What are two ways sequences can be defined?

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

Lol

Step-by-step explanation:

Wdym?

The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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Answer:

A≈  251.33in² ok

Answer:

251.33

Step-by-step explanation:

A=2πrh+2πr2=2·π·4·6+2·π·42≈251.32741

The quadrilateral whose vertices are A(2, 3); B(4, -2);C(-1,-4); D(-3, 1) is a square.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Given A(2, 3); B(4, -2);C(-1,-4); D(-3, 1)

Length of AB = \(\sqrt{(4-2)^2+(-2-3)^2}\) = √29 units

Length of BC = \(\sqrt{(-1-4)^2+(-4--2)^2}\) = √29 units

Adjacent sides are equal.

So the quadrilateral must be square or rhombus.

Now, find the length of diagonals.

If the diagonals are equal, then it is square. If they are not equal, then it is rhombus.

AC = \(\sqrt{(-1-2)^2+ (-4-3)^2}\) = √58 units

BD = \(\sqrt{(-3-4)^2+(1--2)^2}\) = √58 units

Diagonals are equal.

So it is a square.

Hence the quadrilateral is a square.

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Answer:

let the third side be x

Using pythagoras theorem we get,

(58)^2 = (42)^2 + (x)^2

3364=1764+x^2

x^2=3364-1764

x^2= 1600

x=√(1,600)

x=40

\(\pink{\sf Third \: side \: of \: the \: triangle = 40}\)

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

Here,

In given triangle,

Now, by Pythagoras' theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

\( \sf : \implies (58)^{2} = (42)^{2} + P^{2}\)

\( \sf : \implies 58 \times 58 = 42 \times 42 + P^{2} \)

\( \sf : \implies 3364 = 1764 + P^{2}\)

\( \sf : \implies P^{2} = 3364 - 1764\)

\( \sf : \implies P^{2} = 1600\)

By squaring both sides :

\( \sf \sqrt{P^{2}} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{(40)^{2}}\)

\( \sf : \implies P^{2} = 40 \)

\(\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 40}\)

━━━━━━━━━━━━━━━━━━━━━

There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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Answer:

a, c, d

Step-by-step explanation:

Answer:

d answer is right .....

the answer is A.

(-2, -2) and (2,2)

Answer:

The equation is 19+3.5h=10+4.75h. The answer is 7.2 hours.

Step-by-step explanation:

The equation for this problem would be 19+3.5h=10+4.75h. All you have to do is find h. So subtract 3.5h from both sides and 10 from both sides. You will get the equation 1.25h=9. Divide 1.25 from both sides and you will end up with h=7.2 hours.

Answer:

184

Step-by-step explanation:

80% of 230

0.8x230

8×23

=184

Answer:

True.

Step-by-step explanation:

I don't nessicarly know the explanation behind it, but if a negative number is being multiplied by another negative number, the product will always be positive.

Answer:

True.

Step-by-step explanation:

Negative x Negative=Positive.

I'm not sure why, but it's mathematical law.

Hope I helped!

Last week Bob was paid total of $480 for the items that he produced that week and this week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

Let's start with the simplest case:

he produced 36 or less items this week.

In this case he produced less than 36 items last week too.

So he was paid the same amount of dollar per item. Using assumptions (1) and (2), we have:

$480 + 2X = $510

⇒2X=510-480$

⇒2X=$30

⇒2X=$30/2

⇒X=$15

He was paid $15 per item.

Last week he received his $480.

480/15= 32 items.

This week he received his $510.

510/15=34 items. Other cases have no solution.

seems your question is incomplete., but most probably the complete question was

If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?(1) Last week Bob was paid total of $480 for the items that he produced that week.(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

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Answer:

it would be a positive 2/5

Step-by-step explanation:

Answer:

2/5 just not negative anymore!

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

175= 25+2a

The number of laps that Swimmer A swam was 50 laps.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let we suppose that:

Then, according to the given data, we have:

x + y = 175 laps

y = 25 + 2x (25 more than twice of laps of A is the number of laps of B).

Thus, we get a system of two equations as:

\(x + y = 175\\y = 25 + 2x\\\)

From second equation, putting value of y in first equation, we get:

\(x + (25 + 2x) = 175\\3x + 25 = 175\\3x = 150\\\\x = \dfrac{150}{3} = 50 \: \rm laps\)

As x is the number of laps Swimmer A swam, thus, the number of laps that Swimmer A swam was 50 laps.

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Answer: what’s the problem

Step-by-step explanation:

with what problem there isn't one posted

The correct statement is that probability refers to the proportion of times an event is expected to occur in the long run.

The area under a pmf or pdf curve corresponds to its (b) probability. The total area under a pmf or pc equals (b) 1. The probability of landing on any curve is always equal to (c) something between 0 and 1.

The correct option for which of the following is NOT right about probability is: Probability is the frequency of the event interested over the total number of possible events.

Let's discuss the given terms one by one.

Probability:Probability is defined as the branch of mathematics that deals with the study of random events. It is the study of random variables, processes and events that occur in real-time.

Proportion:A proportion is defined as the fraction of a quantity of a population or a sample. It is used to estimate a value based on the sample or population.

PMF (Probability Mass Function):The probability mass function or PMF is a function that is used to describe the probability distribution of a discrete random variable.

The PMF is defined as a function that assigns probabilities to the possible outcomes of a random variable.

PDF (Probability Density Function):The probability density function or PDF is a function that is used to describe the probability distribution of a continuous random variable.

The PDF is defined as the derivative of the cumulative distribution function (CDF).Uniform distribution:The uniform distribution is a probability distribution that is used to describe events that have a constant rate of occurrence.

The probability density function (PDF) for the uniform distribution is a horizontal line that is constant across the entire range of the distribution. It is defined as follows:

PDF of a uniform distribution, f(x) = 1/(b - a), for a ≤ x ≤ b

.Probability is the frequency of the event interested over the total number of possible events is NOT right about probability.

The correct statement is that probability refers to the proportion of times an event is expected to occur in the long run.

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The vector v1 from point O to point E is given by <Δx, Δy, Δz>.

The vector v1 from point o to point e is the directed line segment that connects point o to point e. In other words, it is the vector that starts at point o and ends at point e.

To find the vector v 1, you can subtract the coordinates of point o from the coordinates of point e. Thus, v 1 = (xe - xo)i + (ye - yo)j + (ze - zo)k, where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

To find the vector v1 from point O to point E, you need to follow these steps:

Step 1: Identify the coordinates of point O and point E. Let's assume the coordinates of point O are (x1, y1, z1) and point E are (x2, y2, z2).

Step 2: Calculate the differences between the coordinates of point E and point O. Subtract the coordinates of point O from point E:
Δx = x2 - x1
Δy = y2 - y1
Δz = z2 - z1

Step 3: Represent the vector v1 from point O to point E using the differences in coordinates:
v1 = <Δx, Δy, Δz>

That's it! The vector v1 from point O to point E is given by <Δx, Δy, Δz>.

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Answer: 51.172, 116.321

Step-by-step explanation:

novels : cookbooks : reference books

Answer:

6 : 33 : 8

Step-by-step explanation:

cookbook = C

novel = N

reference book = R

C : N = 2 : 11

C : R = 3 : 4

C : N : R = ?

Start with C : N = 2 : 11

2 is not divisible by 2, so multiply this ratio by 3.

C : N = 6 : 33

C : R = 3 : 4 multiply by 2 to get

C : R = 6 : 8

C : N : R = 6 : 33 : 8

Answer:

C

Step-by-step explanation:

100/2 = 50. 50-6 = 44

Answer:

x=52 m1= 40 m2= 140

Step-by-step explanation:

x-12+x+88=180 since they are linear pair

2x+76=180 collect like terms

2x=180-76

2×÷2=104÷2

×=52

give me a heart and good rate please<3

Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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The calculation 18/6=108 is not the right representation.

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: One of the option as 18/6=108

But in the question Jenna buys 6 new shirts at $18

Thus the total cost of the shirts is 18*6=108

But 18/6=3

Thus this expression is not the right calculation.

Hence, The 18/6=108 is not the right representation.

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Answer:

See the picture for the answer

Step-by-step explanation

Answer: The base of the triangle is 15 inches

Formula for area of a triangle: A = bh/2

Subsitute values into the formula:

150 = b(20)/2

Now solve for b

150 = b20/2

x 2           x2

--------------------

300 = b20

300/20 = b20/20

15 =

The base of the triangle is 15 inches

Answer:

x = 36

Step-by-step explanation:

Tan (30) = opposite / adjacent

The opposite is known: it is 12 √3

Tan (30o) = 1 / √3

Tan(theta) = opposite/adjacent.

Opposite = 12\(\sqrt{3}\)

Adjacent = x

\(\frac{1}{\sqrt{3} } = \frac{12\sqrt{3} }{x}\)                            Cross multiply

1*x = 12*(\(\sqrt{3}\))^2

x = 12 * 3

x = 36

Answer:

Hi there!

Your answer is;

x = 3 & 2/7ths

Step-by-step explanation:

7(x-3)-2

7x -21 -2

7x -23

The simplified equation is 7x-23

To solve for x:

7x-23

+23

7x= 23

/7

x = 3 & 2/7ths

Hope this helps

Answer:

7x - 23

Step-by-step explanation:

7(x-3) -2    Use distributive property

7x - 21 - 2       combine like terms.

7x - 23    <----- This is your answer

The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

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Answer:

11

Step-by-step explanation:

Here, we replace x and y with the values given that x = 6 and y = 2:

=\(\frac{3(6)+4}{(2)}\)

= \(\frac{18+4}{2}\)

=\(\frac{22}{2}\)

=11

Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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