The number of fish in the Colorado River increased 47% from the previous season. There are currently 25284 fish in the river. How many fish were in the river last season?

Answer:

Step-by-step explanation:

To find the eigenvalues of a matrix M, we need to solve the characteristic equation det(M - λI) = 0, where I is the identity matrix of the same size as M, and λ is the eigenvalue we are trying to find.

For the matrix M = [ -4.5 2.5

-7.5 5.5 ]

the characteristic equation is:

det(M - λI) = det([ -4.5 - λ 2.5

-7.5 5.5 - λ ])

Expanding this determinant using the first row, we get:

(-4.5 - λ) (5.5 - λ) - 2.5 (-7.5) = 0

Simplifying and rearranging, we get:

λ^2 - λ - 6 = 0

This is a quadratic equation with solutions:

λ = (1 ± √(1 + 24))/2

λ = (1 ± 5)/2

So the possible eigenvalues of M are λ = -2 or λ = 3.

Note that we have not yet found the eigenvectors associated with each eigenvalue. To do so, we need to solve the equation (M - λI)x = 0 for each eigenvalue. This will give us a set of linearly independent eigenvectors that span the eigenspace associated with that eigenvalue.

The possible eigenvalues are:

λ1 = 1/2 + (√(11)/2)i

λ2 = 1/2 - (√(11)/2)i

To find the eigenvalues of the given matrix, we need to solve the characteristic equation:

|−4.5 − λ 2.5| = (−4.5 − λ)(5.5 − λ) − (−7.5)(2.5)

|−7.5 5.5 − λ| = λ² − 1λ + 3

Expanding the determinant and simplifying, we get:

λ² − 1λ + 3 = 0

Using the quadratic formula, we can solve for λ:

λ = (1 ± √(1 - 4(1)(3))) / 2

= (1 ± √(1 - 12)) / 2

= (1 ± √(-11)) / 2

Since the discriminant is negative, there are no real eigenvalues. The two eigenvalues are complex conjugates:

λ1 = (1 + √(-11)) / 2

λ2 = (1 - √(-11)) / 2

Therefore, the possible eigenvalues are:

λ1 = 1/2 + (√(11)/2)i

λ2 = 1/2 - (√(11)/2)i

Learn more about eigenvalues

https://brainly.com/question/31650198

#SPJ4

Answer:

69 doritos

Step-by-step explanation:

mountain dew and 360 no scope =69 doritos

Answer:

The answer is letter C.

Step-by-step explanation:

hope this helps

Step-by-step explanation:

SUBTRACTING  '6' from the 'x' of the equation shifts the graph '6' units to the RIGHT .

To eliminate the parameter in the pair of parametric equations x = t - 3 and y = t^2 + 5, the correct equation is y = x^2 - 6x - 14.

To eliminate the parameter t and express y in terms of x, we can substitute the expression for x in terms of t into the equation for y.

Given x = t - 3, we can rearrange it to obtain t = x + 3.

Substituting this value of t into the equation for y = t^2 + 5, we get:

y = (x + 3)^2 + 5.

Expanding this equation, we have:

y = x^2 + 6x + 9 + 5,

y = x^2 + 6x + 14.

Therefore, the correct equation that eliminates the parameter t and expresses y in terms of x is y = x^2 + 6x + 14.

The other options presented (Oy = x^2 - 14, Oy = x^2 + 6x + 14, Oy = x^2 + 14) are not correct as they do not correspond to the elimination of the parameter t and the substitution of x in terms of t in the equation for y.

Learn more about parameter here:

https://brainly.com/question/30896561

#SPJ11

Answer:

Step-by-step explanation:

An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

Learn more about Radius of Cylinder:

https://brainly.com/question/22802718

#SPJ4

Answer:

45

Step-by-step explanation:

I think it's 45. Why do I have to have 25 characters

Answer:

5^2 is 5x5=25 25x 2 = 50 minus 5 is 45 so i think its 45

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer:

Female: 93/328

Adult: 103/328

Baby: 61/328

Step-by-step explanation:

71 + 93 + 103 + 61 = 328

Male: 71/328

Female: 93/328

Adult: 103/328

Baby: 61/328

Answer:

1

Step-by-step explanation:

because it is a linear equation and linear Equations only have 1 solution

An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.

D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.

D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.

D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.

D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.

The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.

To know more about blood refer here:

https://brainly.com/question/30828552#

#SPJ11

Answer:

Angle of elevation = 56.31°

Step-by-step explanation:

The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

Learn more about parallelogram  :

https://brainly.com/question/29147156

#SPJ4

Answer:

THIRD-HALF PHASE IS MARKED WITH THE X.

Step-by-step explanation:

MARK ME AS A BRAINLIST PLZ

Answer: waxing gibbous

Answer:

g(3)=2

Step-by-step explanation:

Use g(x)=f(x-2)-1

the " - 2" inside the parenthesis with the x will shift the whole graph to the right 2 units. (Shown in dashed red on the image) The " - 1 " at the end of the expression will slide the whole graph down one unit (see image shown in purple) The image shown in purple is the final g(x).

to find g(3) (see image in yellow highlight)

g(3)=2

Answer:

b. 216 ft

Step-by-step explanation:

Using pythagorean theorem to find the length of the other leg, sqrt(30^2-24^2)=18. area would be product of both legs divided by 2, so (24*18)/2=216 ft^2. Also all the answer choices are wrong since it should be ft^2 instead of ft, but i think they're just looking for the number 216

The area of the right angle triangle is 216 square ft option (C) 216 square ft is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a right angle triangle shown in the picture:

We can calculate the base length by using the Pythagoras theorem:

base length = √(30²-24²) = 18 ft

Area of the triangle = (1/2)(24×18)

Area of triangle = 216 square ft

Thus, the area of the right angle triangle is 216 square ft option (C) 216 square ft is correct.

Learn more about the right angle triangle here:

brainly.com/question/3770177

#SPJ2

Answer:

1 hour

Step-by-step explanation:

Answer:

BGC and FGE are cmplimentary so FGE = 45 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

-6y = -5x + 36

y = 5/6x - 6

Answer: 47.1

Step-by-step explanation:

1/3πr^2h

=1/3×π×32×5

=15π

= 47.123889803847 feet3

Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction and y-intercept of a line is the point at which the line crosses the y-axis.

Slope: Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b.

Example: A line with a slope of 2 would mean that for every increase of 1 in the x-direction, the y-value would increase by 2.

Y-intercept: The y-intercept of a line is the point at which the line crosses the y-axis. It is typically represented by the b in the equation y = mx + b.

Example: A line with a y-intercept of 4 would cross the y-axis at y = 4.

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

for similar questions on area of the circle.

https://brainly.com/question/14068861

#SPJ8

Answer:

8/a^2

Step-by-step explanation:

Step-by-step explanation:

There are 10 + 20 = 30 total students in the class.

Total marks for the class = 60 * 30 = 1800.

Total marks for the girls = 54 * 20 = 1080.

=> Total marks for the boys = 1800 - 1080 = 720.

Mean mark for the boys = 720 / 10 = 72.

Answer:

10 months

Step-by-step explanation:

30x = 22x + 80

8x = 80

x = 10

Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

The formula used to estimate the sample size for a simple random sample when estimating a population mean is:
n = (Z * σ / E) ^ 2.

1. Determine the desired confidence level for your estimation.
2. Find the corresponding Z-score for the desired confidence level. Common Z-scores for confidence levels include 1.96 for 95% confidence and 2.58 for 99% confidence.
3. Estimate the population standard deviation (σ) using previous data or assumptions.
4. Decide on the desired margin of error (E), which represents the maximum acceptable difference between the sample mean and the population mean.
5. Plug these values into the formula: n = (Z * σ / E) ^ 2.
6. Calculate the sample size (n) using the formula.
Therefore, the formula used to estimate the sample size for a simple random sample when estimating a population mean is n = (Z * σ / E) ^ 2.

where:
n is the sample size,
Z is the Z-score corresponding to the desired confidence level,
σ is the population standard deviation, and
E is the desired margin of error.

To know more about error visit:

https://brainly.com/question/13089857

#SPJ11