If the sequence below is a geometric sequence then what will the next two numbers in the sequence be? Sequence: 3, 9,…

Answer: x=-8

Step-by-step explanation:

\(10x\)

Solution:

If \(f(x) = 3x +3\) and \(g(x) = -3 +2x\), then \(2g(x) +2f(x)\) is:

\(2(-3 +2x) +2(3x +3) \\ -6 +4x +6x +6 \\ (-6 +6) +(4 +6)x \\ 0 +10x \\ 10x\)

Answer:

(2x*+6)(x-2)

2x(x-2)+6(x-2)

2xx+2x(-2)+6x +6(-2)

we know ;

(-). (-) = +

(-). (+) = -

(+). (-) = -

(+). (+) = +

2xx-2x(2)+6x -6(2)

2x^2  - 4x + 6x  -12

2x^2  - 2x  -12

Step-by-step explanation:

Answer:

i cant read it.... explain

Step-by-step explanation:

The confidence interval is 0.039. This means that the value lies between the range of -0.039 and 0.039. Therefore, we can express the confidence interval as the mean plus or minus the margin of error.

This will give us a range in which the true population mean lies.Let's assume that the mean is 0.259. Then the lower limit of the range is given by:Lower limit = 0.259 - 0.039 = 0.22 And the upper limit of the range is given by:Upper limit = 0.259 + 0.039 = 0.298Therefore, the confidence interval is: 0.22 to 0.298Now we can see that option A is the correct answer: 0.259+0.22.

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The recursive equation that represents this situation in the bowling alley is f(n) = 2.75 + 4.75n .

The cost of each game = $4.75

Number of games played = n

Total cost of n number of games played = 4.75n

Cost of shoe rental =$2.75

Total cost for n games = 2.75 + 4.75n

Recursive equation : f(n) = 2.75 + 4.75n

Any combination of the terms that came before it equals the nth term in a string of integers, according to a recurrence relation equation. For a parameter k that is independent of n, only k prior terms of the sequence normally appear in the equation; this number k is referred to as the order of the relation.

If the first k numbers in a sequence have values, the remaining numbers can be calculated by repeatedly applying the equation.

A linear recurrence's nth term is a linear function of the first k terms. The recurrence of the Fibonacci numbers is one prominent illustration.

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To calculate the amount Astrid should withdraw from her college fund of $30000, we need to determine the number of payments (n) for equal withdrawals over four years.

The formula to calculate the number of payments (n) can be derived using the formula for calculating the present value of an annuity.

In this case, the present value (PV) is the college fund amount of $30000, the payment (P) is the equal withdrawal amount, and the interest rate (r) is the annual nominal interest rate divided by the number of compounding periods per year.

By rearranging the formula and solving for n, we can find the desired result.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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The sample space is the set of all possible outcomes that can result from a random experiment. In this case, the random experiment is drawing one card from a deck of ten cards. We need to find the size of the sample space.The total number of cards is 10. Therefore, the size of the sample space is 10 (since there are 10 possible outcomes).The probability of drawing a blue card is the number of favorable outcomes divided by the number of possible outcomes. Since there are 3 blue cards in the deck, the number of favorable outcomes is 3. The number of possible outcomes is 10. Hence, the probability of drawing a blue card is:P(B) = favorable outcomes / possible outcomesP(B) = 3/10P(B) = 0.3Similarly, the probability of drawing an odd-numbered card is the number of favorable outcomes divided by the number of possible outcomes. Since there are 4 odd-numbered cards (1, 3, 5, 7), the number of favorable outcomes is 4. The number of possible outcomes is 10. Hence, the probability of drawing an odd-numbered card is:P(O) = favorable outcomes / possible outcomesP(O) = 4/10P(O) = 0.4

The are 10 elements on the sample space and the probability of drawing a blue card is 0.3.

There are 10 cards in total, so the sample space consists of 10 possible outcomes. Therefore, the number of elements in the sample space is 10.

Now let's calculate the probability of drawing a blue card (B). Since there are 3 blue cards out of 10 total cards, the probability of drawing a blue card is:

P(B) = Number of favorable outcomes / Total number of possible outcomes

= 3 / 10

= 0.3

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Answer:

78.54 (unless you round)

Step-by-step explanation:

A=pi(r^2)

10 divided by 2 is 5, then multiply 5^2 by pi. 25 times pi gets you the answer!! I’m not great at explaining things haha sorry

Answer:

D

Step-by-step explanation:

Proportional mean the same but 100 napkins is cheaper then 50 so it is not proportional

Answer:

The answer is D.

No, the ration found by dividing the price of napkins by the number of napkins is not the same for each pack.

Step-by-step explanation:

The prices and the number of napkins in each package are not proportional to each  other because they all not equal to each other when the number of napkins is divided by the price

Hope this helps!!! :)

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The given room contains 5.4 cubic meters of air.

We must determine the volume of the room to determine how much air it holds. The Volume of a room is calculated by multiplying its length, breadth, and height.  To determine the volume of a given room, multiply its length, breadth, and height as follows:

The volume of the room = length x width x height

= 12 cm x 7.5 m x 6 m

The room's length must be converted from centimeters to meters so that all units have the same value system. We may convert 12 cm to meters by dividing it by 100 since 1 meter equals 100 centimeters:

12 cm = 12/100 m = 0.12 m

Substituting this value in the formula above, we get:

Volume of the room = 0.12 m x 7.5 m x 6 m

= 5.4 cubic meters

Therefore, the given room contains 5.4 cubic meters of air.

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\(\huge\text{Hey there!}\)

\(\mathsf{(2n^4)^3}\\\\\mathsf{= 2n^4 \times 2n^4\times 2n^4}\\\\\mathsf{= 4n^8\times 2n^4}\\\\\mathsf{= 8n^{8\ + \ 4}}\\\\\mathsf{= 8n^{12}}\)

\(\huge\textsf{Thus, your answer should be: \boxed{\mathsf{8n^{12}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

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The features that Michael should include on the graph of the parabola are given as follows:

The parabola for this problem is defined as follows:

y = -0.5(x - 3)² - 1.

Comparing to the vertex form definition, the coordinates of the vertex are given as follows:

(3, -1).

The equation can also be written as follows:

-0.5(x - 3)² = y + 1

(x - 3)² = -2(y + 1).

Then the coefficient p is obtained as follows:

4p = -2

p = -0.5

Then the coordinates of the focus are given as follows:

(3, -1 - 0.5) = (3, -3/2),

The equation of the directrix is then given as follows:

y = 1 - 0.5

y = 1/2.

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Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

                                   4a = 60ft

divide both sides by

                                  4a = 60/4

                                    a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

                               4*a + 4(a + 2*3)

Replace a with 15 to get:

                         =  4*15 + 4(15 + 6) 60 + 4(21) 60+84

                         = 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

                       = 144*1.15

                       = $165.6

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Answer:

362,880

Step-by-step explanation:

Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.

Answer:

c. $33

Step-by-step explanation:

$31 * 6% = $1.86

$31+$1.86 = $32.86

$33 is the closest.

There are two possible outcomes when tossing a coin, head or tail.

Since the coin is fair, both outcomes are equally likely to occur 1/2 or 50% of the time.

If you toss a coin 100 times, there are 2^100 possible heads and tails, or about 1.26 x 10^30. This means that there are approximately 1.26 x 10^30 ways a coin can land heads or tails 100 times.

You can also get 50 heads, 50 tails, or a total of 100 combinations of heads and tails. In other words, no particular outcome is more likely than any other. The probability of any particular combination of heads and tails occurring is very small, but the probability of any combination occurring is 1 or 100%.

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Step-by-step explanation:

A shows the initial value or y intercept.

Why.

A exponential function is shown as

\(a(b {}^{x} )\)

If we are trying to find the y intercept, we first set this equal to y

\(a( {b}^{x} ) = y\)

Set x=0

\(a {b}^{0} = y\)

And solve for y.

Remeber that anything raised to the zero power is 1. So

\(b {}^{0} = 1\)

So we have

\(a(1) = y\)

Anything times 1 is itself so we have

\(a = y\)

This means that the y intercept of a exponential function is (0,a). A gives us the y intercept.

Answer:

124

Step-by-step explanation: Hope it helps

The required answers ar(a)P = $2,000,r = 4.5%,n = 2 (b)$ 2985.17, (c) 4.45%

(A) Using the given information, we can identify the following values:

P = $2,000 (the present value or initial deposit)

r = 4.5% (the annual percentage rate)

n = 2 (the number of times per year that interest is compounded, since it is compounded semi-annually)

(B) To find the future value of the account balance after 9 years, we can use the formula:

\(S(t) = P(1 + r/n)^{nt}\)

where t is the time in years. Substituting the given values:

\(S(9) = $2,000(1 + 0.045/2)^{2*9}= $2,000(1.0225)^{18}\)

= $2,000(1.505016)

= $2985.17

Therefore, Monique will have $$2985.17 in the account in 9 years.

(C) The annual percentage yield (APY) takes into account the effect of compounding on the effective interest rate. It is calculated as:

\(APY = (1 + \frac{r}{n})^n - 1\)

Substituting the given values:

\(APY = (1 + 0.045/2)^2 - 1\)

= 0.0445 or 4.45%

Therefore, the annual percentage yield for the savings account is 4.45% rounded to 3 decimal places.

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Answer:

Where's the grid? From what I gathered it is essential in this question.

Step-by-step explanation:

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:

15.92 rotations

Step-by-step explanation:

We need to find the circumference, then divide the distance of the driveway by the circumference.

C = (pi)(d)

C = (3.14)(16)

C = 50.24

400/50.24 = 7.971783 one way to the mailbox. Since it asks for the "journey to the mailbox", let's double it, giving us 15.9235669