What is the the y-intercept and x-intercept of the line.
4x - 4y= 36

Answer:

417

Step-by-step explanation:

372+45 = 417

Just add both gram values

Except falsifiability all of the following are standards used to determine the best explanation.

Given standards for scientific method,

Now,

It is important for science/mathematics to be falsifiable because for a theory to be accepted it must be able to be proven false. Otherwise, theories that are arrived through testing cannot be accepted. They are only accepted if their falsifiability can be disproved.

A scientific hypothesis, according to the doctrine of falsifiability, is credible only if it is inherently falsifiable. This means that the hypothesis must be capable of being tested and proven wrong.

Thus integrity , simplicity , power are standards used to determine the best explanation for scientific method.

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Answer:

\(\frac{1}{x^{\frac{5}{3}}}\)

Step-by-step explanation:

\(\frac{-5}{3}=-\frac{5}{3}\\x^{-\frac{5}{3}}\\x^{-\frac{5}{3}}=\frac{1}{x^{\frac{5}{3}}}\\\frac{1}{x^{\frac{5}{3}}}\)

➲ Hope this helps.

Answer:  the first one is yes and the second one is no

Step-by-step explanation: that’s the answer i took the test

The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) The difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

Expressions that are equivalent serve the same purpose regardless of appearance. When we employ the same variable value, two algebraic expressions that are equivalent have the same value.

To prove the given difference equation for Pₙ , let's break it down into two parts: the case where the nth throw results in a six and the case where it does not.

(a) Case: The nth throw results in a six

In this case, we need to consider the previous (n-1) throws to determine the probability of having an even number of sixes. Since the (n-1)th throw cannot be a six, the probability of having an even number of sixes in (n-1) throws is Pₙ₋₁.

Now, for the nth throw to be a six, we have a probability of 1/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw is a six, is (1/6) * (1 - Pₙ₋₁).

This is because (1 - Pₙ₋₁) represents the probability of having an odd number of sixes in (n-1) throws.

(b) Case: The nth throw does not result in a six

In this case, we still need to consider the previous (n-1) throws to determine the probability of having an even number of sixes.

Since the nth throw does not result in a six, the probability of having an even number of sixes in (n-1) throws remains the same, which is Pₙ₋₁.

Now, for the nth throw to not result in a six, we have a probability of 5/6. Therefore, the probability of having an even number of sixes in n throws, given that the nth throw does not result in a six, is (5/6) * Pₙ₋₁.

Combining the probabilities from both cases, we get:

Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

To solve the difference equation and obtain an explicit formula for Pn, we can rearrange the equation:

6Pₙ = 1 - Pₙ₋₁ + 5Pₙ₋₁

6Pₙ = 1 + 4Pₙ₋₁

Pₙ = (1 + 4Pₙ₋₁) / 6

Now, we can use this recursive formula to find explicit values for Pₙ. We start with P₀, which represents the probability of having an even number of sixes in 0 throws (which is 1):

P₀ = 1

Then, we can use the recursive formula to calculate P₁, P₂, P₃, and so on, until we reach the desired value of Pₙ.

Hence,

(a) Pₙ = (1/6) * (1 - Pₙ₋₁) + (5/6) * Pₙ₋₁

This is the difference equation that we needed to prove.

(b) the difference equation and obtain an explicit formula for Pn,

Pₙ = (1 + 4Pₙ₋₁) / 6

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Answer:

She sold $1800 worth.

Step-by-step explanation:

290-200=90

90 x 20 because 100÷5=20

90 x 20 = 1800

$1800

Answer:

8

Step-by-step explanation:

yes that's correctjahshsjsjsjsj

Answer: 4

Step-by-step explanation: because 2+2+4 and its not gonna equal anything else

Answer:

1.96%

Step-by-step explanation:

→ Minus the 2 numbers

10.2 - 10 = 0.2

→ Divide by the original 10.2

0.0196078

→ Times by 100

1.96%

1) The property P that we need to prove by induction is as P(p) = length p = length (rem R p) + numR p. 2) For the base case, we need to prove P([]) = length [] = length (rem R []) + numR []. 3) Inductive hypothesis is P(p) = length p = length (rem R p) + numR p. 4) For the step case, we need to prove P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p).

1) The property P that we need to prove by induction is as follows:

For all lists of directions p, the property P(p) is defined as:

P(p) = length p = length (rem R p) + numR p

If we can prove this property P by induction, it implies the goal of the exercise, which is to show that length p = length (rem R p) + numR p.

2) Base case goal:

For the base case, we need to prove the following goal:

For an empty list of directions p = [], the property P(p) holds:

P([]) = length [] = length (rem R []) + numR []

Proof:

P([]) simplifies to:

length [] = length (rem R []) + numR []

Using the definition of the length function and rem function, we have:

0 = length [] + numR []

Since the length of an empty list is 0, and there are no occurrences of R in an empty list, numR [] is also 0. Therefore, the base case goal holds.

3) Inductive hypothesis:

Assuming that the property P holds for a list p, we assume the following inductive hypothesis:

P(p) = length p = length (rem R p) + numR p

4) Step case goal:

For the step case, we need to prove the following goal:

Assuming P(p), we need to show that P(L:p) holds:

P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p)

Proof:

Using the definition of the length function and rem function, we have:

length (L:p) = length (L:(rem R p)) + numR (L:p)

Expanding the length and rem functions, we get:

1 + length p = 1 + length (rem R p) + numR (L:p)

Since L is not equal to R, numR (L:p) remains unchanged:

1 + length p = 1 + length (rem R p) + numR p

By canceling out the common terms on both sides, we get:

length p = length (rem R p) + numR p

This matches the property P(p), so the step case goal holds.

By proving the base case and the step case, we have proven the property P(p) by induction, which implies that length p = length (rem R p) + numR p for all lists of directions p.

Correct Question :

length []=0

length (x:xs)=1+ length xs

​−L1

−L2

Consider the following data types and functions: data Direction =L∣R numR : [Direction] -> Int

numR []=0

numR (L:p)= numR p

numR (R:p)=1+ numR p

Answer the following questions:

1. What precisely should we prove by induction? Specifically, state a property P, including possible quantifiers, so that proving this property by induction implies the (above) goal of this exercise.

2. State (including possible quantifiers) and prove the base case goal.

3. State (including possible quantifiers) the inc्acuctive hypothesis of the proof.

4. State (including possible quantifiers) and prove the step case goal.

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Answer:

The answer is y^4+2y^3+4y^2+5y+10

Step-by-step explanation:

I essentially just factored everything, as I'm certain this is right. :D

Answer:

4:1

Step-by-step explanation:

Answer:

4:1

Step-by-step explanation:

The demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.

For the given question;

R′(x) = 0.06x² − 0.05x + 138

R(x) = ∫R′(x)dx

R(x) =  ∫[0.06x² − 0.05x + 138] dx

R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C

R(x) = 0.02x³ - 0.025x² + 138x + C

If R(0) = 0, revenue is 0.

Put x = 0.

0.02x³ - 0.025x² + 138x + C = 0

c = 0

Thus,

R(x) = 0.02x³ - 0.025x² + 138x

Factorizing the function,

R(x) = 0.02x³ - 0.025x² + 138x

R(x) = x(0.02x² - 0.025x + 138)

R(x) = xp(x) . Thus,

p(x) = 0.02x² - 0.025x + 138

Therefore, the demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.

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Answer:

The number cube has 6 equally likely outcomes, so the probability of rolling a 1 or a 6 on any given roll is 2/6 = 1/3.

If Kenya rolls the number cube 90 times, we can use the expected value formula to find the expected number of times that a 1 or a 6 will land face up:

Expected number of 1's or 6's = (number of rolls) x (probability of rolling a 1 or a 6)

Expected number of 1's or 6's = 90 x (1/3)

Expected number of 1's or 6's = 30

Therefore, a reasonable prediction for the number of times that a 1 or a 6 will land face up is 30.

A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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Answer:

Step-by-step explanation: This is just rearranging the formula. Divide by m on both sides, then find the square root. The answer is E

Answer:

fx) = \(3x+4\)

Step-by-step explanation:

1. step:

solve the bracket

fx) = 3(\(x\) - 1) 2 + 5

\(fx) = 3x-1+2+5\)

2. step:

use the BEDMAS form.

fx) = \(3x-3+7\)

fx) = \(3x+4\)

Answer:

Are sure the question is correct please

because the answer is not in the objective answers which is - 7/2 yz.

Please check your out again carefully.

Answer:

Step-by-step explanation:

He made a mistake in step one turning the 7 into a -7

\(x^{2}\) - 3x + 7 = 0

Solving:

\(1x^{2}\) - 3x + 7 = 0  ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.

\(1x^{2}\) + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.

a = 1, b = -3, c = 7

x = - (-3) ±√\((-3)^{2}\) - 4 x 1 x 7

                 2 x 1

x = 3 ± √\((3)^{2}\) - 4 x 7

                2

x = 3 ± √9 - 4 x 7

                2

x = 3 ±√9 - 28

             2

x = 3 ± √-19

         2

The square root of a negative number does not exist in the set of real numbers.  

x = ∉ R

Answer:

b=95

Step-by-step explanation:

180=34+(b-30)+(b-14)

190=2b

b=95

34+(95-30)+(95-14) = 180

Answer:

b-30+b-14+34=180

2b+4-14=180

Step-by-step explanation:

2b=190 ,b=95

Answer: If the x2-9 is x^2-9, then this is the answer. If not and it's supposed to be 2x then the answer is x=2 or x=−7 or x=9/2

Step-by-step explanation:

3(x−2)(x2−9)(x+7)=0

3x4+15x3−69x2−135x+378=0

Step 1: Factor left side of equation.

3(x−2)(x+3)(x−3)(x+7)=0

Step 2: Set factors equal to 0.

x−2=0 or x+3=0 or x−3=0 or x+7=0

x=2 or x=−3 or x=3 or x=−7

The required answer is: Y(s) = (4πe^(-4s) + sy(0) + y′(0)) / (s² + 16π²)

To find the Laplace transform of the solution, we first need to solve the differential equation y′′+16π2y=4πδ(t−4) with the initial conditions. Using the Laplace transform, we have:

s^2 Y(s) - s y(0) - y'(0) + 16π^2 Y(s) = 4π e^(-4s)

Applying the initial conditions y(0) = y'(0) = 0, we have:

s^2 Y(s) + 16π^2 Y(s) = 4π e^(-4s)

Factoring out Y(s), we get:

Y(s) = (4π e^(-4s)) / (s^2 + 16π^2)

Now, we can use partial fraction decomposition to simplify the expression. We can write:

Y(s) = A/(s+4π) + B/(s-4π)

Solving for A and B, we get:

A = (4π e^(-16π)) / (8π) = (1/2) e^(-16π)

B = (-4π e^(16π)) / (-8π) = (1/2) e^(16π)

Therefore, the Laplace transform of the solution is:

Y(s) = (1/2) e^(-16π) / (s+4π) + (1/2) e^(16π) / (s-4π)
To find the Laplace transform of the solution for the given initial value problem:

y′′ + 16π²y = 4πδ(t - 4)

Step 1: Take the Laplace transform of both sides of the equation.

L{y′′ + 16π²y} = L{4πδ(t - 4)}

Step 2: Apply the linearity property of Laplace transform.

L{y′′} + 16π²L{y} = 4πL{δ(t - 4)}

Step 3: Use Laplace transform formulas for derivatives and delta function.

s²Y(s) - sy(0) - y′(0) + 16π²Y(s) = 4πe^(-4s)

Since the initial conditions are not provided, let's keep y(0) and y'(0) in the equation.

Step 4: Combine terms with Y(s).

Y(s)(s² + 16π²) = 4πe^(-4s) + sy(0) + y′(0)

Step 5: Solve for Y(s), the Laplace transform of the solution y(t).

Y(s) = (4πe^(-4s) + sy(0) + y′(0)) / (s² + 16π²)

This is the Laplace transform of the solution to the given initial value problem.

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The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

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The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)

What is parabola?

A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.

Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.

To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:

2 = a(0 + 1)(0 - 4)

2 = -4a

Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.

To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:

0 = a(-2 - h)² + k

0 = a(3 - h)² + k

Solving for h and k, we get:

h = 1/2

k = 4

Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:

y = a(z - 1/2)² + 4

We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:

4 = a(0 - 1/2)² + 4

4 = a(1/4)

a = 16

Therefore, the equation of the parabola in factored form is:

y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.

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Answer:

328

Step-by-step explanation:

Since 41 is a prime number, you would have to multiply 8 by 41 and get 328.

Answer:The LCM is 328

Step-by-step explanation:Find the multiples of 8 and 41.

Multiples of 8:  8, 16, 24, 32, 40, 48, 56,64,72,80,88,96,102,110,118, etc

(For this keep adding 8 into you find a same number which is 328)

Multiples of 41: 41, 82, 123, 164, 205, 246, 287,328

They both have the number 328.

Hope it helps.

Answer:-96

Step-by-step explanation:

Answer:

answer is x=14

Step-by-step explanation:

40% of 70 =x

30% of 80=280%

280/100%×100%

=28/2×100

=14

The polynomial that passes through the points is y = x⁴ + 2x³ + 3x² - x + 1

From the question, we have the following parameters that can be used in our computation:

(-3, 58), (-2, 15), (1, 6), (2, 43), (5, 946)

Given that there are 5 points

This means that the degree of the polynomial is 4

And it can be represented as

y = ax⁴ + bx³ + cx² + dx + e

Using the points, we have

a(-3)⁴ + b(-3)³ + c(-3)² + d(-3) + e = 58

a(-2)⁴ + b(-2)³ + c(-2)² + d(-2) + e = 15

a(1)⁴ + b(1)³ + c(1)² + d(1) + e = 6

a(2)⁴ + b(2)³ + c(2)² + d(2) + e = 43

a(5)⁴ + b(5)³ + c(5)² + d(5) + e = 946

So, we have

81a - 27b + 9c - 3d + e = 58

16a - 8b + 4c - 2d + e = 15

a + b + c + d + e = 6

16a + 8b + 4c + 2d + e = 43

625a + 125b + 25c + 5d + e = 946

When evaluated, we have

a = 1 and b = 2 and c = 3 and d = -1 and e = 1

So, we have

y = x⁴ + 2x³ + 3x² - x + 1

Hence, the polynomial is y = x⁴ + 2x³ + 3x² - x + 1

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