determine whether the geometric series is convergent or divergent. [infinity] 1 ( 3 )n n = 0

Answer:

decrease

Step-by-step explanation:

the percent change measures FROM the first value. A change from 50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50). A change from 75 to 50 is a change of -33.3% (25 is still the difference between the two. 25 is 33.3% of 75

Answer:

\(5(x - 2) = x + 1 \\ 5x - 10 = x + 1 \\ 5x - x = 1 0+ 1 \\ 4x = 11 \\ x = \frac{11}{4} \)

Answer:

(x + 1)(x + 2) = 7x - 1

{1, 2, 3} and {3, 4, 5}

Step-by-step explanation:

Let the three consecutive integers be x, x + 1, and x + 2.

(x + 1)(x + 2) = 7x - 1

x² + 3x + 2 - 7x + 1 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0  or  x - 1 = 0

x = 3  or  x = 1

For x = 1,

x = 1, x + 1 = 2, x + 2 = 3

For x = 3,

x = 3, x + 1 = 4, x + 2 = 5

Answer: {1, 2, 3} and {3, 4, 5}

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

Step-by-step explanation:

All the sides of an equilateral triangle are equal. Hence;

Perimeter of an equilateral triangle = 3S

S is one of the side length

Given;

S = 4n-2

Perimeter of the triangle = 3(4n-2)

This can also be expressed as P = S + S + S

P = (4n-2) + (4n-2) + (4n-2)

This shows that both methods are correct

Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Step-by-step explanation:

hope this helped

Answer:

the answer is c.

Step-by-step explanation:

there's no explanation

(Apologies since this super late; I hope future students will find this helpful)

Answer:

In a scalene triangle, none of the angles are congruent.

Step-by-step explanation:

As shown, the angles in each scalene triangle all have different measurements. Hence, you can conclude that none of the angles in a scalene triangle are congruent.

You can also see the image below if you'd like to confirm this :)

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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T the limit is -oo. To evaluate the limit, we can use L'Hôpital's rule, which states that if we have an indeterminate form of the type 0/0 or oo/oo, then we can differentiate both the numerator and denominator with respect to the variable t until the indeterminate form disappears.

Let's apply L'Hôpital's rule to the given limit:

lim t→0 <5e^t,sin(3t)/t › (t − 3)³>

= lim t→0 [(5e^t)(t-3)^3 - (sin(3t))(3t^2)(t-3)^2] / (t^4)

= [(5e^0)(0-3)^3 - (sin(0))(3(0)^2)(0-3)^2] / (0^4)    {Substituting t=0}

= (-135)/0o

= -oo

Therefore, the limit is -oo.

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Answer:

2267.96 grams

Step-by-step explanation:

Claculator

Answer:

I belive it's 2267.96 grams and 2268 grams rounded

Step-by-step explanation:

used calculator

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

\(\sqrt[3]{x}\)

\(x^3\)

is

Step-by-step explanation:

Answer:

6hours/1 day

Step-by-step explanation:

I REALLY hope this helps

Best of luck

Answer:

He often said "Diesel Be Good"

Step-by-step explanation:

Answer: 31 7/8

Step-by-step explanation:

Firstly, we add the whole part which is 31 into the fraction making it an improper fraction. Then solve the problem by making a common denominator of 3/4  from the whole fraction into 6/8 and adding it to the previous fraction, then subtracting the spilled amount. To make the improper fraction a whole fraction/normal, just divide by the denominator. That's all!

31 x 8 = 248

248 + 6 = 254

254 - 7 = 247

247 ÷ 8 = 31 + \(\frac{7}{8}\)

OR 31 \(\frac{7}{8}\)

Answer:

D: 12

Step-by-step explanation:

1) So what I did at first was convert the fractions into decimals.

(Personally, this makes it easier, for me at least)

2) The problem states that for every 0.25 cups of broccoli, 0.60 grams of fiber are added as well to the mix. You can also convert this into a fraction. (It doesn't matter which one is the numerator/denominator, but for this example, I used the 0.25 cups of broccoli as the numerator.

3) Next step would be making another fraction. This time, the fraction is for the 5 cups of broccoli. Since we don't know the amount of grams for the fiber, we will replace it with an "x".

4) Realize, that |  \(\frac{0.25}{0.60} =\frac{5}{x}\) |  To figure out the answer to this part, you can cross-multiply

5) Then at last, divide both sides by \(0.25\) and you'll get:

Sorry this may have taken a long time; I just wanted to make sure everything was correct. Hope you do well on math, whether it's a test, or just homework. Good luck! :D

The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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50%

since 98/2 = 49

Thats it

Answer:

\(\huge\boxed{\sf \$\ 205}\)

Step-by-step explanation:

Work hours = 28 hours

Earning = $8 per hour

1 hour = $8

28 hours = $8 × 28

28 hours = $224

He has earned $224 last month.

Spent = $19

Left:

= Earning - Spent

= $224 - $19

= $205

\(\rule[225]{225}{2}\)

The MLE for the effect of schooling on wages (ß) is obtained using the log-likelihood function, assuming independent and normally distributed wages. MLE's unbiasedness, variance, advantages over OLS, and behavior with non-normal error terms are discussed.

(a) The log-likelihood function is given by:

L(ẞ) = -n/2 * ln(2π) - n/2 * ln(1) - 1/2 * Σ\((Yi - \beta xi)^2\)

To find the MLE, we maximize the log-likelihood function with respect to ẞ. Taking the derivative with respect to ẞ and setting it equal to zero, we obtain the MLE:

dL(ẞ)/dẞ = Σ(xi(Yi - ẞxi)) = 0

Solving this equation gives us the MLE for ẞ, denoted as B.

(b) To show that B is unbiased, we need to demonstrate that E(B) = ẞ, where E(.) denotes the expected value. Taking the expected value of the MLE equation, we have:

E(Σ(xi(Yi - Bxi))) = Σ(xi(E(Yi) - Bxi)) = 0

Since E(Yi) = ẞxi, the above equation simplifies to:

Σ(xi^2)(E(Yi) - Bxi) = 0

Expanding this equation, we get:

B * Σ(xi^3) - Σ(xi^2E(Yi)) = 0

Solving for B, we find that B = Σ(xi^2E(Yi))/Σ(xi^3). Thus, B is unbiased.

The variance of B can be calculated as Var(B) = 1/Σ(xi^3). Therefore, Var(B) depends on the third moments of the explanatory variable.

(c) The maximum likelihood method offers several advantages over ordinary least squares (OLS). First, MLE does not require assumptions about the distribution of the error term ε, while OLS assumes that ε follows a normal distribution. This makes MLE more flexible and applicable to a wider range of data. Additionally, MLE provides efficient estimates when the data deviates from normality. Furthermore, MLE allows for hypothesis testing and model selection using likelihood ratio tests.

When the error term ε is not normally distributed, the MLE still provides consistent estimates, meaning that the estimates converge to the true parameter values as the sample size increases. However, the estimates may no longer be the most efficient or have desirable statistical properties. In such cases, alternative estimation methods, such as generalized maximum likelihood estimation (GMLE) or robust MLE, may be employed to account for the non-normality of the error term and obtain more robust estimates.

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The value of x is 16.2degrees

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given;

(x+14), (9x-4)

Now,

According to supplementary angles;

(x+14)+ (9x-4)=180

10x+18=180

10x= 180-18

10x= 162

x= 16.2

Therefore, in these angles the value of x will be 16.2degree

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Answer:

n=9.354

Step-by-step explanation:

n=

\( \frac{290}{31} \)

n=9×

\( \frac{11}{31} \)

So n=9.354

Answer:

x^3+8x^2+15x+25+51

x-2

Answer:

(A)CPCTC

Step-by-step explanation:

Issa knows that ΔRED ≅ ΔTAN by the SSS theorem.

If two triangles are congruent, their corresponding parts will always be congruent. In fact, their corresponding angles will be equal.

Therefore, Issa concluded that ∠R ≅ ∠T by the fact that Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

The correct option is A.

Similarly, we can also conclude that:

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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The number of games that will be played will be 8 games.

It should be noted that the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by

y = 3.50x + 6.00.

The games that you can bowl for $34 will be:

y = 3.50x + 6.00.

34 = 3.50x + 6.00.

Collect like terms

3.50x = 34 - 6

3.50x = 28

Divide

x = 28 / 3.50

x = 8

Therefore, the number of games will be 8 games.

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