589 in base five is

Answer:

84.6

Step-by-step explanation:

Using the monthly payment formula, it is found that:

A. You can afford a car at a price of $13,742.36.

B. The monthly payments are of $109.15.

The monthly payments are given by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The variables involved in the equation are listed and explained as follows:

For item a, the parameters are given as follows:

A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

Hence the maximum value of the car is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

0.0181919241P = 250

P = 250/0.0181919241

P = $13,742.36

For item b, the parameters are given as follows:

P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).

Hence the monthly payments are given as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

A = 6000 x 0.0181919241

A = $109.15.

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Answer:

1st Table : Linear

2nd Table : Non-Linear

Step-by-step explanation:

To determine if the function is Linear or not , we find the change in y with a certain change in x

So for the 1st Table:

When x changes from x = 2 to x = 4 increased by 2

Then  y changes from y = 3 to y = 0 decreases by 3

When x changes from x = 4 to x = 6 increased by 2

Then  y changes from y = 0 to y = -3 decreases by 3

Since change in y is the same for the same change in x , Then the Function is Linear

So for the 2nd Table:

When x changes from x = 1 to x = 2 increased by 1

Then  y changes from y = 1 to y = 4 increased by 3

When x changes from x = 2 to x = 3 increased by 1

Then  y changes from y = 4 to y = 9 increased by 5

Since change in y is not the same for the same change in x , Then the Function is Non-Linear

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The flowchart that is used to prove GR ║ F_K is presented as follows;

∠RND and ∠FDP are supplementary  ⇒    ∠RND + ∠FDP = 180°

Given                            [tex]{}[/tex]                                 Definition of supplementary

∠KDN  ≅ ∠FDP                 [tex]{}[/tex]                    ⇒    ∠KDN = ∠FDP

Vertical angles are congruent[tex]{}[/tex]                    Definition of congruent angles

∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°    

Definition of same side interior angles[tex]{}[/tex]                    Substitution property

[tex]{}[/tex]                                           GR ║ F_K

The relationships between the angles formed by a transversal and two parallel lines are;

Definition of congruency;

Two lines, shape or figure are said to be congruent if they have the same size and shape.

Supplementary angles;

Supplementary angles are angles that have a sum of 180°

Substitution property of equality

The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.

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The expressions are:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

15 x squared minus 18 end quantity over 6.

= 15x² - 18 / 6

= 3(5x² - 6)/ 6

= (5x² - 6)/ 2

and, 5 x squared minus 18 end quantity over 2

= 5x² - 18/2

and, 5 x squared minus 6 end quantity over 2

= 5x² -6 /2

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The counterexample for "Two supplementary angles are not congruent." is

angle 100° and angle 80° are supplementary angels

angle 90° and angle 90° are supplementary angels

The instances show supplementary angles that are not congruent

A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.

Counterexamples provides instances that opposes the statement

In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement

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a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.

b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 3x² - 18x + 56.

Giving the temperature in degrees Fahrenheit in x days after Sunday.

The day that represents Thursday is given by:

x = 4.

Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:

f(4) = 3(4)² - 18(4) + 56 = 32 ºF.

Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.

The numeric value is of 35 when:

3x² - 18x + 56 = 35

The solutions to the quadratic equation are:

x = 1.6, x = 4.4.

Hence the days are:

Monday and Thursday.

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Answer:d

Step-by-step explanation:d

Answer: 3/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 12 and 16 is 4

Divide both the numerator and denominator by the GCD

12 ÷ 4

16 ÷ 4

Reduced fraction: 3/4

Therefore, 12/16 simplified to lowest terms is 3/4.

Answer:.

Step-by-step explanation:

The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then

(x,y)=( (mx₂+nx₁)/m+n ,  (my₂+ny₁)/m+n )

Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3

Therefore, we have

P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))

P(x,y)=(2.6,6)

Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

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The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

According to the question,

We have the following information:

Cost of 1 pound of grapes = $3.75

Cost of 1 pound of apples = $4

Total cost made by selling = $251.75

And the weight of the apples and grapes sold = 64

Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.

So, we have:

x+y = 64

x = 64-y ....(1)

3.75x+4y = 251.75

Putting the value of x in this equation:

3.75(64-y)+4y = 251.75

3.75*64-3.75y+4y = 251.75

240+0.25y = 251.75

0.25y = 251.75-240

0.25y = 11.75

y = 11.75/0.25

y = 47 pounds

Now, putting this value of y in equation 1:

x = 64-y

x = 64-47

x = 17 pounds

Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

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The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.

From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(bench press weight, squat weight).

From the table given by the first image at the end of the answer, the points are listed as follows:

(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).

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If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of  different random samples of four accounts that are possible is 230,300.

Given data:

Number of population of bank account = 50

Random sample = 4 accounts

Now let find the different random samples of four account that are possible

Different random sample = 50! / (50 -4)! × 4!

Different random sample = 50! / 46! × 4!

Different random sample = 230,300

Therefore the different random samples is 230,300.

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Answer:

d the last one I think

Step-by-step explanation:

I am not really sure

Answer:

D.) 6.67 X 10^2

Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph

Answer: (f+g)(x) = 6x²- 4x + 6

Step-by-step explanation:

We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)

Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)

We are left with (f+g)(x) = 6x²- 4x + 6

For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

As given in the question,

Given :

Pair of parallel lines are AG and BH.

CF is the transversal.

Transversal CF intersect line AG at point D and

Transversal CF intersect line BH at point E

Four pair of corresponding angles

Two pair of alternate interior angles

Corresponding pair of angles in the pair of parallel lines are congruent.

∠ADE ≅ ∠BEF

∠ADE and ∠BEF are corresponding angles.

Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

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The focus of parabola is (4 , -1) and directrix is 5

The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Focus: The point (a, 0) is the focus of the parabola

Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.

Given equation of parabola is :

y = - 1/12 (x - 4) - 2

Comparing it with standard equation,

h = 4

k = 2

a = -1/12

using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)

=> focus = (4 , 2+(12/4×-1))

=> focus = (4 , 2-3)

=> focus = (4 , -1)

and directrix is : y = 2-(1/4×-1/12)

y = 2 + 12/4

y=2 + 3 => 5

So, the focus is (4,-1) and directrix is 5

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Answer:

Step-by-step explanation:

13+(-3)^2+4(-3)+1- {-10-(-6)}

_________________________

[4+5}/ [4^2-3^2(4-3)-8]+12

15/3=5

Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.

How to get distance/displacement using velocity?

According to given data:

A particle moves with velocity (dx)/(dt) = 3t² in x- direction

and (dy)/(dt) = 12t in y-direction

Integrating both sides of these derivatives with respect to t

x=  ∫3t² dt = (3t³)/3 + A = t³ + A

where A is integration constant

y= ∫12t d t = (12t²)/2 + B = 6t² + B

where B is integration constant

At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.

Therefore, the difference in position of a from t = 0 t = 3 is

27 + A - (0 + A) = 27 units.

Similarly,

At t = 0 , we get y = B and at t = 3 we get

y = 6 * 3² + B = 54 + B

Therefore, the difference in position of y from t = 0 tot t = 3 is

54 + B - (0 + B) = 54 units.

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The mean score of all the students is 79.5 and it is round off into one decimal place.

Mean

Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given,

In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.

Here we need to find the mean score of all students.

In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,

=> 30 x 87.7 = 2631

Similarly, the total score for 21 students is,

=> 21 x 67.7 = 1421.7

So, the 51 students, cumulative score is

=> 2631 + 1421. 7 = 4052.7

Therefore, the mean score is calculated as,

=> 4052.7/51

=> 79.464

When we round off the value into one decimal place then we get

=> 79.5

Therefore, the mean value of all the students is 79.5.

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The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways

The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:

nCr = n!/(r!(n - r)!)

The total number of cards that we have in a deck of cards = 52.

There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways

After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).

Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:

Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card

Plugging in the relevant values gives;

Number of ways = (13 × 6) × 48 × 44 × 40

= 6,589,440 ways

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The equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following statement - "4 less than a number is given w".

Assume the number to be [x].

We can write the equation representing the statement -

"4 less than a number is given w" as a mathematical expression as -

[w] = x     where x ∈ (- ∞, 4)

Therefore, the equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

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The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°

We have different trigonometric ratios such as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.

This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;

tan θ = 10/50

where θ is the true bearing angle. Thus;

tan θ = 0.2

θ = tan⁻¹0.2

θ = 11.31°

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Answer:

-3

Step-by-step explanation:

we sure y2-y1/x2-x1 to find slope

6+6/-4+0

12/-4

-3 is the slope

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The percent that Desmond average speed increase is 25%.

From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.

It should be noted that the percentage increase in speed will be:

= Change in speed / Initial speed × 100

= (30 - 24) / 24 × 100

= 6/24 × 100

= 25%

The percentage is 25%.

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The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

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

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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