Luigi will roll two cubes with faces numbered 1 through 6. Eace face of each cube has one number on it. No number repeats on a cube Luigi records the product of the numbers that land face up. What is the probability that the product of the two numbers will be an odd number less than 20? ОА. ОВ. 8 ΟΟΟ m Ga A-N-ONS

You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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I recommend that Ronald Lau build the pilot plant first to maximize his expected payoff. The expected payoff for this decision is $55,000.

To help Ronald Lau maximize his expected payoff, we can use decision analysis to evaluate the potential outcomes and probabilities of each decision.

The first decision is whether to build the new facility directly or to build the pilot plant first and then decide whether to build the complete facility.

If the new facility is built directly, the expected payoff is $200,000 × 0.5 + (-$190,000) × 0.5 = $5,000.

If the pilot plant is built first, the expected payoff is:

$5,000 + $200,000 × 0.75 × 0.6 + (-$190,000) × 0.25 × 0.6 = $55,000

or

$5,000 + (-$190,000) × 0.75 × 0.4 + $200,000 × 0.25 × 0.4 = -$45,000

The best decision is to build the pilot plant first since this decision has a higher expected payoff of $55,000 compared to the expected payoff of $5,000 for building the new facility directly.

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Answer:the answer is 32

Step-by-step explanation: 2 to the 5th power =2*2*2*2*2=32

Answer:

A.) y=7 hope this helps you

The differential equation is: \(\frac{d^2y}{dt^2} - \frac{21}{5}\frac{dy}{dt} - \frac{72}{5}y = 0\) with the general solution \(y = c_1e^{7t} + c_2e^{-3t}\).

To find a differential equation whose general solution is given by \(y = c_1e^{7t} + c_2e^{-3t}\), we can proceed as follows:

Let's assume that the differential equation is of the form:

\(\frac{d^2y}{dt^2} + a\frac{dy}{dt} + by = 0\)

where \(a\) and \(b\) are constants to be determined.

First, we differentiate \(y\) with respect to \(t\):

\(\frac{dy}{dt} = 7c_1e^{7t} - 3c_2e^{-3t}\)

Then, we differentiate again:

\(\frac{d^2y}{dt^2} = 49c_1e^{7t} + 9c_2e^{-3t}\)

Now, we substitute these derivatives back into the differential equation:

\(49c_1e^{7t} + 9c_2e^{-3t} + a(7c_1e^{7t} - 3c_2e^{-3t}) + b(c_1e^{7t} + c_2e^{-3t}) = 0\)

We can simplify this equation by collecting the terms with the same exponential factors:

\((49c_1 + 7ac_1 + bc_1)e^{7t} + (9c_2 - 3ac_2 + bc_2)e^{-3t} = 0\)

For this equation to hold true for all values of \(t\), the coefficients of the exponential terms must be zero:

\(49c_1 + 7ac_1 + bc_1 = 0\)  ---(1)

\(9c_2 - 3ac_2 + bc_2 = 0\)  ---(2)

Now we have a system of two linear equations with two unknowns \(a\) and \(b\). We can solve this system to find the values of \(a\) and \(b\).

From equation (1):

\(c_1(49 + 7a + b) = 0\)

Since \(c_1\) cannot be zero (as it is a coefficient in the general solution), we have:

\(49 + 7a + b = 0\)  ---(3)

From equation (2):

\(c_2(9 - 3a + b) = 0\)

Similarly, since \(c_2\) cannot be zero, we have:

\(9 - 3a + b = 0\)  ---(4)

Now we have a system of two linear equations (3) and (4) with two unknowns \(a\) and \(b\). We can solve this system to find the values of \(a\) and \(b\).

Subtracting equation (4) from equation (3), we get:

\(42 + 10a = 0\)

\(10a = -42\)

\(a = -\frac{42}{10} = -\frac{21}{5}\)

Substituting the value of \(a\) into equation (4), we get:

\(9 - 3\left(-\frac{21}{5}\right) + b = 0\)

\(9 + \frac{63}{5} + b = 0\)

\(b = -\frac{72}{5}\)

Therefore, the differential equation whose general solution is \(y = c_1e^{7t} + c_2e^{-3t}\) is:

\(\frac{d^2y}{dt^2} - \frac{21}{5}\frac{dy}{dt} - \frac{72}{5}y = 0\)

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(a) Let S be a subset of an n-dimensional vector space V. Suppose S contains less than n vectors. Then, the maximum number of linearly independent vectors in S is also less than n. Therefore, the dimension of the span of S is less than n, and hence, S cannot span V.

(b) The nullity of a matrix is the dimension of its null space, which is the set of all solutions to the homogeneous equation Ax = 0, where A is the matrix. The smallest possible nullity for a 4 x 7 matrix is 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of rows.

(c) The smallest possible nullity for a 7 x 4 matrix is also 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of columns. This follows from the rank-nullity theorem, which states that the rank plus the nullity of a matrix equals its number of columns.

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Answer:

B.) No, because not all of the pairs represent the same ratio.

Step-by-step explanation:

B.) No, because not all of the pairs represent the same ratio.

Answer:

The shortest path to take is \(20\sqrt{3}\ cm\) or \(34.64\ cm\)

Step-by-step explanation:

This question requires an attachment (See attachment 1 for question)

Given

Cube Dimension: 20cm * 20cm

Required

Shortest path from A to B

For proper explanation, I'll support my answer with an additional attachment (See attachment 2)

The shortest path from A to B is Line labeled 2

But first, the length of line labeled 1 has to be calculated;

This is done as follows;

Since, the cube is 20 cm by 20 cm

\(Line1^2 = 20^2 + 20^2\) (Pythagoras Theorem)

\(Line1^2 = 2(20^2)\)

Take square root of both sides

\(Line1 = \sqrt{2(20)^2}\)

Split square root

\(Line1 = \sqrt{2} * \sqrt{20^2}\)

\(Line1 = \sqrt{2} * 20\)

\(Line1 = 20\sqrt{20}\)

Next is to calculate the length of Line labeled 2

\(Line2^2 = Line1^2 + 20^2\) (Pythagoras Theorem)

Substitute \(Line1 = 20\sqrt{20}\)

\(Line2^2 = (20\sqrt{2})^2 + 20^2\)

Expand the expression

\(Line2^2 = (20\sqrt{2})*(20\sqrt{2}) + 20 * 20\)

\(Line2^2 = 400*2 + 400\)

Factorize

\(Line2^2 = 400(2+1)\)

\(Line2^2 = 400(3)\)

Take square root of both sides

\(Line2 = \sqrt{400(3)}\)

Split square root

\(Line2 = \sqrt{400} * \sqrt{3}\)

\(Line2 = 20 * \sqrt{3}\)

\(Line2 = 20 \sqrt{3}\)

The answer can be left in this form of solve further as follows;

\(Line2 = 20 * 1.73205080757\)

\(Line2 = 34.6410161514\)

\(Line2 = 34.64 cm\) (Approximated)

Hence, the shortest path to take is \(20\sqrt{3}\ cm\) or \(34.64\ cm\)

Answer:

44.72 cm

Step-by-step explanation:

1. This was marked correct by RSM

2. Unfold the cube, so that points A and B and on points diagonal from each other on a 40 cm x 20 cm rectangle. Now draw a line connecting points A to B. That is the hypotenuse of both triangles. Now according to the pythagorean theorem, the hypotenuse is √2000, which is equal to 5√20.

3. The answer is 44.72 cm

The equation Chad should program is \(y = -0.04x^2 + 20x.\)

The equation that Chad should program into his rocket launcher to win is:

\(y = -0.04x^2 + 8x\)

This is a quadratic equation in standard form, where the coefficient of x^2 is negative, indicating that the path of the rocket is a downward facing parabola. The coefficient of x^2 is -0.04, which means that the parabola is relatively flat, ensuring that the rocket will travel a horizontal distance of 20 feet when it reaches a height of 100 feet.

To sketch the rocket’s path, we can plot points on the graph of the equation. For example, when x = 0, y = 0, so the rocket starts at the origin. When x = 50, y = 200, so the rocket reaches its maximum height at x = 50 and y = 100. When x = 100, y = 0, so the rocket lands 20 feet away from the launch pad at ground level. We can connect these points to sketch the path of the rocket.

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Answer:

(6x^2)(x^4 +x^2 + 1)

Step-by-step explanation:

6x^6 + 6x^4 + 6x^2

split it up into parts

6x^6 = (6x^2) * x^4

6x^4 = (6x^2) * x^2

6x^2 = (6x^2) * 1

so you can take out 6x^2 to get

(6x^2)(x^4 +x^2 + 1)

Answer:

To find the extreme value of the function f(x) = 6x^2 - 180x + 1000, we can first take the derivative of the function and set it equal to zero:

f'(x) = 12x - 180 = 0

Solving for x, we get x = 15. Substituting this value back into the original function, we get:

f(15) = 6(15)^2 - 180(15) + 1000 = 1250

So the extreme value of the function is 1250, which represents the maximum profit in thousands of dollars that can be earned by selling a certain number of items.

More specifically, the value x = 15 is the value of x that maximizes the profit, and the maximum profit is $1,250,000. This means that if the company sells 15 items, they will make the most profit possible.

Step-by-step explanation:

it would be 4, waxing gibbous

The general solution to the given differential equation is:

y = c1e^(-9t) + c2e^(-5t) where c1 and c2 are arbitrary constants.

To find the general solution to the given differential equation, we can assume a solution of the form y = e^(rt), where r is a constant to be determined.

First, let's find the derivatives of y with respect to t:

y' = re^(rt)

y'' = r^2e^(rt)

Now, substitute these derivatives into the differential equation:

5(r^2e^(rt)) + 60(re^(rt)) + 225(e^(rt)) = 0

Simplifying the equation:

(r^2 + 12r + 45)e^(rt) = 0

For the equation to hold for all values of t, the expression in the parentheses must be equal to zero:

r^2 + 12r + 45 = 0

This is a quadratic equation, which can be factored as:

(r + 9)(r + 5) = 0

Setting each factor equal to zero:

r + 9 = 0  or  r + 5 = 0

Solving for r, we get:

r = -9  or  r = -5

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Answer:

7.7 km

Explanation:

Use cosine rule as here given two sides and one angle.

Cosine rule states:

a² = b² + c² - 2bc cos(A)

While solving, treat a = 7.5 km as to that opposite angle is given of 68°

then b = missing side, c = 5.2 km, A = 68°

Applying rule:

7.5² = b² + 5.2² - 2(b)(5.2) cos(68)

56.25 = b² + 27.04 - 3.8959b

56.25 - 27.04 = b² - 3.8959b

b² - 3.8959b = 29.21

b² - 3.8959b - 29.21 = 0

apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]

\(\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0\)

\(\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}\)

\(\sf b = 7.69 291 \quad or \quad b = -3.797\)

\(\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)\)

As length cannot be negative. Hence the value of b is only 7.7 km

The answer is 7.7 km.

Let's apply the Cosine Law in this situation.

a² = b² + c² - 2bc cos(A)

Now, substitute the values based on the given diagram.

Here, using the Quadratic Equation, we can solve :

Answer:

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  m∠B = 69°

Step-by-step explanation:

measure of ∠B = 3(2x + 5) = 6x + 15

The sum of the angles = 92 = 2x + 5 + 6x + 15

92 = 8x + 20

72 = 8x

x = 9

m∠A = 2(9) + 5 = 18 + 5 = 23

m∠B = 6(9) + 15 = 54 + 15 = 69

Check:  23 + 69 = 92  and 23(3) = 69

The solution is :

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  

m∠B = 69°

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here we have,

given that,

measure of ∠B = 3(2x + 5) = 6x + 15

The sum of the angles = 92 = 2x + 5 + 6x + 15

92 = 8x + 20

72 = 8x

x = 9

m∠A = 2(9) + 5 = 18 + 5 = 23

m∠B = 6(9) + 15 = 54 + 15 = 69

Check:  23 + 69 = 92  and 23(3) = 69

Hence, The solution is :

Equation:  2x + 5 + 6x + 15 = 92

Solution:  x = 9

m∠A =23°  

m∠B = 69°

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Answer:     M=3

Step-by-step explanation:

The slope-intercept form is y=mx+b, where mis the slope and b is the y-intercept. y=mx+b

Simplify the right side.

The most complete and accurate choice is (c) Both (a) and (b) are correct.

To prove the equation E(X^2) = ∫0∞ 2x(1 - F(x)) dx, we can use either approach (a) or (b) to show the validity of the equation.

Approach (a) uses Tonelli's theorem, which allows us to interchange the order of integration for nonnegative random variables. It starts by expressing E(X^2) as the double integral of X(ω)^2 with respect to the joint distribution P. By applying Tonelli's theorem, we interchange the order of integration and rewrite it as ∫[0,∞] 2x ∫[X(ω)≥x] dP dx. The inner integral represents the probability that X(ω) is greater than or equal to x, which can be written as 1 - F(x). Evaluating the outer integral gives ∫[0,∞] 2x(1 - F(x)) dx, thus proving the equation.

Approach (b) directly uses the fact that for a nonnegative random variable U, E(U) = ∫0∞ (1 - F_U(u)) du, where F_U(u) is the distribution function of U. By letting U = X^2, we have E(X^2) = E(U) = ∫0∞ (1 - F_X^2(u)) du. Since the distribution of U is F_X(u), we can replace F_X^2(u) with F_X(u) in the integral, resulting in ∫0∞ (1 - F_X(u)) du. Finally, by substituting x = u, we obtain ∫0∞ 2x(1 - F(x)) dx, which matches the desired equation.

Therefore, the most complete and accurate choice is (c) Both (a) and (b) are correct because both approaches are valid and provide a rigorous proof of the equation E(X^2) = ∫0∞ 2x(1 - F(x)) dx.

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The most complete and accurate choice is (c) Both (a) and (b) are correct.

To prove the equation E(X^2) = ∫0∞ 2x(1 - F(x)) dx, we can use either approach (a) or (b) to show the validity of the equation.

Approach (a) uses Tonelli's theorem, which allows us to interchange the order of integration for nonnegative random variables. It starts by expressing E(X^2) as the double integral of X(ω)^2 with respect to the joint distribution P. By applying Tonelli's theorem, we interchange the order of integration and rewrite it as ∫[0,∞] 2x ∫[X(ω)≥x] dP dx. The inner integral represents the probability that X(ω) is greater than or equal to x, which can be written as 1 - F(x). Evaluating the outer integral gives ∫[0,∞] 2x(1 - F(x)) dx, thus proving the equation.

Approach (b) directly uses the fact that for a nonnegative random variable U, E(U) = ∫0∞ (1 - F_U(u)) du, where F_U(u) is the distribution function of U. By letting U = X^2, we have E(X^2) = E(U) = ∫0∞ (1 - F_X^2(u)) du. Since the distribution of U is F_X(u), we can replace F_X^2(u) with F_X(u) in the integral, resulting in ∫0∞ (1 - F_X(u)) du. Finally, by substituting x = u, we obtain ∫0∞ 2x(1 - F(x)) dx, which matches the desired equation.

Therefore, the most complete and accurate choice is (c) Both (a) and (b) are correct because both approaches are valid and provide a rigorous proof of the equation E(X^2) = ∫0∞ 2x(1 - F(x)) dx.

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Answer:

5 faces 5 vertices 8 edges

Step-by-step explanation: i just finished it.

Answer:

This shape has  

✔ 5

faces.

This shape has  

✔ 5

vertices.

This shape has  

✔ 8

edges.

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

I did the instruction, and I got it correct.

The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

From the given image, we see that;

Hypotenuse = 13

Adjacent = 12

Opposite = 5

Thus;

tan θ = 5/12

θ = tan⁻¹(5/12)

sin θ = 5/13

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Based on the table of values, the slope and y-intercept include the following:

In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is equal to -1/2.

From the information provided in the table above, the slope and data points on this line include the following:

In Mathematics and Geometry, the slope of any straight line can be calculated by using this expression;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have;

Slope (m) = (1 - 0)/(1 + 1)

Slope (m) = 1/2

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Answer:

13

Step-by-step explanation:

4 numbers

average is 10

10 * 4 = 40

13 + 6 + 8 = 27

40 - 27 = 13

The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

What is Equation of Straight line ?

Equation of Straight line as follows , y = mx+b

where m is slope of the line.

Given ,

The equation of line k is y+10=3(x+3).

Perpendicular to line k is line , which passes through the point (5,–5)

So, the given equation could be,

y = 3x+9-10

y = 3x-1

m = 3

So, the slope of the another line = -1/3

So, the equation could be ,

when it passes through the point (5,-5) is

y - (-5) = -1/3  ( x - 5 )

y+ 5 = -1/3  ( x-5)

3 (y+5) = -1 (x-5)

3y+15 = -x + 5

3y+x+15-5 = 0

3y+x+10 = 0

Hence, The equation of a line is 3y+x+10 = 0 when it passes through the point (-5,5).

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Answer:

2x^3 - 2x^2 - 9x + 3

Step-by-step explanation:

(2x^3 − 3x + 2) - (2x^2 + 6x − 1) =

2x^3 − 3x + 2 - 2x^2 + (-6x) − (-1) =  ==> distribute the negative sign to 2x^2,

                                                               6x, and -1 in (2x^2 + 6x − 1)

Adding a negative number is equivalent to subtracting by a positive number.

Subtracting a negative number is equivalent to adding by a positive number.

Hence:

2x^3 − 3x + 2 - 2x^2 - 6x + 1 =  

2x^3 - 2x^2 - 3x - 6x + 2 + 1 =  ==> rearrange the expression in which like

                                                      terms are matching

2x^3 - 2x^2 - 9x + 3 ==> simplify

Answer:

80

Step-by-step explanation:

The null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

Null hypothesis is a statistical hypothesis that claims there is no significant difference between a specified population parameter and the observed sample statistics. While alternative hypothesis is a statistical hypothesis that suggests that there is a significant difference between a specified population parameter and the observed sample statistics.In the given scenario, the null hypothesis and the alternative hypothesis will be:

Null hypothesis (H0): At most 70% of people who eat fast food more than 2x a week are overweight. (This means less than 70% are overweight)Alternative hypothesis (Ha): More than 70% of people who eat fast food more than 2x a week are overweight.

:We can evaluate the null hypothesis by testing the probability of a sample occurring, assuming the null hypothesis is true. If the probability of a sample is very low, it implies that it is unlikely that the sample was obtained assuming that the null hypothesis was true, and we can reject the null hypothesis and accept the alternative hypothesis

.In conclusion, the null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

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Answer:

0

Step-by-step explanation:

There is no gradient there.

Answer:

A: 8.4

Step-by-step explanation:

Order of operations: BEDMAS. Brackets, exponents, division, multiplication, addition, and substraction.

Using this you need to do 2(1.2) first.

2(1.2)=2.4

Then 4.5-2.4=2.1

Then finally 4(2.1)=8.4

Hope that helps

please give brainliest

Answer:

pretty sure it's 8.4 don't come at me if it's not

Step-by-step explanation:

-2(2.1) = -2.4

4(4.5-2.4) = 4(2.1)

4(2.1) = 8.4