use exponential fitting to find a closed formula for the sequence: 4, 5, 7, 11, 19, 35, 67, ...

Step-by-step explanation:

the correct answer is Option C (⁷/2.)

hope this helps you.

x -2 and x 5 provide the solution to the system of inequalities.

A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities. Finding the variable values that will make each inequality true simultaneously is necessary to solve a system like this.

(x+2)(x-5) 0, according to the inequality formula.

The inequality's zeros will be provided by the inequality's zeros, as demonstrated:

(x+2)(x-5) < 0.

(x+2) < 0

x < -2

Similarly;

x - 5 < 0

x < 5

Thus, x -2 and x 5 provide the solution to the system of inequalities.

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Answer C and D.

Asymptotes are hypothetical lines that the entire function graph or a specific region of the graph approaches very closely. When graphing a function, the asymptotes are highly useful since they make it easier to visualize which lines the curve shouldn't cross.

Given a cable company uses the function f(x)= (29x+49)/ x to represent the average monthly cost of their cable where x is the number of months a consumer has cable. This function asymptotes if x = 0 let's solve it for x = 0

F(x) = (29*0 +49) /0...(1)

Let's solve this function for y= 29

29 = (29x + 49)/ x

29x = 29x + 49.......(2)

Therefore from equations 2 and 1, we can conclude that function is asymptote at x= 0 and y = 29.

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Answer:

1.50

Step-by-step explanation:

Answer:

\(\huge\boxed{\$ \ 1.725}\)

Step-by-step explanation:

Costing Price = $ 11.50

Tax = 15% of $11.50 :

=> \(\sf \frac{15}{100} * 11.50\)

=> \(\sf 0.15 * 11.50\)

=> $1.725

So, Sales tax is $1.725

The random nature of the process is why Gina doesn't get the theoretical probability. If she were to repeat this experiment say 1000 or perhaps 10,000 times, then her experimental probability value should get closer to 1/2. It likely won't land *exactly* on 1/2 because again of the random nature of the outcomes.

For more information, check out the Law of Large Numbers.

Answer:

The theoretical probability of spinning a head = 1/2 = 0.5

Therefore, if Gina spins a penny 100 times, the theoretical number of times it will land head side up = 0.5 x 100 = 50 times

Gina's experimental probability is 38/100 = 0.38

Therefore, the experimental probability is less than the theoretical probability.

The main difference between experimental and theoretical probability is that experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly), whereas theoretical probability is based on possible outcomes based on assumptions.

If Gina continued to spin the penny, as the number of times she spun it increased, you would expect for the experimental probability to get nearer to the theoretical probability of 0.5.

A) The function that represents the average of the class is;

y = 65(1.011)^(x)

B) The average of the class after one week will be expressed as;

y = 70.17

The general formula for the nth term of a exponential function is;

y = ab^(x)

where;

a is initial amount

b is growth factor

x is the amount of periods being considered

Now, we are told that the initial score for the exam was 65. Thus;

a = 65

The growth factor is 1.1% and this is; b = 1.011

Thus, the function that represents the average of the class is;

y = 65(1.011)^(x)

The average of the class after one week will be expressed as;

y = 65(1.011)^(7)

y = 70.17

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Answer:

The person has a higher average speed, so the person moves faster than the bird.

Step-by-step explanation:

We have to work with the measures in the same units, i am going to use distance in kilometers and time in minutes.

A certain species of birds migrates 24,000 miles in 90 days.

24000 miles = 24000*1.61 = 38640 kilometers.

90 days = 90*24*60 minutes = 129 600 minutes.

Average speed is distance divided by time, so

38640/129600 = 0.298 kilometers per minute.

A person can speed walk 40 kilometers in 100 minutes.

40/100 = 0.4 kilometers per minute

0.4 > 0.298, so the person moves faster.

Answer:

D.

Step-by-step explanation:

6a² = surface area for cube

6(5)² = 150

2\(\pi\)(r)(h)+2\(\pi\)r²  = surface area cylinder

2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi

150 + 20pi = 212.8318531

Answer:

35%

Step-by-step explanation:

Hope I can help!

Answer:

6400.00%

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

integers are like whole numbers but can also be negative

Answer:

A

Step-by-step explanation:

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

it takes the bears 12 days to eat honey together.

Step-by-step explanation:

1/x+9+1/x+16=1/x

(solve this using cross multiplication)

= x^2 = 144

x=12

The number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

We can define a constant as "Manpower" needed for doing that specific work.

Each worker has his/her own strength. That strength is applied per unit of time.

Let we define:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

(we used multiplication as it represents linear use of strength to finish the task, so using that strength for a finite units of time means you stacked up your strengths that many times to finish that work)

Here, we have:

Assume that:

Then, we get:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

\(M = x \times S\\M = y \times T\)

If bear A and bear B both do the work together, then their strenghts will add up.

That means, the combined strength would be S + T per day

The manpower the work needs is still M, therefore, the time needed is:

\(M = \text{Time needed} \times (S + T)\\\\\text{Time needed} = \dfrac{M}{S+T}\)

This is the time needed for both bears to do the work together.

Also, it is given that:

It takes a bear 9 more days to eat a barrel of honey alone than it takes the bear and a second bear to eat the barrel of honey together.

or

Time needed by bear A to do work = 9 + time needed by both bears to do the work

or

\(x = 9 + \dfrac{M}{S + T}\)

Also, it is given that:

It takes the first bear 7 fewer days to eat a barrel of honey alone than it takes the second bear to eat a barrel of honey alone.

or

Time taken by bear A to do the work = Time taken by bear B for that work - 7 days

or

\(x = y - 7\)

Thus, we got these equations:

\(M = S \times x\\M = T \times y\\\\x = \dfrac{M}{S + T} +9\\\\x = y - 7\)

call them first, second, third and fourth equation as per their ordering.

From the first and second equation, we get:

\(S = \dfrac{M}{x}\\\\T = \dfrac{M}{y}\)

Putting these values in the third equation, we get:

\(x = \dfrac{M}{M/x + M/y} + 9\\\\\\x = \dfrac{xy}{x+y} + 9\\\\(x-9)(x+y) = xy\\x^2 -9x -9y + xy = xy\\x^2 -9x = 9y\)

From the fourth equation, we know that:

\(x = y - 7\)

or \(y = x +7\)

Putting this value of y in the  equation \(x^2 -9x = 9y\), we get:
\(x^2 -9x = 9(x+7)\\x^2 -9x = 9x + 63\\x^2 -18x -63 =0\\\\x^2 -21x + 3x -63 = 0\\x(x-21) + 3(x - 21) = 0\\(x+3)(x-21) = 0\\(x+3) = 0, (x-21) = 0\\x = -3, x = 21\)

'x' represents time in number of days. So it cannot be negative.

Thus, the value of x obtained is 21.

Also, we need: Time needed for both the bears to do the work together.

This time is the value of \(\dfrac{M}{S+T}\), which is equal to \(x - 9\) days (from the third equation)

Thus, the time needed  for both the bears to do the work together = \(x-9 = 21-9 = 12 \; \rm days\)

Thus, the number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

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The range is the smallest number minus the largest number on a number line. Hope that helped!

The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

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Answer:

874.9022

hope this helps

The given decimal rounded to the nearest ten-thousandth is 874.9022.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

The given decimal number is 874.902237102.

The decimal is rounded to the nearest ten-thousandth is 874.9022.

Therefore, the given decimal rounded to the nearest ten-thousandth is 874.9022.

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The 11th term of the geometric sequence 1, 4, 16,... is 4¹⁰.

A sequence is a grouping of objects in a particular order that permits repetitions. It has members, just like a set does. The length of the sequence is determined by the number of items.

Consider the geometric sequences 1, 4, 16......

For a geometric sequence a, ar, ar²,.....

Where a is the first term, and r is the common ratio of the sequence.

Then for the sequence 1, 4, 16,...

a = 1 and r = 4

The nth term of a geometric sequence is given as:

aₙ = ar⁽ ⁿ ⁻ ¹⁾

Therefore, the 11th term of the sequence will be:

a₁₁ = 1 × r¹¹ ⁻ ¹

a₁₁ = (4)¹⁰

a₁₁ = 4¹⁰

Hence, the 11th term of the sequence is 4¹⁰.

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It should be noted that the number of sample size based on the information will be 300.

In order to calculate the sample size, we can use the following formula:

n = z² * p * (1-p) / E²

n = 1.96² * 0.5 * (1-0.5) / 0.05²

= 300

A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.

In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".

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Answer:

y = - x + 6

Step-by-step explanation:

\( point \: slope: y - y_{1} = m(x - x_{1})\)

as y is the y coordinate of the final point , y1 is the y coordinate of the initial point, m is the slope or gradient of the line, x is the x coordinate of the final point, and x1 is the x coordinate of the initial point.

given (-1,7) and (2,4). 7 = y1, 4 = y, -1 = x1, 2 = x.

when substituted into the equation the unknown variable is the slope which we are solving for.

y-y1=m(x-x1) ; y = 4, y1 = 7, x = 2, x1 = -1

(given)

4-7 = m(2--1)

(substitution property of equality)

-3 = m(2--1)

(subtraction property of equality)

-3 = m(3)

(subtraction property of equality)

-3 = 3m

(multiplication property)

-1 = m.

(division property of equality)

m = -1

(symmetric property of equality)

_____________________________

once m is solved you just need the initial values to solve for the actual equation.

y - y1 = m (x - x1) ; y1 = 7, m = -1, x1 = -1

(given)

y - 7 = -1 (x - -1)

(substitution property of equality)

y - 7 = -1 (x + 1)

(subtraction property if equality)

y - 7 = -x - 1

(distributive property of equality)

y = -x - 1 + 7

(addition property of equality)

y = -x + 6

(addition property of equality)

Answer:

get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.

fjnjerng ertekjrtker terkjtkert ertkjrenktmermt erktnkermter

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

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Find the perimeter of the equilateral triangle.

9x - 16

Step-by-step explanation:

18 ball=3team

18=3x

x=18/3

x=6

the answer is 18:3

if (:) this sigh of urs indicate divide

The depreciation schedule for the new machines of University Car Wash, using the activity-based method, is as follows:

Year   Initial Cost   Depreciation    Accumulated    Net Book Value

                                  Expense        Depreciation

1         $267,000        $60,750            $60,750            $206,250

2        $267,000        $24,300            $85,050             $181,950

3        $267,000        $26,325             $111,375            $155,625

4        $267,000        $54,675           $166,050           $100,950

5        $267,000        $50,625          $216,675             $50,325

6        $267,000        $26,325         $243,000             $24,000

A depreciation schedule is a table that shows the annual depreciation expense, the accumulated depreciation over the years, and the net book value of each asset, including the initial cost.

An activity-based method of depreciation uses the machine hours or other activity bases used to determine each year's depreciation expenses.

Cost of machines = $267,000

Residual value = $24,000

Depreciable amount = $243,000 ($267,000 - $24,000)

Estimated useful life = 6 years or 12,000 total hours

Hourly depreciation rate = $20.25 ($243,000/12,000)

Year   Annual Depreciation Expense

1           $60,750 (3,000 x $20.25)

2          $24,300 (1,200 x $20.25)

3          $26,325 (1,300 x $20.25)

4          $54,675 (2,700 x $20.25)

5         $50,625 (2,500 x $20.25)

6         $26,325 (1,300 x $20.25)

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The value of a should be less than -1.

The equation of a parabola is given by the following function,

\(y=f(x)=\pm a(x-h)^2+k\)

where,

(h, k) denotes the coordinates of its vertex,

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

\(f(x) = x^2\)

\(g(x)=ax^2\)

For the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.

Hence, the value of a should be less than -1.

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Answer:

a = 5

Step-by-step explanation:

a = 5

all you have to do is divide both sides by 3

Answer:

A=5

Step-by-step explanation:

Divide each term by 3 and simplify :)

Hope I helped!

The number of words Gillan can read in 1 minute is,  165

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Gillan read 3,135 words in 19 minutes

The number of words read each minute = w

Now, it has given,

Total words = 3135

Time taken = 19 minutes

For words per minute,

we need to take ratio of total words and total time taken,

Ratio =  Total words/Time taken

         =   3135/19

         =   165

Hence, the number of words in 1 minute is 165

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Answer:

Step-by-step explanation:

y = 3x + 9