Question 21 Suppose that 12 inches of wire costs 36 cents. At the same rate, how much (in cents) will 5 inches of wire cost? ​

The value of x= 35.5, y= 43.75 and z= 62.75

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the three angles are x, y and z.

x+ y + z = 180............(E3)

The sum of the measures of the second and third angles is three times the measure of the first angle.

So, y+ z = 3x

3x- y- z= 0.............(E1)

and, third angle is 19 more than the second

z= y+ 19

y- z= -19..........(E2)

So, E1+E2, and E3-E2,

3x- 2z= -19

x+ 2z= 161

Now, adding above

4x = 142

x= 35.5

and, y + z = 106.5, y- z = -19

Again, adding

2y= 87.5

y= 43.75

and, z= 62.75

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The completed sentences that describe the height reached by the ball specified by the function, f(x), that indicates the balls height, based on the number of bounces, x, f(x) = 64·(0.75)ˣ, which is similar to a geometric progression, is presented as follows;

The variable, x, represents the number of times the ball bounces.

The variable f(x) represents the height of the ball after x bounces.

The parameter, 64, represents the initial height of the ball.

The parameter, 0.75, represent the percentage of height left from each previous bounce.

A geometric progression is a number sequence, arranged such that the ratio between a term and the previous term is a constant, known as the common ratio of the geometric progression.

The exponential function that models the specified situation of finding the height of the ball is presented as follows;

f(x) = 64·(0.75)ˣ

The initial height from which the student drops the ball = 64 feet

The height the ball reaches after one bounce = 48 feet

Height of the ball after 2 bounces = 36 feet

The exponential function, f(x) = 64·(0.75)ˣ, is similar to the equation for a geometric progression, aₙ = a₁·r⁽ⁿ⁻¹⁾

Where;

a₁ = The first term = The initial height

r = The common ratio = 48/64 = 36/48 = 0.75

n = The number of times the ball bounces, in addition to the time the ball is dropped from the initial height, therefore;

x = n - 1, therefore;

x = The number of times the ball bounces

n = x + 1

The terms that complete the sentences are therefore:

The variable that represents the number of time the ball bounces = x

The variable that indicates the height of the ball after x bounces = f(x)

The initial height of the ball = The parameter 64

The percentage of the height the ball bounces to after the previous bounce = 0.75

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There is a Rotation of 180 degrees

What is Co-ordinate Geometry?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

We are given that point A is (4, 5) this means that the point lies in the First Quarter of the Co-ordinate System

and the transformed point lies in the Third Quarter of the Co-ordinate System

So, it can be very well said that there is a Rotation of 180 degrees

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Answer: 5

Step-by-step explanation: To find the distance between 2 points, we should use this formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

So, using that it would be written as:

[tex]\sqrt{9 + 16}[/tex] (after simplified)

Now, we need to find the square root of 25

The square root of 25= 5

So, that is how I got my answer.

Answer:Above $297 we need to add 34%. Thus the result :

297 X 34/100 =100,98

Result = 297 + 100,98 = 397,98

Step-by-step explanation:Good luck

Step-by-step explanation:

I just answered this with all explanations.

Answer:

960.00

Step-by-step explanation:

Interest = principle x rate x time

interest = 6000 x .04 x 4

960.00

Answer:

I = $ 960.00

Step-by-step explanation:

I = Prt

Since we are figuring out how much money was earned in interest, we will need to convert our R (which is the interest rate) into decimals, which will be, r = R/100 = 4%/100 = 0.04 per year.

Step 1. Divide R by 100, in this case, R is 4, so it will be 0.04.

Step 2. Times 6000 (the money that was deposited) by 0.04, then times it with 4 (the years) and you will get 960.

I = 6000 × 0.04 × 4 = 960

I = $ 960.00

I hope this helps you!

Answer:

5

Step-by-step explanation:

In an isosceles triangle two of the angles are equal and the corresponding sides are also equal

Here ∠A = ∠B

AC = BC

3x + 4 = 10

3x = 6

x = 2

Side AB = x + 3 = 2 + 3 = 5

****

The line segment's unit of measure is 75.6 inches.

What is the conversion factor?

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.

Here, we have

Given

12in/1ft

We have to convert this into inches.

So, we apply here conversion factor and we get

= 6.3ft × 12in ÷1ft

= 75.6 inches

Hence, the line segment's unit of measure is 75.6 inches.

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Answer:

(1,2)

(3, -1)

Step-by-step explanation:

2x + 5y = 12

4x -y = 2  Multiply this through by 5 and then add to the equation above

2ox - 5y = 10  

2x + 5y = 12        

22x = 22  Divide both sides by 22

x = 1

Substiture in 1 for x in either of the two original equations

2x +5y = 12

2(1) + 5y = 12  

2 + 5y = 12  Subtract 2 from both sides

5y = 10  Divide both sides by 5

y = 2

(1,2)

2nd Problem

2x - 5y = 11 Multiply through by 2      4x - 10 y = 22

3x  + 2y = 7    Multiply through by 5    15x + 10 y = 35

Add the two bold equation together

4x - 10y = 22

15x +10y = 35              

19x = 57  Divide both sides by 19

x = 3            

Substitute in 3 for x in one of the original equations to solve for y.          

2x - 5y = 11

2(3) - 5y = 11

6 - 5y = 11  Subtract 6 from both sides

-5y = 5  Divide both sides by -5

y = -1

(3,-1)

Answer:

(a) A(w) = w(950-2w) = 950w-2w^2

(b) w = 237.5

(c) A = 112812.5

Step-by-step explanation:

First of all the maximum area is always a square. You can get the answer first to check your work later.

950/4 = 237.5

One side is not needed so add that length to the non-parallel side.

237.5+237.5=475 feet is the length and 237.5 feet is the width(s)

A=475*237.5

A=112812.5 square feet

Doing the algebra...

P=l+2w

950=l+2w

950-2w=l

A=lw

A=(950-2w)w

A=950w-2w^2

Step-by-step explanation:

[tex]( {x}^{2} - x)(x + 5)[/tex]

[tex]x(x - 1)(x + 5)[/tex]

[tex]x = 0[/tex]

[tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

[tex]x + 5 = 0[/tex]

[tex]x = - 5[/tex]

So our zeroes are 0,1, and -5

2.

[tex] {x}^{3} + 4 {x}^{2} - 5x[/tex]

To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.

det ( -1 2 0

        -1 0 1

         1  0 1 )   = 4

Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.

Therefore, the polynomial forms the basis of P.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.

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Answer:

Hi, the answer to your question is ×=20

X = 20

when we solve the given equation,

9/12 = 15/x

hence,

X = 15*12/9

X = 20

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number line with open circle on point negative 5 and arrow shaded to the right is the right description for the graph of the inequality.

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

let the number be x

so that 2.5 > -0.5x

dividing through by -0.5 we revert the inequality sign

2.5/-0.5 < x

-5 < x

Taking x to the other side we revert the inequality sign back to greater than

x > -5

In conclusion, number line with open circle on point negative 5 and arrow shaded to the right is the description of the graph

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Answer: D

Step-by-step explanation: I have proof! i got it right on test and i have a picture.

The bacteria after 24 hours will be equal to 450000.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.

The number of bacteria will be calculated as,

N = 125×(60×60)

N = 125×3600

N = 450000

Therefore, the bacteria after 24 hours will be equal to 450000.

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Answer:

1.2+2.56.7×3218°÷456.7820

The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,

so formula becomes,

Total amount = amount (1+r/200)^2t

T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])

5000 = 2500 (1+3/100)^2t

2 = [tex](1+0.03)^{2t}[/tex]

2 = [tex]1.03^{2t}[/tex]

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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The difference between the largest and the smallest fraction is 0.24.

A fraction is a component of a whole.

Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.

In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, first, we will figure out the smallest and the greatest fraction:

We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4

LCM of denominators: 2*2*2*3*3*5 = 360

216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360

Smallest: 216/360

Largest: 300/360

Subtract smallest from largest:

300/360 - 216/360

84/360

7/30

0.2333

Round off: 0.24

Therefore, the difference between the largest and the smallest fraction is 0.24.

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Answer:

The answer is 9

Step-by-step explanation:

The given triangle is equivalent triangle

We know that in equivalent triangle all angles are equal to 60°

So,

(7x - 3)° = 60°

7x - 3° = 60°

7x - 3° + 3° = 60° + 3°

7x = 63°

x = 63°/7°

x = 9°

Thus, The value of x is 9°

For Verification Only;

(7x - 3)° = 60°

[7(9) - 3]° = 60°

(63 - 3) = 60°

60° = 60°

Hence,

L.H.S = R.H.S

Answer:

(3+2)

Step-by-step explanation:

Perimeter of a square = 4L

L is the length of one side of the square

Given the expression 12 + 8 that represents the perimeter of a square, factoring out 4 from both terms;

12 + 8

= (4*3)+(4*2)

= 4(3+2)

Comparing with 4L

4L = 4(3+2)

Divide both sides by 4

4L/4 = 4(3+2)/4

L = (3+2)

Hence the expression that represents one side of the square is (3+2).

Hope this helps!!! :)

The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).

The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.

The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.

In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.

The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.

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The domain of the function are all real numbers between -1 and 0. {x∈R|-1≤x≤0}

What is a function ?

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.

The domain of function are set of values of x for which the function covers.

For the given function, from the graph the function starts from x =-1 and ends at x = 0.

So, the domain of the function are all real numbers between -1 and 0.

{x∈R|-1≤x≤0}

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1. d. 8/52 (Ace ∪ 5)

2. h. 0 (Ace ∩ 5)

3. b. 20/52 (Even')

4. c. 36/52 (Even ∪ black)

5. a. 3/52 (Face ∩ Diamond)

What is probability?

Probability means the quality or state of being the outcome; the extent to which something is likely to happen or take place. Probability means the possibility of any outcome which can take place in any event.

Solution:

1. Probability of Ace ∪ 5 = (No. of Aces + no. of cards with face value 5)/52 = 8/52

2. Probability of Ace ∩ 5 = (Intersection of Ace and face value of card 5)/52 = 0

∵ Intersection of ace and 5 is 0 as there is no intersection in between the 2 subevents.

3. Probability of Even complement = No. of cards with odd values/52                    

 {A,3,5,7,9,A,3,5,7,9,A,3,5,7,9,A,3,5,7,9}/52      =20/52

4. Probability of Even ∪ black = {(2,4,6,8, 10)×4 types of cards odd black spades + odd black clubs = 20+16/52

                                          = 36/52

5.  Probability of Face ∩ Diamond = No. of face cards in diamonds/52

                                                        = {Jack, Queen, King}/52

                                                        = 3/52

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Answer:The answer is B

Step-by-step explanation:

The reason that the answer is b is because he wants to keep the prices low from them getting charged by the bank

With the given coordinates (-3, 1) and (0, 4), the slope is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

Here,

1) (-3, 1) and (0, 4)

Δy=(4-1)=3 and Δx=(0(-3))=3

So, m= Δy/Δx =3/3 =1

2) (-6, 27) and (2, 3)

Δy=(3-27)=24 and Δx=(2-(-6))=8

So, m= Δy/Δx =24/8 =3

3) (5, 27) and (0, -8)

Δy=(-8-27)=-35 and Δx=(0-5)=-5

So, m= Δy/Δx =(-35)/(-5) =7

4) (1, 0) and (-7, -24)

Δy=(-24-0)=-24 and Δx=(-7-1)=-8

So, m= Δy/Δx =(-24)/(-8) =3

5) (-3, 20) and (-5, 32)

Δy=(32-20)=12 and Δx=(-5-(-3))=-2

So, m= Δy/Δx =12/(-2) =-6

6) (5, -4) and (0, -9)

Δy=(-9-(-4))=-5 and Δx=(0-5)=-5

So, m= Δy/Δx =(-5)/(-5) =1

7) (-8, -2) and (-1, -4.5)

Δy=(-4.5-(-2))=-2.5 and Δx=(-1-(-8))=7

So, m= Δy/Δx = -2.5/7

8) (-7, -2) and (6, 11)

Δy=(11-(-2))=13 and Δx=(6-(-7))=13

So, m= Δy/Δx =13/13 =1

9) (-2, -6.5) and (4, -8)

Δy=(-8-(-6.5))= -1.5 and Δx=(4-(-2))=6

So, m= Δy/Δx = -1.5/6 = -1/4

Therefore, slope of a line with the coordinates (-7, -2) and (6, 11) is 1.

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