Español Tom opened a savings account with $600 and was paid simple interest at an annual rate of 2%. When Tom closed the account, he was paid $36 in interest. How long was the account open for, in years? If necessary, refer to the list of financial formulas. Dy years ?

The value of k for which the system has no solution is k = -16.

To determine the value of k for which the system has no solution, we can examine the system of equations:

x + y + 4z = 0 ...(1)

x + 2y - 2z = 0 ...(2)

4x + 9y + kz = 6 ...(3)

To have no solution, the system of equations must be inconsistent.

The coefficient matrix of the system is:

[tex]\left[\begin{array}{ccc}1&1&4\\1&2&-2\\4&9&k\end{array}\right][/tex]

The determinant of this matrix is given by:

|A| = (1 × 2 × k) + (1 × (-2) × 4) + (4 × 1 × 9) - (4 × 2 × 4) - (9 × (-2) × 1) - (k×1 ×1)

= 2k - 8 + 36 - 32 + 18 - k

= k + 16

For the system to have no solution, the determinant must be equal to zero:

k + 16 = 0

k = -16

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The largest possible constant r ∈ (0, 1) such that the function f : [0, r] → [0, r] defined by f(x) = x^2 is a strict contraction is r = 1/2.

To prove this, we need to show that there exists a positive constant k < 1 such that |f(x) - f(y)| ≤ k|x - y| for all x, y ∈ [0, r] with x ≠ y.

Let x, y ∈ [0, r] with x ≠ y. Then, we have:

|f(x) - f(y)| = |x^2 - y^2| = |(x - y)(x + y)| ≤ |x - y|(r + r) = 2r|x - y|

Therefore, if we choose k = 2r < 1, then |f(x) - f(y)| ≤ k|x - y| for all x, y ∈ [0, r] with x ≠ y.

Now, we need to find the largest possible constant r such that k < 1. We have k = 2r < 1, so r < 1/2.

Thus, the largest possible constant r ∈ (0, 1) such that f(x) = x^2 is a strict contraction is r = 1/2.

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All possible values of b1, b2, b3, b4, and b5 for which the given overdetermined linear system is inconsistent are given by,

b T ≠ [1 + 3c1 - 4c3, 1 - 2c1 + c2 + 4c3, 1, 1 - 4c1 + 4c3, 1 + 5c1 + c2 - 3c3]T

for any constants c1, c2, and c3.

An overdetermined linear system Ax = b must be inconsistent for some vector b.

The given system is, x1 - 3x2 = b1 x1 - 2x2 = b2 x1 + x2 = b3 x1 - 4x2 = b4 x1 + 5x2 = b5

It can be written in matrix form as

Ax = b

where,

A = 1 -3 0 0 0 1 -2 1 0 -4 1 5

and,

x = x1 x2 and

b = b1 b2 b3 b4 b5

Since A has more rows than columns, so it's an overdetermined system.

In an overdetermined system, the matrix A does not have an inverse, thus we can't solve Ax = b exactly.

So, we have to use least-squares to get an approximate solution. However, the least-squares solution doesn't exist if and only if b is outside the column space of A.

i.e. there is no solution to the system Ax = b, so it's inconsistent.

The column space of A is the set of all linear combinations of the columns of A. Hence, we need to find the column space of A.

First, let's find the reduced row echelon form of A using Gaussian elimination.

Row 1 ÷ 11 -3 0 0 0 1 -2 1 0 -4 1 5

Row 2 -R1 + R2 0 1 0 0 0 1 -1 1 4 0 2

Row 3 -R1 + R3 0 4 1 0 0 0 3 1 -4 0 4

Row 4 -R1 + R4 0 -1 0 1 0 0 -1 5 4 0 5

Row 5 -R1 + R5 0 8 1 0 1 0 3 6 -3 0 10

Row 4 + 4R2 0 0 0 1 0 0 3 1 0 0 13

The RREF is given by, 1 0 0 0 -9/11 -3/11 5/11 -1/11 -4/11 0 0 19/11 0 1 0 0 3/4 1/4 -1/4 0 -3/4 0 2/4 0 0 0 0 0 0 0 0 0

The columns corresponding to the pivot columns form a basis for the column space of A, which is a subspace of R5. Hence, we can express the basis as, B = {b1, b2, b3, b4}, where

b1 = (1, 1, 1, 1, 1)b2 = (-3, -2, 1, -4, 5)

b3 = (0, 1, 0, 0, 1)

b4 = (-4, 4, -4, 4, -3)

Thus, the column space of A is spanned by these 4 vectors.

If b belongs to the column space of A, then the system Ax = b will be consistent, otherwise, it'll be inconsistent.

i.e. there is no solution to the system Ax = b.

The coefficients of b in terms of the basis B are given by,

B T b = [1, -3, 0, -4; 1, -2, 1, 4; 1, 1, 0, -4; 1, -4, 0, 4; 1, 5, 1, -3]b T

Thus, the system Ax = b is inconsistent when b is not in the column space of A.

i.e. when,

b T ≠ c1b1 + c2b2 + c3b3 + c4b4

for any constants c1, c2, c3, and c4.

Substituting the values of b1, b2, b3, and b4 in the above equation, we get,

1b1 + 0b2 + 0b3 + 0b4 ≤ 1 1b1 - 2b2 + 0b3 + 4b4 ≤ 1 1b1 + 1b2 + 0b3 + 0b4 ≤ 1 1b1 - 4b2 + 0b3 + 4b4 ≤ 1 1b1 + 5b2 + 1b3 - 3b4 ≤ 1

So, the values of b1, b2, b3, b4, and b5 for which the given system is inconsistent are given by,

b T ≠ [1, 1, 1, 1, 1]T + c1[-3, -2, 1, -4, 5]T + c2[0, 1, 0, 0, 1]T + c3[-4, 4, -4, 4, -3]T

for any constants c1, c2, and c3.

Hence, all possible values of b1, b2, b3, b4, and b5 for which the given overdetermined linear system is inconsistent are given by,

b T ≠ [1 + 3c1 - 4c3, 1 - 2c1 + c2 + 4c3, 1, 1 - 4c1 + 4c3, 1 + 5c1 + c2 - 3c3]T

for any constants c1, c2, and c3.

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Answer:

7/9    

Step-by-step explanation:

7/9

Answer:

7/9

Step-by-step explanation:

Brainliest maaaybe? :)

Answer:

[tex]2l + 2w[/tex]

Step-by-step explanation:

We know that a rectangle has four sides. And each pair of opposite sides are equal. We can set the length to [tex]l[/tex] and the width to [tex]w[/tex]. Since we know that both variables have a side that is equal to it, we know that the sum of the sides is[tex]l+l+w+w = 2l + 2w[/tex].

The largest positive step size for which Heun's method is stable in the given initial value problem with x'(t) = -λx(t), x(0) = xo, where λ = 17, is h ≤ 0.034.

Heun's method, also known as the improved Euler method or the explicit trapezoidal method, is an explicit numerical method used for solving ordinary differential equations. The stability of Heun's method depends on the step size chosen for the integration.

The stability criterion for Heun's method is that the step size, denoted as h, should satisfy the condition h ≤ 2 / (|λ|), where λ is the coefficient of the equation being solved. In this case, λ = 17.

Substituting the value of λ into the stability criterion, we have h ≤ 2 / (|17|) = 2 / 17 ≈ 0.1176. Therefore, the largest positive step size for stability is h ≤ 0.1176.

However, to find the largest positive step size, we need to consider the accuracy of the numerical solution as well. A smaller step size typically provides a more accurate solution. Hence, we choose the largest step size that satisfies both the stability criterion and the desired level of accuracy.

In this case, the largest positive step size for which Heun's method is stable and provides a reasonable level of accuracy can be chosen as h ≤ 0.034.

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Answer:

x = 3

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{\sqrt{3} }[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by [tex]\sqrt{3}[/tex] )

x = 3

The distribution of IQ scores is normal, with a mean of μ = 100 and a standard deviation of σ = 10.

Percentage of probability that a randomly selected person will have an IQ less than 90.Solution:We have to find the probability that a randomly selected person will have an IQ less than 90.Using the Z-score formula:Z = (X - μ) / σWhereX = 90μ = 100σ = 10Putting the values into the equation we have:Z = (90 - 100) / 10Z = -1

Using the standard normal distribution table we find that the area to the left of the z-score -1 is 0.1587.That means:P(Z < -1) = 0.1587To find the percentage, we convert it to a percentage by multiplying by 100.0.1587 × 100 = 15.87%Therefore, the probability that a randomly selected person will have an IQ less than 90 is 15.87%.

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Answer:

If both sides of the triangle are exactly equal (which can be assumed they are because of the right angle), then that means EF = FG

Given that information, we can determine that EF is 6.1.

Now, all you have to do is add 6.1 + 6.1 to get 12.2.

EG = 12.2.

Answer: quadratic

Step-by-step explanation:

I guess if you can search up a picture of each function, you will be able to understand it. A linear graph is linear (as its name suggests), as a result, it never "goes back" to the value that has showed up. For example, the linear function y=3x+2. If you plug in a random value of y (let's say 10), then solve for x, you will only get 1 value of x. The data table that you have indicates that the y value of 0 has appeared twice. Thus, the function cannot be linear. The same thing applies to an exponential function. A quadratic function, however, can have to x values that result in the same y value. For example, the function y = [tex]x^2[/tex]-1. When you set y equal to zero....

0 =  [tex]x^2[/tex]-1

0 = (x+1)(x-1)

x = -1 or 1.

Hope this helps :)

Answer:

71

Step-by-step explanation:

The critical value for the 40% level of significance is 1.96. Therefore, we can reject the Null hypothesis at the 40% level of significance.

In hypothesis testing, the critical value is used to determine the threshold for rejecting or not rejecting the Null hypothesis. The critical value depends on the desired level of significance and the distribution being used. In this scenario, we are conducting a one-sample t-test with a known population standard deviation.

To determine the critical value, we need to consider the level of significance. In this case, the level of significance is 40%, which corresponds to an alpha value of 0.40. Since the test is a one-tailed test (we want to test whether the mean waiting time is significantly more than 3 minutes), we divide the alpha value by 2, resulting in 0.20.

Using a t-distribution table or a statistical calculator, we find that the critical value for an alpha of 0.20 with degrees of freedom equal to the sample size minus 1 (99) is approximately 1.96.

Therefore, if the test statistic falls beyond the critical value of 1.96, we can reject the Null hypothesis at the 40% level of significance.

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Answer:

7uwwjwjwjwjai9qiwjwwiwjb2wuw8ejvewusikwvww

The answer to the questions is given in parts.

The standard normal distribution is a normal distribution of data that has been standardized so that it has a mean of 0 and a standard deviation of 1.

The area under the standard normal curve that lies to the right of various values of Z can be calculated using a table of standard normal probabilities, or by using a calculator or computer program. Here, we are given four values of Z and we need to determine the area under the standard normal curve that lies to the right of each value. We can use a standard normal table or a calculator to find these areas.

(a) The area to the right of Z = 0.24 is 0.4052 (rounded to four decimal places).

(b) The area to the right of Z=0.02 is 0.4901 (rounded to four decimal places).

(c) The area to the right of Z=-0.49 is 0.6879 (rounded to four decimal places).

(d) The area to the right of Z=1.89 is 0.0294 (rounded to four decimal places).

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(a) To find the number of committees of six that contain three men and three women, we can use the concept of combinations.

The number of ways to choose three men out of five is given by the combination formula:

[tex]\({{5}\choose{3}} = \frac{5!}{3!(5-3)!} = 10\)[/tex]

Similarly, the number of ways to choose three women out of seven is given by:

[tex]\({{7}\choose{3}} = \frac{7!}{3!(7-3)!} = 35\)[/tex]

Since the choices for men and women are independent, we can multiply these two values to get the total number of committees with three men and three women:

[tex]\(10 \times 35 = 350\)[/tex]

(b) To find the number of committees of six that contain at least two men, we can consider two cases:

1. Committees with exactly two men:

The number of ways to choose two men out of five is [tex]\({{5}\choose{2}} = 10\)[/tex].

The number of ways to choose four women out of seven is [tex]\({{7}\choose{4}} = 35\)[/tex].

So, the number of committees with exactly two men is [tex]\(10 \times 35 = 350\)[/tex].

2. Committees with three men or more:

We have already calculated the number of committees with exactly three men and three women in part (a), which is 350.

To get the total number of committees with at least two men, we sum the results from the two cases: .

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Answer:

793.6

Step-by-step explanation:

793.545=793.55=793.6

Answer:

y+48=90

y= 90-48

y= 42

Step-by-step explanation:

ok

by using the property

sum of two opposite interior angles of triangle is equal to exterior angle

Answer:

Step-by-step explanation:

12 boxes of hay

Answer:48 bunches of hay

Step-by-step explanation:4 hunches for $9, therefore 108/9=12 and 4x12=48 bunches of hay

The equation of the quadratic graph is: [tex]y = \frac{1}{8}(x - 3)^2 + 4[/tex]

In a quadratic graph, the focus and the directrix determine the shape and position of the parabola. The focus (3,4) represents the vertex of the parabola, and the directrix y=8 is a horizontal line.

To evaluate the equation of the quadratic graph, we use the vertex form of a quadratic equation, which is [tex]y = a(x - h)^2 + k[/tex], where (h,k) represents the vertex.

The focus coordinates indicate that the vertex is at (3,4). Thus, h = 3 and k = 4.

Since the directrix is a horizontal line, its equation takes the form y = c, where c is a constant. In this case, the directrix equation is y=8, meaning the distance from the vertex to the directrix is 4 units (8 - 4 = 4).

Using the formula [tex]a =\frac{1}{4p}[/tex], where p is the distance from the vertex to the focus (or directrix), we find that [tex]p = \frac{4}{2} = 2[/tex].

Substituting the values into the vertex form equation, we get:

[tex]y = a(x - 3)^2 + 4[/tex]

To evaluate the value of a, we use the formula a = 1 / (4p), where p = 2. Substituting this value, we have:

[tex]a = \frac{1}{4*2} = \frac{1}{8}[/tex]

Therefore, the equation of the quadratic graph is:

[tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex]

Hence, the equation of the quadratic graph with a focus of (3,4) and a directrix of y=8 is [tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex].

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Answer:

Apartment 1 is his best option

Answer: Apartment 1

Step-by-step explanation:

To find the concentration of H+ or H3O+ ions ([H+] or [H3O+]) given a pH value , you can use the formula:

[H+] = 10^(-pH)

Let's calculate the values for two different pH values: pH = 4.0 and pH = 4.8.

For pH = 4.0:

[H+] = 10^(-4.0)

[H+] ≈ 1 × 10^(-4)

Therefore, the concentration of H+ ions ([H+]) at pH 4.0 is approximately 1 × 10^(-4) or 0.0001.

For pH = 4.8:

[H+] = 10^(-4.8)

[H+] ≈ 1.6 × 10^(-5)

Therefore, the concentration of H+ ions ([H+]) at pH 4.8 is approximately 1.6 × 10^(-5) or 0.000016.

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Answer:

# 1 the missing side is 11,  20+12+12= 44

Step-by-step explanation:

Answer:

1. 5

2. 4

3. 2

4. 10

Step-by-step explanation:

i did this already. so i knew the answers

Answer:

√3

Step-by-step explanation:

                               opposite side         (√3)/2

tan 60 degrees = ------------------------- = ------------ = √3

                                  adjacent side          1/2

The predicted number of visitors when the temperature is 78° is 888.6 visitors.

The least-squares regression line of the number of visitors, y, at a national park and the temperature, x, is modeled by the equation,

D = 85.2 + 10.3x

We need to find the predicted number of visitors when the temperature is 78°.

Substitute x = 78 in the given equation of regression line:

D = 85.2 + 10.3x= 85.2 + 10.3(78)= 85.2 + 803.4

D = 888.6

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Given that the least-squares regression line of the number of visitors, y, at a national park and the temperature, x, is modeled by the equation D=85.2+10.3x.

We need to find the predicted number of visitors when the temperature is 78°.

Option D (fourth) is correct.

To find out this we just need to substitute the given value of x = 78 into the equation of the regression line. So, we get the predicted number of visitors when the temperature is 78° as below:

[tex]D = 85.2 + 10.3 \times 78[/tex]

[tex]D = 85.2 + 803.4[/tex]

D = 888.6

Therefore, the predicted number of visitors when the temperature is 78° is 888.6 visitors.

Hence, option D is correct.

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Answer:

$50(1.05) = $52.50

Jody had to pay $52.50 to Tong for the month.

The Z-transform of the given sequence y[n] = 3u[n] - 1.5 8[n-1] is Y[z] = (3z)/(z-1) - (1.5z)/(z-1). To simplify y[n], we need to find the inverse Z-transform of Y[z].

The Z-transform is a useful tool for analyzing discrete-time signals and systems. In this case, we are given the sequence y[n] = 3u[n] - 1.5 8[n-1], where u[n] is the unit step function and 8[n-1] represents the delayed unit impulse function.

To find the Z-transform of y[n], we can use the linearity property of the Z-transform. Since the Z-transform of u[n] is 1/(1-z^(-1)), and the Z-transform of 8[n-1] is z^(-1), we can substitute these values into the expression for y[n] to obtain:

Y[z] = 3(1/(1-z^(-1))) - 1.5(z^(-1))/(1-z^(-1))

To simplify Y[z], we need to combine the terms with a common denominator. By finding a common denominator of (1-z^(-1)), we can rewrite Y[z] as:

Y[z] = (3z - 1.5)/(z-1)

Now, to obtain y[n], we need to find the inverse Z-transform of Y[z]. The inverse Z-transform can be computed using techniques such as partial fraction expansion or by referring to Z-transform tables.

The simplified expression for y[n] would be:

y[n] = 3δ[n] - 1.5δ[n-1]

where δ[n] represents the discrete-time unit impulse function. The graph of y[n] would have an impulse of magnitude 3 at n = 0 and an impulse of magnitude -1.5 at n = 1.

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