The U.S. public debt as of October 2010 was $9.06 × 1012. What was the average U.S. public debt per American if the population in 2010 was 3.08 × 108 people? Round the multiplier to the nearest hundredth.

( 4.625, - 3.75 )

the midpoint of (x₁, y₁ ) and (x₂, y₂ ) is

[[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

here (x₁, y₁ ) = (5.5, - 4.75 ) and (x₂, y₂ ) = (3.75, - 2.75 )

[ [tex]\frac{1}{2}[/tex](5.5 + 3.75 ), [tex]\frac{1}{2}[/tex](- 4.75 - 2.75 ) ]

= (4.625, - 3.75 ) ← midpoint of HX

The equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip.

The equation will be written as:-

S = 150m + 650

Here, 650 is how much she already saved and 150 is how much per month.

Therefore, the equation that represents the total amount of money Layla has saved, s, after m months is s = 150m + 650.

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B

since both equations express y in terms of x we can equate the right sides

2x + 7 = 25 - x ( add x to both sides )

3x + 7 = 25 ( subtract 7 from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

substitute x = 6 into either of the 2 equations for y

y = 2x + 7 = ( 2 × 6 ) + 7 = 12 + 7 = 19

solution is (6, 19 )

The rate of change of y (miles traveled) with respect to x (time in hours) is 59, the coefficient of x. The appropriate choice is ...

... C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 shows that Megan's rate of change in distance traveled is 59 miles for every hour driven at cruise control, after the first 13 miles. So, the correct answer is C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 represents Megan's total distance traveled after driving the first 13 miles without cruise control. The variable y stands for the total number of miles driven, and x represents the number of hours driven at a constant speed using cruise control. To identify the rate of change in the distance traveled, we look at the coefficient of x in the equation, which is 59. This coefficient indicates how many miles are added to the initial 13 miles for every hour of driving at cruise control. Therefore, for every hour, Megan will drive 59 miles after the initial 13 miles are accounted for. It is important to note that the initial 13 miles are a fixed distance and do not change with time. Thus, the correct statement describing the rate of change in the distance traveled is C. For every hour, she will drive 59 miles after the first 13 miles.

I believe so.  :) correct me if i'm wrong.

Answer:

y = 0.75x+20

Step-by-step explanation:

Given that there is an admission ticket fixed and extra cost of 0.75 per ticket for the rides.

This means even if there is no ride used, enterer has to pay a fixed amount for admission.

Let us find out this admission cost from the given information

If y is the total cost and x no of rides

a) x is the no of rides and y the total cost

b) y = 0.75x+20 is the linear equation to calculate the cost for anyone who only pays for festival admission and rides

(c)

Total cost = Admission charges +0.75 * no of ride tickets.

then y = 0.75x+C

where C is the admission fee

Kendall bought 18 tickets i.e. x= 18 and y = 33.50

33.50 = 0.75(18)+C

33.50=13.50+C

C = 33.50-13.50 = 20.00

Hence admission fee = 20

26.25 hours = 26 hours 15 minutes

substitute y = 40 into the equation and solve for x

- 4x + 120 = 15 ( subtract 120 from both sides )

- 4x = - 105 ( divide both sides by - 4 )

x = 26.25 hours = 26 hours 15 minutes

(a) [tex]a_{n}[/tex] = 4n + 8

(b) row 13 has 60 seats

(a)

the sequence of seats is an arithmetic sequence whose n th term is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

where [tex]a_{1}[/tex] is the first term and d the common difference

here the sequence is 12, 16, ....

with [tex]a_{1}[/tex] = 12 and d = 16 - 12 = 4, thus

[tex]a_{n}[/tex] = 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8

(b)

calculate the number of rows n when 60 seats

solve 4n + 8 = 60 ( subtract 8 from both sides )

4n = 52 ( divide both sides by 4 )

n = 13 ← number of rows

Given P is T, q is F and r is F.

Let us find p ↔ q first.

↔ is called bi-conditional operator and is true when p and q both are matched.

Since here p is T and q is F, p↔q is F. ( Since p and q are not matching)

~p v r = ~T v F = F v F = F

Hence (p↔q)→(~pvr) = F → F = T     (Since conditional operator → is false if and if first proposition is T and second proposition is F, for all other values it is T)

The number of rows will be a divisor of 550 such that the quotient is 3 more.

... 550 = 1×550 = 2×275 ≈ 5×110 = 10×55 = 11×50 = 22×25

Factors 22 and 25 differ by 3.

The number of rows of seats is 22.

_____

The number of seats in a row is 25.

The theater has 22 rows of seats. To find this, we solve the equation x(x - 3) = 550, where x is the number of seats per row, leading to x = 25 seats per row and 22 rows after subtracting 3.

To find out how many rows of seats are in the theater with a seating capacity of 550, where the number of rows is 3 less than the number of seats in each row, we can set up an equation to solve for the number of rows. Let the number of seats per row be represented by x, and the number of rows will then be x - 3. Since the total number of seats in the theater is the product of the number of rows and the number of seats per row, we have the equation x(x - 3) = 550.

Now, we will factor this quadratic equation to find the value of x.:

x² - 3x - 550 = 0

Factoring this, we find that it breaks down into (x - 25)(x + 22) = 0. We can then find the value of x by setting each factor equal to zero:

We ignore the negative solution since we cannot have a negative number of seats. Hence, there are 25 seats in each row. To find the number of rows, we subtract 3 from the number of seats per row: 25 - 3 = 22 rows.

Therefore, the theater has 22 rows of seats.

Answer:

$21,000

Step-by-step explanation:

The cost of car=$ 28,000

A car is depreciated by 25%

Now, the price of car=$28000(1-)[tex]\frac{25}{100}[/tex]

The price of the car= $28000([tex]\frac{100-25}{100}[/tex])

The price of the car= $28000([tex]\frac{75}{100}[/tex])

The price of the car= $280×75

The price of the car= $21,000

The car worth today $21,000

Hence the correct answer is $ 21,000

y- coordinate 0f A' = 2

note that the coordinates of A(1, 2 ) and the centre of dilatation (4, 2) both have the same y- coordinate 2

This means they are both on the horizontal line y = 2

and so the y- coordinate of A' will also be 2

Solution: We are given data points and associated residuals:

Data Point           Residual          Absolute value(Residual)

(20,6)                     -2.00                      2.00

(15,5)                       6.75                       6.75

(5,3)                        -1.25                       1.25

(10,10)                     4.50                       4.50

From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.

Therefore, the data point and its associated residual is:

(15,5)  and 6.75    

Answer:

Data Point: (10,10); Residual = 4.50

2000 times 0.60 = 1200 doctors

3/5=0.6

x= 2000* 3/5

x=2000*0.6

x=1200

so... 1200 doctors use brand X aspirin.

The value for X, the measure of angle MKL, is not specifically given in the question. Since angle JKL is a straight angle of 180 degrees, X can be any value up to 180 degrees.

In mathematics, a straight angle is defined as an angle of 180 degrees. In the scenario described with angle JKL, it is mentioned that this is a straight angle. Given that angle MKL is a part of the straight angle, its degree measure X is a component of those 180 degrees. The specific value of X is not given in the question, and it can be any number less than or equal to 180, provided the other part of the angle KJM is equal to 180- X.

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The measure of angle MKL is 60 degrees.

Finding the Measure of Angle MKL

To determine the value of X in this problem, we first need to understand that a straight angle measures 180 degrees. The problem states that angle JKL is a straight angle, so:

Angle JKL = 180 degrees

Next, we have the measure of angle JKM given as 120 degrees. Since angle JKL is made up of angle JKM and angle MKL, we can set up the following equation to find the measure of angle MKL, which is X:

Angle JKM + Angle MKL = Angle JKL

Substituting the known values:

120 degrees + X = 180 degrees

To find X, subtract 120 degrees from both sides:

X = 180 degrees - 120 degrees = 60 degrees

Therefore, the measure of angle MKL is 60 degrees.

-103  

if he lost the same weight each week that means -412 (the weight he lost) ÷ 4 (number of weeks) = -103 (amount of weight lost in one week)

Answer: -1 1/8

Step-by-step explanation: When you have a problem like this, you have to divide.

So you turn the improper fraction into a mixed number which (4 1/2 turns into 9/2) and then you do KCF (Keep Change Flip). So you keep the 9/8, change division into multiplication, and since we are going to put the four over a 1 like this 4/1, we need to change it into 1/4. Then you multiply across. 9x1=9 and 2x4=8 so it would be 9/8. But it's an improper fraction right? So you do long division, and you get -1 1/8.

The Pythagorean theorem is used for finding the distance between two points. You can consider the line from the origin to (12, 5) to be the hypotenuse of a right triangle with sides 12 and 5 (parallel to the x- and y-axes, respectively). Then the relation between these and the hypotenuse length is

... d² = 12² + 5² = 144 + 25 = 169

... d = √169 = 13

The point (12, 5) is 13 units from the origin.

Okay...... so for this problem you need to use the Pythagorean Theorem. So...

12^2 + 5^2

144+25

169

this = square root of 13

so.... The point (12,5) is 13 units from  the origin.

Set up the equations:

2x+3y=80

1x + 4y = 100

solve for x and y:

1x + 4y = 100

x = 100-4y

plug into first equation

2(100-4y)+3y=80

200-8y+3y=80

y=120/5=24

x = 100-4y=100-96=4

So the charges are (x,y)=(4,24)

So the correct answer (B)

Answer:

-5.27

Since when multiplying a positive and negative integer the answer will become negative

The product of -1.24 and 4.25 is -5.27, found by performing the mathematical operation of multiplication.

Given the question, you are asked to calculate the product of -1.24 and 4.25.

Which in this case, -1.24 * 4.25 equals -5.27

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Look for the adjacent letters A.F or F.A in the names of the pair of angles.

The appropriate choice is ...

... BAF and FAD

Answer:

BAF and FAD

Step-by-step explanation:

In order for an angle to have A.F as a side, it must have the letters A.F or FA in its name.

In DAF, the angle is made of rays AD and A.F.  In DAB, the angle is made up of rays AD and AB.  This is not the correct pair.

In EAF, the angle is made of rays AE and A.F.  In CAE, the angle is made up of rays AC and AE.  This is not the correct pair.

In BAF, the angle is made of rays AB and A.F.  In EAD, the angle is made up of rays AE and AD.  This is not the correct pair.

In BAF, the angle is made up of rays AB and A.F.  In FAD, the angle is made up of rays A.F and AD.  This is the correct pair.

(1, 3 )

to determine if the given points are a solution to the equation

They must lie on the given line to be a solution

the only one that is on the line is (1, 3 ) and is therefore the only solution

Answer:

Given: A Δ ABC in which , AB ≅ BC, BE − median of ΔABC, m∠ABE = 40°30'

To Find: ∠ABC, ∠ CE B,∠A E B

Solution: In Δ ABC , BE is the median.

So, AE= EC

Now, In Δ A E B and Δ CE B

AE = EC [ BE is median]

BE is common.

AB=BC [given]

Δ A E B ≅Δ CE B { SSS Congruency]⇒S→side

So, ∠ABE=∠C BE  [ C PCT]

∴ ∠ABC=2×∠ABE=2×40°30'=81°

∠B EA =∠C E B [ C P CT]

Also,∠B A C = ∠BC A=k° [As AB =BC , if opposite sides are equal , then angle opposite to them are equal]

∠A+ ∠B+∠C=180°[ angle sum property of triangle]

k°+81°+k°=180°

2 k°=180°-81°

2 k°=99°

k°=99°/2

k°=49°30'[1°=60']

In Δ A E B, ∠ABE=40°30',∠A=49°30',∠A E B=?

∠ABE+∠A+∠A E B=180°[ angle sum property of triangle]

40°30'+49°30'+∠A E B=180°

90°+∠A E B=180°

∠A E B=180°-90°

∠A E B=90°

As, ∠B EA =∠C E B

So,∠C E B= 90°

So, BE is perpendicular bisector.

The measure of the angle ∠ABC and ∠BCA are both 69°45'. and ∠FEC measures 99°.

∠ABE and ∠BEC are opposite angles formed by the intersecting lines AB and BE, and BC and BE respectively.

Therefore, they are congruent.

The sum of the interior angles of a triangle is always 180°. So, we can find ∠ABE by subtracting ∠BEC from 180°.

Since m∠ABE = 40°30', we have:

∠BEC = ∠ABE = 40°30'

Since AB ≅ BC, the two sides are congruent.

This means that ∠ABC and ∠BCA are also congruent angles. Let's call their measure x.

Using the fact that the sum of the angles in a triangle is 180°, we can set up an equation:

∠ABC + ∠BCA + ∠BAC = 180°

Since ∠BCA = ∠ABC = x, we can substitute these values in:

x + x + 40°30' = 180°

Adding the like terms:

2x + 40°30' = 180°

Subtracting 40°30' from both sides:

2x = 180° - 40°30'

2x = 139°30'

Dividing both sides by 2:

x = 69°45'

So, ∠ABC and ∠BCA are both 69°45'.

To find ∠FEC, we can use the fact that the sum of the angles in a triangle is 180°. Since ∠BEC = ∠ABE = 40°30', we can find ∠FEC:

∠FEC = 180° - ∠BEC - ∠BCE

Substituting the values we know:

∠FEC = 180° - 40°30' - 40°30'

Simplifying:

∠FEC = 180° - 81°

∠FEC = 99°

Therefore, ∠FEC measures 99°.

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Answer:

The correct answer is:

New students laughing at Steve

10 × 10 = 100

Add all the students laughing at Steve

10 + 100 = 110

Add Steve

110 + 1 = 111

There were 111 students in total laughing.

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

400/16= 25

answer: it's a 16 to 25 ratio

one worker covers 25 dogs

25 : 1

the ratio of dogs : employees = 400 : 16

to simplify the ratio divide both parts by 16

400 : 16 = 25 : 1 ← in simplest form

the answer is b and d!

The examples of the Law of Detachment are:

1. If it snows tomorrow, then my dentist appointment will be canceled.

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

3. If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.

It states that if a conditional statement (if-then statement) is known to be true and its hypothesis (the "if" part) is true, then the conclusion (the "then" part) can be validly inferred as true.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then the conclusion must also be true. In both the first and third examples, the statements follow this pattern.

So, the examples of the Law of Detachment are:

If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

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Answer:

x=-11/12

Step-by-step explanation:

Given an equation for x

x -2/3(3x - 4) + 3x = 5/6

We are asked to find the value of x.

We use equation rules to solve

To get rid of denominator in fraction, let us multiply the whole equation by 6.

6x-4(3x-4) +18x = 5

Simplify:

-6x+18x+16 =5

12x = 5-16 = -11

x = -11/12

Answer:

- 11/6

Step-by-step explanation:

I had a test and this was one of the questions and the answer it said was (3x1/3) x 42 so you dont have to figure it out. hope this helps anyone who needs it. :)

67!/2 = k = 18 235 555 459 094 342 644 124 929 548 302 732 213 583 817 657 024 762 296 850 814 250 133 981 218 471 936 000 000 000 000 000

about 1.82×10⁹⁴

Answer:

k=64

Step-by-step explanation:

To find out the greatest integer such that 2^{k}is a factor if 67!

We divide the quotients by 2 and then finally add all the quotients.

67/2 = 33.5 --------> 33

33/2 = 16.5 ---------> 16

16/2 = 8 --------> 8

8/2= 4 ---------> 4

4/2  = 2--------> 2

2/2 = 1 ----------> 1

k= 33+16+8+4+2+1

   = 64

Hence, 64 is the greatest integer such that 2^{k} is a factor of 67!.

A

the equation of a line in ' slope-intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = 5x + 3 is in this form with slope m = 5

function Q has equation y = 2x + 4

the slope of function P is 3 more than function Q