Find a recursive rule for the nth term of the sequence.

5, 20, 80, 320, ...

Answer:

A = 101250 meter²

Step-by-step explanation:

Answer:

Maximum area enclosed will be 101250 meter².

Step-by-step explanation:

Let the length of the rectangular plot is x meters and the width is y meters.

900 meters is the length of the fence which represents the length of the three sides of the plot.

Therefore,

x + 2y = 900

y =  meters

Now the area of the rectangular plot will be

A = Length × Width

  = (x)(y)

  = 

  = 450x - 

We know for the maximum area we will differentiate the area and equalize it t the zero.



= 450 - x

For the maximum area, 

Therefore, 450 - x = 0

x = 450

and y = 

y = 

y = 450 - 225

  = 225 meters

Now the area enclosed A = 450 × 225

A = 101250 meter²

Answer:

1) f = 16

2) h = 10

Step-by-step explanation:

all interior angles of a triangle add up to 180 degrees.

1) 46 + 67 + (4f+3) = 180

reduce:

4f+3 = 67

4f = 64

f = 16

2) 60 + 3h + 90 = 180

3h = 30

h = 10

Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.

Answer:

8/50 = 0.16

Step-by-step explanation:

Answer:

0.16

Step-by-step explanation:

Hope this helps have a nice day:)))

Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

Hello,

(gof)(x)= f(g(x)

is the composition which produces the greater output

Step-by-step explanation:

(fog)(x)= g(f(x))

=g(2x-6)

=5(2x-6)+1

=10x-29

(gof)(x)=f(g(x))

=f(5x+1)

=2(5x+1)-6

=10x-4

But for all real, 10x-29 < 10-4

Answer:

(2, - 1 )

Step-by-step explanation:

The solution to the system is at the point of intersection of the 2 lines.

They intersect at (2, - 1 ) ← solution

Answer:

1427832.087y4441x6.7

Answer: x=13°    y=9°

Step-by-step explanation:

1.

\((4y+27)^0=63^0\ ( As\ interior,\ cross-lying\ angles)\\4y+27^0=63^0\\4y+27^0-27^0=63^0-27^0\\4y=36^0\\\)

Divide both parts of the equation by 4:

\(y=9^0\)

2.

If two parallel lines are intersected by a secant, then the sum of the unilateral angles is 180°:

\(((5x-8)^0+63^0)+(6x-31)^0=180^0\\\\5x-8^0+63^0+7x-31^0=180^0\\\\12x+24^0=180^0\\\\12x+24^0-24^0=180^0-24^0\\\\12x=156^0\\\\\)

Divide both parts of the equation by 12:

\(x=13^0\)

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information.

To calculate the proportion of candy bars with fewer than 200 calories, we need to know the total number of candy bars and the number of candy bars that have fewer than 200 calories.

Without this information, we cannot determine the proportion. The number of candy bars with fewer than 200 calories could vary greatly depending on the specific dataset or context.

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information regarding the total number of candy bars and the number of candy bars that fall into that category.

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The slope of the line of best fit in this context represents the rate of change in the number of hot cocoas sold for every unit increase in the day's high temperature.

In other words, it represents how much the sales of hot cocoa increase or decrease with respect to changes in the day's high temperature. If the slope is positive, it means that as the temperature increases, Justin sells more hot cocoas, and if the slope is negative, it means that as the temperature decreases, Justin sells more hot cocoas.

The magnitude of the slope indicates the degree to which the number of hot cocoas sold is affected by changes in the temperature.

The slope of the line of best fit in this context represents the rate of change in the number of hot cocoas sold for every unit increase in the day's high temperature.

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Answer:

y = 3x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)

m = \(\frac{-16-14}{-2-8}\) = \(\frac{-30}{-10}\) = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 14 ) , then

14 = 24 + c ⇒ c = 14 - 24 = - 10

y = 3x - 10 ← equation of line

The given statement "An objective of engineering analysis is to confirm the model behaves in the manner we expected it to" is False because identifying the problems is also an objective.

While confirming the expected behavior of a model is a part of engineering analysis, it is not the sole objective. The main objective of engineering analysis is to use mathematical and scientific principles to design, evaluate, and optimize engineering systems and components.

This involves creating mathematical models of the system or component and using various analysis methods to understand and improve its behavior.

In addition to confirming the expected behavior, engineering analysis also involves identifying and understanding potential problems or limitations of the system, determining the effects of different design parameters, and assessing the system's performance under different conditions.

The results of the analysis can then be used to make informed decisions about design modifications or improvements to achieve the desired performance or behavior. Therefore, while confirming expected behavior is important, it is only one aspect of the broader objective of engineering analysis.

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Mia's total distance driven is given by the function C(m) = 55m, where m represents the number of hours she has been driving, and the common difference is not applicable in this context.

In this scenario, Mia is driving at a constant speed of 55 miles per hour. We can represent the total distance driven, denoted as "C(m)," using a function where "m" represents the number of hours Mia has been driving.

The function C(m) = 55m indicates that the total miles driven is equal to 55 times the number of hours Mia has been driving.

For example, if Mia drives for 2 hours, we can calculate the total distance driven by substituting m = 2 into the function:

C(2) = 55 \(\times\) 2 = 110 miles.

This means that after driving for 2 hours, Mia would have covered a distance of 110 miles.

The common difference mentioned in the question seems to be unrelated to this scenario.

In the context of arithmetic sequences or series, the common difference represents the constant amount by which each term in the sequence increases or decreases.

However, in the given scenario, there is no sequence mentioned, so the concept of a common difference does not apply.

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Answer:

a) 210×0.10=21

b) 48×0.10=4.8

Step-by-step explanation:

210-21=189

48-4.8=43.2

the probability that someone prefers the lemon-flavored water over both competitors' brands is approximately 13.3%

we need to look at the overlap between the two groups that preferred the lemon-flavored water over competitor A and competitor B. According to the survey results, 35% of the 1000 people surveyed preferred the lemon-flavored water over competitor A, and 38% preferred it over competitor B. However, we also know that 47% did not prefer the lemon-flavored water over either competitor's brand.
To calculate the probability that someone prefers the lemon-flavored water over both competitors' brands, we need to use conditional probability. We can start by subtracting the percentage of people who did not prefer the lemon-flavored water over either competitor's brand from 100% to get the percentage of people who preferred at least one of the three drinks.
100% - 47% = 53%
Next, we can find the probability that someone prefers the lemon-flavored water over both competitors' brands by multiplying the percentages of people who preferred the lemon-flavored water over competitor A and competitor B.
35% × 38% = 13.3%
In conclusion, based on the survey results, we can say that there is a 13.3% probability that someone prefers the lemon-flavored water over both competitor A and competitor B.

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Answer:

1/5

Step-by-step explanation:

Simplify the expression until it can no longer be simplified:

40/200

4/20

1/5

Hope this helps. Have a nice day you amazing bean child.

New car prices to fall within is $18,300 - $41,900

Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.

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Answer:

y= -6/5+3

Step-by-step explanation:

do m=y-y/x-x, so slope is -6/5

gives you y intercept, so y=-6/5+3

This is my explanation thus sucks and half the timem you guys dont even have the right answer . So this is my answer for you at leatst try to get it tight because if you dont try you wont suceed

Answer: The Horizontal line at 5

Step-by-step explanation: For Y to be a function, there cannot be different points on the same x value. The horizontal line is the only one that has one y value per x value.

Hope this helps!

Answer: C

Step-by-step explanation:

7/8 = x/56

x = 7 x 7

so, 49/56 = rod

so, 49 pieces will be made

hope it helps :)

The cheapest aspect of the party that she can eliminate to keep from overdrawing her account is: c. Catering.

Using this formula

Party to eliminate=Beginning account balance-Total expenses

Where:

Beginning account balance =$708

Total Expenses:

Decorations  $76.92

Catering        $150.66

Musicians      $242.15

Refreshments $123.36

Venue            $260.47

Total expense $853.56

Party to eliminate=$708-$853.56

Party to eliminate= $145.56

Based on the above calculation we are going to eliminate catering  so as to keep from overdrawing her account because the expenses is  higher than $145.56.

Therefore the correct option is C.

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Answer:

C

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  (2, 6)

Step-by-step explanation:

The function is constant where its graph is horizontal. That portion of the graph lies between x=2 and x=6. In interval notation, the function is constant in the interval (2, 6).

This question has no direct question, so here are some facts if you want them:

This equation can be expressed as a linear equation.

The equation can be expressed as: y =40x + 500

The y-intercept is 500, and the slope is 40.

If you type in a graphing website like desmos, then you can actually graph the line if you wanted (or needed) to.

I'm not really sure what the question is, but maybe if you needed help, here you go.

Answer:

115/12, or 9 7/12

Step-by-step explanation:

Let's start by turning all of these into improper fractions.

2 3/6 becomes 15/6

2 2/3 becomes 8/3

4 5/12 becomes 53/12

Now we need to get a common denominator by turning them all to x/12

15/6 becomes 30/12, because we multiply it by 2/2

8/3 is a bit trickier because we have to multiply it by 4 in order to reach x/12, but it turns out to be 32/12 after multiplying it by 4/4

53/12 is already x/12, so we don't have to simplify this one.

30/12 + 32/12 + 53/12 = 115/12, or 9 7/12

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)

So, the dressmaker has 360 in of ribbon.

Answer:

x = 424.3

Step-by-step explanation:

we will answer this in 2 parts
first, we will prove the triangle is equilateral, using the known sum of all angles in a triangle.
then, we will find x using pythagorean theorem.
there is another way, involving trigonometric functions, i will show it too, at the end.
first, this is a right triange, as given in the drawing. so the known angles are 90 degrees and 45 degrees, leaving the third angle to be 45 as well.
this means the triangle is equilateral, so the sides of it are x, x, 600
now, since it is a right triangle, we can apply the pythagorean theorem, we get: x² + x² = 600²
from this we get:

2x² = 360000
x² = 180000
x = √180000 = 424.264
as we are asked to round to the nearest tenth, we write:

x = 424.3

bonus way - trigonometric functions
in a right triangle, the ratio between a side and the hypotenuse, is cos(α) where α is the angle between them, meaning:

x/600 = cos(45°)
and:
x = 600 × cos(45°) = 424.3