Tell whether the function shows growth or decay.

Answer:

The correct answer is B.

Its geometric as you are multiplying by -3 each time

Answer:

Step-by-step explanation:

If we pay attention to the sequence, we would observe that [tex]f(n)[/tex] is increasing by a reason of [tex]-3[/tex], because

[tex]12(-3)=-36\\-36(-3)=108\\108(-3)=-324\\-324(-3)=972[/tex]

So, basically, each term is being multiplied by [tex]-3[/tex], that's what makes the sequence, which is a geometric sequence, because it's being built by a factor, that is, a number which multiplies each term.

When you have to deduct if you have a arithmetic sequence or a geometric sequence, you need to observe if such sequence is increasing or decreasing faster. Like this case, you can see that the numbers are increasing rapidly, that means it's built based on a factor, not a difference, because when we use a difference to form a sequence, that will grow slower and it would be an arithmetic sequence.

Therefore, the given sequence is geometric, which reason is -3.

Answer: The length is 10ft, the width is 7ft.

Step-by-step explanation:

Let L be the length

Let w be the width

The equation for the perimeter is:

2L+2w=34

We also know that L=2w-4

So we can insert L=2w-4 into 2L+2w=34

2(2w-4)+2w=34

4w-8+2w=34

6w=42

w=7

If the width is 7, we can insert it into 2L+2w=34 to find out the length

2L+14=34

2L=20

L=10

The width is 7 ft, the length is 10 ft.

The length and width of the rectangle are 10 feet and 7 feet respectively. This is determined by setting up and solving equations based on the given information about the relationship between the length and width and the perimeter of the rectangle.

Given that the length (L) of the rectangle is 4 less than twice the width (W), we can represent this as:

L = 2W - 4

. We also know that the perimeter (P) of the rectangle is 34 feet. The formula for the perimeter of a rectangle is

P = 2L + 2W

. Substituting L in the perimeter equation gives

P = 2(2W - 4) + 2W = 34

. Simplifying the equation leads to

4W - 8 + 2W = 34

, and then

6W = 42

when you add 8 to both sides. Solving for W gives

W = 7 feet

. Substituting W = 7 into the length equation gives

L = 2(7) - 4 = 10 feet

. Therefore, the width and length of the rectangle are 7 feet and 10 feet respectively.

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Step-by-step explanation:

Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

The solution is Option D.

The solutions to the quadratic equation A = x² - 7x + 13 = 0 is given by

x = ( 7 + √3i ) / 2 and x = ( 7 - √3i ) / 2

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² - 7x + 13 = 0   be equation (1)

On simplifying the equation , we get

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ - ( -7 ) ± √ ( ( 49 ) - 4 x ( 13 ) ) ] / 2

On simplifying the equation , we get

x = [ 7 ± √ ( 49 - 52 ) ] / 2

x = [ 7 ± √ ( -3 ) ] / 2

x = ( 7 ± √3i ) / 2

Therefore , the value of x = ( 7 ± √3i ) / 2

Hence ,

The solution to the equation is x = ( 7 + √3i ) / 2 and x = ( 7 - √3i ) / 2

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Answer:

-1.

Step-by-step explanation:

The graph decreases by 5 for every year, so it has a perfect linear dependence of |1|. The graph is also negative, so the correlation coefficient has to be negative.

Answer:

-1

Step-by-step explanation:

The Correlation Coefficient is defined to measure the strength of the relationship between two variables. Different kinds of correlation coefficient exist, each with has their description and own limit of usability and components Value of Correlation Coefficient always lies within -1 to +1.

If Correlation Coefficient has a value -1 then it has an absolute negative correlation, while if the correlation coefficient has a value of +1 it shows an absolute positive correlation. A correlation of value 0.0 shows there is no correlation between the movements of the two variables.

The Correlation coefficient is measured by the Scatter plot or by Pearson Correlation Coefficient. In the Scatter Plot, we plot the graph between these two variables. If both variables are either increases or decrease then there is a Positive Correlation, and its value is positive that is greater than 0 but less or equal to 1 but if one variable increases and other decreases or vice- versa then there is a Negative Correlation and its value is less than zero but greater than or equal to -1. If the value of Correlation coefficient is less than -1 and greater than +1 then we possibly do mistake in calculating values.

The Pearson Correlation coefficient is determined by the covariance of both the variables divided by the product of standard deviation of the given variable.

It is represented by greek letter rho(ρ)

[tex]\rho_{(X,Y)}=\frac{Cov(X,Y)}{\sigma_X\sigma_Y}[/tex]

where,

cov= covariance of variables X and Y

[tex]\sigma_X[/tex] = standard deviation of X

[tex]\sigma_Y[/tex] = standard deviation of Y.

The formula of the Pearson Correlation Coefficient can also be expressed in mean and expectation which is given by,

[tex]\rho_{(X,Y)}=\frac{E(X-\mu _X)(Y-\mu_Y)}{\sigma_X\sigma_Y}[/tex]

where,

[tex]\mu_X[/tex] = mean of X

[tex]\mu_Y[/tex] = mean of Y

E = Expectation.

Here the given graph is a strong negative linear relationship type. It has a perfect negative correlation.

Here, Option A. is incorrect because it is use for strong positive linear relationship

Option B. and C. is not a possible value for Correlation Coefficient.

Therefore, Option D. is correct.

That is, Correlation Coefficient ( r ) is equal to -1.

When one variable increases and other variable decreases, a negative linear relationship exists.

Answer:

The range could be written in inequality form will be [tex]-2500\leq x\leq -100[/tex].

Step-by-step explanation:

Slitsnails live in the deep water. It is given that they live between a depth of 100 ft to 2500 ft.

Let [tex]x[/tex] represents the depth of water from the water surface.

As we go down the water, the depth will be negative.

So, the depth could vary from 100 ft to 2500 ft.

The minimum depth should be 100 ft and the maximum depth is 2500 ft.

Thus, the range could be written in inequality form as,

[tex]-2500\leq x\leq -100[/tex]

In a graph, the inequality can be shown as,

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The inequality representing the range of elevations for Slitsnails is x ≥ 100 and x ≤ 2500. The graph of the inequality shows the range on a number line.

The range of elevations for Slitsnails is from 100ft to 2500ft. To write an inequality, we'll use the variable x to represent the elevation. The inequality can be written as:

x ≥ 100 and x ≤ 2500

To graph this inequality, we'll plot the values on a number line. We'll start at 100 and draw a closed circle to represent that the value is included in the range. Then, we'll draw an arrow to the right to show that the values continue up to 2500, but do not include 2500. The graph will look like:

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Answer:

-16x^9z^12

Step-by-step explanation:

you . multiply the exponents with the three in this type of equation.

Answer:

The slope of the line is 3/4

Step-by-step explanation:

There is a difference of 3 in the y coordinate and 4 for the x coordinate from each exact point.

Answer:

8.9 x 10^3

:D

Step-by-step explanation:

For this case, we must indicate which of the given functions is not defined for[tex]x = 0[/tex]

By definition, we know that:

[tex]f (x) = \sqrt {x}[/tex] has a domain from 0 to infinity.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.

Thus, we observe that:

[tex]y = \sqrt {x-2}[/tex] is not defined, the term inside the root is negative when [tex]x = 0[/tex].

While [tex]y = \sqrt {x + 2}[/tex] if it is defined for [tex]x = 0.[/tex]

[tex]f(x)=\sqrt[3]{x}[/tex], your domain is given by all real numbers.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root.

So, we have:

[tex]y = \sqrt [3] {x-2}[/tex] with x = 0: [tex]y = \sqrt [3] {- 2}[/tex] is defined.

[tex]y = \sqrt [3] {x + 2}[/tex]with x = 0: [tex]y = \sqrt [3] {2}[/tex]in the same way is defined.

Answer:

[tex]y = \sqrt {x-2}[/tex]

Option b

The function that are undefined for (x=0) is  [tex]y = \sqrt[3]{x-2}[/tex] and [tex]y = \sqrt{x-2}[/tex] and this can be determined by putting (x=0) in all the given expressions.

Given :

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

Function 2 - [tex]y = \sqrt{x-2}[/tex]

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

Function 4 - [tex]y = \sqrt{x+2}[/tex]

Evaluate each function at (x = 0) to determine which function is undefined for (x = 0).

Function 1 - [tex]y = \sqrt[3]{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 2 - [tex]y = \sqrt{x-2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{-2}[/tex]

Therefore, it can be concluded that the above function is not defined for (x=0).

Function 3 - [tex]y = \sqrt[3]{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt[3]{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

Function 4 - [tex]y = \sqrt{x+2}[/tex]

put (x = 0) in above function:

[tex]y = \sqrt{2}[/tex]

Therefore, it can be concluded that the above function is defined for (x=0).

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Answer:

distance = 427.5 miles

Step-by-step explanation:

We can determine the distance by multiplying the miles per gallon by the number of gallons.

distance = mpg * gallons

distance = 28.5 mpg * 15 gallons

distance = 427.5 miles

Answer:

427.5 miles of gas

Step-by-step explanation:

This problem will require using multiplication to determine the distance in total.

We can multiply amount of gas car can hold times the miles per gallon to find the total distance.

Create an equation.

amount of gas car can hold * miles per gallon = distance

Solve by inputting numbers.

15 * 28.5 = 427.5

Answer:

3216.99

Step-by-step explanation:

A = 4 [tex]\pi[/tex] [tex]r^{2}[/tex]

d = 2r

A =[tex]\pi[/tex] [tex]d^{2}[/tex]

= [tex]\pi[/tex] * 32^2 = 3216.99  

50 and this is a filler

Answer:

50

Step-by-step explanation:

because each item is worth 2% so 50 items is 100% and 3 items wrong is minus 6%. which is a 94

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\\\text{We have}\ 5x+3y=8\qquad\text{subtract 5x from both sides}\\\\3y=-5x+8\qquad\text{divide both sides by 3}\\\\y=-\dfrac{5}{3}x+\dfrac{8}{3}\to m_1=-\dfrac{5}{3}\\\\\text{Therefore}\ m_2=-\dfrac{1}{-\frac{5}{3}}=\dfrac{3}{5}\\\\Answer:\ \boxed{b.\ \dfrac{3}{5}}[/tex]

--------------------------------------------------------

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\ 3x-5y=10\qquad\text{subtract 3x from both sides}\\\\-5y=-3x+10\qquad\text{divide both sides by (-5)}\\\\y=\dfrac{3}{5}x-2\to m_1=\dfrac{3}{5}\\\\\text{Therefore we have}\ m_2=\dfrac{3}{5}.\\\\Answer:\ \boxed{D.\ y=\dfrac{3}{5}x}[/tex]

Answer:

Answer Left Panel: 3/5 or B

Answer Right Panel: D

Step-by-step explanation:

Left Panel

Right Panel

The slope of a line parallel to another line is the same as the given line.

The set 'S' of natural numbers less than 8 in roster form is written as: S = {1, 2, 3, 4, 5, 6, 7}. Natural numbers start from 1 and exclude 0, negative integers, fractions, and decimals.

In mathematics, when we want to represent a set in roster form, we list all of its elements within braces and separate each element with a comma. So, the set 'S' representing natural numbers less than 8, in roster form, would be written as: S = {1, 2, 3, 4, 5, 6, 7}. Remember, it's important to note that natural numbers start from 1 and extend indefinitely, and they excludes 0 and any negative integers, fractions, or decimals.

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Given

Step 1: They multiplied 3 on both sides of the equation to get rid of the denominator (you can do this because the denominators were the same number, which was 3)

Step 2: They distributed 6 into (x + 2)

Step 3: They added 1 on both sides

Step 4: They subtracted 6x on both sides to get "x" on one side of the equation

Step 5: They divided -4 on both sides to get "x" by itself

Answer:

D. -17/2

Step-by-step explanation:

1/2 - 4 (1/2 + 1)^2

First we evaluate what is inside the parentheses

1/2 - 4  (3/2) ^2

Now we square what is inside the parentheses

1/2 - 4(9/4)

Now multiply

1/2 -9

Get a common denominator  9 = 9 *2/2 = 18/2

1/2 - 18/2

-17/2

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

--------------------------------------------------------------------------------------

[tex]\dfrac{1}{2}-4\left(\dfrac{1}{2}+1\right)^2=\dfrac{1}{2}-4\left(1\dfrac{1}{2}\right)^2=\dfrac{1}{2}-4\left(\dfrac{1\cdot2+1}{2}\right)^2\\\\=\dfrac{1}{2}-4\left(\dfrac{3}{2}\right)^2=\dfrac{1}{2}-4\cdot\dfrac{3^2}{2^2}=\dfrac{1}{2}-4\cdot\dfrac{9}{4}=\dfrac{1}{2}-1\cdot\dfrac{9}{1}\\\\=\dfrac{1}{2}-9=\boxed{-8\dfrac{1}{2}=-\dfrac{8\cdot2+1}{2}=\boxed{-\dfrac{17}{2}}}\to\boxed{D.}[/tex]

Answer:

$.32

Step-by-step explanation:

To find the unit price, we take the cost and divide by the units.  We will take the cost and divide by 128 ounces since that is how many ounces in a gallon.

$5.12 / 128 ounces

$.04 per ounce

I need to find the price of an 8 ounce glass of milk, so I multiply by 8 ounces

$.04 per ounce * 8 ounces = $.32

My 8 ounce glass of mile costs $.32

Answer:

nooooooooooooooooooo

Step-by-step explanation:

if you divide -2 by 6, you get -0.3333333333... and since their negative -2/6 is a bigger number because -0.397 goes more left on the x axis.

Answer: choice B) 70 degrees

Minor arc AB is equal in measure to the central angle BPA, which cuts off the arc in question.

Final answer:

By applying the given formula d = sqrt(3h/2), we find that Addison can see 2.82 miles farther to the horizon than Kaylib, based on their eye-level heights above sea level.

Explanation:

The question asks how much farther Addison can see to the horizon compared to Kaylib based on their different eye-level heights above sea level, using the formula d = sqrt(3h/2). To solve this, we need to first calculate the distance each person can see to the horizon and then find the difference between the two distances.

Let's calculate the distance for Kaylib:
h = 48 ft, so d = sqrt(3 * 48 / 2) = sqrt(72) = 8.49 miles.

Now let's calculate the distance for Addison:
h = 85¹⁄₃ ft, which we convert to a decimal: 85.333 ft, so d = sqrt(3 * 85.333 / 2) = sqrt(128) = 11.31 miles.

The difference between Addison's horizon and Kaylib's is 11.31 miles - 8.49 miles = 2.82 miles.

Addison can see 2.82 miles farther to the horizon than Kaylib.

Answer: B

Step-by-step explanation:

6 cupcakes is 1/4 of 24 ( 24 / 6 = 4).

This means you would need 1/4 the amount of flour.

Divide the amount needed for 24 cups by 4:

15.25 / 4 = 3.8125

Round answer as needed.

Answer:

3.8125 (108g) of flour are required

Step-by-step explanation:

We can use ratio's to solve this problem

432 g                 x  g

------------     =   -----------

24 cupcakes    6 cupcakes

Using cross products

432*6 = 24x

Divide each side by 24

432*6/24 = 24x/24

108 =x

108 grams

If we needed to use 15.25  units? instead

15.25                 x  

------------     =   -----------

24 cupcakes    6 cupcakes

15.25 * 6 = 24x

Dividing by 24 on each side

15.25 *6/24 = 24x/24

3.8125 =x

Answer:

9%

Step-by-step explanation:

1/11 students

1 divided by 11

=0.09090909090909

to convert the decimal to a percentage, multiply 100 to .09

9%

Answer:

how much did the stuff cost to rent per hour

Answer:

Step-by-step explanation:

Final answer:

The second car, starting 1/2 hour late and traveling at 55 miles per hour, will take 2.25 hours to catch up to the first car. This means it will catch up before the first car, traveling at 45 miles per hour, reaches the destination 135 miles away in 3 hours.

Explanation:

The question involves calculating the time it will take for the second car, traveling at an average speed of 55 miles per hour and starting 1/2 hour later, to catch up to the first car, which left on time traveling at an average speed of 45 miles per hour to a destination 135 miles away. To solve this, we need to find when both cars have traveled the same distance.

Finally, since the first car travels at 45 miles per hour, we calculate if it arrives before being caught: Time of travel for the first car to reach 135 miles is 135 miles / 45 miles per hour = 3 hours. Since 2.25 hours (the catch-up time) is less than 3 hours (the travel time to the destination), the second car will indeed catch up to the first car before it arrives at the football game.

Answer:

1.0

Step-by-step explanation:

The answer is 1.0 It is not a tenth but 99 is closer to 100. witch is 1.0 Do you try looking it up. This is a site i used. It is great. It is called calculator soup.

Answer:

So the center is at (20,.05) and the radius is 9

Step-by-step explanation:

The equation of a circle can be written in the form

(x-h) ^2 + (y-k) ^2 = r^2

where (h,k) is the center and r is the radius

Lets write our equation in that form

( x-20)^2 + (y-0.05)^2 =81

( x-20)^2 + (y-0.05)^2 =9^2

So the center is at (20,.05) and the radius is 9

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 20)² + (y - 0.05)² = 81 is in this form

with centre = (20, 0.05) and r = [tex]\sqrt{81}[/tex] = 9

Answer:

The perimeter is 22.

Step-by-step explanation:

If you turn this shape into a rectangle, the perimeter doesn't change.

The width is given, it is 7.5. The height is BC+DE = 3.5

Then the perimeter is twice the width plus twice the height:

7.5*2 + 3.5*2 = 15+7 = 22