WILL GIVE BRAINLIEST : Please calculate the following:

How many jelly beans fit in a one quart jar?

How many chips are in a batch of chocolate chip cookies?

Write out your calculations.

To determine whether the sequence converges or diverges, we can use the ratio test:

lim n→[infinity] |(4 + 9(n+1)^2)/(n+1 + 7(n+1)^2) * (n + 7n^2)/(4 + 9n^2)|

= lim n→[infinity] |(4 + 9(n+1)^2)(n + 7n^2)/(n+1 + 7(n+1)^2)(4 + 9n^2)|

= lim n→[infinity] |(36n^3 + 85n^2 + 36n + 4)/(63n^3 + 98n^2 + 35n + 7)|

= lim n→[infinity] |(36/n^2 + 85/n^3 + 36/n^4 + 4/n^5)/(63/n^2 + 98/n^3 + 35/n^4 + 7/n^5)|

= 36/63

= 4/7

Since the limit of the ratio is less than 1, the series converges by the ratio test. To find the limit, we can use algebraic manipulation:

an = (4 + 9n^2) / (n + 7n^2)
= (4/n + 9n) / (1 + 7/n)

As n approaches infinity, both (4/n) and (7/n) approach zero, so we can simplify:

lim n→[infinity] an = lim n→[infinity] (9n) / (1 + 7/n)

= lim n→[infinity] (9n^2) / (n + 7)

= lim n→[infinity] (9)

= 9

Therefore, the sequence converges to 9.

To learn more about sequence visit:

brainly.com/question/30262438

#SPJ11

The sequence with nth term, \(a_n = \frac{ 4 + 9n² }{n + 7n²}\) is convergent sequence because the limit of sequence ( n→∞ ), \(\lim_{n→∞}a_n = \frac{9}{7} \\ \) is exits.

A sequence is a list of elements (usually numbers) that exhibits a particular order. Each element of sequence is called term.

Convergence of a sequence: We apply a limit at infinity when determining the convergence of a sequence \(b_n\). A limit at infinity is a limit of the form,\(\lim_{n→∞} f(n)\\ \), and we have to evaluate, \(\lim_{n→∞}b_n = L \\ \), to know the convergence of bn. If L exists, then the sequence is said to be convergent. We have a sequence with nᵗʰ term, \(a_n = \frac{ 4 + 9n² }{n + 7n²}\)

We have to check whether it is convergent or divergent. So, consider

\(\lim_{n→∞}a_n = \lim_{n→∞}\frac{ 4 + 9n² }{n + 7n²} \\ \)

if we apply n→∞ then we get an undetermined form (∞/∞). So, using the L'Hospital rule, \(= \lim_{n→∞ }\frac{ \frac{d(4 + 9n²)}{dn }}{\frac{ d(n + 7n²)}{dn}} \\ \)

\(= \lim_{n→∞ } \frac{18n }{1 + 14n}\\ \)

\(= \lim_{n→∞ } \frac{18 }{\frac{1}{n} + 14} \\ \)

\(= \frac{18}{14}\)

\(= \frac{9}{7}\)

= L > 0

That L is exist, so it is a convergent sequence. Hence, sequence \(a_n\) is convergent .

For more information about convergent sequence, visit:

https://brainly.com/question/30894178

#SPJ4

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

For such more question on interest

https://brainly.com/question/25720319

#SPJ8

She sampled 25 patients and obtained a sample average of 179.1 minutes. The null hypothesis (H0) states that the true population mean is equal to 180 minutes.

In hypothesis testing, Stephanie first sets up the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, H0: μ = 180, where μ represents the population mean of exercise minutes per week. The alternative hypothesis Ha would be H1: μ < 180, indicating that the average exercise time is less than 180 minutes.

Stephanie then collects a sample of 25 patients and calculates the sample mean, which is found to be 179.1 minutes. To determine if this sample mean is significantly different from the hypothesized population mean, she performs a hypothesis test using the appropriate statistical method, such as a t-test.

Based on the sample mean and assuming the null hypothesis is true, Stephanie can calculate the test statistic and corresponding p-value. If the p-value is less than the significance level (e.g., α = 0.05), she would reject the null hypothesis in favor of the alternative hypothesis. This would imply that there is enough evidence to support Stephanie's claim that her patients get less than 180 minutes of exercise per week, on average.

However, if the p-value is greater than the significance level, Stephanie would fail to reject the null hypothesis. In this case, there would not be sufficient evidence to conclude that the average exercise time is significantly less than 180 minutes. It's important to note that the conclusion of the hypothesis test is based on the calculated p-value and the chosen significance level.

Learn more about null hypothesis here:

https://brainly.com/question/19263925

#SPJ11

Answer:

x=16

Step-by-step explanation:

3*4=12

4*4=16

Answer:

52

Step-by-step explanation:

12-3n=-7n-4(n+5)

Step 1: distribute

12-3n=-7n-4n-20

Step 2: Combine like terms

12-3n=-11n-20

Step 3: Move N to one side

12-3n=-11n-20

  +11n +11n

12+8n=-20

Step 4: Get normal numbers to the other side

12+8n=-20

-12         -12

8n=-32

Step 5: Take away the number infront of N by dividing each side by the number of Ns

8n=-32

/8     /8

n= -4

Step 6: Plug N into: 32-5n

32-5(-4)

Step 7: Get rid of parenthesis by multiplying. Negative times Negative is positive.

32+20

Step 8: Finish the problem

Answer is 52

The system Ax = b has 2 free variables.

Given that A is a 5x7 matrix, and the transformation x → Ax is onto, we can determine the number of free variables in the system Ax = b.
Identify the dimensions of the matrix A:

A is a 5x7 matrix, which means it has 5 rows and 7 columns.
Determine the transformation type:

Since the transformation x → Ax is onto, it implies that every element in the codomain \((R^5)\) has a corresponding element in the domain\((R^7)\).

In other words, the system Ax = b has a solution for every b in \(R^5.\)
Determine the rank of matrix A:

Since the transformation is onto, the rank of A must be equal to the number of rows in the codomain, which is 5.
Calculate the number of free variables:

The number of free variables is the difference between the total number of columns in A and the rank of A.

In this case, it's 7 columns minus 5 (the rank of A).
Number of free variables = 7 - 5 = 2.

For similar question on matrix.

https://brainly.com/question/1279486

#SPJ11

we can use survivorship to make judgements in following ways:

1. Life expectancy

2. Reproductive strategies

3. Population growth

Survivorship curves are graphical representations of the survival rates of individuals in a population over time. They are a useful tool for understanding and predicting the life expectancy of a population, as well as the reproductive strategies that a species employs.

Here are some ways in which survivorship curves can be used to make judgments:

- Life expectancy: The shape of a survivorship curve can give us an idea of the typical lifespan of individuals in a population. If the curve shows a steep decline in survival rates early in life, this suggests that many individuals are dying at a young age, indicating a shorter average lifespan. On the other hand, if the curve shows a gradual decline in survival rates over time, this suggests that individuals are living longer on average.

- Reproductive strategies: Survivorship curves can also provide information about the reproductive strategies employed by a species. Species that have a high survival rate early in life tend to produce fewer offspring, but invest more resources in each individual to ensure its survival. Species with a lower survival rate early in life tend to produce more offspring, but invest fewer resources in each individual.

- Population growth: By examining the shape of a survivorship curve, we can make judgments about the future growth or decline of a population. If the curve shows a steep decline in survival rates later in life, this suggests that the population is aging and may be in decline. If the curve shows a elatively constant rate of decline over time, this suggests that the population is stable.

In summary, survivorship curves can be a useful tool for making judgments about the lifespan, reproductive strategies, and future growth of populations. By analyzing these curves, we can gain insights into the dynamics of different populations and make more informed decisions about how to manage and conserve them.

To know more about Survivorship:

https://brainly.com/question/14140061

#SPJ11

The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

for such more question on  net profit

https://brainly.com/question/4177260

#SPJ8

The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.

To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).

First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.

Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.

Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:

a * a^-1 ≡ 1 (mod pq)

Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:

a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)

Now, we can use the Chinese Remainder Theorem to combine these congruences and get:

a^(p-1)(q-1) ≡ 1 (mod pq)

Therefore, we know that the order of a must divide (p-1)(q-1).

To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).

Assume for contradiction that there exists such a k. Then, we have:

a^k ≡ 1 (mod pq)

This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.

Know more about prime here:

https://brainly.com/question/20532807

#SPJ11

The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.

To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).

First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.

Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.

Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:

a * a^-1 ≡ 1 (mod pq)

Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:

a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)

Now, we can use the Chinese Remainder Theorem to combine these congruences and get:

a^(p-1)(q-1) ≡ 1 (mod pq)

Therefore, we know that the order of a must divide (p-1)(q-1).

To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).

Assume for contradiction that there exists such a k. Then, we have:

a^k ≡ 1 (mod pq)

This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.

Know more about prime here:

https://brainly.com/question/20532807

#SPJ11

Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

7(2x - 5) = 21

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 21 does indeed equal 21.

∴ x = 4 is the solution to the equation.

Answer:

(1.5,2.5) I think

Step-by-step explanation:

I put it into demos

In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.

As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.

Learn more about speed here:

https://brainly.com/question/13263542

#SPJ11

Answer:

B

Step-by-step explanation:

because in this question

ABCD are exactly the same formula

but only B is the standard form

Answer:

Step-by-step explanation:

Given

Factors to form the Polynomial

Standard Form (on multiplying)

The correct statement describing step 3 is:

C. Adjust the width of the compass to BQ, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.

Correct option is C.

In the given construction,

step 1 involves drawing an arc from point Q to intersect the sides PQ and QR at points A and B, respectively.

Step 2 involves drawing a segment NT and using the same width of the compass to draw an arc from point N to intersect the segment NT at point X.

To continue the construction and construct an angle MNT congruent to angle PQR,

step 3 requires adjusting the width of the compass to BQ. This means the compass should be set to the distance between points B and Q. Then, from point X, an arc is drawn that intersects the arc drawn from N at a point Y.

By completing this step, the construction creates an angle MNT that is congruent to the given angle PQR.

Correct option is C.

For more questions on intersects

https://brainly.com/question/28744045

#SPJ8

Answer:

They look similar but their not

Step-by-step explanation:

because of their length and

The first triangle is a Scalene because all the side are different and

The second triangle is a isosceles because it has to side of equal length.

Answer:

the ansewr is b

Step-by-step explanation:

Answer: Rs 1469

Step-by-step explanation:

Coat of item = RS 1300

Value added tax = 13%

The price of the item will then be calculated as:

= 1300 + (1300 × 13%)

= 1300 + (1300 × 0.13)

= 1300 + 169

= Rs 1469

9514 1404 393

Answer:

  -8x +12

Step-by-step explanation:

The distributive property can help you simplify the product.

  (4)(-2x +3) = (4)(-2x) +(4)(3) = -8x +12

Answer:

13

Step-by-step explanation:

3|2(2)-9|-2

First evaluate inside the absolute value

3|4-9|-2

3|-5|-2

Taking the absolute value of -5

3*5-2

Multiply

15 -2

13

Steps to solve:

3|2(2) - 9| - 2

3|4 - 9| - 2

3|-5| - 2

3(5) - 2

15 - 2

13

Best of Luck!

Answer:

C

Step-by-step explanation:

f(x) = x - 2

f(2) = (2) - 2

f(2) = 0

A + B are wrong cuz..

f(-2) = -2 - 2

f(-2) = -4

Answer:

acute

triangle

Step-by-step explanation:

Answer:

acute

triangle

Step-by-step explanation:

Answer is given below in picture

I hope it helps.

Answer:

\(x=3\\y=4\)

OR

\((3,4)\)

Step-by-step explanation:

The solution of the given system of equations is (3, 4).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y = 2x-2 ------(i) and y = -3x+13 ------(ii).

From equation (i) and (ii), we have

2x-2=-3x+13

2x+3x=13+2

5x=15

x=3

Substitute x=3 in equation (i), we get

y=2(3)-2

y= 4

So, the solution is (3, 4)

Therefore, the solution of the given system of equations is (3, 4).

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ3

Answer:

Step-by-step explanation:

The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.

To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).

The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.

The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.

The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.

An answer is- More information is needed before t can be found.  So, option(D) is the correct answer.

Here initial rotation speed is given, the final rotation speed is given, and the asking for time( in a sec) is.

If we use,

A) θ=θ0+ω0t+(1/2)αt2

For this equation, we don't have any details about the value of angular displacement and angular acceleration, so it is not useful.

B) We use,

ω=ω0+αt

For this equation, we don't have any details about angular acceleration, so it is not useful.

C) We know that,

ω2=ω02+2α(θ−θ0)

In this equation, time is not included, hence it is not useful.

D) So, more information is needed.

Thus, option (D) is the correct answer.

Read more about speed:

https://brainly.com/question/13943409

#SPJ4

The complete question is:

Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?

A) θ=θ0+ω0t+(1/2)αt2

B) ω=ω0+αt

C) ω2=ω02+2α(θ−θ0)

D) More information is needed before t can be found.