leon drew two fraction game cards that were between 1 6 and 1 2 . the sum of the two cards chosen lies within what range

Answer:

36

Step-by-step explanation:

You multiply354 and 16 then divide

The left-hand side of the equations equals zero since x₁'(t) - x₂'(t) = 0 and y₁'(t) - y₂'(t) = 0. Therefore, the solution (x(t),

Given two solutions of a linear nonhomogeneous system, (x₁(t), y₁(t)) and (x₂(t), y₂(t)),  the solution is indeed a solution of the corresponding homogeneous system.

Let's consider the linear nonhomogeneous system:

x' = p₁₁(t)x + p₁₂(t)y + g₁(t),

y' = p₂₁(t)x + p₂₂(t)y + g₂(t).

We have two solutions of this system: (x₁(t), y₁(t)) and (x₂(t), y₂(t)).

Now, we need to show that the solution (x(t), y(t)) = (x₁(t) - x₂(t), y₁(t) - y₂(t)) satisfies the corresponding homogeneous system:

x' = p₁₁(t)x + p₁₂(t)y,

y' = p₂₁(t)x + p₂₂(t)y.

Substituting the values of x(t) and y(t) into the homogeneous system, we have:

(x₁(t) - x₂(t))' = p₁₁(t)(x₁(t) - x₂(t)) + p₁₂(t)(y₁(t) - y₂(t)),

(y₁(t) - y₂(t))' = p₂₁(t)(x₁(t) - x₂(t)) + p₂₂(t)(y₁(t) - y₂(t)).

Expanding and simplifying these equations, we get:

x₁'(t) - x₂'(t) = p₁₁(t)x₁(t) - p₁₁(t)x₂(t) + p₁₂(t)y₁(t) - p₁₂(t)y₂(t),

y₁'(t) - y₂'(t) = p₂₁(t)x₁(t) - p₂₁(t)x₂(t) + p₂₂(t)y₁(t) - p₂₂(t)y₂(t).

Since (x₁(t), y₁(t)) and (x₂(t), y₂(t)) are solutions of the nonhomogeneous system, we know that:

x₁'(t) = p₁₁(t)x₁(t) + p₁₂(t)y₁(t) + g₁(t),

x₂'(t) = p₁₁(t)x₂(t) + p₁₂(t)y₂(t) + g₁(t),

y₁'(t) = p₂₁(t)x₁(t) + p₂₂(t)y₁(t) + g₂(t),

y₂'(t) = p₂₁(t)x₂(t) + p₂₂(t)y₂(t) + g₂(t).

Substituting these equations into the previous ones, we have:

x₁'(t) - x₂'(t) = p₁₁(t)x₁(t) - p₁₁(t)x₂(t) + p₁₂(t)y₁(t) - p₁₂(t)y₂(t),

y₁'(t) - y₂'(t) = p₂₁(t)x₁(t) - p₂₁(t)x₂(t) + p₂₂(t)y₁(t) - p₂₂(t)y₂(t).

The left-hand side of the equations equals zero since x₁'(t) - x₂'(t) = 0 and y₁'(t) - y₂'(t) = 0. Therefore, the solution (x(t),

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\({ \green{ \tt{the \: origin}}}\)

The name given to the ordered pair (0,0) is the origin.

Answer:

a) The orgin

Step-by-step explanation:

Now we have to,

→ find the name of the ordered pair.

The coordinates are,

→ (0,0)

{It is the origin, where both axis collides}

Hence, the option (a) is correct.

Answer:

72000

Step-by-step explanation:

Multiply 120,000 by 0.6 OR multiply 120,000 by 0.4 and subtract 120,000 by the product.

Both equal 72,000

Hope this helps my fellow mike winsowski memer

-Scorpio

The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

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Answer:

f(x) = −6(x+ 1)(x +5)

Step-by-step explanation:

x-intercepts at (−1, 0) and (−5, 0)

so the roots are -1 and -5 (where the graph intersects the x-axis)

this will give us that f(x) = (x- root1)(x-root2) = (x- -1)(x- -5) = (x+1)(x+5)

y-intercept at (0, −30) is telling us that when x= 0 the y = -30

y = a ( x+1)(x+5) , in general

y = a(0+1)(0+5), is the equation if x=0

-30 = a·1·5, we need y= -30 when x= 0

-30 = 5a , divide both sides of the equation by 5

-6 = a

The correct choice is :

f(x) = −6(x+ 1)(x +5)

f(x) = −6(x − 1)(x − 5)

f(x) = −5(x +1)(x +5)

f(x) = −5(x − 1)(x − 5).

The conditions under which the Farmer Jack should build his fence is; B. The length of the fence must be greater than or equal to 15 ft. or less than or equal to 7 ft.

We are told that the length of the entire fence is 44 ft long. Thus it means that the perimeter is 44 ft long.

Now, since the fence is a rectangular shape, it means that;

a + b = 44/2

a + b = 22  ----(1)

Now, we are told that the area has to be greater than 105 sq. ft. Thus;

ab > 105    ------(2)

From eq 2; a > 105/b

Thus; (105/b) + b = 22

Multiply through by b to get;

105 + b² = 22b

b² - 22b + 105 = 0

Solving using quadratic equation calculator gives;

b  ≤ 7 or b ≥ 15

Thus, we can conclude that the length of the fence must be greater than or equal to 15 ft. or less than or equal to 7 ft.

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The probability that the next person will pay with a debit card is:

P =  0.63

We want to find he probability that the next customer will pay with a debit card.

That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.

We know that:

15 paid in cash.

50 paid with debit card.

15 paid with credit card.

For a total of 15 + 50 + 15 = 80

Then the probability is:

P = 50/80 = 0.63

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Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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To solve for x, we need to use the properties of angles in a circle. We know that the measure of the central angle JIH is 74 degrees. We are also given that the measure of arc JH is (3x-39) degrees.

The angle ∠JIH is given as 74°, and the measure of arc JH is (3x-39)°. In a circle, the measure of an angle formed by an inscribed arc is half the measure of the arc. Therefore, we have: 74° = 1/2 * (3x-39)°. To solve for x, we can simplify the equation: 148 = 3x - 39, Adding 39 to both sides, we get: 187 = 3x . Dividing both sides by 3, we find: x = 62.3. Therefore, the value of x is approximately 62.3 when the measure of arc JH is (3x-39)°.

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Answer:

vhbsdvidbvdvuib math

Step-by-step explanation:

zdztj

Umm i think you forgot to add the question.

The minimum number of choices in a scoring procedure that the student must eliminate before it is advantageous to guess among the rest is 4. Option E is the correct option.

Suppose that there are n choices remaining for a particular question.

The probability of answering this question correctly is 1/n if the student guesses and the probability of leaving the question unanswered is (n-1)/n.

The expected score for guessing is therefore (7/n) × (1/n) + (2/n) × ((n-1)/n) = (7 + 2(n-1))/n² = (9 - 2/n)/n.

The expected score for leaving the question unanswered is 2/n.

The student should guess if and only if the expected score for guessing is greater than the expected score for leaving the question unanswered.

That is, we must have (9 - 2/n)/n > 2/n, or equivalently 9 > 2n, or n < 4.5.

Thus, if the number of choices remaining is 4 or more, the student should not guess; if the number of choices remaining is 3 or fewer, the student should guess.

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The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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Answer:

The trapezoid(??) is worth 15. The moon(??) is worth 11.

Step-by-step explanation: 15 = 11+2+2

Answer:

126 mm / 3 = 42 mm

The length of each side of this equilateral triangle is 42 mm.

The future value of $500 in 24 years, assuming an interest rate of 6 percent compounded semiannually, is $1,962.82.

To calculate the future value, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

Where:

FV = Future value

PV = Present value (initial investment)

r = Interest rate

n = Number of compounding periods per year

t = Number of years

In this case, the present value (PV) is $500, the interest rate (r) is 6 percent (or 0.06), the number of compounding periods per year (n) is 2 (semiannually), and the number of years (t) is 24.

Plugging these values into the formula, we get:

FV = $500 * (1 + 0.06/2)^(2*24)

     = $500 * (1 + 0.03)^(48)

     = $500 * (1.03)^(48)

     ≈ $1,962.82

Therefore, the future value of $500 after 24 years, compounded semiannually at an interest rate of 6 percent, is approximately $1,962.82.

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The number of times that the actual flag is wider than Reagan's model would be = 3 times.

Rectangle: What is it?

A rectangle is a particular kind of quadrilateral with opposite sides that are parallel and equal to one another and four right angles, according to the definition.

The rectangular flag measures 39 inches in length in actuality.

Reagan's model measured 13 inches in length.

The formula: = Length of actual flag / Length of model = 39/13 = 3 will tell you how many times broader the model is than the real flag.

The real flag is three times wider than Ronald Reagan's model, for a total of four times.

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We used the formula for the standard deviation of the sample mean. The standard deviation of the sample mean is the standard deviation of the population divided by the square root of the sample size.

The population of values has a normal distribution with mean μ=68.4 and standard deviation σ=72.6. You intend to draw a random sample of size n=210. We are supposed to find the mean and standard deviation of the distribution of sample means.Mean of the distribution of sample means is:μx = μ = 68.4Standard deviation of the distribution of sample means is:σx = σ / sqrt(n)= 72.6 / sqrt(210)= 5.3 (approx)

Therefore, the mean of the distribution of sample means is 68.4, and the standard deviation of the distribution of sample means is 5.3 (approx).Note: Here, we used the formula for the standard deviation of the sample mean. The standard deviation of the sample mean is the standard deviation of the population divided by the square root of the sample size.

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Answer:

-18

Step-by-step explanation:

If you're looking for the y-intercept for this equation this means that x = 0.

So substitute x as 0 in the equation and you'll get the following.

y + 3 = 5 (0 - 3)

y + 3 = -15

y = -18

In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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There would be 56 exchange relationships if eight bakeries each tried to sell their products directly to seven supermarkets.

To calculate the total number of exchange relationships that would be established, we can multiply the number of bakeries by the number of supermarkets.

In this case, there are eight bakeries and seven supermarkets.

Total number of exchange relationships = Number of bakeries × Number of supermarkets

Total number of exchange relationships = 8 × 7 = 56

Therefore, there would be 56 exchange relationships established between the bakeries and the supermarkets.

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y=-1/3x+3 is equation of the line that passes through the given points (9,0) and (0,3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+c, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

x₁=9, y₁=0,x₂=0,y₂=3

Apply in slope formula

m=3-0/0-9

m=-1/3

So slope of line passing through (9,0) and (0,3) is -1/3.

y=-1/3x+c

Put (9,0) in x and y place

0=-1/3(9)+c

0=-3+c

c=3

y=-1/3x+3

Hence y=-1/3x+3 is equation of the line that passes through the given points (9,0) and (0,3)

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Using the Factor Theorem, the length of one side of the garden is:

(3x - 4) feet.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

The area of a rectangle is given by the multiplication of it's dimensions. In this problem, it is given by:

A = 9x² - 24x + 16.

The root of 9x² - 24x + 16 = 0 is x = 4/3 with multiplicity 2, hence:

\(x_1 = x_2 = \frac{4}{3}\)

Hence the area can be written as:

\(A = 9\left(x - \frac{4}{3}\right) \times \left(x - \frac{4}{3}\right)\)

Then, to find one side:

9(x - 4/3) = 9x - 12 = 3(3x - 4).

Hence (3x - 4) feet is one side.

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Answer:

the number is 2, 2,7, 11, 0

Step-by-step explanation:

this is an indefinitie solution.

The quadratic equation 2x² + 7x + 11 = 0 has imaginary roots as the graph of this equation does not intersect the x-axis.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as it's degree is two.

To know the type of solution of a quadratic equation we'll observe what is

the discriminant which is b² - 4ac.

2x² + 7x + 11 = 0 is ax² + bx + c = 0.

b² - 4ac.

= 49 - 4.2.11

= 49 - 88.

= - 39.

Now, - 39 < 0 so the quadratic equation has imaginary roots as the graph of this equation does not intersect the x-axis.

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Answer:

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

x in (-oo:+oo)

(3/4)*x+2 = 5 // - 5

(3/4)*x-5+2 = 0

3/4*x-3 = 0 // + 3

3/4*x = 3 // : 3/4

x = 3/3/4

x = 4

The sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals is not binomial. This is because the binomial distribution has specific requirements that must be met, including a fixed number of trials, independent outcomes, and a constant probability of success. the probability of observing a sample proportion of 0.75 or higher is approximately 0.16.        

Assuming that the sample size is sufficiently large and the proportion of people who respond "yes" in the population is not too close to 0 or 1, the sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals can be approximated by a normal distribution using the Central Limit Theorem. This means that the distribution of the sample proportion will be approximately normal with a mean equal to the population proportion and a standard deviation equal to the square root of [p(1-p)/n], where p is the population proportion and n is the sample size.

For example, let's say that we know that 60% of the population believes that gun laws should be more stringent. If we take samples of 4 individuals and calculate the proportion of people who respond "yes" in each sample, the sampling distribution of these proportions can be approximated by a normal distribution with a mean of 0.6 and a standard deviation of sqrt[(0.6)(0.4)/4] = 0.15.

Using this normal approximation, we can calculate probabilities and confidence intervals for the sample proportion. For example, if we take a sample of 4 individuals and find that 3 of them respond "yes," the sample proportion is 0.75. We can calculate the probability of observing a sample proportion of 0.75 or higher by standardizing the sample proportion using the mean and standard deviation of the sampling distribution:

z = (0.75 - 0.6)/0.15 = 1

Using a standard normal distribution table or calculator, we can find that the probability of observing a standard normal random variable greater than or equal to 1 is approximately 0.16. This means that the probability of observing a sample proportion of 0.75 or higher is approximately 0.16.

In summary, while the sampling distribution of the proportion of people who respond "yes" in samples of 4 individuals is not binomial, it can be approximated by a normal distribution using the Central Limit Theorem under certain conditions. This approximation allows us to calculate probabilities and confidence intervals for the sample proportion, even when the exact distribution is unknown.

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