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The formula of the sequence based on geometric progression is  2(3/8)ⁿ⁻¹

The term geometric progression is defined as let a, r are real numbers and an infinite sequence of the form{arⁿ⁻¹} is said to be a geometric sequence this one is refers n'th term of the sequence.

Here we have know that the sequence is written as,

=> {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

Here the value of r is calculated as,

=> (3/4) / (2/1) = 3/4 x 1/2 = 3/8

Then the general formula by using the geometric progression is written as,

=> 2 x (3/8)ⁿ⁻¹

Complete Question:

Find the formula for the general term a subscript n of the sequence {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

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Answer:

13 × 21=293

10/100×293=$29.3

[tex]\begin{cases} x-2y=3\\ 2x+4y=6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x-2y=3}\implies x=2y+3 \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{2(\underset{x}{2y+3})+4y=6}\implies 4y+6+4y=6\implies 8y+6=6 \\\\\\ 8y=0\implies y=\cfrac{0}{8}\implies \boxed{y=0}\hspace{5em}\stackrel{2(0)+3}{\boxed{x=3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (3~~,~~0)~\hfill[/tex]

Tom Sullivan's new account balance after all the transactions that has occurred as per the information provided will be $1,580.49.

Unpaid balance = $1,392. 8

Periodic rate = 2.5%

New purchase = $152.87

New Balance = $1,392. 8 + 2.5% + $152.87

A financial institution's account balance is the sum of money it has on hand during the current accounting period. It is the balance carried forward from the previous month plus the net difference between the credits and debits posted in any given accounting cycle.

An account balance offers current and convenient information about how much money you currently have on hand. An account balance offers a convenient way to manage the money coming in and going out while keeping track of all transactions.

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Answer:

Based on the weights assigned to these grades, Emily's weighted average in the class would be 77.6 marks.

10 transactions have occurred in 2 months.

In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.

To create a frequency distribution:

Count the number of occurrences for each value (in this case, transactions).

Group the values into ranges (if applicable).

Tabulate the frequency (number of occurrences) for each value or range.

For this set of numbers, the frequency distribution is:

Transactions | Frequency

6 | 1

7 | 2

8 | 2

9 | 3

10 | 2

So, in 10 months, 10 transactions have occurred in 2 months.

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The greater ratio of boys to students in the class of Mrs. Henderson's class is, 0.67

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Mrs. Henderson has 16 boys in her class of 24 students

Mr. Gregory has 18 boys in his class of 30

Greater ratio = ?

Ratio in Mrs. Henderson =  number of boys/total students

                                         =   16/24

                                         =   2/3

                                         =    0.67

Ratio in Mrs. Gregory =  number of boys/total students

                                    =  18/30

                                    =   3/5

                                    =    0.6

Hence, the ratio is greater in Mrs. Henderson's class  0.67

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Answer:

14.16%

Step-by-step explanation:

[tex]=(\frac{44.27-38}{44.27} )(100)=(\frac{6.27}{44.27} )(100)=\frac{627}{44.27} =14.16[/tex]

Hope this helps

The initial coordinates of the polygon will change by the rule -

(x, y) → (x - 8, y).

Given is on a coordinated plane, polygon GHIJ translates 8 units to the left to form polygon G1 H1 I1 J1.

Since the polygon is shifted to left, this means only the {x} - coordinate will change. So, the coordinates will change as -

(x, y) → (x - 8, y)

Therefore, the initial coordinates of the polygon will change by the rule -

(x, y) → (x - 8, y).

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According to the concept of fraction, the estimated sum of two mixed number is 7 5/9

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts.

Here we know that Grace rounds one number to 7 and the other number to 4.

And here we have to find the number she rounds to 7.

Let us consider that x be the number.

And here we have know that

=> x - 7/4 = 7

=> x = 28/7

=> x = 4

Then the resulting number is calculated as,

=> 4 - 7/4 = 16 -7/4

=> 9/4

Then the rounded number is to 7 is 7 5/9.

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The solution to the inequality is (2, -2)

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

y<-x and 2x+y>2

Express them as equations

So, we have

y = -x and 2x + y = 2

This gives

2x - x = 2

Evaluate

x = 2

Recall that

y = -x

So, we have

y = -2

Hence, the solution is (2, -2)

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The width and height of the model are;

Width of model = 13.5 inches

Height of model = 2.25 inches

A scale model is defined as a physical model that is geometrically similar to an object. Scale models are usually smaller than large prototypes such as vehicles, buildings, or people. However, these scale models may be larger than small prototypes such as anatomical structures or subatomic particles.

Now, we are given that the dimensions of the new medical complex are;

Length = 400 ft

Width = 180 ft

Height = 40 ft

Thus, for a scale model with length of 30 in(2.5 ft) long, the scale factor is; Scale factor = 2.5/400

Thus;

Width of model = 180 * (2.5/400)

= 1.125 ft = 13.5 inches

Height = 30 * (2.5/400)

= 0.1875 ft = 2.25 inches

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The range of the data varies from 30 to 80. The correct answer is 30 < y < 80. The option C is correct

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Given that there is a graph in which the y-axis represents relative humidity and the x-axis represents time.

The range will be the variation of the y value on the graph from minimum to maximum.

The y value varies from 30 to 80 from minimum to maximum respectively. The inequality can be written as 30 < y < 80.

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Answer:

14

Step-by-step explanation:

36 - 8 = 28

28 / 2 = 14

The volume of the cone with mentioned dimensions of height and diameter are 10,048 cubic inches.

The volume of come can be calculated by the formula -

V = πr²h/3, where V represents volume of the cone, r represents radius of the cone and h represents height of the cone. Furthermore, radius is half of the diameter. Hence, calculating radius first.

Radius = 40/2

Performing division on Right Hand Side of the equation

Radius = 20 inches

Keep the values in formula of cone to find the volume of the cone

Volume of the cone = (3.14 × 20² × 24)/3

Performing division on Right Hand Side of the equation

Volume of the cone = 3.14 × 20² × 8

Performing multiplication on Right Hand Side of the equation

Volume of the cone = 10,048 inch³

Thus, the volume of cube is 10,048 cubic inches.

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Logistic regression models the probability of a binary outcome, while CART models segment data into categories. For example, CART is preferable when data has complex interactions, as it can partition data into multiple categories.

Logistic regression and classification and regression trees (CART) are two different machine learning models used for binary classification problems. Logistic regression models the probability of one class or the other based on a linear combination of input variables. This makes it useful for predicting a binary outcome, such as whether a customer will purchase a product or not. On the other hand, CART is a decision tree model that divides data into categories. It uses a tree-like structure to split the data into segments based on the input features. This makes it useful for dealing with data with complex interactions, as it can partition data into multiple categories. For example, a CART model would be preferable to a logistic regression model if there are multiple underlying factors that affect the binary outcome. In this case, a CART model could more accurately identify the categories that are associated with a particular outcome. Overall, CART models are superior for dealing with data with complex interactions, whereas logistic regression is better for simpler data.

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The average speed in kilometers per hour is 34.61 KMPH if an athlete runs 100 meters in 10.4 seconds .

What is speed ?

Speed is a measure of how fast an object is moving or how quickly an action is taking place. It is usually measured in units of distance per unit of time, such as miles per hour (mph) or kilometers per hour (kph).

Given ,

An athlete runs 100 meters in 10.4 seconds.

And we have to find the average speed in kilometers per hour.

So, average speed = total distance / total time taken

= 100 / 10.4

= 1000/104 meters/sec

So, we have to change units from meters/sec to kilometers per hour

So we multiply with 18/5 .

= 1000 / 104  *  18/5

= 200 * 9 / 52

= 1800 / 52

= 34.61 kmph.

Hence, The average speed in kilometers per hour is 34.61 KMPH if an athlete runs 100 meters in 10.4 seconds .

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Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.

An equation in algebra is an equality claim that includes one or more variables or unknowable things.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation.

Tony : d = 108m

Tony walks 108 meters per minute

Mark : (10,1100),(20,2200)

slope = (2200 - 1100) / (20 - 10) = 1100/10 = 110 meters per minute

Therefore, Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.

The complete question is:

Tony writes an equation to represent the distance he walks in meters, d, in relation to the number of minutes he walks, m. d = 108m Mark has created a table to record the number of minutes it took him to walk different distances in meters. Time (minutes) Distance (meters) 10 1,100 20 2,200 40 4,400 Assuming that Tony and Mark both walk at a constant rate, the unit rate for Tony is meters per minute and the unit rate for Mark is meters per minute. On a graph, the line representing Tony’s distance covered with respect to time would be Mark’s line. So, Tony’s walking speed is Mark’s.

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m = (1--4) / (4-8)

m = 5 / -4

m = -1.25

y = mx + c

1 = -1.25(4) + c

1= -5 + c

c = 6

y = -1.25x + 6

The passing score of the student when the standard deviation and mean are given is calculated to be 111.1.

Standard deviation = 17

Mean = 120

Percentage of students failed in the exam = 30%

Let us find Z such that P(Z< (X - 120)/17) = 0.3

By referring the table, the Z value corresponding to 0.3 probability is observed to be -0.525.

This means that (X - 120)/17 = -0.525

(X - 120) = 17 × -0.525

(X - 120) = -8.925

X = 120 - 8.925 = 111.07 ≈ 111.1

Thus, the required passing score is calculated to be 111.1.

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Answer:

option (D) is the correct one ...

CD is about 2.83 in length when C: (-3 , -4) D: (1 , -2) in coordinate geometry.

In coordinate geometry, the distance formula, which is the square root of (x2 - x1)2 + (y2 - y1)2, can be used to determine the length of CD.

In this instance, point C's coordinates are (-3, -4) and point D's coordinates are (1, -2). Using the distance formula with these values as input, we obtain:

√((1 - (-3))^2 + ((-2) - (-4))^2) = √(4 + 4) = √8 = 2.8284271247461903

In simpler terms, you can use the distance formula, which is the square root of the sum of the differences of their x- and y-coordinates squared, to determine the separation between two points in a coordinate plane.

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The slope is of m = 7 and the y-intercept is of b = 10.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by one, y increases by 7, hence the slope m is given as follows:

m = 7.

Hence:

y = 7x + b.

When x = 1, y = 17, hence the intercept b is given as follows:

7 + b = 17

b = 10.

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False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.

aggregate aiming to figure out the amount total number, or time needed. The amount in front of you or being thought about is quite active. the final outcome, its significance, or its import. three accountings: principal, interest, and the third. Word forms include amounts, amounting, and amounted. supple noun How much something is, much you have, the amount that you require or how many you get is its quantity. He needs that much cash to get by.

given

It is true that robo-advisors typically charge less than a traditional financial advisor.

It is true that robo-advisors typically require larger account minimums than a traditional financial advisor.

It is true that robo-advisors automate the investing process using an algorithm.

False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.

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The approximate surface area of the given cylinder is 2010cm^2. The solution has been obtained using area of cylinder.

What is area of cylinder?

The entire area a cylinder occupies in three dimensions is known as the cylinder's area. The combined areas of the two circular bases and the curving surface make up the cylinder's surface area. In right cylinders, the axis line creates a right angle to the base, and the two circular bases are perfectly over one another. It is referred to as an oblique cylinder if one of the circular bases is misaligned and the axis does not make a right angle with the base.

We are given radius(r) as 10cm and height(h) as 22cm.

We know that area of cylinder (A) = 2πrh + 2πr^2

So, using this, we get

⇒A = 2*3.14*10*22 + 2*3.14*10*10

⇒A = 1381.6 + 628

⇒A = 2009.6 = 2010cm^2

Hence, the approximate surface area of the given cylinder is 2010cm^2.

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As per the Pythagoras theorem, the width of the farmer's field  is 74.83 meters.

In math the term Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

The general form of the Pythagoras theorem is written as,

=> hypotenuse² = opposite side² + adjacent side²

Here we have know that a farmer is tilling his rectangular field.

Where the known length of the field is 54 meters and distance between opposite corners is 90 meters.

As we all know that here we have here is a triangle.

And then here we need to use Pythagorean Theorem is calculated as,

=> 50² + w² = 90²

When we simplify this one then we get,

=> 2500 + w² = 8100

=> w² = 5600

=> w = 74.83

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If 11 is Subtracted from both sides, the resulting inequality is 9 > -4

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

Initially, you have 11 > −2

If you subtract 11 from both sides, you will have:

11 -2 > −2-2

9 > -4

Thus, the resulting inequality will be 9 > -4

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Answer: The estimated population of smallmouth bass in lake clay can be calculated using the Lincoln-Petersen index.

This method is based on the idea that the proportion of tagged fish among all the fish caught will be proportional to the proportion of the total population that was tagged.

Formula: N = (C1 * N1) / (C2 - 1)

where N is the estimated population, C1 is the total number of fish caught, N1 is the number of tagged fish caught, and C2 is the number of tagged fish caught among all fish caught.

In this case:

C1 = 175 (total number of smallmouth bass caught)

N1 = 50 (number of smallmouth bass initially tagged)

C2 = 7 (number of tagged smallmouth bass caught among all fish caught)

So, the estimated population of smallmouth bass in Lake clay is:

N = (C1 * N1) / (C2 - 1) = (175 * 50) / (7-1) = 8750

Therefore, the estimated population of smallmouth bass in Lake clay is 8750.

Step-by-step explanation:

The average salary of xyz university = $138330

The average salary of abc university  is $115275 as provided in the question and also mentioned condition on the average salary of xyz university.

given that the average salary of xyz universtiy is greater than abc univeresity by 20% of the average salary of abc university.

so 20% of average salary of abc university = 0.2 * 115275 = 23055

so the average slary of xyz university is 23055 greater than average slary of abc university

so the avergae salary of xyz university is given by:

= 115275 + 23055

=> 138330

so the average salary of xyz university = $138330

To know more about  The average salary of xyz university = $138330

The average salary of abc university  is $115275

given that the average salary of xyz universtiy is greater than abc univeresity by 20% of the average salary of abc university.

so 20% of average salary of abc university = 0.2 * 115275 = 23055

so the average slary of xyz university is 23055 greater than average slary of abc university

so the avergae salary of xyz university is given by:

= 115275 + 23055

=> 138330

so the average salary of xyz university = $138330

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Complete question :

xyz university claims that their graduates earn more than abc university graduates on average. the average salary of abc university as advertised on their website is $115,275. Find the average salary of xyz university given that the difference betwwen the salary is 20 % of avergae salary of abc university.

Therefore $138330 is the average income at xyz university.

According to the information in the question and the conditions on the average pay at xyz university,

the average salary at ABC University = $115275.

the average income at xyz University = 20% higher than the average at ABC University.

,20% of ABC University's average income = 0.2 x 115275,

= 23055.

The average pay at XYZ University is = 115275 + 23055

= 138330

The xyz university's average income is $138330.

the average pay at ABC University = $115275

20% of ABC University's average income = 0.2x115275

= 23055.

the average pay at XYZ University = 115275 + 23055

= 138330

Therefore $138330 is the average income at xyz university.

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Complete question :

xyz university claims that their graduates earn more than abc university graduates on average. the average salary of abc university as advertised on their website is $115,275. Find the average salary of xyz university given that the difference betwwen the salary is 20 % of avergae salary of abc university.