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The net growth of of population of butterflies led to 560 butterflies.

We know that the population of butterflies is 500.

The population experiences a net growth of 12%.

The net growth can be defined as increase in number of individuals in a population .

So, the gain in the population of butterflies = 12% of 500= (12/100) × 500= 60 Butterflies

So, the new population of butterflies after the gain is 500 + 60 = 560 Butterflies.

This can be calculated by another method which is

112% of 500= (112/100)*500 = 560 butterflies

Hence, the required answer is 560 butterflies.

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Answer:

4802 rounded to the nearest 1000 is 5000

Answer:

5,000

Step-by-step explanation:

We are rounding all of the elements in the equation, 2 rounds to 0, 0 rounds to 0, 8 rounds to 9, 9 rounds to 5,000.

Hence, the present age of the father is 30 years, and the present age of the son is 4 years.

To find someone's age, you need to know their date of birth and the current date. Then, you can calculate the difference between the two dates to determine their age. Here are the steps you can follow:

Ask the person for their date of birth.

Use a calendar or an online tool to determine the current date.

Calculate the difference between the two dates in years.

If the person has not had their birthday yet this year, subtract one year from the result.

Let's assume the present age of the son is "x" years.

According to the problem statement, the present age of the father is 10 years more than 5 times the age of the son, which can be mathematically represented as:

[tex]Father's present age = 5x + 10[/tex]

Also, it is given that the father was 28 years old two years ago. So, his present age would be 28 + 2 = 30 years.

Now, equating the two expressions for the father's age, we get:

[tex]5x + 10 = 30[/tex]

Solving for x, we get:

[tex]5x = 20\\x = 4[/tex]

Therefore, the present age of the son is 4 years.

And the present age of the father is:

[tex]5x + 10 = 5(4) + 10 = 30 years.[/tex]

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A Linear and Quadratic pair of  parent functions are inverses of each other on the domain x > 0.

In mathematics, a parent function is a basic representation of a function type without manipulations such as translation and dilation. For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simply shifting and stretching parallel to the axes. Function is defined as the set of all input values have at least one output value.

According to the question,

a. A pair of linear functions :

let the function be y = x.

Domain : (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Inverse of linear function is linear domain and range set of all real numbers.

Option A is the correct answer.

b. A cubic function and a cube root function :

Let y = x³

Domain: (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Inverse function  , x = ∛y ,

Domain: (-∞ , ∞) set of all real numbers

Range : (-∞ , ∞) set of all real numbers

Option B is not a correct answer.

c. a quadratic function and a square root function :

Domain of square root function: y = √x is [ 0, ∞)

Range of square root function: y = √x is [ 0, ∞)

Domain of quadratic function is (-∞ , ∞) set of all real numbers.

Range : all possible values of y.

Option C is not a correct answer.

D. A logarithmic function and an exponential function :

Domain : ( 0, ∞)

Range : set of all real numbers

Exponential function:

Domain : set of all real numbers

Range : ( 0, ∞)

Option D is not a correct answer.

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Answer:

The given equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing this with the given equation:

y = x - 2

We can see that the slope (m) is 1 and the y-intercept (b) is -2.

Answer:

These angles are complementary and congruent, so x = 15.

Step-by-step explanation:

[tex]3x + 45 = 90[/tex]

[tex]3x = 45[/tex]

[tex]x = 15[/tex]

Let x be Mary’s age

Let x-3 be Ned’s age

Let x+2 be Carla’s age

(x+2)-10=(x-10)+[(x-3)-10]

x+2-10=x-10+x-3-10

x-x-x=-10-3-10-2+10

-x=-15

x=15

Mary is 15, Ned is 12, and Carla is 17.

Answer: The volume of the metal cube 1x1x1 m is:

V_cube = l × w × h = 1 m × 1 m × 1 m = 1 m^3

The volume of the metal block that is to be cut from the cube is:

V_block = l × w × h = 3 cm × 3 cm × 4 cm = 36 cm^3

We need to convert the volume of the block to cubic meters, as the volume of the cube is given in cubic meters. We can use the conversion factor 1 m = 100 cm to convert cubic centimeters to cubic meters.

V_block = 36 cm^3 ÷ (100 cm/m)^3 = 0.000036 m^3

The number of blocks that can be cut from the cube is:

N_blocks = V_cube ÷ V_block = 1 m^3 ÷ 0.000036 m^3 = 27,777.78

Since we can only have a whole number of blocks, the maximum number of blocks that can be cut from the cube is 27,777.

The remaining volume of the cube after cutting the metal block is:

V_remain = V_cube - V_block × N_blocks = 1 m^3 - 0.000036 m^3 × 27,777 = 0.999 m^3

The surface area of the remaining cube can be calculated as follows:

S_remain = 6 × (l × w) = 6 × (h^2) = 6 × (0.999 m)^2 = 5.994 m^2

Therefore, the complete number of blocks that can be cut from the metal cube is 27,777. The volume of each block is 36 cm^3 or 0.000036 m^3. The remaining cube has a volume of 0.999 m^3 and a surface area of 5.994 m^2.

Step-by-step explanation:

Answer:

6.6km

Step-by-step explanation:

Area of trapezium = 0.5(a+b)h

201 = 0.5(17+b)17

201 = 8.5(17+b)

201 = 144.5 + 8.5b

201 - 144.5 = 8.5b

56.5 = 8.5b

b = 6.65km

Using a calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

To find the equation, we need to insert the points (x,y) in the calculator. The same is true for any regression equation such as quadratic or exponential. However, as the problem states, a line of best fit is calculated in this problem.

From the table presented in the problem, the points are given as follows:

(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).

Inserting these points into the calculator, the line of best fit for the ice cream sales in the function of the daily temperature is given by:

y = 6.5x - 279.1.

Here

x is the daily temperature, in F.

y is the sales, in dollars.

The complete question is-

The table compares the average daily temperature and ice cream sales each day

Temperature ("F) Ice Cream Sales

$112

$135

$138

$146

$166

$180

$188

$199

$220

$280

58.2

642-

64.3

66.8

684

71.6

72.7

76.2

77.8

82.8

Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth

09=38x-1092

09=-38xx-1092

Oý=65x-279.1

O ý= -65x-279.1

and also attached an image of the question.

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Step-by-step explanation:

It is a triangle.....all of the interior angles of ANY triangle su to 180 degrees.

soooo

  x  +   65 + 50   =   180

   x   =   180 - 65 - 50 = _________ degrees

Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.

Theοretical prοbability is a type οf prοbability that is based οn mathematical reasοning and analysis. It is the prοbability οf an event οccurring based οn the assumptiοn that all οutcοmes are equally likely.

Fοr example, if yοu rοll a fair six-sided dice, each οutcοme (1, 2, 3, 4, 5, οr 6) is equally likely tο οccur.

Therefοre, the theοretical prοbability οf rοlling a 1 is 1/6, the theοretical prοbability οf rοlling a 2 is 1/6, and sο οn.

Here we have

The faces οf a fair 6-sided cube are numbered 1 thrοugh 6.

The cube is rοlled 120 times,  

Since the cube is fair, each οf the six faces has an equal prοbability οf appearing οn any given rοll.

Hence, the theοretical prοbability οf rοlling a 3 οn a single rοll is 1/6.

Here we can use the fοrmula fοr expected value tο find the number οf times we shοuld expect tο rοll a 3:

Expected value = (number οf trials) x (prοbability οf success)

Expected value = 120 x (1/6) = 20

Therefοre,

Based οn the theοretical prοbability, we shοuld expect tο rοll a number 3 20 times οut οf 120 rοlls.

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A recursive sequence is a sequence in which terms are defined using one or more previous terms that are given.

If you know the term n of an arithmetic sequence and you know the common difference, d, you can find the term [tex](n + 1)[/tex] by tossing the recursive formula to [tex]n + 1 = a \ n + d[/tex]

We have then:

[tex]5, 15, 30, 50[/tex]

[tex]an = (\dfrac{5}{2} ) \times (n) \times (n + 1)[/tex]

Answer:

the recursive formula for 5, 15, 30, 50, is:

an = (5/2) x (n) x (n + 1)

Three lollipops are more expensive than two pencils.

Given that three erasers cost as much as 2 lollipops.

Let e denote the cost of an eraser and l denote the cost of a lollipop.

A pencil costs as much as two erasers, which implies that the cost of a pencil is two times the cost of an eraser. Therefore, the cost of a pencil is 2e.

Likewise, three erasers cost as much as 2 lollipops, which implies that the cost of an eraser is (2/3) l.

Therefore, the cost of a pencil is 4/3 times the cost of a lollipop.

Thus, the cost of two pencils is 4/3 * 2l = 8/3 l.

The cost of three lollipops is 3l.

Now, we must determine whether 8/3 l is greater than 3l or vice versa.

8/3 l = 2.67 l

Since 2.67 l < 3 l, the conclusion is that three lollipops are more expensive than two pencils.

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Answer: The divisors of 20 are 1, 2, 4, 5, 10, and 20. Out of these, only the numbers 1, 2, 4, and 5 are possible outcomes when rolling a standard 6-sided dice.

The probability of rolling any of these four numbers is the total number of favorable outcomes (4) divided by the total number of possible outcomes (6), which gives:

Probability = Favorable outcomes / Total outcomes = 4/6 = 2/3

Therefore, the probability of rolling a 6-sided dice and getting a number that is a divisor of 20 is 2/3 or approximately 0.667.

Step-by-step explanation:

The probability of rolling a six-sided die and getting a result that divides by 20 is 2/6, or around one-third of the time.

There is a 1/3 chance that you will roll a number that divides by 20 when using a six-sided die. There are 6 possible outcomes when a 6-sided die is rolled, however only the numbers 4 and 5 may divide by 20. There are hence 2 positive events and a total of 6 occurrences that could take place. When the number of successful outcomes is divided by the total number of possible outcomes, the probability is 2/6, or 1/3

Because just one-third of results are likely to meet the criteria, the likelihood of rolling a number on a 6-sided die that is a divisor of Twenty is minimal.

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Answer:

7.654 ft

Step-by-step explanation:

The volume of a hemisphere is [tex]V=\frac{2}{3}\pi r^3[/tex]. Rearranging this equation gives [tex]r=\sqrt[3]{\frac{3V}{2\pi} }[/tex]. Plug in V=939 to find the value of r.

The probability of drawing a lettered card from a deck of shuffled 52 cards is 50%.

There are 52 cards in a deck, and 26 of them are lettered cards (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) while the other 26 cards are suited cards (clubs, spades, hearts, diamonds).

If the deck is well shuffled, each card is equally likely to be drawn.

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is simply the number of lettered cards divided by the total number of cards:

P(Drawing a lettered card) = Number of lettered cards / Total number of cards

= 26 / 52

= 1/2

= 0.5

Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is 0.5 or 50%.

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Option B. It defines the joint probability as the probability of the intersection of two events.

A joint probability refers to the probability of two or more events occurring simultaneously. In other words, it is the probability that two or more events will occur together.

The joint probability of two events A and B is denoted as P(A ∩ B), which represents the probability of the intersection of events A and B. This is the probability that both A and B occur at the same time.

For example, if we toss a coin and roll a dice, the probability of getting heads on the coin and a 4 on the dice would be the joint probability of these two events occurring together. This joint probability can be calculated by multiplying the probability of getting heads (1/2) and the probability of rolling a 4 (1/6), giving a joint probability of 1/12.

Therefore, option (b) is the correct answer, as it defines the joint probability as the probability of the intersection of two events.

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Step-by-step explanation:

Using similar triangles:

6ft height is to 5 feet shadow as   tower height is to 40 ft tower shadow

6/5  = h / 40     <====solve for 'h'

40 * 6/5 = h  =  tower height = 48 feet tower height

Answer:

104

Step-by-step explanation:

9^2+3(9)-4 = 104

Number of remaining rods can she choose as the fourth rod is 10

For the rods to form a quadrilateral with positive area, the fourth rod must satisfy the triangle inequality. That is, the sum of the lengths of any two sides of the quadrilateral must be greater than the length of the remaining side.

Let's start by looking at the rod with length 3 cm. The only other rod that can be paired with it to form a triangle is the rod with length 7 cm, since all the other rods are either shorter or longer than 4 cm. Similarly, the only other rod that can be paired with the rod with length 15 cm is the rod with length 7 cm.

Therefore, to form a quadrilateral with positive area, Joy must choose a rod that is longer than 7 cm but shorter than 18 cm (since the sum of 7 cm and 15 cm is 22 cm). There are 10 rods that satisfy this condition: 8 cm, 9 cm, 10 cm, 11 cm, 12 cm, 13 cm, 14 cm, 16 cm, 17 cm, and 18 cm.

So Joy can choose 10 rods as the fourth rod to form a quadrilateral with positive area.

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The given question is incomplete, the complete question is:

Joy has 30 thin rods, one each of every integer length from 1 cm through 30 cm. She places the rods with lengths 3 cm, 7 cm, and 15 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

Answer:

40, 60 and 80.

Step-by-step explanation:

Let x = t he size of the smallest angle

x + 2x + x + 20 = 180  The sum of the interior angles of a triangle is 180

4x + 20 = 180  Subtract 20 from both sides

4x = 160  Divide both sides by 4

x = 40

The smallest angle is 40.  The largest angle is 80.  The other angle is 60.  The total is 180

Helping in the name of Jesus.

Pythagorean Theorem can be used to find the missing side that is equal to 21.3.

Distance formula states that the distance between two points is equal to the square root of the sum of the squares of the differences of the coordinates.

The missing side can be found by using the Pythagorean Theorem, which states that the square of the length of the hypotenuse (longest side of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Therefore, the missing side is equal to the square root of the sum of the squares of the sides we already have:

b² = (16)² + (14)²

= 256 + 196

= 452

b = √452

= 21.3

We can also use the distance formula here.

The distance between (16, 14) and (0, 0) =

√(16² + 14²)

= √(256 + 196)

= √452

= 21.3.

This confirms that the missing side is equal to 21.3.

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Question:

Find the length of the missing side. If necessary, round to the nearest tenth.

21.3

30

15

7.7

(it is a triangle and it has a right angle and you are looking for b and the numbers on the triangle are 16 [this is the longest side and slanted] and 14 [this is straight with no slant)

Answer:

(9x)/(2-2x)

Step-by-step explanation:

let f-1(x) = y

then, f(y) = x

so, (2y)/(9+2y) = x    

 ***remember the thing inside the () in  f(x) can change! y can go in x's place, any number or any other variable can go in x's place! BUT, nothing else can be changed in the function***                

   now just solve for y!

multiply both sides by (9+2y): 2y = 9x + 2xy

bring the y's together (subtract both sides): 2y-2xy =9x

hey! we can factor the left side (where the y's are): 2y(1-x) = 9x

get all the x's together  (divide both sides) : 2y = (9x)/(1-x)

get y alone (divide both sides by 2): (9x)/(1-x) * (1/2)

*finally*  distribute/simplify: (9x)/(2-2x)

you can double-check the answer on desmos!

                          ~ lmk if u got Qs   :>

The most appropriate way to report the distance driven using the car’s odometer is  181.7.

An odometer  is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. The device may be electronic, mechanical, or a combination of the two.

According to the question

A car’s odometer measures distance to the nearest 0.1 miles.

i.e it measures only 1 digit after decimal

Therefore,

the most appropriate way to report the distance driven using the car’s odometer is  181.7 miles as it has only 1 digit after decimal.

Hence, the most appropriate way to report the distance driven using the car’s odometer is 181.7 .

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Length of rectangular plot is 144ft

A rectangle is a geometric shape that is characterized by having four straight sides and four right angles. It is a type of quadrilateral, which means that it has four sides. The opposite sides of a rectangle are parallel and of equal length, which makes it a type of parallelogram.

Given;

From the image attached below;

Diagonal length, AB=306 ft

Base length, BC=270ft

As triangluar plot is right angled triangle.

According to pythagoras' theorem

AB²=BC²+CA²

Putting the values, we get

Length side of rectangle, BC=√306²-270²

BC=√20736

BC=144ft

Hence, Length of rectangular plot is 144ft

The right angle is inscribed in rectangular plot. The base and height of right angle is one base and height of the rectangular plot. Hence, the lengths of the legs of a right triangle related to the lengths of the sides of a​ rectangle.

Image is attached below

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Answer:

a) x = 2

b) x = 10

c) x = 10/3

d) x = 11/2

e) x = 24

Step-by-step explanation:

a) x = 8-6

x=2

b) x=20/2

     x=10

c) 3x = 9+1

3x=10

x=10/3

d) 2x=11

x=11/2

e) x = 6*4

x=24

Answer: Square

Step-by-step explanation:

A square has 4 parallel sides and has 4 90 degree angles