A maple tree grows 1.5 feet each year. The table shows the yearly growth for a pibe tree

The given equation is a second order differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

Isaac Newton listed three kinds of differential equations given -

[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]

Given is a differential equation as follows -

d²a/db² + a = 4b + 10sin(b)

The given equation is -

d²a/db² + a = 4b + 10sin(b)

Let y = a and x = b, then we can write -

d²y/dx² + y = 4x + 10sin(x)

A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -

d²y/dx² + P(x) dy/dx + Q(x) y = f(x)

For the equation given -

d²y/dx² + y = 4x + 10sin(x)

On comparing, we get -

P(x) = 0

Q(x) = 1

f(x) = {4x + 10sin(x)}

Therefore, the given equation is a second order differential equation.

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The probability that the team will win more than 9 games this season, given the average number of wins for the team, is 4 %

The Z-score formula is:

Z = (x - mean) / standard deviation

Where x is the number of wins we're interested in (9), mean is the average number of wins (7.6), and standard deviation is the standard deviation of the number of wins (1.3)

Z = (9 - 7.6) / 1.3

= 2.3 / 1.3

= 1.77

This means that 9 wins is 1.77 standard deviations above the mean. The result is the probability of a team winning more than 9 games this season, which is around 0.04 or 4% from the standard normal distribution table.

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Answer:

The answer would be the second and fourth options.

Step-by-step explanation:

This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!

20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.

In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.

The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.

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Answer:

7/8 = 87.5%

Step-by-step explanation:

You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).

Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.

The probability of not getting orange is 87.5%. The correct option is C.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.

Probability = Number of favourable outcomes / Number of samples

Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

You only have one of eight (1/8) evenly divided orange sections.

The rest is not orange,

P = (1 - 1/8

P =  7/8

P = 87.5%

Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.

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Answer:

To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.

In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.

Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:

(0, x)

(1, 4/5x)

(2, 3/5x)

(3, 2/5x)

This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.

For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.

By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.

Step-by-step explanation:

The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]

this would cancel out on the right hand side such that we would have:

[tex]\frac{2n}{(d + g)} =a[/tex]

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The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 6

The equation of the line that is parallel to the line y = - 5x + 6 is written as,

y = - 5x + c

The equation passes through (-4, -1), then we have

- 1 = - 5 (-4) + c

- 1 = 20 + c

- 21 = c

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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The length of y in the triangle is 18.55 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The side y of the triangle can be found using sine law.

Therefore,

a / sin A = b / sin B = c / sin C

Applying the sine law,

y / sin 106 = 15 / sin 51

cross multiply

y sin 51° = 15 sin 106°

divide both sides by sin 51°

y sin 51° / sin 51° = 15 sin 106° / sin 51°

y = 15 sin 106° / sin 51°

Therefore,

y = 15 × 0.96126169593 / 0.77714596145

y = 14.4189254391 / 0.77714596145

y = 18.5536589719

Hence,

y = 18.55 units

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The range of the absolute function will be from 0 to 9. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The domain means all the possible values of x and the range means all the possible values of y.

From the graph, the range of the absolute function will be from 0 to 9.

Then the correct option is A.

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The complete question is attached below.

Answer:

-3,950

Step-by-step explanation:

First -5,000(1-0.21)

Then multiply -5,000 x 0.79 = -3,950

Check the picture below.

Percentage of chocolates Jim given to his family is 11.11%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Jim made 45 treats for his birthday. He gave 5 away to his family before taking the rest to school.

Now, percentage of chocolates Jim given to his family

= 5/45 ×100

= 0.1111 ×100

= 11.11%

Therefore, percentage of chocolates Jim given to his family is 11.11%.

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Answer: (-3,0) and (0,-2)

Step-by-step explanation:

Set of value that belong to the Domain are: Values of Independent, Variable, Input Values

Set of value that belong to the Range are: Output Values, Values of Dependent Variables.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

Domain :

Values of Independent Variable

Input Values

Range :

Output Value

Values of Dependent Variables.

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Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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957÷3=319 this divide answer i hope help you

The perimeter and the area of the fountain is calculated to be

94.25 feet and 625.32 square feet respectively

The perimeter of the fountain consisting of two semicircles and a quarter circle is

= perimeter of semicircle * 2 + perimeter of circle * 1/4

= π d + 2 π r * 1/4

for semicircle, diameter, d = 20 ft

for circle, radius r, = 20 ft

substituting the values

= 20π + 2 * π * 20 * 1/4

= 20π + 10π

= 30π

= 94.25 feet

Area of the fountain

= area of semicircle * 2 + area of circle * 1/4

area of semicircle * 2 = area of circle of radius 10 ft

for semicircle, radius, r = 10 ft

for circle, radius r, = 20 ft

= π 10² + π 20² * 1/4

= 100π + 100π

= 200π

= 625.32 square feet

The area of the fountain is 625.32 square feet

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Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.

Step-by-step explanation:

From the given values and conditions, We need to form a equations and equate both sides to solve for the miles, The answer is 300 miles.

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.

x= miles

60+0.6x=0.8x

0.8x-0.6x=60

0.2x=60

x=60/0.2

=300 miles

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Answer:

  -9447840

Step-by-step explanation:

You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.

The n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

where a1 is the first term and r is the common ratio.

Using the given values, we have ...

  -160 = a1·(-1/3)^(11 -1)

  a1 = (-160)·(-3)^10 = -9447840

The first term is -9447840.

Answer:

9:15

Step-by-step explanation:

Time needed to deliver 100 letters: 100 : 40 = 2,5 hours = 2:30min
Your break: 6:45 + 2:30 = 9:15

The product of given numbers is 60x³(x−3)²(x+2)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra,

Multiply the numbers:

6x²x(x−3) * (x−3)10(x+2)

Multiply 6 and 10

60x²x(x−3) (x−3)(x+2)

Multiply x terms

60x³(x−3) (x−3)(x+2)

Multiply (x-3) terms

60x³(x−3)²(x+2)

So, the product of given numbers is 60x³(x−3)²(x+2)

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The null hypothesis is rejected.

The mean is not greater than $175.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

Sample size (n) = 6

Sample mean ([tex]\bar x[/tex]) = $80

Sample standard deviation(s)=6.3

Significance level(α)=0.05

We have to test the claim that the true mean greater than $175.

The null and alternative hypotheses:

H₀ : μ = 175

H₁ : μ > 175

Here, Population Standard deviation is unknown and sample size is less than 30.

So we will use t- distribution.

Test Statistic t,

t   = ([tex]\bar x[/tex] - μ) / {s/√n}

t  =  (80−175) / (6.3 /√6)

t   =  (80−175) / (6.3 / 2.45)

t  = − 95 / 2.57196423

t = −36.937

degree of freedom (df) = n−1

                                     = 6−1

                                     = 5

p-value at  t = −36.937, df = 5 and α = 0.05

Absolute value of −36.937 = 36.937

Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.

So, p-value = 1

Since, p-value > α

That means, we fail to reject the null hypothesis (H₀).

Therefore, the true mean is not greater than $175.

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In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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