HELP ME PLEASE I WILL GIVE BRAINLIEST!

By using the ratio test, the infinite series  converges for any real value x since the limit is less than 1

Ratio test can be applied to show that the infinite series \(Σ(n!)^(1/n)\)converges for any real value x

\(lim n → ∞ |(n + 1)!^(1/(n + 1)) / n!^(1/n)|\\= lim n → ∞ [(n + 1)! / n!)^(1/(n + 1) - 1/n)]\\= lim n → ∞ [(n + 1)^(1/n)] / (n + 1)\\= lim n → ∞ [(1 + 1/n)^(n)]^(1/n) / (n + 1)\\= e^0 / ∞\)

= 0

Using the ratio test, we have limit that is less than 1.

Hence,  the series \(Σ(n!)^(1/n)\) converges for any real value x.

2.  Showing limit lim₁=0, for any real number a n! n=0 using the part 1 above

\(a_n/n! - 0| = |a/(n-1)! × (n/(n-1)) × (1/n) × (1/(n-2)) × ... × (1/2) × (1/1)|\\= |(a/(n-1)) × (1/n) × (1/(n-2)) × ... × (1/2) × (1/1)|\\ < = |(a/(n-1)) × (1/n) × (1/n) × ... × (1/n) × (1/n)|\\= |a/n^(n-1)|\)

Since n → ∞, the right-hand side is getting close to 0, since the denominator grows much faster than the numerator.

By using the squeeze theorem, \(lim a_n/n! = 0\) for any real number a.

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Hello,

\( \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2 \times 5 {}^{2} } = 5 \sqrt{2} \)

                                                  Question 1)

Given

Interest I = $18

Principle P = $200

t = 1.5 years

To determine

Interest rate r = ?

Using the formula

\(P = Irt\)

\(r=\frac{I}{Pt}\)

susbtituting I = 18, t = 1.5 and P = 200

\(r=\frac{18}{\left(200\times 1.5\right)}\)

\(r = 0.06\)

or

r = 6%       ∵ 0.06 × 100 = 6%

Therefore, we conclude that the interest rate required to  accumulate simple interest of $18.00  from a principal of $200 over 1.5 years is 6% per year.

                                                    Question 2)

Given

Interest I = $60

Principle P = $750

Interest rate = 4% = 0.04

To determine

Time period t = ?

Using the formula to calculate the time period

\(P = Irt\)

\(t\:=\:\frac{P}{Ir}\)

\(t=\frac{60}{\left(750\times 0.04\right)}\)

\(t = 2\) years

Therefore, the time required to  accumulate simple interest of $ 60.00

from a principal of $ 750 at an interest rate of 4% per year  is 2 years.

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

The correct answer is a. the average distance between M and µ that would be expected if H0 was true.

The denominator of the z-score test statistic measures the average distance between the sample mean (M) and the population mean (µ) that would be expected if the null hypothesis (H0) was true.

Option a. "the average distance between M and µ that would be expected if H0 was true" is the correct description of what is measured by the denominator of the z-score test statistic. It represents the standard error, which is a measure of the variability or dispersion of the sample mean around the population mean under the assumption of the null hypothesis being true.

Option b. "the actual distance between M and µ" is not accurate because the actual distance between M and µ is not directly measured by the denominator of the z-score test statistic.

Option c. "the position of the sample mean relative to the critical region" is not accurate because the position of the sample mean relative to the critical region is determined by the numerator of the z-score test statistic, which represents the difference between the sample mean and the hypothesized population mean.

Option d. "whether or not there is a significant difference between M and µ" is not accurate because the determination of a significant difference is based on comparing the calculated test statistic (z-score) to critical values, which involve both the numerator and the denominator of the z-score test statistic.

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Answer:

3x-2

Step-by-step explanation:

12x-8/4 = 3x-2 is one side length of a square

The true statement about the residual plot is (a) The regression line is a good model because there is no pattern in the residuals.

For a residual plot to be considered a good model, the points on the plot must be at random and they must not follow a specific pattern

From the graph, we can see that the points are scattered

Hence, the true statement about the residual plot is (a)

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Heron's formula makes use of s, which is described as the semi-perimeter of the triangle. Before we can use Heron's formula, let us solve first for the value of s via the equation

The lengths of the triangle are given in the problem. Just plug it in on the equation above and compute.

Now, let's move on using Heron's formula to solve the area of the triangle. We have

Therefore, the area of the triangle is 5.3 square units.

Answer:

<30,-20>

Step-by-step explanation:

4u + 2v

4< 6,-4> + 2< 3,-2>

<24,-16> + < 6,-4>

<30,-20>

In an experimental study, random error due to individual differences can be reduced if a(n) control group is implemented.

One effective way to reduce random error due to individual differences in an experimental study is to include a control group. A control group serves as a baseline comparison group that does not receive the experimental treatment. By having a control group, researchers can isolate and measure the effects of the independent variable more accurately.

The control group provides a point of reference to assess the impact of individual differences on the study's outcome. Since both the experimental group and control group are subject to the same conditions, any observed differences can be attributed to the experimental treatment rather than individual variations.

This helps to minimize the influence of confounding variables and random error associated with individual differences.

By comparing the outcomes of the experimental group and control group, researchers can gain insights into the specific effects of the treatment while controlling for individual differences. This improves the internal validity of the study by reducing the potential bias introduced by individual variability.

In summary, including a control group in an experimental study helps to reduce random error due to individual differences by providing a comparison group that is not exposed to the experimental treatment. This allows researchers to isolate and measure the effects of the independent variable more accurately.

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To find the value of x, we multiply the given values for molar and seconds by the distance cubed in meters. This results in an answer of 0.039 m²

To solve for x, we simply need to multiply (3.5×10³ m⁻²s⁻¹) and (0.33m)³ together. This gives us:

x = (3.5×10³ m⁻²s⁻¹) * (0.33m)³

x = 0.039 m²

Therefore, the answer is 0.039 m², with units of square meters.


To solve for x, we use the formula x = (3.5×10³ m⁻²s⁻¹) * (0.33m)³. This involves multiplying the values for molar and seconds by the distance cubed in meters. The calculation is straightforward and yields an answer of 0.039 m². This means that the area is 0.039 square meters. It's important to use the correct units when working with equations that involve different measurements, as this can affect the final result. Overall, it's a simple problem to solve using basic mathematical operations.


To find the value of x, we multiply the given values for molar and seconds by the distance cubed in meters. This results in an answer of 0.039 m², with units of square meters. It's important to use the correct units when working with equations that involve different measurements to get an accurate result. The calculation is straightforward and can be easily solved using basic mathematical operations.

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Answer:

2 and 5

Step-by-step explanation:

A linear pair angles are angles on a straight line, whose sum equals to 180°.

Examining the diagram given, angle 2 and angle 5 are on a straight line. Thus, they are a linear pair. Their sum would equal 180°.

Form the options given, the angles that would form a linear pair are:

Angles 2 and 5.

The number of ways to choose 2 items from a set of n items is
[(n-1)(n-2)]/2.

Combinations represent the choice of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. We use the symbol ⁿCr to represent the number of distinct r-selections or combinations among a set of n objects.

The formula for combinations is given by

Here we have

Number of items = n

The number of items that need to be chosen = 2

By given combination formula,

Number of ways are there to choose 2 items from a set of n items

=>  ⁿC₂ = n!/ 2![n- 2]!  

= (n - 1) × (n - 2) × (n - 3) .... (n - (n-1))/ [ 2! (n -2 - 1) × (n - 2 - 2) ..... ]    

= (n - 1) × (n - 2) × (n - 3) .... (n - (n-1))/ [ 2! (n -3) × (n -4) (n -5) ..... ]

= (n - 1)(n-2)/2 × 1

= [(n-1)(n-2)]/2    

Therefore,

The number of ways to choose 2 items from a set of n items is
[(n-1)(n-2)]/2  

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Answer:

52 degrees

Step-by-step explanation:

the triangle has to equal 180 to be a perfect triangle so you would add 64+64=128 then subtract that from 180 to get 52.

Total amount that Subway collect in franchise fees  = $2,189,250,000

Total number of subway franchisees = 42,000

Average annual store revenue           = $417,000

Total paying percentage of franchisees               = 12.5%

12.5% of average revenue = (417000×12.5)÷100

                                              = $52,125

Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees

                                         = 42,000×52,125

                                         = $2,189,250,000

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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.

Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".

Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.

Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.

The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.

The franchise fee:

Now, according to the question:

Total number of subway franchisees = 42,000

Average annual store revenue = $417,000

Total paying percentage of franchisees = 12.5%

∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100

                                                    = $52,125

Total subway collection in franchise fee

= total number of franchisees × amount of fees per franchises

= 42,000×52,125

= $2,189,250,000

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Aisha has a maximum of 23 coins altogether which is equal to dd dimes plus qq quarters. This can be written as an inequality as dd + qq ≤ 23.

Aisha has a maximum of 23 coins altogether, which consists of a certain number of dimes (denoted as dd) and quarters (denoted as qq). Since the maximum number of coins Aisha can have is 23, this can be expressed as an inequality, dd + qq ≤ 23. This inequality states that the total number of dimes and quarters Aisha has must be less than or equal to 23. To solve this equation, we can use a trial and error method, where we make reasonable assumptions for the number of dimes and quarters Aisha has and see if the sum of them is less than or equal to 23. If it is, then our assumptions are correct, otherwise we need to make new assumptions. For example, if we assume that Aisha has 7 dimes and 11 quarters, then 7 + 11 = 18, which is less than 23, so our guess is correct. However, if we assume that Aisha has 8 dimes and 12 quarters, then 8 + 12 = 20, which is greater than 23, so our guess is incorrect. As we can see, this method can be used to solve any inequality, as long as we make reasonable assumptions for the variables.

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a) The correlation between the ages of husbands and wives would be negative if men always marry women who are 3 years younger than themselves. b) The correlation between the ages of husbands and wives would be positive if men always marry women who are 2 years older than themselves. c) The correlation between the ages of husbands and wives would depend on the distribution of ages in the population.

a) If men always marry women who are 3 years younger than themselves, there would be a negative correlation between the ages of husbands and wives. The correlation coefficient would be negative, indicating an inverse relationship.

b) If men always marry women who are 2 years older than themselves, there would be a positive correlation between the ages of husbands and wives. The correlation coefficient would be positive, indicating a direct relationship.

c) If men always marry women who are 1.1 times as old as themselves, the correlation between the ages of husbands and wives would depend on the distribution of ages in the population.

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Option A: 0.1 is incorrect. Option B: 0.09 is incorrect. Option C: 0.009 is incorrect. Option D: 0.001 is incorrect. The correct answer is 0.71.

Suppose that in a specific population, the average age is usually distributed with a mean of 40 and standard deviation of 36. The retirement age is 65. We are required to find out the probability that an individual, who is randomly chosen, will be within retiring age in 5 years.Let us begin by calculating the z-score.z = (x-μ)/σWhere, μ = 40, σ = 36 and x = 65 - 5 = 60.z = (60 - 40)/36z = 0.5556Using the Z table, we can obtain the probability associated with the z-score.

The area under the normal distribution curve between the mean and the z-score equals the required probability.P(z < 0.5556) = 0.7099Therefore, the probability that a randomly selected individual will be within retiring age in 5 years is 0.7099 or 0.71 (rounded to two decimal places).

Therefore, option A: 0.1 is incorrect. Option B: 0.09 is incorrect. Option C: 0.009 is incorrect. Option D: 0.001 is incorrect. The correct answer is 0.71.

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To find (dw/dy)x and (dw/dy)z at the point (w, x, y, z) if w=x^2y^2 yz-z^3 and x^2 y^2 z^2=12, we will start by finding the partial derivatives. We will use the chain rule of differentiation to calculate the partial derivative of w with respect to y, holding x and z constant.

We will also use the chain rule of differentiation to calculate the partial derivative of w with respect to z, holding x and y constant. We will find the partial derivatives at the point (w, x, y, z) using the given equations.Using the product rule of differentiation, we can find that;dw/dy = 2xy²yz + x²y²z.  (eqn 1)And, using the product rule of differentiation again, we can find that;dw/dz = y²z² - 3z².   (eqn 2)Using the equation, x² y² z² = 12, we can substitute for z² in eqn 2 to get;dw/dz = y²(12/(x²y²))-3(12/(x²y²)).          (eqn 3)

Using the equation, w = x²y² yz-z³, we can substitute for z³ as (xyz)²/3. Hence, w = x²y² yz - (xyz)²/3. Since x²y² z² = 12, y = (12/(x²z²))^(1/2).We can now substitute these values into eqn 1 to obtain;(dw/dy)x = 2xy²z(12/(x²z²)^(1/2)) + x²y²z.(12/(x²z²)^(1/2))Dividing through by y gives;(dw/dy)x = 2xz(12/(x²z²))^(1/2) + 12/x^(3/2)z^(1/2).Hence, (dw/dy)x = 2√3 + 2√3 = 4√3.The value of (dw/dy)x is 4√3. Similarly, substituting for y and z in eqn 4 gives;(dw/dz) = (12/4) - (36/48) = 3 - (3/4) = 9/4.The value of (dw/dy)z is 9/4.Answers: (dw/dy)x = 4√3 and (dw/dy)z = 9/4.

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The theoretical probability of landing on tails is P = 0.5, and out of the 250 contestants, around 125 will win the game.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The degree to which something is likely to happen is basically what probability means.

If the coin is fair, each of the two outcomes will have a probability of 0.5 as there are two possible outcomes (this is the theoretical probability for a fair coin, where all the outcomes have the same probability).

Then, for a sample N, we can expect that about 0.5N of the participants win.

We have Sample = 250, then

= 0.5 x 250

= 125

Around 125 of the contestants win the game

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Answer:

its -6 please give brainliyest

The solution is (4,2)

The System of Equation is to find the intercept of both graphs.

In the graphs as shown in the picture, the graphs intercept both at (4,2). It's easier to look at the graph and answer rather than solving an equation.

After all, we have to find the slope to solve the equations.

We can try solving the equations but if you want, let me know.

I can solve the equations but the graphs make it obvious. So if you want me to solve the equation then let me know in the comment.

Answer: C

Step-by-step explanation:

i just took a test

Answer:Answer:

x + y = 10

6x + 8y = 72

Step-by-step explanation:

Number of packages = 10

Total batteries = 72

For AA:

batteries per package = 6

Let number of packages = x

For AAA:

batteries per package = 8

Let number of packages = y

Number of AA packages + number of AAA packages = 10

Sum of AA + sum of AAA equals 72 batteries

x + y = 10

6x + 8y = 72

Step-by-step explanation:

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

-6

Step-by-step explanation:

The pattern here is that you substract 15 every time you move a number (left to right) , therefore: 9-15 = -6

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

The mean is a statistics tool used to find the approximate "middle" in a set of data.

Statistic is a branch of mathematics that deal with the collection analyzes interpretation and presentation of data it is used to summarize analyze and compare data in order to draw conclusion and make decisions statistical method are used in a wide variety of field including economics finance business engineering medicine psychology social science and many others.

It is calculated by adding the values of the data set and dividing the sum by the number of items in the data set. The mean is also known as the average, and it can be used to compare sets of data and to measure the central tendency of a data set.

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Answer:

6y-2y=3y+2

4y=3y+2

4y-3y=2

1y=2

y=2

Answer:

4

x value increases  by 2 in the time it takes y value to increase by 8

8/2 = 4

Answer:

eli= £180, freda = £260, geoff = £360

Step-by-step explanation:

eli : freda : geoff

9   :    13    :  18

9 + 13 + 18 = 40 parts

800 / 40 = 20

therefore 1 part = £20

20 x 9 = £180

20 x 13 = £260

20 x 18 = £360

Answers:

===========================================================

Explanation:

Let x be some positive real number.

Since each person gets a share of the money based on their ages, we can say that

The ratio 9x:13x:18x reduces to 9:13:18 when dividing everything by x.

Add up their shares, set the sum equal to 800 pounds, and solve for x.

9x+13x+18x = 800

40x = 800

x = 800/40

x = 20

We can then use this to find each person's share

As a check: 180+260+360 = 800 which confirms we have the correct split among the three people.

Notice how the ratio 180:260:360 fully reduces to 9:13:18 when you divide each part by the GCF 20.