A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is _____ (Hours,Miles,Mph) Simplify your answer.

Answers

Answer 1

Answer:

The speed of the plane in still air is 590Mph

The speed of the wind is 60Mph

Step-by-step explanation:

Let

s= the speed of the plane in still air

w= the speed of the wind

Flying with the wind:

5525=(s+w)*8.5

5525=8.5s + 8.5w (1)

Flying against the wind:

4505=(s-w)*8.5

4505=8.5s - 8.5w (2)

Add (1) and (2) to eliminate w

5525=8.5s + 8.5w

4505=8.5s - 8.5w

10,030=17s

Divide both sides by 17

10,030/17=17s/17

590=s

s=590Mph

Substitute the value of s into (1)

5525=8.5s + 8.5w

5525=8.5(590) + 8.5w

5525=5,015 + 8.5w

5525-5015=8.5w

510=8.5w

Divide both sides by 8.5

60=w

w=60Mph

The speed of the plane in still air is 590Mph

The speed of the wind is 60Mph


Related Questions

Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. If they start at the same position, chosen at zero, and bike in straight opposite directions, what will the distance between them be after 45 minutes?

Answers

Answer:

45 minutes is 3/4 of an hour, so find 3/4 of 12.  

Divide 12 by 4 to get 1/4 of 12. That is 3.  

3/4 is 3 of those, so multiply it by 3 to get 9.

So, she will have biked 9 miles.  

Answer:

180 miles.

Step-by-step explanation:

First, we have to find out how far Claire is after 45 minutes:

12 x 45 = 540

Now, we need to find out how far Han is after 45 minutes:

8 x 45 = 360

Lastly, we need to subtract how far Claire went by how far Han went:

540 - 360 = 180

Final answer:

The distance between Claire and Han after 45 minutes will be 180 miles.

Hope this helped! Have a nice day!

If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105

Answers

Answer:

  z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

  y = kxz

We can find k from the given values.

  40 = k(10)(9)

  40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

  y = (4/9)xz

  9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

  z = 9·105/(4·55)

  z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)

Find an equation of variation where y varies jointly as x and the square of z, and where y=70, when x=21 and z=5.

Answers

Answer:

[tex]y = 181.75xz^2[/tex]

Step-by-step explanation:

Given

y jointly varies to x and z^2

Required

Find the equation

We start by writing out the variation;

[tex]y\ \alpha\ xz^2[/tex]

Write as equation

[tex]y = kxz^2[/tex]

Substitute values of x,y and z

[tex]70 = k * 21 * 25^2[/tex]

[tex]70 = k * 21 * 25 * 25[/tex]

[tex]70 = k * 13125[/tex]

Divide both sides by 7

[tex]\frac{70}{13125} = \frac{k * 131251}{13125}[/tex]

[tex]\frac{70}{13125} = k[/tex]

[tex]187.5 = k[/tex]

[tex]k = 181.75[/tex]

Substitute k in [tex]y = kxz^2[/tex]

[tex]y = 181.75xz^2[/tex]

Find the table with unit rates greater than the unit range in the graph. Then arrange these tables in order from least to greatest unit rate?

Answers

Answer:

Except table 2, all tables have greater unit rate than the graph.

The required arrangements of tables is  

Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6

Step-by-step explanation:

Formula for unit rate :

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rat of graph is

[tex]m=\dfrac{20-0}{11-0}=1.8181...[/tex]

Similarly, we need to calculate the unit rate for each table.

[tex]m_1=\dfrac{26-13}{14-7}=\dfrac{13}{7}=1.85714[/tex]

[tex]m_2=\dfrac{18-9}{10-5}=\dfrac{9}{5}=1.8[/tex]

[tex]m_3=\dfrac{34-17}{18-9}=\dfrac{17}{9}=1.88..[/tex]

[tex]m_4=\dfrac{42-21}{22-11}=\dfrac{21}{11}=1.9090..[/tex]

[tex]m_5=\dfrac{38-19}{20-10}=\dfrac{19}{10}=1.9[/tex]

[tex]m_6=\dfrac{50-25}{26-13}=\dfrac{25}{13}=1.923[/tex]

[tex]m_7=\dfrac{46-23}{24-12}=\dfrac{23}{12}=1.9166..[/tex]

Except table 2, all tables have greater unit rate than the graph.

The required arrangement of tables is  

Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6

Answer:

table 3 table 5 table 4 table 7 table 6

Step-by-step explanation:

I just took the test


Liam is making chocolate chip cookies. The recipe calls for 1 cup of sugar for every 3 cups of flour. Liam only has 2 cups of flour.
​How much sugar should Liam use?
Explain why your answer is correct.

Answers

Answer:

2/3 cups of sugar

Step-by-step explanation:

Answer:

2/3 cups of sugar

Step-by-step explanation:

If 3 cups of flour: 1 cup of sugar

2 cups of flour: x cup of sugar

Cross multiply

3x = 2 × 1

3         3

x = 2/3

My answer is correct because every 3 cups of flour is a full cup (1) but because he has 2 cups of flour, the cup of sugar is going to be less than 1 because 3 cups of flour is bigger than 2 cups of flour.

Please answer both questions

Answers

Answer:

which question......

m to the b gimme gimme points :3

What is the length of the diagonal of a TV that measures 2.25 feet high and 4 feet wide?

Answers

Answer:  Rounded, the diagonal is 4.6 feet

Step-by-step explanation: Use the Pythagorean Theorem:  c² = a² + b²

Then take the square root of c² to find the length

2.25² =5.0625  This is a²

4² = 16  This is b²    Add a² + b²  to get c²

5.o625 + 16 = 21.0625 This is c²

√21.0625 = 4.589389938 This is the square root.

Round this to common measurements or "significant digits"  4.6 feet.

Plz help me with the hw I do not have points please help me please I will give you the questions and send it on the comment -4=-1/8e

Answers

Answer:

32

Step-by-step explanation:

-4=-1/8e

multiply both sides by -8

-8(-4)=-1/8(-8)e

32=e

Answer:

-32

Step-by-step explanation:

1/8 x8/1=1, so you would also multiply -4 by 8 and get -32

Guess the rule and write down the missing number: 1 5 6 11 _ 28

Answers

Answer:

1 5 6 11  17 28

Step-by-step explanation:

Hi there! :)

Answer:

17 is the missing number.

Step-by-step explanation:

The rule is to add the previous two numbers together to get the next number. For example:

1 + 5 = 6

5 + 6 = 11

Using this rule to solve for the missing number gets us:

6 + 11 = 17

We can check this work as well:

11 + 17 = 28.

Therefore, 17 is the missing number.

ASAP PLZZZ Find the area of the shaded polygons:

Answers

Step-by-step explanation:

You can use the Pick's theorem:

[tex]A=i+\dfrac{b}{2}-1[/tex]

where

i - number of lattice points in the interior located in the polygon

b - number of lattice points on the boundary placed on the polygon's perimeter

[tex]1.\\i= 5;\ b=12\\\\A=5+\dfrac{12}{2}-1=5+6-1=10\\\\2.\\i=3;\ b=4\\\\A=3+\dfrac{4}{2}-1=3+2-1=4\\\\3.\\i=5;\ b=10\\\\A=5+\dfrac{10}{2}-1=5+5-1=9[/tex]

Answer:

Of course, the Pick's theorem is the way to solve this question, but consider:

Another approach is using topography:

Gauss's Area Calculation Formula:

[tex]$A=\frac{1}{2} \sum_{i=1}^{n} (x_{i} \cdot y_{i+1}-y_{i} \cdot x_{i+1})$[/tex]

Taking the purple one:

We have 6 points. I will name them:

[tex]A(0, 4);B(0, 0);C(1, 1);D(4, 0);E(4, 4);F(1, 2);[/tex]

[tex]$D=\begin{vmatrix}0& 0& 1 & 4& 4 & 1 & 0\\ 4& 0 & 1 & 0& 4 & 2 & 4 \end{vmatrix}$[/tex]

[tex]D=28-8=20[/tex]

[tex]$A=\frac{20}{2} =10$[/tex]

Help help help help
Plz

Answers

Answer:

Step-by-step explanation:

Probability of getting any number less than 6 = 2/6 =1/3

So, It is unlikely

Answer:

2/6 or 1/3

Step-by-step explanation:

the two umbers less than 6 or 2 and 4. In total on the dice there is 6 numbers. so 2/6 is tha answer and then we spimlify

If a store is selling packs of gum at 3 for $0.99, how much would 12 packs cost?

Answers

Answer:

$3.96.

Step-by-step explanation:

3 cost $0.99, so 12 packs would cost 12/3 = 4 times as much.

0.99 * 4 = 3.96.

12 packs would cost $3.96.

Hope this helps!

Hello! The answer will be below! :3

The answer to your question is 3.96.

Because we have to take the info that’s given like we first have to divide.

12 divided by 3 is 4

Now we multiply.

0.99 * 4 = 3.96

So the answer is 3.96

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Using a System to Break Even

A company’s weekly revenue, in thousands, is modeled by the equation R = -p2 + 14p, where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.


Part B
Create a system of equations for the break-even point(s) of the company’s product to assist with the decision of hiring the distributor. Assume the distributor’s cost is the only cost that needs to be considered.

Answers

Answer: P^2 - 10p + 24 = 0

Step-by-step explanation:

Given that a company’s weekly revenue, in thousands, is modeled by the equation

R = -p2 + 14p,

where p is the price of the product it makes. The company is considering hiring an outside source to distribute its products, which will cost the company 4p + 24 thousand dollars per week.

If the company want to break even, the cost of hiring distributors will be equal to the revenue per week.

Therefore,

-P^2 + 14p = 4p + 24

Collect the like terms

-P^2 + 14p - 4p - 24 = 0

-P^2 + 10p - 24 = 0

Multiply all by minus sign

P^2 - 10p + 24 = 0

Determine the quotient. Write your answer in scientific notation.
(8.4 * 10%) + (1.2 x 102)

Answers

Answer:

0.84+122.4x is your answer. hope this helped

Step-by-step explanation:

0.84+122.4 i believe is the correct answer

What is (12!) - (10!)?

Answers

Answer:

step 1

12! =479001600

step2

10!=3628800

step 3

479001600-3628800=

475372800

Can someone answer a-c please!

Answers

Okay

Here an example for factoring the zero

A. X^2+x -20=0

(X+3) (x-4)=0

X+3=0 X-4=0

X=-3 Or x= 4


Here an an example for quadratic form


X-2=0

Formula for quadratic form is

Ax^2 +bx +c =0

Discriminant =b^2 -4ac


0^2 -4(1)(-2)=8

So 8 is not perfect square


Here we a solution

X= -b+-√b^2-4ac/2a

X= -0+_ √0^2-4(1)(-2)/2(1)


X=-0+_ √8/2

X= +_2 √2/2

Cancel 2

+_ √2



And last question which one you prefer so you can choice any


Hopefully this help you :)


Please solve for x and y. If you do, also write the steps you used.

Answers

Answer: a = 8, x = 56, y = 68

Step-by-step explanation:

Was there a description that stated this was a parallelogram?

Since that information was not provided....

I used the Law of Cosines to find x = 56°.

Congruent sides implies congruent angles so Center-Q-R = 56°.

Triangle Sum Theorem results in y = 68°

Vertical angles results in S-Center-P = 68°

Triangle sum Theorem results in S-P-Center = 68°

Now we can see that alternate interior angles are congruent, therefore PQRS is a parallelogram. Diagonals are bisected at the intersection so a = 8

Rewrite the formula to determine the number of tickets they need to sell

Answers

Answer:

n = [tex]\frac{p}{(d-c)}[/tex]

Step-by-step explanation:

The goal is to solve for n meaning n needs to be by itself. In the current formula, n is multiplied by (d-c). Get n by itself by dividing both sides by (d-c).

Which of the following graphs represents the equation below? y= 0.666667x + 3

Answers

Answer:

the last graph

Step-by-step explanation:

the y intercept is clearly shown as three and then using rise over run you can see that the slope is 2/3 or 0.667

Hiroto paid $4.28 in sales tax for the items that he purchased.


Percents
Total
















100%



































If the sales tax rate was 6.25 percent, what was the total cost of the items before tax was added?
$0.27
$0.68
$26.75
$68.48

Answers

Answer:

  $68.48

Step-by-step explanation:

You want to find cost such that ...

  6.25% × cost = $4.28

Dividing by the coefficient of cost, we get ...

  cost = $4.28/0.0625 = $68.48

Answer:

the answer would be 68.48

Step-by-step explanation:

help me plz on this i just need the answer Use the given parent function f(x)=|x| to graph g(x)=|x|+5. Use the ray tool and select two points to graph each ray.

Answers

Answer:

no

Step-by-step explanation:

the answer is no because the quantum formula states that a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states.

in 50 gram portion of cereal 8 grams of it are sugar which of the following represents the present of the 50 grams that is sugar
a)4
b)8
c)16
d)24

Answers

Answer:

C

Step-by-step explanation:

8/50= 0.16

Answer:

C = 8/50 = 0.16 * 100 = 16

Step-by-step explanation:

In your own words, what does it mean when something has an extrinsic value? What is an
example of an item having extrinsic value?
Answer using complete sentences.​

Answers

Answer:

Extrinsic value means to have the motivation or desire to do something by yourself. To have the motivation to complete a task or goal without outside help.

Step-by-step explanation:

One way of having extrinsic value is that you go to school and you want to go to Germany. Your school fortunately has a student exchange program, so you apply hoping that you get in.

Now you go home, you get the best grades so people recognize you. You teach yourself German and you do all the things that you need to do in order to go.

What makes this extrinsic is that no one forced you to go, you did all this work by will. Your own motivation.

Use the Venn diagram to list the elements of the set in the roster form

Answers

Answer:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Step-by-step explanation:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

If Triangle Q S R is congruent to triangle Y X Z describes two triangles, which other statement is also true? A: Triangle Q R S is congruent to Triangle X Y Z // B: Triangle Q R S is congruent to Triangle Y Z X // C: Triangle Q R S is congruent to Triangle Z X Y // D: Triangle Q R S is congruent to Triangle X Z Y

Answers

Answer:

ANSER  IS B FIRST IS INCORRECT

Step-by-step explanation:

The true statement:

ΔQRS ≅ ΔYZX.

Triangle QRS is congruent to Triangle YZX.

The correct option is C.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

Triangle QSR is congruent to triangle YXZ.

ΔQSR ≅ ΔYXZ.

From the given choices:

The correct order of the congruent triangles.

ΔQRS ≅ ΔYZX.

Therefore, ΔQRS ≅ ΔYZX.

To learn more about the congruent;

https://brainly.com/question/12413243

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Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone in 90 minutes. Richie’s brother slept in one day, leaving Richie to deliver alone for 30 minutes. How long must the two of them work together to finish delivering the newspapers?

Answers

Answer

30 minutes

Step-by-step explanation:

Answer: approximately 26.66667  minutes

This converts to 26 minutes, 40 seconds

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

Explanation:

Let's say there are 360 newspapers that need to be delivered.

The two brothers can get the job done in 40 minutes if they work together. Their rate is 360/40 = 9 newspapers per minute.

Richie can do the full job alone in 90 minutes. So his rate would be 360/90 = 4 newspapers per minute. In 30 minutes, he delivers 30*4 = 120 newspapers. This leaves 360 - 120 = 240 left over.

Divide this over the rate of 9 papers per minute to get 240/9 = 26.66667 approximately. It takes about 26.66667 minutes to finish up delivering the 240 remaining newspapers if the brothers work together.

The portion 0.66667 multiplies with 60 to get 0.66667*60 = 40.0002 which rounds to 40 (we have rounding error going on). This means

26.66667 minutes = 26 minutes, 40 seconds

Use the De Morgan law that states: ~(p ∧ q) is equivalent to ~ p ∨ ~ q to write an equivalent English statement for the statement. It is not the case that a gun and a nose are both weapons. A gun is not a weapon or a nose is not a weapon. guns are not noses. A gun is a weapon but a nose is not. A gun is not a weapon and a nose is not a weapon.

Answers

Answer:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Step-by-step explanation:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

The equivalent statement for the given statement -  It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.

What is De Morgan's Law?

The De Morgan's law states that → ~(p ∧ q) is same as (~ p ∨ ~ q). Theoretically, we can write it as → Not (A and B) is the same as Not A or Not B.

Given is the following statement - It is not the case that a gun and a nose are both weapons.

Now, we know that the De Morgan's law states that → Not (A and B) is the same as Not A or Not B. In the statement given -

A = gun

B = nose

~(p ∧ q) = Not(A ∧ B)

So, we can write it as -

~(p ∧ q) =  Not(A ∧ B) = A gun is not a weapon or a nose is not a weapon.

where -

A gun is not a weapon → ~p

or →

a nose is not a weapon → ~q

Therefore, the equivalent statement for the given statement -  It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.

To solve more questions on De Morgan's Law, visit the link below-

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Write an ordered pair for each point graphed below.

Answers

Answer:

[tex]\boxed{(-1,4)}[/tex]

Step-by-step explanation:

The point is located in Quadrant II of the graph, where x-values are negative and y-values are positive.

Each marking on the graph represents one unit of distance. The two axes meet at the origin, where the coordinate point is equal to [tex](0,0)[/tex].

So, you can count backwards once from the origin to get your x-value ⇒ [tex]-1[/tex] and count up upwards four times from [tex]x=-1[/tex] to get your y-value ⇒ [tex]4[/tex].

Finally, place these in a coordinate point [tex](x,y)[/tex] ⇒ [tex]\boxed{(-1,4)}[/tex].

Answer:

(-1, 4)

Step-by-step explanation:

The point lies on the line x = -1.

The point lies on the line y = 4.

Where both lines intersect, that is the coordinate.

(x, y)

(-1, 4)

Bert’s cab company charges $1.00 plus an additional $3.00 per mile for a ride. Madeline’s cab company charges $3.00 plus an additional $2.00 per mile for a ride. Write a system of linear equations that shows the cost in dollars, y, for a cab ride of x miles for each cab drive At what distance, in miles, will the cost be the same for both companies? Show your work

Answers

Answer: (2,7) at 2 miles they both will cost $7


BERT
y=1+3x

MEDELINE
y=3+2x

LINEAR EQUATION
1+3x=3+2x
-2x both sides
1+x=3
-1 both sides
x=2

y=1+3(2)
multiply 3*2
y=1+6
y=7

i hope it’s correct <3 comment if any questions ;)

1. What solid is represented by this net? (Image 1). A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid 2. Choose all the solids from the list below. A. Rectangle B. Circle C. Cone D. Pyramid E. Prism F. Cylinder 3. The volume of the following figure = ___________ cm3. (Image 2) A. 288 B. 72 C. 216 D. 144

Answers

Answer:

1) TRIANGULAR PRISM

3) d. 144 cm3

Step-by-step explanation:

1) When figuring out what shape a net is, look at the two shapes that are different. In this case, its the triangles. Then take a look at the other shapes. If it has a rectangle base then you know its a prism. If it has a different shpes base then you know its pyramid. Now just combine the two key words you found. Triangle + Prism = Triangular Prism

2) A solid is something that is firm and stable. So it is not a liquid or solid. Pretty much everything that you listed is a solid.

3) The formula for finding the volume of a triangular prism is bxhxl divided by 2. So it would be 8x3x12= 288 divided by 2= 144 cm3

Answer:

Triangular prism.

Step-by-step explanation:

Other Questions
Find the slope of the line that passes through (1, 14) and (4,9)Which two numbers in the points represent y values? Select both in thelist 1)Determine que accin realiza la funcin definida como: f(x) = -7x - 7 a) Multiplica la variable independiente por -7 y luego resta 7 b) Multiplica la variable independiente por 7 y luego resta 7 c) Multiplica la variable dependiente por -7 y luego resta -7 d) Multiplica la variable dependiente por -7 y luego resta -7 2)Dada la funcion F(x) = -3x + 6 el valor de F(5) es 2. A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is A) more than the total kinetic energy of the cylinder. B) less than the total kinetic energy of the cylinder. C) equal to the total kinetic energy of the cylinder. If the car decelerates uniformly along the curved road from 27 m/s m/s at A to 13 m/s m/s at C, determine the acceleration of the car at B Please Help!!!Family Size. You selected a random sample of n = 31 families in your neighborhood and found the mean family size for the sample equal to 3.1, the standard deviation for the sample is 1.42? What is the 90% confidence interval for the estimate? Which of the following are reasons that Globalization has occurred?O AImprovements in shipping and air cargo have driven down transportation costsB. Innovations in computing and telecommunicationsC.Barriers that are created by different currencies have been liftedODinternational agreements and treaties between countries have encouraged greater trade. What's the difference between velocity time graph and distance time graph Which is the biggest lake in nepal? 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If you dont know the exact location, you can use your imagination. You just need to show you can give directions. a.Le nom de votre village natal / ville natale.b: L o se trouve le village natal / la ville natale.c. Le nom de march de votre village natal/ville nataled. Comment est le march?e. Le jour de march de votre village natal / ville natalf. Que font les gens pendant le jour de march?g. L'heure ou le march commence.1. Comment devient le village pendant le jour de mLes marchandises qu'on vend et chete au journatal/ville natale.ur anneler les achete Which one doesnt belong? Why? Explain. A client has made the decision to leave her alcoholic husband. She is feeling very depressed. Which nontherapeutic statement by the nurse conveys sympathy A perfectly competitive firm sells 15 units of output at the going market price of $10. Suppose its average fixed cost is $15 and its average variable cost is $8. Its contribution margin (i.e., contribution to fixed cost) is explain relative velocity. The heat of vaporization delta Hv of dichloromethane (Ch2CL2) is 28.0 kJ/mol . Calculate the change in entropy delta S when 473 g of dichloromethane boils at 39.8 degree. Genent Industries, Inc. (GII), developed standard costs for direct material and direct labor. In 2017, GII estimated the following standard costs for one of their major products, the 30gallon heavyduty plastic container. Budgeted quantity Budgeted price Direct materials 0.3 pounds $20 per pound Direct labor 0.7 hours $20 per hour During July, GII produced and sold 4,000 containers using 1,500 pounds of direct materials at an average cost per pound of $17 and 2,875 direct manufacturing labor hours at an average wage of $20.50 per hour. July's direct material flexiblebudget variance is ________. An Article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the familys financial situation, 37% would like to talk about school, and 30%would like to talk about religion. These and other sampling were based on 522 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. Express the answer in the form P hat+- E Describe the key elements of the Second Great Awakening. P(x) has factors (x-2), (x+1), and (x-3). Decide if there is only one polynomial that has these factors. Justify your answer. Question 3 of 10Whichtypeofenergy works by removing electrons from atoms to produceelectricity?A. WindB. SolarC. GeothermalD. Nuclear