write a recursive formula for the given arithmetic sequence, and then find the specified term.a={2,6,10,...}a_1=Answera_n = a_{n-1} + Answera_8 =Answer

Answer:A= -2.50x + 45

Step-by-step explanation:

Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:

\(\huge{\textbf{\textsf{{\color{skyblue}{An}}{\blue{sw}}{\red{er}}{\color{red}{:}}}}}\)

1697 ➳ MDCXCVII

Answer:

MDCXCVII

Step-by-step explanation:

Answer:

Domain { -1,3}

Range { 2,5,6}

Step-by-step explanation:

The domain is the inputs or the x values

Domain { -1,3}

we dont list repeated values  more than once

The range is the output values

Range { 2,5,6}

Answer:

Step-by-step explanation:

domain:{-1, 3}

range:{2, 5, 6}

We can get the rental cost for each movie and each video game is 1.75 &  6.75 respectively by using simultaneous equations.

What is simultaneous equations?

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations.

We have,

First month --- >  rented 3 movies and 5 video games for $39.

Second month --- >  rented 9 movies and 7 video games for $63.

Let's consider,

x = price of each video games

y = price of each movies

Therefore,

              3x + 5y = 39    ..........................(i)

              9x + 7y = 63   ...........................(ii)

Multiplying the first equation by 3 and subtracting with second equation we get,

              9x + 15y = 117    ..........................(iii)

              y = 54 / 8 = 6.75

by putting the the value of y in equation (i),

               3x + 5(6.75) = 39

               3x  = 39 - 33.75 = 5.25

                x = 1.75

By calculating this simultaneous equations we get values of,

                x = 1.75 & y = 6.75

Therefore the rental cost for each movie and each video game is 1.75 &  6.75 respectively.

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Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

Answer:

13/4

Step-by-step explanation:

The lengths for which the area will be less than 175 cm² are less than 25 cm

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

Width = 7 cm

Area = Less than  175 cm²

The formula of area is represented as

Area = Length * Width

Using the above as a guide, we have the following:

Length * Width < 175

substitute the known values in the above equation, so, we have the following representation

Length * 7 < 175

Divide by 7

Length < 25

Hence, the length is less than 25

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Answer:

24 miles....you travel 24 miles per hour

Step-by-step explanation:

you multiply your mph by the amount of hours to get the answer

Answer:

Dividing the current value by the previous value ALWAYS equals 1.05.

Since the growth rate is constant, it is linear.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The relationship is linear when the rate of change is constant. It means the sequence of the dependent variable forms an arithmetic sequence.

We see the the sequence of Projected Value is not arithmetic but geometric sequence with common ratio of 1.05.

It will have equation:

This is therefore exponential.

Answer:

Option B.

Step-by-step explanation:

Irrational number: It can not be expressed in the form of p/q, where p,q are integers and q≠0. For example : \(\sqrt{2},\sqrt{3},2.3456..., \pi \text{ etc}.\)

Money cannot be expressed in square root of a prime number but sometimes we get not recurring non repeating decimal amount. So, budgeting with money has less chances to get an irrational number.

Area of a circle is

\(A=\pi r^2\)

where, r is radius.

It contains \(\pi\) which is an irrational number. So, it is most likely o encounter an irrational number.

Area of square is square of its side. So, it has less chances to get an irrational number.

Buying food that has a cost per pound has less chances to get an irrational number because monitory terms are generally rational.

Therefore, the correct option is B.

Answer:Option

Step-by-step explanation:

The probability that a student is a graduate student given they are a history major is approximately 0.16.

The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.

We are given the following information:

Total number of students who are history major: 463

Total number of graduate students: 261

Number of graduate students who are history major: 73

We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:

P(graduate | history) = P(graduate and history)/P(history)

P(graduate | history) = 73/463

P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)

Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.

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Answer:

Factors=5xy=5,x,y

=7

Step-by-step explanation:

Pls mark as branliest thanks

Step-by-step explanation:

5xy+7

=1(5xy+7)

Factors are 1&5x+7

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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All possible values of r for which this infinite geometric series is defined is the interval (-1,1).

The infinite geometric series is given by:

\(\[2 6r 18r^2 54r^3 \dotsb\]\)

This is a geometric series, so it is defined when the absolute value of the common ratio (r) is less than 1. The common ratio of this series is r, so the series converges when |r| < 1. Mathematically, this can be expressed as follows:

|r| < 1

-1 < r < 1

Therefore, all possible values of r for which this infinite geometric series is defined is the interval (-1,1).

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Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Answer:

53

Step-by-step explanation:

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1 times 2 is equal to 2.

Multiplication is a mathematical operation that combines two numbers (known as "factors") to produce a third number (known as the "product"). It is represented using the symbol "x" or the asterisk (*).

For example, consider the multiplication of the numbers 2 and 3:

2 x 3 = 6

Here, 2 and 3 are the factors, and 6 is the product. Multiplication is a type of arithmetic operation that can be used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

In summary, multiplication is a mathematical operation that combines two numbers to produce a third number, and it is represented using the symbol "x" or the asterisk (*). It is an important operation in mathematics, used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

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Answer:

23.28 hours

Step-by-step explanation:

He earns 5.8 per hour of part-time work. You can find this by doing 87/15
Because we now know that he earns 5.8 per hour we can just do 135/5.8 (23.28) < this is rounding to the nearest hundreth

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively

Given the following functions a(x) = 7x + 10 and b(x) = 12x - 18

Take the sum

(a+b)(x) = a(x) + b(x)

(a+b)(x) = 7x + 10 + 12x - 18

(a+b)(x) = 19x- 8

Take the difference

(a-b)(x) = a(x) - b(x)

(a-b)(x) = 7x + 10 - 12x + 18

(a-b)(x) = -5x + 28

For the composite function a[b(x)].

a(12x- 18) = 7(12x-18) - 10

a[b(x)] = 84x - 126 - 10

a[b(x)] = 84x - 136

Hence the value of the sum, difference and composite function a[b(x)] are 19x - 8, -5x + 28 and 84x - 136 respectively

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Answer:

90

Step-by-step explanation:

since mean = sum of terms / number of terms, we can find the total sum of the tests currently to see how much it needs to be raised

76 * 6 = 456

x = score of the new test

(456 + x)/7 = 78

x =90

Answer:

Step-by-step explanation:

The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).

What is domain?

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

According to question:

In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.

To find the values that make the denominator equal to zero, we can factor it as follows:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.

Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)

The range of a function consists of all possible output values of the function, given the domain of the function.

To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.

As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.

Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.

Range: (-∞, 0) ∪ (0, ∞).

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Answer:

A

I hope this helps

The annual interest rate is 8%

The length of the investment in years is 6 yr.

The periodic interest rate is 2%

The number of periods of the investment periods \(=\frac{24}{\text { periods. }}\)

As per the details share in the above question are as follow,

Given time period of t=5 years

Where the Interest rate of =8 % (Quarterly compounding)

Note: for quarterly compounding n=4

(a) So the annual interest rate will be of 8 %

(b) Further the length of Investment in years 6 years

(C) The Periodic interest rate

\($(\gamma)=\left(\frac{8}{4}\right)=2 \%$\)

(d) Number of periods for investment \($=n t$\)

\(\Rightarrow 4 \times 6=\frac{24}{\text { periods. }}\)

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Answer:

36

Step-by-step explanation:

Do the brackets first:

(7+9)=16

(4×5)=20

Now we add our 2 brackets to get our final answer

16+20=36