There are two cheesecakes in the fridge. The first cheesecake was cut into 10 slices and 4 slices were sold. How much cake is left in the fridge?

Since the value of L is a finite positive number (2), we can conclude that the Root Test is inconclusive for this series.

To determine the convergence or divergence of the series using the Root Test, we compute the limit L = lim √(|an|) as n approaches infinity. For the given series Σ(4n - 1)/(2n + 2)^2, we evaluate L as follows:

L = lim √(|(4n - 1)/(2n + 2)^2|)

Taking the absolute value, we have:

L = lim √((4n - 1)/(2n + 2)^2)

Next, we simplify the expression under the square root:

L = lim √(4n - 1)/√((2n + 2)^2)

L = lim √(4n - 1)/(2n + 2)

Since both the numerator and denominator approach infinity as n increases, we apply the limit of their ratio:

L = lim (4n - 1)/(2n + 2)

By dividing the numerator and denominator by n, we get:

L = lim (4 - 1/n)/(2 + 2/n)

As n approaches infinity, both terms in the numerator and denominator become constants. Therefore, we have:

L = (4)/(2) = 2

Since the value of L is a finite positive number (2), we can conclude that the Root Test is inconclusive for this series. However, this does not provide information about the convergence or divergence of the series. Additional tests are needed to determine the nature of convergence or divergence.

To learn more about convergence click here, brainly.com/question/29258536

#SPJ11

Answer: 5x + 15 = y

Step-by-step explanation:

mx+b = y

find rise over run

(y_2-y_1)/(x_2-x_1) = m

(-5-5)/(-4+2)

simplify

-10/-2

10/2

5 = m

plug in a point and find b

5(-2) + b = 5

-10 + b = 5

b = 15

5x + 15 = y

Answer:

So what are you asking me to do

Answer:

A.

Step-by-step explanation:

Solution:

Given:

The graph of the function is given below;

The end behavior:

From the graph, the end behavior of the graph shows that as x tends to negative infinity, the function f(x) tends to negative infinity. Also, as x tends to positive infinity, the function f(x) tends to positive infinity.

The turning points:

The maximum number of turning points of a polynomial function is always one less than the degree of the function. A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising).

The graph has a maximum and minimum point. Increasing and decreasing, and decreasing and increasing.

Hence, the graph of the function has two turning points.

The number of zeros:

The zeros of a function also referred to as roots or x-intercepts, occur at x-values where the value of the function f(x) = 0.

Hence, the zeros exist at;

Therefore, the function has three zeros.

Answer:

\(\frac{11}{2}\)

Step-by-step explanation:

To obtain the inverse of f(x)

let y = f(x) and rearrange making x the subject, that is

y = 2x - 1 ( add 1 to both sides )

y + 1 = 2x ( divide both sides by 2 )

\(\frac{y+1}{2}\) = x

Change y back into terms of x with x = \(f^{-1}\)(x) , thus

\(f^{-1}\)(x) = \(\frac{x+1}{2}\)

Evaluate g(3) and substitute the value obtained into \(f^{-1}\)(x)

g(3) = 3² + 1 = 9 + 1 = 10, then

\(f^{-1}\) (10) = \(\frac{10+1}{2}\) = \(\frac{11}{2}\)

Answer:

x = 50

Step-by-step explanation:

I hope this helps!

Answer:

0.02

Step-by-step explanation:

Step-by-step explanation:

the multiplication result is found by row×column multiplications.

1st row × 1st column = a

2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a

1st row × 2nd column = b

2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b

1st row × 3rd column = c

2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c

Answer:

(2, 3 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = - 5 → (1)

5x + 4y = 22 → (2) [ rearranged equation ]

Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y

8x - 12y = - 20 → (3)

15x + 12y = 66 → (4)

Add (3) and (4) term by term to eliminate y, that is

23x = 46 ( divide both sides by 23 )

x = 2

Substitute x = 2 in either of the 2 equations and evaluate for y

Substituting into (2)

5)2) + 4y = 22

10 + 4y = 22 ( subtract 10 from both sides )

4y = 12 ( divide both sides by 4 )

y = 3

Solution is (2, 3 )

The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

Know more about Isothermal Expansion here,

https://brainly.com/question/30329152

#SPJ11

Answer:

a) 67

b) 122

c) que angulo

d) 40

Step-by-step explanation:

The value of partial derivative ∂w/∂v when u=0, v=0 is 0.

To find ∂w/∂v when u=0, v=0, we can use the partial derivative formula:

∂w/∂v = (∂w/∂x) * (∂x/∂v) + (∂w/∂y) * (∂y/∂v)

First, let's find the partial derivatives of w with respect to x and y:

∂w/∂x = 2xy

∂w/∂y = x^2

Next, let's find the partial derivatives of x and y with respect to v:

∂x/∂v = 5(-1) = -5

∂y/∂v = 4u = 0 (since u=0)

Now we can plug in the values we have:

∂w/∂v = (2xy × ∂x/∂v) + (x^2 × ∂y/∂v)

At u=0, v=0, we have x=5u-5v=0 and y=4uv-6=0. Plugging in these values gives:

∂w/∂v = (2(0)(0)× -5) + ((0)^2×0) = 0

Click the below link, to learn more about the partial derivative formula:

https://brainly.com/question/30560681

#SPJ11

Answer: C. \(B=\left[\begin{array}{ccc}1\\3\\-5\end{array}\right]\)

Step-by-step explanation: I got this right on Edmentum.

Several operations such as addition, subtraction, multiplication, etc. can be performed on matrices. The value of matrix B is:

\(B =\left[\begin{array}{c}1&3&-5\end{array}\right]\)

Given that:

\(A =\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right]\)

\(AB =\left[\begin{array}{c}24&-46&-2\end{array}\right]\)

Let matrix B be:

\(B =\left[\begin{array}{c}a&b&c\end{array}\right]\)

The product of A and B is as follows:

\(\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right] \times\left[\begin{array}{c}a&b&c\end{array}\right]\)

Multiply the rows of A to the column of B. So, we have:

\(AB =\left[\begin{array}{ccc}2a+4b-2c\\4a-5b+7c\\2a+7b+5c\end{array}\right]\)

This means that:

\(\left[\begin{array}{ccc}2a+4b-2c\\4a-5b+7c\\2a+7b+5c\end{array}\right] = \left[\begin{array}{c}24&-46&-2\end{array}\right]\)

By comparison, we have:

\(2a + 4b - 2c = 24\) --- (1)

\(4a - 5b + 7c = -46\) --- (2)

\(2a + 7b + 5c = -2\) --- (3)

Multiply (1) and (3) by 2

\(2a + 4b - 2c = 24\) --- (1)

\(4a + 8b - 4c = 48\) ----- (5)

\(2a + 7b + 5c = -2\) --- (3)

\(4a + 14b + 10c = -4\) ---- (6)

So, we have:

\(4a - 5b + 7c = -46\) --- (2)

\(4a + 8b - 4c = 48\) ----- (5)

\(4a + 14b + 10c = -4\) ---- (6)

Make 4a the subject in each of the equations

\(4a = -46 + 5b - 7c\)

\(4a = 48 - 8b + 4c\)

\(4a = -4 - 14b - 10c\)

\(4a = 4a\). So, we have:

\(-46 + 5b - 7c = 48 - 8b + 4c\)  and  \(-46 + 5b - 7c = -4 - 14b - 10c\)

Simplify both expressions

\(-46 + 5b - 7c = 48 - 8b + 4c\)

\(5b + 8b - 7c - 4c = 48 + 46\)

\(13b - 11c = 94\)

\(-46 + 5b - 7c = -4 - 14b - 10c\)

\(5b+14b - 7c + 10c = 46-4\)

\(19b + 3c = 42\)

Make c the subject

\(c = \frac{42 -19b}{3}\)

Substitute \(c = \frac{42 -19b}{3}\) in \(13b - 11c = 94\)

\(13b - 11 \times (\frac{42 - 19b}{3}) = 94\)

Multiply through by 3

\(39b - 11 \times (42 - 19b) = 282\)

Open bracket

\(39b - 462 + 209b = 282\)

Collect like terms

\(39b + 209b = 282+462\)

\(248b = 744\)

Solve for b

\(b = \frac{744}{248}\)

\(b = 3\)

Solve for c

\(c = \frac{42 -19b}{3}\)

\(c = \frac{42 - 19 \times 3}{3}\)

\(c = \frac{-15}{3}\)

\(c = -5\)

Solve for a in \(4a = -4 - 14b - 10c\)

\(4a = -4 - 14 \times 3 - 10 \times -5\)

\(4a = 4\)

Divide by 4

\(a = 1\)

Recall that matrix B is:

\(B =\left[\begin{array}{c}a&b&c\end{array}\right]\)

Hence, the value of matrix B is:

\(B =\left[\begin{array}{c}1&3&-5\end{array}\right]\)

Read more on matrix operations at:

https://brainly.com/question/16956653

Answer:

48 by 10 because

\(480\div 10 = 48\)

therefore the wall dimensions are 48 by 10

a. the matrix:

| a0 b0 c0 |

| a1 b1 c1 |

| a2 b2 c2 |

b. the matrix:

| p0 q0 r0 |

| p1 q1 r1 |

| p2 q2 r2 |

To find the transition matrix from basis C to basis B, we need to express each vector in basis C as a linear combination of vectors in basis B and then write the coefficients in matrix form.

(a) Transition matrix from C to B:

To express each vector in C as a linear combination of vectors in B, we solve the following system of equations:

1 = a0 * 1 + a1 * x + a2 * x^2

(x - 1) = b0 * 1 + b1 * x + b2 * x^2

(x - 1)^2 = c0 * 1 + c1 * x + c2 * x^2

We solve this system of equations and find the coefficients a0, a1, a2, b0, b1, b2, c0, c1, c2. Then we form the matrix:

| a0 b0 c0 |

| a1 b1 c1 |

| a2 b2 c2 |

(b) Transition matrix from B to C:

To express each vector in B as a linear combination of vectors in C, we solve the following system of equations:

1 = p0 * 1 + p1 * (x - 1) + p2 * (x - 1)^2

x = q0 * 1 + q1 * (x - 1) + q2 * (x - 1)^2

x^2 = r0 * 1 + r1 * (x - 1) + r2 * (x - 1)^2

We solve this system of equations and find the coefficients p0, p1, p2, q0, q1, q2, r0, r1, r2. Then we form the matrix:

| p0 q0 r0 |

| p1 q1 r1 |

| p2 q2 r2 |

(c) To complete part (c), please provide the polynomial p(x) that you want to write in terms of the basis C or B.

Learn more about matrix here

https://brainly.com/question/30389982

#SPJ11

Answer:

A cylinder

Step-by-step explanation:

When you rotate the rectangle you are make a circle but since its volume the original height of the rectangle is the height of the circle which would mean a cylinder.

Answer:

CYLINDER

Step-by-step explanation:

Answer:

isnt like 40 the answer (im sorry if im wrong 3rd grader)

Step-by-step explanation:

Please find attached photograph for your answer. Don't forget to mark me Brainliest if you like my answer

The acceleration vector when t = 2, is (-1/4, -12).

option B.

The acceleration vector of the point is calculated as follows;

The position vector of the point at time t = y r(t) = (x(t), y(t)) = (ln(2t), 3 - t³).

The velocity vector is calculated as follows;

v(t) = r'(t)

v(t)  = (dx/dt, dy/dt)

v(t) =  (d/dt(ln(2t)), d/dt(3 - t³))

v(t) = (1/t, -3t²)

Acceleration is change in velocity with time, so the acceleration vector is calculated as follows;

a(t) = v'(t) = (d/dt(1/t), d/dt(-3t²))

a(t) = (-1/t², -6t)

The acceleration vector when t = 2, is calculated as follows;

a(2) = (-1/2², -6(2) )

a(2) = (-1/4, -12)

Learn more about acceleration vector here: https://brainly.com/question/31134791

#SPJ1

Answer:

(0, 5000)

The value of the account at the start of the year is 5000

Step-by-step explanation:

Given the equation that represents the  value, y, of one account that was left inactive for a period of x years as;

y = 5000(0.98)^x

The y-intercept of the equation occurs at x = 0

Substitute x = 0 into the expression

y = 5000(0.98)^0

y = 5000(1) (any value raise to power of zero is 1)

y = 5000

Hence the y intercept is (0, 5000)

This means that the value of the account at the start of the year is 5000

Answer:

The number -5 is not a rational number because it is a negative integers.

Step-by-step explanation:

Hopes This Helps :)

Answer: 2.6

Step-by-step explanation:

1. We know that A to C is 14

2. B to C is 11.4 so we're going to find the remainder to equal 14.

3. 14 minus11.4 which equals 2.6

4. AB is 2.6

So, P(C|F) is approximately equal to 0.6667, rounded to four decimal places.

To find P(A|E) and P(C|F) using the tree diagram, we need to determine the conditional probabilities.

Looking at the tree diagram, we can see that the event E occurs in two out of the four branches, and the event A occurs in one of those branches. Therefore, we can calculate P(A|E) as follows:

P(A|E) = P(A ∩ E) / P(E)

From the tree diagram, we see that P(A ∩ E) is the probability of the branch that leads to both A and E, which is 0.15.

To calculate P(E), we sum up the probabilities of the branches that lead to E, which are 0.15 and 0.05.

P(E) = 0.15 + 0.05 = 0.20

Now we can calculate P(A|E):

P(A|E) = P(A ∩ E) / P(E) = 0.15 / 0.20 = 0.7500

So, P(A|E) is equal to 0.7500.

Similarly, we can calculate P(C|F) using the same approach:

P(C|F) = P(C ∩ F) / P(F)

From the tree diagram, we see that P(C ∩ F) is the probability of the branch that leads to both C and F, which is 0.20.

To calculate P(F), we sum up the probabilities of the branches that lead to F, which are 0.10 and 0.20.

P(F) = 0.10 + 0.20 = 0.30

Now we can calculate P(C|F):

P(C|F) = P(C ∩ F) / P(F) = 0.20 / 0.30 = 0.6667

So, P(C|F) is approximately equal to 0.6667, rounded to four decimal places.

Learn more about decimal here:

https://brainly.com/question/28393353

#SPJ11

Answer:

The answer is D.

Sum means addition. So, you would be adding a and b. Remember this; a - b = difference, a * b = product, a ÷ b = quotient, and a + b = sum. Good luck!

Answer:

d) a+b

Step-by-step explanation:

For this question we can think of a and b as different numbers just for the sake of making the question easier. For example "a" could be 2 and "b" could be 3 (a=2 and b=3).

(However, keep in mind that "a" and "b" can be any number and that we don't know their values. But we can assign some values to them in order to solve the question more easily)

So if a=2 and b=3 in our example the notation for their sum would be 2+3. If we just put a for 2 and b for 3 we get a+b, which is the answer

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

Learn more about Gram-Schmidt process here;

https://brainly.com/question/17132977

#SPJ4

Answer:

slope of p= -7/12

slope of q= -3/6.8

slope of r= -16/6.4

slope of m= 6.2/15.5

slope of n= 6.8/17

Step-by-step explanation:

The slopes of the line are given as 2.5 for p and q and -2.5 for r, m and n respectively.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The slope of the given lines can be obtained as follows,

(a) In order to find slope of line p,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-3 - 8)/(0.4 - (-4))

⇒ m = -2.5

(b)  In order to find slope of line q,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (13 - 0)/(6.8 - 12)

⇒ m = -2.5

(c)  In order to find slope of line r,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (13 - (-3))/(6.8 - 0.4)

⇒ m = 2.5

(d) In order to find slope of line m,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-15.5 - 0)/(0 - 6.2)

⇒ m = 2.5

(e)  In order to find slope of line n,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-5 - 12)/(- 6.8 - 0)

⇒ m = 2.5

Hence, the slopes of first two lines are 2.5 and of the remaining three are 2.5.

To know more about slope click on,

https://brainly.com/question/3605446

#SPJ2

Answer:1) 29.4

2)4.2

Step-by-step explanation:

0.7×42=29.4

0.3×14=4.2

To determine the critical value for the F-test at 95% confidence, we need the degrees of freedom for the numerator (df) and the denominator (df), along with the significance level (α) to find the critical value from an F-distribution table.

The F-test is used to compare the variances of two populations. In this case, we need additional information such as the sum of squares (SS), mean squares (MS), and the p-value to calculate the critical value for the F-test accurately.

Without the values for df, SS, MS, F, and p, it is not possible to provide a specific calculation for the critical value at 95% confidence.

The critical value for the F-test at 95% confidence depends on the degrees of freedom, sum of squares, mean squares, F-statistic, and p-value. To determine the specific critical value, these values are required. Without the given data, it is not possible to provide an exact answer.

To know more about numerator , Visit:

https://brainly.com/question/1217611

#SPJ11

The 3 to the power of three halves equal to square root of 27 sqrt(27).

What is the square root?

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

A square root is a number that can be multiplied by itself to give the original number.

3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.

To calculate this value, you can use a calculator or you can use the following formula:

3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417

Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).

To learn more about the square root visit,

https://brainly.com/question/428672

#SPJ1

The years when the spending be more than $66 billion is in 4 years time.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:

y=12.7x+15.2

66 = 12.7x + 15.2

Collect like terms

12.7x = 66 - 15.2

12.7x = 50.8

Divide

x = 50.8 / 12.7

x = 4

The number of years is 4.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1