Evaluate 9.1p + 8.9r when p = 6 and r =7.

You determine the limit by [tex]\lim_{n \to \infty} a_n = -1[/tex].

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.

Divide the denominator and numerator by 3n as shown.

[tex]\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}[/tex]

[tex]= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1[/tex]

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70 times smaller is the bacterial cell than the amoeba cell.

What is 10^n?

As a result, a power of 10 is represented in long form as the number 1 followed by n zeros, where n is the exponent and is bigger than 0; for instance, 10⁶ is represented as 1,000,000. The number 1 n places after the decimal point represents the power of 10 when n is less than 0; for instance, 10⁻² is represented as 0.01.

Given that, the length of a bacterial cell is about 5 x 10⁻⁶ m, and the length of an amoeba cell is about 3.5 x 10⁻⁴ m.

To calculate times of smaller, divide the length of amoeba cell with bacterial cell.

Therefore, (3.5 x 10⁻⁴)/(5 x 10⁻⁶) = 70.

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Answer:

so the experts answer is correct but its not in scientific notation the answer is: 7 x 10^1

Step-by-step explanation:

Answer: [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The vertex is halfway between the [tex]x[/tex]-intercepts.

So, the answer is [tex]\frac{2+3}{2}=\frac{5}{2}[/tex].

The solution to the expression 9.1p + 8.9r is 116.9 when p = 6 and r = 7

From the question, the mathematical expression is given as

9.1p + 8.9r

The values of the variables are given as

p = 6 and r = 7

Substitute p = 6 and r = 7 in the given expression 9.1p + 8.9r

So, we have the following representation

9.1p + 8.9r = 9.1 * 6 + 8.9 * 7

Evaluate the products in the above equation

9.1p + 8.9r = 54.6 + 62.3

Evaluate the sum in the above equation

9.1p + 8.9r = 116.9

Hence, the value is 116.9

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The area of the triangle given in this problem is of:

A = 84 cm².

The area of a triangle of base b and height h is given by the multiplication of these two dimensions divided by two, which is equivalent to the multiplication of these measures by 0.5, hence:

Area = 0.5 x base x height.

For the triangle given at the end of the answer, these dimensions are given as follows:

Then the area of the triangle is obtained by the multiplication as follows:

Area = 0.5 x 8 x 21 = 4 x 21 = 84 cm².

The triangle from which we calculate the area is given by the image shown at the end of the answer.

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 y = 3/8x + 1/4 is equation of linear equation .

What in mathematics is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                   The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.

                 There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.

3/2x -4y+1=0

  -4y = -3/2x - 1

    y = 3/8x + 1/4

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The complete question is -

Which equation is equivalent to 3/2x -4y+1=0

Answer:

[tex]5mn^{2} (2+ 5m^{2} n)[/tex]

Step-by-step explanation:

I assumed the polynomial is [tex]10mn^{2} +25m^{3}n^{2}[/tex]

FIRST: Highlight the common factors{ 5 , m and[tex]n^{2}[/tex])

[tex]5mn^{2} (2+ 5m^{2} n)[/tex]

The probability that the second ball is greater than the first ball is 5/8

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

As to even odd

first ball can be anything. Second would have to be the first is not thus 5/9.

As second smaller than first

if first is 9, probability is 8/8, 100%, if 7 probability s 6/8 so in general take first ball, value k,

then the probability is sum (k - 1) / (n = 10 - 1) for k=1,2,…,9 so that’s all in 45/8 times 1/9 so 45/72 or 5/8.

Even a clear ball has Color so unless you have an invisible ball in your collection, both balls will be some amount of color or color.

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The transformation that has changed the parent function f(x) = (0.5)^x to the exponential graph passing through points (1,2) and (2,1) is given as follows:

f(x - 2).

The parent function for this problem is given as follows:

f(x) = (0.5)^x.

Hence the points on the graph of the parent function are given as follows:

The points on the transformed function are given as follows:

(1,2) and (2,1).

Meaning that the value assumed at x = -1 is now assumed at x = 1, while the value assumed at x = 0 is not assumed at x = 2, meaning that the function was shifted right two units, and the transformation is defined as follows:

f(x - 2).

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Answer:

143. Divide 91/7 = 13, then take the number of oil changes per day and times it by 11. 13 x 11 = 143.

Step-by-step explanation:

Answer:

113.75

Step-by-step explanation:

Since 11 days is only 4 days away from 11, divide 91 / 4 = 22.75. Add this number to 91 to get the answer.

In order to achieve at least two integers with common digits, we must choose at least 10 integers.

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction.

All three-digit integers in the range of 100 to 999 are taken into consideration.

The ten numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are all feasible.

In the worst case, there are no common digits among the nine chosen integers. It is feasible, for instance, that no two of the nine integers 111, 222, 333, 444, 555, 666, 777, 888, and 999 share any digits.

There is only one digit that was not stated in the previous nine integers, therefore if we choose a tenth three-digit integer, it must share at least one digit with the first nine integers. However, a three-digit integer cannot start with a 0, so the first digit must be something else.

One of the previous nine integers must have also used the three-digit integer. In order to achieve at least two integers with common digits, we must choose at least 10 integers.

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According to the given speed, the minimum rate of climb must be maintained to meet the required climb rate to 4,800 feet as specified on the instrument departure procedures is option (d) 870 feet per minute.

Speed:

In math speed refers the rate of change of position of an object in any direction.

Given,

Here we have using an average ground speed of 120 knots and taking off on runway 14.

Now, we need to find in what minimum rate of climb must be maintained to meet the required climb rate (in feet per nm) to 4,800 feet as specified on the instrument departure procedures.

While we looking into the given question, we have identified that,

Speed = 120

Distance = 4800

Then the  minimum rate of climb must be maintained to meet the required climb rate  is calculated as,

Here we also note in the bottom left corner of the overhead view of the departure requires 435 ft/nm climb gradient to 4800' for obstacle clearance.

Therefore, the minimum rate is 870 feet per minute.

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The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

Given that,

A conical tank is filled with water at a pace of 9 feet per minute. The tank is 10 feet tall and has a base radius of 5 feet. It stands pointed down.

We have to find how quickly does the water level rise when it is 6 feet deep.

We know that,

dv/dt= 9 feet³/min

x=5 feet

y=10 feet

And we have x/y=1/2 ----->equation(1)

We know the formula

V=1/3πx²y

Differentiating on both sides

dv/dt=9

1/3πy(2x) dx/dt+π/3(x²)dy/dt

=π/3[2xy dx/dt+x² dy/dt]

From equation(1)

x/y=1/2       or     y=2x

dy/dt= 2dx/dt

Now,

9=π/3[xy dy/dt+x² dy/dt]

9= π/3 dy/dt[xy+x²]

dy/dt=9×3/π×(18+9)

dy/dt=27/π×27

dy/dt= 1/π

dy/dt=0.318 feet/min

Therefore, The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

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On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207

There are two approaches to define arithmetic progressions (AP):

The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.

9,15,25..............

15-9 = 6

25-15 = 10

a4 - 25 = 14 => a4 = 39

a5-39 = 18 => a5 = 57

a6-57 = 22 => a6 79

...

...

...

...

...

a10 - 169 = 38 => a10 = 207

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The inequality to describe the number of subscriptions Andre must sell to reach his goal is  3s + 25 ≥ C.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.

∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.

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Answer:

The answer to you question is 18 and  20

18 and 20

Yes, the permutation test is used in this problem to conduct a hypothesis testing about comparing  the 95th percentile of the income of country a and that of country b.

Yes, the permutation test can be used in this problem. The permutation test is a nonparametric test that can be used to compare two or more groups to determine if there is a statistically significant difference between them. In this case, we can use the permutation test to compare the 95th percentile of the incomes of the two countries. The permutation test would involve randomly permuting the data for each country, then calculating the 95th percentile for each permutation. The difference in the 95th percentile between the two countries in the original data can then be compared to the differences in the 95th percentile of the permuted data to see if the difference is statistically significant.

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As per the empirical rule, the percent of data in the shaded region is 68%.

In statistics, the empirical rule states that When you use a standard normal distribution also known as Gaussian Distribution we have to consider the following

=> Around  68% of values fall within one standard deviation of the mean.

=> Around 95% of the values fall within two standard deviations from the mean.

=> Other all of the values are about 99.7% that fall within three standard deviations from the mean.

Therefore, this facts are the 68 95 99.7 rule. And it is also called the Empirical Rule because the rule originally came from observations.

Here we have given the the data is normally distributed. And we need to find the percent of data is in the shaded region.

While we looking into the following diagram and according to empirical rule,68% of the data falls within one standard deviation of the mean.

Because, the center part is the shaded region,

So, it can be calculated as,

=> 34 + 34 = 68%

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The domain for the given graph is obtained as {1, 2, 3, 4}.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

From the graph of the given exponential function,

The set of ordered pairs can be written as follows,

{(1, 10), (2, 20), (3, 40), (4, 80)}

Since the domain is the set of first elements for a given pair of ordered set.

The domain is given as {1, 2, 3, 4}.

Hence, the domain obtained from the given graph is {1, 2, 3, 4}.

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The graph missing in the question is attached here.

The person can buy a total of 36 distinct systems from three models of the basic unit, three models of keyboard, and four models of printer.

Given, a person buying a personal computer system is offered a choice of three models of the basic unit, three models of keyboard, and four models of printer.

we have to find the number of distinct systems that can be purchased.

Using the concept of Permutations and Combinations, we get

Choose One model of basic unit from three models, Choose one model of keyboard from three models of keyboards and also choose one model of printer from four models of printers.

C(3 , 1)×C(3 , 1)×C(4 , 1)

= 3×3×4

= 36

So, the total of 36 systems can be purchased.

Hence, the total of 36 systems can be purchased.

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Piecewise linear functions, f(x) as common core algebra, Evaluate each of the following :

(1) f(-3) = 12

(2) f(4) = 2

(3) f(0)= 8

(4) f(3)= 8

A piecewise linear function is a function defined on the interval [xₘᵢₙ ,xₘₐₓ]. A piecewise linear function is a function that consists of straight line segments. This is a piecewise function whose pieces are affine (linear) functions. Graphs of piecewise linear functions consist of line segments and rays.

We have given that,

f(x) = 5x - 3 ; x< -2

= x+8 ; -2≤x< 3

= 1/3(x) + 7 ; x ≥3

we see here that , f(x) is a piecewise linear function defined on interval [-2,3).

Now, we solve the following

(1) f(-3) , here x = -3< -2 i.e we take f(x) =5 x -3

=> f(-3) = 15 - 3 = 12

(2) f(4) , x= 4 >3 so, f(x) = 1/3(x) + 7

=> f(4) = 1/3(4) + 7 = 14/7 = 2

(3) f(3) , x = 3 so, f(x) = 1/3(x) + 7

=> f(3) = 1/3(3) + 7 = 8

(4) f(0) , x = 0 or -2 < x < 3 so, f(x) = x+8

=> f(0) = 0+8 = 8

Hence, we evaluate the given functions.

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Complete question:

piecewise linear functions common core algebra 2 homework answers

5x - 3 x&lt;-2 1. For f (x) = x+8 -25x&lt;3 answer the following questions. -x+7 x23 (a) Evaluate each of the following by carefully applying the correct formula: (1) f ( -3 ) (ii) f (4) (iii ) f ( 3 ) (iv ) f (0 )

The value of x in the triangle is 70°

Given:

the equation m<A + m<B = 130°

We know that:

m<A + m<B + m<C = 180° (sum of angles in a triangle)

Since m<A + m<B = 130°, we have

130° + m<C = 180°

m<C = 180° - 130°

m<C = 50°

Considering the middle triangle, let the unlabeled angle be y:

m<C + m<C + y + 40° = 180° (sum of angles on a straight line)

50 + 50 + y + 40 = 180°

y = 180° - 140° = 40°

x + x + y = 180° (sum of angles in a triangle)

2x + y = 180°

2x + 40° = 180°

2x = 140°

x = 140/2

x = 70°

Thus, the value of x is 70°

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The equation for such line is 5x - y - 22 = 0, using properties of parallel line and slope of a line.

What are the properties of two parallel line ?

1. These lines never intersect each other.

2. These lines have same slope .

General Equation for a line :

y = mx +c

Where m is slope of a line and c in constant .

As in que , we are given one line ,

so we can find slope of that line , using differentiation

3dy/dx - 15 = 0

slope : (1dy/dx) = 5

From 2nd property :

Slope of another line = 5 and passing point is (5,3)

Put all these information in general equation for a line:

3 = 5*5 + c

c = -22

So, the equation for a line with slope (m):5, constant(c):(-22) is

y = 5x - 22  

or 5x - y - 22 = 0

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An isosceles triangle is a type of triangle which has two of its sides to be equal, viz-a-viz two of its internal angles are equal. The required proof in the given question are stated below:

A triangle is a trigon with just three straight sides, thus three internal angles. Thus, the sum of its internal angles equals [tex]180^{o}[/tex]. Some common examples are. equilateral, isosceles, right angled, scalene, etc.

An isosceles triangle is one which has two of its sides equal, so that the measure of two of its internal angles are also equal.

Therefore, the expected proof in the question are:

              STATEMENT                                             REASON

1. AB = BC = CD = DE = EA        Similar sides of a regular pentagon  

2. AB = DE                                  Congruent of sides of similar triangle

3. BC = CD                                 Congruent of sides of similar triangle

4. <ABC = <EDC                         Congruent angles of similar triangle

5. AC = CE                                 Congruent sides of an isosceles triangle

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Answer:

The answer is 20

Step-by-step explanation:

6/8 = 15/y

(6) × y = (8) × (15)

6y = 120

6y/6 = 120/6

y = 20

Thus, The value of y is 20

Answer:

[tex] \sf \: y = 20[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

Now the value of y will be,

[tex] \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} [/tex]

[tex] \sf \rightarrow \: 6y = 15 \times 8[/tex]

[tex] \sf \rightarrow \: 6y = 120[/tex]

[tex] \sf \rightarrow \: y = \frac{120}{6} [/tex]

[tex] \sf \rightarrow \boxed{ \sf y = 20}[/tex]

Hence, the value of y is 20.

The linear regression equation that represents this set of data is given as follows:

y = -27.3x + 843.2.

The estimate of the calendar year in which the number of new cases would reach 604 is of:

2019.

The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.

From the table given at the end of the answer, the points of the function are given as follows:

(0, 832), (1, 827), (2,800), (3,750).

Inserting these points into the calculator, the equation is given as follows:

y = -27.3x + 843.2.

The number would reach 604 when:

y = 604

-27.3x + 843.2 = 604

x = (843.2 - 604)/27.3

x = 8.7

2011 + 8.7 -> during the year of 2019.

The table is given by the image shown at the end of the answer.

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A gallon which is a liquid measuring unit of US in cooking measurements, there are eight cups in half of a gallon.

A gallon is the most commonly used unit of measure for measuring the volume of liquids. US gallons are legally defined as 231 cubic inches, or exactly 3.78 liters .

Ounces : fluid ounces (fl oz, fl. oz ) is a unit of volume commonly used to measure liquids. To convert from gallons to ounces, multiply the value in gallons by 128. So, 1/2 gal = (1/2) × 128 = 64 oz or ounces, 1/2 gallons = 64 ounces. Now, let's measure a cup in gallons, 1 cup is equal to 8 ounces ,then 8 cups are 64 ounces. From the above discussion we conclude that 8 cups = 64 ounces = 1/2 gallon. So, 8 cups is 1/2 gallon.

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Eigenvalues are a unique collection of scalar values connected to the set of linear equations that are most often found in the matrix equation.

Eigenvalues are the unique set of scalar values connected to the set of linear equations most likely found in the matrix equations. Also known as characteristic roots, the eigenvectors are. After applying linear transformations, the vector is non-zero and can only be altered by its scalar factor.

The term "eigenvalue equation" refers to an equation in which the operator multiplies the function by a constant when applied to a function. An eigenvalue is the resultant numerical value, and an eigenfunction is the function itself.

Given:

The given value is

[tex]$$A=\left[\begin{array}{lll}0 & 1 & 0 \\0 & 0 & 1 \\a & b & c\end{array}\right]$$[/tex]

where a, b, c are arbitrary constants.

If [tex]$\lambda$[/tex] is an eigen value of A Then,

[tex]$& E_\lambda={ker}(A-\lambda I) \\[/tex]

Now,

Last two rows are linearly independent.

So, we have

[tex]${dim} E_\lambda=1$[/tex]

Therefore,

[tex]${gemu}(\lambda)=1$$[/tex]

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(-12, -1) is a solution to both y= 4x - 8 and y = 8x - 4.

Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is considered a solution to the problem. Finding the solution or solutions to an equation is known as solving it.

Unique, infinitely many solutions and no solutions are three types of solution.

If we put x=-12 and y=-1 in both of the given equation we will get L.H.S=R.HS . So (-12, -1) is the required solution.

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