an article in the new york times noted that the human population has shown a significant increase in height. when the relationship of height to reproductive success in humans was examined across three decades (1935-1967), height had a positive correlation to the number of children born and the number of surviving children. these observations suggest that

The common ratio and the 1st term will be 2/3 and 81. And the least number of terms for which the sum exceeds 240 will be 11.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The amount of the first 2 terms of a remarkable grouping is 135 and the amount of the third and fourth terms is 60. Then the equations are given below.

a + ar = 136                 ...1

ar² + ar³ = 60

r²(a + ar) = 60               ...2

From equations 1 and 2, then we have

r² x 135 = 60

r² = 60/135

r² = 4/9

r = 2/3

Then the value of 'a' is given as,

a + (2/3)a = 135

a = 81

Then the least number of terms for which the sum exceeds 240 will be given as,

Sₙ > [a₁ (1 - rⁿ)] / (1 - r)

240 > [81(1 - 0.66ⁿ)] / (1 - 0.66)

240 > 243(1 - 0.66ⁿ)

0.9876 > 1 - 0.66ⁿ

0.66ⁿ > 1 - 0.9876

n log 0.66 > log 0.012345

n > 10.57

n = 11

The common ratio and the 1st term will be 2/3 and 81. And the least number of terms for which the sum exceeds 240 will be 11.

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Answer:

-1

Step-by-step explanation:

The number never changes when you divide by 1. So -1/1=-1.

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Answer:

  0.4 m = 40 cm

Step-by-step explanation:

You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.

The scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.

This lets us write a proportion for the height of the model tower:

  [tex]\dfrac{h}{40\text{ m}}=\sqrt[3]{\dfrac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^{-6}}=\boxed{0.40\text{ m}}[/tex]

Logan should make his tower 0.4 meters, or 40 cm high.

Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 and crosses the y- axis at (0, - 7 ) ⇒ c = - 7

that is the y- intercept c = - 7

Answer:

FG≅LJ

GH≅JK

HF≅KL

Step-by-step explanation:

The difference between a set of expected and observed values is known as residual standard deviation, which refers to the standard deviation of the residual values.

In the given question we have to explain the standard deviation of the residual values in the regression output.

Regression analysis is a statistical technique used to demonstrate the relationship between two different variables and to assess how well one variable can be predicted based on the behaviour of another.

The standard deviation of points surrounding a fitted line or the standard error of estimate are other names for residual standard deviation.

The difference between a set of expected and observed values is known as residual standard deviation, which refers to the standard deviation of the residual values.

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a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Now,

Since, The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Let the average distance of Venus from the sun = x

So, We can formulate;

⇒ 57.9 = 3.8 + x/2

Solve for x as;

⇒ 57.9 = 3.8 + x/2

⇒ 57.9 - 3.8 = x/2

⇒ x/2 = 54.1

⇒ x = 54.1 × 2

⇒ x = 108.2

Thus, The average distance of Venus from the sun = 108.2 million kilometers.

Therefore, a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

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Answer:

∴ x = 5

Step-by-step explanation:

(18x)° = 180° - 90° (adjacent angles on a straight line)

  18x = 90

  ∴ x = 5

The solution of the expression -3√7r³-6√7r² is -3√7r²(r+3)

Expression:

An expression also known as the algebraic expression consists of unknown variables, numbers and arithmetic operators.

Given,

Here we have the expression -3√7r³-6√7r²

Now, we have to solve this expression step by step.

In order to solve this expression, we have to write the given expression as,

=> - 3√7r³- 6√7r²

Here the value √7 is common, so we have to take it as the common term and then rewrite the given expression as,

=> √7(-3r³-6r²)

Now, we have to take the number -3, as the common term then we get he expression like the following,

=> -3√7(r³+3r²)

Now we have to take the variable r² as the common term, then we get,

=> -3√7r²(r+3)

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Answer:

E

Step-by-step explanation:

they are equal to each other

https://brainly.com/question/4316749The symbol used to represent the square root of a non-negative number is √ and is called the radical symbol or sign or root symbol and the non-negative square root is called the principal square root.

Every positive real number has two square roots, positive and negative.

For this reason, we use the square root symbol √ to represent the dominant (non-negative) square root. Negative sign before radical −√ for negative square root.

Every nonnegative real number a has a unique nonnegative square root called the principal square root, denoted by √ in which √ is called the root symbol.

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No it is not a right angled triangle.

acc to our question-

Hence, no sides are equal to 90 degrees.

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Answer:

of poor quality

Step-by-step explanation:

it broke after a few days

0.6%  is the probability of getting a king .

What is probability ?

Probability of K from full 52 card pack = 4/52 = 1/13

Probability of A from the remaining 51 cards = 4/51

“And" in probability means you Multiply.

1/13 x 4/51 = 4/663 = 0.6%

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Answer:The answer would be the A

Step-by-step explanation:

Answer:

40x + 20y < 480

Step-by-step explanation:

the inequality: 40x + 20y <(with a line under the < sign)480

Answer:

Step-by-step explanation:

Given:

N₀ = 298 pages

N = 20 pages

You can apply the formula:

Number of days

D = [N₀ / N] + 1 = [298 / 20 ] + 1 =

= [14.9] + 1 = 14 + 1 = 15 day,

where the square brackets are the integer part of the number

If a book has 298 pages, and I read 20 pages a day, then it will take 15 days to read the entire book.

Total pages in the book= 298

Total pages that I daily read= 20

Then it will take 15 days to read the entire book.

The formula for this problem:

The solution to this type of problem can be figured out with the help of unitary method.

20 pages of a book can be read in = 1 day

1 page of a book can be read in = 1/20 days

298 pages of a book can be read in = 1/20×298 days = 14.9 days

But days cannot be 14.9, so it will be 15 days which is the nearest value of 14.9.

15 days it will take to read the entire book.

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Following equation represents a circle with its Centre at the origin is ,

[tex]x^2 +y^2=25[/tex].

What is circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

What does origin mean math?

The origin is the point at which all lines in a coordinate system intersect. When x and y are both equal to zero, the axes intersect. The origin's coordinates are (0, 0).

What is equation?

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

What is Pythagoras theorem?

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, [tex]a^2 + b^2=c^2[/tex], are equal to the squares on the legs.

If we take any point P(x, y) on the circle, then OP = 5 is the radius of the circle.

But OP is also the hypotenuse of the right-angled triangle OPN, formed when we drop a perpendicular from P to the x-axis.

Now in the right-angled triangle, ON = x and NP = y. Thus, using the theorem of Pythagoras,

[tex]x^2 + y^2 = 5^2 = 25[/tex].

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Answer:

1) The new price would be $595

2 )The discount is $105 off

Step-by-step explanation:

1) 700 x 0.85 = 595

2) 700 x 0.15 = 105

Answer:

2.543%

Step-by-step explanation:

295x1.02543=$302.50

295+2.543%=302.50

Answer: Simplification of Fractions.

Step-by-step explanation:

The distance between friend's house and home is 14.263 miles.

What is distance?

The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line.

What is tan?

the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Given,

The distance he covered to west (base) = 17 miles

angle = 24°

tan 24°= perpendicular/base

tan 24° = perpendicular/17

p = 0.836/17

=14.263 miles.

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According to the equation it takes 6 years for the population to reach 1,458 elk.

Equation:

An equation is made up of two expressions connected by an equal sign. For example, 2x – 5 = 16 is an equation.

Given,

A biologist is studying the elk population in a county park. She starts with only 2 elk and observes that the number of elk triples every year.

Here we need to find the equation that will shows the number of years, y, it will take for the population to reach 1,458 elk.

Let us consider n be the number of years take  for the population to reach 1,458 elk.

So, according to the given question, we have written as,

f(n) = 2 x 3ⁿ

Here we know that the value of f(n) = 1458, then the equation is written as,

1458 = 2 x 3ⁿ

When we simplify this, then we get,

3ⁿ = 729

We know that, 729 = 3⁶,

Therefore, it can be written as,

3ⁿ = 3⁶

Therefore, it take 6 years for the population to reach 1,458 elk.

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Answer:

y = 100x + 400

Step-by-step explanation:

What we know:

     - You started with 400

     - You get 100 a week

What we need to find out:

 - The equation or rate to know how much money acquired in specific time

Step 1 ( of 1 ): Equation

-   if you let y represent the total of money you acquire then the equations starts as

y=

-  Then we know that we get 100 a week so let x represent the amount of weeks so

y = 100x

-  Lastly we know that we started with 400 so then we just add that to the equation to make it

y = 100x + 400

A summary measure that is computed to describe a characteristic of an entire population is called a parameter.

Descriptive statistics are those approaches that collect, present, and characterize a set of data in order to accurately describe the different properties of that set of data. A population characteristic can be estimated or a population decision can be made based solely on sample results, according to the definition of inferential statistics.

The totality of the items or things being considered constitutes a population.

The portion of the population that has been chosen for analysis is known as a sample.

A parameter is a summary measure that is computed to describe a characteristic of an entire population.

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The rational roots of the given polynomial f(x)= 20x4 + x3 + 8x2 + x - 12 are x = -4/5 and x = 3/4.

All possible rational roots of f(x) are in the form p/q where p is a factor of constant term and q is the coefficient of leading term. Here, p= -12 and q= 20

Factors of -12= -/+(1,2,3,4,6,12)

Factors of 20= -/+(1,2,4,5,10,20)

So the rational roots = -/+ (1, 2, 3, 4, 6, 12)/ (1, 2, 4, 5, 10, 20)

Solving for x when f(x) = 0,

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

Equating all factors to zero, we get

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x = i, x = -i

Hence, the rational roots are x = 3/4, x = -4/5.

The given question is incomplete, the complete question is

What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?

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Answer:

the slope is 1

Step-by-step explanation:

x1,y1=(3,-1)

x2,y2=(-3,-5)

[tex]m = y2 - y1 \div x2 - x1[/tex]

-5--1/-3-3

-6/-6

m=-6/-6

simplify the fraction -1/-1

since 2 negatives = positive

m=1/1

simplify

m=1

Answer:

9

How I got the Answer:

We have,        

  p = 0.30        

   q = 1 - p = 0.70          

    n = 449

Here,

npq = 4449*0.3*0.7 = 9

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Answer:

[tex]m= -2\frac{1}{13}[/tex]

Step-by-step explanation:

2m-27/3=5m

x3.             x3

2m-27=15m

-2m.     -2m

-27=13m

/13.   /13

-27/13=m

-2 1/13=m

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