What are the solutions of 6t-1> 4t+13

The balance in Adam's account at the end of June which has the credit card with an apr of 14.63% is $627.27.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

The Adam’s credit card has an Apr of 14.63%,The table below shows his use of that credit card over three months.

For the purchase add the previous balance and for payment subtract the previous balance. I have mentioned another column for remaining balance in the above table.

The total of this transaction when multiplied with number of days, we get the total balance, 56498.48.

Now the monthly average balance is,

\(m=\dfrac{56498.48}{90}\\m=627.76\)

Thus, the balance in Adam's account at the end of June which has the credit card with an Apr of 14.63% is near to $627.27.

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Adam’s balance at the end of June is $629.42.

The adjusted balance method is an accounting method that bases finance charges on the amount(s) owed at the end of the current billing cycle after credits and payments post to the account.

Balance at the end of April = 626.45 + 37.41 + 44.50 = $708.36

Interest levied on $708.36= 708.36* (14.63/12) * 1/100

Interest levied on $708.36 = $8.64

So, balance on May 1st= 708.36+ 8.64 = $717

Balance at the end of May = 717-65.50+24.89-104.77 = $571.62

Interest levied on $571.62 = $571.62 * (14.63/12) * 1/100

Interest levied on  $571.62=$6.97

So, balance on June 1st = $578.59

Balance at the end of June = 578.59-23.60 + 15+51.85 = $621.84

Interest levied on $621.84 = $621.84* (14.63/12) * 1/100

Interest levied on $621.84 =$ 7.58

So balance at the end of the june = 621.84 + 7.58 = $629.42

Therefore, Adam’s balance at the end of June is $629.42.

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we know the cos(α), and we also know the sin(α) is positive, that only happens on the I and II Quadrants, now, our cosine is negative, and our sine is positive, that means, α is in the II Quadrant.

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{-9}}{\underset{hypotenuse}{12}} \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{12}\\ a=\stackrel{adjacent}{-9}\\ o=\stackrel{opposite}{y} \end{cases}\)

\(y=\pm\sqrt{ 12^2 - (-9)^2}\implies y=\pm\sqrt{ 144 - 81 } \implies \stackrel{ \textit{II Quadrant} }{y=+\sqrt{ 63 }} \\\\\\ ~\hfill~\boxed{(-9~~,~~\sqrt{63})}~\hfill~\)

Answer:

-7.5

Step-by-step explanation:

-140-18+8=20y

-150=20y

y=-7.5

\( - 140 = 18 + 4(5y - 2) \\ = > - 140 = 18 + 20y - 8 \\ = > - 140 - 18 + 8 = 20y \\ = > - 150 = 20y \\ = > y = \frac{ - 150}{20} \\ = > y = - 7.5\)

y = -7.5

Answer:  27

Step-by-step explanation:

\(a_{1}=6\\a_{2}=a_{n-1}+7=a_{2-1} +7=a_{1} +7=6+7=13\\a_{3}=a_{n-1}+7=a_{3-1} +7=a_{2} +7=13+7=20\\a_{4}=a_{n-1}+7=a_{4-1} +7=a_{3} +7=20+7=27\)

Given:

Amanda can read 30 pages in one hour.

Total number of pages are 300.

a)

Let y and x be the hours that Amanda study and pages left to study.

Given that y=0 , x=300

Graph:

The probability of the spinner landing on 5 is 1/8.

The spinner is divided into 8 equal sections, and each section represents a number from 1 to 8. Since there is only one section with the number 5, the favorable outcome is landing on 5.

To calculate the probability, we need to determine the ratio of the favorable outcomes (landing on 5) to the total number of possible outcomes (numbers 1 to 8 on the spinner).

The total number of possible outcomes is 8, as there are 8 numbers on the spinner. Therefore, the probability of landing on 5 can be calculated as follows:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 (favorable outcomes) / 8 (total possible outcomes)

Simplifying the expression:

Probability = 1/8

In other words, if we were to spin the spinner many times, we would expect it to land on 5 approximately 1 out of every 8 spins, on average.

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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Answer:

Shorter leg = 5

Longer leg = 8

Step-by-step explanation:

Shorter leg = 3

Longer leg = x+3

area = (x * (x+3)) / 2 = 20

x² + 3x -40 = 0

(x + 8) (x - 5) = 0

x = -8 or x = 5    ... leg length > 0         x = 5

Shorter leg = 5

Longer leg = 8

The expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet is 7.7.

First, you need to calculate the row totals, column totals, and the grand total from the provided data.

Row Totals:

Under 45 feet: 12 + 4 + 4 = 20

45-120 feet: 35 + 5 + 30 = 70

Over 120 feet: 3 + 2 + 5 = 10

Column Totals:

For: 12 + 35 + 3 = 50

Undecided: 4 + 5 + 2 = 11

Against: 4 + 30 + 5 = 39

Grand Total: 20 + 70 + 10 = 100

Then, the expected frequency for the specified group can be calculated as:

Expected Frequency = (Row Total for 45-120 feet * Column Total for Undecided) / Grand Total

= (70 * 11) / 100 = 7.7

The expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet is 7.7.

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Answer:

\(9x+24=5\)

Step-by-step explanation:

Hi there!

\(\displaystyle\frac{3}{4}x+2=\frac{5}{12}\)

To get rid of the fraction \(\displaystyle \frac{3}{4}\), multiply both sides of the equation by 4 (the denominator:

\(4(\displaystyle\frac{3}{4}x+2)=4(\frac{5}{12})\\\\\frac{4*3x}{4} +4*2=\frac{4*5}{12} \\\\3x+8=\frac{5}{3}\)

Now, to get rid of the fraction \(\displaystyle\frac{5}{3}\), multiply both sides of the equation by 3 (the denominator):

\(\displaystyle3(3x+8)=3(\frac{5}{3})\\\\3*3x+3*8=\frac{3*5}{3} \\9x+24=5\)

I hope this helps!

Answer:

Step-by-step explanation:

1. The Probability that she selected 2 comedies and 1 action movie = (36/455) or 0.07912  

2. if two comedy movies were added to the list in place of the 2 mystery movie , the probability that she selected 2 comedies and 1 action movie = (18/91) or 0.1978

- I hope that makes sense, I hope its helpful, please let me know if it does.

Answer:

Then the probability of the comedies being chosen would go up because there would be more of them.

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2^6)^-5 is the expression that should be multiplied

Answer:

Here is the solution solution-

(-15x+6y)-(-10x+7y)

= -15x+6y+10x-7y

= (-15x+10x)+(6y-7y)

= -5x-y

Answer:

yes

Step-by-step explanation:

hope this helps :)

Answer:

y=-5x

Step-by-step explanation:

this is because slope intercept form is y=mx+b

if m= -5 and b=0 the answer would be

y=-5x+0

simplified it would be

y=-5x

Answer:

D. None of the Above

Step-by-step explanation:

They don't relate whatsoever

Answer: 4

Step-by-step explanation:

Mean means to add up the values and divide it by the number of values there is so 9 + 1 + 8 + 3 + 2 + 1 = 24, then 24 / 6 is 4.

By using the vertex of the quadratic equation, we will get the equation:

y = -2*(x + 6)^2

For a quadratic equation with a leading coefficient "A" and a vertex (h, k), the equation can be written as:

y = A*(x - h)^2 + k

Here we can see that the vertex is (-6, 0), so we have:

y = A*(x + 6)^2

We also can see that the parabola passes through the point (-4, -8), replacing these values above we will get:

-8 = A*(-4 + 6)^2

-8 = A*(2)^2

-8 = 4A

-8/4 = A

-2 = A

Then the quadratic equation is:

y = -2*(x + 6)^2

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Answer:

Pt. 1: D

Pt. 2: what are the options for part 2?

Step-by-step explanation:

Harold needs 71 tomato plants.

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

Given that;

Harold wants to make a tomato patch.

And, It will have 7 long rows of plants, each with 8 plants in the row, and 3 short rows of plants, each with 5 plants in the row.

Now, For the total number of tomato plants Harold needs, we can multiply the number of plants in each row by the number of rows for each section (long and short) and then add the results as,

Hence, the expression for number of tomato plants Harold needs is:

⇒  (7 long rows x 8 plants per row) + (3 short rows x 5 plants per row) Simplifying the expression, we get:

⇒ 56 + 15 = 71

Therefore, Harold needs 71 tomato plants.

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Since the measure of angle DOC = 44 degrees and it's the central angle of arc DC, the measure of arc DC = 44 degrees

Answer:

Step-by-step explanation:

Answer:



Step-by-step explanation:

Given: The table of linear function.

x :  -3  , 0 , 3,  6

y :  -6 , -2 , 2,  6

Slope=change in y over change in x



Passing point: (0,-2)

Point slope form:







Slope of the linear function

Linear function is

Hence, The slope of linear function is

The slope of the given linear function which graph represents the data is 3/2.

The slope of a linear function can be calculated by finding the difference between two points on the graph and dividing it by the difference of the corresponding x-values of those points.

In this case, the two points are (2, -2) and (6, 4).

The difference between these y-values = 6,

and the difference between the x-values = 4.

Therefore, the slope of the linear function which graph represents the data = 6/4

= 3/2

This means that the linear function has a slope of 3/2 which summarizes that for every two units that x increases, y increases by three units.

If x increases from 0 to 4, y increases from -5 to 1, which is a difference of 6 units (4 x 3/2 = 6).

The linear function can be written as y = 3/2x -5.

This means that for any given x-value, the corresponding y-value can be calculated by multiplying 3/2 by the x-value and subtracting 5.

If x = 2, the y-value is -2,that is

(2* 3/2)- 5= -2

Therefore, the slope of the linear function which graph represents the data is 3/2.

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Answer:

\((2,8]\)

Step-by-step explanation:

Given

The attached piece wise function

Required

The domain

To do this, we simply consider the inequalities that bound the values of x.

The inequalities are:

\(2 < x < 4\)     \(4 < x < 8\)   and   \(x \ge 8\)

Combine the first two inequalities:

\(2 < x < 8\)    and   \(x \ge 8\)

For the inequality to be true, we must have:

\(2 < x \le 8\)

In interval notation, the inequality is:

\((2,8]\)

They are probably vulnerable to divorce within 7 years. People make the decision to go with divorce for a variety of reasons. Finances influence many divorces, but every case is unique, and people choose to end their marriages for various pertinent and personal reasons. You know how challenging this circumstance might be if you consider getting divorced.

It's likely that you've heard of the "seven-year itch." This refers to the idea that couples frequently decide to get divorced after spending about seven years together. Nothing mystical occurs at this stage of a marriage, but there are a number of factors that may increase the likelihood that a couple will file for divorce at or near this time in their relationship.

An average couple stays together for seven years before deciding to end their relationship. Extramarital affairs frequently serve as the catalyst for divorce proceedings. The phrase "seven-year itch" refers to this situation in which one partner becomes dissatisfied in the marriage and seeks fulfillment elsewhere.

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The surface area of the open-top rectangular box is 2L^2 + 6Lh.

The surface area of an open-top rectangular box consists of the area of its base and the areas of its four sides. The base is a rectangle with dimensions w (width) and l (length), and the box has a height h.

To calculate the surface area, we need to find the areas of the base and the four sides.

1. The area of the base is given by lw.

2. The four sides of the box consist of two pairs of equal-sized rectangles. Each pair has a width w and a height h, and a length equal to the length of the base, l.

Therefore, the total surface area (SA) can be expressed as:

SA = lw + 2wh + 2lh

Given that the base width is double the base length (w = 2l), we can substitute this into the equation:

SA = lw + 2(2l)h + 2lh

SA = lw + 4lh + 2lh

SA = lw + 6lh

Comparing this expression to the given options, we can see that the correct answer is:

SA = \(2L^2\)+ 6Lh  (option a)

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Answer:

I believe its (- 2, 2 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then multiply the coordinates of B by the scale factor 2, that is

B(- 1, 1 ) → B'(2(- 1), 2(1) ) → B'(- 2, 2 )

They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.

Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

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sqrt(-49) is not a real number

Square root of any negative number is not a real number

The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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