Let X be the continuous random variable with probability density function, f(x) = A(2 - x)(2 + x); 0 <= x <= 2 ==0 elsewhere
P(X = 1/2) ,
Find the value of A. Also find P(X <= 1) , P(1 <= X <= 2)

The probability of obtaining a head on the next toss of a coin after obtaining two heads from two tosses is still 1/2 or 50%.

This is because each coin toss is an independent event, and the outcome of one toss does not affect the outcome of another toss. Therefore, the fact that two heads have been obtained in the previous two tosses does not change the probability of obtaining a head on the next toss, which is always 1/2 or 0.5 for a fair coin.

Probability is the likelihood of an event occurring. The values are between 0 and 1. The closer it is to 1, the greater the probability.

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Answer:

missing side = 50

Step-by-step explanation:

using Pythagoras theorem,

30² + 40² = (missing side)²

900 + 1600 = (missing side)²

(missing side)² = 2500

missing side = √2500

missing side = 50

Answer:

C

Step-by-step explanation:

to determine which ordered pair is not a solution , substitute the coordinates of the point into the inequalities and check the validity. Note that both inequalities must be true for the point to be a solution.

A (- 3, 3 )

3  ≥ - 3 - 5

3 ≥ - 8  ← true

3(3) < - 6(- 3) + 3

9 < 18 + 3

9 < 21 ← true

------------------------------------------

B ( - 1, 2 )

2 ≥ - 1 - 5

2 ≥ - 6 ← true

3(2) < - 6(- 1) + 3

6 < 6 + 3

6 < 9 ← true

------------------------------------------

C (4, 5 )

5 ≥ 4 - 5

5 ≥ - 1 ← true

3(5) < - 6(4) + 3

15 < - 24 + 3

15 < - 21 ← false

-------------------------------------------

D (- 6, 0 )

0 ≥ - 6 - 5

0 ≥ - 11 ← true

3(0) < - 6(- 6) + 3

0 < 36 + 3

0 < 39 ← true

--------------------------------------------

Both inequalities are true in A, B , D

Both inequalities in C are not true so (4, 5 ) is not a solution to the system

Answer:

Step-by-step explanation:

Simply divide the numbers, the result is the quotient

The quotient of the given expression when 1,224 divided by 9 is 136.

The quotient is defined as the number obtained on dividing a number with some number.

The number left after the division is called as the remainder.

Example: When 37 is divided by 5, the quotient is 5 and the remainder is 2.

The quotient of the following expression can be calculated as:

When 1224 is divided by 9, it gets divisible in 136 times completely, leaving no remainder.

So, it can be said that 136 is the quotient when 1,224 divided by 9.

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Answer:

30 square feet

Step-by-step explanation:

scale F = 43.744532

Answer:

c ) it either shows diameter or radius

d) I am not sure

C. When elements are represented in a Venn diagram (using circles), the placement of elements inside or outside the circles indicates their relationship to the sets being represented.

D. Yes, the elements written at the intersection of both circles form a subset of the two sets.

C. Place an element inside a circle to indicate that it is a member of the set indicated by the circle.

An element that is positioned at the intersection of two circles denotes an element that is a part of both sets that are symbolized by those circles.

Outside the circles: In a Venn diagram, an element that is positioned outside every circle does not belong to any of the sets being represented.

D. This is so because these components are a part of the intersection of the two sets and as such, they are a part of both sets. In set theory, all of the components that are shared by two sets are contained in their intersection. Due to their simultaneous membership in both sets, the elements at the intersection are a subset of both sets.

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The given expression is:

Answer:

Step-by-step explanation:

Answer:

150.72

Step-by-step explanation:

The volume of a cylinder is 2πrh. We have r = 3 and h = 8 so volume is 48π or 150.72.

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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We are given

We want to write using a calculator

Solution

We first note that

on calculator

Now, we come back to the question

Thus, the answer is (4.5E11)/(6E2)

Option B

The flux is positive, it means that the vector field F is flowing out of the closed surface. Flux = ∫0^5 ∫0^2π ∫0^5 (z^3/4) r dr dθ dz = (π/4) ∫0^5 z^4 dz = (π/4)(5^5/5) = 125π/4.The flux of the vector field F across the surface S is zero.

To see why the flux is zero, we can use the Divergence Theorem. This theorem tells us that the flux of a vector field across a closed surface is equal to the volume integral of the divergence of the vector field over the region enclosed by the surface. Since the upper hemisphere of x^2 + y^2 + z^2 = 25 is a closed surface, we can use the Divergence Theorem to compute the flux of F across it.

First, we need to find the divergence of F. Using the product rule for differentiation, we have

div(F) = (d/dx)(0) + (d/dy)(0) + (d/dz)(z^4/16) = z^3/4.

Next, we need to find the volume enclosed by the upper hemisphere of x^2 + y^2 + z^2 = 25. This region is a half-sphere of radius 5, so its volume is (1/2)(4/3)π(5^3) = 250π/3.

Now we can use the Divergence Theorem to compute the flux of F across the upper hemisphere. The theorem tells us that the flux is equal to the volume integral of the divergence over the enclosed region, so we have

Flux = ∫∫S F · dS = ∭V div(F) dV = ∭V (z^3/4) dV

Since the integrand only depends on z, we can use cylindrical coordinates with z as the axis of symmetry to evaluate the integral. The limits of integration for z are 0 to 5, and the limits for the other variables are 0 to 2π and 0 to 5. Thus we have

Flux = ∫0^5 ∫0^2π ∫0^5 (z^3/4) r dr dθ dz = (π/4) ∫0^5 z^4 dz = (π/4)(5^5/5) = 125π/4

Since the flux is positive, it means that the vector field F is flowing out of the closed surface. However, since we are only interested in the flux across the upper hemisphere and not the entire sphere, we need to subtract the flux across the lower hemisphere to get the net flux across the upper hemisphere. The lower hemisphere has the same surface area as the upper hemisphere, but the direction of the normal vectors is pointing downward, so the flux across it is negative. Therefore, the net flux across the upper hemisphere is zero, as stated at the beginning.

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Answer:

3.75

Step-by-step explanation:

-0.8(q-0.5)=-2.6

-0.8q+0.4=-2.6

-0.8q=-2.6-0.4

-0.8q=-3

0.8q=3

q=3/0.8

q=3.75

Answer:

5(5) 5 times 5 = 25

Step-by-step explanation:

The particular solution to the given differential equation with the initial condition x = 1 when y = 0 is:

(1/3)y³ - (9/2)y² = 9/2 x² - 2x - 5/2

To find the particular solution to the given differential equation, we need to integrate both sides and apply the initial condition.

Starting with the differential equation:

2 + y² dy = 9(x dx + y dy)

We can rearrange the equation to isolate the terms involving y:

y² dy - 9y dy = 9x dx - 2

Combining like terms:

(y² - 9y) dy = 9x dx - 2

Now, we integrate both sides of the equation:

∫(y² - 9y) dy = ∫(9x dx - 2)

Integrating the left side:

∫(y² - 9y) dy = (1/3)y³ - (9/2)y²

Integrating the right side:

∫(9x dx - 2) = 9/2 x² - 2x

Therefore, the equation becomes:

(1/3)y³ - (9/2)y² = 9/2 x² - 2x + C

To find the particular solution, we substitute the initial condition x = 1, y = 0:

(1/3)(0)³ - (9/2)(0)² = 9/2 (1)² - 2(1) + C

Simplifying:

0 = 9/2 - 2 + C

Solving for C:

C = 2 - 9/2

C = 4/2 - 9/2

C = -5/2

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See attachment for the graph of the equation 8x - y = -4

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The equation is given as:

8x - y = -4

The above equation is a linear equation.

So, we start by making y the subject of the formula

y = -4 - 8x

Multiply through by -1

y = 4 + 8x

Rewrite the above equation as:

y = 8x + 4

So, we plot the graph of the equation y = 8x + 4

See attachment for the graph of the equation y = 8x + 4

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The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions is

4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions shown below

Explanation in detail:

Two expressions are shown here.

Expression 1 : 2x/x-1

Expression II for 5x/2x+4.

The product of expressions I and II must be calculated.

(2x / x-1 ) ÷ (5x / 2x+4)

applying the upcoming regulation

a ÷ b = a× 1/b

(2x/x-1)×( 2x+4 / 5x)

(2x) (2x+4) / (x-1)(5x) (5x)

(2) (2) (x+2) / (x-1)(5) (5)

The solution to the previous question is 4(x+2) / 5(x-1).

The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

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Answer:

x = 5

Step-by-step explanation:

vertical angles are congruent , so

∠ A = ∠ B , that is

5x - 1 = 4x + 4 ( subtract 4x from both sides )

x - 1 = 4 ( add 1 to both sides )

x = 5

Given the matrix A = [1 2 -1 1; 0 2 0 3; 1 1 -3 1].

Here we have to find the basis for the kernel and image of TA, and also to find the rank and nullity of TA.

Let's solve the problem using the following steps:Basis for kernel:

We know that the kernel of a matrix A is the solution of the equation Ax = 0. So,

we can solve this equation to find the kernel of A as: Ax = 0 x [1;2;-1;1] = 0 x [0;2;0;3] = 0 x [1;1;-3;1] = 0

So, we can write the augmented matrix for this equation as: [1 2 -1 1 | 0] [0 2 0 3 | 0] [1 1 -3 1 | 0]

Applying row operations on this augmented matrix, we can reduce it to the following form: [1 0 0 1 | 0] [0 1 0 3/2 | 0] [0 0 1 -1 | 0]

From this, we can write the solution as:

\([x1; x2; x3; x4] = x1[-1; 0; 1; 1] + x2[-2; -3/2; 0; 0] + x3[1; 0; -1; 0] + x4[-1; 0; 0; 1]\)

So, the basis for the kernel of A is given by the set

{[-1; 0; 1; 1], [-2; -3/2; 0; 0], [1; 0; -1; 0], [-1; 0; 0; 1]}.

Basis for image:To find the basis for the image of A, we need to find the columns of A that are linearly independent. So, we can write the matrix A as: [1 2 -1 1] [0 2 0 3] [1 1 -3 1]

Applying row operations on A, we can reduce it to the following form: [1 0 0 1] [0 1 0 3/2] [0 0 1 -1]

From this, we can see that the first three columns of A are linearly independent. So, the basis for the image of A is given by the set {[1;0;1], [2;2;1], [-1;0;-3]}.Rank and nullity:

From the above calculations, we can see that the basis for the kernel of A has 4 vectors and the basis for the image of A has 3 vectors.

So, the rank of A is 3 and the nullity of A is 4 - 3 = 1.

Hence, the required basis for the kernel and image of TA are {-1,0,1,1}, {-2,-3/2,0,0}, {1,0,-1,0}, {-1,0,0,1} and {[1;0;1], [2;2;1], [-1;0;-3]}

respectively. The rank of TA is 3 and the nullity of TA is 1.

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Answer:

I think the burger costs $3.5

Step-by-step explanation:

I divided $10.60 with the three burgers

Given :

One root of a third degree polynomial function f(x) is –5 + 2i.

To Find :

The number and nature of all roots for this function.

Solution :

We know, there are exactly three roots in any third degree polynomial.

Also, we know complex roots always comes in pair i.e. the other root is the conjugate of each other .

So, other root is , -5 - 2i .

Also, since complex roots come in conjugate pair. So, third root cannot be complex.

Therefore, 2 roots are complex and 1 is real.

Answer:

f(x) has two imaginary roots and one real root.

Step-by-step explanation:

B on edge.

Answer:

1/36

Step-by-step explanation:

If the cubes are numbered from 1 to 6 there is just one way that the sum of both of them equals 12 and this is when Marsha gets 6 in the first cube and 6 in the other.

Thus, to know what the probability that the total of numbers facing up will equal 12 we would have to calculate the probability that the first cube is 6 AND the second one is also 6.

The probability that the first cube has the number 6 is: 1/6

The probability that the second cube has the number 6 is: 1/6

We need to multiply this numbers because they both have to be 6 (rule of multiplication),

so: \(\frac{1}{6}(\frac{1}{6} )= \frac{1}{36}\)

Thus, the probability that the sum of them equals 12 is 1/36

1. A confidence interval for the single population of the 50 twins is necessary to determine the average height and likely range.

2. A confidence interval between the two populations is necessary to compare the average ages of the two different tree species.

3. A confidence interval for the single population of the waves at the beach is necessary to determine the average height and likely range.

4. A confidence interval between the two populations is necessary to compare the incomes of the students before and after graduating.

5. A confidence interval between the two populations is necessary to compare the average GPAs of the Senior and Freshmen students.

For the first scenario, a confidence interval for a single population is appropriate in the context of answering the proposed question. The researcher wants to determine whether the height of 50 twins (25 sets of twins) is significantly different than 70 inches, and therefore a confidence interval for the single population of the 50 twins is necessary to determine the average height and likely range.

For the second scenario, a confidence interval between two populations is appropriate in the context of answering the proposed question. The Environmental Protection Agency is looking to compare the average ages of Coastal Redwoods and Giant Sequoias in Californian National Parks and Forests, and therefore a confidence interval between the two populations is necessary to compare the average ages of the two different tree species.

For the third scenario, a confidence interval for a single population is appropriate in the context of answering the proposed question. A UCSB student wants to get a "likely" range for the average height of waves at Campus Point Beach, and therefore a confidence interval for the single population of the waves at the beach is necessary to determine the average height and likely range.

For the fourth scenario, a confidence interval between two populations is appropriate in the context of answering the proposed question. UCSB wants to compare the income of students before and after graduating from the school, and therefore a confidence interval between the two populations is necessary to compare the incomes of the students before and after graduating.

For the fifth scenario, a confidence interval between two populations is appropriate in the context of answering the proposed question. The Economics department studies whether student GPAs are different for Seniors and Freshmen in the department, and therefore a confidence interval between the two populations is necessary to compare the average GPAs of the Senior and Freshmen students.

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In Luther v. Borden, 1849, it is true that the Supreme Court abdicated its role in clarifying whether the people had the right to abolish their state governments. The great statesman Daniel Webster argued that people do indeed possess the right to overthrow their government.

Luther v. Borden, 1849 was a United States Supreme Court case that decided whether the court should intervene in a political question, specifically the Rhode Island Dorr Rebellion of 1841 to 1842. In this case, the court declined to do so and ruled that the authority to decide whether a rebellion against a state government exists or not, rests solely with the United States government. The Court refused to support either side in the rebellion and thus upheld the lower court's decision.

The decision is well-known for declaring that the federal government must guarantee a "republican form of government" in the states. In this context, Webster argued that people possess the right to overthrow their government as they possess the ultimate sovereignty. True.

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Answer:

21.14 lbs.

Step-by-step explanation:

So you plug in x=6.

y=3.27(6)+1.52=21.14

Answer:

b < 5

Step-by-step explanation:

subtract 2 from each side

Answer:

b < 5

Step-by-step explanation:

b + 2 < 7

    -2    -2

b < 7

Answer:The answer to the first question is b = 3.

The answer to the second question is t = 8.

The answer to the third question is m = 2 and n = 7.

The answer to the fourth question is y = 84.

The answer to the fifth question is b = 5 and c = 3.

Step-by-step explanation:

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the figure = 2(1/2 * 4 cm * 3 cm) + (8 cm * 3 cm) + (8 cm * 4 cm) + (8 cm * 5 cm) = 108 cm²

The volume of figure = area of base * height = (1/2 * 4 cm * 3 cm) * 8 cm = 96 cm³

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

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