The graph below shows a linear relationship between x and y. Assume that both the x-axis and the y-axis have the same scale. Determine the value of the constant rate of change of y with respect to x (This is a numerical value.) Write a formula that expresses change in y in terms of change in x. Suppose that y = 1.5 when x=1 Write a formula that expresses y in terms of x.

A solution of the first order IVP consisting of this differential equation is   y = [tex]\frac{1}{x^2-5}[/tex] and the domain of y considered as a function over the reals is (-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

We have to find the domain of y considered as a function over the reals.

The differential equation is  y' + 2x[tex]y^2[/tex] = 0

The solution of the given differential equation is y = 1/([tex]x^2[/tex] + c)......(1)

The given initial value; y(-3) = 1/4

Replace the initial value in the first-order DE solution provided. To obtain the equation for y, locate the constant c and then re-substitute 'c'.

Now put x = -3 and y(-3) = 1/4 in equation 1

[tex]\frac{1}{4}=\frac{1}{(-3)^2+c}[/tex]

[tex]\frac{1}{4}=\frac{1}{9+c}[/tex]

9+c = 4

Subtract 9 on both side, we get

c = -5

Now substitute the value of c again in equation 1

y = [tex]\frac{1}{x^2-5}[/tex]

To find the domain of y we can write it as

y = [tex]\frac{1}{(x)^2-(\sqrt{5})^2}[/tex]

Now the simplified form is

y = [tex]\frac{1}{(x-\sqrt{5})(x+\sqrt{5})}[/tex]

Now the domain of y over R is

(-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

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The complete question is:

y = 1/([tex]x^2[/tex] + c) is a one parameter family of solutions of the first order DE y' + 2x[tex]y^2[/tex] = 0. Find a solution of the first order IVP consisting of this differential equation and the given initial condition.

y(-3) = 1/4

Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)

The solution to the equation is i , -i , 4i , -4i

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x⁴ + 17x² + 16 = 0   be equation (1)

On simplifying the equation , we get

Substitute the value of x² = u

u² + 17u + 16 = 0

The roots of the quadratic equations are

u = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

u = [ -17 ± √ ( 289 - 4 ( 1 ) ( 16 ) ) ] / 2

On further simplification , we get

u = [ -17 ± √ ( 289 - 64 ) ] / 2

u = ( -17 ± √ 225 ) / 2

u = ( -17 ± 15 ) / 2

The two values of u are

u = ( -17 - 15 ) / 2

u = -16

And , u = ( -17 + 15 ) / 2

u = -1

Substitute the value of x² = u , we get

x² = -16

Taking square roots on both sides of the equation , we get

x = ± √ ( -16 )

x = ± 4i

And ,

x² = -1

x = ± i

So , the values of x are i , -i , -4i and 4i

Hence , the equations are solved

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Work Shown:

A = P*(1+r*t)

A = 5000*(1+0.12*30/12)

A = 6500

The amount $6500 is what you pay back

Divided over 30 months gives 6500/30 = 216.67 dollars per month.

Side note: The value t is in years, so 30 months = 30/12 years.

Answer:

So, there are 5,280 feet in a mile, so you will want to find out how many times 5, 280 will go into 23,760. To do this, you will divide.

23,760/5,280 = 4.5

There are 4.5 or 4 1/2 miles in 23,760 feet!

Step-by-step explanation:

Hope it helps! =D

The inequality that best represent the expression is x ≥ 12

A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The sign for greater than is >

The sign for less than <

The sign for greater than or equal to is ≥

The sign for less than or equal to is ≤

There must be at least 4 people in the group. This means that a group member must greater or equal to 4. There are 3 groups.

Represent the value of the number of friends by x

then, x/3 ≥ 4

therefore x ≥ 12

this means that the number of friends must be greater or equal to 12

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The margin of error at a 90% confidence level for this sample is approximately 0.086.

What is meant by margin of error?

The standard error of the sample proportion is calculated using the following formula:

Standard error = √((sample proportion * (1 - sample proportion)) / sample size)

Plugging in the values for the sample proportion (62/75) and sample size (75), you get a standard error of approximately 0.072.

Multiplying the standard error by the critical value gives the margin of error:

The margin of error = critical value * standard error

= 1.645 * 0.072

= 0.086

Hence, the margin of error at a 90% confidence level for this sample is approximately 0.086.

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The equation that matches the hanger diagram is 2x=5

From the question, we have the following parameters that can be used in our computation:

The hanger diagram added as an attachment

From the diagram, we hav

Left = x + x

Right = 1 + 1 + 1 + 1 + 1

This gives

Left = 2x

Right = 5

So, we have

2x = 5

hence, the equation is 2x = 5

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The center of mass is (2,1) since m1 has a mass of 10 and is located at (4,2). The center of mass is the average of the locations of the masses, weighted by the masses.

We can calculate the center of mass of these two spheres by using the formula c = (m1*L1 + m2*L2) / (m1 + m2). m1 is the mass of the first sphere, and L1 is the location of the first sphere. In this case, m1 is 10, and L1 is (4,2). We assume that m2 is 0 and L2 is (0,0). Plugging these values into the formula, we get c = (10*(4,2) + 0*(0,0)) / (10 + 0), which is (2,1).  This is because the center of mass is the average of the locations of the masses, weighted by the masses. In this case, the only mass is 10, and it is located at (4,2). Therefore, the center of mass is simply (4,2) since it is the only mass that contributes to the calculation.

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The complete question: find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1 = 10, L1 = ( 4,2)

Answer:

An agency that occurs when a principal and an agent categorically agree to enter into an agency agreement with each other is known as which of the following?

The property of an isosceles trapezoid is that the diagonals are congruent. That is option C.

An isosceles trapezoid is defined as the type of quadrilateral whereby line of symmetry bisects one pair of opposite sides.

The unique characteristics of an isosceles trapezoid include the following:

Therefore, the property of an isosceles trapezoid that is listed above is that Diagonals are congruent which means that they are equal.

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The properties of isosceles trapezoid are

Two pairs of parallel sides

Two pairs of parallel sides

An isosceles trapezoid has left and right sides that are equal in length or identical in length, therefore the base angles are also equal.

The diagonals are identical because the lengths of the left and right sides are equal and the base angles are equal.

Additional varieties of trapezoids include

Generally, all trapezoids have two parallel sides.

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The missing numbers are -80 and -20.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

There is a number line in the question.

In a number line, numbers are arranged in equal intervals.

The constant interval here = -40 - -60 = 20

x - -100 = 20

x + 100 = 20

x = 20 - 100

x = -80

First missing number is -80.

y - -40 = 20

y + 40 = 20

y = 20 - 40

y = -20

Hence the numbers missing are -80 and -20.

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The approximate length of the pendulum is 2 feet.

Two or more expressions with an Equal sign is called as Equation.

Given that period (T) of a pendulum is related to the length (L) of the pendulum and

acceleration due to gravity (g) by the formula T=2π√L/g.

g=32 ft/s2

t=1 sec

We need to find L

1=2×3.14√L/32

32=6.28√L

32/6.28=√L

5.09=√L

Square on both sides

L=25.9 inches

L=2 feet because 12 inches = 1ft.

Hence, the approximate length of the pendulum is 2 feet.

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Step-by-step explanation:

y÷15 or y/15 = 6

let's ignore the remainder for a moment.

y/15 = 6

y = 6×15 = 90

now, what does "remainder" mean ?

it means after a clean division there is a result, and there is still this additional remainder left.

the actual result of

a/b is

a/b = c + remainder/b

where c is an integer, and remainder is also an integer.

so, a = b×c + b×remainder/b = b×c + remainder

therefore,

y = 6×15 + 8 = 98

to check

98/15 = 6 remainder 8

so, it is correct

314÷y = 18 remainder 8

314 = 18y + 8

306 = 18y

y = 306/18 = 17

check

314 / 17 = 18 remainder 8

so, it is correct.

Standard Deviation, σ: 3.152

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given, Data set: 8, 7, 10, 10, 17, 13, 7, 10

variance:

σ² = Σ(xi - μ)²/N

σ²=  ((8 - 10.25)² + … + (10 - 10.25)²)/8

σ²= 79.5/8

σ²  =9.9375

σ = √9.9375

σ = 3.1523

The sampling mean most likely follows a normal distribution. In this case, the standard error of the mean can be calculated using the following equation:

σ =  σ/√N

σ = 1.114

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Answer: To determine how many months it will take for an initial investment of Rs1000 to grow to Rs1200 at a 10% interest rate, we can use the formula:

Time = (ln(final value / initial value)) / (ln(1 + interest rate))

where ln is the natural logarithm function.

Plugging in the given values:

Time = (ln(1200/1000)) / (ln(1 + 0.10))

Time = (ln(1.2)) / (ln(1.10))

Time = 0.18232 / 0.09531

Time = 1.913 months

It will take approximately 1.913 months for an investment of Rs1000 to grow to Rs1200 at a 10% interest rate.

Step-by-step explanation:

The equivalent expression for 1/2(2a - 6b+ 8) will be a - 3b + 4

Expressions that are equivalent do the same thing even though they have different appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are substituted for the variable and both expressions yield the same result, you can also tell if two expressions are equivalent.

This will be:

1/2(2a - 6b+ 8)

= a - 3b + 4

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Complete question

Distribute to create an equivalent expression with the fewest symbols possible 1/2(2a - 6b+ 8) =

Answer:

1/2

Step-by-step explanation:

Triangle XYZ has endpoints (0,0) (0,8) and (4,6)

Triangle X'Y'Z' has endpoints (0,0) (0,4) and (2,3)

As you can see, all the coordinates from Triangle XYZ are halved to get the coordinates of Triangle X'Y'Z', so the scale factor is 1/2.

Answer: 602.88 square feet

Equation for surface area of cylinder:

A = 2πrh+2πr^2

r = 6, because radius is half of the diameter

h = 10

A = 2(3.14)(6)(10) + 2(3.14)(6)^2

A = 376.8 + 226.08

A = 602.88 square feet

Following are the answers to all the asked questions for classifying types of cost.

a. Electricity costs of $0.025 per kilowatt-hour - variable cost

b. Warehouse rent of $6,000 per month plus $0.50 per square foot of storage used - mixed cost

c. Thread - variable cost

d. Lubricants used to oil machinery - variable cost

e. Janitorial costs of $2,000 per month - fixed cost

f. Advertising costs of $10,000 per month - fixed cost

g. Sales salaries - fixed cost

h. Color dyes for producing different colors of sweatshirts - variable cost

i. Salary of the production supervisor - fixed cost

j. Patterns for different designs. Patterns typically last many years before being replaced - fixed cost

k. Maintenance cost with sewing machine company. The cost is $2,000 per year plus $0.001 for each machine hour of use - mixed cost

l. Property taxes on factory, building, and equipment - fixed cost

m. Cotton and polyester cloth - variable cost

n. Hourly wages of sewing machine operators - variable cost

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The number of ways to choose 6 letters from a set of 13 is given as follows:

a) Order does not matter: 1716.

b) Order matters: 1,235,520.

A combination is used when the order does not matter, hence, for item a, the number of ways is obtained as follows:

C(13,6) = 13!/(6!7!) = 1716.

A permutation is used when the order matters, hence, for item b, the number of ways is obtained as follows:

P(13,6) = 13!/7! = 1,235,520.

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The Correlation Coefficient -0.12 shows that The taller the baby, the lighter the baby.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.

Given:

Correlation Coefficient = -0.12

As, The range of a correlation coefficient ranges from -1 to 1.

When the number is closer to -1 or closer to 1, there is a substantial association, and when the number is closer to 0, there is no link.

The correlation coefficient in this instance is -0.12, indicating a marginally negative correlation. The negative sign indicates that when one component changes, the other decreases, making a baby that is taller and lighter.

Hence, The taller the baby, the lighter the baby.

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The general form of exponential formula is y = a * b^x, the  population of the city in 2018 6.058454 million.(c) the population of the city be 8 million19.38548963 years.

In this problem, a = 5.21 million and b = 1 + 2.86%/100 = 1.0286.

In 2012, the population was 5.89 million.

In 2018, the population will be 5.89 * 1.0286 ^ (2018 - 2012) = 5.89 * 1.0286 ^ 6 = 6.058454 million.

To find when the population will be 9 million, your equation becomes:

9 = 5.21 * 1.0286 ^ x divide both sides of this formula by 5.21 to get:

9/5.21 = 1.0286 ^ x take the log of both sides of the equation to get:

log(9/5.21) = log(1.0286^x) since log(1.0286^x) = x * log(1.0286), the equation becomes:

log(9/5.21) = x * log(1.0286)

Divide both sides of this equation by log(1.0286) to get:

log(9/5.21) / log(1.0286) = x

Solve for x to get:

x = 19.38548963.

Confirm by replace x in the original equation to get:

9 = 5.21 * 1.0286 ^ 19.38548963 becomes 9 = 9.

This confirms the value of x is good.

The population will grow to 9 million in 19.38548963 years.

To find when the population will double, the equation becomes:

2 = 1 * 1.0286 ^ x

Simplify to get:

2 = 1.0286 ^ x

Take the log of both sides of this equation to get:

log(2) = log(1.0286 ^ x)

Since log(1.0286 ^ x) = x * log(1.0286), this equation becomes:

log(2) = x * log(1.0286)

solve for x to get:

x = log(2) / log(1.0286) = 24.5808602.

to confirm this is true, replace x in the original equation to get:

2 = 1.0286 ^ 24.5808602 which becomes 2 = 2.

This confirms the value of x is true.

The population will double in 24.5808602 years.

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a) 0.04550 has four significant figures.

b) 5.0003 has four significant figures.

c) 1.000 x [tex]10^5[/tex] has four significant figures.

d) 0.00002 has one significant figure.

e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.

f) 7 has one significant figure.

Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.

Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.

For example, in the given number 5.006, there is four significant number,

since all zeros between integers are always significant.

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62.8363 cm is the total circumference of the given circle.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

Given a circle that has an arc of 165 degrees and also given that arc has a circumference of 28.8cm

Circumference of 165 Degrees arc = 28.8cm

Circumference of 1 Degree arc = 28.8/165

Circumference of 1 Degree arc =0.17454

Since the total angle in a circle is 360 degrees

Thus from the fraction,

Circumference of 360 Degrees arc = 0.17454*360

Circumference of 365 Degrees arc = 62.8363 cm

Therefore, the total circumference of the given circle is 62.8363 cm.

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These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear function is given below.

y = 2x – 6

The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.

As when the put the given points in the equation , than it satisfies the given condition.

Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

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Variable x and y for the rectangle is given by

x = (3x + 3)/6 + 1

y = (3x + 3)/6

Yes that's right. You have to equate the expressions for widths and for the lengths, since left and right widths (and lengths) have the same dimensions.

You may rewrite the equation for y=3x+3÷6 as

y = (3x + 3)/6

And now you have an expression for y, we can substitute it to the other equation you got:

x = y + 1

x = (3x + 3)/6 + 1

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After solving the given equation we know that students worked for 17 hours a week.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, the given equation is:

g=−0.0007h+0.018h+3.02

Now, we know that g is 2.72, so we can calculate for h as follows:

2.72=−0.0007h+0.018h+3.02

2.72 = -0.0173h + 3.02

- 0.3 = -0.0173h

h = -0.3/-0.0173

h = 17.34

Rounding off: 17 hours

Therefore, after solving the given equation we know that students worked for 17 hours a week.

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A binomial setting is one in which there are a fixed number of trials, the outcome in each trial is either a success or a failure, the probability of success or failure is known, and the probability doesn't change from trial to trial.

A binomial setting is one in which we know the number of repetitions (n=20), the outcome of each trial can be considered either a success or a failure (p=0.4, q=1-p=0.6), and the probability of success or failure of any trial does not change from trial to trial (p=0.4, q=1-p=0.6).

For example, if we toss a coin 20 times, and we know the probability of success (head) is 0.4 and the probability of failure (tail) is 0.6, then this is a binomial setting. We can calculate the probability of getting exactly 10 heads in 20 tosses using the binomial formula: P(X=10) = (20C10) * (0.4^10) * (0.6^10) = 0.1775.

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21.931% of Nicole's monthly pay goes to rent.

percent = (638/2900) x 100

percent = 0.21931 x 100

percent = 21.931%