the number of fish in a lake decreased by 25 % between last year and this year there were 60 fish in the lake what is the population this year?

Step-by-step explanation:

A set-builder notation describes or defines the elements of a set instead of listing the elements. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements. The same set could be described as { x/x is a counting number less than 10 } in set-builder notation.

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

If the data were transformed and points with the coordinates

(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.

To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.

Let's calculate the logarithms for the given data:

x     y            log(y)

1     12          log(12) = 1.079

2     83        log(83) = 1.919

3     580      log(580) = 2.763

Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)

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Answer:

Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)

Therefore,y=2z

z=x-8

y=2x-16

substituting the values of x,y and z into the question,we have

x+(2x-16)+(x-8)=100

Simplifying,we have

4x-24=100

adding 24 to both sides of the equation,

4x=100+24

4x=124

dividing both sides of the equation by the co-efficient of x,we have

4x/4=124/4

4.31=124

therefore,x=31.

The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-3 is greater than -4 on the number line but less than -2 on the number line. Therefore, the number is -3

hope I helped.

Answer: -7.7%

Step-by- A P E X

Answer:

3 is correct answer

Step-by-step explanation:

root 2 and pi are irrational numbers

Answer:

(100/500) *200 =40%

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

4-3 = 1

Answer:

1

Step-by-step explanation:

4-3=1

If you had 4 lollipops and you gave your friend 3 lollipops, how many would you have? 4-3=1 You could try it out at home.

Answer:

The first thing you do is make the denominators equal on both sides.

Step-by-step explanation:

As a example if you have the equation:

\(\frac{1}{2}\) + \(\frac{2}{5}\) =

you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10

this would make the equation

\(\frac{x}{10} + \frac{x}{10} = ...\)

next you have to do the same with the numerator.

so sence you multiplied the \(\frac{1}{2}\) by five you will get \(\frac{5}{10}\)

same with the other fraction except you multiplied it by two.\(\frac{2}{5}\) x 2 = \(\frac{4}{10}\)

next you add and simplify if needed

Answer:

3 simple steps

Step-by-step explanation:

1.     Make sure the bottom numbers ( the denominators ) are the same

       IF DIFFERENT find the LCD

2.    Add the top numbers (the numerators )

3.    simplify the fraction if needed

ex:  1/4 +1/4 = 2/4  (bottoms were the same) simplify  1/2

       1/3 + 1/6    LCD of 3 and 6 so make the bottom numbers 6

                         so multiply  1/3 x  2 = 2/6

        now you have 2/6 + 1/6 = 3/6    simplify 1/2

Answer:

f(-3) = 9

Step-by-step explanation:

Step 1: Define

f(x) = -2x² - 7x + 6

f(-3) = x = -3

Step 2: Substitute and evaluate

f(-3) = -2(-3)² - 7(-3) + 6

f(-3) = -2(9) + 21 + 6

f(-3) = -18 + 21 + 6

f(-3) = 3 + 6

f(-3) = 9

Answer:

Step-by-step explanation:

Answer:

559

Step-by-step explanation:

Step-by-step explanation:

5⁴÷(1/5)²

=5⁴÷5‐²

=5⁴+²

=5⁶

=15,625

Answer:

Step-by-step explanation:

5^4/5-2

=5^4-(-2)

=5^6

=15,625

Bianca's speed was 20 mph, while Arlene's speed was 15 mph.

Given that two cyclists, Arlene and Bianca, complete a 60-mile course, and Bianca's speed was 5 mph faster than Arlene's, and she finished the course 1 hour sooner, to determine what was each cyclist's speed the following calculation must be performed:

Therefore, Bianca's speed was 20 mph, while Arlene's speed was 15 mph.

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To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer:

See below

Step-by-step explanation:

Not sure what they are looking for here....unless there is more info

\(\sqrt[14]{y}\)  =  \(y^{1/14}\)     perhaps?

Answer:   71º

Step-by-step explanation:

I cant remeber the therum but basically its just the opposite, super simple!!

Answer:

Step-by-step explanation:

circumference=75 ft.

2πr=75

r=75/2π=75/(2×3.14)≈11.937

radius=11.94 ft

Diameter=2r=2×11≈23.87 ft

Answer:

mark me brainlest

Step-by-step explanation:

The area of sector is = pi* r^2*β\360 …. . . .(1

Where

Pi=3.14

r = radius

β= angle=36

So. Put value in equation 1

5.024=3.14 * r^2*36/360

5.024*360/(3.14*36)= r^2

16=r^2

r=4

Answer:

A = 1/4

Step-by-step explanation:

Answer:

A = 1/4 is the correct answer

Answer:

The answer for this question is 2 ft

Step-by-step explanation:

12ft÷6ft=2

Answer:

Radiation

Step-by-step explanation:

the sun sends out light

note-this should be in science

Convection warms the land, oceans, and surrounding atmosphere from the Sun.

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Answer:

of which class is it ?

Step-by-step explanation:

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Answer:

  384 cubic centimeters

Step-by-step explanation:

We are given the base area and total area of a square pyramid and asked to find the volume. The typical volume formula for a pyramid requires that we know the height of it. We can use the formula for the surface area to find the slant height of a face, and we can use the slant height to find the height perpendicular to the base.

__

  total surface area = base area + area of 4 faces

  area of 4 faces = total surface area - base area

  area of 4 faces = 384 cm² -144 cm² = 240 cm²

  area of 1 face = 240 cm²/4 = 60 cm²

__

The side length of the square base is ...

  A = a²

  a = √A = √(144 cm²) = 12 cm

and the slant height of one face is ...

  A = 1/2as

  s = (2A)/a = (2×60 cm²)/(12 cm) = 10 cm

__

The distance from the center of the base to the edge of the base is (12 cm)/2 = 6 cm. That is one leg of the right triangle whose hypotenuse is the slant height of the face. The other leg of the triangle is the height of the pyramid:

  H² = s² -(a/2)² . . . . Pythagorean theroem solved for one leg

  H = √(10² -6²) = 8 . . . . cm . . . . height of the pyramid

__

Now we know the base area of the pyramid (B), and we know its height (H), so we can use the formula ...

  V = 1/3BH

  V = 1/3(144 cm²)(8 cm) = 384 cm³

The volume of the pyramid will be 384 cm³.