Factor by completing the square: x^4-x^2+16

The country's debt is $48,231.51  per person.

The national debt seems to be the total of a country's yearly budget deficits less any surpluses. A deficit develops once the government spends more money than it collects. The government borrows money to finance the deficit by selling debt obligations to investors.

Given that a country's gross debt was around $ 15 trillion at the end of the year, the following computation must be performed to estimate this amount in dollars per person assuming that the country's population is approximately 311 million.

15 trillion = 15,000,000,000,000

15,000,000,000,000 / 311,000,000 = X

15,000,000 / 311 = X

48,231.51 = X

The country's debt is $48,231.51  per person.

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Using permutations and combinations, The number of different ways this can be done is 316250 ways.

A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.

We will solve it using permutations and combinations

a. The number is ²⁵P₄=  25! / (25 - 4)!

25! / 21! = 25 × 24 × 23 × 22 = 303600 ways.

b. The number is ²⁵C₄= 25! / 4! . (25 - 4)!

= 25! / 4! . 21! = 25 × 24 × 23 × 22 / 4 × 3 × 2

= 12650 ways

Total number of ways to select persons are =

303600 + 12650

= 316250

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Answer:53 + 47 = 100

Step-by-step explanation:

i tink it is right

Answer:

calculators already simplified the issue of adding

Step-by-step explanation:

0 steps to reach floor 0.

a.

floor 0 to floor 1 = floor 0 + 14 = 0 + 14 = 14

floor 1 to floor 2 = floor 1 + 14 = 14 + 14 = 28

floor 2 to floor 3 = floor 2 + 14 = 28 + 14 = 42

floor 3 to floor 4 = floor 3 + 14 = 42 + 14 = 56

floor 4 to floor 5 = floor 4 + 14 = 56 + 14 = 70

b.

when we look at the calculation for the stairs to floor 1, then we see

floor 1 = floor 0 + 14 = 0 + 14 = 14

and for floor 2

floor 2 = floor 1 + 14 = floor 0 + 14 + 14 = 0 + 14 + 14 = 28

and for floor 3

floor 3 = floor 2 + 14 = floor 0 + 14 + 14 + 14 = 42

and so on.

we see

floor n = s(n) = s(0) + 14×n = 0 + 14×n = 14n

s(n) = 14n

we can rewrite:

|x - 1| if x >1

as

(x - 1)   with x > 1.

Remember how the absolute value function works:

In this case, we have the function:

|x - 1| if x >1

Then the minimum value (not included) that this can take is:

|1 - 1| = 0

So it is only 0 or positive, then we can use the first bullet point only, then we can rewrite:

|x - 1| if x >1

as

(x - 1)   with x > 1.

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Answer:

3/100

Step-by-step explanation:

[tex]\frac{0.45}{15}=\frac{45/15}{100}=3/100[/tex]

The roots of f(x)=5x^2-80x+69, f(x)=-9x^2+81x+6 is mathematically given as

This is further explained below.

Generally,  the equation for the function is  mathematically given as

f(x)=5x^2-80x+69

Therefore

Set5 x^2-80 x+69 equal to 0 .

5 x^2-80 x+69=0

Solve for x.

Use the quadratic formula to find the solutions.

[tex]\frac{-b+\sqrt{b^2-4(a c)}}{2 a}[/tex]

Substitute the values a=5, b=-80, and c=69 into the quadratic formula and solve for x.

[tex]\frac{80 \pm \sqrt{(-80)^2-4 \cdot(5 \cdot 69)}}{2 \cdot 5}[/tex]

[tex]x=\frac{40 \pm \sqrt{1255}}{5}[/tex]

The final answer is the combination of both solutions.

[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]

In conclusion, we implore the same format to solve for

f(x)=-9x^2+81x+6

Roots

x=9.07347, -0.07347

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Answer:20-pack of hot dogs

Step-by-step explanation:

It says (The greatest number of hot dogs that you can buy in store for 20-pack  Its $3.05.You will have $16.95 left over) YOUR WELCOME

The measure of each angle of the triangular sign is; 60°

There are different types of triangles such as;

Now, out of these three types of triangles, the only one that has all three sides and three angles equal is equilateral triangle.

Now, we know that the sum of angles in a triangle is 180 degrees. Thus, if the measure of each angle of an equilateral triangle is x, then we can say that;

x = 180/3

x = 60°

Thus, we conclude that the measure of each angle of the triangular sign is; 60°

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Answer: 32 i think

Step-by-step explanation:

assuming there was one original bacteria, then multiplying it by two, or splitting it in two five times means 32

The amount invested at 15% was $900 whereas the $300 was invested in the 11% account

How do we represent the amounts invested in each account?

The fact that $900 more was invested in 15% account means that if the amount invested in the 11% is x, then amount in the other would be x+900

interest on 15% account=15%*(x+900)

interest on 15% account=0.15x+135

interest on 11% account=11%*x=0.11x

total interest=0.15x+135+0.11x

total interest on both accounts=0.26x+135

total interest earned=$213

213=0.26x+135

213-135=0.26x

78=0.26x

x=78/0.26

x=$300(amount invested in the 11% account)

amount invested in the 15% account=$300+$900

amount invested in the 15% account=$1200

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The ratio of their perimeters = 11/6

The ratio of their areas = 121/36

Similar figures are defined as two or more figures that have different sizes but the same shape. By implication, they have the same interior angle measures but different corresponding side lengths that are proportional to each other.

Thus, the ratios of their side lengths are all the same or congruent.

To find the perimeter of two similar figures, A and B, the following ratio is used:

Side length of figure A/Side length of figure B = Perimeter of figure A/Perimeter of figure B

To find the perimeter of two similar figures, A and B, the following ratio is used:

(Side length of figure A)²/(Side length of figure B)² = Area of figure A/Area of figure B.

Given:

Side length of the red figure = 11

Side length of the blue figure = 6

Therefore:

11/6 = Perimeter of red figure/Perimeter of blue figure

Perimeter of red figure/Perimeter of blue figure = 11/6

(11)²/(6)² = Area of red figure/Area of blue figure.

Area of red figure/Area of blue figure = 121/36

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If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

Time = Distance/speed

Time taken to row upstream:

(30/2) /(9 - x)

15/(9-x)

Time taken to row downstream:

15/(9 + x)

Total time spent is 6 hours hence,

15/(9- x) + 15/(9 + x) = 6

Cross multiplying

15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)

= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)

=270 = 6(81 - x²)

270/6 = 81- x²

45 = 81- x²

x² = 81- 45

x²= 36

x =√36

x = 6

Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

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Applying the midpoint formula, the coordinates of B are: (-5, -8).

The midpoint formula is:

M(x, y) = [(x1 + x2)/2, (y1 + y2)/2].

Given the following:

M(x, y) = (-2, -6)

A(x1, y1) = (1,−4)

B(x2, y2) = (?, ?)

Plug in the values

M(-2, -6) = [(1 + x2)/2, (-4 + y2)/2]

Isolate each coordinate

-2 = (1 + x2)/2

(-2)(2) = 1 + x2

-4 = 1 + x2

-4 - 1 = x2

-5 = x2

x2 = -5

-6 = (-4 + y2)/2

(-6)(2) = -4 + y2

-12 = -4 + y2

-12 + 4 = y2

-8 = y2

y2 = -8

Therefore, applying the midpoint formula, the coordinates of B are: (-5, -8).

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The expected gross winning is 0.255 dollars.

According to the question, twenty thousand raffle tickets were sold. There are different prizes awarded for the purchase of one ticket.

Therefore, the probability for the expected gross winning is written as:

Expected Gross = [tex]\frac{3000+(2)(750)+()3(200)}{20000} = \frac{5100}{20000}[/tex]        

                           =  51/200

                           = 0.255 dollars

Hence, the expected gross winning is 0.255 dollars.

What is Probability?

Probability can be used in mathematics for the calculation of the occurrence of the events. It is the ratio of the favorable events to the total number of the occurred events. And the value of the probability is always less than one.

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Answer: The answer would be for "B" that it's 6 units to the left and 0 units down and for "C" It would 1 to the left and -5 units down!

Step-by-step explanation: I used a graph to help me determine these coordinates :D

Answer: At times when your not sure of what to do with a big set of measurements shown in a table, you can use a Histogram to arrange and display the data in a more user friendly and understandable format. It makes it easy to see where most of the values fall in a measurement scale, and how much difference there is.

Step-by-step explanation:

=======================================================

Explanation:

The domain is the set of allowed x inputs.

The left-most part of the graph is at x = -9. There is no right-most part since it goes on forever in that direction due to the arrow.

So we can say [tex]x \ge -9[/tex] or [tex]-9 \le x[/tex] or [tex]-9 \le x < \infty[/tex]

That third inequality mentioned then turns into the interval notation [tex]\big[-9, \infty\big)[/tex]

Use a square bracket to include -9 as part of the domain. It's included because of the closed filled in circle, in contrast to a open hole.

We always will use a curved parenthesis for either infinity since we cannot actually reach it (it's not a number to reach).

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

Now onto the range. This is the set of possible y outputs.

The graph stretches forever downward, so there is no lower bound. The upper bound, or highest part, is when y = 3

The range as a compound inequality is [tex]-\infty < y \le 3[/tex] which condenses to the interval notation of [tex]\big( -\infty , 3 \big][/tex]

Once again, use a square bracket to include the endpoint 3.

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

The absolute max is the highest point of the graph. It's the peak of the mountain. In this case, the absolute max is y = 3. This is the relative max also. The relative max is the maximum within a certain specified interval.

There is no absolute min since the graph goes downward forever. There is no lowest point. This also rules out a relative min as well.

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

The function is increasing when it goes uphill as you move to the right.

The graph shows the function increases on the interval -9 < x < -3 which condenses to the interval notation (-9, -3). This is NOT ordered pair notation which unfortunately looks identical to interval notation when using curved parenthesis for both endpoints.

In contrast, the function decreases when it goes downhill (when moving to the right). This occurs when [tex]4 < x < \infty[/tex] which shortens down to the interval notation of [tex](4, \infty)[/tex]

The graph is flat or constant when it's neither increasing nor decreasing. The graph is constant when -3 < x < 4 which translates to the interval notation of (-3, 4)

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

Now onto the x and y intercepts

The x intercepts are where the graph crosses the horizontal x axis.

We have the two locations of x = -6 and x = 6 as the x intercepts

The y intercept is at y = 3, which is where it crosses the y axis. This also happens to be the max value mentioned earlier, though the y intercept won't always be the max.

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

Lastly, let's compute f(8)

Locate 8 on the x axis. Then draw a vertical line through this. The vertical line crosses the curve at (8, -3). Then move to the left until hitting y = -3 on the y axis

So x = 8 plugged in leads to y = -3 as the output.

Therefore, f(8) = -3

The absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

An absolute value inequality is an inequality that has an absolute value sign with a variable inside.

Example:  | x + 2 | > 4

We have,

Financing a car for 5 years.

Monthly payment = $225

Since 5 years = 5 x 12 months = 60 months.

The cost of the car:

= 60 x $225

= $13500

Absolute deviation = $35

This means monthly payments can be increased maximum up to $35.

So if the monthly payment is increased maximum we have the monthly payment as:

= $225 + $35

= $260

If $260 is the monthly payment then,

The number of months the car finance can be done is:

= $13500 / $260

= 51.9 months

The absolute value inequality for the range of months is:

52 < | x | ≤ 60

Where x is the number of months to finance the car.

Thus the absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.

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Using integrals and probabilities, it is found that:

a) The value of a is of a = 8.

b) The reliability of the refrigerator for the first year is of 93.75%.

c) There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

The distribution is given as follows:

f(t) = t/a, 0≤t≤4.

The cumulative distribution function(cdf) is of 1, hence:

[tex]\int_{0}^{4} f(t) dt = 1[/tex]

[tex]\int_{0}^{4} \frac{t}{a} dt = 1[/tex]

[tex]\left(\frac{t^2}{2a}\right)_{t = 0}^{t = 4} = 1[/tex]

Applying the Fundamental Theorem of Calculus:

8/a = 1

a = 8.

Hence:

The value of a is of a = 8.

The probability that the refrigerator lasts more than one year is:

[tex]P(t > 1) = \int_{1}^{4} \frac{t}{8} dt[/tex]

[tex]P(t > 1) = \left(\frac{t^2}{16}\right)_{t = 1}^{t = 4}[/tex]

P(t > 1) = 1 - 1/16

P(t > 1) = 15/16

P(t > 1) = 0.9375 = 93.75%.

The reliability of the refrigerator for the first year is of 93.75%.

For item c, the probability that a refrigerator will fail during the first month is:

[tex]P\left(t < \frac{1}{12}\right) = \int_{0}^{\frac{1}{12}} \frac{t}{8} dt[/tex]

[tex]P\left(t < \frac{1}{12}\right) = \left(\frac{t^2}{16}\right)_{t = 0}^{t = \frac{1}{12}}[/tex]

Hence:

P(t < 1/12) = 1/(144 x 16) = 0.0004.

There is a 0.0004 = 0.04% probability that a refrigerator will fail during the first month.

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The expression of the number squares are as follows;

1) 4² = 4 * 4 = 16

2) 11²  = 11 * 11 = 121

3) 100²  = 100 * 100 = 10000

4) 3²  = 3 * 3 = 9

5) 10²  = 10 * 10 = 100

6) y²

1) Four squared is expressed as;

4² = 4 * 4 = 16

2) Eleven squared is expressed as;

11²  = 11 * 11 = 121

3) One Hundred squared is expressed as;

100²  = 100 * 100 = 10000

4) Three squared is expressed as;

3²  = 3 * 3 = 9

5) Ten squared is expressed as;

10²  = 10 * 10 = 100

6) y squared is expressed as; y²

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Using proportions, it is found that the car uses gas at a rate of 31.25 miles per gallon.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The gas consumption of the car is given by the proportion of number of miles divided by the number of gallons, hence:

(5/8)/(1/50).

To divide two fractions, we multiply the numerator by the inverse of the denominator, hence:

5/8 x 50 = 31.25.

The car uses gas at a rate of 31.25 miles per gallon.

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Considering the definition of an inequality, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "t" the time parked, in hours. If you want to determinate the interval of hours parked for which Garage A is cheaper than Garage B,  the inequality that expresses the previous relationship is

5 + 3t < 11 + 2t

Solving:

3t - 2t < 11 -5

t < 6

Finally, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.

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Using a point, (24, 150) on the proportional graph, the constant of proportional, k = y/x = 6.25.

A proportional graph represents a proportional relationship between two variables, x and y. Variable y is dependent on variable x. x is the independent variable, and y is the dependent variable.

A proportional graph passes through the origin (0, 0). A proportional graph has a constant of proportionality, k, which is the same for every point on the graph, k = y/x. That is k remains the same, irrespective of the points on the line you chose to pick.

The graph in the image above is a proportional graph as it passes through the origin (0, 0).

To find the constant of proportional, k, any point on the line can be used.

For example, using point (12, 75) we have:

Constant of proportional, k = y/x = 75/12

Constant of proportional, k = 6.25

Also, we can also use the point, (24, 150):

Constant of proportional, k = y/x = 150/24

Constant of proportional, k = 6.25

In conclusion, using a point, (24, 150) on the proportional graph, the constant of proportional, k = y/x = 6.25.

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Answer:

c = 8.75b

Step-by-step explanation:

Since each box costs the same,

The cost of one box = Total cost of 23 boxes ÷ 23

= 201.25 / 23 = 8.75

For b boxes, the total cost would be $8.75b

This should be equal to c which is the variable used to represent the total cost

So the equation is

c = 8.75b

A. The function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

B. We can assume a reasonable domain for the situation as [1, 2, 3, ... 6).

C. A reasonable range for the situation is {375}.

A domain refers to the set of all possible inputs (independent variables) for the function, including real numbers except zero.

The range refers to the difference between the largest and smallest output values (dependent variables) of a function.

Note that the range depends on the domain.

Initial deposit = $450

Weekly deposits = $75

For (w) weeks, the total deposits = 450 + 75w

Function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

A reasonable domain (input value for w) = 6 (six weeks).

A reasonable range (output value for 6 weeks) is 375 (900 - 525).

Thus, the function for the amount Kyle has after (w) weeks is f(w) = 450 + 75w.

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Answer:

Yes

Step-by-step explanation:

Perpendicular lines form 90-degree angles

The solution to the above question is -147

-3[(w-6) ^2+x] ^2 where the value of w = 5 and x amounts to 6

Using algebraic identity: (a-b) ^2 = (a^2 -2ab+b^2)

= -3 [(w^2 -2w*6 +6^2) + x] ^2

= -3 [(w^2 -12w+36) + x] ^2

now substitute the value of w = 5

= -3 [(5^2 -12*5+36) + x] ^2

= -3 [(25 -60+36) + x] ^2

= -3 [1+ x] ^2

Using algebraic identity: (a+ b) ^2 = a^2 +2ab + b^2

= -3 [1^2+2x*1+ x^2]

= -3 [1+2x+ x^2]

now substitute the value of x = 6

= -3 [1+2*6+ 6^2]

= -3 [1+12+ 36]

= -3 [49]

= -147

The above answer can be derived through direct substitution also. Both the methods will any way give the same answer.

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The length of AB of the given triangle ABC is 23.41cm.

So, Pythagoras's Theorem is used: a²+b² = c²

If we swap the values,

Then,

Therefore, the length of AB of the given triangle ABC is 23.41cm.

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