Alexa Alexa brought 32 apples for $4.16 at the rate what 1 Apple cost​

Answers

Answer 1

Answer:0.13

Step-by-step explanation:i think

Answer 2

The cost of each apple is given by the rate. Then the cost of each apple will be $0.13 per apple.

What is the rate?

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Alexa brought 32 apples for $4.16.

Then the cost of each apple rate will be given as,

Rate = $4.16 / 32

Rate = $0.13 for each apple

The cost of each apple is given by the rate. Then the cost of each apple will be $0.13 per apple.

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Related Questions

find the area and perimeter of the rectangle with vertices (4, -7), (-3, -7), (-3, 3), and (4, 3).​

Answers

Answer:

Area:  42

Perimeter = 26

Step-by-step explanation:

Distance from (4,-7) to (-3,-7) = 7

Distance from (-3,-7) to (-3,3) = 6

These are the length and width of the rectangle.

Area: 7 * 6 = 42

Perimeter = 2*(7+6) = 26

945 divided by 6.6
[tex]945 \div 6.6[/tex]

Answers

143.1818 is the answer

Answer:

143.1818

Step-by-step explanation:

Solve the inequality. Graph the solution.
6n < 90

Answers

Answer:

any number less than 15 will work n<15

Step-by-step explanation:

I divided the 6n so I could do 90/6 then equals 15=n so if I do 6 times 15 it would be 90 so that would no be true 90<90 so that means n has to be less than 15

n<15

in a parallelogram wxyz, wxy= 72 degrees, zwy= 80 degrees.Calculate

a- wzy

b- xwz

c - wyz​

Answers

Answer:

Part a) m∠WZY=72°

Part b) m∠XWZ=108°

Part c) m∠WYZ=28°

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

see the attached figure to better understand the problem

Part a) Find the measure of angle WZY

we know that

m∠WZY≅m∠WXY ----> by opposite angles

we have

m∠WXY=72°

therefore

m∠WZY=72°

Part b) Find the measure of angle XWZ

we know that

m∠XWZ+m∠WXY=180° ----> by consecutive angles

we have

m∠WXY=72°

substitute

m∠XWZ+72°=180°

m∠XWZ=180°-72°

m∠XWZ=108°

Part c) Find the measure of angle WYZ

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

In the triangle WZY

m∠ZWY+m∠WZY+m∠WYZ=180°

we have

m∠ZWY=80°

m∠WZY=72°

substitute

80°+72°+m∠WYZ=180°

152°+m∠WYZ=180°

m∠WYZ=180°-152°

m∠WYZ=28°

In a parallelogram, finding angles involves rules like opposite angles being equal and adjacent angles being supplementary. wzy = 72 degrees, xwzc = 80 degrees, and wyz = 108 degrees.

Given:

wxy = 72 degrees

zwy = 80 degrees

To find:

wzy: Opposite angles in a parallelogram are equal, so wzy = wxy = 72 degrees

xwzc: Opposite angles in a parallelogram are equal, so xwzc = zwy = 80 degrees

wyz: Adjacent angles in a parallelogram are supplementary. Therefore, wyz = 180 - wxy = 180 - 72 = 108 degrees

Betty has $15 to buy plants for her greenhouse. Each plant costs $6. How
many plants can she buy? Do not include units in your answer.

Answers

Answer:

2

Step-by-step explanation:

If 15 dollars is what she has. you take 6 for one plant away from that 15 to become 9. Then she can buy one more. 2 plants now for 12 dollars. since she only has 3 left, she can't buy another.

Answer:

the answer to your qestoin is 2

please help wit all the questions!! leave explanation below thanks!

Answers

Answer:

4. The relationship is proportional because, for every 12 students, there is one chaperone and when you multiply 12 by the number of chaperones you get the same numbers that the table shows.

1. the relationship is proportional.

45/1= 45

45/2 = 90

45/3 = 135

45/3 = 180

2. the constant of 2 is 10. the constant of 3 is 2.

the relationship between x and y is that x divided by y equals the constant.

4. x divided by y equals the constant, or

x÷y=c(constant)

hope that helps and sorry for taking so long

Choose the answer that best translates
the algebraic expression below.

9a


9 more than a number
9 less than a number
9 times a number
9 divided by a number

Answers

Answer:

9 times a number

Step-by-step explanation:

If a number and a variable are next to each other, you multiply.

Write an equation in slope-intercept form of the line that passes through (6,-2) and (12,1)

Answers

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

[tex]y =\frac{1}{2}x-5[/tex]

Step-by-step explanation:

Given points are:

(x1,y1) = (6,-2)

(x2,y2) = (12,1)

The slope intercept form is:

[tex]y=mx+b[/tex]

We have to find the slope first

[tex]m =\frac{y_2-y_1}{x_2-x_1}\\=\frac{1-(-2)}{12-6}\\= \frac{1+2}{6}\\=\frac{3}{6}\\=\frac{1}{2}[/tex]

Putting the value of slope

[tex]y = \frac{1}{2}x+b[/tex]

To find the value of b, putting (12,1) in the equation

[tex]1 = \frac{1}{2}(12)+b\\1 = 6+b\\b = 1-6\\b=-5[/tex]

Putting the values of m and b

[tex]y =\frac{1}{2}x-5[/tex]

Hence,

Equation in slope-intercept form of the line that passes through (6,-2) and (12,1) is:

[tex]y =\frac{1}{2}x-5[/tex]

Keywords: Equation of line, slope-intercept form

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Final answer:

To write the equation in slope-intercept form, find the slope and y-intercept using the given points. The slope is 1/2, and the y-intercept is -5. The equation is y = (1/2)x - 5.

Explanation:

To write an equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The slope can be calculated using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the slope is (1 - (-2)) / (12 - 6) = 3/6 = 1/2.

Now, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we get y = (1/2)x + b.

To find the value of b, we can substitute the coordinates of one of the given points (6, -2) into the equation. -2 = (1/2)(6) + b. Solving for b, we get b = -2 - 3 = -5.

Therefore, the equation in slope-intercept form of the line that passes through (6, -2) and (12, 1) is y = (1/2)x - 5.

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A ball is thrown vertically upward from the ground with an initial velocity of 122 ft/sec. Use the quadratic function
h(t) = -16t2 + 122t +0 to find how long it will take for the ball to reach its maximum height, and then find the
maximum height. Round your answers to the nearest tenth.

Answers

Answer:

232.6 metres after 3.8 seconds.

Step-by-step explanation:

h(t) = -16t² + 122t

a = -16  b = 122  c = 0

Substitute into the quadratic formula

(Ignore the Â)

[tex]x =  \frac{-b±\sqrt{b^{2}-4ac}}{2a} [/tex]

[tex]x =  \frac{-122±\sqrt{122^{2}-4(-16)(0)}}{2(-16)} [/tex]

[tex]x =  \frac{-122±122}{-32} [/tex]

Split the equation at the ±

[tex]x =  \frac{-122+122}{-32}[/tex]        [tex]x =  \frac{-122-122}{-32} [/tex]

[tex]x =  \frac{0}{-32}[/tex]                    [tex]x =  \frac{-244}{-32} [/tex]

[tex]x = 0[/tex]                                       [tex]x = \frac{61}{8}[/tex]

The two x-intercepts at 0 and 61/8. The midpoint of the x-intercepts is the axis of symmetry, which is the x-coordinate of the vertex.

Midpoint = [0 + (61/8)] / 2

Midpoint = 61/16   <= This is the time for maximum height

t = 61/16

t = 3.8125  => Round to t = 3.8

To find the maximum height, substitute t=61/16 into the equation

h(t) = -16t² + 122t

h(61/16) = -16(61/16)² + 122(61/16)

h(61/16) = 232.5625  => Round to h = 232.6

Therefore, the ball will reach the maximum height of 232.6 metres after 3.8 seconds.

lauren planted 20 flowers, but her neighbors dog ate 7 of them. what percent of the flowers did the dog eat​

Answers

35 percent got eaten.

To solve: you’d take the number of flowers eaten, 7. And you’d divide it by the overall number, 20. Then you’d get 0.35, which would be your percent.

4p+10=p-14 what is the solution and how do you check the solution

Answers

Answer:

p=-8

Step-by-step explanation:

Its on the picture

-3x+3y=9 2x−7y=−14 ​

Answers

X equals negative 1.4 and y equals 1.6.
Work shown in photo and answers were checked in calculator.

realize the following operations in order for the response to be in a+bi:

[tex] \frac{4 + 2i}{1 - 3i} [/tex]

Answers

Answer:

(7i-1)/5

Step-by-step explanation:

(4+2i)/(1-3i)

the opposite of 1-3i is 1+3i

multiply that

[(4+2i)(1+3i)]/[(1-3i)(1+3i)]

=[(4+2i+12i+6i^2)]/[(1-3i+3i-9i^2)]

=[(4+14i+6(-1))]/[(1-9(-1))]

=(4+14i-6)/(1+9)

=(-2+14i)/10

factor out the 2,

[-2(1-7i)]/10

-(1-7i)/5

(-1+7i)/5

(7i-1)/5

Remember that i^2=-1, because sqrt(-1)*sqrt(-1)=-1.

(30 POINTS) see image and evaluate

Answers

Answer:

1/400

Step-by-step explanation:

i put it in the calculator and got 1/400

Answer:

I believe it's 1/400 or 0.0025

WILL POSSIBLY MARK BRAINLIEST IF GOOD ANSWER!!!

The table shows the number of desks in each classroom
at three different schools. Which expressions represent the total number of desks? Select all that apply.



Thanks**!​

Answers

Answer:

Hahahahahaha how we Answer without any options

Answer: a, c, and d

Step-by-step explanation:
for anybody that needs it now ^^

it says the total number of all the desks from all classrooms and schools
a. 2 x (12 x 35) + 15 x 20) -- correct

b. 2 x (12 + 12 + 15) -- incorrect

c. (2 x 12) x 25 + 15 x 20 -- correct

d. 15 x 20 + (2 x 12) x 25 -- incorrect

why is b incorrect?
b says 2 times 12 + 12 + 15 --- 2 x (12 + 12 + 15) only shows two times the number of classrooms -- not the total number of desks from each classroom in each school (i cant english im sorry)

Tyler is going on a hiking trip . At the end of the first day he has 5,250 feet left to climb . He plans to climb 500 feet each day

Answers

Answer:

12 days

Step-by-step explanation:

At the end of the first day he has the distance left to climb = 5,250 feet

He plans to climb the distance each day = 500 feet

Number of days to complete his trip = [tex]\frac{5,250}{500}[/tex]

                                                             = 10.5 ≈ 11 days

He has already climbed for one day, so he will finish his trip in 1 + 11  = 12 days.

Solve the system of equations:

3x + 2y = 4

3x + 6y = -24

I'm really confused on how to solve these types of problems! I was wondering if you can explain this to me.

Answers

The solution of the system of equations is (6 , -7)

Step-by-step explanation:

There are two method to solve the system of equations

Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variableSubstitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

3x + 2y = 4 ⇒ (1)

3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

-3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

x = 6

The solution of the system of equations is (6 , -7)

I hope this explanation help you

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What is 3y+4+3y-6=34​

Answers

Answer:

Y=10

Step-by-step explanation:

Answer: y

=

6

Hopefully this helps!

the number 42,__2 rounded to the hundred place is 42300. what is the least possible sum of the two missing digits? justify your answer.

Answers

Least possible sum of missing digits is 3 that is 3 + 0 and missing numbers are 30

Solution:

Given that number 42,__2 rounded to the hundred place is 42300 .

Need to determine least possible sum of the two missing digits.

first lets see what all numbers can be rounded to 300  

number from 251 to 349 can be rounded to 300 as 251 is more close to 300 than 200 and 349 is closer to 300 than 400.  

But in our case at ones place we are having 2 , so possible numbers having 2 at ones place and in between  251 to 349 are 252 , 262 , 272 , 282 , 292 , 302 , 312 , 322 , 332  and 342.

but we are only concern numbers at hundred and tens place

so now we have 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 and 34.  

Out of this set we want numbers whose sum is least . So if you carefull observer that number is  30 having least sum as 3 + 0 = 3 .

So missing numbers in 42,__2 is 30 and number is 42,302.

Hence we can conclude that least possible sum of missing digits is 3 that is 3 + 0 and missing numbers are 30.

What is the median of $9.84, $11.75, $12.50, $12.98, $13.88

Answers

Answer: $12.50

Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.

To find the median of these numbers, let's start by writing our data set from least to greatest.

$9.84, $11.75, $12.50, $12.98, $13.88

So the median will be the middle number or $12.50.

The median is the middle number of a data set.

$9.84, $11.75, $12.50, $12.98, $13.88

If their isn't a perfect middle number then you take 2 middle numbers and find the number that is between them.

________

Best Regards,

Wolfyy :)

What is the sum of the solutions of x2 + 9x + 20 = 0?



What is the product (or multiplication) of the solutions of 6x2 + 7x = 3?

Answers

Answer:

Sum of the solutions of [tex]x^2+9x+20=0[/tex] is -9.

Product of the solutions of [tex]6x^2+7x=3[/tex] is [tex]-0.50[/tex]

Step-by-step explanation:

1. [tex]x^2+9x+20=0[/tex]

Given:

The expression whose sum of the solution is required is given as:

[tex]x^{2} +9x+20=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the sum of the solutions is given as:

Sum = [tex]\frac{-b}{a}[/tex]

Here, [tex]a=1,b=9,c=20[/tex]

Therefore, the sum of the solutions = [tex]-\frac{9}{1}=-9[/tex]

2. [tex]6x^2+7x=3[/tex]

Rewriting the above equation in a standard quadratic equation, we get:

[tex]6x^2+7x-3=0[/tex]

For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the product of the solutions is given as:

Product = [tex]\frac{c}{a}[/tex]

Here, [tex]a=6,b=7,c=-3[/tex]

Therefore, the product of the solutions = [tex]\frac{-3}{6}=-0.50[/tex]

A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6
each and four-topping pizzas that cost $10 each. They order c cheese pizzas and f four-topping pizzas.
Which expression represents the total cost of all the pizzas they order?

Answers

The cheese pizzas is $6.00 each. The four-topping pizzas are $10.00 each.

The expression would be $6c + $10f because the c and f are variables and the variables stand for the amount of pizzas they ordered.
Final answer:

The total cost of all the pizzas that the softball team order can be calculated as 6c + 10f, where c represents the number of cheese pizzas ordered, and f represents the number of four-topping pizzas ordered.

Explanation:

To determine how much the softball team is spending on pizzas, we need to multiply the cost of each type of pizza by the number of each type they are ordering. For the cheese pizzas, that cost $6 each, the cost will be:
6c (where 'c' is the number of cheese pizzas).
For the four-topping pizzas, that cost $10 each:
The cost will be 10f (where 'f' is the number of four-topping pizzas).

Now, to calculate the total cost, we add up the cost of the cheese pizzas and the four-topping pizzas:
Total cost = 6c + 10f

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Which of the following best represents the average rate at which a person can
quickly walk?
01) 3 steps per hour
O2) 3 steps per second
03) 30 steps per minute
O4) 30 steps per second

Answers

The answer is 2, 3 steps per second.

The Roasted Bean charges
$17,00 per pound for Fair Trade Organic Mexican
coffee and $15.00 per pound for Fair Trade Organic
Peruvian coffee. How much of each type should be
used to make a 28-lb blend that sells for $16.00 per
pound?

Answers

Answer:

14 pounds of each type should be used to make a 28 pounds blend that sells for $16 per pound.

Step-by-step explanation:

The Roasted Bean charges $17 per pound for Fair Trade Organic Mexican coffee and $15 per pound for Fair Trade Organic Peruvian coffee.

Let x pounds of Mexican coffee and y pounds of Peruvian coffee are mixed to prepare a 28 pounds blend that sells for $16 per pound.

So, x + y = 28 ........... (1)

Again, [tex]\frac{17x + 15y}{x + y} = 16[/tex]

⇒ 17x + 15y = 16x + 16y

x = y .......... (2)

Now, from equation (1) we have 2x = 28

x = 14 pounds  

And y = 14 pounds. (Answer)

twice the difference of a number and 4 is less than the sum of the number and five. Solve please

Answers

Answer:

[tex] - 2x + 4 < x + 5 \\ - 2x - x < 5 + 4 \\ - 3x < 9 \\ x = - 3[/tex]

hope this helps you

After solving the inequality, the value obtained will be equal to x < 9.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question,

The given statement is,

Twice, the difference between a number and 4 is less than the sum of the number and five.

In mathematical form, it can be written as:

Let the unknown number be x.

2x - 4 < x + 5

Let's solve the equation for x.

2x - x < 5 + 4

x < 9

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simplify -3w-5(4x-4w)-4x

Answers

-3w-5(4x-4w)-4x

multiply the bracket by -5

(-5)(4x)=-20x

(-5)(-4w)=20w

-3w-20x+20w-4x

-3w+20w-20x-4x ( combine like terms)

answer:

17w-24x or -24x+17w


An item on sale costs 70% of the original price. If the original price was $30, what is the sale price​

Answers

Answer:

$21

Step-by-step explanation:

70%=0.7

30*0.7=21

Answer:

$9.00

Step-by-step explanation:

Subtract 70 percent from 30 dollars

Megan and molly have an age gap of 6 years. Megan is older. If molly is 8 years old, then how old is Megan?

Answers

Answer:

Megan is 14

Step-by-step explanation:

Megan is M

Molly is Mo

Mo = 8

M = x

6 + mo = x

6 + 8 = 14

If Molly is 8 years old and there is a 6-year age gap between her and Megan, then Megan must be 6 years older than Molly.

Therefore, Megan is 8 + 6 = 14 years old.

This age gap of 6 years means that Megan was born 6 years before Molly.

Age gaps are calculated by subtracting the younger person's age from the older person's age.

It's important to note that Megan is the older of the two, and the age difference remains constant as they both get older.

Understanding age differences is essential in various contexts, from family dynamics to social relationships and legal matters.

In this case, it's a straightforward calculation, but age gaps can have significant implications in more complex situations, such as legal age requirements, generational differences, and even compatibility in personal relationships.

In this instance, Megan is 6 years older than Molly, and that age gap will remain consistent as they both grow older.

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A salesperson earns 4% commission on furnace sales. What is the commission that the salesperson earns on the sale of $33,000 worth have furnaces? Suppose the salesperson doubles his sales of furnaces. What would be true about the commission? Explain without using any calculations.

Answers

The commission that the salesperson earns on the sale is $1320

The commission would be double when he doubles his sales of furnaces

Step-by-step explanation:

The given is:

A salesperson earns 4% commission on furnace salesThe furnace sales have worth $33,000

We need to find the commission that the salesperson earns

∵ The salesperson earns 4% commission on furnaces sale

∵ The furnaces sale have worth $33,000

- Find the 4% of 33,000

∴ The salesperson earns 4% of 33,000

∵ 4% × 33,000 = [tex]\frac{4}{100}[/tex] × 33,000 = 1320

∴ The salesperson earns $1320

The commission that the salesperson earns on the sale is $1320

∵ The salesperson doubles his sales of furnaces

∴ The commission would be double

That because the commission is a constant percent from his sales of furnaces, so if the amount of his sales of furnaces doubles , then his commission also doubles, it is a direct proportion relationship

Commission = constant (4%) × amount of furnaces sale

The commission would be double when he doubles his sales of furnaces

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The resistance, R of a wire varies directly as the length, l, and inversely as the diameter, d, squared. If R is 1.50ohms when l=2.0 m and d=1.5 mm, what is the resistance of a wire made of the same material that is 8.0 m long and has a diameter of 3.0 mm?

Answers

Answer:

resistance is 1.5 ohms (1.5 Ω)

Step-by-step explanation:

R varies directly with l

R varies inversely with [tex]d^2[/tex]

We can set-up a proportionality statement as shown below:

[tex]R=k\frac{l}{d^2}[/tex]

Now, Given,

R = 1.50

l = 2

d = 1.5

We substitute and find k (the proportionality constant):

[tex]R=k\frac{l}{d^2}\\1.5=k\frac{2}{1.5^2}\\1.5=\frac{2k}{2.25}\\2k=1.5*2.25\\2k=3.375\\k=1.6875[/tex]

Now, we will use this value of k to solve the problem.

Given,

l = 8

d = 3

and

k = 1.6875

We find R:

[tex]R=k\frac{l}{d^2}\\R=1.6875\frac{8}{3^2}\\R=\frac{1.6875*8}{9}\\R=1.5[/tex]

The resistance is 1.5 ohms (1.5 Ω)

Other Questions
Choose the sentence that has no errors.A. Although, "Amazing Grace" was written in the 1700s, it remains a well-loved song today.B. Although 'Amazing Grace' was written in the 1700s, it remains a well-loved song today.C. Although Amazing Grace was written in the 1700s, it remains a well-loved song today.D. Although "Amazing Grace" was written in the 1700s, it remains a well-loved song today. The vertices of A ABC are (-2,-4),(-4-2) and (- 6. - 4) respectively. Translate ABCABC by the vector (2,3) and reflect the image on the line x=0. Find the co-ordinates ofthe vertices of the image under the combined transformation and draw all the trianglesin the graph. 1) Se___(criticar) duramente el discurso del presidente.2) Se__(prohibir) las reuniones pblicas.3) Se __(aprobar) las nuevas leyes.4) Se__ ( informar) al pueblo sobre la difcil situacin.5) Se__ (llamar) a los lderes para hablar del conflicto.6) Se__(pedir) a los candidatos evitar los ataques personales. The records for the Clothing Department of Metlocks Discount Store are summarized below for the month of January. Inventory, January 1: at retail $24,800; at cost $16,600 Purchases in January: at retail $136,600; at cost $78,695 Freight-in: $7,100 Purchase returns: at retail $3,000; at cost $2,200 Transfers in from suburban branch: at retail $13,000; at cost $9,300 Net markups: $8,100 Net markdowns: $3,900 Inventory losses due to normal breakage, etc.: at retail $500 Sales revenue at retail: $94,300 Sales returns: $2,500 Compute the inventory for this department as of January 31, at retail prices. List and briefly describe four components of innate immunity (include one barrier defense and three internal defenses) Stossel Company sells 300 units for $200 each to Liberty Inc. for cash. Stossel allows Liberty to return any unused product within 30 days and receive a full refund. The cost of each product is $120. Stossel estimates that ten units will be returned, the costs of recovering the units will be immaterial, and the returned units are expected to be resold at a profit. What amount of Sales Returns and Allowances should Stossel record in the year of the sale?(a)$2,000.(b)$0.(c)$800.(d)$1,200. a5 Lines 47 through 53 reveal the(1) traveler's acceptance of the change in thesituation(2) boy's misunderstanding of his grandfather'sillness(3) traveler's resentment about delaying hisappointments(4) boy's confidence in the doctor's expertise The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. make a system of equations to find the smallest number of busses the orchestra can rent. Let x= the number of busses and y= the number of vans make an equation representing the number of vehicles needed. __________ make an equation representing the total number of seats in vehicles for the orchestra members. __________ Solve the system of equations. How many busses does the orchestra need to rent? ____________ How many 12-passenger vans does the orchestra need to rent? ____________ -3x+3y=9 2x7y=14 State incorporation grants corporations the following express powers excepta.the power to lend money.b.the power to make charitable donations.c.the power to acquire property.d.the power given in the statement of corporate purpose in the articles of incorporation.e.the power to make contracts and borrow money. The SAT was developed in order to provide children from public schools with a chance to demonstrate their fitness for college and to show they are as able as students from private high schools. It is therefore ironic that The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 10.4degrees. If skyscraper B is 1472 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation. On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).How do the areas of triangle ABC and DEF compare?The area of ABC is 1 square unit less than the area of DEF.The area of ABC is equal to the area of DEF.The area of ABC is 1 square unit greater than the area of DEF.The area of ABC is 2 square units greater than the area of DEF. It is claimed that mutual funds have two advantages. The first is that mutual funds allow people with small amounts of money to diversify. The second is that mutual funds provide the skills of professional money managers who buy stocks they believe will be the most profitable and thereby increase the return that mutual fund depositors earn on their savings.a. Economists strongly agree with both claims.b. Economists are skeptical of both claims.c. Economists are skeptical of the first claim, but strongly agree with the second.d. Economists strongly agree with the first claim, but are skeptical of the second. A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of Rin=80 L/minutes (min). The fluid mixes instantaneously and is pumped out at a specified rate Rout. Let y(t) denote the quantity of salt in the tank at time t. Assume that Rout=40L/min. (a) Set up and solve the differential equation for y(t). (b) What is the salt concentration when the tank overflows? According to the current empirical literature, what factor(s) can influence the development of the executive function? Choose ALL correct answers. a. bilingualism b. poverty c. parenting style d. maternal prenatal nutrition Under the PATRIOT Act, the FBI can issue a ____ to compel banks, Internet service providers, and credit reporting companies to turn over information about their customers without a court order simply on the basis that information is needed for an ongoing investigation. Explain how you can write an equation for a line with slope 1/2 that crosses the y-axis at the point (0,-1). What is one way that the text cites as a problem associated with how students practice time management, as they prepare for their speeches? a. Incorrect estimation of time of the amount of time it takes to prepare for their speeches b. Preparing for the wrong speech c. Using an egg timer rather than the timer feature on thier cell phones all of these d. No answer text provided. Assume the lunch plate industry in Oahu, a perfectly competitive industry, is in long-run equilibrium with a market price of $5. If demand for lunch plate increases and this industry is a decreasing-cost industry, long-run equilibrium will be reestablished at _______ price.