Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?

The answer for this process of long division is, therefore:

To find the result for this long division, we needed to divide the first term of the polynomial by the x in the divisor. Then, if we see the first graph, we have:

Then, we need to multiply this term by the divisor (x - 3), and then, subtract the result from the first two terms of the dividend. We can see as follows:

Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

Let AB be the segment where

The coordinate M(2, 9) and C(4, 12)

and we have to find the point E.

Let us assume the other point is (x, y)

As we know that

The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.

Mid - point formula:

m = [tex]\frac{x_{1}+x_{2} }{2}[/tex]

n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]

So,

Substituting M(2, 9) into C(4, 12):

2 = [tex]\frac{4+x_{2} }{2}[/tex]

9 = [tex]\frac{12+y_{2} }{2}[/tex]

Solve the Equation:

[tex]x_{2} = 0\\y_{2} = 6[/tex]

Express solutions in ordered pairs:

(0,6)
Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

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The height is 9.875 feet from which the goalkeeper catches the ball.

The player kicks soccer from a height of 2 feet

x = 0 and y = 2

Maximum height of 20 feet after traveling 40 feet

x = 40, y = 20

So let y = a(x - 40)² + 20  ( the path of parabola)

Since x = 0 , y = 2

So, 2 = a(0 - 40)² + 20

2 = 1600a + 20

-18 = 1600a

a = - 9/800

Thus, y = -9/800(x - 40)² + 20

Since the soccer is caught by the goalkeeper 70 feet from where it was kicked

x = 70

So at this time,

y = -9/800 ( 70 - 40)² + 20

  = -9/800 × 900 + 20

  = - 81/8 + 20

  = 79/ 8

  = 9.875 feet

Therefore the height at which the goalkeeper catches the ball is 9.875 feet.

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P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.

Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.

To determine P (B U C),

Given that B and C are independent.

Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675

To determine P (B U C),

Given that B and C are mutually exclusive.

Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.

Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

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Answer:

C

Step-by-step explanation:

- 2 = 5x + 3 ( subtract 3 from both sides )

- 5 = 5x ( divide both sides by 5 )

- 1 = x

[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.

The number of integers from 31 to 40 is 10

Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.

From the question, we are to determine the number of integers there are from 31 to 40.

First, we will list all the whole numbers from 31 to 40.

The whole numbers from 31 to 40 are

31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.

All of these numbers are positive whole numbers. Thus, they are integers.

The number of integers listed above is 10.

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1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.

2) The sets that positive integers belong to among the available are;

possibilities

Choices A, B, C, and D

1) There are two basic categories into which numbers are often divided:

- Rational numbers

- Irrational numbers

The four examples above are all different categories of rational numbers.

Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.

Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.

In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers

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The correct answer is Tim

She drives at a variable speed for 2minutes

mean = sum of the heights / number of grandchildren

Answer:

Result of [tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex] is [tex]\tt{} - {2x}^{2} + 6x - 6.[/tex]

Step-by-step explanation:

[tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex]

[tex]\tt{} {3x}^{2} + 2x - 5 - {5x}^{2} + 4x - 1[/tex]

[tex]\tt{} - {2x}^{2} + 6x - 6[/tex]

The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)

Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:

y = y' + Δy · cos ωt     (1)

Where:

The equation for the velocity of the body in simple harmonic motion is found differentiating (1):

v = - ω · Δy · sin ωt      (2)

If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:

v = - 1 · 5 · sin (2π / 3)

v = - 5 · sin (2π / 3)

v = - 5 · √3 / 2

v = - 5√3 / 2

The velocity is equal to - 5√3 / 2.

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Answer:

Bds $ 1.98

Step-by-step explanation:

1386 bds / $ 700   *  $ 1 = 1.98 Bds

Given:

The distance between two stations in map, D= 9cm.

The distance between two stations in real life, d=3 km.

Now, to find the scale of the map take the ratio of D/d .

So, the scale of the map is 1 km=3 cm.

45 represents the slope while -900 is the y-intercept of the function

Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing

From the question, we are told that he averaged an elevation of 45 meters per hour

What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope

To get the y-intercept of the function, we can see this as a distance of -900 meters

The reason for this is that we can see the summit of the mountain as 0 m

So we can represent the equation as;

The expression used to depict area will be 9 / (3x - 1).

A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.

The given expression for area = 27x - 9

Factorize 27x - 9

Taking 9 as greatest common factor outside, we get

27x - 9 = 9(3x - 1)

We know that the area of rectangle with dimensions length by breadth is given by:-

Area = Length x Breadth

Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).

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Complete Question:

What are possible dimensions of the rectangular area at the right? if area is 27x-9.

Given: The figure shown

To Determine: The value of EF

Solution

Using intersecting chord theorem that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

Applying the theorem to the given would give us

Therefore

2. Let us label the the image given

Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:

a verbal reasoning score,

a quantitative reasoning score,

an analytical writing score.

Let average verbal reasoning score represent by v

Let average quantitative reasoning score represent by q

Let average analytical writing score represent by a

In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points

i.e.,

Average quantitative reasoning score - average verbal reasoning = 1.3

q - v = 1.3 ...(1)

The average verbal reasoning score exceeded the analytical writing score by 150.5 points.

i.e.,

Average Reasoning score - average analytical writing = 150.5

v - a = 150.5 ...(2)

The sum of the three average scores was 305.9.

i.e.,

v + q + a = 305.9 ...(3)

Simplify the equation (1), (2) and (3) to get the value of q,v and a;

Add equation (1) and (2)

(q-v) + (v-a) = 1.3 + 150.5

q + a = 151.8 ....(4)

Substitute the value of (q+a=151.8) in the equation (3);

v + q + a = 305.9

v + 151.8 = 305.9

v = 305.9 - 151.8

v = 154.1

Substitute the value of v = 154.1 in the equation (2);

v - a = 150.5

154.1 -a = 150.5

a = 154.1 - 150.5

a = 3.6

Now, substitute the value of a = 3.6 in the equation (4)

q + a = 151.8

q + 3.6 = 151.8

q = 151.8 - 3.6

q = 148.2

Answer :

The average verbal reasoning score was 154.1

The average quantitative reasoning score was 148.2

The average analytical writing score was 3.6

Answer:

Find the following probabilities if you are dealt cards from a standard 52-card deck. Round your answers to three decimal places.

a. If a card is randomly selected, what is the probability that the card is a heart?

13/52 = 1/4

b. If a card is randomly selected, what is the probability that the card is either a club or a spade?

26/52 = 1/2

c. If a cards is randomly selected, what is the probability that the card is both a club and a spade?

0

d. If two cards are randomly selected, what is the probability of drawing a three first, then drawing a jack?

4/52·4/51 = 4/663 = 0.006033182503

e. If two cards are randomly selected, what is the probability of drawing a heart first, then drawing a diamond?

13/52·13/51 = 13/204 = 0.06372549019

f. If two cards are randomly selected, what is the probability of drawing a face card followed by drawing an ace?

12/52·4/51 = 4/221 = 0.01809954751

g. If two cards are randomly selected, what is the probability of drawing a diamond first, then drawing an eight?

12/52·4/51 + 1/52·3/51 = 1/52 = 0.01923076923

The most appropriate choice for pattern will be given by

Option E is the correct option

What is pattern?

Repeated arrangement of number or shape is called pattern.

Here,

Let the boxes be counted row wise

The question is all about filling all the blank boxes with orange colour.

Let the pattern be solved column wise

In the first column,

In first figure

The 2nd, 3rd and 4th boxes are filled with orange colour

Then in the second figure 5th box is filled with orange colour

To complete filling all the boxes with orange colour, 1st, 6th, 7th, 8th and 9th boxes are left. That is shown in the third figure.

In the third column

In first figure

The 5th, 6th and 9th boxes are filled with orange colour

Then in the second figure

1st, 2nd, 4th, 7th and 8th boxes are filled with orange colour

To complete filling all the boxes with orange colour, only the 3rd box is left

That is shown in third figure

Now, in the second column,

In the first figure,

1st, 7th and 8th boxes are  filled with orange colour.

Then in the second figure 3rd, 6th and 9th are filled with orange colour

To complete filling all the boxes with orange colour, 2nd, 4th and 5th boxes are left.

That is shown in option E

So option E is correct

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Hello!

First, let me explain the difference between discrete and continuous.

Discrete: only some numbers of the interval are on the input. For example, in the interval 1 - 10, consider only the integers.

Continuous: all the numbers of the interval are on the input. For example: in the interval 1 - 10, all values are considered (integers and decimals).

Knowing it, let's analyze your exercise:

The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven.

We can represent miles as integers and also decimals, right?

• 2 miles

• 5.750 miles

So, it means that all values can be considered.

So, this is a continuous domain.

This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the

value of the variable x is 7.

let x = the money invested at 8%

y = the money invested at 12%

an actor invests some money at 8% and 36,000 more than four times the amount at 12%

x = 36000 + 2y

total annual interest earned from the investment is 26400

0.08*x + 0.12*y = 26400

by solving the system of equations

x = 36000 + 2y

0.08*x + 0.12*y = 26400

solving the equations,

0.08(36000+2y)+0.12y=26400

2880+0.16y+0.12y=26400

y=84000

x=204000

The amount for 8% will be 84000, and the amount for 12% will be 204000.

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The absolute value inequality is given by | x-130745 | > 10000

and the possibility of Car B is  x < 120745  or  x > 140745

What is absolute value inequality?

Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.

x = price of car B

x-130745 = difference in price from car A to car B

If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.

In short,

x-130745 > 0 when x > 130745

x-130745 < 0 when x < 130745

Using absolute value will give us

|x-130745| = positive difference in price

The result of an absolute value is never negative

We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar

 | x-130645 | > 10000

Part b.

We'll use the idea that if |x| > k, then x < -k or x > k

to get the following

|x-130745| > 10000

x-130745 < -10000 or x-130745 > 10000

x < -10000+130745  or  x > 10000+130745

x < 120745  or  x > 140745

Car B has a price less than $120,745

OR

Car B has a price greater than $140,745

So basically anything that is not between 120745 and 140745. The price has to be positive of course.

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The current area of Mr. Milstein's kitchen table is:

The new width of Mr. Milstein's kitchen table = 5 feet

The area of the new kitchen table if the length is l is given by

Note that the area of the proposed kitchen table should be larger than the current one.

Therefore,

The correct option is F

When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.

Notice that the triangle get's inverted on each reflection around the lines.

The quadratic equation with roots -7, 3/4 in standard form is

4x² + 25x - 21 = 0.

A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.

We know the roots of a quadratic equation are also factors of a quadratic equation.

If x = a and x = b are two roots of a quadratic equation then x - a = 0 and

x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.

Given that -7 and 3/4 are the roots.

∴ { x - (-7)}{ x - 3/4) = 0.

(x + 7)(x - 3/4) = 0.

x² + 7x -(3/4)x - 21/4 = 0.

x² + (25/4)x - 21/4 = 0.

4x² + 25x - 21 = 0.

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Given:

The equation is:

Find-:

Restrictions for this equation

Explanation:

The equation is:

The denominator is not equal to zero. If the denominator is zero, then the function is undefined.

Then the restriction is:

For the function value of x is:

The value of "x" is:

So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1

To find h(-6), replace x = -6 into the function, as follows:

h(x) = -x - 3

h(-6) = -(-6) - 3

h(-6) = 6 - 3

h(-6) = 3