Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?

Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

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The Pythagorean theorem can be solved using a C programme, therefore yes. The Pythagorean theorem states that the hypotenuse's square length of a right triangle equals the sum of the squares of its other two sides. The slope is the side that faces the right angle.

Therefore, given the lengths of the two shorter sides (a and b), the length of the hypotenuse can be calculated using the formula: c = sqrt(a^2 + b^2).

Here is an example C program that calculates the length of the hypotenuse of a right triangle given the lengths of the other two sides:

#include <stdio.h>

#include <math.h>

Above command is for library

int main() {

 double a, b, c;

Above command to initiate the variable.

  printf("enter the first side's length.: ");

 scanf("%lf", &a);

To enter the value in program

 printf("enter the second side's length.: ");

 scanf("%lf", &b);

Enter the value and print the value

  c = sqrt(a*a + b*b);

Arithmetic command

   print("The hypotenuse's length is: %lf\n", c); return 0;}

Print the value and return the program value to zero.

This program prompts the user to enter the lengths of the two shorter sides of the triangle, calculates the hypotenuse length using the Pythagorean theorem, and then prints the result.

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Answer:

2n^2-8n-24

Step-by-step explanation:

Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.

Hope this helped tho! :)

For acceptable x values of √12(x-1)+√√2(x-1)², the option is equivalent to the quotient given here (x-1) ² is [tex]$2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex] .

The equivalent of the quotient displayed above for allowable x values is

[tex]$\sqrt{1} \cdot 2(x-1)+\sqrt{\sqrt{2}}(x-1)^2$[/tex]

[tex]$2(x-1)+\sqrt[2 \cdot 2]{2}(x-1)^2$\\[/tex]

[tex]\$2(x-1)+\sqrt[4]{2}(x-1)^2$\\$(2 x-2)+\sqrt[4]{2}\left(x^2+2 x(-1)+(-1)^2\right)$\\$(2 x-2)+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x-2+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x+\sqrt[4]{2}\left(x^2-2 x+1\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-\sqrt[4]{2} \cdot 2 x+\sqrt[4]{2}\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}\right)-2$\\$2 x+\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}-2$[/tex]

[tex]$f(x)=\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\frac{d}{d x}\left(\sqrt{12(x-1)}-\sqrt{2(x-1)^2}\right)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\sqrt{12(x-1)}=2 \sqrt{3} \sqrt{x-1}$[/tex]

[tex]$\sqrt{2(x-1)^2}=\sqrt{2}(x-1)$\\$=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex]

Values that might result in a fraction's denominator being equal to zero are excluded. Finding these omitted values is crucial for resolving a rational statement because you cannot divide by 0.

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Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.

Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.

Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.

Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.

For example, the square root of 16 is 4, since 4 x 4 = 16.

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Answer:

Step-by-step explanation:

b

The solution for each system of equations is given as follows:

1) x = -4, y = -8.

2) x = 5, y = -1.

3) x = -7, y = 2.

4) No solution.

5) x = 2, y = -6.

6) x = -3, y = 4.

The system of equations are solved using the elimination method, writing  one variable as a function of another, replacing in the other equation, and then obtaining each variable.

For item 1, we eliminate x, as follows:

x = 12 + 2y.

Hence the solution for y is obtained as follows:

5(12 + 2y) + 3y = -44

60 + 10y + 3y = -44

13y = -104

y = -104/13

y = -8.

Then the solution for x is given as follows:

x = 12 + 2y = 12 + 2(-8) = -4.

For item 2, we have that:

y = 19 - 4x.

Hence:

7x - 2(19 - 4x) = 37

7x - 38 + 8x = 37

15x = 75

x = 5.

Hence the solution for y is of:

y = 19 - 4(5) = -1.

For item 3, we can simplify the second equation by two, hence:

-x + y = 9.

y = 9 + x.

Hence:

3x + 8(9 + x) = -5

3x + 72 + 8x = -5

11x = -77

x = -7.

Hence the solution for y is of:

y = 9 - 7 = 2.

For item 4, we have that:

x = 7 + 3y.

Hence:

2(7 + 3y) - 6y = 12

14 + 6y - 6y = 12

0y = -2. (no solution, division by zero).

For item 5, we have that:

y = -2 - 2x.

Hence:

5x + 3(-2 - 2x) = -8

5x - 6 - 6x = -8

-x = -2

x = 2.

Hence the solution for y is of:

y = -2 - 2(2)

y = -6.

For item 6, we simplify the second equation by two, hence:

2x + y = -2

y = -2 - 2x.

Replacing on the first equation, we have that:

2x + 5(-2 - 2x) = 14.

2x - 10 - 10x = 14

-8x = 24

8x = -24

x = -3.

Hence the solution for y is obtained as follows:

y = -2 - 2(-3)

y = -2 + 6

y = 4.

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Answer:

3(x+1)(x-3)

Step-by-step explanation:

Well, this isn't an equation, but we can factor it like this:

[tex]3x^2-6x-9=3(x^2-2x-3)=3(x+1)(x-3)[/tex]

Answer:

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

Find the difference in time and the difference in the number of batches.

The two numbers will help to find the rate of change in that time interval.

This is same as finding the slope of a line with points (2.5, 8) and (4, 11):

draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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The three equations for this problem are:

Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z

so the

let's use the third equation to get the value of x,y and z:

If you get the values and substitute, then the answer would be:

4 chocolate cakes, 5 fruit cakes, 2 sponge cakes

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[tex]sin(C)=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{9}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2 - 4^2}=a\implies \sqrt{65}=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(C)=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{\sqrt{65}}}\implies tan(C)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies tan(C)=\cfrac{4\sqrt{65}}{65}[/tex]

Numbered meridians are semicircles.

On a map of the planet, the Prime Meridian is an illustrative line. It serves as the origin of the longitude system of measurement. Meridians, a system of fictitious north-south lines, make up longitude. The planet Earth rotates like a ball. The Earth's axis serves as the spin's focal point.

The North Pole and the South Pole are where the axis intersects the surface of the planet. The North Pole and the South Pole are the points on each meridian. Meridians are used to calculate how far away from the prime meridian you are in degrees east or west.

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The required probability as calculated from the data given above is found to be as 1 / 9.

Given,

The spinner is having the letters as A, B and C.

The possibility of getting any of these letters when the spinner is rolled is same.

Therefore , the sample space will be as follows ,

6 + 3 = 9

This is due to the fact a die has 6 sides.

Then the probability of getting a B will be ,  1/9

Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.

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The total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.

To find the total weight of the wall and the average dead load per foot of wall length, we need to calculate the total area of the wall and the area of the windows, then use that information to determine the weight of the remaining brick veneer.

First, we calculate the total area of the wall by multiplying the length and height:

40 ft * 11 ft = 440 ft²

Next, we calculate the area of the windows by multiplying the total area of the wall by 25% (the percentage of the wall that is windows):

440 ft² * 0.25 = 110 ft²

Now we can find the area of the brick veneer by subtracting the area of the windows from the total area of the wall:

440 ft² - 110 ft² = 330 ft²

To find the weight of the brick veneer, we can assume a weight of 150 lb/ft². We can calculate this by multiplying the area of the brick veneer by the weight per square foot:

330 ft² * 150 lb/ft² = 49,500 lb

Now to find the average dead load in lb/ft of the length of the wall, we divide the total weight of the wall by the total length of the wall:

49500 lb / 40 ft = 1237.5 lb/ft

So the total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.

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On solving the provided question, we got to know that -  to plot the graph, required equation is 3x +y -8 = 0

a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples -  2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value. To plot the graph,we need to find the equation first.

and to find the equation -

(y - y1) = m( x - x1)

y1 = -4

x1 = -2

y = 3

x = -5)

equation  -

(-3)(x-1) = y-5

-3x + 3 = y-5

3x - 3 = 5-y

3x +y -8 = 0

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Pyramids have been a symbol of great architecture inventions of the mankind. Egyptian People were the first once to design pyramids on a very large level.

Let a be the Side of Area of base of Pyramid . The base of a pyramid is a square shaped quadrilateral

The Volume of the Pyramid with base area   and height  is given by the equation (1)

[tex]Volume = (1/3)Ah....(1)[/tex]

[tex]A = a^{2}[/tex]

[tex]a = Side[/tex]

A = [tex]a^{2}[/tex] = [tex]44cm^{2}[/tex]

[tex]h = 12.6[/tex]

Putting these values in equation (1) we get

[tex]Volume = (1/3)X44X12.6[/tex]

[tex]Volume[/tex] [tex]= 184.8cm^{3}[/tex]

Hence , the volume of the pyramid is 184.8cm³

The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number

1. Cost of a paperback = 25 cents = $0.25

Cost of a hardcover book = $1.25

There were 54 paperbacks and 163 hardcover books sold.

Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25

2. Cost for round trip airfare = $398.60

Cost of room per night = $115.70

Cost of room for two nights = 2 × $115.70 = $231.40

Cab fare from airport to hotel = $40.00

Total fare from airport to hotel and the return = 2 × $40.00 = $80.00

Total cost = $398.60 + $231.40 + $80.00 = $710

3. Total working hour of Paula = 48 hours

Earning for first 35 hours = $14.50/h × 35

                                          = $507.50

Remaining hours = 48 - 35 = 13 hours

Earning for next 13 hours = ($14.50/h × 1.5) × 13

                                          = $282.75

Total earnings =  $507.50 + $282.75 = $790.25

4. Number of cards Will has = 26

Number of cards Liam has = 19

When they combine, total cards = 26 + 19 = 45

When father also shared, total number of cards = 3 × 45 = 135

Number of cards Nestor has = 4 × 8 = 32

Total number of cards = 135 + 32 = 167

Hence all the questions are cleared using multiplication as one of the basic operations.

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No, 10, 12, and 15 are not the lengths of the sides of a right triangle.

A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).

The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.

In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:

10^2 + 12^2 = 15^2

100 + 144 = 225

244 ≠ 225

Therefore, 10, 12, and 15 are not the side lengths of a right triangle.

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Answer: The probability of a random student to have either ginger or blonde hair is 19/28.

Step-by-step explanation: Before anything is done, let's look and see what information the problem gives us and what we need to find out. We know that there's a 5/14 chance for a student to be ginger, and a 9/28 chance for them to be blonde. We need to find out the combined chance, as we want to know what the chances are for a student to have either hair color.

In order to do this, all we need to find is the sum of both fractions. Because the fractions have different denominators, we need to change one of them to match the other. 14 multiplied by 2 is equal to 28.

If we multiply both the numerator and denominator of 5/14 by 2, we get 10/28. Now, all we have to do is add that to 9/28. When we do that, we get 19/28.

19/28 cannot be simplified, so it is our final answer. Hope this helps!

In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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The average rate of change is equivalent to 2.

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.

Given is the table as shown below -

[x] :  0  1  2  3  4

[y] :  -2 -3 1  3  6

The rate of change in the interval 0 < x < 4 is -

AROC = (6 + 2)/(4 - 0)

AROC = 8/4

AROC = 2

Therefore, the average rate of change is equivalent to 2.

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The domain of a logarithm function is (0, ∞). The range of the logarithm function is all real numbers.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

log (0.1) = -1

log (0.023) = -1.638

The value of log x can be any real number.

The possible value of the logarithm function is any real number. Thus the range of the function is (-∞, ∞).

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The third term of the arithmetic sequence will be negative 14.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term is 20 and the common difference is calculated as,

aₙ = aₙ₋₁ - 17

aₙ - aₙ₋₁ = - 17

d = - 17

Then the third term is calculated as,

a₃ = 20 + (3 - 1) (-17)

a₃ = 20 + 2 (-17)

a₃ = 20 - 34

a₃ = - 14

The third term of the arithmetic sequence will be negative 14.

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Using the concept of fraction, the percentage edited on the video is 62.5 percent.

What is Percentage

Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.

In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;

percentage edited = (2.5 / 4) × 100

Percentage = 0.625 × 100

Percentage = 62.5 %

From the above, Thorton has edited 62,5 percent of the video for his school project.

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The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.

The following are the rationales:

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Answer:

i am not to sure but if i am corroct it IS polynomial

Step-by-step explanation:

hope this helps

The length of the sides of cube will be;

⇒ 2 cm

A cube is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six squared faces with eight vertices and twelve edges is called cuboid.

Given that;

The surface area of a cube = 24 cm².

We know that;

The surface area of a cube with side 'a' is,

⇒ S.A = 6a²

Here, The surface area of a cube = 24 cm²

Hence, We get;

⇒ 24 = 6a²

⇒ 24/6 = a²

⇒ a² = 4

⇒ a = √4

⇒ a = 2 cm

Thus, The side of cube = 2 cm

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Answer:

Approx 3.92

Step-by-step explanation:

The conjugate is -7+6i. The correct option is third.

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

Given:

On a coordinate plane,

the y-axis is labeled imaginary and the x-axis is labeled real.

Point z is at (negative 7, negative 6).

Z(-7, -6)

So, the equation,

-7-6i

So, the conjugate of the equation is,

-7+6i

Therefore, -7+6i is the conjugate of the points.

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