The amount M (in trillions of dollars) of mortgage debt outstanding in the United States from 1990 through 2009 can be approximated by the function M = f(t) = 0.0037(t + 14.979)2, where t = 0 represents the year 1990.

a) Describe the transformation of the common function f(x) = x2. Then sketch the graph over the interval 0 ≤ t ≤ 19.

b) Predict the mortgage debt in the year 2014.

Values that will satisfy the given inequality be 5,6 and 7.

What do you mean by natural number?

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Given inequality:

n > 4

Values that will satisfy the given inequality be 5,6 and 7.

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

[tex]3^4x=9^3x+7[/tex]

Simplify:

[tex]81x=729x+7[/tex]

Subtract 729x from both sides:

[tex]81x-729x=729x+7-729x[/tex]

[tex]-648x=7[/tex]

Divide both sides by -648:

[tex]\dfrac{-648x}{-648} =\dfrac{7}{-648}[/tex]

[tex]\fbox{x = $\dfrac{-7}{-648}$}[/tex]

The terminal ray of an angle measuring negative startfraction 10 over 9 endfraction pi lies in the Second quadrant. this angle measures 200°.

The standard Cartesian coordinate plane is divided into four quadrants as shown in the figure above.

Angle measure: This is the unit of measure used to determine the distance between two lines joined at a common vertex. Subtract 360 to find the quadrant in degree units.

We have given that,

the angle = - 10π/9°

As we know that , π = 180°

so, - 10π/9° = (-10×180/9)° = - 200°

Now, we check the quadrant for angle - 200°

For this follow the above steps,

So, the required quadrant is second .

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Answer: 7w + 6

Step-by-step explanation:

Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.

Answer:

y = 3/5x + 2

Step-by-step explanation:
Parallel lines have the same gradient, so

y = 3/5x + c

Put in your point (-5,-1):

(-1) = 3/5(-5) + c

-1 = -3 + c

-1 + 3 = c

2 = c

So

y = 3/5x + 2

While virtually all time series exhibit a random​ component, not all time series exhibit other components is a true statement.

It's accurate to say that while almost all time series show a random component, not all time series show additional components.

A time series is a collection of observations of discrete data points gathered over a period of time by repeated measurements. For instance, calculating the quantity of retail sales for each month of the year would be a time series. This is because sales income is consistently and precisely measured at regular times. Data collected once or irregularly are not time series data.

A time series observation can be divided into three categories: trend (long-term direction), seasonal (systematic, calendar-related motions), and irregular (unsystematic, short term fluctuations).

A time series is a group of data points that have been arranged chronologically in mathematics. Typically, a time series is a sequence that was captured at many equally spaced intervals in time. As a result, it is a collection of discrete-time data.

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Answer:

Irrational

Step-by-step explanation:

An irrational number added to any other real numbers still keep its infinitely long and never repeating decimals, leaving it still irrational.

Answer:

y=-1.25x+7

Step-by-step explanation:

See the image

Answer:

$7,096.55

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] = [tex]\frac{7}{42}[/tex]

[tex]\frac{1}{7}[/tex] = [tex]\frac{6}{42}[/tex]

[tex]\frac{6}{42}[/tex] + [tex]\frac{7}{42}[/tex] = [tex]\frac{13}{42}[/tex]  This Son A and Son B's portion

Son C must be [tex]\frac{42}{42}[/tex] - [tex]\frac{13}{42}[/tex] = [tex]\frac{29}{42}[/tex]

[tex]\frac{29}{42}[/tex] of some number is 29400

[tex]\frac{29}{42}[/tex] x = 29400  Multiple by sides  by [tex]\frac{42}{29}[/tex]

x = [tex]\frac{42}{29}[/tex] x 29400

x = 42579.31  Rounded to the nearest penny

This number is the total

42579.31 x 1/6 = 7096.55 Rounded to the nearest penny

The total urine patient/client has been measuring at home is 2.838 liters.

Given that,

the patient/client has been measuring urine at home with a quart milk carton and states voiding 1 quarts 2 days ago and 2 quarts yesterday.

We know that 1 quart = 0.946 litre

and 2 quarts = 1.892 litre

Therefore total amount = 0.946 + 1.892

                                       = 2.838

Hence the total urine patient/client has been measuring at home is 2.828 litres.

What is Quart?

The quart is an English unit of volume equal to a quarter gallon. It is a quarter of a gallon. Measurement of volume, capacity. Its unit of measurement for liquids, equal to approximately 1.14 litres in the UK, or 0.95 litrs in the US.

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The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

f(x) = 3(2 – x) –2

Put x = -2

f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)

Put x = -1

f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)

Put x = 0

f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)

Put x = 1

f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)

Put x = 2

f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)

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Answer: -3

Step-by-step explanation:

The shortest length of fence that the rancher can use is 6000ft

Given that

x = width of rectangle

y = length of rectangle

A = area of rectangle = x*y = 1500000 [tex]ft^{2}[/tex]

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2([tex]\frac{1500000}{x}[/tex]) = 3x + 3([tex]10^{6}[/tex])[tex]x^{-1}[/tex]

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

There will be a minimum in Quadrant I.

dL/dx = 3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]

dL/dx = 0:

3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 0

3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]= 3

([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 1

[tex]x^{2}[/tex] = [tex]10^{6}[/tex]

x > 0, so x = 1000 feet for shortest length.

Shortest L = 3000 + 3([tex]10^{6}[/tex])([tex](10^{3} )^{-1}[/tex])= 6000 feet.

The shortest length of fence that the rancher can use is 6000ft

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7x²-45x-28

ac=196

[tex]7x^{2}-49x+4x-28[/tex]

[tex]7x(x-7)+4(x-7)[/tex]

(7x+4) (x-7)

[tex]x=-\frac{4}{7}, 7[/tex]

The first term of the geometric progression= 1/5

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Given:

The second term = 3/10

The sixth term = 243/ 160

The formula for the nth term of geometric sequence is given by

an = a1 r^(n-1 ) , a1 = first term , r= common ratio

Substitute n=2

a2 = a1 r^(2-1 ) ..................(1)

3/10 = a1* r

Substitute n=6

243 / 160 = a1 r^5 ..............(2)

dividing equation 2 by 1 , we get

r^4 = 5.0625

=> r = 1.5

Substitute this value of r into equation 1

3/10 = a1 * (1.5)

a1 = 0.2

So, the first term = 1/5

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For a BOAT isosceles trapezoid. The length of the median is 9 ..

An isosceles trapezoid must have two non-parallel sides of equal length. Therefore, use the information provided to apply the following formula: circumference = base 1 base 2 (legs), where the length of the "leg" is one of the two equivalent non-parallel sides . The base angles of an isosceles trapezoid are equal. The center line or median of the trapezoid is parallel to the base and its length is half the total length of the base. We have given that,

length of side BO = 12

length of side TA = 6

The length of Median = 1/2(12+6)

= 1/2(18) = 9

Hence, the required length is 9 .

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Answer:

Step-by-step explanation:

g

Step-by-step explanation:

16.            +.        5

__.                    ____
7(x+4).                7 (x-3)

The answer to ½ ½ is ¼.

The mentioned symbol is representative of fraction. It can be read as 1 by 2 or 1 over 2. It can be interpreted as the ratio or comparative quantity.

For calculating the answer to this problem, we need to multiply the mentioned two fractions. As per the known rule, the multiplication of numerator values and denominator values takes place to multiply the fraction.

Value = ½ × ½

Multiplying the numerators and denominators as 1×1 and 2×2

Value = ¼

Thus, the answer to given symbols is ¼.

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The scale factor of the dilation of the triangle ABC is equal to 2.5.

We know that the triangles ABC and A'B'C' are similar.

The scale factor of the dilution is given by -

scale factor = measure of A'B' / measure of AB.

Now, let's find the measure of AB and the measure of A'B' from the graph given below, using the distance formula as follows-

The distance formula is = [tex]\sqrt{(y_{2} - y_{1})^{2} + (x_{2} - x_{1})^{2}}[/tex]

Hence, the distance AB =[tex]\sqrt{(2-2)^{2} + (2-0)^{2}}[/tex]

                                       = [tex]\sqrt{(0)^{2} + (2)^{2}}[/tex]

                                       = [tex]\sqrt{2^{2}}[/tex]

                                       = 2 units

Similarly, we can find the distance A'B'

The distance A'B' = [tex]\sqrt{(-1+1)^{2} + (1+4)^{2}}[/tex]

                             = [tex]\sqrt{(0)^{2} + (5)^{2}}[/tex]

                             = [tex]\sqrt{(5)^{2}}[/tex]

                             = 5 units

Now, the scale factor = measure of A'B' / measure of AB

                                       = 5/2

                                       =2.5

Thus, the scale factor of the dilation is 2.5.

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The complete question is -

Triangle ABC was dilated and translated to form a similar triangle A'B'C'.

What is the scale factor of the dilation?

Answer: nose

Step-by-step explanation:

The Question is based on concept of Cost Price and selling Price is 5.2$

What is Cost PRice and Selling PRice?

Cost price is the actual price of an object where as selling price is the price in which seller sells it to customer

Solution

Cost Price of batteries = 4$

and shopkeeper can charge upto 30% interest

hence selling price will be 4$ + 30% of 4$

= 4 + 30/100(4)

= 4 + 1.2

5.2$

Hence answer to this Question is 5.2$

and this 5.2$ is the selling price of duracell batteries whereas 4$ was the cost price for the same

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1. The expression can be simplified as follows: 4 × 5 – 32 × 2 ÷ 6 = 20 – 16 ÷ 6 = 20 – 2 = 18.

2. The expression can be simplified as follows: -2(-9 + 3) = -2(-6) = 12.

3. To solve this equation, we need to isolate the variable a. We can do this by dividing both sides of the equation by -13: -a/13 = 18. Dividing both sides of the equation by -13 gives us a = -18 * 13 = -234.

4. To solve this equation, we need to isolate the variable x. We can do this by moving all terms involving x to one side of the equation and all constants to the other side. This gives us: 7 = 5x + 3(x – 2). We can then distribute the 3 to get 7 = 5x + 3x – 6. Combining like terms, we get 7 = 8x – 6, which we can solve by adding 6 to both sides to get 13 = 8x. Dividing both sides of the equation by 8 gives us x = 13/8.

5. To solve this equation, we need to isolate the variable w. We can do this by moving all terms involving w to one side of the equation and all constants to the other side. This gives us: 11w + 2(3w - 1) = 15 w. We can then distribute the 2 to get 11w + 6w - 2 = 15w. Combining like terms, we get 17w - 2 = 15w, which we can solve by adding 2 to both sides to get 17w = 15w + 2. Subtracting 15w from both sides gives us 2w = 2, which we can solve by dividing both sides by 2 to get w = 1.

6. N' is the complement of the set N. This means that N' contains all elements that are not in the set N. Since the set N contains all factors of 18, N' will contain all natural numbers less than 20 that are not factors of 18. Some elements of N' are 1, 2, 4, 5, 7, 8, 11, 13, 14, 16, and 17.

7. The solution to the inequality 17 - 2a ≤ 29 is all values of a that satisfy the inequality. To find these values, we can first subtract 17 from both sides of the inequality to get -2a ≤ 12. Dividing both sides of the inequality by -2 gives us a ≥ -6. This means that the solution is the set of all values of a that are greater than or equal to -6. This solution can be represented on a number line

8.To solve the inequality 17 – 2a ≤ 29, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 17 from both sides, which gives us -2a ≤ 12. Dividing both sides by -2, we get a ≥ -6. To graph this inequality, we can use a number line. We would draw a solid line at -6 and shade the region to the right of the line, since a is greater than or equal to -6.

9. To solve the inequality 12c + 6 > 9c – 15, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 9c from both sides, which gives us 3c + 6 > -15. Next, we need to add 15 to both sides, which gives us 3c + 21 > 0. Finally, we can divide both sides by 3 to get c > -7. To graph this inequality, we can use a number line. We would draw a solid line at -7 and shade the region to the right of the line, since c is greater than -7.

Answer:

25

Step-by-step explanation:

Answer:25

Step-by-step explanation:

The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

Permutations and combinations

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor

given that

we throw a fair die three times

Due to the fact that each die has a 4 on it, the equation would be [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]=[tex]\frac{1}{2}[/tex] if all the dice were added together.

(There are fifteen ways to get 2 fours: 441,414,144,442,424,244.. and so on until 446,464,644; another way to get the solution is using permutations and combinations:

=(1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])+1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])+(5[tex]C_{1}[/tex](1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])/[tex](6C_{1} )^{3}[/tex]

=  [tex]\frac{1+15}{216}[/tex]

=[tex]\frac{2}{27}[/tex]

The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

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1/5 or -1/9 would both be correct

By using the concept of data structure, it can be concluded that-

First option is correct

What is data structure?

Data structure is a group of elements that provides an efficient way of storing and organizing data so that the data can be accessed and used efficiently. Data structure is a very important tool for computer science and computer engineer and especially in IT industry. Nowadays, lots of research work is being done on data structure.

The three main components of data model structure in SAP S/4HANA are,

configuration data, master data and transaction data

First option is correct

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The negation of the given statement " Everyone failed the quiz today " is given by " No one failed the quiz today."

As given in the question,

Given statement is written as:

S : Everyone failed the quiz today.

Negation of the given statement represent the conversion of true statement into false statement or conversion of false statement into true statement.

Here given statement is true statement.

Convert the given statement into false statement.

So Negation of statement S is represented by ~ S.

~S : No one failed the quiz today.

Therefore, the negation of the given statement is equal to " No one failed the quiz today".

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There are 160 possible area codes can be created with this format.

A process determining the number of possible arrangements in a collection of items in which the order of the selection does not matter is called combination.

Given that, When three-digit telephone area codes were first put in place in the United States and Canada, the first number could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any digit from 0 through 9.

So, according to question,

The first digit has about 8 options

The second digit has about 2 options

The third digit has about 10 options

Therefore, the total possible code = 8×2×10=160.

Hence, 160 possible codes are there.

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