Pascals triangle is named after the French mathematician Blaise Pascal despite the fact that its documented existence pre-dated him by over 600 years. Though he did not invent Pascals triangle he did invent a type of machine in 1642 that would end up being historically significant. What was this invention?

Using cοmpοund interest, the Tοtal return equals $ 17,300 and Annual returns fοr the 4-year periοd will be equal tο 13.32%.

The interest yοu receive that is cοmpοunded οn:the primary, οr the sum yοu depοsited οriginallyinterest that yοu have previοusly accrued

Fοr instance, if yοu have a savings accοunt, yοu will receive interest οn bοth yοur initial funds and any priοr interest. On yοur interest, yοu receive interest.

Simple interest is distinct frοm this. At the end οf the periοd, simple interest is sοlely paid οn the principal. Simple interest is typically paid οn term depοsits.

Given the principal = $2700

Amοunt = $20,000

Total return = $20,000 - $2700

= $ 17,300

Annual returns for the 4-year periοd will be equal to,

using compοund interest formula,

[tex]A = P (1 + \frac{r}{n})^{t}[/tex],

Where A = amοunt,

P = principal,

r = rate οf interest,

n = number οf times interest applied per time period,

t = time periοd,

For, 5 years, the value will be -

[tex]20,000 = 2700 (1 + r/100)^5[/tex]

[tex]7.41 = (1 + r/100)^5[/tex]

1.50 = 1 + r/100

1.50 - 1 = r / 100

0.50 = r / 100

r = 5%

For 4 years,

[tex]Annual return = ((202700 (5/4)^4\\A = 13.32 \%[/tex]

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Her new credit score using the given table attached is: 634

Credit score is representative of an individual's credit score and shows the credibility of a person in the market. It is affected by a number of factors like history of repayments, legal status of activities from money, loans taken, etc.

Credit score is calculated by various credit rating agencies and are updated every month depending upon the credit history of such individual. It is calculated out of 900 where higher the score, higher is the credibility of that person.

Now, we are told that last time she checked, that she had a credit score of 659.

Now, from the attached table, the number of points she would lose for taking loan for a store credit card and to buy a new car is;

-10 - 15 = -25 points

Thus;

New credit score = 659 - 25 = 634

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An exponential function is a function in which the independent variable x appears as an exponent.

a is the y-intercept.

b is the rate of change.

The function is exponential growth when b > 1.

The function is exponential growth when b < 1.

y-intercept is the initial value of the function when x is equal to 0.

Asymptote is the line that the function approaches but does not cross.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch or cross.

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The number of coach tickets bought is 2 and the number of first class ticket bought is 2.

Sarah took 4 people including herself to a trip. She was able to purchase coach tickets for $140 and first class tickets for $1000.

She used her total budget for airfare for the trip, which was $2280.

Let's find the number of first class and coach tickets bought.

let

x  = number of first class ticket

y = number of coach ticket

Therefore, using equation

140x + 1000y  = 2280

x + y = 4

multiply equation(ii) by 140

140x + 1000y  = 2280

140x + 140y = 560

860y = 1720

y = 1720 / 860

y = 2

x = 4 - 2

x = 2

therefore,

number of coach tickets = 2

number of first class tickets = 2

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The Area of the given Trapezoid is calculated as: 42 ft²

The area of a trapezoid is calculated using the formula:

A = ¹/₂(b₁ + b₂)*h

where b₁ and b₂ are the lengths of the bases and h is the height

From the given trapezoid, we can see that:

b₁ = 4 + 12 = 16 ft

b₂ = 12 ft

h = √(5² - 4²) = 3

Thus:

Area = ¹/₂(12 + 16) * 3

Area = 42 ft²

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Answer:

Let's use "d" to represent the time the team spent on each drill.

Since the team spent the same amount of time on each drill, and they worked on 5 drills, the total time spent at practice before Jayla arrived can be represented as:

5d

We know that Jayla was 15 minutes late, so when she arrived, the team had already been practicing for 15 minutes. Therefore, the total time she spent practicing is:

40 minutes = 5d - 15

Now we can solve for "d":

5d - 15 = 40

5d = 55

d = 11

So the team spent 11 minutes on each drill.

The equation we used is:

5d - 15 = 40

Answer:

A.) 5.68
B.) 8.4%
C.) 99.6%

Step-by-step explanation:

Answer: 0.0135

0.0009563758

0.00835

Vector W is not a linear combination of the vectors v1, v2 and v3.

w is a linear combination if it is written as a system of equations of the vectors v1, v2 and v3.

Considering the first three lines, the system of equations modeling these variables is given as follows:

From the second equation, the value of y is given as follows:

2y = -1

y = -0.5.

From the third equation, the value of x is given as follows:

x - 0.5 = -1

x = -0.5.

From the first equation, the value of z is given as follows:

-0.5 + z = 2

z = 2.5.

From the fourth equation, we have that:

z = 1.

Which is false, as we found z = 2.5 solving the system of equations, hence Vector W is not a linear combination of the vectors v1, v2 and v3.

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Answer:

The probability of grabbing a tile other than a "B" is approximately 0.818 or 81.8%.

The smallest number with six different digits not including zero that begins with 2 and ends with 3 is: 213457.

The greatest number with six digits not including zero that begins with 3 and ends with 2 is: 398762.

The smallest number with six different digits not including zero that begins with 2 and ends with 3 can be constructed by choosing the remaining four digits from the set {1, 4, 5, 6, 7, 8, 9}, arranging them in ascending order, hence it is of:

213457.

For the greatest number with six digits not including zero that begins with 3 and ends with 2, we arrange them is descending order, hence it is of:

398762.

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Rounding to the nearest tenth, we get the area of the sector is: 6.3 square inches.

Area is the measurement of the amount of space inside a two-dimensional shape, such as a square, circle, or triangle. It is usually expressed in square units, such as square inches or square meters. To find the area of a shape, you need to use a specific formula based on its dimensions and geometry. For example, the area of a rectangle can be found by multiplying its length by its width, while the area of a circle can be found by using the formula pi times the radius squared.

Here,

To find the area of the sector, we need to use the formula:

Area of sector = (central angle/360) x πr²

where r is the radius of the slice.

Plugging in the values we get:

Area of sector = (34/360) x π(8)²

Area of sector = (0.0944) x π(64)

Area of sector = 6.2822 square inches

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Answer:

10x

Step-by-step explanation:

Just add or subtract.

4x + 7x - 1x

4 + 7 - 1 = 10

10x

Answer: i believe its 10x

Step-by-step explanation:

The linear function perpendicular to y - 5 = -3x and that passes through the point (-9, -1) is given as follows:

y + 1 = 1/3(x + 9).

The point-slope definition of a linear function is given as follows:

y - y* = m(x - x*).

The parameters of the equation are given as follows:

The line is perpendicular to y - 5 = -3x, and when two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope m is given as follows:

-3m = -1

m = 1/3.

The coordinates of the point are (-9,-1), hence:

x* = -9, y* = -1.

Hence the equation is:

y + 1 = 1/3(x + 9).

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Answer:

Deductive reasoning

The answer is deductive reasoning.

Answer:

The profit (P) of a company is equal to the revenue (R) minus the cost (C): P = R - C.

Step-by-step explanation:

Option B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.

To determine whether a relation is a function, we need to check whether each input value (the first coordinate of each ordered pair) is associated with exactly one output value (the second coordinate of each ordered pair).

The input value 1 is associated with two different output values (3 and 4), so this relation is not a function.

Therefore, the relation given by set B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.

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The question given is incomplete, the complete question is:

Which of the relations given by the following sets of ordered pairs is not a function?

A. (-4, -4), (-3, -3), (0, 0), (3, -3), (4, -4)

B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10)

C. (5, 1), (4, 1), (3, 1), (2, 1), (1, 1)

D. (-5, -7), (-4, -6), (-3, -5), (-2, -4), (-1, -3)

Answer:

X (minutes) Y (cost in dollars)

10 7.30

20 14.60

30 21.90

40 29.20

50 36.50

60 43.80

The length of the most direct path between Ann and the pile of bottle caps is given as follows:

31 feet.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Ann's location is given by the following ordered pair:

(-4,3).

The location of the pile of bottle caps is given by the following coordinate pair:

(4, -10).

Hence the distance is given as follows:

D = sqrt((4 - (-4))^2 + (-10 -3)^2)

D = 15.5 units.

Each unit represents 2 feet, hence:

15.5 x 2 = 31 feet.

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The inequality that compares Tara's height to Jeff's height is: ℎ > 120

An inequality is a mathematical statement that shows a relationship between two values that are not necessarily equal. It uses symbols such as <, >, ≤, or ≥ to indicate that one value is less than, greater than, less than or equal to, or greater than or equal to another value.

Let ℎ be Tara's height in centimeters. Since Tara is taller than Jeff, her height must be greater than 120 centimeters.

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The graph of the function with asymptotes at x = -2, and x = 3, and x-intercept of (3, 0), indicates that the possible equation graphed is of the form;

[tex]f(x) = \frac{-6\cdot (x -2)}{(x + 2)\cdot (x -3)}[/tex]

An asymptote is the line which the graph of the function approaches when the input value of the function approaches infinity or minus infinity.

The asymptotes of the graph of the function are; x = -2, and x = 3

The possible denominators of the function are therefore; (x + 2) and (x - 3)

The value of the function when x = 0 is -2, therefore;

Numerator ÷ ((0 + 2)×(0 - 3)) = -2

When x = 0, the numerator = ((0 + 2)×(0 - 3)) × -2 = 12

The expressions in the denominator of the function, (x + 2), and (x - 3), and the shape of the graph with a x-intercept of 2, indicates that we get;

The possible numerator is; 6·(x - 2)

The equation for the function graphed is; f(x) = (6·(x - 2))/((x + 2)·(x - 3))

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Answer:

B

1 x 10^3

Step-by-step explanation:

Answer:

Let's suppose that the integer is x.

We know that x leaves a remainder of 1 when divided by 4, so we can express x as:

x = 4n + 1

where n is some integer.

Now we need to find the remainder when x^2 is divided by 8:

x^2 = (4n + 1)^2

x^2 = 16n^2 + 8n + 1

Notice that the first two terms (16n^2 + 8n) are divisible by 8, so we can ignore them.

The remainder when x^2 is divided by 8 is the same as the remainder of 1 when divided by 8:

x^2 ≡ 1 (mod 8)

Therefore, the remainder when the square of the integer is divided by 8 is 1.

Here is the correct equation:

[tex]c = 15 + 65m[/tex]

One packet of raisins costs £1.53 after buying three packets with a £5 note and receiving 41p change.

Total amount paid = £5

Change received = 41p (41 pence)

as he paid £5 note and gets 41p change

100 pence make £1, 41p is equal to £0.41

total amount paid = £5 - £0.41 = £4.59

Ben bought 3 packets of raisins for £4.59

cost of one packet = cost of 3 packets of raisin / 3

cost of one packet = £4.59 ÷ 3 = £1.53

Therefore,  one packet of raisins costs £1.53.

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Answer:

Step-by-step explanation:

To construct the data set, we need to consider the given measures of central tendency:

Mean: 9

Median: 8

Mode: 5

Midrange: 11.5

We can start by finding five values that are less than or equal to the median of 8, and five values that are greater than or equal to the median. Since the mode is 5, we can include it as one of the lower values.

Let's try to find the other four lower values that satisfy the given conditions:

The sum of all values is 10 * 9 = 90 (since there are 10 values and the mean is 9).

The mode is 5, so we need at least two values that are equal to 5.

The midrange is (max + min) / 2 = 11.5, so we need a maximum value that is 3 more than the minimum value.

Here's one possible set of 10 values that satisfy these conditions, listed in ascending order:

{2, 3, 4, 5, 5, 8, 9, 10, 12, 13}

To check that this set of values satisfies the given conditions:

The mean is (2+3+4+5+5+8+9+10+12+13) / 10 = 9.

The median is 8 (the middle value when the values are listed in ascending order).

The mode is 5 (the most common value).

The midrange is (13 + 2) / 2 = 7.5 + 4 = 11.5 (the average of the maximum and minimum values).

The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Let's call the length of the rectangle "l" and the width "w".

We can write two equations based on the given information -

Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)

Area equation: A = 3lw (since the field is divided into 3 equal parts)

We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.

We can use the perimeter equation to solve for one of the variables in terms of the other -

2l + 4w = 600

2l = 600 - 4w

l = 300 - 2w

Now we can substitute this expression for "l" into the area equation -

A = 3lw

A = 3(300 - 2w)w

A = 900w - 6w²

To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -

dA/dw = 900 - 12w = 0

12w = 900

w = 75

So the width of each of the smaller rectangular plots is 75 feet. We can use the perimeter equation to find the length -

2l + 4w = 600

2l + 4(75) = 600

2l = 300

l = 150

Therefore, the dimensions value are obtained as 150 feet by 75 feet.

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Answer:

Step-by-step explanation:

One mathematical sentence that relates to a real-life scenario in business is:

Profit = Revenue - Cost

This formula represents the basic accounting equation, which is used to calculate the profit or loss of a business. In this equation, "Revenue" represents the total amount of money a business earns from its sales or services, and "Cost" represents the total amount of money a business spends on producing its goods or services.

By subtracting the cost from the revenue, we can determine the amount of profit a business has made. If the resulting value is positive, the business has made a profit; if it is negative, the business has suffered a loss.

This mathematical sentence is widely used in business and finance, and is essential for determining the financial health of a business. It can be used to make important decisions, such as whether to invest in new products or services, or to expand the business. Overall, the profit equation is a crucial tool for businesses to ensure their continued success and growth

The correct equation in vertex form for the function is:

g(x) = 2(x-5)² + 9

What is the parabola?

The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.

Option A is the correct equation in vertex form for the function:

g(x) = 2(x-5)² + 9

The vertex form of a parabola is y=a(x-h)²+k, where (h,k) is the vertex of the parabola. We are given that the vertex is located at (5,9), so h=5 and k=9. Substituting these values into the vertex form equation, we get:

g(x) = a(x-5)² + 9

To find the value of a, we can use one of the points that the parabola passes through. Let's use point (7,1):

1 = a(7-5)² + 9

1 = 4a + 9

-8 = 4a

a = -2

Substituting this value of a into the equation, we get:

g(x) = -2(x-5)² + 9

Expanding the square and simplifying, we get:

g(x) = -2x² + 20x - 41

This is not in vertex form, but if we factor out the -2 from the first two terms, we get:

g(x) = -2(x² - 10x + 20.5)

Completing the square inside the parentheses, we get:

g(x) = -2(x-5)² + 50.5

This is also in vertex form, but the constant term is not 9 as given in the problem.

Therefore, the correct equation in vertex form for the function is:

g(x) = 2(x-5)² + 9

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