A solid object has the right triangle with vertices (0, 0), (3, 0), and (0, 4) as its base.

a) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x-axis, is a square. Find the volume of the solid.
b) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x -axis, is a smi-circle. Find the volume of the solid.

The given arguments are proved using logical inference rules.

To show that each of the following arguments is valid, we need to construct a proof using logical inference rules. Here is a proof for the given arguments:

Argument 1:

1. C ⊃ D (Premise)

2. ~(A ∨ B) ∨ C (Premise)

3. ~B ∨ D (Premise)

4. ~(A ∨ B) (Assumption)

5. ~A ∧ ~B (De Morgan's Law, 4)

6. ~B (Simplification, 5)

7. D (Disjunctive Syllogism, 3, 6)

8. ~(A ∨ B) ∨ D (Disjunction Introduction, 7)

9. C (Disjunction Elimination, 2, 8)

10. ~(A ∨ B) ∨ C (Disjunction Introduction, 9)

Therefore, the argument is valid.

Argument 2:

1. C ⊃ D (Premise)

2. ~(A ∨ B) ∨ C (Premise)

3. ~B ∨ D (Premise)

4. ~A ∨ ~B (Assumption)

5. ~(A ∨ B) (De Morgan's Law, 4)

6. C (Disjunction Elimination, 2, 5)

7. C ⊃ D (Premise)

8. D (Modus Ponens, 6, 7)

9. ~B ∨ D (Disjunction Introduction, 8)

10. ~(A ∨ B) ∨ D (Disjunction Introduction, 9)

Therefore, the argument is valid.

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The given second-order linear differential equation, 1y'' + 4y' + y = x^2 - 4x, can be solved using the method of undetermined coefficients. The particular solution is obtained by assuming a form for the solution and determining the coefficients based on the right-hand side of the equation.

To solve the given differential equation by undetermined coefficients, we first consider the homogeneous equation, which is obtained by setting the right-hand side equal to zero: 1y'' + 4y' + y = 0. The characteristic equation associated with this homogeneous equation is [tex]r^2[/tex]+ 4r + 1 = 0, where r represents the roots of the equation. Solving this quadratic equation, we find two complex conjugate roots: r = -2 ± i.

Since the right-hand side of the original equation is a polynomial of degree 2, we assume a particular solution of the form y_p = A[tex]x^{2}[/tex] + Bx + C. Substituting this assumed form into the original equation, we differentiate it twice to obtain the expressions for y''_p and y'_p, and substitute them back into the original equation. This allows us to equate the coefficients of like powers of x on both sides of the equation.

By comparing coefficients, we find that A = 1 and B = -2. However, the term C is a constant and does not contribute to the differential equation. Hence, the particular solution is y_p = [tex]x^{2}[/tex] - 2x.

Finally, the general solution of the differential equation is given by the sum of the homogeneous solution and the particular solution: y = y_h + y_p. Since the homogeneous solution contains complex roots, it can be expressed as y_h =[tex]e^{-2x}[/tex](C_1cos(x) + C_2sin(x)), where C_1 and C_2 are arbitrary constants. Thus, the complete solution is y = [tex]e^{-2x}[/tex]C_1cos(x) + C_2sin(x)) + [tex]x^2[/tex] - 2x.

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The number of students that are in college is 7200 if ​Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in​ dormitories.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

​Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in​ dormitories

Let x be the number of students that are in college.

Then from the question:

The value of x can be found as follows:

x = (6000/5)×6

x = (1200)×6

x = 7200

Thus, the number of students that are in college is 7200 if ​Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in​ dormitories.

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Answer:

B) y=3.5x^2 +0.5

Step-by-step explanation:

the (0,0.5) tells you what the y-intercept is :)

hope this helps :)

Answer:

1±√2=q

or

q=2.41, -0.41

Step-by-step explanation:

we are given the equation q²-2q-1=0, and we want to use the quadratic equation, which is (-b±√(b²-4ac))/2a

a is 1 (there is a 1 in front of q²)

b is -2

c is -1

substitute into the equation:

q=(2±√(4-4*1*-1))/2

solve for the discriminant:

√(4-4(1*-1))

√8

now the equation:

(2±√8)/2=q

simplify:

1±√2=q

or if your application asks for a decimal:

√2≈1.41

so:

1+1.41=2.41=q

or

1-1.41=-0.41=q

Hope this helps!

The division of 32x^3 - 48x^2 - 40x by 8x results in the quotient 4x^2 - 6x - 5 on solving the given equation.

To divide 32x^3 - 48x^2 - 40x by 8x, we divide each term of the dividend by the divisor, 8x.

Dividing 32x^3 by 8x gives us 4x^2, as x^3/x = x^2 and 32/8 = 4.

Dividing -48x^2 by 8x gives us -6x, as -48x^2/8x = -6x.

Dividing -40x by 8x gives us -5, as -40x/8x = -5.

Combining these results, the quotient is 4x^2 - 6x - 5.

The quotient represents the result of dividing the dividend by the divisor, resulting in a polynomial expression without any remainder. Therefore, when dividing 32x^3 - 48x^2 - 40x by 8x, the quotient is 4x^2 - 6x - 5.

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 The answer is not provided in the given options.

To simplify the expression (4x^3 - 3x - 7)(3x^3 + 5x + 3), we can use the distributive property of multiplication.

Multiplying each term in the first expression by each term in the second expression, we get:

(4x^3)(3x^3) + (4x^3)(5x) + (4x^3)(3) + (-3x)(3x^3) + (-3x)(5x) + (-3x)(3) + (-7)(3x^3) + (-7)(5x) + (-7)(3)

Simplifying each term, we have:

12x^6 + 20x^4 + 12x^3 - 9x^4 - 15x^2 - 9x - 21x^3 - 35x - 21

Combining like terms, we get:

12x^6 + (20x^4 - 9x^4) + (12x^3 - 21x^3) + (-15x^2) + (-9x - 35x) + (-21)

Simplifying further, we have:

12x^6 + 11x^4 - 9x^3 - 15x^2 - 44x - 21

Therefore, the correct simplification of (4x^3 - 3x - 7)(3x^3 + 5x + 3) is:

12x^6 + 11x^4 - 9x^3 - 15x^2 - 44x - 21.

Therefore, the answer is not provided in the given options.

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The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

The total number of elements in an array is equal to the product of its number of rows and columns. In this case, the array has 4 rows and 7 columns, so the total number of elements is:

4 x 7 = 28

Therefore, the answer is (c) 28.

The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.

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Answer:

I don't know how to do it the subject

The equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

To express that the point (x, y) is equidistant from both the point (4, 1) and the x-axis, we can set up an equation using the distance formula.

The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, we want the distance from (x, y) to (4, 1) to be equal to the distance from (x, y) to the x-axis. The x-axis can be represented by the equation y = 0.

Let's set up the equation:

√((x - 4)² + (y - 1)²) = √((x - x)² + (y - 0)²)

Simplifying, we get:

√((x - 4)² + (y - 1)²) = √(x² + y²)

To remove the square roots, we can square both sides of the equation:

((x - 4)² + (y - 1)²) = (x² + y²)

Expanding and simplifying further, we have:

x² - 8x + 16 + y² - 2y + 1 = x² + y²

Combining like terms, we obtain:

-8x - 2y + 17 = 0

Therefore, the equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.

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Answer:

I think! 3.5 feet wide

Step-by-step explanation:

the area of the pool is 240 square feet. divide by 68 square feet gives you 3.539= 3.5 feet wide. dont shoot me if I'm wrong lol

The width of the deck is approximately 2.65 feet.

To solve the problem, we need to first find the total area of the pool and deck combined, and then subtract the area of the pool to find the area of the deck.

The total area of the pool and deck can be represented as follows:

(12 + 2x) x (20 + 2x)

where x is the width of the deck.

The area of the pool is:

12 x 20 = 240

So, the area of the deck can be found by subtracting the area of the pool from the total area:

(12 + 2x) x  (20 + 2x) - 240 = 68

Expanding the left side and simplifying, we get:

4x²+ 64x - 208 = 0

Dividing both sides by 4, we get:

x²+ 16x - 52 = 0

Using the quadratic formula, we get:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 16, and c = -52.

Plugging in these values, we get:

x = (-16 ± √(16² - 4(1)(-52))) / 2(1)

x = (-16 ± √(960)) / 2

x = (-16 ± 4√(15)) / 2

x = -8 ± 2√(15)

Since the width of the deck cannot be negative, we can discard the negative solution, and we are left with:

x = -8 + 2√(15)

So, the width of the deck is approximately 2.65 feet.

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Answer:

Step-by-step explanation:

x+3 - x = 3 = width

2(x+3) = 2x + 6 = length

2x + 6 +2x +6 +3 +3 = 4x + 18 = Perimeter of T

Given the random variable X with specific expected values and the equation Y = a + bx + cX, we are asked to find the correlation coefficient p(X,Y).

The correlation coefficient between two random variables X and Y is given by the formula:

p(X,Y) = Cov(X,Y) / sqrt(Var(X) * Var(Y))

To calculate the correlation coefficient, we need to find the covariance (Cov(X,Y)) and the variances (Var(X) and Var(Y)).

Given the expected values, we can calculate the required values as follows:

Cov(X,Y) = E[XY] - E[X]E[Y]

Var(X) = E[[tex]X^2[/tex]] - [tex](E[X])^2[/tex]

Var(Y) = E[tex][(Y - E[Y])^2][/tex]

Using the provided expected values, we can substitute them into the formulas:

Cov(X,Y) = E[XY] - E[X]E[Y] = E[(a + bx + cX)X] - (0)(E[a + bx + cX]) = E[aX + b[tex]X^2[/tex] + c[tex]X^2[/tex]] = a(E[X]) + b(E[[tex]X^2[/tex]]) + c(E[[tex]X^3[/tex]])

Var(X) = E[[tex]X^2[/tex]] - [tex](E[X])^2[/tex] = 1 - [tex](0)^2[/tex] = 1

Var(Y) = E[(Y - [tex]E[Y])^2[/tex]] = E[(a + bx + cX - [tex](E[a + bx + cX]))^2[/tex]] = E[[tex](a + bx + cX)^2[/tex]]

Using the provided values for E[[tex]X^3[/tex]] and E[[tex]X^4[/tex]], we can simplify the expressions further and calculate the values.

Once we have the values of Cov(X,Y), Var(X), and Var(Y), we can substitute them into the correlation coefficient formula to find p(X,Y).

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Answer:

Georgio has to earn $1,800 and borrow $2,700.

Answer:

The experimental probability should get closer to the theoretical probability of 1/6 with more trials.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Experimental probability:

The number of desired outcomes is taken from the results of an experiment.

Theoretical probability:

Found before the experiment happens.

For a large number of trials, the experimental probability will be closer to the theoretical probability.

In this question:

A standard die has 6 sides, one which is 3. So the theoretical probability of rolling a 3 is 1/6.

After six rolls of a standard die, the experimental probability of rolling a 3 is 2/6.

The experimental probability, after six rolls, is 2/6 = 1/3.

What do you expect will happen to the experimental probability if the die is rolled 90 more times?

As the number of trials increase, the experimental probability is expected to get closer to the theoretical probability, which in this case is 1/6.

Based on the illustration above, the value of margin of error M.E is 6.961

Margin of error (M.E) is calculated as the product of critical value (CV) and standard error (SE) of sample mean.

The formula for standard error of sample mean is:

SE = σ/√n

where σ is the population standard deviation and n is the sample size. The formula for margin of error is:

M.E. = CV x SE

where CV is the critical value.

The critical value for a 95% confidence level with 22 degrees of freedom (sample size 23 - 1) is 2.074 (rounded to 3 decimal places).

The sample mean is 37.6 and the population standard deviation is 16.1.

Sample size, n = 23.

Using the formula,

SE = σ/√n

SE = 16.1/√23

SE = 3.365 (rounded to 3 decimal places)

Now, using the calculated value of SE and CV,

ME = CV x SE

ME = 2.074 × 3.365

ME = 6.961 (rounded to 1 decimal place)

Therefore, the margin of error (M.E.) is 6.961 (rounded to 1 decimal place).

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Answer: -9

2 to the power of 0 = 1 then all you have to do is plug in the numbers and simplify

Answer:

-9

Step-by-step explanation:

Well you just subsitute it all and solve from there

s^0= 2^0

p^-2= -3^-2

Anything squared to the power of 0 is 1

so its already 1/smth

the second part is just 3^-2 first which is 1/9 then the negative sign which is -1/9

Given the heights of the female adults in a country is represented by a random variable that follows the normal distribution N(170,30)1. To enter the tallest 20% of the female adults, a man must be at least 184.87 cm tall.

Solution:It is given that, the heights of the female adults in a country can be represented by a random variable that follows the normal distribution N(170,30)Let X be the height of female adults, then X ~ N(170, 30)

Let P be the probability of the tallest 20% female adults.To find the value of x we need to use the standard normal distribution formula which is given byz = (x - μ) / σWhere,z = standard score or z-scorex = the raw scoreμ = the meanσ = the standard deviation

Now, the probability of the tallest 20% female adults is P = 0.20 or 20%We know that the total area under the normal curve is 1 which means P(X < μ) = 0.5So, P( X > μ) = 1 - P(X < μ) = 1 - 0.5 = 0.5Therefore, 0.5 = P(Z < z) at z = 0.84 from standard normal distribution table,0.84 = (x - μ) / σOn substituting the values,0.84 = (x - 170) / 30x - 170 = 0.84 x 30x - 170 = 25.2x = 195.2So, to enter the tallest 20% of the female adults, a man must be at least 184.87 cm tall.2.

To enter the tallest 1% of the female adults, a man must be at least 201.17 cm tall.

Solution: It is given that, the heights of the female adults in a country can be represented by a random variable that follows the normal distribution N(170,30)Let X be the height of female adults, then X ~ N(170, 30)

Let P be the probability of the tallest 1% female adults.

Now, the probability of the tallest 1% female adults is P = 0.01 or 1%We know that the total area under the normal curve is 1 which means P(X < μ) = 0.5So, P( X > μ) = 1 - P(X < μ) = 1 - 0.5 = 0.5Therefore, 0.5 = P(Z < z) at z = 2.33 from standard normal distribution table,2.33 = (x - μ) / σOn substituting the values,2.33 = (x - 170) / 30x - 170 = 2.33 x 30x - 170 = 69.9x = 239.9 cm

So, to enter the tallest 1% of the female adults, a man must be at least 201.17 cm tall.

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To enter the tallest 1% of the female adults, a man must be at least 104.1 cm tall.

The heights of female adults in a country can be represented by a random variable that follows the normal distribution N(170,30).

The questions and their solutions are:

1. To enter the tallest 20% of female adults, a man must be at least [ ] cm tall.

To solve this, we can use the standard normal distribution table.

Let Z be the standard normal distribution.

To find the corresponding Z-score to the 20th percentile, we use the standard normal distribution table.

P(Z < z) = 0.20, where P(Z < z) is the area under the standard normal distribution curve to the left of z.

z = -0.84 (rounded to 2 decimal places).

Using the formula z = (X - µ) / σ, we can solve for X, the height of the woman:

[tex]z = (X - µ) / σX = σz + µX = 30(-0.84) + 170X = 147.8[/tex] (rounded to the nearest tenth of a cm)

Therefore, to enter the tallest 20% of the female adults, a man must be at least 147.8 cm tall.

2. To enter the tallest 1% of female adults, a man must be at least [ ] cm tall.

P(Z < z) = 0.01

z = -2.33 (rounded to 2 decimal places).

Using the formula z = (X - µ) / σ, we can solve for X, the height of the woman:

[tex]z = (X - µ) / σX = σz + µX = 30(-2.33) + 170X = 104.1[/tex] (rounded to the nearest tenth of a cm)

Therefore, to enter the tallest 1% of the female adults, a man must be at least 104.1 cm tall.

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Answer:

400

Step-by-step explanation:

The area of sides and add then up

Given that we randomly select 100 drivers ages 16 to 19 from example 4. We are to determine the probability that the mean distance traveled each day is between 19.4 and 22.5 miles. The probability that the mean distance traveled each day is between 19.4 and 22.5 miles is approximately 1.00.

Probability distribution is a function which represents the probabilities of all possible values of a random variable.

When the probability distribution of a random variable is unknown, we can use the Central Limit Theorem (CLT) to estimate the mean of the population.

Let X be the mean distance traveled each day by the 100 drivers ages 16 to 19.

Then, the distribution of X is approximately normal with the mean μ = 20.4 miles and the standard deviation σ = 3.8 miles.

Therefore, we can calculate the z-score as follows; z = (X - μ) / (σ / √n), where X = 19.4 and n = 100.

z₁ = (19.4 - 20.4) / (3.8 / √100)

z₁ = -2.63 and

z₂ = (22.5 - 20.4) / (3.8 / √100)

z₂ = 5.53

Hence, the probability that the mean distance traveled each day is between 19.4 and 22.5 miles is;

P(19.4 < X < 22.5) = P(z₁ < z < z₂).

Using the z-table, the probability is found to be; P(-2.63 < z < 5.53) ≈ 1.00.

Therefore, the probability that the mean distance traveled each day is between 19.4 and 22.5 miles is approximately 1.00.

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Answer:

angle 3=angle (vertical opposite angle)

angle 3 +angle 2=180°(by linear pair)

136°+angle 2=180°

angle 2=180°-136°

angle 2=44°

angle 2=angle 4(by vertical opposite angle)

Answer:

13.9%

Step-by-step explanation    :

Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.

 0.138613961 ------ when multiplying by 100 you move two spots the decimal point:     13.8613961 %

The tenth digit is 8 the number after that is 6  

If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit.

6 is greater than 5 so we add 1 to 8 and becomes 9

If the digit  after the tenth was 4 instead 6, for example,then it would be 13.8%

Answer:

Hello, Brainly users, hi hows your day going. Great. Yeah thanks for asking. Anyway, the answer is 5.2.

Step-by-step explanation:

Will provide step-by-step explanation as to how I figured it out if I can get brainliest *HINT HINT*. Have a good day. And keep good vibes amid the pandemic

:D

Answer:

5.2

Plz mark me as brainliest.

Answer:

1256 square inches

Step-by-step explanation:

Area of a circle:

A = πr²

Given:

r = 20

Work:

A = πr²

A=(3.14)20²

A = 3.14(400)

A = 1256

Answer:

1256 square inches.

Step-by-step explanation:

20 squared * π = 1256 square inches

The value of ∠FGJ = x⁰ is 45⁰.

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Here, we know that sum of angles on linear pair is 180⁰.

        ∠FGJ = x⁰ and ∠JGH = 135⁰

∠FGJ + ∠JGH = 180⁰

    x⁰ + 135⁰ = 180⁰

    x⁰ = 180⁰ - 135⁰

    x⁰ = 45⁰

Thus, the value of ∠FGJ = x⁰ is 45⁰.

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Answer:

Number 1 is correct

4.5 x 12 = 54

Number 3 is wrong,

Formula of a triangle:

BH x 1/2(basically dividing by 2)

8 x 15 = 120,

120 DIVIDED BY 2 = 60 is your area, not 120.

Your plug in would be for the triangle:

8 x 15 x 1/2

Number 5 is wrong.

11 + 4 = 15

15 x 6 (you forgot to multiply by the height!) = 90

90 divided by 2 ( x 1/2) = 45 is your area, NOT 90.

Your formula for a trapezoid is:

(b1 + b2) x h x 1/2 Don't forget your height next time!

Plug in: (4 + 11) x 6 x 1/2