find a function f(n) that identifies the nth term an of the recursively defined sequence, as an = f(n). a1 = 5 and an+1 = ((n + 1 )an / 5) for n ≥ 1
f(n) =

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Given:

The linearized regression line model;

Given:

y = $200

Substituting the value of y in the model to get x,

Therefore, the best approximation of the number of weeks that will pass before the value of the stock reaches $200 is 6.7

Hence, the correct answer is option C.

The solution is y = -22/3 of the system of equations.

Now, According to the question:

Linear equations in two variables are the algebraic equations which are of the form y = mx + b, where m is the slope and b is the y-intercept.

They are the equations of the first order.

Given, y = (2/3)x + 3x

x = -2

We have to find the solution to the given system of equations.

Put x = -2 to find the value of y

y = (2/3)(-2) + 3(-2)

By further calculation

= (-4/3) - 6

By taking LCM

= (-4 - 18)/3

So we get

= -22/3

Therefore, the solution is y = -22/3

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The complete question is this:

What is the solution to the system of equations? y = 2/3 x + 3x, x = -2

Answer:

B

Step-by-step explanation:

No matter what value you multiply a, the fraction will remain unchanged. That is because you can divide an a out from the numerator and the denominator. Thus, doubling a has no affect on the fraction, and in fact, u can simplify it to just bc. Now, if you halve b, it will simply just halve the actual value. When you halve b, you are simply executing (1/2)(b)(c). Therefore, you can rearrange the expression to be (1/2)(bc), which is just halving bc. If you decrease by 1/2, it's the same thing as being half of the value it was before. Therefore, the answer is b.

The predicted gain (or loss) from a single trial is 53 cents per game on average.

A roulette wheel has the number 1 through 36, as well as 0 and 00. If you wager $1 that an odd number would show up, you will win or lose $1 depending on whether or not that occurrence occurs. If random variable X represents your net benefit, X=1 with probability 18/38 and X=-1 with probability 20/38.

E(X) = 1(18/38) – 1 (20/38) = -$.053

On average, the casino wins  5 cents for each game.

If the stakes are raised, the casino makes even more money:

E(X) = 10(18/38) – 10 (20/38) = -$.53

If the cost is $10 for each game, the casino wins an averaged of 53 cents per game. If 10,000 games are played in a single night, that's a cool $5300.

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The focus of the parabola with the equation \(y = (1/12)x^2\) is at the point (0, 1/96), and the directrix is the horizontal line y = -1/96. In general, the equation of a parabola in standard form is given by \(y = ax^2 + bx + c\), where a, b, and c are constants.

Comparing this with the given equation \(y = (1/12)x^2\), we can see that a = 1/12, b = 0, and c = 0.

For a parabola in standard form, the focus lies at the point (h, k + 1/(4a)), and the directrix is the horizontal line y = k - 1/(4a), where (h, k) is the vertex of the parabola.

In our case, since b = 0, the vertex of the parabola is at the point (0, 0). Using the formula for the focus and directrix, we substitute the values of a and the vertex coordinates into the formulas:

Focus: (0, 0 + 1/(4 * (1/12))) = (0, 1/96)

Directrix: y = 0 - 1/(4 * (1/12)) = y = -1/96

Therefore, the focus of the parabola \(y = (1/12)x^2\)is at the point (0, 1/96), and the directrix is the horizontal line y = -1/96.

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Answer:

Step-by-step explanation:

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

16 students

Step-by-step explanation:

2 pizzas cut into 8ths, 8 slices plus 8 slices = 16

The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

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Based on the amounts Julia paid and the percentage rates, the missing amounts are:

Julia's social security taxes were:

= 6.2% x 2,000

= $124.

Medicare amount:

= 1.45% x 2,000

= $29

Federal income tax:

= 260 / 2,000 x 100%

= 13%

State income tax:

= 120 / 2,000 x 100%

= 6%

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Answer:

540

Step-by-step explanation:

If you divide 540 by 100 (100%) you get 5.4 then multiply it by 10 (10%) to get 54 again. THIS WAS TO CHECK TO GET: 10% or 100% is 10 so multiply 54•10=540

Hope this helps! ;-)

Answer: 7.5

Step-by-step explanation:

\(-15=\frac{x}{-0.5}\\\\-15=-2x\\\\x=\boxed{7.5}\)

The inverse of the equation y = - 4x + 3 is y = (3 - x)/4.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, An equation y = - 4x + 3.

To find the inverse we'll first solve for 'x'.

Therefore,

y = - 4x + 3.

4x = 3 - y.

x = (3 - y)/4.

Now, we'll interchange the positions of 'x' and 'y'.

Therefore,

x = (3 - y)/4 becomes,

y = (3 - x)/4.

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Answer:

Step-by-step explanation:

Answer:

x = 23

Step-by-step explanation:

4x + 8 - 8 = 100 - 8

4x = 92

(4x) / 4 = 92 / 4

x = 23

Answer:

x = 23

Step-by-step explanation:

4x + 8 = 100 ( subtract 8 from both sides )

4x = 92 ( divide both sides by 4 )

x = 23

Answer:13.33333333

Step-by-step explanation:All you have to do is 5 divided by 1.5 times 4. Your welcome random human being (or alien)

Step-by-step explanation:

In the second step while opening the bracket, instead of 'a', there should be - 4a.

Answer:

From Step 2 every step is wrong

Step-by-step explanation:

Ste p 1 : 3a - 5b = 12 - 4(b + a)

Step 2 : 3a - 5b = 12 - 4b - 4a      [ Last term instead - 4a she\he wrote + a ]

Step 3 : 7a  - 5b = 12 - 4b

Step 4 : 7a = 12 + b

\(Step 5 : a = \frac{12 + b}{7}\)

There are 4 ice cream flavors :

chocolate (c), vanilla (v), moos tracks (m), and dark chocolate (d).

There are 3 types of sauces :

hot fudge (h), butterscotch (b), and strawberry (s).

There are 2 types of toppings :

whipped cream (w) and fruit (f)

The sample space are the combinations of ice cream flavors, sauces and toppings with one of each kind.

Listing down the sample spaces as {flavors, sauces, toppings}, will give us :

{c,h,w}, {c,h,f}, {c,b,w}, {c,b,f}, {c,s,w}, {c,s,f}

{v,h,w}, {v,h,f}, {v,b,w}, {v,b,f}, {v,s,w}, {v,s,f}

{m,h,w}, {m,h,f}, {m,b,w}, {m,b,f}, {m,s,w}, {m,s,f}

{d,h,w}, {d,h,f}, {d,b,w}, {d,b,f}, {d,s,w}, {d,s,f}

All in all, there are 24 sample spaces, which is also the product of 4 flavors, 3 sauces and 2 toppins (4 x 3 x 2 = 24)

Answer:

y = 12 when x = 6

Step-by-step explanation:

The equation for inverse proportion is

xy = k where k is a constant

Let x = 9 and y = 8

9*8 = k

72 = k

The equation is xy = 72

Let x=6

6*y = 72

Divide each side by 6

6y/6 = 72/6

y =12

168 US fluid ounces

Hope this helps!

Answer:

95

Step-by-step explanation:

Because you do parenthesis first left to right so 5 x 3=15 then you'll add 9 x 8=72+15=87 then addition and subtraction is next left to right so add 2=89 then+6=95

The place where the company should place the tower should be the circumcenter of the area.

The circumcenter denotes the precise point where the perpendicular bisectors of each triangle's sides intersect.

To ascertain the circumcenter, a systematic procedure is followed. First, the company must draw straight lines connecting the respective centers of the towns, effectively forming the triangular shape. Subsequently, the midpoints of each triangle's sides are determined by measuring and dividing the length of each line segment by two.

These midpoints serve as vital reference points in the subsequent steps. By extending lines perpendicular to the sides at their respective midpoints, the perpendicular bisectors are established. These bisectors intersect at a singular point, which signifies the circumcenter and serves as the optimal placement for the cell tower.

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{-15}

1) Let's solve this expression:

Note that we multiplied by 2 and then by (x+5) so that we could get rid of the denominators.

2) Examining the options, we can state that:

The solution set is S={-15}

Since there's one solution for that.

The chores overshadowed the joy of our Reunion, learned a valuable lesson about managing time and prioritizing obligations

Embarking on a bike ride to visit a friend who lives 3 miles away, little did I know that a looming sense of forgotten chores would soon disrupt my plans. Determined to fulfill my obligations, I mustered the strength to continue riding towards my friend's house, albeit with a heavy heart.

I pedaled towards my destination, the weight of my impending chores grew heavier with each passing moment. Thoughts of unfinished tasks occupied my mind, and I knew that I couldn't stay for long once I reached my friend's place. However, in my haste, a newfound urgency propelled me forward, and I found myself pedaling at a speed 5 mph faster than my initial journey.

With this increased velocity, the return trip promised to be swifter, yet time was slipping away. My mind raced as I calculated the implications of my predicament. The total round trip, comprising both the journey to my friend's house and the hurried return, needed to be accomplished within a tight time frame of 30 minutes.

As I approached my friend's house, I realized that I had no choice but to deliver my news swiftly and immediately turn back around. The momentary joy of reunion would be overshadowed by the pressing chores that awaited me. Regrettably, I bid my friend a hasty farewell, explaining the circumstances that compelled my premature departure.

Once on my bike again, I kicked up the pace, utilizing the extra speed to my advantage. The wind rushed past my face as I hurriedly retraced my path, pushing myself to complete the return trip as swiftly as possible. The seconds ticked away relentlessly, as the pressure mounted to make it back within the allocated timeframe.

In a flurry of determination, I managed to reach home just in the nick of time, fulfilling my duties and responsibilities. Exhausted but relieved, I contemplated the whirlwind of events that had transpired within the span of this half-hour adventure.

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Note the question be like :

A company is hosting a team-building event and has allocated a total of 4 hours for various activities. If Activity A takes 1 hour, Activity B takes 2 hours, and Activity C takes 45 minutes, what is the maximum amount of time that can be dedicated to Activity D while still staying within the allocated 4-hour timeframe?

Answer:

2·v - (u + w) = (5, 0, -10)

Step-by-step explanation:

The given values of the vectors are;

u = (2, -1, 3), v = (4, 0, -2), and w = (1, 1, 3)

The required vector is 2·v - (u + w)

2 × v = 2 × (4, 0, -2) = (8, 0, -4)

(u + w) = (2, -1, 3) + (1, 1, 3) = (3, 0, 6)

Therefore;

2·v - (u + w) = (8, 0, -4) - (3, 0, 6) = (5, 0, -10)

2·v - (u + w) = (5, 0, -10)

Based on the Alternate Interior Angles Theorem, the measure of angle 3 in the image attached below is: 100°

If we have a situation where two parallel lines are intersected by a transversal, according to the Alternate Interior Angles Theorem, the pairs of alternate interior angles formed are congruent.

Angles 7 and 3 lie in the interior sides of the parallel lines but on opposite sides of the transversal, which makes them alternate interior angles. Therefore, based on the Alternate Interior Angles Theorem, we have:

m<3 = m<7

Substitute:

m<3 = 100°

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