a student's exponential model has smaller residuals than their quadratic model. what can you infer about their experiment?

Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].

What is the rate of change?

Rate of change (ROC) refers to how quickly something changes over time. It is thus the acceleration or deceleration of changes (i.e., the rate) and not the magnitude of individual changes themselves.

Here given that,

In [tex]2000[/tex], the world population was calculated to be [tex]6,071,675,206[/tex]. The world population increases at a rate of about [tex]1.2[/tex]% annually.

As the population increases [tex]1.2[/tex] % in every year

i.e., [tex]\frac{1.2}{100}=0.012[/tex]

So, the population in the year [tex]2001[/tex] is

[tex]6,071,675,206(0.012)=72860102.5[/tex]

which is the nearest value in the year [tex]2001[/tex].

Since, the population size increases  [tex]72860102.5[/tex] which is the nearest to the [tex]8000000000[/tex].

Hence, the population increases to [tex]72860102.5[/tex] in the year [tex]2001[/tex] which is nearest to the [tex]8000000000[/tex].

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The ratio of the total number of letters to vowels is 5 : 16.

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another value. The sign that is used to represent ratio is :.

Ratio of the total number of letters to vowels - total number of letters : total number of vowels

total number of letters = 16

total number of vowels = 5

Ratio of the total number of letters to vowels - 5 : 16

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There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:

14, 20, 25, 10, 16, 8, 15, 12, 18, 9

We assume the length of paper has an approximately normal distribution.

Sample size = 10

The sample mean for the given data = 14.7

The standard deviation for the given data = 5.04

Critical value is obtained from standard normal distribution at the level of significance 0.05.

The critical value is 1.96.

The 95% confidence interval for the mean length of all term papers is calculated as follows:

P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95

P(11.58 < µ < 17.82) = 0.95

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Answer:

The answer is 85

Step-by-step explanation:

c/100 = 51/60

(c) × (60) = (51) × (100)

60c = 5100

60c/60 = 5100/60

c = 85

Thus, The value of y is 85

Answer:

[tex] \sf \: c = 85[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

Now the value of c will be,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

[tex] \sf \rightarrow \: c = ( \frac{51}{60} ) \times 100[/tex]

[tex] \sf \rightarrow \: c = \frac{(51 \times 100)}{60} [/tex]

[tex] \sf \rightarrow \: c = \frac{5100}{60} [/tex]

[tex] \sf \rightarrow \boxed{ \sf c = 85}[/tex]

Hence, the value of c is 85.

The formula for the volume of a cone is V = 1/3 π[tex]r^{2}[/tex]h  and the dimensions V = 6.28 [tex]r^{2}[/tex] cubic unit

The area or capacity of a cone is determined by its volume. Cones are three-dimensional shapes.

The volume of a cone =  1/3 π[tex]r^{2}[/tex]h cubic units

Where,

‘r’ is the base radius of the cone

‘l’ is the slant height of a cone

‘h’ is the height  of the cone

A).The formula for the volume of a cone is V = 1/3 π[tex]r^{2}[/tex]h

B).find the dimensions that maximize the volume of the cone.

A cone has a slant height of 6.

V = 1/3 π[tex]r^{2}[/tex]h

V = 1/3 *22/7 * 6 *[tex]r^{2}[/tex]

V = 6.28 [tex]r^{2}[/tex] cubic unit.

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Answer:

The map is displaying 600 miles of land.

Step-by-step explanation:

To find the number of miles of land being displayed on the map, you need to multiply the length of the map in inches by the conversion factor, which is the ratio of inches to miles. In this case, the conversion factor is 2 inches per 200 miles.

So, to find the number of miles of land being displayed on the map, you would do the following calculation: 12 inches * (200 miles / 2 inches) = 600 miles.

Answer:

1+i

Step-by-step explanation:

Divide by 1

(1/1+i)

(1+i)

Identify the components of the numbers and add the real and imaginary parts separately

=(1)+(1)i

=(1)+(1)i

=(1+i)

On solving the provided question, we cans ay that by standard deviation, [tex]SE = 0.1590 (approx.)[/tex]

Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.

By sample standard deviation, we mean standard error. Hence, we have that:

Therefore, Standard deviation[tex]= 0.6929891[/tex]

The sample size [tex](n) = 19.[/tex]

Hence:

[tex]SE = 0.1589826.\\ SE = 0.1590 (approx.)[/tex]

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The value of ∠JKI is  107⁰.

What is an angle of a triangle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that ∠JKI = (5x−3)⁰, ∠KIJ=(2x+8)⁰, and ∠IJK=(x−1)⁰.

The sum of all angles of a triangle is 180⁰.

(5x−3)⁰ + (2x+8)⁰ + (x−1)⁰ = 180⁰

(5x + 2x + x) + ( - 3 + 8 -1) = 180

8x + 4 = 180

Subtract 4 from both sides:

8x = 176

x = 22

Putting x = 22 in ∠JKI = (5x−3)⁰:

∠JKI = (5×22 − 3)⁰

∠JKI = 107⁰

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The expression is x-12.

12 less than a number means subtracting 12 from that number.

So, 12 less than 20 is 8, because is 20−12, 12 less than 12 is 0, because it's 12−12, and so on.

But since the number you need to subtract from is unknown, it's a variable, and you can call it as you like, suppose x. So, using the variable we can write an expression that holds for any number, which always means "take 12 away from my number". If your number is x, the expression would be x-12

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Monomial has a degree of 4 in linear equation.

What in mathematics is a linear equation?

The algebraic equation y=mx+b is known as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                       Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let's define some of the vocabulary words so we can understand what is being asked.

trinomial: 3 terms   → each term is separated by a plus or minus sign

                              Example: 5x² + 3x + 2

monomial: 1 term   →  no plus or minus sign exists in the term.

                              Example: 5x²

degree: the largest exponent → it can be in any of the terms.

                              Example: 5x² has a degree of 2

It is possible that a monomial has an exponent greater than that of a trinomial so the answer is NO!

trinomial:   5x² + 3x + 2      has a degree of 2

monomial: 5x⁴                    has a degree of 4

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After 3 hours Dylan and Sam will be exactly 15 miles apart .

In the question ,

it is given that ,

the speed at which Dylan is jogging in east = 4 miles per hour .

the speed at which Sam is jogging in south = 3 miles per hour .

the distance covered by Dylan is = 4t

the distance covered by Sam is = 3t

we have to find the time when they are 15 miles apart .

Since Dylan walks in east and Sam walks in South  , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,

(3t)² + (4t)² = 15²

9t² + 16t² = 225

225 = 25t²

t² = 225/25 = 9

t = 3

Therefore , the time taken will be 3 hours .

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Answer:

ANSWER BELOW

Step-by-step explanation:

Given,

The length of a rectangle =6x

The width of the rectangle=x

84yd=2(6x+x)

84yd=12X+2X

        =6

X=6

6X=6X6=36

Hence the length is 6 and the width is 36

Answer:

book (Y) = 2

magazine (X) = 4

Step-by-step explanation:

4x + Y = 24

y = 2x

All of the above options a) implement an expansion strategy b)attract capital c)reduce tax burdens d)easy entry into an industry e)take advantage of limited liability ,are correct.

A corporation is generally set up to take advantage of limited liability. This means that the owners of the corporation (the shareholders) are not personally responsible for the debts and obligations of the corporation. The other options you have listed are also potential reasons for setting up a corporation, but they are not the primary purpose of a corporation.

An expansion strategy refers to a company's plan for growth and expansion, and setting up a corporation can be one way to implement this strategy. Attracting capital refers to the process of raising funds for a business, and a corporation may be able to attract more capital because it is a separate legal entity that can issue stocks and bonds. Reducing tax burdens refers to the process of minimizing the amount of taxes a business has to pay, and a corporation may be able to do this because it is taxed as a separate entity. Finally, setting up a corporation can also make it easier for a business to enter an industry because it provides a legal framework for the business and can make it easier to raise capital.

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Total 36 storage locations are allocated by the statement declare [tex]a[4,9][/tex] as integer.

The statement declare [tex]A[4,9][/tex] as integer allocates 4 × 9 = 36 storage locations for the array A. Each storage location is capable of holding a single integer value.

In this statement, the array A is declared with two dimensions, 4 and 9. The first dimension, 4, represents the number of rows in the array, and the second dimension, 9, represents the number of columns. This means that the array A has a total of 4 rows and 9 columns, for a total of 4 × 9 = 36 storage locations.

Here's an example of how the array A might be structured in memory:[tex]A[0,0] \ A[0,1] \ A[0,2] \ A[0,3] \ A[0,4] \ A[0,5] \ A[0,6] \ A[0,7] \ A[0,8]\\A[1,0] \ A[1,1] \ A[1,2] \ A[1,3] \ A[1,4] \ A[1,5] \ A[1,6] \ A[1,7] \ A[1,8]\\A[2,0] \ A[2,1] \ A[2,2] \ A[2,3] \ A[2,4] \ A[2,5] \ A[2,6]\ A[2,7] \ A[2,8]\\A[3,0] \ A[3,1] \ A[3,2] \ A[3,3] \ A[3,4] \ A[3,5] \ A[3,6] \ A[3,7] \ A[3,8][/tex]

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The correct B. 495.

A group of k elements can be chosen from a group of n elements in  ways.

n = 12

r = 4

Probability

Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen

nCr = n1 / (n-r)! r1

12C4 = 12! / (12-4)! 4!

12C4 = 12x11x10x9x8! / 8! 4!

12C4 = 11880 / 24

12C4 = 495

The correct B. 495.

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The total cost with sales tax would be $ 96.30

The required absolute value of the given complex number is |-3 + 2i| = √13.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

The complex number is given in the question as:

-3 + 2i

We have to determine the absolute value of the given complex number.

The absolute value of a complex number a+ib is denoted as |a+ib| and is given by √(a²+b²)

As per the given question, we have

⇒ |-3 + 2i| = √((-3)²+2²)

⇒ |-3 + 2i| = √(9 +4)

⇒ |-3 + 2i| = √13

Therefore, the required absolute value of the given complex number is |-3 + 2i| = √13.

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26 points are scored in the fifth game.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

First four games, a netball team scores an average of 31 points per game.

x/4=31

Let x represents four games

x=124

After the fifth game, the average for the first five games is 30

y/5=30

Let y represents five games

y=150

We need to find the number of points scored in fifth game.

x-y

124-150

26

Hence, 26 points are scored in the fifth game.

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Answer:

option c

Step-by-step explanation:

Answer:

[tex]\textsf{b)} \quad \dfrac{(y+3)^2}{25}-\dfrac{(x-1)^2}{15}=1[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of vertical hyperbola}\\\\$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $(h, k\pm a)$ are the vertices. \\\phantom{ww}$\bullet$ $(h\pm b, k)$ are the co-vertices. \\\phantom{ww}$\bullet$ $(h, k\pm c)$ are the foci where $c^2=a^2-b^2$.\\\end{minipage}}[/tex]

Given:

As the x-values of the given center, vertex and focus are the same, the hyperbola is vertical (opening up and down).

Given the center is (1, -3):

Use the vertices formula (h, k±a) to find a:

[tex]\begin{aligned} (h, k \pm a) = (1, -3 \pm a) &= (1, 2)\\\implies -3 \pm a &= 2\\a &= 5\end{aligned}[/tex]

Use the foci formula (h, k±c) to find c:

[tex]\begin{aligned} (h, k \pm c) = (1, -3 \pm c)&=(1, -3 \pm 2\sqrt{10})\\c &= 2 \sqrt{10}\end{aligned}[/tex]

Use the found values of a and c with Pythagoras Theorem to find b²:

[tex]\begin{aligned}c^2 &=a^2+b^2\\\implies (2 \sqrt{10})^2&=5^2+b^2\\40&=25+b^2\\b^2&=15\end{aligned}[/tex]

Therefore:

Substitute the found values into the hyperbola formula to create an equation of the hyperbola with the given parameters:

[tex]\dfrac{(y+3)^2}{25}-\dfrac{(x-1)^2}{15}=1[/tex]

Two or more figures are said to be similar when they have common properties. The value of MP is 18 units.

More than one figure are said to be similar if they have some relatable common properties, either considering their length of sides or measure of their internal angles. But similarity is not the same as congruence.

In the given question, it can be deduced that ΔMNP is similar to ΔQRP. Thus, relating the corresponding sides of the two triangles we have;

[tex]\frac{12}{30}[/tex] = [tex]\frac{5x-2}{11x+1}[/tex]

cross multiply to have

30(5x-2) = 12(11x+1)

150x - 60 = 132x + 12

collect like terms

150x - 132x = 12 + 60

18x = 72

x = 4

So that,

MP = 5x - 2

      = 5(4) - 2

      = 20 -2

MP = 18 units

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Answer:

[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Step-by-step explanation:

We can use the quotient rule:

[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

In this case, u and v both are functions. By applying formula above, we will have:

[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]

Then apply power rule to derive functions, we have to know that:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]

Therefore, we will have:

[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]

Expand the terms in:

[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Hence, that's the answer. You can keep in unfactored form or factored form as you desire!

The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

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The  situations that can be represented by the opposite of -25 are:

-25 can be seen as represention of the given  situations fro the problem, and exploring the given options, we can see that 25 feet below the sea level with that ones balance can be gets reduced by $25.

But when exploring the But the opposite of (-25)  then we can see that 25 feet above the sea level, and in this case the amount will be raised by $25. and the height by 25 feet with the increase in the debt by $25.

Therefore, option B ,C and E are correct.

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missing options:

A. A scuba diver is 25 feet below sea level. B. Leon gets paid $25. C. An airplane descends 25 feet. D. Sara has a $25 debt. E. A bird flies 25 feet above sea level

This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

The probability of getting a specific number of heads in a given number of flips follows a binomial distribution, which describes the probability of getting a certain number of successes in a given number of independent trials. The probability of getting a specific number of heads in ten flips can be calculated using the formula:

P(x heads in n flips) = (n choose x) * p^x * (1-p)^(n-x)

where p is the probability of getting a head on each flip and x is the number of heads.

For example, the probability of getting exactly 3 heads in ten flips is:

P(3 heads in 10 flips) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3) = 0.241

This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

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The polynomial 25x² + 36y²  is the sum of the squares.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, 25x² + 36y² which can be written as,

= 5²x² + 6²y².

= (5x)² + (6y)² it is the sum of the squares, The difference of squares would be (5x)² - (6y)².

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Answer:

[tex]y = \frac{1}{10}x[/tex]

Step-by-step explanation:

⭐ What is slope-intercept form?

First, we need to find the value of "m" using the slope formula.

⭐ What is the slope formula?

Substitute the two coordinates you are given into the slope formula.

[tex]m = \frac{1-2}{10-20}[/tex]

[tex]m = \frac{-1}{-10}[/tex]

[tex]m = \frac{1}{10}[/tex]

Substitute the value of "m" into the slope-intercept form equation.

[tex]y = \frac{1}{10}x + b[/tex]

Next, we need to find the value of "b". To do so, substitute a coordinate that you are given into the equation and solve for "b".

I am going to use (10,1), but you can also use (20,2).

[tex]1 = \frac{1}{10} (10) + b[/tex]

[tex]1 = 1 + b[/tex]

[tex]0 = b[/tex]

Substitute the value of "b" into the slope-intercept form equation.

[tex]y = \frac{1}{10}x[/tex]

On solving the provided question we can say that - 112 child tickets were sold that day

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, finding a way to respond to them has been a major driving force behind the development of mathematics.

Call the number for children and the number for adults to get:

[tex]5.20c+8.50\\ a=1097.60[/tex]

and

a=4c

indicating that there were four times as many adults as youngsters.

Using this value in place of a

into the first equation we get:

[tex]5.2c+8.5(4c)=1097.6\\ 5.2c+34c=1097.6[/tex]

rearranging:[tex]c=1097.639.2=28[/tex]

and so:

[tex]a=4c=4⋅28=112[/tex]

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