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Consider the equation below.



The equation was solved using the following steps.

Answer:

H + P = 14

3.50H + 2.50P = 43

Step-by-step explanation:

Given that

H denotes half gallons of ice cream

P denotes packages of ice cream cones

Now  

H + P = 14

And,  

3.50H + 2.50P = 43

So, the systems of equations would be

H + P = 14

3.50H + 2.50P = 43

The total compound interest obtained is $756.6.

We are given an initial amount equal to $4,800. This is the principal amount that is denoted by the variable "P". The rate of interest is 5% per annum and is denoted by "r". The interest is compounded annually and denoted by "I". The time duration is 3 years, denoted by the variable "t". Let the final amount be represented by the variable "A". We can use the given formula.

A = P(1 + r)^t

A = $4,800*(1 + 0.05)³

A = $4,800*(1.05)³

A = $4,800*1.157625

A = $5,556.6

The compound interest earned is the difference between the initial and the final amount.

I = A - P

I = $5,556.6 - $4,800

I = $756.6

Hence, the interest amount is $756.6.

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Answer:

$49.72

Step-by-step explanation

14.50x15=217.5

217.5/3=72.5

72.5-22.78=49.72

14.50 (Cost per hour)

X 15 (Hours they work)

----------

217.5 (pay per day)

217.5 ÷ 3 (amount of people) = 72.5

Sally Sarah and Sam earn $72.5

72.5 - 22.78 (cost for shoes) = 49.72

Sarah will have 48.72 left

George has put rice on the 10th square, he has placed a total of 1,023 grains of rice on the chessboard.

What is geometric progression ?
A geometric progression, also known as a geometric sequence, is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number called the common ratio.

The general form of a geometric progression is:

\(a, ar, ar^2, ar^3, ...\)

where:

a is the first term of the sequence

r is the common ratio between successive terms

Given by the question:
To find the total number of grains on the first 10 squares, we can use the formula for the sum of a geometric series, which is:

\(sum = a(1 - r^n) / (1 - r)\)

where:

a is the first term (in this case, 1)

r is the common ratio (in this case, 2)

n is the number of terms (in this case, 10)

Using this formula, we can calculate the sum of the grains of rice on the first 10 squares as:

\(sum = 1(1 - 2^10) / (1 - 2)\)

\(sum = 1(1 - 1024) / (-1)\)

\(sum = 1023\)

Therefore, once George has put rice on the 10th square, he has placed a total of 1,023 grains of rice on the chessboard.

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The point where the medians of a triangle are concurrent is called the centroid.

The centroid is the point of intersection of the three medians of a triangle. A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side. The centroid is often considered as the center of mass of the triangle, as it is the point at which the triangle would balance if it were a physical object with uniform density. The centroid is also the point that is two-thirds of the way along each median, measured from the vertex to the midpoint of the opposite side. The centroid has several important properties, such as dividing each median into two segments with a 2:1 ratio, being the point of intersection of the triangle's medians, and being the center of gravity of the triangle.

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Answer:

To find the interest earned on a savings account by depositing $9800 for 15 months at 5% simple interest, we can use the formula:

Interest = (Principal x Rate x Time) / 100

Where:

Principal = $9800

Rate = 5%

Time = 15 months

First, we need to convert the time from months to years by dividing 15 by 12:

Time = 15/12 = 1.25 years

Now, we can substitute the values into the formula:

Interest = (9800 x 5 x 1.25) / 100

Interest = $612.50

Therefore, the interest earned on the savings account is $612.50.

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1.) The total number of ways in which the books can be arranged so that mathematics and physics cannot touch = 478,961,280.

2.) The total number of ways the books can be arranged when math and physics books touch = 479,001,600

Permutation is defined as the expression that shows how objects can be arranged in a definite order.

The total number of mathematics books = 5

The total number of astronomy books = 4

The total number of physics = 3

The total number of books that the student has in possession = 5+4+3 = 12.

The arrangement of the books so that math and physics cannot touch = 12!-8!

= 479001600 - 40320

= 478,961,280

The arrangement of the books so that math and physics can touch = 12! = 479,001,600

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Answer:

C

Step-by-step explanation:

Hey, so i know you might not need help now, but i got the answer right on mine and it was C.

Hope this helps!

From the given equation the value of r is 8.

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.

To solve this equation for r, we need to isolate r on one side of the equation. First, we add 14 to both sides of the equation:

4r-14+14 = (9/4)r+14

4r = (9/4)r+14

Then, we subtract (9/4)r from both sides:

4r - (9/4)r = (9/4)r+14 - (9/4)r

(5/4)r = 14

Finally, divide both sides of the equation by (5/4) to isolate r:

r = 14/(5/4) = 8

Therefore, the value of r is 8.

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From the asymptotes of the function, the end behavior is given by:

In this problem, the function is given by:

\(f(x) = \frac{4x}{x - 16}\)

For the vertical asymptote, it is when the denominator is of zero, hence:

x - 16 = 0 -> x = 16.

For the horizontal asymptote, we find the limit as x goes to infinity, hence:

\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{4x}{x - 16} = \lim_{x \rightarrow \infty} \frac{4x}{x} = \lim_{x \rightarrow \infty} 4 = 4\)

Hence the end behavior is given by:

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Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

A completely randomized model in a single factor study means that the assignment of treatments is completely random, with no underlying pattern or bias.

When analyzing the difference in means between treatments in a single factor, a completely randomized model means that each individual or unit in the study has an equal chance of being assigned to any of the treatment groups.

In other words, the assignment of treatments is completely random, with no underlying pattern or bias.

This type of experimental design is important because it helps to minimize the effects of confounding variables and other sources of bias.

By randomly assigning treatments to study participants, researchers can be confident that any observed differences in the outcome variable are due to the treatment itself, rather than to other factors that may vary between the groups.

In statistical analysis, a completely randomized model can be used to test whether there are significant differences in the means between the different treatment groups.

This can be done using methods such as analysis of variance (ANOVA) or t-tests, depending on the number of treatment groups and the type of outcome variable being measured.

Overall, the completely randomized model is an important tool for ensuring that the assignment of treatments in a single factor study is unbiased and that the resulting data are suitable for statistical analysis.

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Answer:

A, B, C

Step-by-step explanation:

The top right corner is the positive side of the graph. If it goes below the X axis or to left of the Y axis, it is negative. (thus, the negative numbers)

Answer:

A, B, C, F, E, D

Step-by-step explanation:

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

If the measures of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:

x + (x + 10) + (2x - 6) = 180

Combine the terms:

4x + 4 = 180

Subtract 4 from both sides:

4x = 176

Divide by 4:

x = 44

Now, we can find the measures of the other two angles:

x + 10 = 44 + 10 = 54
2x - 6 = 2(44) - 6 = 88 - 6 = 82

The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

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The terminal point is (0.5, 0.866), and the value of the tangent is 0.173.

For any angle a, the coordinates of the terminal point are given by:

x = cos(a)

y = sin(a).

In this case, the angle is a = pi/3

Then the coordinates of the terminal point are:

x = cos(pi/3) = 0.5

y = sin(pi/3) = 0.866

So the terminal point is ( 0.5, 0.866)

And the tangent of that angle is equal to the quotient between the y-component and the x-component:

tan(pi/3) = 0.866/0.5 = 0.173

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Answer:

Terminal point: (1/2,sqrt3/2); tan 0 = sqrt3

Step-by-step explanation:

I am sorry if this is not right but I am pretty sure it is!

(Edit: It was right on the program!)

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Infinity cannot be directly represented on a graph since graphs are used to represent finite quantities.

However, concepts such as vertical asymptotes, horizontal asymptotes,

and an extended number line can be used to indicate or infer infinite behavior or values.

Infinity, being a concept representing an unbounded and limitless quantity, cannot be directly represented on a conventional graph.

Graphs are typically used to visualize and represent finite quantities or a range of values within a given domain.

However, there are some instances where infinity or infinite behavior can be indicated or inferred on a graph using specific notations or symbols.

Here are a few examples,

Vertical Asymptotes,

For functions, if a graph approaches a vertical line (often denoted by dashed lines) but never intersects it, it suggests an asymptote.

Asymptotes can represent values such as positive or negative infinity,

indicating that the function approaches those values as the independent variable approaches a particular point.

Horizontal Asymptotes

Similar to vertical asymptotes, a horizontal asymptote (represented by a horizontal line) can be used to indicate the behavior of a function

as the independent variable goes towards positive or negative infinity.

If the function approaches a constant value as x approaches infinity, that value can be represented as a horizontal asymptote.

Extended Number Line

Another representation of infinity can be seen on an extended number line, where infinity is often denoted by the symbol ∞.

This extended number line includes positive and negative numbers, as well as infinity as a conceptual endpoint,

indicating values that are unbounded in magnitude.

Infinity remains an abstract concept that lies beyond the scope of conventional graphing techniques.

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Answer:

supply

Step-by-step explanation:

Answer: if the j is supposed to be there, the answer is -9+24j. if the j is not there then just -9+24.

Step-by-step explanation: we distribute the -3 to the 3 and the -8. (-3x3=-9) and (-3x-8=24). when you multiply for divide by a single negative it is negative. when there are two negatives the answer will come out positive.

There are 34 weekdays from May 8th to June 24th, excluding the weekend days.

There are 48 days altogether from May 8 through June 24.

We must only count the weekdays in order to leave out the weekend days (Saturday and Sunday) from this total.

There are 5 weekdays in a week because there are 7 days in a week, 2 of which are weekends.

We may divide the total number of days by 7 and then multiply the result by 5 to get the number of weekdays between May 8 and June 24:

Number of weekdays = (total number of days ÷ 7) x 5

= (48 ÷ 7) x 5

= 6.857 x 5

= 34.285

Therefore, there are 34 weekdays from May 8th to June 24th, excluding the weekend days.

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Answer:

The equation of the line that passes through the point (1,3) with a slope of 66

is

y=66x-63

Answer:

c is the odd one.

Answer:

C

Step-by-step explanation: