Solve the system of equations.

The finance charge for Julie's installment loan of $4,600 at 13% for 36 months is D. $979.64.

The finance charge represents the interest and other administrative charges for granting a loan to an individual or organization.

The finance charge is always described in terms of the APR (annual percentage rate) that accrues on the loan, depending on the amount and the period.

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 13%

PV (Present Value) = $4,600

FV (Future Value) = $0

Results:

PMT = $154.99

Sum of all periodic payments = $5,579.64

Total Interest = $979.64

Thus, Julie will pay a finance charge of $979.64.

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Option D. $979.64

The area of the figure is 1875 sq.in.

In this question, we need to find the area of the given figure.

the area of the figure = area of rectangle + area of two triangles.

For rectangle,

length =  50 inch and width = 30 in.

Using the formula for the area of rectangle,

A1 = length * width

A1 = 50 * 30

A1 = 1500 sq.in.

For triangle,

base = 1/2 * length of rectangle

so, base = 25 in and height = 15 inch

Using the formula for the area of triangle,

A2 = 1/2 * base * height

A2 = 1/2 * 25 * 15

A2 = 187.5 sq.in.

so, the area of the figure would be,

A = A1 + (2 * A2)

A = 1500 + (2 * 187.5)

A = 1875  sq.in.

Therefore, the area of the figure is 1875 sq.in.

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The distance from B to AC can be constructed as shown in the figure.

The distance from G to EF can be constructed as shown in the figure.

The distance from Q to SR can be constructed as shown in the figure.

What is the distance of a line from a point?

A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.

For the figure 1, the distance from B to AC, will be the perpendicular line through point B on side AC, so side BD will be the distance.

For the figure 2, the distance from G to EF, will be the perpendicular line through point G on side EF, so side GH will be the distance.

For the figure 1, the distance from Q to SR, will be the perpendicular line through point Q on side SR, so side QT will be the distance.

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The probability that in any given period of 400 days there will be an accident on one day is 0.2707

Given that;

In a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.

n = 400, p = 0.005

Poisson distribution is given by;

e P(x) = (λˣe^λ ) / x!

Here, Mean(λ) = np

                        = 400*0.005

                        =2

The probability that there will be an accident on one day;

(P(x = 1)) = (λxe-λ)/x!

             = 2*e-2

             = 0.2707

The probability that in any given period of 400 days there will be an accident on one day is 0.2707

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Directly proportional to x.

Acc to our question-

Hence,Directly proportional to x.

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31 Americans should be surveyed  by Z mean.

What does critical value of Z mean?

If the prior population proportion is unavailable then the formula to find the sample size is given by

           n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]

where z* = Critical z-value

E = margin of error

Given,  Confidence level = 98%

The critical z-value for 98% confidence interval is 2.326  ( BY z-table)

Margin of error : E= 0.21

             n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]

             n = 0.25 * ( 11 .07)²

             n = 0.25 * 122.5449

             n =  30.363225  ≈ 31

Hence,  31 Americans should be surveyed.

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Answer:

t =2.45s

Step-by-step explanation:

H=-16t2+96t

then, -16t2= -96t

divide both sides by 16

-16t2/16 = -96t/16

-t2 = -6

t2=6

t=√6

t=2.45

The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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Answer:

39.94

Step-by-step explanation:

Ask? :)

Answer:40,000        porque dice que redondees a la centecima mas cercana              

The length of backyard in drawing is 37 inch when 74 feet long in real life and scale of drawing is 1 inch: 2 feet.

A proportion is a form of ratio in which the denominator also contains the numerator. For example, the fraction of male deaths would be deaths to men divided by deaths to males + deaths to females (i.e. the total population). A population proportion is a percentage of the population that possesses a specific feature. Assume you have 1,000 persons in your population, with 237 of them having blue eyes. Blue eyes account for 237 of every 1,000 persons, or 237/1000.

Here,

as the given scale is 1 inch: 2 feet.

actual length of backyard=74 feet

length of backyard in drawing is x inch,

1/2=x/74

2x=74

x=37 inch

The length of the backyard in the drawing is 37 inches, although it is 74 feet long in real life, and the scale of the drawing is 1 inch: 2 feet.

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Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

__

Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

Answer:

  AD = 32

Step-by-step explanation:

You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.

The value of x can be found by recognizing that the measure of any angle in a square is 90°.

  (6x -12)° = 90°

  6x = 102 . . . . . . . . divide by °, add 12

  x = 17

The sides of a square are congruent, so ...

  AD = CD = (x +15) = 17 +15 = 32

The length of AD is 32 units.

The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.

given:

Per lesson charges= $25

Recital f= $50

Total money can be spend= $175

let the number of lessons taken be x.

So, the inequality is

25x + 50 < 175

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Answer:ok

Step-by-step explanation:

Answer: 1/5 25/48

maybe?

The person can make 60 trips.

Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

Thus, A × B = 5 × 12

Performing multiplication on Right Hand Side of the equation to find the number of trips

Total number of trips = 60

Hence, there are 60 trips that could be made.

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The equation which has infinitely many solutions from the given answer choices is; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

It follows from the task content the the equation with infinitely many solutions among the given answer choices is to be determined.

An equation of the type; a(1)x + b(1) = a(2)x + b(2) is said to have infinitely many solutions if; a(1) = a(2) and b(1) = b(2).

Hence, the equations which have infinitely many solutions among the given answer choices are; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

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Answer:

L

Step-by-step explanation:

The number of communication channels, 10 channels would five people require.

To find number of communication channels, we use;

On the other hand, it might be a sign of the scope and intensity of the project communication management needed in huge projects and so-called megaprojects. This could, for example, entail allocating specific resources to project communication responsibilities in accordance to the number of available channels for communication. These factors may be especially important for teams working on sensitive projects and projects where information flow may be unclear or even fraudulent.

Number of potential communication channels = n x (n-1)/2

Given n = 5;

→ x = 5*(5 - 1)/2

     = 5*2

     = 10

The number of communication channels, 10 channels would five people require.

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The recursive formula is an = a(n-1) +4. A recursive formula is one that defines each term in a sequence by using the term before it (s)

The sequence's first term

The pattern rule for obtaining any term from its preceding term

Recursive Arithmetic Sequence Formula

To find the nth term of an arithmetic sequence, use the recursive formula:

an = an-1 + d for n ≥ 2

Where

an is the nth term of a A.P.

d is the common difference.

Given:

14, 18, 22, 26, 30, …

a1 = 14

and, d = 18-14

d = 4

a2 = a1 + 4

a2 = 14 + 4 = 18

Similarly, going this way

an = a(n-1) +4

Hence, the recursive formula is an = a(n-1) +4

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Submitting an online survey is one example of volunteer sampling.

When researchers look for volunteers to participate in studies, they use voluntary sampling. Volunteers can be recruited in person, online, through public postings, and through a variety of other means. When using voluntary sampling, a researcher usually makes little effort to control the sample composition.

The customer satisfaction survey is a common form of voluntary sampling. When a company provides a service or a product, it frequently asks customers to rate their satisfaction. The sample is voluntary and biased because the company asks all customers to volunteer their opinions.

Researchers in academia frequently seek volunteer samples by asking students to participate in research or by looking for people in the community.  Volunteer samples are used for a variety of different types of research because they are inexpensive.

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Using the section formula, point F lie on 3/5 in the number line.

In the given question,

On a number line, point D is at -3, and point E is at 6.

The point F lies on segment DE .

The ratio of DF to FE is 2 : 3.

We have to find where point F lie on the number line.

Since point D lies is at -3 at x axis so the point should be ( -3,0).

Point E lies is at 6 at x axis so the point should be ( 6,0).

F lies on segment DE. So let the point of F is (X, Y)

The ratio is 2:3.

Now firstly finding the value of X using section formula

X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]

where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3

Now putting the value

X = {2×6+(-3)3}/(2+3)

Simplifying

X = (12-9)/5

X = 3/5

Now firstly finding the value of Y using section formula

Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]

where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3

Now putting the value

Y = (2×0+3×0}/(2+3)

Y = 0/5

Y = 0

Hence, point F lie on 3/5 in the number line.

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Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

So, the distance of the building from John and Fred is:

Now, we get the formula:

Calculate as follows:

John's distance:

Fred's distance:

Therefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

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To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

Unit conversion is the expression of the same function in a new unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles to kilometers/feet, or another length measurement. A conversion factor is a numerical equation that allows for the equal conversion of feet to another dimensional analysis unit.

A conversion factor is a number that is used to multiply or divide one set of units into another. When converting to an equivalent value, the proper conversion factor must be utilized. For example, to translate inches to feet, the correct conversion value is 12 inches equals 1 foot. The converting value for minutes to hours is 60 minutes equals 1 hour.

From the information given:

To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.

The conversion factors are:

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Answer: 300

Step-by-step explanation:

[tex]\sum^{3n}_{k=1} k=\frac{3n(3n+1)}{2}\\\\\sum^{n}_{k=1} k=\frac{n(n+1)}{2}\\\\\therefore \frac{3n(3n+1)}{2}-150=\frac{n(n+1)}{2}\\\\3n(3n+1)-300=n(n+1)\\\\9n^2 +3n-300=n^2 +n\\\\8n^2 +2n-300=0\\\\4n^2 +n-150=0\\\\(n-6)(4n+25)=0\\\\n > 0 \implies n=6\\\\\therefore 4n=24\\\\\implies \sum^{4n}_{k=1} k=\sum^{24}_{k=1} k=\frac{24(25)}{2}=300[/tex]

Considering a circle whose equation is x² + y² – 2x – 8 = 0. The statements that are true about it is as follows

Information given in the question

a circle whose equation is x² + y² – 2x – 8 = 0

Equation of a circle is given as

(x - h)² (y - k)² = r²

The equation of the circle is written in standard form by completing the square of each of the quadratic equation involved

x² + y² – 2x – 8 = 0

x² - 2x + 1 + y² + 0 = 8 + 1

(x – 1)² + (y - 0)² = 3²

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Answer:

y=-1/5x+3

Step-by-step explanation:

I think this the answer

Answer:

y = -1/5x - 3

Step-by-step explanation:

→ Find the x intercept

( - 15 , 0 )

→ Find y intercept

( 0 , -3 )

→ Find gradient

y = -1/5x + c

→ Substitute coordinate pair in

y = -1/5x - 3

Answer:

Step-by-step explanation:

-8-6y=-8-2y

+2y +2y

-8-4y=-8

+8 +8

-4y=0

Y=0

Answer:
1 : 10 is the answer.

Step-by-step explanation:

Total number of eggs in 2 boxes = 6 x 2 = 12

Total number of eggs in 20 boxes = 120

12 : 120

1 : 10

Answer:

1:6

Step-by-step explanation:

The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]

What are mixed numbers?

A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.

Given,     [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]

             [tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]

             [tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]

              [tex]= \frac{26}{9} +\frac{50}{9}[/tex]

               [tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]

Hence, the required answer for the given term is  [tex]8\frac{4}{9}[/tex] .

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