When you start from a given set of rules and conditions and determine what must be true, you are using reasoning.
A. conjunctive
B. inductive
C. deductive
D. conductive

Answer:

  a. 31 months

  b. $818.32

  c. $168.32 interest

Step-by-step explanation:

Given that Joe makes a minimum payment of $21.45 on his credit card purchase of $650 with an APR of 19.85%, you want to know ...

If the balance is reduced by $21.45 per month, it will take ...

  $650/($21.45/mo) ≈ 30.3 months

to pay off the balance.

Joe will be making payments for 31 months.

The total amount Joe pays for his sound system is the sum of its initial cost and the total of interest payments. That sum is ...

  cost + interest = total paid

  $650 +168.32 = $818.32

Joe will pay a total of $818.32.

The total amount of interest Joe pays is $168.32.

__

Additional comment

If the total payment each month is $21.45, then it will take 43 months to pay off the system, for a total cost of $909.61, of which $259.61 is the cost of the credit. (The finance charge is paid first from this payment amount, so the amount that goes to reduce the balance is less.)

The hours that it take a pipes to feel the same pool is 120 hours.

Rate demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this situation, 5 pipes can fill the pool in 24 hours.

The rate for a pipe will be:

= Number of hours × Number of pipe

= 24 × 5

= 120 hours

The time taken is 120 hours.

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Ф {0, [3√3/2(3√3-π)]}

The poster above has good diagrams ; so , I will just go through the calculations .

The region of integration is with in the circle x ^2+y^2=2y but outside the circle   x^2+y^2=1.

I would convert to polar . With polar , we have  x^2+y^2=r^2 ,x=rcosФ and        y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r,  and you get r=2sinФ(1).  
This is the upper circle in the previous posters diagrams .

The other equation of a circle becomes :
x^2 + y^2 =  1  ⇒ r^2 = 1 ⇒ r =  1   (2)      
These two curves intersect at :
r= 2sinФ =1 ⇒     sinФ=1/2  ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6    
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X  coordinate of the center of mass is zero  
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2  ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ  They say the area mass density is inversely proportional to the distance from the origin .

This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=

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Using the slope, the required value of k is 48.

In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.

A line's slope can be used to determine how steep it is.

Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).

Given is a line that crosses through the origin:

y = mx

Let,s take x = -12 and y = -2.

y = mx

-2 = -12m

m = -2/12

m = -1/6

m is the slope.

The equation now:

y = mx

y = -1/6x

Now, insert:
x = k and y = 8

y = mx

8 = -1/6x

x = 6*8

x = 48

Therefore, using the slope, the required value of k is 48.

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A selective industrialization is a phenomenon in which those sectors or elements where it is desired to centralize or focus the industrialization itself are selected.

This has been a type of industrialization where industrialization is projected in sectors that are previously selected and defined.

Some of the characteristics of selective industrialization are:

¡Hope this helped!

Selective industrialization is a strategy that involves focusing on the development of specific industries or sectors in a country's economy.

This approach is often used by developing countries to promote economic growth and development by targeting key industries that have the potential to drive growth and create jobs.

In the context of an Expo, selective industrialization could refer to showcasing and promoting specific industries or sectors that a country or region specializes in or wants to develop further.

This could involve exhibiting products, technologies, and innovations related to those industries, as well as networking with potential investors, partners, and customers to explore opportunities for collaboration and growth.

Answer:lol

Step-by-step explanation:lol

Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

A function that will match the given graph is; f(x) = 2(x - 5)²(x + 2)

In polynomial graphs, we know that the roots are the points where the graph crosses or touches the x-axis.

In this given graph, we see that the graph touches the x-axis at x = 5 and then crosses the x-axis at x = -2. Thus;

The roots of the equation are -2 and 5.

However, when the graph changes sign at a point on the x-axis, it means that point represents double roots. Thus, we will now have three roots which are -2, 5 and 5. The factors of the polynomial are;

(x + 2), (x - 5)²

Now, we see that when x = 0, y = 100 from the graph. Thus;

a(0 + 2)(0 - 5)² = 100

a(50) = 100

a = 100/50

a = 2

Thus, the equation would now be;

f(x) = 2(x - 5)²(x + 2)

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With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n       (Step 2. Combine like terms; 9n + 3n = 12n)

-9n                  -9n    (Step 3. Subtract 9n from both sides to isolate the variable)

______________

  -27 = 3 + 3n            

     -3      -3               (Step 4. Subtract 3 from both sides)

________________

-30 =       3n                        

 -----         ----

  3            3              (Step 5. Divide 3 from both sides)

________________

 -10 = n

Therefore, n = -10

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c is the answer. jdjsisiao

Answer:

y = -1/2x - 2

Step-by-step explanation:

y = mx+b, m = -1/2, and b (the y-intercept) is -2.

The height of the triangular cross section is equal to 2.5 cm.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H or Volume = base area × length

Where:

Next, we would determine the base area of this rectangular prism by using the formula for the area of a triangle:

Area of triangle = 1/2 × base area × height

Area of triangle = 1/2 × 4 × h

Area of triangle = 2h

Now, we can determine the height of this rectangular prism as follows;

Volume = base area × length

35 = 2h × 7

Height, h = 35/14

Height, h = 2.5 cm.

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The fraction in simplest form is  [tex]\frac{8}{125}[/tex].

What is a fraction?

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

Given, [tex](\frac{2}{5})^{3}[/tex]

= [tex]\frac{2}{5} *\frac{2}{5} *\frac{2}{5}[/tex]

= [tex]\frac{8}{125}[/tex]

Hence, the fraction in simplest form is  [tex]\frac{8}{125}[/tex].

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stem                            leaf

0                               7, 7, 8, 8

1                                   3 , 3

2                                   5, 2

What is stem and leaf plot ?

A stem and leaf plot, also known as a stem and leaf diagram, arranges data in a way that makes it simple to see how often certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display stem and leaf values.

For instance, the stem and leaf plot key is used to represent 46 as 4 on the stem and 6 on the leaf.

in 2|5 , 2 is the stem side and 5 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

in 2|2 , 2 is the stem side and 2 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

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Error Analysis 1:(x-3)/(x+7)

Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.

Error Analysis 1:

(x²-x-6)/(x²+9x+14)

=(x-3)(x+2)/(x+2)(x+7)

=(x-3)/(x+7)

Error Analysis 2:

(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)

=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

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The proof that  Δ SVW ≅ Δ UTW is given by ASA congruence criterion.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

The symbol of congruence is’ ≅’.

Given:W is the midpoint of SU

⇒ SW = WUTU ⊥ SU and SU ⊥ SV

To prove:Δ SVW ≅ Δ UTW

Proof:In Δ SVW and Δ UTWSW = UW (given)

∠S ≅ ∠U (given)

∠ SVW ≅ ∠ UTW (vertically opposite angle)

Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)

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omgggg thats what she said

Answer:true, false, false, true

Step-by-step explanation:

The values on a number line that are less than -2 include -3, -4 etc

A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.

The horizontal straight lines known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

It should be noted that -3, and above are less than -2.

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(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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Answer:

x = 58, y = 61

Step-by-step explanation:

We can use two properties of a parallelogram to solve this

1. The opposite angles of a parallelogram are equal

2. The sum of the 4 interior angles of a parallelogram equal 360

Using property 1,

Using property 2
(2x - 3) + y + (y + x) + y = 360

3x + 3y + 3 = 360

3x + 3y = 360 - 3 = 357

Divide both sides by 3 to get
x + y = 357/3
x + y = 119  [2]

Add [1] and [2] together to eliminate y and get

x - y + x + y = -3 + 119

2x = 116

x = 116/2 = 58

Use equation [2]

x + y = 119
58 + y = 119

y = 119 - 58

y = 61

The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by [tex]P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}[/tex] where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

[tex]\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}[/tex]

The required answer is 15.41%.

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Answer:

307.50

Step-by-step explanation:

277.50 + .1(300)

277.50 + 30

307.50

Answer:

(-2, 1.5)

Step-by-step explanation:

When graphed their solution is (the point where both the line intercept/touch) (-2,1.5)

I graphed this equations online**

The value will be 13.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

According to the given graph of

⇒ f(x) = 3ˣ

The point for f(x) = 12

We can see that such x is situated between 2.2 and 2.3

Thus the solution for this be;

⇒ (2.2 + 2.3)/2

⇒ 2.25

As above the solution of 3ˣ = 12

Is x = 2.25 which is about 2

Now, put x = 2.3

Therefore;

3²°³  = 12.51 ≈ 13

Thus it is about 13.

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The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

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Answer:

I was willing to pay $20 more for the toy than I actually paid.

Step-by-step explanation:

Let us take the maximum bid be y

So,

(y × 60) ÷ 100 = 30

60y/100 = 30

60y/100 × 100 = 30 × 100

60y = 3000

60y/60 = 3000/60

y = 50

60% of $50 is $30

So,

50 - 30 = 20

Thus, I was willing to pay $20 more for the toy than I actually paid.

They must make 18,000 pencils in a month to break even.

Let,      n = number of pencils they sell

           R = revenue

           C = cost

           P = profit

We know that,

          P = R - C

At the break-even point,

              P = 0

            ⇒R - C = 0

            ⇒ R = C

Putting the value,  

            C = [tex]\frac{3500 - 1500}{3000}[/tex] n + 1500

        ⇒ C = 0.667n + 1500

and,       R = 0.75n

When   R = C

           ⇒ 0.75n = 0.667n + 1500

           ⇒  0.0833n = 1500

           ⇒     n   =  18000

 ∴ They must make 18,000 pencils in a month to break even.

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