Solve the given initial-value problem. y',' + 5y"-8y'-12y-0, y(0)-y'(0)-0, y"(0)-1 y(x)

Conner's work is correct.

\((3^56^8)(3^96^{10})=(3^53^9)(6^86^{10})=3^{5+9}6^{9+10}=3^{14}6^{19}\)

Given piecewise function has a jump discontinuity at 0 or x=0 i.e. B.

What exactly is a piecewise function?

A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x≥0 ,

     -x  if x><0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As jump discontinuity is defined as where the endpoint of one segment and the start of the following segment may have the same x coordinate but have different values of f(x). In the piecewise linear function, such a difference is known as a jump discontinuity.

and in the given graph that happened at x=0 or 0.

Hence,

         Given piecewise function has a jump discontinuity at 0.

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Answer:

2:1

Step-by-step explanation:

We can set up a ratio using a side from Figure A and a side from Figure B. Let's use the shorter side of the parallelogram...

4:2

We can simplify this down to...

2:1

Answer:

$60

Step-by-step explanation:

There's not enough information. We need to know how often the interest is compounded. I'll assume it's yearly. If not, you can apply the same method to what it actually is.

If it's compounded yearly that means it's going to be compounded 5 times so the equation becomes.

5*(300*4%)

which is:

5*(300*.04)

which becomes:

5*12

Which is:

$60

The Interquartile range of the given set is 1.5.

What is Interquartile range ?

The variation between the third and first quartiles is defined by the interquartile range. The numbers that partition the entire series into four equal sections are known as quartiles. There are therefore 3 quartiles. The lower quartile is represented by the letter Q₁, the higher quartile by the letters Q₁, and the middle quartile by the letter Q₃.

Given set : 81, 82, 83, 83, 84, 84, 84, 85

Here, It is already in increasing order but the number of values is 8 which is even.

So, Q₁ part = 81, 82, 83, 83

Q₁ will be the median of 82 and 83.

So, Q₁ = (82+83)/2

          = 82.5

Similarly, Q₃ part =84, 84, 84, 85

So, Q₃ will be the median of 84 and 84.

hence, Q₃ = (84+84)/2

                 = 84

We know that, Interquartile range = Q₃ - Q₁

                                                          =  84 - 82.5

                                                          = 1.5

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Answer:

16

Step-by-step explanation:

6 percent of 15= 0.9

0.9*18≈16

Answer:

ABCD has congruent diagonals.

ABCD is a rhombus.

ABCD has four congruent angles

Step-by-step explanation:

The following statements would be considered true

1. The quadrilateral ABCD could have the congruent diagonals as the diagonals are perpendicular

2. ABCD would be treated as the rhombus as it is a  regular quadrilateral

3. ANd, It Have the four congruent angles that means the four angles be 90 degrees

The other statements would be false.

Answer:

A,B,E

Step-by-step explanation:

Edge 2021

Answer:

Step-by-step explanation:

Hmm

Answer:

i don't know

Step-by-step explanation:

Answer: d.

restricted lifestyle

Step-by-step explanation:

on ed

The option that is not an advantage of renting is;

D: Restricted lifestyle

When we rent a home, it means that we are paying the owner of the home some money periodically which could be yearly, monthly weekly e.t.c to make use the house.

Now, renting a home could be advantageous for different reasons and so let us look at each option given;

A) Ease of mobility; Sometimes we need to rent a home close to our place of work or business for ease of movement and as such this is an advantage.

B) Fewer responsibilities; Sometimes when we don't have too many responsibilities, renting a small home for a specific purpose could be very beneficial.

C) Lower Initial Costs; Renting a home is always cheaper initially than buying a home.

D) Restricted lifestyle; This is not an advantage of renting a home because renting a home is not meant to restrict your lifestyle but improve it.

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The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8

Let

x = price of blue fabric per yard

y = price of green fabric per yard

"The blue fabric costs $2 more per yard than the green fabric" means:

x = y + 2  (Equation 1)

" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:

6x + 9y = 57  (Equation 2)

Substitute equation 1 into equation 2:

6x + 9y = 57

6 (y + 2) + 9y = 57

6y + 12 + 9y = 57

15 y = 45

y = 3

Substitute y = 3 into equation 1

x = 3 + 2 = 5

Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.

The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8

Complete question:

LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?

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Step 1

Use the law that the sum of angles on a straight line is 180° to find y given that x = 42°

Step 2

Using the law

x + y = 180°

After substitution

42 + y = 180

y = 180 - 42

y =138°

y = log2 ( -x)

Since the log function must have a positive input, the domain must be x < 0

Domain ( - inf, 0)

The range is the values that y can take. The log goes from - infinity to infinity

Range (-inf, inf)

The asymptote is at x=0 since log must be greater than zero

Moving along a circle that is encircled by a square is point p. The bottom-left corner of the square is fixed at point q. Drag the point p around the circle in the applet below to investigate this issue.

As Point P moves from A to \($B \rightarrow$\)

(d) Distance, increases then decreases.

As point P moves from B to \($C \rightarrow$\)

(a) Distance Decreases

As point P moves from C to \($D \rightarrow$\)

(b) Distance tier eases then increases.

a As Point P moves from D to\($A \rightarrow$\)

(c) Distance increases.

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer: To determine the percent of birds in Forest A that are robins, we need to know the number of robins and the total number of birds in Forest A. Let's assume that we have conducted a bird survey and found the following information:

Number of robins in Forest A = 50

Number of other birds in Forest A = 150

Total number of birds in Forest A = 50 + 150 = 200

To calculate the percentage of birds in Forest A that are robins, we can use the following formula:

Percentage = (Number of robins / Total number of birds) x 100%

Plugging in the values, we get:

Percentage = (50 / 200) x 100% = 25%

Therefore, 25% of the birds in Forest A are robins.

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

x=(14)(sin22)

x=5.24...

x=5.2

The answer is A.

Step-by-step explanation:

Answer:

............................................ ............

Answer: I am unable to solve this problem.

Conceptually, the arithmetic and geometric average returns are different measures used to describe the performance of an investment or an asset over a specific period.

The arithmetic average return, also known as the mean return, is calculated by adding up all the individual returns and dividing by the number of periods. It represents the average return for each period independently.

On the other hand, the geometric average return, also called the compound annual growth rate (CAGR), considers the compounding effect of returns over time. It is calculated by taking the nth root of the total cumulative return, where n is the number of periods.

When to use each measure depends on the context and purpose of the analysis:

1. Arithmetic Average Return: This measure is typically used when you want to evaluate the average return for each individual period in isolation. It is useful for analyzing short-term returns, such as monthly or quarterly returns. The arithmetic average return provides a simple and straightforward way to assess the periodic performance of an investment.

2. Geometric Average Return: This measure is more suitable when you want to understand the compounded growth of an investment over an extended period. It is commonly used for long-term investment horizons, such as annual returns over multiple years.

The geometric average return provides a more accurate representation of the overall growth rate, accounting for the compounding effect and reinvestment of returns.

In summary, the arithmetic average return is suitable for analyzing short-term performance, while the geometric average return is preferred  evaluating long-term growth and the compounding effect of returns.

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Answer:

the answer is 3GB

Step-by-step explanation:

30-21=9 9/3 = 3

Answer:

x = 15

Step-by-step explanation:

MULTIPLY 1/4 with each number in the parentheses:

1x/2 - 7/2 = 4

ADD 7/2 to both sides:

x/2 = 15/2

MULTIPLY both sides by 2:

x = 15

Substituting the given values into the formula, we get logistic growth as

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

A pattern of population expansion known as logistic growth sees population growth begin slowly, pick up speed, then slow to a stop as resources run out. It can be shown as an S-shaped curve or a logistic function.

The formula for logistic growth can be expressed as:

\(P(t) = K / (1 + A * e^{(-r * t)})\)

where:

P(t) is the population at time t,

K is the carrying capacity,

A = (K - P₀) / P₀,

P₀ is the initial population,

r is the growth rate per unit of time, and

e is the base of the natural logarithm (approximately 2.71828).

Given the information you provided:

r = 0.013 (per year)

K = 2392

P₀ = 127

First, let's calculate the value of A:

A = (K - P₀) / P₀ = (2392 - 127) / 127 = 18.748

Now, substituting the given values into the formula, we get:

\(P(t) = 2392 / (1 + 18.748 * e^{(-0.013 * t)})\)

Remember to round the parameters to three decimal places when performing calculations.

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Answer:

$27.48

Step-by-step explanation:

He buys 1 shirt at 12.94 and gets one at 6.47

He does this 2 times and the total is 25.88

That times 1.062 to factor in the 6.2 percent tax rate is 27.48

So first you do:

.5 x 12.94=6.47

Next:

6.47 x 2=12.94

Then:

12.94 x 3=38.82

Now you have to do the tax:

38.82 x .062=2.41

After you get the answer for tax you have to add that to the price with out tax:

So, 38.82+2.41

=41.23

So you answer is 41.23 including the discount and tax

The value of f(-2)  is 15.

Hence option D is correct.

The given expression is

\(\int\limits {f(x)} \, dx\) = (1/3)x³ - 2x² +3x - 5

To find expression of f(x)

Differentiate it with respect to x

f(x) = x² - 4x + 3

Now put x = -2

f(-2) = (-2)² - 4(-2) + 3

       = 4 + 8 + 3

       = 15

Hence,

f(-2)  = 15

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Answer:

9

Step-by-step explanation:

2*3=6

so 3*3=9

Square root of 4 is not a polynomial. It is a quadratic function. Functions containing other operations like square root is not a polynomial.

A polynomial need not have any square root.  polynomial is a finite sequence form. it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Polynomial are sums and differences of polynomial terms. For an expression to be a polynomial term, any variables in the expression must have whole number powers. It should not have any square root, cube root or any negative values. Quadratic function can have square root cube roots and fraction values.

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It will take 10.5 months for 15 grams of a solution to increase to 60 grams if the solution has a k factor of 0.5453.

The k factor is a measure of how quickly a solution grows. A k factor of 0.5453 means that the solution will grow by 54.53% each month. To calculate how long it will take for 15 grams of solution to increase to 60 grams, we can use the following formula:

time = (60 grams - 15 grams) / 0.5453

This gives us a time of 10.5 months.

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A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.

The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.

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Descartes' Rule of Signs states that the number of positive real zeros of a polynomial can be determined by counting the number of sign changes in the polynomial's coefficients, and that the number of negative real zeros is at most the number of sign changes.

The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials are mathematical expressions made up of variables (also known as indeterminates) and coefficients.

A polynomial function in an equation is a function that only employs non-negative integer powers or only positive integer exponents of a variable. Examples of such functions include the cubic equation, the quadratic equation, and others. The exponent of the polynomial 2x+5 is 1, for instance.

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