An electrician charges a rate of $60 per hour plus a per job fee of $25. If
the electrician works on the weekend, he charges an additional 50% of
his hourly rate. Write an expression that represents the total cost for a
weekend job in 2 different ways.

Answers

Answer 1

The expression that represents the total cost on weekend job is 25x + 90y.

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

Given that,

The hourly charge of the electrician is $60.

And, the job fee is $25.

The additional percent charged on weekend is 50%.

Suppose the number of jobs on weekend is x and the total hour worked is y.

Then, as per the given case, the following expression can be written for the weekend cost as,

25x + 60y + (50% of 60y)

= 25x + 60y + 50/100 × 60y

= 25x + 90y

Hence, the expression for the total cost for a weekend job is given as 25x + 90y.

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Related Questions

(03.06 MC)

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 3), (2, 6), (3, 12), (4, 24)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)

Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)

Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)

Answers

A) The data models a geometric sequence

B) Using a recursive formula, the time she will complete station 5 is; 2

C) Using a explicit formula, the time she will complete station 9 is; 512

How to find the Recursive Formula?

A)  From the given coordinates (1, 3), (2, 6), (3, 12), (4, 24), we can say that when x increases by 1, y is multiplied by 2. Thus, as the quotient between consecutive terms is the same, the data depicts a geometric sequence.

B) The recursive formula for a geometric sequence with common ratio r and first term a₁ is given by the formula:

f(n) = a₁(r)ⁿ⁻¹

Since a₁ = 2 and r = 1, then we have;

f(1) = 2(1)¹⁻¹

f(1) = 2

f(5) = 2

C) The explicit formula from the calculations above will be;

aₙ = 2ⁿ

Thus;

a₉ = 2⁹

a₉ = 512

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Tessa has a new beaded necklace. 18 out of the 45 beads on the necklace are blue. What
percentage of beads on Tessa's necklace are blue?

Answers

Answer: 40%

Step-by-step explanation: 18/45 = x/100

divide 100 by 45 and you get 2.22 repeating.

multiply 2.22 by 18 and you get 40%

In triangle , the measure of angle is 50° and the measure of angle 70°. What is the measure of the exterior angle to angle ?

Answers

Answer:

60

Step-by-step explanation:

50+70=120

180-20=60

Answer:

120°

Step-by-step explanation:

Your question didn't include an image or angle names, so it was pretty confusing to get what you were asking for. If you were asking for the exterior angle of the missing angle, then here's your answer:

The 3 angle measures of a triangle will always equal 180.

Since we've already got two angles, all we need to do is a simple equation to get our missing angle:

180-(50+70)=60

Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:

180-60=120

And there's your answer, 120°

There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!

the mean of five positive integers is 1.5 times their median. four of the integers are 8, 18, 36 and 62, and the largest integer is not 62. what is the largest integer?

Answers

The largest number of the five positive integers is 146.

Mean:

The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.

Median:

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.

Here we have to find the largest integer.

Data given:

Four of the five integers are 8, 18, 36, and 62.

It is given that mean of five numbers 1.5 times their median.

mean = (8+18+36+62 + x)/5

median = 36

mean = 1.5 × median

(124 + x) / 5 = 1.5 × 36

124 + x = 5 × 54

x = 270 - 124

  = 146

Therefore we get the largest number as 146.

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I need help with this asap please ​

Answers

Answer: C

Step-by-step explanation:

-2 and 2 add up to 0

Answer:

c

Step-by-step explanation:

-2 + 2 =0

Evaluate the expression and enter your answer in the box below.
|42|

Answers

Answer:

42

Step-by-step explanation:

because the distance between 42 and zero is 42

y= 3x + -2
y= x -4

HELP ME

Answers

Answer:

y=-3x+2 y=-x-4

Step-by-step explanation:

a person casts a shadow that aligns with a shadow of a tree. the person is 5.5 feet tall and casts a shadow 8.25 feet long. the trees shadow measures 22.5 feet long

Part A: write and equation you can use to find the trees hight.

Part B: How tall is the tree? How far is the person standing from the tree?

Answers

An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.

The height of this tree is equal to 15 feet.

The distance of this person from the tree is equal to 14.25 feet.

What are the properties of similar triangles?

In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):

22.5/8.25 = x/5.5

Where:

x represents the height of the tree.

How tall is the tree?

22.5/8.25 = x/5.5

Cross-multiplying, we have:

8.25x = 22.5 × 5.5

8.25x = 123.75

x = 123.75/8.25

x = 15 feet.

How far is the person standing from the tree?

The distance of this person from the tree can be calculated as follows;

Distance = Length of tree's shadow - Length of person's shadow

Distance = 22.5 - 8.25

Distance = 14.25 feet.

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Jack has 18 fewer points than Aria, who has x points.​

Answers

Answer: x-18

Step-by-step explanation:

|-2c-3| > -4
Absolute value inequality

Answers

The solutions of the absolute value inequality.

|-2c-3| > -4

are all the real numbers.

How to solve the absolute value inequality?

Here we have a really trivial inequality, which is:

|-2c - 3| > -4

Notice that we have an absolute value there, and the absolute value is defined as:

|x| = x   if x ≥ 0

|x| = -x if   x < 0

Then the absolute value |x| is always equal to or larger than zero, so:

|x| > -4

Is true for any value of x.

Then our inequality:

|-2c - 3| > -4

Is true for any value of c, because the left side is always equal to or larger than 0, and 0 > -4

So c can be any real number.

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A circle is centered at (−5, 8) and has a radius of 7. Which of the following is the equation of this circle? Group of answer choices (x + 5)2 + (x − 8)2 = 49 (x + 5)2 + (x − 8)2 = 7 (x − 5)2 + (x + 8)2 = 7 (x − 5)2 + (x + 8)2 = 49

Answers

The equation of the circle centered at (−5, 8) and having a radius of 7 is (x + 5)² + (y - 8)² = 49.

What is the equation of the circle centered at (−5, 8) and has a radius of 7?

The standard form of the equation of a circle is expressed as;

x² + y² = r²

The horizontal (h) and vertical (k) translations represents the center of the circle.

Hence;

(x - h)² + (y - k)² = r²

Given the data in the question;

Center of the circle: (−5, 8)

h = -5k = 8r = 7Equation of the circle = ?

Now, plug the values of h, k and r into the equation above and simplify,

(x - h)² + (y - k)² = r²

( x - (-5) )² + ( y - 8 )² = 7²

(x + 5)² + (y - 8)² = 49

Therefore, the equation of the circle is (x + 5)² + (y - 8)² = 49.

Hence, option A is the correct answer.

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What is the value of the rational expression below when x is equal to 5?
15-x
x-10
OA. 10
O.B. -2
OC. 2
O D. -10

Answers

Answer: A. 10

Step-by-step explanation:

Plug in x which is 5 to equation 1

15-5=10

Plug in x which is 5 to equation 2

5-10= -5

the polynomial that represents the volume of the box is 6x3 32x2 2x - 40. find the volume of the box if x is 4 inches.

Answers

the polynomial that represents the volume of the box is is 6x^3 +5x^2 -3x-2

V=lwh

l=x+1

w=2x+1

h=3x-2

V=(x+1)(2x+1)(3x-2)

V=(x*2x+x*1+1*2x+1*1)(3x-2)

V=(2x²+x+2x+1)(3x-2)

V=(2x²+3x+1)(3x-2)

V=2x²*3x+2x²*(-2)+3x*3x+3x*(-2)+1*3x+1*(-2)

V=6x³-4x²+9x²-6x+3x-2

V=6x³+5x²-3x-2

complete question is

Find the volume of the box. Use the formula V = lwh.

Rectangular box with sides x plus 1, 2x plus 1, and 3x minus 2.

6x3 – 2

6x3+ x – 2

6x3 – 13x2 – 3x – 2

6x3 + 5x2 – 3x – 2

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Find the slope of the line through (7,-6),perpendicular to y=4x+2

Answers

Answer:

4y+x+17=0

Step-by-step explanation:

y=4x+2

For a point to be perpendicular to a line

then the product of the two gradients must be negative one (I.e, m1×m2=-1)

where m1= 4

m2=-(1/m1)

m2=-1/4

point (7,-6)

x1=7 y1=-6

from the general equation of a line

y-y1=m(x-x1)

y-(-6)=-1/4(x-7)

y+6=-1/4(x-7)

y+6=-1/4x+7/4

y+1/4x=(7/4)-6

y+1/4x=-17/4

y+1/4x+17/4=0

4y+x+17=0

POSSIBLE POINTS: 20
A prestigious program accepts 2 out of every 9 applicants per yer. If the program accepted 360 applicants, how many applicants were NOT accepted?
A.1260
B.1620
C.2520
D.3240
E.3600

Answers

The correct option is A. It can be solved by the concept of ratio and proportion.

What is ratio?

It is the way of representation of a quantity relative to the other quantity. Its symbol is :. For example size of 2 relative to 5 is represented by 2:5 or 2/5.

Total number of applicantas = 9

Accepted applicants             = 2

Not accepted applicants      = 9-2 = 7

Take the ratio of accepted to the not accepted applicants = 2/7

Now, if new not accepted applicants are x then accepted applicants are 360. To keep the ratio constant, the following equation must be satisfied:

[tex]\frac{2}{7}=\frac{360}{x}\\x=\frac{7}{2}\times 360\\x=1260[/tex]

Hence, the correct option is A. It can be solved by the concept of ratio and proportion.

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Pennylvania ha 51 mile of coat along Lake Erie and 57 mile horeline along the Delaware Etuary. The total ditance around Pennylvania i about 1000 mile. How much of that ditance around Pennylvania i not horeline?

Answers

the total distance around Pennsylvania is not shoreline will be 892 miles.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Pennsylvania has 51 miles of coast along Lake Erie and a 57-mile shoreline along the Delaware Estuary.

The total distance around Pennsylvania is about 1000 miles.

So the distance around Pennsylvania is not shoreline will be 1000-(57+51) = 892miles

Hence, the total distance around Pennsylvania is not shoreline will be 892 miles.

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What is 35.7 divided by 0.07

Answers

Answer:

510

Step-by-step explanation:

Answer: The answer is 510

Step-by-step explanation:

35.7/0.07 = 510

The sum of two numbers is 19. The second number is 2 more than twice the first number.

Answers

Answer: 5[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

19=(x+(2x+2))
Subtract 2 from each side
17=x+2x
17=3x
Divide each side by 3
[tex]\frac{17}{3}[/tex] = x
5 [tex]\frac{2}{3}[/tex] = x

Question 5 of 15
Solve: 6+ x/2 = 1/4(x − 4) – 1
OA. There are infinitely many solutions.
OB. x=-16
OC. x= 32
OD. X=-32

PLEASE HELP ME HURRY❗️❗️❗️❗️❕

Answers

Answer: x= -32

Step-by-step explanation:

6+x/2=1/4(x-4)-1

6 +x/2 = 1/4x -1 -1         distribute

6+ x/2 = 1/4x -2            combine like terms

(6+x/2) = (1/4x -2)        Find GCF for denominator

4(6+x/2) = 4(1/4x -2)      GCF is 4 so multiply by 4 on both sides

24 +x = x-8                 add 8 on both sides

32+x=x                        subtract x

32=-x                           divide by -1 on both sides

-32= x

 

if the measure of an interior angle of a regular polygon is 120 degrees, how many sides does the polygon have?

Answers

Answer:

6 sides

Step-by-step explanation:

since the measure of an interior angle of a polygon can be found with the formula 180(n-2) / n where n is the number of sides we can substitute 120 to the answer and cross multiply to find that

120n = 180(n-2)

120n = 180n-360

360 = 60n

n = 6

Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k. What test can you use to check whether the true average is 59k?.

Answers

To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted.

What is an Average?

In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.

It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.

When we analyze the  given question, we find that,

The total number of students were 49,

The true average was found to be 59k,

and the Sample average is found to be 44k.

Thus, in  the present question we will use the One- sample T-test.

We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.

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Solve each inequality. Use the number line provided to test intervals.

Thank you!! :)

Answers

Answer: x ∈ {-0.5, -5, -12.5}

Step-by-step explanation: To solve the inequality 2x³ + 21x² + 60x + 25 > 0, we first need to find the values of x that make the inequality true. We can do this by setting the expression equal to 0 and solving for x.

We can start by factoring the expression to make it easier to solve. Notice that 2x³ + 21x² + 60x + 25 is a polynomial with a leading coefficient of 2 and a constant term of 25. This means that it has the form (x + a)(x + b)(x + c), where a, b, and c are constants.

We can start by factoring out the common factor of 2x from the first two terms: 2x³ + 21x² + 60x + 25 = 2x(x² + 10.5x + 12.5). Now we can see that the expression has the form (x + a)(x + b)(x + c), where a = 0.5, b = 5, and c = 12.5.

So, we can rewrite the expression as (x + 0.5)(x + 5)(x + 12.5) = 0. Now we can solve for x by setting each factor equal to 0 and solving for x:

x + 0.5 = 0 => x = -0.5

x + 5 = 0 => x = -5

x + 12.5 = 0 => x = -12.5

Therefore, the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5.

Now we need to determine which of these values make the inequality 2x³ + 21x² + 60x + 25 > 0 true. To do this, we can substitute each of the values of x into the inequality and see which ones make the inequality true.

When x = -0.5, the inequality becomes 2(-0.5)³ + 21(-0.5)² + 60(-0.5) + 25 > 0, which simplifies to -0.5 + 5.25 - 15 + 25 > 0. This is true, because the left-hand side is 29 > 0.

When x = -5, the inequality becomes 2(-5)³ + 21(-5)² + 60(-5) + 25 > 0, which simplifies to -125 + 525 - 300 + 25 > 0. This is also true, because the left-hand side is 225 > 0.

When x = -12.5, the inequality becomes 2(-12.5)³ + 21(-12.5)² + 60(-12.5) + 25 > 0, which simplifies to -391.25 + 1181.25 - 750 + 25 > 0. This is also true, because the left-hand side is 1147.5 > 0.

Therefore, the solution to the inequality is x ∈ {-0.5, -5, -12.5}. This means that the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5. The inequality is satisfied when x is any of these values.

So far, you proved that one pair of parallel sides in a parallelogram

must be congruent. Add to your proof to prove that both pairs of

parallel sides in a parallelogram must be congruent.


Geometry

Answers

Both the pairs of opposite sides in a parallelogram are parallel and congruent.

According to the question,

We've proved that one pair of sides in parallelogram must be congruent

Let ABCD is a parallelogram ,

We know that AB // CD

Here, AC is transversal for the parallel lines AB and CD

So, ∠BAC = ∠DCA    (Using interior angle property) --------(1)

Similarly , We also know that BC // AD

=> ∠BCA = ∠DAC -----------(2)

Now , In ΔABC and ΔADC,

∠BAC = ∠DCA from (1) AC is common side∠BCA = ∠DAC from (2)

Therefore , ΔABC ≅ ΔADC    (as per ASA congruence rule)

Therefore , AB = CD and BC=AD   (Corresponding sides of congruent triangles are equal)

Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.

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Find the GCF if 8 and 15
A.1
B.2
C.3
D.5

Answers

1 is the greatest common factor of 8 and 15 .

What is GCF ?

GCF stand for greatest common factor.It is a set of numbers is the largest factor that each and all the number share. GCF is also often used to find the common denominator.

First we need to write common factor of each number.

The common factors of 8 = ( 1,2,4,8)

The common factor of  15= (1,3,5,15)

1 is the  only one common factor here which is divides both 8 and 15.

So 1 is the only and GCF of 8 and 15.

Thus, 1 is the right answer.

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josh and dan each want to save $600 to attend a sports camp. josh has saved 60% of the amount. dan $320 .who saved more money?

what number solud you multipluy both sides by to solve for x

Answers

The amount of money that Josh has is more than the amount of money that Dan has.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Josh and Dan each need to save $600 to go to a games camp. Josh around has saved 60% of the amount. Dan has $320.

The amount of money that Josh has is given as,

⇒ 60% x $600

⇒ 0.6 x $600

⇒ $360

The amount of money that Josh has is more than the amount of money that Dan has.

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Step by step please help asap !!!!!!!

Answers

Answer:

3,31

Step-by-step explanation:

i dont got steps for this but i think thats the right answer

Solve the equation for y.
x = 4y-2
y=

Answers

Answer:

Step-by-step explanation:

In someone infected with measles, the virus level N (measured in number of infected cells per mL of blood plasma) reaches a peak density at about t = 12 days (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of N(t) from t = 0 to t = 12 (as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells x time). The function N has been modeled by the function f(t) = -t(t - 21)(t + 1). Use this model with six subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms of measles.

Answers

The total amount of infection needed to develop symptoms of measles is 7840

Consider the model,

N(t)= f(t)=-t(t-21)(t+1).

The area of the graph of N(t) from t=0 to t = 12 is,

N(t)dt

Use six subintervals and their midpoints to estimate the above as follows:

Here, a=0,b=12, n=6

The length of each subinterval is,

h= b-a/n = 12-0/6

=2

So, the midpoints of each subinterval are 1, 3, 5, 7, 9, and 11.

Use Midpoint Rule,

A = [N(t)dt]

= At[ƒ (1) + ƒ (3) + ƒ (5) +ƒ(7)+ƒ(9)+ƒ(11)] =2[40+216+480+784+1080+1320]

= 7840

Thus, the total amount of infection needed to develop symptoms of measles is 7840.

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A cardboard carrying box has the dimensions shown below. How many square inches of cardboard are needed to make the box?

Answers

This is a surface area problem. Find the area of each side. Front/back are 2(12x5), or 2x60, so 120. Left/right are 2(6x5), or 2x30, so 60. Top/bottom are 2(12x6), or 2x72, so 144. Add these 3, 120+60+144=324. The number of square inches of cardboard is 324 square inches. Peace!

A common guideline for constructing a 95% confidence interval is to place upper and lower bounds one standard error on either side of the mean.
True
False

Answers

False. Because a 95% confidence interval is two standard errors on either side of the mean.

What is a 95% confidence interval?

If 100 separate samples were taken and a 95% confidence interval was calculated for each sample, then around 95 of the 100 confidence intervals would contain the actual mean value (), according to the definition of a 95% confidence interval.

For a 95% confidence interval, the value lies within 2 standard deviations of the normal distribution.

For upper and lower bounds one standard error on either side of the mean is 68%.

So, the 95% confidence interval is two standard errors on either side of the mean.

Hence, the given statement is False.

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the european central bank uses main refinancing operations as the predominant form of open market operations, which are similar to the fed's repo transactions.True or False Q4.The 5th term of an arithmetic series is 4k, where k is a constant.The sum of the first 8 terms of this series is 20k + 16(a) (i) Find, in terms of k, an expression for the common difference of the series.(ii) Show that the first term of the series is 16 - 8kGiven that the 9th term of the series is 24, find(b) the value of k,(c) the sum of the first 20 terms. according to social psychologist fritz heider, when we incorrectly believe that a person's behavior is due to their disposition, rather than underlying context, we have committed a . Which of the following is the approximate internal rate of return for an investment that costs $45,880 and has net cash flows of $4,000 for 20 years?Reason: 45,880/4000=11.47. Look at Table B.3 in the 20 year row for the present value factor closest to 11.47. You'll see 6% three disaccharides are important in the human diet: sucrose, lactose, and maltose. click and drag the monosaccharides to build each of the disaccharides below. an older male patinet complains to his nurse that his immediate family doesnt take his health care seiously. which tool might be most heplful in determing the functionality of this family Find the value of c guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6]. Give the net ionic equation for the reaction (if any) that occurs when aqueous solutions of sodium sulfide and iron(II) nitrate are mixed. O Na+(aq) + NO3(aq) - NaNO3(s) O No reaction occurs. OS2-(aq) + Fe2+(aq) FeS(s) O 2 Nat(aq) +52-(aq) + Fe2+(aq) + 2 NO3(aq) 2 Nat(aq) + 2NO3 (aq) + 2 FeS(s) O 2 Na(aq) + 52 (aq) + Fe2+(aq) + 2 NO3 (aq) Fe2+(aq) + 52 (aq) + 2 NaNO3(s) What reason is given for the Railway to be built? in The Ghost and The Darkness what is the best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar? what fundmental changes orrcured in the american political system that allowed the nation to become more democratic by 1840 what can joseph do to increase his chances of ats selection? check all that apply. focus on adjectives like efficient, reliable, and personable. use variations of the job title. concentrate on the skills section. group keywords together in a summary. use terms from the posted job advertisement or job description. alpha polonium crystalizes in a simple cubic unit cell with an edge length of 336 pm. whatis the density of alpha polonium (in g/cm^3)? In 2015, the United States:A. imported more services than it exported.B. imported more goods than it exportedC. traded mainly with developing nations such as Mexico and India.D. had a small trade surplus in goods and services. find the mass of aluminum requried to produce 1.32 l of hydrogen gas at stp from the single replacement reaction of aluminum and sulfuric acid The following problem refers to a geometric sequence:If a1= 5 and r = 3 find anan=___ Use the AS-AD model below to answer the following questions. In each case assume the economy starts in long- and short-run equilibrium. Suppose a revolution in Iran results in a significant reduction in the world's supply of oil. Drag the appropriate line in the correct direction to show the short-run effect on the AS-AD model. This will: Suppose the government takes no action to help the economy. Suppose, instead, the government decides to take action to help the economy. You can recommend: If the U.S. government makes the appropriate policy response, what happens to price levels and output in the long run. in linear programming, what are restrictions that limit the degree to which a manager can pursue an objective? part 2 a. constraints b. resource rules c. gatekeepers d. limitations the value of the marginal product is found by multiplying the marginal of labor by the market of the product. What volume of 12 gas forms when 21 L Cl2 react at STP?