What’s the 69th term of the arithmetic sequence -13, -33, -53

Answer:

In the picture above

Step-by-step explanation:

....

R = 1/3.

a. R = Does not converge
b. R = Cannot be determined without knowing the value of sum.gif
c. R = 1
d. R = 1
e. R = 1/3

To find the radius of convergence, R, of the series, we need to use the ratio test. The series is given by:

sum(n=1 to infinity) of a_n

where a_n is given by:

a_n = x^n * n^43^n

Applying the ratio test, we get:

lim (n → ∞) |a_n+1 / a_n| = lim (n → ∞) |x^(n+1) * (n+1)^43 * 3^(n+1) / (x^n * n^43 * 3^n)|

= lim (n → ∞) |x * (n+1)^43 * 3 / n^43|

= |x| * lim (n → ∞) ((n+1)/n)^43

= |x|

The series converges if the limit is less than 1 and diverges if the limit is greater than 1. Therefore, we need to solve the inequality |x| < 1 to find the radius of convergence, R.

a. If x = infinity, then the series diverges.

b. If x = sum.gif, then the series converges if |sum.gif| < 1. We cannot simplify this expression further without knowing the value of sum.gif.

c. If x = 1, then the series becomes:

sum(n=1 to infinity) of n^43

This is a p-series with p = 43 > 1, which converges. Therefore, R = 1.

d. If x = -1, then the series becomes:

sum(n=1 to infinity) of (-1)^n * n^43

This is an alternating series with decreasing terms. We can apply the alternating series test to show that it converges. Therefore, R = 1.

e. If x = 3, then the series becomes:

sum(n=1 to infinity) of n^43 * 3^n

This is a geometric series with a common ratio r = 3 > 1. Therefore, the series diverges.

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The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Answer:

x=12

Step-by-step explanation:

You have to do 60/5 which is 12
so x=12

Answer:

x=12

Step-by-step explanation:

5x=60

divide both sides by 5

x=12

answer: x=12

Answer:

100

Step-by-step explanation:

before coming to the head we have like 40 bones there

Answer:

40 + 12.5y = vv

vv = the amount of points needed for a free movie ticket
y = Visits to the movie theater

Step-by-step explanation:

40 + 12.5y =vv could be an equation for this

Answer:

c

Step-by-step explanation:

The first equation is for a parabola but with x less than zero, so half a parabola on the negative side.

The second equation is -1*the square root of x. It will always be a negative number since you cant get a negative from a square root.

d and c are similar, but c has the half parabola on the correct side.

Answer:

C.

Step-by-step explanation:

Because when you first graph f(x)={x²+2,x<0} As shown in the first image the line is slanted to 2 in y axis just like Option C in the blue line and when you graph f(x)={-√x, x≥0} As shown in the second image the line is slanted down from 0 in x axis just like Option C in red line

Answer:

Step-by-step explanation:

10 percent of 3000 = 300

3000+300=3300

3300+300=3600

3600+300=3900

interest = 3900-3000

= R900

he will pay R900 interest over 3 years.

i think this is the answer.

Answer:

x374874593893

Step-by-step explanation:

eaddthemalltogethertogethtatjbifmwhumebry38578494029 aso add the m

First part

numerator f cubed g to the power of negative 2

The numerator can be written as

Second part

denorminator h raised to the power of negative 1

The numerator can be written as

combining part one and two

Open parentheses fraction - fraction - close parentheses to the power of 4

This gives

simplifying the expression to remove negative exponent

Simplifying the numerator

simplfying the denorminator

combining simplfied values for numerator and denorminator in the general form we have

Hence, the simplified form of the expression is

a)Approximately 1.76% of adults

b) about 35 people

c)About 12.9% of adults

d)Approximately 106.95

Solution:

a. Approximately 1.76% of adults in the USA have stage 2 high blood pressure, which is a systolic bp of 160 or higher.

b. If you sampled 2000 people, you would expect about 35 people to have a systolic bp greater than 160.

c. About 12.9% of adults in the US qualify for stage 1 high blood pressure, which is specified as systolic bp between 140 and 160.

d. If you are in the 30th percentile for blood pressure among US adults, your systolic bp is approximately 106.95, rounded to two decimal places.

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Answer:

30 degree

Step-by-step explanation:

sum of the interior angles of a hexagon=720degree

one angle of the hexagon=720/6=120degree

one angle of the rhombus=90 degree

therefore, x=120-90=30

Answer:

Set your calculator to degree mode.

\( \tan( \alpha ) = \frac{23}{35} \)

\( \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31\)

The angle of elevation of the sun is about 33°.

Anjelique has travelled further than Jamila because she has travelled 120 kilometres, whereas Jamila has travelled 115 kilometres.

In terms of length, a mile equals 1760 yards or 1.6 kilometres. This is a commonly used unit to determine how far apart two places are. A mile is a unit of measurement for distance that is used all over the world that is equal to 5280 feet, or around 1.609 kilometres.

Another unit of measurement, the kilometre, is made up of 1000 metres (0.62 miles) and is frequently used to determine how far apart two sites are from one another.

1-mile equals 1.609 kilometres.

Given,

Anjelique travels 75 miles = 75×1.6 = 120kms

Jamila travels = 115kms

120kms>115kms

Therefore, Anjelique has travelled further than Jamila.

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The complete question is:

Anjelique travels 75 miles Jamila travels 115 kilometres show that Anjelique travelled further than Jamila.

The method that could be used instead of cross multiplication to solve the equation *3-3x+5 is distributing x + 3 and then 3x + 5 to both sides of the equation.

Instead of using cross multiplication, one alternative method to solve the equation *3-3x+5 is to distribute x + 3 and then 3x + 5 to both sides of the equation.

To explain this method, let's consider the equation step by step:

Original equation: *3-3x+5

Cross multiplication: 5(x+3) = 2(3x+5)

Distributive property: 5x + 15 = 6x + 10

Subtraction property of equality: 5x - 6x = 10 - 15

Simplification: -x = -5

Multiplication property of equality: (-1)(-x) = (-1)(-5)

Simplification: x = 5

Now, instead of cross multiplication, we can distribute x + 3 and then 3x + 5 to both sides of the equation:

Original equation: *3-3x+5

Distributive property: 5(x + 3) = 2(3x + 5)

Expanding the expressions inside the parentheses:

5x + 15 = 6x + 10

Now we can proceed with solving the equation as before:

Subtraction property of equality: 5x - 6x = 10 - 15

Simplification: -x = -5

Multiplication property of equality: (-1)(-x) = (-1)(-5)

Simplification: x = 5

By distributing x + 3 and 3x + 5 to both sides of the equation, we obtain the same result as the original method. This alternative method is another way to solve the equation without using cross multiplication.

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Answer:

The answer is C

Step-by-step explanation:

Answer:

y = 2/5 x - 3.1

Step-by-step explanation:

Slope of the line passing through the points (0, 2) and (5, 4) = (4-2)/(5 - 0) = 2/5

Since required line is parallel to the line passing through the points (0, 2) and (5, 4).

Therefore, slope of required line (m) = 2/5

Required line passes through the point ( 4, - 1.5)

Therefore equation of line in slope point form is given as.

y - (-1.5) = m(x-4)

y + 1.5 = 2/5(x - 4)

5y + 7.5 = 2x - 8

5y = 2x - 8 - 7.5

5y = 2x - 15.5

y = 2/5 x - 3.1

Answer:

am da got lebonne jems haha 23

f(g(x)) simplifies to x/6.

g(f(x)) simplifies to 6x - 15.

To find the composition of functions f(g(x)) and g(f(x)), we substitute the expression for g(x) into f(x) and vice versa.

f(g(x)):

Replace x in f(x) with g(x):

f(g(x)) = f(6/x + 3)

Now, we substitute the expression for g(x) into f(x):

f(g(x)) = f(6/(x) + 3) = 1/(6/(x) + 3 - 3) = 1/(6/(x)) = x/6

Therefore, f(g(x)) simplifies to x/6.

g(f(x)):

Replace x in g(x) with f(x):

g(f(x)) = g(1/(x-3))

Now, we substitute the expression for f(x) into g(x):

g(f(x)) = g(1/(x-3)) = 6/(1/(x-3)) + 3 = 6(x-3) + 3 = 6x - 18 + 3 = 6x - 15

Therefore, g(f(x)) simplifies to 6x - 15.

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The radius of the sphere with a volume of 4,500π cubic inches is 15 inches, not 2,000 inches as the student had incorrectly calculated.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The volume of the sphere is given as 4,500π cubic inches.

The formula for volume of the sphere is -

V= 4/3πr³

Substituting the values in the equation -

4,500π = 4/3πr³

4,500 = 4/3r³

The mistake in the student's calculation is in the step where they simplified 4/3πr³ to 4,500.

To correct this, we need to isolate r³ by dividing both sides by 4/3 -

4,500 = (4/3)r³

4,500 ÷ (4/3) = r³

4,500 × 3/4 = r³

3,375 = r³

Then, we can take the cube root of both sides to find r -

r = ∛3,375 = 15

Therefore, the radius of the sphere is 15 inches.

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Answer:

La ingeniería es la opción más preferida y la contabilidad es la opción menos preferida entre los diferentes estudios.

Step-by-step explanation:

Los resultados obtenidos de la encuesta a estudiantes que siguen diferentes carreras luego de completar su 4 grado en la escuela secundaria. Cuando los estudiantes terminan sus estudios de secundaria, prefieren dedicarse más a la ingeniería. La escala salarial de los ingenieros es alta y también la demanda de ingenieros es alta en el país. La segunda mejor opción para los estudiantes serán los estudios comerciales, luego elegirán medicina, contabilidad y otros estudios. Las opciones están disponibles para que los estudiantes elijan su carrera preferida en la que identifiquen su interés.

Answer:

√104

Step-by-step explanation:

missing side = \(\sqrt{15^2-11^2} = \sqrt{225-121} = \sqrt{104}\)

Answer:

107

Step-by-step explanation:

The pattern is +10

Your finding the 9 term to your going +10 9 times from 27. Which simplifies to +80.

27 + 90 = 107

Answer:

D) Figure M

A) Figure J

Step-by-step explanation:

Answer:

pi/6

got it right on plato

Answer:

4/11

Step-by-step explanation:

4x -9 =2

perform inverse operations

+9 to both sides

4x = 11

divid both sides by 4

x = 4/11

Answer:

x<4 and x>4

Step-by-step explanation:

4x-9<7 or 3x-10>2

Start with 4x-9<7

You want to get the variable alone. Since 9 is negative add it to both sides

4x-9(+9)<7(+9)

4x<16

You have to divide the 4 from both sides for the variable to be alone.

4x(/4)<16/4

x<4

Next 3x-10>2

Get the variable alone.

3x-10(+10)>2(+10)

3x>12

Divide 3 on both sides

3x(/3)>12(/3)

x>4

There are 1287 different ways Ms. Bell can create a 5-Member committee of seniors from her class.

Ms. Bell's mathematics class consists of 6 sophomores, 11 juniors, and 13 seniors. The task is to determine the number of different ways Ms. Bell can create a 5-member committee of seniors, with each senior having an equal chance of being selected.

To solve this problem, we can use combinations. The number of ways to select a committee of 5 seniors from a group of 13 can be calculated using the combination formula:

C(n, k) = n! / (k!(n - k)!)

Where n represents the total number of elements (seniors in this case), and k represents the number of elements to be selected (5 in this case). The exclamation mark denotes the factorial of a number.

Using the combination formula, the number of ways to select a 5-member committee from 13 seniors is:

C(13, 5) = 13! / (5!(13 - 5)!) = 13! / (5! * 8!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 1287

Therefore, there are 1287 different ways Ms. Bell can create a 5-member committee of seniors from her class.

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\(\longrightarrow{\green{a\:=\:2}}\) 

\(\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}\)

➡\(\:4a + 1 = a + 7\)

Combining like terms, we have

➡\(\:4a - a = 7 - 1\)

➡\(\:3a = 6\)

➡\(\:a = \frac{6}{3} \)

➡\(\:a = 2\)

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

➪ \( \: 4 \times 2 + 1 = 2 + 7\)

➪ \( \: 8 + 1 = 9\)

➪ \( \: 9 = 9\)

➪ \( \: L.H.S.=R. H. S\)

Hence verified.

\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}\)

Answer:

C

Step-by-step explanation:

5-10x+25=0

5+25=10x

30=10x

x=3