the 41st term of the sequence 25,27.5,30,32.5... is

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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The table of integrals can be a useful tool for simplifying the integration process, but it's important to have a solid understanding of calculus concepts in order to use it effectively.

The table of integrals is a tool used in calculus to simplify the process of finding antiderivatives. It lists various functions and their corresponding antiderivatives, or integrals.

To use the table of integrals, you first need to identify the function you are trying to integrate. Then, find a similar function in the table and use the corresponding antiderivative to solve your integral.

It's important to note that not all functions have a corresponding antiderivative listed in the table, and in those cases, other integration techniques must be used.

Additionally, it's always a good idea to double check your work and make sure the answer makes sense in the context of the original problem.

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If we use the table of integrals, the solution would be In | tan(x+7) + sec(x+7)|+C. Option A

Using the table of integral, we say

∫ (1/cos(x +7)) dx ⇒ ∫sec (x+7) dx

u = x+7   ⇒ du = dx

= ∫sec (u) du

Expand the fraction by tan (u) + sec (u)

= ∫(sec(u) (tan(u) + sec (u))/ tan (u) + sec (u)

= ∫((sec(u) tan(u) + sec²(u))/ (tan (u) + sec (u))) du

Substitute v= tan(u) + sec (u) ⇒ dv = (sec(u) tan(u) + sec²(u))du

= ∫(i/v)dv

= In(v)

Undo substitution v = tan(u) + sec(u)

=In(tan(u) + sec(u))

= In(tan(x+7) + sec(x +7))

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Answer: g=1.2

Step-by-step explanation:

Answer:

I don't get what you're asking for

Step-by-step explanation:

I don't know.

Answer:

1/3a

Step-by-step explanation:

\( \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} \)

The input that would give an output value of -1/3 is 19

A linear equation is an equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The table of values that completes the question is added as an attachment

A system of linear equations is a collection of at least two linear equations.

In this case, the linear equation is given as

y = -1/3x + 7

From the complete question, the output value is given as:

y = 2/3

Substitute y = 2/3 in y = -1/3x + 7

2/3 = -1/3 * x + 7

Subtract 7 from both sides of the equation

-1/3 * x = 2/3 - 7

Take the LCM

-1/3 * x = (2 - 7 * 3)/3

Evaluate the product

-1/3 * x = (2 - 21)/3

Evaluate the difference

-1/3 * x = -19/3

Multiply both sides by -3

x = 19

Hence, the input that would give an output value of -1/3 is 19

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Answer:

answer is 19

Step-by-step explanation:

If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

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The values will be Loan amount=$186900, When simple interest is 6% then monthly payment=$1453.66 per month, When simple interest is 7% monthly payment=$1609.4 per month

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.

Simple interest formula is given as:

SI=P*R*T/100

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

In order to calculate the total amount, the following formula is used:

Amount (A) = Principal (P) + Simple Interest (SI)

Now,

Initial amount=$237000

Down-payment=20%=20/100*237000=$47400

Amount left=237000-47400=$186900

So, Loan amount=$186900

For interest rate=6%

Total amount=186900+186900*6*30/100

=186900+336420

Total amount=$523320

Therefore, monthly payment=523320/360

monthly payment=$1453.66 per month

For interest rate=7%

Total amount=186900+186900*7*30/100

=186900+392490

Total amount=$579390

Therefore, monthly payment=579390/360

monthly payment=$1609.4 per month

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Answer:

1341.75

Step-by-step explanation:

I did the math :)

The guy above me is correct

Answer:

1) Ninety-six and two hundred forty one thousandths.

2) One hundred five and thirty-six hundredths.

3) Seven and four tenths.

4) Eighty four and twelve hundredths.

5) Five and seventy-five hundredths.

Step-by-step explanation:

Example:

123.456

1 is in the hundreds place

2 is in the tens place

3 is in the ones place

4 is in the tenths place

5 is in the hundredths place

6 is in the thousandths place

One hundred twenty three and four hundred fifty-six thousandths.

The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.

Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.

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Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

Answer:

p = 4.5

Step-by-step explanation:

0.5p - 3.45 = -1.2.

0.5p = -1.2 + 3.45

0.5p = 2.25

0.5p/0.5 = 2.25/0.5

p = 4.5

therefore p is equal to 4.5

Answer:

25 sodas if the type of soda chosen is cherry sodas

Answer:

\((c,b) are the coordinates of N\)

Step-by-step explanation:

as N is the mid-point of QR

BY USING MID-POINT FORMULA

\(N(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})\)

PUTTING THE VALUES OF COORDINATES

\(N(x,y)=(\frac{0+2c}{2},\frac{2b+0}{2})\)

\(N(x,y)=(\frac{2c}{2},\frac{2b}{2})\)

\(N(x,y)=(c,b) are the coordinates\)

O HOPE THIS WILL HELP YOU :)

1. 8^3 * 8^2, 8^5, and (2^3)^5

2. 6^9, and 6^5 x 6^4

Answer:

8+2√6x / 8-3x

Step-by-step explanation:

yes

Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

Answer:

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Step-by-step explanation:

A binomial is a polynomial with 2 terms and trinomial is a term with 3 terms.

Given

\((4x+3)\\and\\(2x^2-5x-3)\)

Distributive property can be used to find the result.

Writing mathematically

\((4x+3)(2x^2-5x-3)\\= 4x(2x^2-5x-3)+3(2x^2-5x-3)\\= 8x^3-40x^2-12x+6x^2-15x-9\)

Combining alike terms

\(= 8x^3-40x^2+6x^2-12x-15x-9\\= 8x^2-34x^2-27x-9\)

Hence,

The product of given binomial and trinomial is:

\(8x^3-34x^2-27x-9\)

Answer:

y-5=1/6(x-1)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-5)/(-5-1)=-1/-6=1/6

slope is 1/6

y-y1=m(x-x1)

y-5=1/6(x-1)

The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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At confidence, how large a sample should be taken to obtain a margin of error for the estimation of a population proportion? We now assume that past data are not available for developing a planning value for

Preliminary estimate for proportion (Not Known) is equal to 0.5

Margin of error = E = 0.03

Level of significance = 1-0.99 = 0.01

Z critical value is considered as (by using Z table) = 2.576

So, the sample size formula is taken as

n = [p(1 – p)]\(\left[Z/E]^{2}\)

=[0.5*(1-0.5)] [2.576/0.03]\(^{2}\)

=1,843.03                    

Hence, the sample size is approximately will be 1,844

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Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Answer:

The answer is "1.6 and \(\frac{11}{12}\)".

Step-by-step explanation:

The joint pdf by x and y

\(1< x<2\\ 0< x< 1\)

In point a:

\(\to K \int^1_{y=0} \int^2_{x=1}  (2y - \frac{x}{4}) dx, dy =1\\\\ \to k \int^{1}_{y=0} 2y - \frac{x^2}{8} \int^{2}_{1} dy=1\\\\\to k \ \ y^2 \int^1_{0} - \frac{1}{8} (3) =1 \\\\ \to k \ (1-\frac{3}{8}) =1\\\\\to k= \frac{8}{5}\\\\\)

       \(= 1.6\)

In point b:

In the original pdf of x

\(\to fx(x)= k \int^{1}_{y=0} (2y-\frac{x}{4}) dy =k\)

\(= k \int^{2}_{1} (x-\frac{x^2}{4}) dx =k\\\\= k \frac{x^2}{2} - \frac{x^3}{12})^2_{1} =k\\\\= k \frac{1}{2} \times 3 - \frac{1}{12} \times 7 =k \\\\ =\frac{3}{2} - \frac{7}{12}\\\\= \frac{11}{12}\)

Answer:

The correct answer is C, Graph D.

x^2 - 4x + 4 = (x - 2)^2.

Answer:

it is 6(y-2)

Step-by-step explanation:

Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

Answer:

number a should be half of 82 which is 41

for question b is two times 26 which is 52

The number of items must be made for the average cost to fall to $5 wil be; 900.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

We are given that function = 40x +700 represents the average cost (in dollars) of making items.

Then the item made for function average cost to fall to $5.

= 40x + 700

= 40(5) + 700

= 200 + 700

= 900

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Step-by-step explanation:

What do you think would happen to the median if we included students

from grades 10-12