if f(x)=-3x+5, find f(-2)

The total amount of interest that the student paid for the unsubsidized Stafford loan with an interest rate of 6.8%, compounded monthly is,

⇒ $476.24.

Thus, The correct answer is Option C.

A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, or other entities in finance.

Given that;

Borrowed money = $2,560

The fixed monthly payment = $84.34

Hence, The total amount that the student paid for 3 years after the grace period is,

= $84.34 × 3 × 12

= $3036.24

Thus, The amount of interest will be;

⇒ Total amount paid - Sum borrowed

Hence, We get;

Interest =  $ 3,036.24- $2,560

            = $ 476.24

Therefore, $476.24 is the total amount of interest the student paid.

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As per the unitary method, Roxanne's dad make did make 36 blueberry pancakes.

Here we know that Roxanne's dad made 108 mini pancakes in total, with 3 times as many blueberry pancakes as chocolate chip pancakes.

And we need to  solve this problem, we can use the unitary method, which is a simple way to solve problems involving ratios.

As we all know that the unitary method involves dividing the total number of items (108 pancakes) by the ratio (3 blueberry to 1 chocolate chip).

=> 3:1 = 108

When we simplify this gives us the result that 36 blueberry pancakes were made. Therefore, Roxanne's dad made 36 blueberry pancakes

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The correlation coefficient for the data shown in the scatter plot is- 0.9.

The correlation coefficient is a measure of the strength of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. The correlation coefficient can be used to measure the strength of the linear correlation between two variables, as well as identify whether a relationship between two variables is positive or negative. It can also be used to compare the strength of different relationships between multiple variables.

The scatter plot shows a strong negative linear relationship between the two variables, indicating that as one variable increases, the other variable decreases. Therefore, the correlation coefficient is likely to be close to -1, making -0.9 the best estimate.

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Answer:

To prove that AD is a bisector of BC, we need to show that AD divides BC into two congruent segments.

Since AB ≅ AC, we have ∠BAC ≅ ∠CAB by the isosceles triangle theorem.

Since BD ≅ CD, we have ∠CBD ≅ ∠CDB by the same reasoning.

Now, we can use the angle bisector theorem, which states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.

Applying the angle bisector theorem to triangle BCD with angle ∠BCD, we get:

BD/DC = AB/AC

Since AB ≅ AC and BD ≅ CD, we can substitute and simplify to get:

BD/CD = 1

This implies that BD ≅ CD.

Therefore, AD divides BC into two congruent segments, and AD is a bisector of BC.

Hope this helps!

Measure of MP is 10 units.

Angle bisector theorem states that if a line segment is drawn from a vertex of a triangle to the opposite side such that it bisects the angle, then the two parts of the opposite side which are divided by the line segment is proportional to the other two sides of the triangle.

Given is a triangle MNO.

Line segment NP bisects the angle MNO.

MO is divided into two segments MP and PO.

By the Angle Bisector Theorem,

MP / PO = MN / ON

Substituting,

MP / 8 = 15 / 12

MP = (15 / 12) × 8

MP = 10

Hence the measure of MP is 10.

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Answer:

Hi! This question tells us that the book costs $18 and that it costs 3 times more than a DVD. In order to determine the cost of the DVD, all we have to do is divide 18 by 3. 18 divided by 3 is 6. Therefore, the DVD costs $6.

Hope this helps!

Answer:$6

Step-by-step explanation: 18÷3=6

Answer:

23

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Look for the letter that is between 1 and 2 ...very close to 2

=  1.85    <===== very close to '2'

Answer:

Step-by-step explanation:

To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.

To use this formula, we first need to find the slope of the line that passes through the two given points (-4, -2) and (-6, -5). The slope, denoted by m, is given by the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-4, -2) and (x2, y2) = (-6, -5). Substituting these values, we get:

m = (-5 - (-2)) / (-6 - (-4))

= (-5 + 2) / (-6 + 4)

= -3 / -2

= 3/2

So, the slope of the line is 3/2.

Now, we can choose either of the two given points and use it with the slope to write the equation of the line. Let's use the first point, (-4, -2). Substituting the values of x1, y1, and m in the point-slope formula, we get:

y - (-2) = (3/2)(x - (-4))

Simplifying the right side of the equation, we get:

y + 2 = (3/2)(x + 4)

Expanding the right side, we get:

y + 2 = (3/2)x + 6

Subtracting 2 from both sides, we get:

y = (3/2)x + 4

So, the equation of the line that passes through the points (-4, -2) and (-6, -5) is:

y = (3/2)x + 4

The answers are:

a)the number we're looking for is [tex]2^{(-97.5)}[/tex], or approximately [tex]1.629 x 10^{(-30)}.[/tex]

b)the value of a is -13.

c) there were 61 people in the line before the second round of people squeezing in.

What is algebra?

Algebra involves solving equations and manipulating expressions to find the value of unknown quantities. It involves working with numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

11. We can solve this problem by using the properties of exponents and algebra.

Let the number we're looking for be x. Then, we can write the equation:

x * 8⁶⁵ = 16⁵⁰

We can simplify the right side of the equation by using the property:

[tex]a^2 = (a^{1/2})^2[/tex]

So, we have:

[tex]16^{50} = (2^4)^{50} = 2^{(4*50)} = 2^{200}[/tex]

Now we can substitute this into the equation:

[tex]x * 8^{65} = 2^{200}[/tex]

We can simplify the left side of the equation by using the property:

[tex]a^n * b^n = (ab)^n[/tex]

So, we have:

[tex]x * (8^2)^{32.5} = (2^3)^{32.5} = 2^{(3*32.5)} = 2^{97.5}[/tex]

Now we can substitute this into the equation:

[tex]x * 64^{32.5} = 2^{97.5}[/tex]

We can simplify the left side of the equation by using the property:

[tex]a^{(n/2)} = (a^n)^{(1/2)}[/tex]

So, we have:

[tex]x * (2^6)^{32.5} = x * 2^{(6*32.5)} = x * 2^{195}[/tex]

Now we can substitute this into the equation:

[tex]x * 2^{195} = 2^{97.5}[/tex]

We can simplify both sides of the equation by dividing by [tex]2^{195}[/tex]:

[tex]x = 2^{97.5} / 2^{195}[/tex]

[tex]x = 2^{(-97.5)}[/tex]

Therefore, the number we're looking for is [tex]2^{(-97.5)}[/tex], or approximately [tex]1.629 x 10^{(-30)}.[/tex]

12. We can find the equation of the line using the two given points and then use the fact that the line passes through the origin to solve for a.

First, we can find the slope of the line using the two given points:

slope = (y2 - y1) / (x2 - x1)

slope = (3 - 9) / (40 - (2a + 50))

slope = -6 / (-2a - 10)

slope = 3 / (a + 5)

Now we can use the point-slope form of the equation of a line to write the equation of the line passing through the two given points:

y - 9 = (3 / (a + 5))(x - (2a + 50))

Simplifying this equation, we get:

y - 9 = (3x / (a + 5)) - (6a + 150 / (a + 5))

Now we can use the fact that the line passes through the origin to solve for a:

When x = 0, y = 0, so we can substitute these values into the equation:

0 - 9 = (3(0) / (a + 5)) - (6a + 150 / (a + 5))

-9(a + 5) = 6a + 150

Expanding and simplifying:

-9a - 45 = 6a + 150

-15a = 195

a = -13

Therefore, the value of a is -13.

14. Bree can organize her trip in different ways depending on how many countries she decides to visit. If she visits only one country, there is only one way to organize her trip. If she visits two countries, she can either choose to visit the second country or skip it, which gives her 2 possible ways to organize her trip. If she visits three countries, she has 2 options for the second country and 2 options for the third country (visit or skip), giving her a total of 2x2 = 4 ways to organize her trip. Following this logic, we can create a table to show the number of ways Bree can organize her trip for different numbers of countries:

Number of countries | Number of ways to organize a trip

1                                        1

2                                       2

3                                       4

4                                       8

5                                      16

6                                      32

7                                      64

Therefore, Bree can organize her trip in a total of 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 ways.

13. Let's start by working backward. After the second round of people squeezing in, there are 121 people in the line. Let's call the number of people in the line before the second round "x". Then we can set up an equation to represent this situation:

121 = x + (x-1)

The reason we have x-1 in the equation is that between each pair of people in the original line, one person squeezed in during the first round, so we have one less gap between people in the new line.

Simplifying the equation, we get:

121 = 2x - 1

Adding 1 to both sides, we get:

122 = 2x

Dividing both sides by 2, we get:

x = 61

Therefore, there were 61 people in the line before the second round of people squeezing in. But before the first round, there were also gaps between people, so the actual initial number of people in the line is one more than the number of gaps. Since there are x-1 gaps between x people, there were 60 gaps and therefore 61 initial people in the line.

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Answer: The estimated probability of generating a 3 using the random number generator is 1/3, since there are 3 possible outcomes and each is equally likely.

The actual probability of generating a 3 is also 1/3, since the generator is equally likely to generate any of the 3 possible integers.

Therefore, the difference between the estimated and actual probability of generating a 3 is:

1/3 - 1/3 = 0

So there is no difference between the estimated and actual probability of generating a 3.

Step-by-step explanation:

Answer:

43,560ft

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Therefore, for every 1 acre it is equivalent to 43,560 feet.

The measure of side a given the characteristics of the oblique triangle as discussed is; 34.02.

As evident in the task content, A = 151° C = 9° b = 24. Therefore, the measure of angle B = 180° - 151° - 9° = 20°.

Ultimately, the length of side a can be determined using sine rule as follows;

a / sin 151° = b / sin 20°

a = 24 sin 151° / sin 20°

a = 34.02.

Ultimately, the length of side a is; 34.02.

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He would have to pay a total of $30 + $10 xx.

What is the basic arithmetic operation?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

If David used 4 GB over the limit, he used a total of 6 + 4 = 10 GB of data that month. Since he was charged $10 per GB over the included amount, he would have to pay an extra $10 x 4 = $40 in addition to the base $30 cost.

Therefore, he would have to pay a total of $30 + $40 = $70 that month.

If David went over the limit by xx GB, he would have used a total of 6 + xx GB of data that month.

Therefore, he would have to pay an extra $10 x xx in addition to the base $30 cost.

Hence, he would have to pay a total of $30 + $10 xx.

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Answer:

-1/10

Step-by-step explanation:

     [tex]\sf (-3 , \frac{-7}{2}) \ ; \ x_1 = -3 ; \ ; y_1=\frac{-7}{2}[/tex]

     [tex]\sf (2 , -4) ; \ x_2 = 2 \ ; \ y_2 = -4[/tex]

             [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                       [tex]= \dfrac{-4-[-\frac{7}{2}]}{2-[-3]}\\\\\\= \dfrac{-4+ \frac{7}{2}}{2+3}\\\\[/tex]

                        [tex]\sf = \dfrac{ \frac{-4*2}{1*2}+ \frac{7}{2}}{5}\\\\\\= \dfrac{ \frac{-8+7}{2}}{5}\\\\\\= \dfrac{ \dfrac{-1}{2}}{5}\\\\= \dfrac{-1}{2*5}\\\\\\= \dfrac{-1}{10}[/tex]

The equation of the points is y + 4 = -7(x = 24)

From the question, we have the following parameters that can be used in our computation:

(-4,24) and (7,-53)

The slope is calculated as

m = (-53 - 24)/(7 + 4)

m = -7

The equation is then calculated as

y - y1 = m(x - x1)

Substitute the known values in the above equation, so, we have the following representation

y + 4 = -7(x = 24)

Hence, the equation is y + 4 = -7(x = 24)

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Answer:

The step which is used is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step-by-step explanation:

Given point d is is the center of inscribed circle.

To construct the inscribed circle of abc we have several steps of construction

Step 1: First step is to construct the incenter with the help of angle bisectors of two base vertices.

Here given d center of inscribed circle that means the incenter given.

Step 2: After incenter, draw a line perpendicular to one side of triangle that passes through incenter and the label the point of intersection.

This is very important step because after labelling measure the radius(same as the distance between the incenter and labelled point) and draw the circle.  

Hence, after incenter The next step is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step 2 is used draw inscribed circle when incenter already given.

Center C and  [tex]~\overset{\LARGE{\frown}}{AD}[/tex] marked on circle C with ∠AVD being an inscribed angle, the option 3) m ∠AVD = 1/2 [tex]m~\overset{\LARGE{\frown}}{AD}[/tex] is true

It is given that C is a center of circle and  ∠AVD is inscribed angle.

An inscribed angle is an angle with its vertex on the circle, formed by two intersecting chords. This common end point is the vertex of the angle. The measure of an inscribed angle is half the measure of the intercepted arc.

Inscribed Angle = 1/2 of Intercepted Arc

Therefore m ∠AVD = 1/2 [tex]m~\overset{\LARGE{\frown}}{AD}[/tex]

So, the option 3) m ∠AVD = 1/2 [tex]m~\overset{\LARGE{\frown}}{AD}[/tex] is true when center C and  [tex]~\overset{\LARGE{\frown}}{AD}[/tex] marked on circle C with ∠AVD being an inscribed angle

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The complete question is in the image below

Answer:

b = 70 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees.

We know 2 angles, one is 80 degrees, and one is 30 degrees.

80 + 30 = 110 degrees.

180 - 110 = 70 degrees

So, b = 70 degrees.

Types of quadrilaterals are parallelograms, rectangles, squares, rhombi, trapezoids, kites, and isosceles trapezoid.

A polygon having four sides and four angles are called a quadrilateral. Quadrilaterals come in a wide variety of forms, each with its own set of qualities and attributes.

Some of the most typical varieties are listed below:

Parallelogram - A quadrilateral has opposing sides that are equally long and parallel.

Rectangle - A parallelogram with all angles at 90 degrees is referred to as a rectangle.

Square - A rectangle with equally long sides.

Rhombus - A parallelogram with equal-length sides is referred to as a rhombus.

Trapezoid - A quadrilateral with just one set of diagonally opposed sides is called a trapezoid.

Kite - A quadrilateral has two sets of adjacent sides that are of equal length or a kite.

Isosceles trapezoid - An isosceles trapezoid is one with equally long non-parallel sides.

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The odds of winning the Mega Millions jackpot are approximately 1 in 302 million.

The chances of winning the Mega Millions Jackpot, which requires matching each of the five white balls and the gold Super Ball, are around 1 of every 302 million. The chances of winning any award in Uber Millions, which incorporates matching essentially the Super Ball, are around 1 of every 24. The size of the award relies upon the quantity of matching numbers and the Super Ball, with the big stake being the biggest award. The likelihood of winning the bonanza increments somewhat as the quantity of tickets sold increments, however it stays an exceptionally low likelihood occasion. Notwithstanding the slim chances, a great many individuals play the Uber Millions lottery consistently with expectations of becoming quite wealthy.

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Answer:

Step-by-step explanation:

Applying the distance formula, we get that the distance is sqrt(14^2+(-3)^2)=sqrt(205), which is approximately 14.3178211. Rounding to the nearest tenth, we get that the distance is 14.3 units long.

A option (c) marginal distribution summarizes the information from one variable ONLY, without considering ANY information from another variable.

A distribution is a mathematical function that shows the likelihood of different values occurring for a given variable.

Now, a marginal distribution summarizes the information from one variable ONLY, without considering ANY information from another variable. It shows the probability of each value occurring for that variable.

In mathematical terms, we can represent a marginal distribution as follows:

P(X = x) = ∑P(X = x, Y = y) for all possible values of y

Here, X is the variable we're interested in, and Y is the other variable that we're not considering. P(X = x) is the probability of X taking on the value x, and P(X = x, Y = y) is the joint probability of X taking on the value x and Y taking on the value y. The summation is taken over all possible values of y.

Therefore, option (c) is correct.

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Answer:

[tex] \frac{23}{10} [/tex]

Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

The 7th graders mode: 0 (since it appears twice in the sample)

The 7th graders median: 3.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 3 and 4)

The 8th graders mode: 3 (since it appears twice in the sample)

The 8th graders median: 8.5 (since the scores are already sorted, the median is the average of the two middle scores, which are 7 and 10)

Based on these measures of center, Rhonda's claim that 8th graders performed better than 7th graders on the state English test seems to be supported, as the median and mode for the 8th graders are both higher than those for the 7th graders.

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A rational number is one that has a non-zero denominator and can be written as a fraction of two integers.

A rational number is one that has a non-zero denominator and can be written as the ratio of two integers. This indicates that a rational number must have an integer denominator and numerator, and that the denominator cannot be 0.

Rational numbers can be positive or negative, and they include all integers, fractions, and terminating or repeating decimals. A and b can be stated as a/b when both of them are integers and b is not equal to 0. It is essential to understand rational numbers in mathematics, and fields like computer science, physics, and engineering frequently use it in their daily work. as well as computer science.

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Answer:

6,16

Step-by-step explanation:

Answer: x=24

Step-by-step explanation:

Ok, this one is a bit tricky, you just have to keep in mind that directions specifically state that this is a rectangle.

A rectangle's opposite sides will always be the same, so the side opposite to 7 (the bottom of the rectangle) is also 7.

Now we should only be concerned with the triangle that includes the side-length that is x. So now we can use the Pythagorean theorem:

(leg length)^2+(other leg length)^2=(hypotenuse)^2

So if we plug in the values we have:

7^2+x^2=25^2

Solve for x:

49+x^2=625

x^2=625-49

x^2=576

x=[tex]\sqrt{576}[/tex] (square root is the inverse of square)

x=24

Hope this helps :)

After converting from Celsius to Fahrenheit 70 degrees Celsius is equivalent to 158 degrees Fahrenheit.

To convert Celsius to Fahrenheit, you can use the following formula:

°F = (°C x 9/5) + 32

In this case, to convert 70 degrees Celsius to Fahrenheit, we can substitute 70 for °C in the formula:

°F = (70 x 9/5) + 32

Simplifying this expression, we can first perform the multiplication and division:

°F = (126) + 32

Then we can add 126 and 32 to get the final answer:

°F = 158

It's worth noting that the Celsius and Fahrenheit scales are both used to measure temperature, but they have different starting points and different degrees of scale. Celsius is based on the freezing and boiling points of water, where 0 degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point at sea level.

Fahrenheit, on the other hand, is based on a system of degrees devised by Gabriel Fahrenheit, with 32 degrees being the freezing point and 212 degrees being the boiling point at sea level.

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Answer:

45.01

Step-by-step explanation:

You round to the nearest hundredth so since seven is big enough you add a 1 to the hundredth place