Please explain this more in depth. How does the chain rule allow
the first equation to reduce to the second equation? Some simple
explanation of the chain rule would also be helpful.

Answer:

Finding the total accrued amount is necessary before we can determine the interest rate.

Simply multiplying the monthly payment by the number of months in a 12-year period will give us the accrued amount.

144 months in 12 years.

$680 x Monthly Payment

A = 680 * 144

A = $97920

We can use the following formula now that we know the total accrued sum:

A= 97920

P = 72000

t= 12

Let's replace them with our values now.

The percentage value is then obtained by multiplying the r value by 100.

0.03 x 100 = 3%

The interest rate for Alexia is 3%.

Answer:

4 !!!!

Step-by-step explanation:

f (x) =  1/1-x2 g (x) = -(3  x -2 ) - 5  then the number of solutions if the number of   intersections of f(x) and g (x) i drew a graph and there was 4 intersections so thats how i got this answer

I hope i was right

There are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.

An equation is a statement that shows that two mathematical expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.

We can start by considering the case where the expression inside the absolute value is non-negative, i.e., 3x - 2 ≥ 0, which implies x ≥ 2/3. In this case, the equation becomes:

1/(1 - x²) = 3x - 2 + 5

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

Multiplying both sides by 1 - x², we get:

1 = (3x + 3)(1 - x²)

3x³ + x² - 3x - 2 = 0

This equation has one real root.

The root is approximately x = 0.727.

Next, we consider the case where the expression inside the absolute value is negative, i.e., 3x - 2 < 0, which implies x < 2/3. In this case, the equation becomes:

1/(1 - x²) = -(3x - 2) + 5

Simplifying this equation, we get:

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

1 = (-3x + 3)(1 - x²)

3x³ - x² - 3x + 2 = 0

This equation also has one real root, which we can find using the same methods as before. The root is approximately x = -0.727. \

Therefore, there are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.

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Answer:

d. Insured banks pay a premium on the money insured. The FDIC's reserve fund comes from premiums paid by insured banks. The premiums are paid based on the amount of deposits held by the bank and the level of risk the bank poses to the FDIC's insurance fund.

Step-by-step explanation:

First of all sorry for the bad hand writing

so rn I'm using elimination method which I try to eliminate y by multiple number 2 equation with 2

in order to find x

I know my explanation is quite confusing but any way goodluck n hope u understand

The value of k is 13.

Using the remainder theorem, we can find the value of k by substituting the value of x in the given polynomial equation with the value that makes the divisor equal to zero. In this case, the divisor is x-2, so the value of x that makes it equal to zero is x=2.

Substituting x=2 into the polynomial equation, we get:

2(2)^3 + 3(2)^2 - k(2) + 5 = 7

Simplifying the equation, we get:

16 + 12 - 2k + 5 = 7

33 - 2k = 7

-2k = -26

k = 13

Therefore, the value of k is 13.

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Answer: Order of operations

Step-by-step explanation:

Plug in 3 for x so...

y = -2(3)² + 12(3) - 15

Don't forget the order of operations, exponents go first

y = -2(9) + 12(3) - 15

Then multiply

y = -18 + 36 - 15

Simplify

y = 3

We can write the perimeter of the equilateral triangle as -

P = 13x - 19.

Given is a equilateral triangle.

We can write the perimeter of a equilateral triangle as -

Perimeter = (2x + 3) + (4x - 5) + (7x - 17)

Perimeter = 2x + 4x + 7x + 3 - 5 - 17

Perimeter = 13x - 19

Therefore, we can write the perimeter of the equilateral triangle as -

P = 13x - 19.

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The requried, possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
To describe the possible solution sets of the inequality ax + b < cx + d, we need to isolate the variable x on one side of the inequality and simplify.

ax + b < cx + d

ax - cx < d - b

x(a-c) < d - b

x < (d - b)/(a-c)

So the solution set for the inequality is all values of x that are less than the quotient of (d - b) divided by (a-c).

Therefore, the possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).

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It is possible for each of the six quadratic equations to have at least one real root.

This is because the discriminant of a quadratic equation determines the nature of its roots. The discriminant is given by the formula: D = b² - 4ac.

If D > 0, the equation has two distinct real roots.
If D = 0, the equation has one real root (a double root).
If D < 0, the equation has no real roots (two complex roots).

In each of the six equations, the coefficients a, b, and c are non-zero real numbers. This means that the discriminant can be positive, zero, or negative, depending on the values of a, b, and c. Therefore, it is possible for each of the six equations to have at least one real root.

For example, consider the equation ax² + bx + c = 0. If b² > 4ac, then the equation has two distinct real roots. If b² = 4ac, then the equation has one real root (a double root). If b² < 4ac, then the equation has no real roots (two complex roots).

Similarly, the other five equations can also have at least one real root, depending on the values of the coefficients a, b, and c.

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2.75; a kitten who is just born is predicted to weigh 2.75 ounces.

What is Statistics?

Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It enables the identification of trends, patterns, and relationships within the data. The goal of statistics is to make meaningful inferences and predictions based on the data.

It is used in a wide range of fields, including business, economics, social sciences, healthcare, and engineering. The main tools of statistics include probability theory, statistical inference, and statistical modeling.

2.75; a kitten who is just born is predicted to weigh 2.75 ounces.

The w-intercept of the line of fit represents the weight of a kitten at birth, which is the value of w when d equals zero. In this case, the intercept is 2.75, which means that a kitten who is just born is predicted to weigh 2.75 ounces.

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Answer:

Step-by-step explanation:

31 degreese

add 59 with 90 you get 149 then you subtract 149 with 180 a

nd then get 31

Pippin has 37.5% of her sports drink left.

What is Percentage?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Pippin has 32 - 20 = 12 ounces of sports drink left.

To find the percentage of ounces Pippin has left, you need to divide the number of ounces left by the original amount of sports drink (32) and then multiply by 100 to get the percentage:

(12/32) x 100 = 37.5%

Therefore, Pippin has 37.5% of her sports drink left.

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Answer:

1. 2430 feet

2. 1.8 m/s^2

Step-by-step explanation:

See the attached worksheet.

A time versus speed graph contains a small treasure of mathematical rewards. The area under the graph is equal to the distance travelled. The slope of the line segments represents acceleration.

For total distance: If we break the graph into three sections (2 triangles and a rectangle) we can calculate the areas for each. Each area is the distance travelled for that segment. As shown on the workseet, the total area is 2430 miles, the distance travelled by the train for this question.

The slope of the line in the first 10 seconds is 1.8 meters/sec^2, the acceleration of the train over that period.

A majority of the consumers in the sample prefer pepsi over coke.

Based on the given information, a random sample of 100 soft drink consumers tasted an unmarked cup of pepsi and an unmarked cup of coke. Fifty-nine out of the 100 consumers stated that they prefer pepsi over coke.

This means that the majority of the consumers in the sample, or 59%, preferred pepsi over coke. It is important to note that this is only a sample of consumers and may not necessarily reflect the preferences of the entire population of soft drink consumers. However, it does provide some insight into the preferences of a portion of the population.

In conclusion, the results of the taste test indicate that a majority of the consumers in the sample prefer pepsi over coke.

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Question Number 5.

The first and second numbers in the exponential sequence are 10 and 5, respectively.

In the exponential sequence given by a, b, c, d, ..., where a and b are the first two numbers. We know that the third number is given by b * c/a, and the fourth number is given by c * d/b.

the third number = 100

the fourth number = 500,

So b * c/a = 100

c * d/b = 500

rearranging the first equation :

c = 100a/b

Substituting this into the second equation, we then have

d = 500b/a

The sequence is then written as a, b, 100a/b, 500b/a, ...

We then proceed to  find a and b,

a, b, 100a/b, 500b/a, ...

a, b, 100a/b, 500b/a, ... = a, b, 100a/b, 500b/a, ...

100a/b = 100

500b/a = 500

Solving for a and b, we have:

a = 10

b = 5

In conclusion, the first and second numbers in the exponential sequence  are 10 and 5.

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Answer:

15, 3, -1, -12

Step-by-step explanation:

15, 3, -1, -12

Answer:

First answer (15, 3, -1, -12)

Step-by-step explanation:

ez

Answer:

The correct answers are:

As x approaches positive infinity, f(x) approaches positive infinity.

As x approaches negative infinity, f(x) approaches 0.

Step-by-step explanation:

The estimated height of the child at delivery is represented by the y-intercept, which is 72.66.

We may use linear regression to construct an equation that represents the link between this child's height and age. The line of best fit for the supplied data is determined by linear regression, which can be written as:

Age (years) + b * m * Height (cm)

where m denotes the line's slope and b its y-intercept.

The equation that most closely matches the above data can be determined using a calculator or spreadsheet software as follows:

Age (years) + 72.66 Height (cm) = 6.087

Thus, the height of the youngster increases by roughly 6.087 centimetres for every year that their age rises. The estimated height of the infant at delivery is represented by the y-intercept, which is 72.66.

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The probability that X is greater than 1 is less than or equal to 0.5, making the correct answer (C) 0.5.

Markov's inequality states that for a non-negative random variable X and a positive number a, the probability that X is greater than a is less than or equal to the expected value of X divided by a. In mathematical terms, this can be written as:

P(X > a) ≤ E(X) / a

In this case, X follows an exponential distribution with a mean of 1/2.0, or 0.5. Therefore, the expected value of X is 0.5. If we plug in the values for X and an into Markov's inequality, we get:

P(X > 1) ≤ 0.5 / 1

P(X > 1) ≤ 0.5

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The transformations that are occurring between each of the function are given as follows:

f(x) = 14(x - 3) + 1 and g(x) = 7(x + 2) + 1: vertical compression by a factor of 1/2 and shift left 5 units.

f(x) = 6(x + 2) - 3 and g(x) = 8(x - 3) + 6: vertical stretch by a factor of 4/3, shift right 5 units and shift up 9 units.

f(x) = 3(x - 1) + 2/3 and g(x) = 3(3 - x) - 2/3: reflection over the y-axis, shift left 2 units and shift up 4/3 units.

f(x) = 1/3(x + 2) - 4 and g(x) = 1/3(-x - 2) + 6: reflection over the y-axis and shift up 10 units.

f(x) = 4/3(x - 2/3) + 1/3 and g(x) = 2/3(2/3 - x) = reflection over the y-axis, shift down of 1/3 units and vertical stretch by a factor of 2.

The curve of the graph "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is changed.

The transformation rules are defined as follows:

x -> x + a: shift left a unit.

x -> x - a: shift right a unit.

y -> y + a: shift up a unit.

y -> y - a: shift down a unit.

y -> ky, k > 1: vertical stretching by k times.

Vertical compression by a factor of k is achieved by y -> ky, k 1, horizontal compression by a factor of k is achieved by x -> kx, k > 1, and vertical stretch by a factor of k is achieved by x -> kx, k 1.

x -> -x: reflection over the y-axis.

y -> -y: reflection over the x-axis.

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Other fractions could represent the part of the beads on the bracelet that will be green are : 1/3, 2/6, 3/9, 4/12.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

The maximum number of beads the bracelet can have  = 12 beads

The fraction of green beads in the bracelet = 1/3

⇒ 1 bead in every 3 bead is GREEN.

⇒The minimum number of total beads = Number of (green+ Other) bead                                                           = 2 + 1  = 3

Now, the possible number of total beads the bracelet can have is

3, 4, 5 , 6, 7, 8, 9 ,10, 11 and 12.

If there are total 3 beads, the fraction representing the green bead  = 1/3

If there are total 6( =3 +3) beads, the fraction representing the green bead  

= 1 green bead in first 3 beads +  1  green bead in next 3 beads

=   2 green beads in total 6 beads

=   2/6

If there are total 9( = 3 +3 +3) beads, the fraction representing the green bead  = 3/9

If there are total 12( = 3 +  3 +3 +3) beads, the fraction representing the green bead  = 4/12

Hence, other fractions could represent the part of the beads on the bracelet that will be green are :1/3, 2/6, 3/9, 4/12.

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On sοlving the given trigοnοmetric expressiοn using the trigοnοmetric identity, we fοund that it is equal tο tan (π/35).

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn.

There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.

The given trigοnοmetric expressiοn is:

[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex]

tan (a-b) = sin(a-b)  / cοs (a-b)

    = (sin a cοs b - cοs a sin b) / (cοs a cοs b + sin a sin b)

  Dividing the numeratοr and denοminatοr by (cοs a cοs b), we get,

tan (a-b) = (tan (a) - tan (b)) / (1+tan a tan b)

This expressiοn is similar tο the given expressiοn.

Cοmparing,

a = 3π/7

b = 2π/5

[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex]  = tan( 3π/7 - 2π/5) = tan (π/35)

Therefοre on solving the given trigonοmetric expression using the trigonοmetric identity, we found that it is equal tο tan (π/35).

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The ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

To write the ratio as a fraction in simplest form, we will follow the steps below:

Step 1: Write the ratio as a fraction. In this case, we have 3.5cm:1.4cm, which can be written as 3.5cm/1.4cm.

Step 2: Simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF). In this case, the GCF of 3.5 and 1.4 is 0.7. So we will divide both the numerator and denominator by 0.7 to get:

(3.5cm/0.7) / (1.4cm/0.7) = 5/2

Step 3: Convert the fraction to simplest form with whole numbers in the numerator and denominator. In this case, we can multiply both the numerator and denominator by 10 to get:

(5*10)/(2*10) = 50/20

Step 4: Simplify the fraction by dividing both the numerator and denominator by the GCF. In this case, the GCF of 50 and 20 is 10. So we will divide both the numerator and denominator by 10 to get:

(50/10)/(20/10) = 5/2

Therefore, the ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

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The number of copies sold in total is 586,301

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a book sold 42800 copies in its first month of release, this represents 7.3 of the number of copies sold to date, we need to find the number of the copies have been sold to date,

Let the number of copies sold in total be x,

Using the concept of percentage,

7.3 % of x = 42800

7.3 / 100 of x = 42800

x = 100/7.3 (42800)

x = 586,301

Hence, the number of copies sold in total is 586,301

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The numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.

The integers in Set P are {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}.

The absolute values of these integers are {7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4}, which make up Set Q. The intersection of Set P and Set Q are the integers that are in both sets, which are {0, 1, 2, 3, 4}.

Therefore, the numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.

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A 10gm sample of Titanium-44 will have 6.06 grams of mass left after 50 years.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]

From the information, Titanium-44 has a half-life of 63 years we can model,

[tex]5 = 10.e^{63k}.[/tex]

[tex]0.5 = e^{63k}.[/tex]

[tex]63k = ln0.5.[/tex]

63k = - 0.69.

k = - 0.01.

Therefore, The amount of mass left after 50 years is,

[tex]y_{50} = 10.e^{-0.01\times50}.[/tex]

[tex]y_{50} = 6.06[/tex] grams.

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Jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.

An equatiοn in twο variables is an equatiοn that invοlves twο variables, typically x and y, and relates them with cοnstants and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let's represent the vοlume οf jug A by x and the vοlume οf jug B by y.

We knοw that the cοmbined vοlume οf the twο jugs is 800 ml:

x + y = 800 (equatiοn 1)

We alsο knοw that after pοuring water frοm jug A tο jug B, there is 200 ml οf water remaining in jug A. This means that jug B cοntains x ml οf water:

y = x (equatiοn 2)

We can substitute equatiοn 2 intο equatiοn 1 tο eliminate y:

x + y = 800

x + x = 800

2x = 800

x = 400

Nοw that we knοw that the vοlume οf jug A is 400 ml, we can use equatiοn 2 tο find the vοlume οf jug B:

y = x

y = 400

Therefοre, the vοlume οf jug B is alsο 400 ml.

Hence, jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.

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use the slope formula

5 - 9/4-2 = -4/2 = -2

slope = -2

The value of the line segment AB of the trapezoid ABCD will be 25.9 units.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The sum of the parallel sides of the trapezoid is equal to twice the line segment that divides the other two sides in the ratio of 1: 1.

Then the equation is given as,

MN = (AB + CD) / 2

18.7 = (AB + 11.5) / 2

37.4 = AB + 11.5

AB = 25.9 units

The value of the line segment AB of the trapezoid ABCD will be 25.9 units.

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