The formula N = p + 0.04p models the new population, N, of a town with current population p if the town is expecting population growth of 4% next year. Find the new population of a town whose current population is 4300 persons

N=? persons

Answer:

i believe its 24500

Step-by-step explanation:

The solution is,  Chun is correct.

The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.

here, we have,

Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:

 top short : bottom short = top long : bottom long

 5 / 8 = 15 / x

Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...

 top short : bottom long = bottom short : top long

She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.

Chun's proportion correctly gives x=24.

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Answer:

Step-by-step explanation:

[tex]7 \times 3 + 2 = 23 [/tex]

[tex]2 \times 3 + 2 = 8[/tex]

[tex] \frac{23}{8}[/tex]

so if want to have improper fraction this is the answer but to get proper fraction i am continuing

[8 \div 23 \sqrt[23]{80} to get the correct answer.you can get a mixed fraction too when you multiply 8 how many times you will get 23 8×2=16=2whole number 16 as the numerator and 8 as the denominator

X = 5 is the other zeros of polynomial.

What is a polynomial, simply put?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).  

                                       The different types of polynomial equations are - linear equations, quadratic equations, cubic equations, and biquadratic equations. The equations formed with variables, exponents and coefficients are called as polynomial equations.

   g(x) = x³ - x² - 34x + 70

       x = 5

 g(5) = 5³ - 5² - 34 * 5 + 70

         = 125 - 25 -  170 + 70

          = 195  - 195

          = 0

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For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                 G(x)= 3x-5

for F(x)=G(x)

  |3x+2|-6=3x-5

  3x+2-6=3x-5

    3x-4=3x-5

Hence no solution.

The graph is given below.

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For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one other object f if the object x is present in the set of inputs (referred to as the domain) (x) among the range of potential outcomes (called the codomain).

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                G(x)= 3x-5

for F(x)=G(x)

 |3x+2|-6=3x-5

 3x+2-6=3x-5

   3x-4=3x-5

Hence no solution.

The graph is given below.

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Answer: 10,000 or 10^4

Step-by-step explanation: I will assume in the problem that the logarithm is of base-10. We can therefore rewrite the equation in words as 10^4=x. The general form of a logarithm is log base y of x=z. This can be rewritten as y^z=x. We are doing the same thing here. We know that 10^4 is 10,000 so that is our answer.

Hope this helps!

For practice here are some problems (assume all logarithms are our base 10): log x = 3, log x = 1.

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:

r = 0.06/12 = 0.005

Next, we can substitute the given values into the formula and solve for P:

12,000 = P(1 + 0.005/12)^(12*3)

12,000 = P(1.005)^36

P = 12,000/(1.005)^36

P ≈ $9,883.86

Therefore, the amount of money that should be deposited today is approximately $9,883.86.

Step-by-step explanation:

The value of the function at x = -10, x = 2, and x = 5 will be 20,201, 17, and 1,226, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 2x⁴ + x² - 10x + 1

At x = - 10, the value of the function is given as,

f(-10) = 2(-10)⁴ + (-10)² - 10(-10) + 1

f(-10) = 20,201

At x = 2, the value of the function is given as,

f(2) = 2(2)⁴ + (2)² - 10(2) + 1

f(2) = 17

At x = 5, the value of the function is given as,

f(5) = 2(5)⁴ + (5)² - 10(5) + 1

f(5) = 1,226

The value of the function at x = -10, x = 2, and x = 5 will be 20,201, 17, and 1,226, respectively.

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Answer:

A) (5 , 1)

Step-by-step explanation:

The x coordinate goes first, then the y coordinate: (x , y)

In this case, locate Chewy. Chewy is found in the x-coordinate of 5, and a y-coordinate of 1. Therefore, (5 , 1) or A) is your answer.

~

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No, -(p « › q) and p «> -q are not logically equivalent.

When two logical assertions have the same truth value for all conceivable truth value assignments to their constituent propositions, the two statements are said to be logically equivalent. In other words, two assertions are comparable logically if and only if all feasible permutations of the truth values of their component propositions are equal.

First, let's rewrite the statements using the standard logical operators of negation, conjunction, and implication:

-(p « › q) is equivalent to ¬(p ∧ ¬q)

p «> -q is equivalent to ¬p → ¬¬q, which simplifies to p → q

Now, we can construct a truth table with columns for p, q, ¬(p ∧ ¬q), and p → q:

p |      q |   ¬(p ∧ ¬q)    |    p → q

--|----------|------------------|-----

T        T          F               T

T        F          T               F

F       T           T               T

F       F           T               T

We can see that the truth values of the two statements are not always the same.

For example, when p is true and q is false, ¬(p ∧ ¬q) is true and p → q is false.

Therefore, -(p « › q) and p «> -q are not logically equivalent.

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Answer:

Step-by-step explanation:

triangle-

b+h/2=a

5x6/2=30

rectangle-

2.5x12=30

area of drawing-

30+30=60

answer:60cm^2

The factors of given expression are (a+b+2) and (a+b+2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is (a+b)²+4(a+b)+4.

Here, take x=a+b

Now, x²+4x+4

= x²+2×2×x+4 (Algebraic identity (a+b)²=a²+2ab+b²)

= (x+2)²

= (a+b+2)²

= (a+b+2)(a+b+2)

Therefore, the factors are (a+b+2) and (a+b+2).

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The graph that models the situation is on the image at the end, we can see that she scored 8 2-pointers and 1 3-pointer.

Let's define the variables:

x = number of 2-points that she scored.

y = number of 3-points that she scored.

We know that she scored 19 points, then we have the equation:

2x + 3y = 19

And we also know that she scored a total of9 baskets, so we have other equation:

x + y  =9

Then we have a system of equations:

2x + 3y = 19

x + y = 9

The graph of that system is the graph that models the situation, it is shown at the end of the answer.

There you can see that the solution is (8, 1)

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Therefore, the combined volume of the two rectangular prisms is 132 cubic units.

2-D enclosed shapes with four sides, four corners, and four right angles are called rectangles. A rectangle has two equal and parallel opposite sides.

To determine the combined volume of the two rectangular prisms shown in the diagram, we need to find the sum of their individual volumes. The volume of a rectangular prism is given by the formula:

Volume = length x width x height

In the diagram, we can see that the first rectangular prism has a length of 5 units, a width of 3 units, and a height of 4 units. The second rectangular prism has a length of 6 units, a width of 4 units, and a height of 3 units.

To find the volume of the first rectangular prism, we can use the formula:

Volume of first prism = length x width x height

Volume of first prism = 5 units x 3 units x 4 units

Volume of first prism = 60 cubic units

To find the volume of the second rectangular prism, we can use the same formula:

Volume of second prism = length x width x height

Volume of second prism = 6 units x 4 units x 3 units

Volume of second prism = 72 cubic units

Finally, to find the combined volume of the two prisms, we just need to add their individual volumes:

Combined volume = Volume of first prism + Volume of second prism

Combined volume = 60 cubic units + 72 cubic units

Combined volume = 132 cubic units

Therefore, the combined volume of the two rectangular prisms is 132 cubic units.

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The answer for the given polynomial function are given below:

Real zero of the polynomial : x= -7

                                           x= 7/2

                                           x= 7

Not a real zero of the polynomial : x= -49

                                                    x= -7/2

                                                    x= 49

It is a function of a single independent variable involving only non - negative integer powers. For example 5x+7.

What is zero of polynomial?

Zero of polynomial  are the points for which the polynomial becomes zero as a whole.

Given polynomial function is P(x)= (2x-7)(x²- 49)

For the zeros of the polynomial we need to take P(x)=0

                      (2x-7)(x² -49)=0

              Either (2x-7)=0 or (x² -49)=0

                   If, 2x-7=0            

                      2x=7

                       x=7/2

         If, x² -49=0

             x² =49

             x=±√49

             x=± 7

Hence, x= -7, 7/2, 7

so the real zeros of the polynomial are -7, 7/2, 7.

rest of the numbers are not the real zeros of the polynomial.

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Aaron running speed is 2 3/4 miles per hour

What is Speed?

Speed is the ratio of distance to the time in which the distance was covered. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s, km/hr, miles/hr and so on. It is also a measurement of how fast an object is moving through a path.

Where the formula is Speed = Distance/Time

Where Distance covered = 1/8 miles

Time taken = 1/22 of an hour

Speed = (1/8)/(1/22)

Speed = 1/8 *22/1

Speed = 22/8

Speed = 11/4

Spees = 2 3/4 miles per hour

Therefore, Aaron running speed is 2 3/4 miles per hour

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Using the roots of the given equation, x²+x-6=0, the value of the expression, 2β²-3α², is -19

From the question, we are to evaluate the given expression.

In order, to evaluate the expression, we will solve the given quadratic equation

To solve x²+x-6=0, we can use factoring method

Solving the equation

x² + x - 6 = 0

(x + 3)(x - 2) = 0

Setting each factor equal to zero, we get:

x + 3 = 0 or x - 2 = 0

Solving for x in each case, we get:

x = -3 or x = 2

So the solutions to the equation are x=-3 and x=2.

Since α<β

Thus,

α = -3 and β = 2

Then,

2β²-3α²

= 2(2)² -3(-3)²

= 2(4) -3(9)

= 8 - 27

= -19

Hence, the value is -9

Here is the correct question:

If α and β are the roots of the equation x²+x-6=0, where α<β, evaluate 2β²-3α²

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Answer: Krysti's mistake was ordering only 12 small T-shirts when she should have ordered more. To figure out how many small T-shirts she should have ordered, we can start by finding out how many classmates wanted small T-shirts:

60% of 25 classmates = 0.60 x 25 = 15 classmates

So, 15 classmates wanted small T-shirts. If Krysti had ordered one small T-shirt for each of these classmates, she would have needed 15 small T-shirts. However, Krysti only ordered 12 small T-shirts, which means she is short by 3 shirts.

To avoid this mistake, Krysti should have double-checked her calculations and made sure that the number of small T-shirts she ordered matched the number of classmates who wanted small T-shirts.

Step-by-step explanation:

The missing length the right triangle to the nearest tenth is 8.8 units.

The figure in the image is a right traingle.

To solve for the second leg of the right triangle given the first leg and hypotenuse, we can use the Pythagorean theorem.

It states that the sum of the squares of the two legs is equal to the square of the hypotenuse.

a² + b² = c²

Let's denote the second leg by 'b'. Then we have:

2² + b² = 9³

Simplifying the equation:

4 + b² = 81

Subtracting 4 from both sides:

4 - 4 + b² = 81 - 4

b² = 77

Taking the square root of both sides:

b = √77

b = 8.8 units

Therefore, the second leg of the right triangle is 8.8 unit.

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Answer: To solve the problem, we need to subtract the number of points scored on touchdowns from the total number of points to find out how many points were scored on field goals.

133 points - (number of touchdowns x 7 points per touchdown) = points scored on field goals

We don't know the number of touchdowns, but we can use the fact that each touchdown is worth 7 points to write:

133 points - 7x = points scored on field goals

Now we can divide the points scored on field goals by the value of each field goal to find the number of field goals:

(points scored on field goals) / (3 points per field goal) = number of field goals

Putting it all together:

133 points - 7x = points scored on field goals

(points scored on field goals) / (3 points per field goal) = number of field goals

We need to solve for x, the number of touchdowns. We can start by isolating points scored on field goals:

133 points - 7x = points scored on field goals

points scored on field goals = 133 points - 7x

Now we can substitute this expression into the second equation:

(133 points - 7x) / (3 points per field goal) = number of field goals

Simplifying:

44.33 - 2.33x = number of field goals

Since the number of field goals must be a whole number, we can try different values of x until we find an integer solution. For example, if we assume that the Bobcats scored 16 touchdowns, then:

133 points - 7(16) = 21 points scored on field goals

21 points scored on field goals / 3 points per field goal = 7 field goals

Therefore, the Bobcats kicked 7 field goals.

Step-by-step explanation:

The equation would be C = 1.25w, where c is the total cost of w pounds of oranges do not include units or a dollar sign.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

We are given that oranges are being sold for $ 1.25 per pound.

The equation would be as;

C = 1.25w

where c is the total cost of w pounds of oranges and does not include units or a dollar sign.

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Answer: (3,-1) = (0,2) (5,-2) = (2,1) (3,-5) = (0,-2) (-5,-5) = (-2,-2)

Step-by-step explanation:

The inequality represented by the given number line is expressed as;

-3 ≤ x < 1

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Now, a square bracket at one end of an interval indicates that the interval is closed at that end (i.e., the number adjacent to the opening or closing square bracket is included in the interval).

Thus, the inequality here is expressed as;

-3 ≤ x < 1

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Answer:

2n^2

Step-by-step explanation:
The is a Quadratic sequence:

First difference is 6 10 14 18
Second difference is 4 4 4 4
Divide the second term by 2 which is 2n^2

In answering the question above, the solution is If a/b = 1/4 and c/d = 1/3, fraction then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are stated in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You may assess it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a whole number or object.

Let's start by decomposing { into two fractions:

[tex]{ = a/b + c/d\\\\{ = (ad + bc)/bd[/tex]

If [tex]a/b = 1/2 and c/d = 1/3, then ad + bc = (1/2)(bd/2) + (1/3)(bd/3) = bd/3 + bd/6 = 3bd/6 + bd/6 = 4bd/6 = 2/3,[/tex] which works.

If [tex]a/b = 1/2 and c/d = 1/4, then ad + bc = (1/2)(bd/2) + (1/4)(bd/4) = bd/4 + bd/8 = 2bd/8 + bd/8 = 3bd/8,[/tex] which doesn't work.

If [tex]a/b = 1/2 and c/d = 1/5, then ad + bc = (1/2)(bd/2) + (1/5)(bd/5) = bd/4 + bd/25 = 25bd/100 + 4bd/100 = 29bd/100[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/4, then ad + bc = (1/3)(bd/3) + (1/4)(bd/4) = bd/9 + bd/16[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/5, then ad + bc = (1/3)(bd/3) + (1/5)(bd/5) = bd/9 + bd/25,[/tex] which doesn't work.

If a/b = 1/4 and c/d = 1/3, then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

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Answer:

Step-by-step explanation:

Mark decompose 5/6 into three fractions using fractions : 1/3, 5/18, 2/9

What is fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given, fraction

5/6

Multiplying 3 with both numerator and denominator

15/18

= (6 + 5 + 4)/18

= 6/18 + 5/18 + 4/18

= 1/3 + 5/18 + 2/9

Hence, 1/3, 5/18, 2/9 are fractions Mark used to decompose 5/6.

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Answer: 168

Step-by-step explanation:  

The answer as a fraction in lowest terms is 4/81, and the denominator is 81.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

There are 4 green card, 2 red cards, 3 blue cards

Now,

If the first card drawn is red and is replaced before the second draw, then the probability of drawing a red card on the second draw is the same as the probability of drawing a red card on the first draw, which is 2/9 (since there are 2 red cards out of a total of 9 cards).

To find the probability of drawing two red cards, we need to multiply the probability of drawing a red card on the first draw (which we know is 2/9) by the probability of drawing a red card on the second draw, which is also 2/9 (since the first card is replaced).

So the probability of drawing two red cards with replacement is:

(2/9) * (2/9) = 4/81

Therefore, the probability and denominator will be 4/81 and 81.

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Answer:

The answer is 1/25

Step-by-step explanation:

The factored form of the polynomial  f(x) = x³ - 7x² + 9x - 63 is,

(x - 7)(x² + 9).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A polynomial f(x) = x³ - 7x² + 9x - 63.

Now, If x = 7 is an x-intercept then one root(cuts the x-axis) is 7 and one factor is (x - 7).

Now, Factoring(long division) f(x) = x³ - 7x² + 9x - 63 by (x - 7) we have,

(x³ - 7x² + 9x - 63) = (x - 7)(x² + 9).

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