Janice is starting classes at Hellenson University in the fall. The cost of tuition for one year is $14,700. Janice earned an engineering scholarship that covers one-third of her tuition. She has also saved $1,000 to use for this year's tuition. Janice and her parents have agreed to each pay half of the remaining tuition. How much money will they each pay for Janice's tuition this year?

The future value of investment is $560.30, and interest gained in 4 years is 136.8%

The interest regarding loan or investment that increases exponentially with respect to time is called compound interest.

We use compound interest so as to enhance our investment in a large scale.

Given, Amount invested, P= $500

compound interest rate, r= 2.85%

number of time period, t = 4 years

number of times interest applied per time period, n =12 (as interest compound monthly)

Final amount, A

we used compound interest formula, A= P(1+r/n)∧nt

                  A= 500(1+0.0285/12) ∧12×4

          Final amount, A= $560.30

The future value = $560.30

Interested gained in 4 years with compound monthly =2.85x12x4 =136.8%

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Answer: x=8

Step-by-step explanation:

This would be your equation:

x+4=12

Solve.

x=12-4

x=8

The number of subjects that Paige would study D. 2 subjects.

It should be noted that Paige would study for one hour. She spends 1/2 an hour, or 30 minutes, on a subject.

An hour is 60 minutes. If Paige studied 2 subjects, then she would of studied for 60 minutes.

30 + 30 = 60

So, if Paige spends 1/2 hour on Spanish, she would study 2 subjects to reach an hour.

Therefore, the correct option is D.

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Complete question

Paige spends 1 hour on her homework. She spends equal amounts of time on all subjects. If Paige spends 1/2 hour on Spanish, how many subjects does she study?

3 subjects

1 subject

4 subjects

2 subjects

Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.

The standard form of the expression is [tex]0.000286 \times 10^a[/tex].

What is a standard form?

A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.

The given expression is

              [tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]

Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].

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Value of y is -2.The variable mappings that satisfy all of the component equations in a system of equations.

One or more equations involving a number of variables make up a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system.

Explanation:

The equations are provided as follows:

x = 10

3x + 5y = 20

In the second equation, change x to 10

3 * 10 + 5y = 20

Evaluate

30 + 5y = 20

Take away 30 from both sides.

5y = -10

Multiply both sides by 5.

y = -2

Consequently, in the system of equations, y has a value of -2.

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Value of y is -2.The variable mappings that satisfy all of the component equations in a system of equations.

A system of equations is made up of one or more equations with numerous variables. A system of equations' solutions are either the variable mappings that satisfy each of its component equations or the locations where its component equations cross.

The equations are provided as follows:

x = 10

3x + 5y = 20

In the second equation, change x to 10

3 * 10 + 5y = 20

Evaluate

30 + 5y = 20

Take away 30 from both sides.

5y = -10

Multiply both sides by 5.

y = -2

Consequently, in the system of equations, y has a value of -2.

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Answer:

Line A parallel

Line B perpendicular

Line C parallel

Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.

A crucial periodic function in trigonometry is the cosine function.

Utilizing the unit circle will make understanding the cosine function the simplest.

Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.

The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().

According to our answer-

B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period

Determines horizontal phase shift by using

C =determines vertical shift.

When solving the given issue, D = midline = 5

A = amplitude = 2.

B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.

C = 0.

The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.

so,

A*cos(B(x-C)) + D = y

y = 2*cos(3pi(x-0)), plus 5.

y = cos(3pi*x) * 2 * + 5

Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.

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Answer: B

Step-by-step explanation:

Answer: The answer is D. 2 | 0.25

Step-by-step explanation:

I don't really have a good explanation, but I hope it helps!

Proof of ray BC is the angle bisector of angle ABA' is given.

Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.

A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.

Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.

Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.

Therefore, <A'B'C' = <ABC

by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.

Therefore, the ray BC is the angle, bisector of angle ABA'.

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the triangle of the given figures are congruent and ∠1 = ∠2.

What is congruent by SAS?

The side-Angle-Side congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the triangle ΔABD and ΔAED

Here AD is a common side

AB = AE

BC = EC

So both triangles are congruent.

So we can have ∠1 = ∠2

Hence, the triangle of the given figures are congruent and ∠1 = ∠2.

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The value of a+b is 67.5+52.2=120.1 degree.

Which is the value of B?

The middle number, the one immediately following the x, is the b-value. A and C are also numerals, much as the letter B. These can all have any number. They all work together to show you how the quadratic function will be graphed. If you haven't used your y = mx + b equation in a while, dust it off and use the three values you were given for x, y, and m to solve for the b-value, which is the value of the y-intercept. The equation is then solved for the last variable: b, the y-value intercept's.

[tex]\begin{aligned}& 360-90=270 \\& 270-2=135 \\& 180-135=45 \\& \frac{45}{2}=22.5 \\& 90-22.5=67.5 \\& b=67.5^{\circ}\end{aligned}[/tex]

90 *67.8+a 110 =360

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Answer:

x=-1 3/8

Step-by-step explanation:

-2.25 + 0.4x = -2.8

-2.25 + 2.25 + 0.4x = -2.8 + 2.25  ==> add 2.25 on both sides to isolate x

0.4x = -0.55

(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals

8x = -11

x=-11/8

x=-(3+8)/8  ==> turn x into a mixed number

x=-3/8 - 8/8

x=-3/8 - 1 ==> simplify

x=-1 - 3/8

x=-(1 + 3/8)

x=-1 3/8

True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.

When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.

                   While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.

When there is no association in a correlational analysis, what happens?

The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.

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6/7

Step-by-step explanation:

1 - x = 1/7

- x = 1/7 - 1

- x = 1/7 - 7/7

- x = -6/7

x = -(-6/7)

x = 6/7

thus,

1 - 6/7 = 1/7

The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.

What is a sphere?

The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.

Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.

The radius of a sphere is the half of its diameter.

The radius of the bottom ball is 3/2 feet =1.5 feet

The radius of the middle ball is 2/2 feet = 1 feet.

The radius of the top ball is 1/2 feet = 0.5 feet.

The volume of a sphere is 4/3 × ∏r³.

The volume of  bottom ball is  4/3 × ∏ × (1.5)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (1)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (0.5)³  cubic foot.

The total amount of snow is

4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³

=  4/3 × ∏ [1.5³  +1³  + 0.5³ ]

=  4/3 × ∏× 4.5

= 18.84

≈ 19 cubic foot

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The answer is that the Monte Carlo analysis simulates a model’s outcome many times to provide a statistical distribution of the calculated results.

Now, what is  Monte Carlo analysis technique?

Monte Carlo Analysis is a risk management technique used to conduct a quantitative analysis of risks.

This mathematical technique is used to analyze the impact of risks on your project — in other words, if this risk occurs, how will it affect the schedule or the cost of the project?

So, Monte Carlo Analysis gives you a range of possible outcomes and probabilities to allow you to consider the likelihood of different scenarios.

For example, let’s say you don’t know how long your project will take. You have a rough estimate of the duration of each project task. Using this, you develop a best-case scenario (optimistic) and worst-case scenario (pessimistic) duration for each task.

You can then use Monte Carlo to analyze all the potential combinations and give you probabilities of when the project will complete.

Other major benefits of this technique is -

1. It Provides early indication of how likely you are to meet project targets.

2. Can be used to create a more real budget and schedule.

3. Predicts the likelihood of schedule .

4. Gives quantitative measure of risks to assess impacts

5. Provides objective data for decision making.

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Step-by-step explanation: Without more information, it is impossible to determine the experimental probability that a coin will land on heads. The experimental probability of an event is determined by performing experiments and observing the results. For example, if we were to flip a coin 10 times and it landed on heads 6 times, we could say that the experimental probability of the coin landing on heads is 6/10, or 0.6. However, without knowing the results of any experiments, it is impossible to determine the experimental probability of the coin landing on heads.

Answer: We should ASSUME 1/2 or 50%

Step-by-step explanation: Since we don't know the exact number of times the person flipped the coin, we must infer you mean he/she flips the coin once. So, If a coin has 2 sides and the probability is 100% total, we can write an expression to help us solve:

P(Probability)= 100/2

P= 50% or 1/2

How I got 50% or 1/2 is I took the whole probability (100%) and divided it by 2. (2 sides on a coin)

I hope this helped (at least)

Answer: C

Step-by-step explanation:

It should be 5 x 3, considering that rows come before the columns.

Answer: B

Step-by-step explanation:

vertical angles are =

The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61

The regression equation is given as:

y = 0.138x + 1.166

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 21.9 + 1.166 = 4.19

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 20 + 1.166 = 3.93

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 0.7 + 1.166 = 1.26

y = 0.138 * 21.9 + 1.166 = 4.19

y = 0.138 * 0.7 + 1.166 = 1.26

y = 0.138 * 16.7 + 1.166 = 3.47

y = 0.138 * 15.5 + 1.166 = 3.31

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

Residual = 3.7 - 3.65 = 0.05

Residual = 3.69 - 4.19 = -0.5

Residual = 3.8 - 3.65= 0.15

Residual = 4 - 3.93 = 0.07

Residual = 4 - 3.65= 0.35

Residual = 1.11 - 1.26 = -0.15

Residual = 3.69 - 4.19 = -0.5

Residual = 1.11 - 1.26 = -0.15

Residual = 3.5 - 3.47 = 0.03

Residual = 3.92 - 3.31 = 0.61

Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61

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Answer:

The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61

How to determine the residuals?

The regression equation is given as:

y = 0.138x + 1.166

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 21.9 + 1.166 = 4.19

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 20 + 1.166 = 3.93

y = 0.138 * 18 + 1.166 = 3.65

y = 0.138 * 0.7 + 1.166 = 1.26

y = 0.138 * 21.9 + 1.166 = 4.19

y = 0.138 * 0.7 + 1.166 = 1.26

y = 0.138 * 16.7 + 1.166 = 3.47

y = 0.138 * 15.5 + 1.166 = 3.31

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

Residual = 3.7 - 3.65 = 0.05

Residual = 3.69 - 4.19 = -0.5

Residual = 3.8 - 3.65= 0.15

Residual = 4 - 3.93 = 0.07

Residual = 4 - 3.65= 0.35

Residual = 1.11 - 1.26 = -0.15

Residual = 3.69 - 4.19 = -0.5

Residual = 1.11 - 1.26 = -0.15

Residual = 3.5 - 3.47 = 0.03

Residual = 3.92 - 3.31 = 0.61

Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61

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Step-by-step explanation:

According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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The coordinates of C are (8/7, 10/7) if point A is (-4, -2) and point B is

(8, 6)

The section formula aids in finding a point's coordinates so that the line connecting two points can be divided in a ratio. This involves both internal and external activities. P (x, y) = (c, m, plus a, plus n, plus d, plus b, plus n). The Section formula is used to determine the ratio by which a line segment is divided by a point either internally or externally in coordinate geometry. It is used to identify a triangle's centroid, incenter, and excenter. Physics uses this technique to determine equilibrium points, the centers of mass of systems, and other things.

A(-4, -2), B(8, 6)

m:n=3:4

((3(8)+4(-4))/(3+4) , ((3(6)+4(-2))/(3+4))

=((24-16)/7, (18-8)/7)

=(8/7, 10/7)

Therefore, the coordinates of C are (8/7, 10/7)

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Answer:18 1/8

Step-by-step explanation:

5x3=15

5x5/8=25/8=3 1/8

15+3 1/8=18 1/8

Answer:

-------------------------------

Total hours worked is x + y.

Earning from the part time job is 24x, from the internship is 12y.

Inequality for the number of hours:

Inequality for the earning:

This can be simplified by dividing all terms by 12:

Answer:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

Step-by-step explanation:

Part-time job

Internship

The student needs to work less than 15 hours a week:

[tex]\implies x+y < 15[/tex]

The student needs to earn at least $240 a week:

[tex]\implies 24x+12y \geq 240[/tex]

Therefore, the system of inequalities is:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

The second inequality can be simplified by dividing each term by 12:

[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]

[tex]\implies 2x+y \geq 20[/tex]

Therefore, a second system of inequalities is:

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

To solve the system of equalities, graph both inequalities and shade the overlapping region.  

Any (x, y) point in the overlapping region is a solution to the system of inequalities.

The equations of inequalities are y < 4 and y > x.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.

One graph line is parallel to x-axis and it intersect y axis at (0,4).

The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a

The equation of the line parallel to x-axis is y = 4.

The equation of line that passes through origin is y = mx

The line passes through the point (1,1).

Putting x = 1 and y = 1 in y = mx:

1 = m

Therefore the equations of lines are y = x and y = 4

The inequality will be y < x or y > x for the line  y = x.

The inequality will be y < 4 or y > 4 for the line  y = 4.

(-2,0) is a point on the shaded area.

Putting x = -2 and  y = 0 in y > x

0 > -2 true.

The inequality is y > x

Putting x = -2 and  y = 0 in y < 4

0 < 4  true.

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The glide reflection that maps ABC to A'B'C' is given as follows:

The glide reflection is a combination of a reflection with a translation.

The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.

The midpoint of segment A'B' is given as follows:

The slope of this segment is given as follows:

m = (-6 - (-2))/(6 - 4) = -1.

Then the slope of the reflection line is of:

m = 1.

(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).

Then:

y = x + b.

When x = 5, y = -4, then the intercept b is calculated as follows:

-4 = 5 + b

b = -9.

Thus the reflection line is of:

y = x - 9.

Then the translation is given subtracting the coordinates of one of the vertices, as follows:

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