The parallelogram below has an area of 15 1/6 square feet. What is the height of the parallelogram?

the determinant of the given matrix is 81/93750.

In order to find the determinant of the given matrix, let's begin by creating a matrix of 4×4 using the aij (2×2) matrix.

And the formula used to find the determinant of the n × n matrix is given by the following equation:

|A| = ∑ (-1)i+j * aij * Mij

where Mij is the minor of the ith row and jth column of the matrix, and aij is the element of the ith row and jth column of the matrix.

A matrix of 4×4 using the aij (2×2) matrix is shown below:5 0 -30 05 0 -30 05 0 5 05 0 -10 05 0 -15 0

Now we can use the above formula to evaluate the determinant of the given matrix.

|a| = 5[0, -30, 0; 0, 5, 0; -10, 0, 5] + 0[-30, 0, 5; 5, 0, -10; -15, 0, 0] - 30[5, 0, 0; 0, 0, -10; -15, 5, 0] + 0[-30, 5, 0; 5, -10, 0; 0, -15, 0]

On multiplying and simplifying the above expression,

we get |a| = 93750

As per the given information,

|ca| = cn|a|,

where c = -3

and n = 4 (since the given matrix is 4x4).

Therefore,|(-3) a|

= (-3)^4|a||a|

= 81|a| (from the above equation)|a|

= 81/93750

Therefore, the determinant of the given matrix is 81/93750.

To know more about determinant visit:

https://brainly.com/question/16981628

#SPJ11

The solution to the differential equation \(y'' - 6y' + 9y = 324e^{(9t)}\) with initial conditions y(0) = 4 and y'(0) = 5 is:

\(y(t) = (-5/3 + (2/3)t) e^{(3t)} + 9e^{(9t)}\)

To solve the differential equation \(y'' - 6y' + 9y = 324e^{(9t)}\) with initial conditions y(0) = 4 and y'(0) = 5, we can first find the characteristic equation by assuming the solution has the form \(y = e^{(rt)}\):

\(r^2 - 6r + 9 = 0\)

This can be factored as \((r - 3)^2 = 0\), so the characteristic equation has a repeated root of r = 3. Therefore, the general solution to the homogeneous differential equation y'' - 6y' + 9y = 0 is:

\(y_h(t) = (c_1 + c_2t) e^{(3t)}\)

where \(c_1\)and \(c_2\) are constants that depend on the initial conditions.

To find the particular solution to the nonhomogeneous differential equation \(y'' - 6y' + 9y = 324e^{(9t)}\);

We can use the method of undetermined coefficients and assume the particular solution has the form \(y_p(t) = Ae^{(9t)}\), where A is a constant to be determined.

Substituting this into the differential equation, we get:

\(81Ae^{(9t)} - 54Ae^{(9t)} + 9Ae^{(9t)} = 324e^{(9t)}\)

Simplifying:

\(36Ae^{(9t)} = 324e^{(9t)}\)

A = 9

Therefore, the particular solution is:

\(y_p(t) = 9e^{(9t)}\)

The general solution to the nonhomogeneous differential equation is:

\(y(t) = y_h(t) + y_p(t)\)

\(= (c_1 + c_2t) e^{(3t)} + 9e^{(9t)}\)

To find the values of \(c_1\) and \(c_2\), we can use the initial conditions y(0) = 4 and y'(0) = 5. Substituting these into the general solution, we get:

\(y(0) = c_1 e^{(0)} + 9e^{(0)} = c_1 + 9 = 4\)

\(y'(t) = 3(c_1 + c_2t) e^{(3t)} + 9e^{(9t)}\)

\(y'(0) = 3(c_1 + 0) e^{(3(0)}) + 9e^{(9(0)}) = 3c_1 + 9 = 5\)

Solving these equations for \(c_1\) and \(c_2\), we get:

\(c_1 = -5/3\)

\(c_2 = 2/3\)

Therefore, the solution to the differential equation \(y'' - 6y' + 9y = 324e^{(9t)}\) with initial conditions y(0) = 4 and y'(0) = 5 is:

\(y(t) = (-5/3 + (2/3)t) e^{(3t)} + 9e^{(9t)}\)

Learn more about differential equation

brainly.com/question/14620493

#SPJ11

Answer:

the answer is b

Answer:

i

Step-by-step explanation:

Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.

 the answer is i

Step-by-step explanation:

for real this is true

Answer:

  2048

Step-by-step explanation:

You want the value of a10 = 4(2^(10 -1)).

If you don't have powers of 2 memorized, you can put this expression into your calculator or spreadsheet to get it evaluated. You will need parentheses around the exponent.

  4(2^(10-1)) = 4(2^9) = 4(512) = 2048

The value of the expression is 2048.

__

Additional comment

This looks like an instance of the equation for the n-th term of a geometric sequence:

  an = a1·r^(n -1)

where a1 = 4, r = 2, and n = 10.

This is why we have assumed that the "-1" is part of the exponent, and that you simply want the value of the right-side expression.

If this equation means something else, then it needs to be written differently. For example, if a10 means 'a' to the 10th power, it needs to be written as a^10, and we need to be told we're solving for 'a'.

<95141404393>

Answer:

The factors are \(2v+3,2v+3\).

The factors are not \(4v+3,4v+3\)

Step-by-step explanation:

Equation is \(4v^2=-12v-9\).

This equation can be written as follows:

\(4v^2+12v+9=0\)

Here,

\(12v=6v+6v\)

Therefore,

\(4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0\)

So, the factors are \(2v+3,2v+3\).

The factors are not \(4v+3,4v+3\)

Answer:

(-1)* (3)^(n-1)

Step-by-step explanation:

common ratio is 3 and the first term is -1

the explicit formula is a * r^ ( n-1)

i.e., (-1) * 3^(n-1)

Answer:  see image

Step-by-step explanation:

There aren't any instructions so my best guess is that you draw a line from the ball to a zombie and then to another zombie, etc until all of the zombies are wiped out by the ball.

Step-by-step explanation:

you multiply both the top and bottom by the root if it was alone.

let's say if we had (1 - sqrt(2)) in the denominator. here we multiply both the numerator and the denominator by the conjugate.

the conjugate is formed by changing the sign between two terms in a binomial. so in this case the conjugate is

(sqrt(2) -1)

make sure to ask if you need any further guidance :)

Problem 1

PMT = 505.76 = monthly payment

k = monthly interest rate in decimal form

k = 0.043/12 = 0.003583333 (approximate)

n = 5*12 = 60 months

PVOA = present value of ordinary annuity

PVOA = PMT * ( 1 - (1+k)^(-n) )/k

PVOA = 505.76 * ( 1 - (1+0.003583333)^(-60) )/0.003583333

PVOA = 27,261.436358296

When rounding to the nearest dollar, we get $27,261

Your teacher made a mistake in choosing the formula. S/he mixed up present value ordinary annuity with annuity due. The (1+k) portion at the end is ignored. I rewrote the 1/( (1+k)^n ) sub-portion as (1+k)^(-n) to avoid a bit of clutter.

--------

To type this into excel we will write

=PV(0.043/12,5*12,505.76,0,0)

That will produce the result of -27,261.44. The negative is to indicate a cash outflow.

Don't forget about the equal sign up front when writing excel formulas.

=====================================================

Problem 2

L = loan amount = 23099

k = interest rate per month = 0.051/12 = 0.00425 exactly

n = number of months = 5*12 = 60 months

PMT = monthly payment

PMT = (Lk)/(1 - (1 + k)^(-n) )

This formula is the result of solving PVOA = PMT * ( 1 - (1+k)^(-n) )/k for "PMT". The PVOA value is the loan amount in this case.

Let's plug in the values mentioned

PMT = (Lk)/(1 - (1 + k)^(-n) )

PMT = (23099*0.00425)/(1 - (1 + 0.00425)^(-60) )

PMT = 436.965684557303

PMT = 437 when rounding to the nearest whole number

--------

To do this in excel, we type in

=PMT(0.051/12,5*12,23099,0,0)

The output should be -436.97 which rounds to -437.

The value is negative to represent a cash outflow, but your teacher mentions to post the answer as a positive value.

The composite function g(x) is g(x) = 12x/(2x - 1)

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

f(x) = x/(x - 6)

f(g(x)) = 2x

This means that

f(g(x)) = g(x)/(g(x) - 6)

So, we have

g(x)/(g(x) - 6) = 2x

Rewrite as

y/(y - 6) = 2x

This gives

y = 2x(y - 6)

Open brackets

y - 2xy = -12x

This gives

y = -12x/(1 - 2x)

So, we have

y = 12x/(2x - 1)

Hence, the function g(x) = 12x/(2x - 1)

Read more about composite function at

https://brainly.com/question/10687170

#SPJ1

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

The slope is the rate at which the pool is being filled.

A slope of 2 means a filling rate of 2 inches per minute.

Answer: The height of the water increases 2 inches per minute.

Answer:

118

Step-by-step explanation:

The key piece of information to focus on is that there are around 120 fruits. 15 is the biggest of the given divisors, and the gaps between multiples of 15 is the greatest (compared to 4 and 6) which will narrow down our options. Therefore we can first try approaching the problem by finding multiples of 15 that are close to 120.

The question says that when the number (let's call it A) is divided by 15, it leaves 13. Therefore we can express A as such:

A-13 = 15x OR 15x + 13 = A

Where 'x' represents a whole number showing that the number is divisible by 15.

The closest multiples of 15 to 120 are 105 (15*7), 120 (15*8), and 135 (15*9).

A is one of these numbers + 13, let's see which ones are closest:

105+13 = 118, 120+13 = 133, 135+13 = 148

118 is very close to 120, so let's check it with the other numbers:

118/4 = 29 r 2

118/6 = 19 r 4

The exact number of fruits is 118.

Hope this helped!

Answer:

118

Step-by-step explanation:

We are told that there are about 120 fruits.

Fruits divided equally among 4 students

Multiples of 4:  4, 8, 12, ... 112, 116, 120, 124, ...

Therefore, 116, 120 and 124 are closest to 120.

Add the given remainder of 2 to these numbers:

Fruits divided equally among 6 students

Multiples of 6:  6, 12, 18, ... 108, 114, 120, 126 ...

Therefore, 114, 120 and 126 are closest to 120.

Add the given remainder of 4 to these numbers:

Fruits divided equally among 15 students

Multiples of 15:  15, 30, 45, ... 105, 120, 135, ...

Therefore, 105, 120 and 135 are closest to 120.

Add the given remainder of 13 to these numbers:

Therefore, as the total of 118 fruits is common to all three groups the exact number of fruits is 118.

Check

Divide 118 by each group of students:

As the remainders concur with the given amount of fruit left over for each group of students, this verifies that the exact number of fruits is 118.

Answer: 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

easy flip them and make it into mixed fractions  hope it helps

The probability that none of the 29 houses will be burglarized is approximately 0.5368 or 53.68%.

To solve this problem, we need to use the binomial probability formula:

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where:
- P(X = k) is the probability of getting k successes
- n is the number of trials
- k is the number of successes
- p is the probability of success on each trial
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

In this case, we want to find the probability that none of the 29 houses will be burglarized, which means we want k = 0. We know that p = 0.02 (since the probability of a house being burglarized is 2%). So we can plug these values into the formula:

P(X = 0) = (29 choose 0) × 0.02 × (1-0.02)⁽²⁹⁻⁰⁾
P(X = 0) = 1 × 1 × 0.98²⁹
P(X = 0) = 0.5368

Therefore, the probability that none of the 29 houses will be burglarized is approximately 0.5368 or 53.68%.

To learn more about probability here:

brainly.com/question/30034780#

#SPJ11

Answer:

C. Mediterranean Sea

Step-by-step explanation:

The Mediterranean Sea is south of western Europe. The Atlantic doesn't really touch Europe, the Pacific is east of Europe, and the Baltic sea is in northern Europe.

Answer:

x = -9

y = 4

Step-by-step explanation:

-2x - 5y = -2

-x - 5y = -11

Time the second equation by -2

-2x - 5y = -2

2x + 10y = 22

5y = 20

y = 4

Now put 4 in for y and solve for x

-2x - 5(4) = -2

-2x - 20 = -2

-2x = 18

x = -9

Let's check

-2(-9) - 5(4) = -2

18 - 20 = -2

-2 = -2

So, x = -9 and y = 4 is the correct answer.

Answer:

C

Step-by-step explanation:

It is C. Have a great day!

Answer:

Paul has 6.6 miles to go after his snack.

Step-by-step explanation:

Speed is the rate of moving. The speed can be calculated by dividing the distance traveled by the amount of time it took.

speed= distance/time  , v=d/t

So,from Paul's average speed we can calculate how much distance he has passed after 3 hours.

distance_3h=v*t=13.8 miles per hour * 3 hours

distance_3h=41.4 miles

There are total 48 miles to the beach, so Paul have to go 48miles-distance_3h after his snack, which gives:

48-41.4=6.6 miles

There are two possible volumes for the rectangular prism: 36 cubic units or 25 cubic units.

To find the volume of the rectangular prism with a space diagonal of 13 units and integer unit dimensions, we can follow these steps:

1. Recall that the space diagonal of a rectangular prism can be found using the Pythagorean theorem in 3D: d² = l² + w² + h², where d is the space diagonal, and l, w, and h are the length, width, and height of the prism.

2. Given that the space diagonal is 13 units, we have: 13² = l² + w² + h².

3. Since the dimensions are integers, we need to find the combination of l, w, and h that satisfies this equation. Possible combinations are: (2, 3, 6) and (1, 5, 5), as these are the only sets of integers that satisfy the equation.

4. Now, we can calculate the volume of the rectangular prism using the formula: Volume = l × w × h.

For the combination (2, 3, 6), the volume is: 2 × 3 × 6 = 36 cubic units.
For the combination (1, 5, 5), the volume is: 1 × 5 × 5 = 25 cubic units.

So, there are two possible volumes for the rectangular prism: 36 cubic units or 25 cubic units.

Learn more about "rectangular prism": https://brainly.com/question/24284033

#SPJ11

The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.

To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) =  = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.

Learn more about vector equation

https://brainly.com/question/31044363

#SPJ11

Step-by-step explanation:

Calculating the discount is easy. For example, if an item had a discount of 10% and the original price was $100.

10% is equivalent to 10/100

10/100 multiplied by 100 (original) is 10

The discount would be $10 off

Hope this helped

Answer:

Independent: The people who attend.

Dependent: The copies she has to make.

Step-by-step explanation:

She will make a certain amount of copies depending of how many people attend.

Answer:

B

Step-by-step explanation:

Please mark me brainleist

Answer:

the answer is C, I got it too from the website, I got the answer from it

Answer:

The formula for the volume of a hemisphere is V = (2/3)πr³. Solving for r, we get r = (3V/4π)^(1/3). Substituting V = 2507 in³, we get r ≈ 7.5 in. The diameter of a hemisphere is twice its radius, so the diameter of this hemisphere is approximately 15 inches to the nearest tenth of an inch.

Step-by-step explanation:

The projected misstatement of this sample would be $50,000, calculated as follows: ($4,000 / $5,000) x $10,000.

In a probability-proportional-to-size sample, each item's chance of being selected is proportional to its recorded amount, so larger accounts have a higher probability of being selected. In this case, the auditor selected an account with a recorded amount of $5,000, but found that it had an audited amount of $4,000.

To project the misstatement of this sample, the auditor needs to estimate the total misstatement in the population by multiplying the audited amount by the inverse of the sampling fraction, which is the sampling interval divided by the recorded amount of the selected item. So, the projected misstatement is ($4,000 / $5,000) x $10,000 = $8,000 x 6.25 = $50,000. This means that the auditor estimates the total misstatement in the population to be approximately $50,000 based on this sample.

For more questions like Probability visit the link below:

https://brainly.com/question/30830663

#SPJ11

Answer:

0.5

Step-by-step explanation:

I did the same question