determine whether the series converges or diverges. [infinity] 3n 7 5n n = 1

Answer:

36

Step-by-step explanation:

There are 6 sides on each die so you just multiply that by 6 to get the total number possible outcomes

6 * 6 =36

Answer:

(D)

Step-by-step explanation:

A is true because c*b=cb and c*-a=-ca.

B is true because a*-c=-ac and a*b=ab.

C is true because 4a*4b is 16*ab so 16ab.

D is NOT true because bc*a=bca and bc*3=3bc so bca-3bc is NOT bca-3

By using the commutative property, the given expression should be simplified as follows: B. 4/3 + 2/3 + 3/4 = 2 + 3/4 = 2 3/4.

The Associative Property of Addition states that when three (3) numbers are added, the end result would always be the same regardless of the way the numbers are grouped.

The Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the Commutative Property of Addition, we have;

4/3 + 3/4 + 2/3

Re-arranging the expression, we have;

4/3 + 2/3 + 3/4 = (4 + 2)/3 + 3/4

4/3 + 2/3 + 3/4 = 2 + 3/4

4/3 + 2/3 + 3/4 = 2 3/4

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Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is much larger than one.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

Firstly, it is important to clarify that when people say ‘‘The Sun Will Rise Tomorrow’ they are implying only how It only appears to an observer on earth that the sun rises and sets. In reality the sun neither rises nor sets it only appears to do so because the earth takes one day (24 hours to rotate on its axis). It has appeared to do this for as long as the earth has existed (approx. 4.5 billion years). Although for the purpose of this short reflection, the idiom will signify part of the day-night process -being able to see the sun rise from the perspective of a human on earth.

Although the chances might be extremely high, they are not certain. Even thought it may be very improbably unless an infinite amount of days in which the sun has risen has occurred, the probability will not exactly be one. Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic and philosophy of mathematics, said, “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.” Although we may reasonably argue that the earth while rise tomorrow to a 99.99999999% chance, there still is that 0.000000001 which states that it would not in fact rise.

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The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

From the question, we have the following parameters that can be used in our computation:

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

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Complete question

What is √(2 + 2x) - 6 = 2

The product of -3/5 and (-1 1/3) is 4/5.

To find the product of -3/5 and (-1 1/3), we need to convert the mixed number (-1 1/3) into an improper fraction.

The mixed number (-1 1/3) can be rewritten as a fraction by multiplying the whole number (-1) by the denominator (3) and adding the numerator (1) to get -4/3. So, (-1 1/3) is equivalent to -4/3.

Now we can calculate the product:

-3/5 * -4/3

To multiply fractions, we multiply the numerators and denominators separately:

(-3 * -4) / (5 * 3)

= 12 / 15

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator, which is 3:

12 ÷ 3 / 15 ÷ 3

= 4/5

Therefore, the product of -3/5 and (-1 1/3) is 4/5.

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Answer:

sin(-θ) = -0.809

Step-by-step explanation:

To find this, simply perform the operation that is being asked, make theta negative.

If you want to find out what theta is in the first place, do this:

θ = arcsin(0.809)

θ = 54

Then to find sin of negative theta, substitute:

sin(-θ), or, sin(-54)

should equal to:

sin(-θ) = -0.809

The probability of the horse winning the race is 4/11 or approximately 0.36 or 36%.

The odds in favor of a horse winning a race is expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of the horse winning the race is 4:7.

This means that for every 4 favorable outcomes, there are 7 unfavorable outcomes.

To determine the probability of the horse winning the race, we can use the formula:

Probability = favorable outcomes / total outcomes

In this case, the total number of outcomes is the sum of the favorable and unfavorable outcomes, which is 4 + 7 = 11.

Therefore, the probability of the horse winning the race is:

Probability = 4 / 11

This means that the horse has a probability of approximately 0.36 or 36% of winning the race.

In summary, the odds in favor of a horse winning a race of 4:7 means that there are 4 favorable outcomes for every 7 unfavorable outcomes.

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Answer:

there is a website where you can make triangles and that would get it 4 u

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The only consecutive integers that satisfy the Pythagorean theorem are 3, 4, and 5.

___

4^2 ≠ 2^2 + 3^2

16 ≠ 4 + 9 . . . . . . . an attempt at applying the Pythagorean theorem to the given numbers fails.

a) At the moment the information is first learned (x = 0 weeks), 100% of the information is remembered.

b) After 1 week, approximately 69.79% of the information is remembered.

c) After 8 weeks, approximately 40.67% of the information is remembered.

d) After one year, approximately 40.0036% of the information is remembered.

a. When we substitute 0 for x in the function f(x) = 60e^(-0.7x) + 40, we get:

f(0) = 60\(e^{(-0.7*0)\) + 40

= 60e⁰ + 40

= 60(1) + 40

= 60 + 40

= 100

b. When we substitute 1 for x in the function, we get:

f(1) = 60\(e^{(-0.7*1)\) + 40

= 60\(e^{(-0.7)\) + 40

Using the calculator, we can evaluate this expression to find the percentage of information remembered after 1 week.

f(1) ≈ 60(0.4966) + 40

≈ 29.79 + 40

≈ 69.79

c. To find the percentage of information remembered after 8 weeks, we substitute x = 8 into the function:

f(8) = 60\(e^{(-0.7*8)\) + 40

≈ 60(0.0111) + 40

≈ 0.6667 + 40

≈ 40.67

d. Similarly, to find the percentage of information remembered after one year (52 weeks), we substitute x = 52 into the function:

f(52) = 60\(e^{(-0.7*52)\) + 40

≈ 60(0.00006) + 40

≈ 0.0036 + 40

≈ 40.0036

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The population you're focusing on for your experiment is "Americans over the age of 30."

the population in your experiment would be "Americans over the age of 30." Here's the breakdown:

1. You are interested in the preference of Coke over Pepsi among Americans.
2. You specifically want to test this preference for those who are over the age of 30.
3. You plan to conduct an experiment with 100 people from this population.

A population in statistics is the complete set of individuals or objects that have one or more characteristics in common . A population can be finite or infinite, existent or hypothetical. A sample is a subset of the population that is selected for a study

Therefore, the population you're focusing on for your experiment is "Americans over the age of 30."

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Answer:

x=4

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

First, round the number to the ones place.

We get 175.

Then, divide it by 3.

     5  8

  _____

3| 1  7  5

  -1  5

   ___

       2  5

     - 2  4

      ____

            1

quotient = 58

remainder = 1

So, the estimated quotient is 58.

Hope it helps!

Also, please mark my answer as brainliest.

The probability that a student picked at random would pick a room filled with cupcakes or computers using probability concept is 0.26.

Probability is the ratio of required outcome to the total possible outcomes.

Mathematically,

Probability = Required outcome / Total possible outcomes

Room filled with computers or cupcakes = Number of rooms filled with computers + Number of rooms filled with cupcakes = 12 + 3 = 15

Total number of rooms = 12+3+12+3+29 = 59

P(computers or cupcakes) = 15/59 = 0.259

Therefore, the probability that a student picked at random would pick a room filled with cupcakes or computers is 0.26.

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When the result of a signed arithmetic operation is too big or too small to fit into the destination, the overflow flag is set.

In more detail, in signed arithmetic, the most significant bit (MSB) of a number represents its sign: 0 for positive numbers and 1 for negative numbers. When performing arithmetic operations, such as addition or subtraction, the result may exceed the range that can be represented by the destination data type.

For example, adding two large positive numbers may result in a value that exceeds the maximum positive value that can be stored. Conversely, subtracting a large negative number from a small positive number may result in a value that is smaller than the minimum negative value that can be represented.

To detect such scenarios, processors set the overflow flag. This flag is a status flag that indicates whether an overflow has occurred during the arithmetic operation. It helps to identify cases where the result is too large (positive overflow) or too small (negative overflow) to fit within the destination data type. Software can then check the overflow flag to handle these situations appropriately, such as by truncating the result or reporting an error.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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Answer:

no

when you enter the point into the equation and solve, it does not work

Answer:

NO

Step-by-step explanation:

Answer:

17/20

Step-by-step explanation:

The ratio 8.5 to 10 as a fraction in simplest form is 17/20. 8.5/10 = 85/100 = 17/20

(8.5:10 = 85:100 = 85/100 = 17/20)

Answer:

Step-by-step explanation:

Here's a table of values (but it sounds as though you were given the beginnings of such a table):

x    y = 3/x

0   undefined

1     3

3     1

9     3/9 = 1/3

and so on

The table of the values for y = 3 / x is (x, y) = (1, 3), (2, 1.5), (3, 1), (4, 0.75), (-1, -3)

Given:

y = 3 / x

y = 3 / x

Assume x = 1

y = 3/1

y = 3

Assume x = 2

y = 3/2

y = 1.5

Assume x = 3

y = 3/3

y = 1

Assume x = 4

y = 3/4

y = 0.75

Assume x = - 1

y = 3/-1

y = -3

Therefore, the value of y from the equation y = 3/x depends on the value of x

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The rocket will reach the maximum height in 1.5 seconds, and the maximum height of the rocket is 35.96 ft.

Parabolic function is a function of the form f(x) = ax² + bx + c. It is a quadratic expression in the second degree in x.

Given that, a toy rocket is shot vertically into the air from a launching pad 3 feet above the ground with initial velocity of 48 ft/sec and the function is given by, h(t) = -16t²+48t+3

h(t) = -16t²+48t+3

= 3 feet

= 48 ft/sec

We find the vertex of the function,

Vertex = -b/2a = -48/-32 = 1.5

= 1.5 seconds

= (c-b²)/4a = (3-2304)/4*(-16) = 2301/64 = 35.96 ft

Hence, The rocket will reach the maximum height in 1.5 seconds, and the maximum height of the rocket is 35.96 ft.

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Answer:

y = 15x^3 + 16x^2 - 55x + 24

Step-by-step explanation:

y = (3x +8)(5x - 3)(x - 1)

y = (15x^2 - 9x + 40x -24) * (x - 1)

y = (15x^2 + 31x - 24) * (x-1)

y = 15x^3 - 15x^2 + 31x^2 - 31x - 24x + 24

The x-intercepts of a graph are the points where the graph crosses the x-axis.

The x-intercepts are: \(\mathbf{x = ,-\frac83, \frac 35\ and\ 1}\)

The function is given as:

\(\mathbf{y = (3x + 8)(5x - 3)(x - 1)}\)

First, we plot the graph of \(\mathbf{y = (3x + 8)(5x - 3)(x - 1)}\)

See attachment for the graph

Next, write out the x-values when the graph crosses the x-axis.

From the graph, we have:

\(\mathbf{x = -\frac 83}\)

\(\mathbf{x = \frac 35}\)

\(\mathbf{x = 1}\)

Hence, the x-intercepts are: \(\mathbf{x = ,-\frac83, \frac 35\ and\ 1}\)

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The required number of possible plates are 26x26x10x10x10x10x15.

To calculate the number of possible plates, we need to multiply the number of possibilities for each character slot. The first two slots are letters, and there are 26 letters in the alphabet, so there are 26 choices for each of those slots. The next four slots are digits, and there are 10 digits to choose from, so there are 10 choices for each of those slots. Therefore, the total number of possible plates is:

26 x 26 x 10 x 10 x 10 x 10 x 15 = 45,360,000

The extra factor of 15 comes from the fact that both letters can repeat, so there are 26 choices for the first letter and 26 choices for the second letter, but we've counted each combination twice (once with the first letter listed first and once with the second letter listed first), so we need to divide by 2 to get the correct count. Thus, the total count is 26 x 26 x 10 x 10 x 10 x 10 x 15.

So, option c is the correct answer.

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The average value of y for the part of the curve y=3x-x^2 in the first quadrant is 4.5.


To find the average value of y for the part of the curve y=3x-x^2 in the first quadrant, we need to integrate the function from x=0 to x=3 (since the curve intersects the x-axis at x=0 and x=3 in the first quadrant) and divide by the length of the interval (3-0=3).

The integral of the function is:

∫(3x-x^2)dx = (3/2)x^2 - (1/3)x^3 + C

Evaluating this integral from x=0 to x=3, we get:

[(3/2)(3)^2 - (1/3)(3)^3] - [(3/2)(0)^2 - (1/3)(0)^3]
= (27/2 - 27/3) - (0 - 0)
= 27/6
= 4.5

So the average value of y for the part of the curve y=3x-x^2 in the first quadrant is 4.5.

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Answer:

\(x = 60\)

Step-by-step explanation:

Step 1:  Convert into an equation

Nine less than one forth of a number is 6

\(1/4x - 9 = 6\)

Step 2:  Add 9 to both sides

\(1/4x - 9 = 6\)

\(1/4x - 9 + 9= 6+ 9\)

\(1/4x = 15\)

Step 3:  Multiply both sides by 4

\(1/4x * 4 = 15 * 4\)

\(x = 60\)

Answer:  \(x = 60\)

Answer:

picture #1 - 50.27 square units

picture #2 - 113.10 square units

picture #3 - 380.13 square units

Step-by-step explanation:

picture #1 - area = πr^2 -> π*4^2 = 50.27 square units

picture #2 - area = πr^2 -> π*6^2 = 113.10

picture #3 - area = πr^2 -> π*11^2 = 380.13

By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "\(x2 + 2x - 3 = 0\\\)" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

\(0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35\)

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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Answer:

24cm^2

Step-by-step explanation:

3cm times 8cm = 24cm^2

Answer:

A=b*h

Step-by-step explanation:

base=5

height=3

5*3=15

15 is the answer