margo is repaying a loan from her parents. she has already paid $315 and still owes them $1245. write an equation to find the original amount a of the loan

In linear functions, there is a constant difference between the y-values on a table. This means that it increases or decreases by the same amount per every equal interval.

For instance: 2, 4, 6, 8 ⇒ Constant difference of 2 every 1 term

To find the constant difference for this set of values, determine the constant difference (y), and by what interval this difference occurs (x).

Looking at the first two rows of the table, we now know that for every increase in 3 in the x-values yields an increase of 15 in the y-values.

We can write it like a fraction, with difference in y on top and difference in x at the bottom:

\(\dfrac{15}{3}\) ⇒ \(5\)

Congratulations! We have now found the slope of the line.

Linear equations are typically organized in slope-intercept form:

\(y=mx+b\)

Plug in our slope, and solve for the y-intercept by using one of the given points from the table:

\(y=5x+b\\-10=5(-1)+b\\-10=-5+b\\b=-5\)

Plug this back into the equation:

\(y=5x-5\)

To find n, plug in 20 as y and solve:

\(20=5n-5\\25=5n\\n=5\)

n = 5

Answer:

Figure D

Step-by-step explanation:

dilation by a factor of 1/2: (x,y) -> (1/2 x , 1/2 y)

rotation 180°: (1/2 x , 1/2 y) -> (-1/2 x , -1/2 y)

The Answer Is 4 Minutes and 33 Seconds

Have A Good Day :)

Answer:

4 min 33

Step-by-step explanation

Answer:

7. (2,1) 8. (8,2)

Step-by-step explanation:

Step: Substitute4z−7foryin5y+3z=11:

5y+3z=11

5(4z−7)+3z=11

23z−35=11(Simplify both sides of the equation)

23z−35+35=11+35(Add 35 to both sides)

23z=46 Divide both sides by 23

x=2

Substitute2forxiny=4z−7:

y=4z−7

y=(4)(2)−7

y=1

Step: Solve2x+4y=24for x:

2x+4y+−4y=24+−4y(Add -4y to both sides)

2x=−4y+24

x=−2y+12

−2y+12forxin−2x+8y=0:

−2x+8y=0

−2(−2y+12)+8y=0

12y−24=0(Simplify both sides of the equation)

12y−24+24=0+24(Add 24 to both sides)

12y=24 Divide both sides by 12

y=2

Substitute2foryinx=−2y+12:

x=−2y+12

x=(−2)(2)+12

x=8

Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403  probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

Probability: -

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Conditional Probability :

Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)

In which

In this problem:

Event A: Commute to school each day.

Event B: Spends more than $25 a week.

80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8

Of those, 83% spend more than $25 a week on gasoline, hence .

                     P(B|A) = 0.83

Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

13

Step-by-step explanation:

use Pythagorean

it is usually, 5, 12, 13

It would cost $516.60 for four people to stay at the motel for one week, considering the 10% discount for seven consecutive days.

To calculate the cost of lodging for four people staying at the motel for one week, we'll consider the discounted rate for seven consecutive days.

The regular rate for a room accommodating four people is $82.00.

To find the discounted rate for seven days, we need to apply a 10% discount. To do this, we calculate the discount amount:

Discount = 10% of $82.00

= 0.10 * $82.00

= $8.20

Now, we subtract the discount from the regular rate to obtain the discounted rate:

Discounted Rate = Regular Rate - Discount

= $82.00 - $8.20

= $73.80

Therefore, the cost of lodging for four people staying at the motel for one week (seven consecutive days) would be $73.80 per day.

To calculate the total cost for the entire week, we multiply the daily rate by the number of days:

Total Cost = Daily Rate * Number of Days

= $73.80 * 7

= $516.60

Thus, it would cost $516.60 for four people to stay at the motel for one week, considering the 10% discount for seven consecutive days.

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The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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The expression representing height of kite from ground is Height = sin 50° × 40.

The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -

sin theta = perpendicular ÷ hypotenuse

Keep the values in mentioned trigonometric relation to find the expression -

sin 50 = height ÷ 40

Height = sin 50° × 40

Finding the height using formed equation -

Height = 0.77 × 40

Performing multiplication

Height = 30.64 meters

Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.

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The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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Nausea doesn't appear to be a problematic adverse reaction to this drug.

To evaluate and check the claim that 3% of users have nausea, here we have to implement the use of a hypothesis test

The null hypothesis consist of users who develop nausea is 3%.

The alternative hypothesis consist of users who have nausea greater than 3%.

The test statistic is stated and evaluated as  

\(z = (p - P) / \sqrt{(P * (1 - P) / n)}\)

here,

p = sample proportion,

P = hypothesized proportion,

n = sample size.

From the given values from the question,

p = 154 / 6027 = 0.0256 and P = 0.03.

n = 6027.

Staging the values obtained in the formula we get

\(z = (0.0256 - 0.03) / \sqrt{(0.03 * (1 - 0.03) / 6027) }\)

= -2.07

The given critical value for z is 2.33.

After calculating and analyzing the test statistic = -2.07 is less than the critical value = -2.33, therefore we can’t proceed with null hypothesis as it will fail in the process.

Nausea doesn't appear to be a problematic adverse reaction to this drug.

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Answer:

12.255

Step-by-step explanation:

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

The student's lifetime value for a four-year degree at this college is $80,000.

The student's lifetime value for a four-year degree can be calculated as follows:

Determine the cost per semester: $10,000 per semester

Determine the number of semesters for a four-year degree: 4 years * 2 semesters/year = 8 semesters

Multiply the cost per semester by the number of semesters to get the total cost of tuition: $10,000 * 8 = $80,000

Therefore, the student's lifetime value for a four-year degree at this college is $80,000.

It is important to note that this calculation only considers the cost of tuition and does not take into account other costs such as room, board, books, and supplies, which can add significantly to the total cost of obtaining a degree.

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Answer:

x = 20 , y =43

Step-by-step explanation:

1- 7x-3 + 3x-17 = 180

10x = 200, x = 20

Y = 3x-17  x is 20 so Y=60-17=43

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.

A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.

Some features of circuit training exercise are-

Benefits of doing circuit training exercise-

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The complete question is -

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)

Answer

0.24

Step-by-step explanation:

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

-5a²+13ab should be subtracted.

Based on the given conditions, formulate,

\(→- {a}^{2} - 4 {a}^{2} + 13ab\)

\(→-({a}^{2} - 4 {a}^{2}) + 13ab\)

Taking the coefficients or numbers, we get,

\(→(- 1 - 4) {a}^{2} + 13ab\)

\(→ - 5 {a}^{2} + 13ab\)

Given :

What should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b² ?

Solution :

Let the required expression to be subtracted be x

⇢ a² – 7ab + 3b² – x = – 4a² + 6ab + 3b²

⇢ a² – 7ab + 3b² – (– 4a² + 6ab + 3b²) = x

⇢ a² – 7ab + 3b² + 4a² – 6ab – 3b² = x

Combining the like terms :

⇢ a² + 4a² – 7ab – 6ab + 3b² – 3b² = x

⇢ 5a² – 13ab = x

⇢ x = 5a² – 13ab

Therefore,

5a² – 13ab should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b².

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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Answer:

24

Step-by-step explanation:

40 divided by 5 = 8

8 x 3 = 24

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Answer:

0.28 easy

Step-by-step explanation:

Answer:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Step-by-step explanation:

Given:

92÷5

Hailey's workings:

92 divided by 5.

5 goes into 9 1 time.

9 minus 5 = 4.

5 goes into 42 8 times.

42 minus 40 = 2.

The answer is 18 R 2.

The true statements about Hailey's work are:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Answer:

The answer is 3

Step-by-step explanation:

If you combine like terms you get 22x - 6 = 60

Then you set the numbers and x's apart = 22x = 66

Then you divide and get 3

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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