⚠️please help I have been stuck for forever⚠️
1. Seats in a theater are curved from the front row to the back. The front row has 15 chairs, the second has 20
and the third has 25, and so on.

a. Write a recursive rule for this series (2 points):

b. Write an explicit rule in simplified form for this series:
Show the steps to simplify. (2 points)

c. Using the explicit formula, find the number of chairs in row 9 (show work) (3 points):


d. The auditorium can hold 18 rows of chairs. Write a sigma notation for this series, and then use either series
formulas to calculate how many chairs can fit in the auditorium. Show all your work. (5 points)

Answer:

Step-by-step explanation:

x-y=7

-3x+9y=-39

Divide the second equation by 3

-x +3y = -13

Add this to the first equation

x-y=7

-x +3y = -13

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

0x +2y = -6

Divide by 2

2y/2 = -6/2

y = -3

Now find x

x-y = 7

x -(-3) = 7

x+3 = 7

Subtract 3 from each side

x = 4

(4,-3)

Or by substitution

x-y=7  

solve for x

x = 7+y

-3x+9y=-39

Substitute y+7 in for x

-3(7+y) +9y = -39

Distribute

-21 -3y +9y = -39

Combine like terms

-21 +6y = -39

Add 21 to each side

6y = -18

Answer:

The system has no real  solutions.

Step-by-step explanation:

9514 1404 393

Answer:

  not generally

Step-by-step explanation:

The basic log function has a vertical asymptote where its argument is zero. It has a positive slope for all positive arguments. It tends to infinity as the argument tends to infinity. There is no horizontal asymptote.

__

A log function can be made part of a larger expression in a way that would give the expression a horizontal asymptote. For example, the function ...

  f(x) = 1/log(x)

has a horizontal asymptote at f(x) = 0. (This asymptote is approached very slowly.)

By using the correlation coefficients, it is found that the two conclusions which the researcher can make from the given data are:

The correlation coefficient is a statistical measure of the strength of a linear relationship among two variables. Its assuming values can range from -1 to 1. If it is positive, the relation is positive, which is, they are direct proportional. And if it is negative, they are inverse proportional. If the absolute value of the correlation coefficient is greater than 0.6, it means the relationship is strong.

In this case, since the correlation is 0.486, thus, the conclusion is that the relation among the variables is positive, that means the higher the proportion of calories from sweeteners in the diets, the higher the mortality. And the other conclusion is that the relationship between the variables is not strong enough.

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Although part of your question is missing, you might be referring to this full question: A researcher found a study relating the mortality rates for women aged 65 to 74, y, to the proportion of calories from sweeteners in their diets, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r squared equals 0.486. Select two conclusions that the researcher can make from this data.

Answer:

slope is -1

y= -1x+3

Step-by-step explanation:

rise over run

slope going down to the right is negative

Answer:

The slope is -1

Answer:

12.5 Km / hour

Step-by-step explanation:

Average speed (s) is calculated as

s = \(\frac{distance}{time}\)

distance covered is 50 Km and time taken is 4 hours, then

s = \(\frac{50}{4}\) = 12.5 Km/ hour

From the slope of the graphs we can say that Robert and Elizabeth will reach the top at the same time , Mei will reach 10 mins after them and Jordan will reach the top in the least time.

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.

The slope of the graphs will give the speed at which the stairs are climbed.

For Elizabeth :

slope (s) = (y2 - y1)/(x2 - x1) = (400 - 0)/(10-0) = 400/ 10 = 40 stairs/ min

For Jayden :

Slope (s) =  (y2 - y1)/(x2 - x1) = (400 - 0)/(10-5) = 80 stairs/ min

Both for Robert and Mei will have the same slope but Mei started her journey 10 minutes late

Slope (s) =  (y2 - y1)/(x2 - x1) = (400 - 0)/(10-0) = 400/ 10 = 40 stairs/ min

From the slope of the graphs we can say that Robert and Elizabeth will reach the top at the same time , Mei will reach 10 mins after them and Jordan will reach the top in the least time.

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Answer:

146.2

Step-by-step explanation:

We have number 1462.

We know that in a number as we go the right once, that value will be 1/10 the values as the left so just move each number to the right once.

We get

146.2

Answer:

x^2 + 10

Step-by-step explanation:

Factors considered for potential aquifers: permeability, porosity, recharge. Avoid areas near contamination or high population density.

Examining the geology of a region for potential useable aquifers involves considering various characteristics and factors. Permeability, the ability of rocks or sediments to transmit water, is a key attribute. Highly permeable formations like sandstone or limestone facilitate water movement, making them favorable for aquifer development. Porosity, the amount of empty space within rocks or sediments, indicates the storage capacity of an aquifer. High porosity allows for greater water storage.

Recharge rates, the rate at which water replenishes the aquifer, are also important. Areas with consistent and sufficient rainfall or access to water sources like rivers and lakes tend to have higher recharge rates, making them suitable for aquifer utilization.

However, it is crucial to consider natural and human factors to determine areas to avoid. Proximity to contamination sources, such as industrial activities or landfills, can pose a risk to the water quality of an aquifer. Additionally, regions with high population density often face increased demands for water, which may lead to excessive groundwater extraction, causing depletion and long-term sustainability concerns.

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The solution for the equations `1/4 = 2x` and `1/4 ÷ x = 2` is `x = 1/8`.

To show that the equations `1/4 = 2x` and `1/4 ÷ x = 2` have the same solution, we need to find the value of x in each equation, then check if the values obtained are equal or not. We will begin by solving each equation.Solving `1/4 = 2x`To find the value of `x` in the equation `1/4 = 2x`, we will isolate `x` by dividing both sides by 2:`1/4 = 2x` (original equation)`1/4 ÷ 2 = 2x ÷ 2` (divide both sides by 2)`1/8 = x`

So the solution for the equation `1/4 = 2x` is `x = 1/8`.Solving `1/4 ÷ x = 2`To find the value of `x` in the equation `1/4 ÷ x = 2`, we will isolate `x` by dividing both sides by `1/4`:`1/4 ÷ x = 2` (original equation)`1/4 ÷ 1/4 ÷ x = 2 ÷ 1/4` (divide both sides by `1/4`)`x = 1/8`

So the solution for the equation `1/4 ÷ x = 2` is `x = 1/8`.Since the solution for each equation is the same (`x = 1/8`), we can conclude that the two equations have the same solution.

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The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.

Given:

To find: Distance of ship from the base of the lighthouse.

Finding:

Let 'x' be the distance of the ship from the base of the lighthouse and θ be the angle of depression.

Then, tanθ = \(\frac{160}{x}\)

=> x = \(\frac{160}{tan26}\)

=> x = \(\frac{160}{0.487}\)

=> x = 328.54m

Hence, The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.

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Answer:

Answer:

21.9

Step-by-step explanation:

Similarity Theorem

15/13=x/19

1.15384615=x/19

19*1.15384615=x

21.9230769=x

Final Answer

21.9

Proof answer

15/13=21.9/19

1.2= 1.2

The stretch of an exponential decay function is y = 2(1/5)ˣ

From the question, we have the following parameters that can be used in our computation:

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

There are 48 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

Explanation: We are given that a standard deck of 52 cards. (a) The first card is an Ace and (b) the second card is not a Queen. In a standard deck of 52 cards, there are four aces. If the first card drawn is an ace, then there are 51 cards left in the deck and 12 cards that are queens. Hence, there are 51 − 12 = 39 cards that are not queens. So, we can say that, There are 4 aces × 39 cards that are not queens = 156 ways to choose two different cards from a standard 52-card deck such that the first card is an Ace and the second card is not a Queen.

However, we have to remove the case where both cards are aces and the second card is a queen. So, we subtract 1 from the previous answer to get, 156 − 1 = 155 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

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Answer:

6 miles

Step-by-step explanation:

To find the miles in an hour, we must found the unit rate. A fraction is a division problem, so we would set this up as a fraction. The numerator is the distance, and the denominator is the time it takes to travel the distance.

10.5/1.75=6

7.5/1.25=

4.5/0.75=

Answer:  6 miles

Step-by-step explanation:

Christy went jogging and covered 4.5 miles in 0.75 hr
and in 1.75 hr she covered 10.5
To find distance she covered in 1 hour = 10.5 - 4.5 (because 1.75 hr - 0.75 hr)

:)

In a nonexperimental method, relationships between variables are studied by making observations or measures of the variables of interest.

Research without either the manipulation of an independent variable, the random assignment of individuals to conditions or orders of conditions, or both, is referred to as non-experimental research.

The non-experimental study is entirely dependent on variables that the researcher has no control over. By whatever means, they cannot manipulate, control, or change the subjects. Thus, all they can do is continue their research while monitoring and interpreting their subjects.

It is safe to assume that a non-experimental research design is used when there is no specific cause-effect study problem and the researcher simply wants to grasp a topic in depth without constraining it with variables. They examine the natural phenomena as they take place.

Therefore, in a nonexperimental method, relationships between variables are studied by observing or measuring the variables of interest.

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Answer:

No, it is not.

Step-by-step explanation:

Functions do not result in a 90 degree corner.  Functions are 100% straight.

Answer:

y= −3 /2 x+ −7 /2

slope= -3/2

Step-by-step explanation:

y−1= −3 /2 (x+3)

y= −3 /2 x+ −7 /2

according to y=mx+b slope intercept form

-3/2 is the slope

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

208

Step-by-step explanation:

8 times 8 +6 times 24=208

Answer:

Step-by-step explanation:

338.33 ft

The Cartesian coordinates corresponding to the polar coordinates 7, 7π/6 are approximately (-3.5, 6.062).

To convert polar coordinates to Cartesian coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the polar coordinates are given as 7, 7π/6.

Plugging these values into the formulas, we have:

x = 7 * cos(7π/6)

y = 7 * sin(7π/6)

To evaluate these trigonometric functions, we need to convert the angle from radians to degrees. The angle 7π/6 is approximately equal to 210 degrees. Using the trigonometric identities, we can rewrite the above equations as:

x = 7 * cos(210°)

y = 7 * sin(210°)

Evaluating the cosine and sine of 210 degrees, we find:

x ≈ 7 * (-0.866) ≈ -3.5

y ≈ 7 * (-0.5) ≈ -3.5

Therefore, the Cartesian coordinates corresponding to the polar coordinates 7, 7π/6 are approximately (-3.5, 6.062).

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The number we should pick near average value is 252 or 253.

In this given scenario, we have 10 players, everyone wagers 100 bucks and everyone picks 0-100. The person who picks to half the average wins the prize. To determine what number we should pick and why, let's start by solving the problem step-by-step.

Step 1: Find the average value of all picks.To find the average, we add up all the picks and divide by the number of players. We have 10 players, so: Sum of all picks = 0 + 1 + 2 + ... + 99 + 100 = 5050

Average value = (sum of all picks) / (number of players)= 5050 / 10= 505

Step 2: Half the average value. To half the average value, we divide it by 2:

Half of average = (average value) / 2= 505 / 2= 252.5

Step 3: Choose the number closest to half the average. Now that we know that the half of the average value is 252.5, we should choose the number closest to it. The person who picks the number closest to 252.5 wins the prize. If we pick a number less than 252.5, we will not win because someone who chose a number greater than 252.5 will win. If we pick a number greater than 252.5, we will not win because someone who chose a number less than 252.5 will win.So, the number we should pick is 252 or 253. Both numbers are equally close to 252.5. If we want to win, we should choose one of these numbers.

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False, system requirements do not serve as benchmarks to measure the overall acceptability.

A system requirement is a configuration that depicts a system's ability or feature to satisfy the customers' genuine requirements.

It is regarded as a "must have" in a system for a software application to run effectively. If these conditions are not met, the system may experience installation and performance problems.

System needs are therefore seen as a requirement for pa systems to periodically access specific software. System requirements can't be used as a primary yardstick to gauge how desirable the finished system will be as a result.

Therefore, this claim is untrue.

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Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Hey there!

1/2(8 - 6y) + 1/5(10y - 25)

DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES

= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)

= 4 - 3y + 2y - 5

COMBINE the LIKE TERMS

= (-3y + 2y) + (4 - 5)

= -3y + 2y + 4 - 5

= -1y - 1

≈ -y - 1

Therefore, your answer is: -y - 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

the x-coordinate of the centroid is (1/2) and the y-coordinate of the centroid is (π/4).

The centroid of the region bounded by the graphs of y = arcsin(x), x = 0, and y = π/2 can be found by calculating the average of the x-coordinate and y-coordinate of the region's points.

To find the x-coordinate of the centroid, we integrate x with respect to y over the given region and divide it by the area of the region. Since the region is bounded by the graphs of y = arcsin(x), x = 0, and y = π/2, the limits of integration for y are from 0 to π/2. Integrating x with respect to y gives us \(x^{2}\)/2.

To find the y-coordinate of the centroid, we integrate y with respect to x over the given region and divide it by the area of the region. The area of the region can be found by integrating y = π/2 with respect to x from 0 to 1, which gives us the area as 1. The integral of y with respect to x over the given region is π/4.

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Answer:

12 to 8, 6 to 4

Step-by-step explanation: