithmetic, we're given

\(x-3\equiv0\pmod7\implies x\equiv3\pmod7\)

\(y+3\equiv0\pmod7\implies y\equiv-3\equiv4\pmod7\)

Then x = 7a + 3 and y = 7b + 4 for integers a and b.

Substitute these into the quadratic expression and simplify:

\(x^2+xy+y^2+n\equiv0\pmod7\)

\((7a+3)^2+(7a+3)(7b+4)+(7b+4)^2+n\equiv0\pmod7\)

\(49a^2+42a+9+49ab+28a+21b+12+49b^2+56b+16+n \equiv 0\pmod7\)

\(37+n\equiv 0\pmod7\)

\(n\equiv-2\equiv5\pmod7\)

which means the smallest positive integer n we are looking for is 5.

We have evidence to suggest that the true mean amount of soft-drink filled is more than 2 liters.

To answer this question, we need to perform a hypothesis test.

Let's define our null and alternative hypotheses as:

- H0: μ ≤ 2 (the true mean amount of soft-drink filled is less than or equal to 2 liters)

- Ha: μ > 2 (the true mean amount of soft-drink filled is greater than 2 liters)

We will use a one-tailed t-test, since we are only interested in whether the true mean amount of soft-drink filled is greater than 2 liters.

Next, we need to calculate the test statistic and the p-value.

Let's assume we have a sample of soft-drink amounts and their mean is 2.05 liters, with a standard deviation of 0.1 liters.

Using this sample information, we can calculate the t-statistic as:

t = (x - μ) / (s / √n) = (2.05 - 2) / (0.1 / √n)

Assuming a significance level of 0.05 and using a t-distribution with n-1 degrees of freedom, we can find the critical value of t by using a t-table or a statistical software. For a one-tailed test with 49 degrees of freedom, the critical value of t is approximately 1.677.

Using a statistical software or a t-table, we can find the p-value associated with our test statistic. Assuming a sample size of n = 50, we find that the p-value is approximately 0.025.

Since the p-value (0.025) is less than the significance level (0.05), we reject the null hypothesis. There is evidence to suggest that the true mean amount of soft-drink filled is greater than 2 liters.

In conclusion, at the 0.05 level of significance, we have evidence to suggest that the true mean amount of soft-drink filled is more than 2 liters.

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Refer to attachment for your answer

Answer:

x = 12

Step-by-step explanation:

-x + 8 = x - 16

add x to both sides

8 = 2x - 16

add 16 to both sides

24 = 2x

divide by 2 on both sides

x = 12

Answer:

x = 12

Step-by-step explanation:

you can do any of the following as the first step:

a)  add 'x' to each side to get:  8 = 2x - 16

b)  subtract 'x' from each side to get:  -2x + 8 = -16

c) subtract 8 from each side to get:  -x = x -24

d) add 16 to each side to get:  -x + 24 = x

if we choose to solve the equation in (a) we will get:

8 = 2x - 16

8 + 16 = 2x - 16 + 16 which simplifies to:

24 = 2x

divide each side by 2 to get x = 12

solving any of the above 4 equation will give you x = 12

The statement that is consistent conceptually with what a computed Pearson's r value represents is:

"The Pearson's r value represents the degree to which X and Y scores covary together relative to how much X and Y scores vary separately."

Pearson's correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, X and Y. It quantifies how closely the data points of X and Y align on a straight line. The magnitude of the correlation coefficient represents the degree to which the variables covary together. Additionally, the statement acknowledges that the coefficient compares the variability in X and Y scores separately to the variability when considering both variables together.

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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Answer: 9500000

Step-by-step explanation: 95 × 100000 = 9500000

*Multiply the value by 100000*

Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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Answer: {x|4<x<10}

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

35/10 = 3.5

To determine the entropy (=H(Y)) and transmitted information (=I(X:Y)=H(Y)−(H(Y/X)) with the given data, we can calculate the probabilities of each response and use them to calculate the entropy.

(1) For the first table, we have the following probabilities:

P(R2) = 0.125, P(R3) = 0.125, and P(R4) = 0.25.

Using these probabilities, we can calculate

H(Y) = -[P(R2)log2(P(R2)) + P(R3)log2(P(R3)) + P(R4)log2(P(R4))] = -[(0.125log2(0.125)) + (0.125log2(0.125)) + (0.25log2(0.25))] ≈ 1.5.

Similarly, we can calculate H(Y/X) using the joint frequencies:

P(R2/X) = 0.125/0.5 = 0.25, P(R3/X) = 0.125/0.5 = 0.25, and P(R4/X) = 0.25/0.5 = 0.5. Thus, H(Y/X) = -[P(R2/X)log2(P(R2/X)) + P(R3/X)log2(P(R3/X)) + P(R4/X)log2(P(R4/X))] = -[(0.25log2(0.25)) + (0.25log2(0.25)) + (0.5log2(0.5))] ≈ 1.5.

Therefore, I(X:Y) = H(Y) - H(Y/X) ≈ 1.5 - 1.5 = 0.

(2) To calculate H(X) - H(X/Y), we need to calculate the probabilities of each stimulus. From the first table, P(X=5) = 0.5 and P(X=0) = 0.5. Using these probabilities, we can calculate

H(X) = -[P(X=5)log2(P(X=5)) + P(X=0)log2(P(X=0))] = -[(0.5log2(0.5)) + (0.5log2(0.5))] = 1.

H(X/Y) can be calculated by using the joint frequencies:

P(X=5/Y=R2) = 0.125/0.5 = 0.25, P(X=0/Y=R2) = 0.125/0.5 = 0.25, P(X=5/Y=R3) = 0.125/0.5 = 0.25, P(X=0/Y=R3) = 0.125/0.5 = 0.25, P(X=5/Y=R4) = 0.25/0.5 = 0.5, and P(X=0/Y=R4) = 0.25/0.5 = 0.5.

Thus, H(X/Y) = -[P(X=5/Y=R2) log2(P(X=5/Y=R2)) + P(X=0/Y=R2) log2(P(X=0/Y=R2)) + P(X=5/Y=R3) log2(P(X=5/Y=R3)) + P(X=0/Y=R3) log2(P(X=0/Y=R3)) + P(X=5/Y=R4) log2(P(X=5/Y=R4)) + P(X=0/Y=R4) log2(P(X=0/Y=R4))]

= -[(0.25log2(0.25)) + (0.25log2(0.25)) + (0.25log2(0.25)) + (0.25log2(0.25)) + (0.5log2(0.5)) + (0.5log2(0.5))] = 1.5.

Comparing the results, we can see that the answers of (1) and (2) are not the same.

(3) and (4) can be calculated in a similar manner as (1).

(5) To identify the table that shows perfect information transmission, we need to look for the table with the highest transmitted information (=I(X:Y)).

From the calculations, we can see that table 3 has the highest transmitted information (≈1.5). This is because the responses R2 and R3 are evenly distributed for both stimuli (X=0 and X=5), resulting in higher uncertainty and thus higher transmitted information.

In conclusion, the entropy and transmitted information can be determined using the probabilities and joint frequencies provided. The answers in (1) and (2) are not the same. Table 3 shows the perfect information transmission due to the evenly distributed responses for both stimuli.

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Given DC is tangent to circle N at point C: m∠DCN < m∠BAN and BE is tangent to Circle N at point A, is True

(1) From the diagram, we can see that angles ∠DCN and ∠BAN are vertical angles, so they are equal in measure. Since DC is tangent to Circle N at point C, we know that m∠DCN is a right angle. Therefore, m∠DCN = 90° and m∠BAN = 90° - m∠DCN. Since m∠DCN is positive, we have m∠BAN < 90°, which implies that m∠DCN < m∠BAN. So, statement (1) is true.

(2) Since DC is tangent to Circle N at point C, we know that angle ∠CBE is a right angle, and hence BE is perpendicular to CE. Also, we know that CE is the radius of Circle N, so it is perpendicular to NB. Therefore, BE is tangent to Circle N at point A. So, statement (2) is true.

(3) The length of NB cannot be determined from the given information. We only know that CE = 6, but we do not know the radius of Circle N or the position of point B along the circle. Therefore, we cannot determine the length of NB. So, statement (3) cannot be determined.

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Complete question:

Given DC is tangent to circle N at point C, which statements are true?

- m∠DCN < m∠BAN

- BE is tangent to Circle N at point A.

- NB ≈ 6.1

Answer:

f(x) = 3x – 1

Step-by-step explanation:

f(x) = 3x – 7 also known as y = 3x – 7

Translated 6 units up:

y (+ 6) = 3x – 7

y + 6 = 3x – 7

y = 3x – 13

2 units right:

y = 3(x + 2) – 7

y = 3x + 6 – 7

y = 3x – 1

Answer:

Step-by-step explanation:

the function f(x)=3x-7 is:

vertically compressed by a factor of three

down 7 units

now we translate it 6 units up

so... f(x)=3x-7⇒f(x)=3x-7+6⇒f(x)=3x-1

to translate a linear function horizontally, you have to consider:

f(x-h)=mx+b, where h is the horizontal shift,

thus, to translate f(x)=3x-1     2 units right, we do it :

f(x-2)=3x-1  

f(x)+f(-2)=3x-1  

f(-2)=3*(-2)-1

f(-2)=-6-1

f(-2)=-7

f(x)+(-7)=3x-1  

f(x)-7=3x-1  

f(x)=3x+6

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer: $51.10

Step-by-step explanation:

Formula: Price x Percentage not needed to pay(discount)

= 146 x 0.35

= $51.10

Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

7

Step-by-step explanation:

42/6=7

The time at which the pool was full is 4:00 when the water is in the 4 inches tank .

In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.

The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.

which means,

To fill 4 inches it takes = 25 min

To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches

To fill 48 inches it takes = 48 × 25/4

                     = 300 min

                          = 5 hours

So, 5 hours after 11:00 will be 4:00

Hence, the time at which the pool was full is 4:00

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Answer:

282.743 yd²

Step-by-step explanation:

Surface Area of the Cylinder: Top Base + Bottom Base + Side

Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²

Area of Bottom Base (Circle): same as top base = 25π yd²

Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =

2π(5 yd)*(4 yd) = 40π yd²

Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²

Answer:

D. y = { -x + 2 x ≥ 1}

          { x + 1  x < 1}

Step-by-step explanation:

First is to eliminate A and C, why?

This is because of the end points shown on the graph.

As shown, if you look at the point of (2,1) it is black, this means that not only is it closed but it is also means ≤ or ≥ symbol.

You are now left with B and D

The difference between these two is the symbols; they are facing the opposite directions.

While B says x ≤ 1, and x > 1

While D says x ≥ 1, and x < 1

The direction of the symbols depends on the direction of the lines and what is part of it (some what like a shaded area)

So you answer would be D

Answer:

B

Step-by-step explanation:

First, round the figures 18 and 709 to 1 significant figure = 20 x 700

20 x 700 = 14000

Best estimate: \(\(18 \times 709 \approx 14,000\)\) by rounding \(\(18\) to \(20\) and \(709\) to \(700\)\). The correct option is B.

When precise data isn't available or necessary, an estimate is a rough approximation of a value obtained through skewed calculations or calculated  guesses that helps with quick assessments.

To estimate \(\(18 \times 709\)\),  round both numbers to the nearest tens and then multiply:

\(\(18\) rounds to \(20\)\\\(709\) rounds to \(700\)\)

Estimate: \(\(20 \times 700 = 14,000\)\)

So, the best estimate is 14,000.

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The complete question is - What is the best estimate of 18×709?

A.9,000

B.14,000

C.18,000

D. 22,000

(9 : 3) = 3(6 - 7) = (-1)

Next product

4(6 - 7) = 4(-1) = -4

Next sum

(9 : 3) + 4(6 - 7) = 3 + (-4) = -1

Answer:

-1 or B

Step-by-step explanation:

took the test

Answer:

52 cm ^ 2

Step-by-step explanation:

the big rectangle area: 12 x 4 = 48 cm ^2
the small triangle area: 1/2 Bh = 1/2 (4 ) (3) =  12/2 = 6 cm^s

Area of the shade: 48 + 6 = 52 cm^2

Answer:

A) 6

Step-by-step explanation:

The angle 12x is the same angle as the one below 108 degrees. They are supplementary angles so they add up to 180 degrees. 180-108 = 72, 12x = 72 divide each side by 12, x = 6 :)

Answer:

B. (x-3)^2

Step-by-step explanation:

x^2-6x+9 = (x-3)^2

(a-b)^2=a^2-2ab+b^2

(a+b)^2=a^2+2ab+b ^2