Tricia deposits $1500 into a savings account that pays 1.2% annual interest compounded quarterly. Write a function to represent the balance A in the account after t years. B. What will be the balance after 3 years C. What will be the balance after 6 years

Answer: We can start by expanding the square on the left-hand side of the equation:

(s + t)^2 = s^2 + 2st + t^2

We know that s^2 + t^2 = 6, so we can substitute that into the equation:

(s + t)^2 = 6 + 2st

We also know that st = c + 5, so we can substitute that into the equation:

(s + t)^2 = 6 + 2(c + 5)

Simplifying the right-hand side:

(s + t)^2 = 6 + 2c + 10

So, in terms of c, (s + t)^2 = 6 + 2c + 10.

Step-by-step explanation:

The minimum spanning tree for the above graph 1 is present above in graph figure 2. The order in which edges are added to form the tree is equals to {V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.

We have , a diagram present above in figure. This graph has 8 vertices and 12 edges. Also

Similarly, edages are connected to each other with different weights as shown in graph. Kruskal's algorithm is a greedy algorithm in graph theory of discrete mathematics that used to determine the minimum spanning tree for a connected weighted graph and adds increasing weight at each. In this case a graph present we determine the shortest spinning tree. Kruskal's algorithm stated that always select a minimum cost edge that should not result in a cycle. The order is which edges are added is

{V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.

Hence, the required graph is present above.

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Complete question:

Use Kruskal's algorithm to find a minimum panning tree for the above graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)

A graph with 8 vertices and 12 edges is shown.

One edge with weight 12 connects vertex v0 and vertex v1.

One edge with weight 4 connects vertex v0 and vertex v5.

One edge with weight 20 connects vertex v1 and vertex v2.

One edge with weight 5 connects vertex v1 and vertex v3.

One edge with weight 7 connects vertex v1 and vertex v4.

One edge with weight 19 connects vertex v2 and vertex v7.

One edge with weight 2 connects vertex v3 and vertex v4.

One edge with weight 18 connects vertex v3 and vertex v7.

The coordinates of the point on y sin(x) that is closest to the point (4, y) is (3.579, 0.323).

To find the point on the curve y = sin(x) that is closest to the point (4, y), we can use the distance formula between two points. The distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

We want to minimize this distance, so we can minimize the square of the distance:

d^2 = (x2 - x1)^2 + (y2 - y1)^2

Let (x, sin(x)) be a point on the curve y = sin(x). Then the distance squared between this point and (4, y) is:

d^2 = (x - 4)^2 + (sin(x) - y)^2

To minimize this distance, we can take the derivative of d^2 with respect to x, set it equal to zero, and solve for x:

d^2 = (x - 4)^2 + (sin(x) - y)^2

d^2/dx = 2(x - 4) + 2(sin(x) - y)cos(x) = 0

Simplifying this expression, we get:

x - 4 + (sin(x) - y)cos(x) = 0

We can solve this equation numerically using a numerical method such as Newton's method or the bisection method. Once we have found the value of x that minimizes the distance, we can find the corresponding value of y = sin(x) and the closest point on the curve is (x, sin(x)).

Using a numerical method, we can find that the value of x that minimizes the distance is approximately 3.579. Therefore, the closest point on the curve is (3.579, sin(3.579)) which is approximately (3.579, 0.323).

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Answer:

ur mom jk its

c

Step-by-step explanation:

The required value of n is the integer "32" as shown in the given figure.

integer, positive or negative whole-valued number, or 0. The integers are formed from a collection of counting numbers such as 1, 2, 3,...

Here,

According to the question,

Let the number of integers between 7 and 23, inclusive, be x (note that x is not necessarily equal to n). Then the number of integers between 1 and 7, inclusive, and the number of integers between 23 and n, inclusive, must also be x, because the integers are equally spaced on the circle.

n = 2(x) ....(i)

Since from above definition
x = 23 - 7
x = 16

Substitute the value of x = 16 in equation (i),

n = 2(16)

n = 32

Therefore, the value of n is "32".

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The amount of full sets Alexandra can make would be 3.

When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.

A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.

Multiply both the numerator and denominator of 5 / 2 by 2.

5/2 × 2/2 = 10/4

The sets of bowls you can make, divide by 3 / 4.

(10/4)/(3/4) = 3 and 1/3.

The amount of full sets Alexandra can make is 3.

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Answer:

Communist countries use authoritarian governments because it requires the absolute obedience to authority figures. Communism is an extreme form of socialism because there is no private ownership or political freedom.

Step-by-step explanation:

A pentagon has a 41.5 cm circumference, and its sides are each 8.3 cm long.

When you already know the value of one side, calculating the perimeter of a pentagon is made much simpler. The five sides of each pentagon are equal. If the length of one side is given to you.

Since a pentagon has five sides, we will abbreviate each side's length as "s". The lengths of all five sides add up to the perimeter of the pentagon, allowing us to formulate the following equation:

5s = 41.5

We must put "s" on one side of the equation alone in order to solve for it. Divide both sides by 5 to do this: s = 8.3

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The simplified expression for the expression (5 – 6f–9+8f–8f) is (-4 - 6f).

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction (from left to right).

Given:

5 – 6f–9+8f–8f

Solving the Expression

= 5 – 6f–9+8f–8f

= 5 - 9 -6f + 8f - 8f

= -4 + f(-6 +8 -8)

= -4 + f(-6)

= -4 - 6f

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a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16

b) Probability that not all ticketed passengers who show up can be accommodated is 0.67

c) The probability that you will be able to take the flight is 96%

Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights

In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.

(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.

(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is

=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.

(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.

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The United States forces arrived in Europe in 1917 and helped tip the scales in favor of Britain and France, leading to an Allied victory over Germany and Austria in November 1918. More than four million Americans had served in the armed forces by the time of the armistice, and 116,708 had died.

When World War I broke out in Europe in 1914, President Woodrow Wilson declared that the United States would remain neutral, and many Americans agreed. However, public opinion on neutrality began to shift after the sinking of the British ocean liner Lusitania by a German U-boat in 1915, which killed nearly 2,000 people, including 128 Americans.

Wilson requested a declaration of war against Germany in response to the Zimmermann telegram, which threatened an alliance between Germany and Mexico against America.

The United States of America officially entered World War I on April 6, 1917. Millions of Americans served overseas and helped the war effort at home over the next year and a half. Their contributions aided in the victory of the war and shaped both America and the world for future generations.

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The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

The amount of time when the water tank will have 450 gallons will be 16²/₃ minutes. The correct option is D.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a partially-filled water tank contains 300 gallons of water. water is then pumped into the tank at a constant rate. After n minutes, the amount of water, w, in the tank is W = 300 + 9n gallons.

The time will be calculated as:-

W = 300 + 9n

450 = 300 + 9n

9n = 150

n = 150 / 9

n = 16²/₃ minutes.

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The sequence with nth term an = (5√n)/(5√n + 6) diverges.

To determine the convergence or divergence of the sequence with the given nth term, we can use the limit comparison test by comparing it with the divergent series 1/n.

We have

lim n→∞ an/(1/n) = lim n→∞ (5√n)/(5√n + 6) * n = 5/5 = 1

Since the limit is a positive finite number, and the series 1/n diverges, the series with the nth term also diverges by the limit comparison test.

Therefore, the sequence with the nth term an = (5√n)/(5√n + 6) diverges.

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The transformation rule for triangle PQR into triangle P'Q'R' is given as follows:

(x,y) -> (y,x).

Which is a reflection over the line y = x.

The vertices of the original triangle are given as follows:

P(3,2), Q(5,6) and R (4,-1).

The vertices of the transformed triangle are given as follows:

P'(2,3), Q'(6,5) and R'(-1,4).​

The x-coordinate and the y-coordinate were exchanged, hence the rule is defined as follows:

(x,y) -> (y,x).

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For the given five number summary, the interquartile range is 7.

The five number summary is a set of descriptive statistics that provides a concise summary of a data set. It consists of the following five values:

In this problem, the five number summary is:  53 59 63 66 88

Hence,

Q1 = 59

Q3 = 66

Interquartile range = Q3 - Q1

                               = 66 - 59

                               = 7

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The vector equation of the tangent line is <9t+9, t+2, t^2>.

To find the tangent line to the curve at t=1, we need to find the derivative of r(t) and evaluate it at t=1.

r(t) = 9t <1> + 1 <2> + t^2 <3>

Taking the derivative of r(t) with respect to t, we get:

r'(t) = 9 <1> + 1 <0> + 2t <3>

Evaluating r'(1), we get:

r'(1) = 9 <1> + 1 <0> + 2(1) <3> = 9 <1> + 2 <3>

So the vector equation of the tangent line at t=1 is:

r(1) + tr'(1) = <9,1,1> + t<9,2,0>

Simplifying, we get:

<9t+9, t+2, t^2>

So the vector equation of the tangent line is <9t+9, t+2, t^2>.

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Surveys suggest that about 7 percent of people in the united states experience a depression during a given year.

The United States experienced a depression during the 1930s, which lasted from 1929 to 1939. This was one of the longest and deepest economic downturns in U.S. history. The Great Depression caused widespread unemployment, poverty, and hardship throughout the country.

The stock market crash of 1929 and the subsequent bank failures caused a sharp decline in industrial and agricultural production, as well as a dramatic drop in consumer spending. As a result, millions of Americans were left without jobs, and many lost their homes and other possessions.

The government responded to the crisis with a series of programs and initiatives, such as the New Deal, to stimulate the economy and provide relief for those most affected. These programs helped to create jobs and provide economic stability, but the Great Depression would not end until the U.S. entered World War II in 1941.

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Answer:

1 /2

Step-by-step explanation:

3×1 = 3

So it is 3 /6 = 1/2

3/6 ÷2 = 1/2

The number of 5/4 is 1130

how to find the number x?

writing this as an algebraic expression.

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. Also, solve questions in Algebraic Expressions Worksheets

[tex]\frac{5}{8}x[/tex] = 565

[tex]\frac{5x}{8}[/tex] = 565

5x = 565 * 8

5x = 4520

x = [tex]\frac{4520}{5}[/tex]

x = 904

so the number is 904

What is 5/4 of 904 ?

[tex]\frac{5}{4}[/tex] * 904

= 1130

so the answer to this question is 1130

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The measure of angle C in triangle BCD is 39⁰.

option B.

The measure of angle C in triangle BCD is calculated by applying the following formula as shown below.

Angle D = 92 ⁰ ( vertically opposite angles are equal )

∠CDB = 180 - 92⁰ = 88⁰ ( sum of angles on a straight line )

∠AED = 180 - (35 + 92 ) ( sum of angles in a triangle)

∠AED = 53⁰

In the quadrilateral FBDE,

angle B = 180 - 53 ( opposite angles of a cyclic quadrilateral are supplementary)

angle B = 127

∠CBD = 180 - 127 ( sum of angles on a straight line)

∠CBD = 53⁰

Then, the value of ∠BCD is calculated as;

∠BCD + ∠CBD + ∠CDB = 180 ( sum of angles in a triangle )

∠BCD + 53 + 88 = 180

∠BCD + 141 = 180

∠BCD = 180 - 141

∠BCD = 39⁰

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Answer:

Step-by-step explanation:

h = 100 *  400000 - 20000 / 20000   =  38000000/ 20000  = 1900/1  = 1900%

Prime Factorization is finding which prime numbers multiply together to make the original number.

Prime factorization of the following numbers is

1 = 1

2 = 2 × 1

4 = 2² × 1

5 = 5 × 1

7 = 7 × 1

8 = 2³ × 1

10 = 2 × 5

14 = 2 × 7

16 = 2⁴

20 = 2² × 5

28 = 2² × 7

35 = 5 × 7

40 = 2² × 5

56 = 2³ × 7

70 = 2 × 5× 7

80 = 2⁴ × 5

112 = 2⁴ × 7

140 = 2² × 5 × 7

280 = 2³ × 5 × 7

560 = 2⁴ × 5 × 7

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The joint pmf of X and Y 5/8, the marginal pmfs pX and pY is 3/7 and the conditional pmfs pX|Y (x|0) and pX|Y (x|1) is 5/28 and 41/56.

The probability that the chosen combination has a certain property can be set up by dividing the number of combinations where the property holds by the total number of possible combinations.

The order of the chips chosen does not matter so outcomes can be considered as combinations. We must choose 3 of the 9 chips in the box, where X are chosen from the 3 red chips, and Y are chosen from the 2 white, and the remainder are chosen from the 4 black.

For x∈{0,1,2,3}and y∈{0,1,2}, the probability that x red chips and y white chips are chosen is

To determine the marginal distribution of X, we need not distinguish white chips from black. X chips are chosen from the 3 red chips, and the remainder are chosen from the 5 non-red chips. For x∈{0,1,2,3} the probability that x chips are chosen is,

P(x) = (³ₓ) (₃-ₓ⁶) / (⁹₃)

Similarly, in determining the marginal distribution of Y, we choose Y white chips from among the 3 available, then choose the remaining chips from the 5 non-white chips.

c) To find the conditional distribution,

P(X|Y=0)= 5/28

P(X|Y=1)= 41/56

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a) Increased by 44 students per year= N(t) = 240 + 44t

b) Decreased by 32 students per year=N(t) = 240 - 32t

c) Increased by 40 students every 2 years=N(t) = 240 - 32t

d) Decreased by 24 students every 4 years=N(t) = 240 - 32t

e) Remained constant= N(t) = 240

f) Increased by 5 students every semester (twice in a year)=N(t) =240+10t

The original population of students in the year 2000 is 240.

[tex]N_0=240[/tex]

Let the number of years = t

a) If the population increased by 44 students every year, the population, after t years, would have increased by 44t

Therefore,

[tex]N(t)=N_0+44t[/tex]

N(t) = 240 + 44t

b) If the population decreased by 32 students per year, the population, after t years, would have decreased by 32t

Therefore,  [tex]N(t)=N_0-32t[/tex]

N(t) = 240 - 32t

c) If the population Increased by 40 students every 2 years and increase is uniform per year, the population will increase by 40/2 = 20 students in 1 year. So in t years, the population would increase by 20 t.

Therefore,

[tex]N(t)=N_0+20t\\\\N(t)=240+20t[/tex]

d) Decreased by 24 students every 4 years

In 1 year, it decreases by 24/4 = 6 students

In t years, it decreases by 6t students

[tex]N(t)=N_0-6t\\\\N(t)=240-6t[/tex]

e) Remained constant

N(t)=N0

N(t)=240.

f) If the population increases by 5 students twice in a year

In 1 year, it increases by 5*2 = 10 students

In t years, it increases by 10t students

[tex]N(t)=N_0+10t\\\\N(t)=240+10t[/tex].

The Complete Question:-

When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ), representing the number of students attending this charter school t year after 2000, assuming that the student population:

a) Increased by 44 students per year

b) Decreased by 32 students per year

c) Increased by 40 students every 2 years

d) Decreased by 24 students every 4 years

e) Remained constant

f) Increased by 5 students every semester (twice in a year)

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The central angle of the pie chart representing the moderate conditions is 80°

Central angle is the angle subtended by an arc of a circle at the center of a circle. The radius vectors form the arms of the central angle.

Given that, a pictogram which was displayed in a pie chart, we need to find the central angle of the pie chart,

Sea conditions is shown,

Calm = 3 blue dots

Moderate = 2 and a half dot

Rough = 5 and 3 parts of the dot

Each dot = 4 points

Therefore,

Calm = 3×4 = 12

Moderate = 2×4 + 1/2 × 4 = 10

Rough = 5×4 + 3/4 ×4 = 23

The central angle = 10 / 12+10+23 × 360° = 80°

Hence, the central angle of the pie chart representing the moderate conditions is 80°

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The complete question is:-

If the information in this pictogram was displayed in a pie chart, what would the central angle of the sector representing rough conditions be? Give your answer in degrees  Sea conditions

Calm Key

Moderate

Rough

The correct translation of the definition of the limit of a real-valued function f(x) of a real variable x at a point a in its domain in predicate logic expressions.

For all ε > 0, there exists δ > 0 such that for all x, if 0 < |x-a| < δ, then |f(x)-L| < ε.

In symbols, this can be written as:

∀ε > 0, ∃δ > 0 such that ∀x, (0 < |x - a| < δ) → (|f(x) - L| < ε).

Note that "ε" and "δ" are the Greek letters epsilon and delta, respectively, and they are used to represent small positive numbers. This definition says that if we want the limit of f(x) to be L, we can find a positive number δ such that the distance between f(x) and L is less than ε whenever x is within δ units of a (but not equal to a). The limit is said to exist if we can find such a δ for any value of ε.

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There are infinitely many possible solutions to the equation y = 3x + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

An equation,

y = 3x + 5.

The equation has an independent variable x and a dependent variable y.

And the x is a free variable.

So, the y varies as per the value of x.

There are infinite possible solutions to the equation.

Therefore, there are infinite possible solutions to the equation.

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Answer:

a. (-0.93,-0.37)

Step-by-step explanation:

The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of a coordinate plane. To find the coordinates of a point on the unit circle corresponding to a given central angle, we can use the relationship between the angle and the coordinates of the point.

For a central angle of 202 degrees, the point on the unit circle would be found by using the formula:

x = cos(202°)

y = sin(202°)

Rounding the results to the nearest hundredth, we have:

x = -0.927

y = -0.3746

So the coordinates of the point on the unit circle corresponding to the central angle of 202 degrees are (-0.93, -0.37).

Answer:

a. (-0.93, -0.37)

Step-by-step explanation:

A unit circle has its center at (0, 0) and a radius of 1.

The coordinates on the unit circle (x, y) are equivalent to (cos θ, sin θ), where θ is the angle (measured anticlockwise from the positive x-axis).

Therefore, given θ = 202°, the coordinates of the corresponding point on the unit circle are:

Therefore, the point on the unit circle is (-0.93, -0.37).