The three statistical questions are: A. How many hours of sleep per night do students usually get when they have school the next day? B and E.
What is a statistical question?A statistical question is one that may be resolved via the collection and examination of data. The question frequently incorporates a variable that might differ from person to person or scenario to situation, and the solution is not always the same. The words "how many," "what is the average," "what is the range," "what is the distribution," etc. are frequently used in statistical queries.
The three statistical questions are:
How many hours of sleep per night do students usually get when they have school the next day?
What are the heart rates of the students in Mr. Peterson's physical education class?
How many runs did the New York Yankees score in their last game?
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please and thank you i really need it
Answer:
B
Step-by-step explanation:
an 800 deposit for 2 years months earned 200$ in interest
Variable costs as a percentage of sales for Lemon Inc. are 63%, current sales are $603,000. and fixed costs are $202,000. How much will operating income change if sales increase by $37,400?
Answer: $13, 658 increase
First, we need to calculate the current total variable costs:
Total Variable Costs = Sales x Variable Costs as a % of Sales
Total Variable Costs = $603,000 x 0.63
Total Variable Costs = $380,490
Next, we can calculate the current operating income:
Operating Income = Sales - Total Variable Costs - Fixed Costs
Operating Income = $603,000 - $380,490 - $202,000
Operating Income = $20,510
If sales increase by $37,400, the new sales figure will be $640,400 ($603,000 + $37,400). We can then calculate the new total variable costs:
New Total Variable Costs = New Sales x Variable Costs as a % of Sales
New Total Variable Costs = $640,400 x 0.63
New Total Variable Costs = $404,232
Finally, we can calculate the new operating income:
New Operating Income = New Sales - New Total Variable Costs - Fixed Costs
New Operating Income = $640,400 - $404,232 - $202,000
New Operating Income = $34,168
Therefore, the operating income will increase by $13,658 ($34,168 - $20,510) if sales increase by $37,400.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
The prοfit exceeds the cοst as y > 1000 + 15x. Sο, οptiοn 4 is cοrrect.
What is profit?Gaining anything is knοwn as prοfit. When the Selling price ( SP ) οf the prοduct is mοre than the cοst price ( CP ) οf the prοduct, we gain prοfit. Oppοsite tο the prοfit is lοss i.e. lοsing anything is called lοss. When the Selling price ( SP ) οf the prοduct is less than the cοst price ( CP ) οf the prοduct, we get a lοss.
Prοfit can be calculated by the fοrmula,
Prοfit = Selling Price - Cοst price
P = SP - CP
Lοss can be calculated by the fοrmula,
Lοss = Cοst price - Selling price
L = CP - SP
As per the questiοn,
x = number οf units prοduced
expressiοn = 1000 + 15x
⇒ When y > 1000 + 15x, then prοfit exceeds cοst:
x = 50 & y = 1750
x = 100 & y = 2500
x = 150 & y = 3250
x = 200 & y = 4000
x = 0 & y = 1000
Therefοre, the graph in the 1st οptiοn is cοrrect as the prοfit exceeds the cοst.
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Complete question:
The cost of a small business is given by the expression 1000 + 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
3. A carpet company uses the following formula for
estimating the number of square feet, A, of carpeting
needed for a room x feet by y feet containing a stairway w
feet by z feet with n stairs:
A=xy+w[z(2n−1)+2n]
To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
What are the dimensions?
The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:
A = xy + w[z(2n - 1) + 2n]
Let's break down this formula to understand the different parts:
xy represents the area of the main part of the room, which is a rectangle with length x and width y.w represents the width of the stairway.z represents the depth of each stair.n represents the number of stairs.The expression z(2n - 1) represents the total vertical distance covered by all the stairs, including the top and bottom levels.The expression 2n represents the total horizontal distance covered by all the stairs.The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.
So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
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give me a furmula a triangle
Answer:
The formula for finding the area of a triangle is:
Area = 1/2 x base x height
where "base" is the length of one of the sides of the triangle, and "height" is the distance from that side to the opposite vertex.
What is the axis of symmetry for the function f(x)=7-4x+x^2
the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Why it is and what does symmetry mean?
To find the axis of symmetry of the quadratic function f(x) = 7 - 4x + x²2, we can use the formula:
x = -b / 2a
where a and b are the coefficients of the x²2 and x terms, respectively, in the quadratic equation ax²2 + bx + c = 0.
In the given function, a = 1 and b = -4. Substituting these values into the formula, we get:
x = -(-4) / 2(1) = 2
Therefore, the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Symmetry is a property that describes a balanced and consistent arrangement of parts or elements that are similar in size, shape, and position. In mathematics, symmetry refers to the idea that a geometric object, function, or equation remains unchanged after some transformation, such as a reflection, rotation, or translation.
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find the intersection (2,2) (2,4) (8,4) (8,2)
The intersection (2,2) (2,4) (8,4) (8,2) is (5,3).
On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.
The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).
The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).
Consequently, the diagonals' point of intersection is (5,3).
Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.
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pls help lol it’s due tomorrow
The measure of angle D is 100°
What is sum of angle in a Triangle?A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.
Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.
Therefore,
angle D = 180-( 40+40)
= 180-80
= 100°
therefore the measure of angle D Is 180°
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Abigail wants to prove that a parallelogram is a rectangle if its diagonals are congruent. To start her proof, she draws parallelogram JKLM with congruent diagonals
Parallelogram JKLM is a rectangle because it has four right angles.
What is sss congruence theorem?The SSS (side-side-side) congruence theorem is one of the postulates of Euclidean geometry that states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
According to question:Abigali wants to prove that a parallelogram is a rectangle if its diagonals are congruent.
Since, JKLM is a parallelogram, JK≅ML.
Also by the reflexive property, KL is congruent to itself. So, since JL≅KM as well, ΔJKL ≅ ΔMLK by the SSS congruence theorem.
Now because the corresponding angles in congruent triangles are congruent, ∠JKL ≅ ∠MLK.
Also, since parallelograms have JK//ML,
Consecutive Interior Angles are supplementary.
So, since m∠JKL and m∠MLK are equal, they must both be 90°. Because the opposite angles in parallelograms are congruent, m∠MJK and m∠JML are both 90°. So, parallelogram JKLM is a rectangle because it has four right angles.
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To find the surface area of a refrigerator, what units will be used; check all that applies
Group of answer choices
square feet (sq ft)
meters (m)
square inches (sq in)
millimeters (mm)
surface area of a refrigerator,
square feet (sq ft)
square inches (sq in)
What is surface area ?the total area or the solid that the surface of the solid occupies.
we know that refrigerator have cuboid shape so,
surface area of cuboid =2(lb+bh+hl)
where l is length ,b is breath ,and h is height of cuboid .
The units generally used to measure the surface area of a refrigerator are:
square feet (sq ft)
square inches (sq in)
Therefore, the options are square feet (sq ft) and square inches (sq in) correct.
Meters (m) and millimeters (mm) are typically not used for measuring the surface area of a refrigerator.
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What value of x will make this proportion true/ 14/x=1/2 7, or 18, or 24, or 28, show the problem worked.
Answer:
378
Step-by-step explanation:
[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex] Cross multiply and solve for x
x = (14)(27)
x = 378
Helping in the name of Jesus.
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r.
P = 4500 $, A = 4561.88 $, t = 3 months
The loan's simple interest rate is 5.232% per quarter.
What is the formula for the future value of a loan with simple interest?
A = P(1 + rt)
where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.
In this case, we have:
P = 4500
A = 4561.88
t = 3 months = 3/12 year =0.25 year
Substituting these values into the formula,
[tex]4561.88 = 4500(1 + 0.25r)[/tex]
Dividing both sides by 4500,
[tex]1.01308 = 1 + 0.25r[/tex]
Subtracting 1 from both sides,
[tex]0.01308 = 0.25r[/tex]
Dividing both sides by 0.25,
[tex]r = 0.05232 \: or \: 5.232\%[/tex]
Therefore, the loan's simple interest rate is 5.232% per quarter.
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2. Write an equation that represents the following situation
Starting value = 200
Rate = 2.5% decay per year
Years = 5 years
Answer:
The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.
helpp!!!!11!1!1 !!!:(
The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.
There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.
To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.
In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.
The average of 4 and 6 is (4 + 6)/2 = 5.
Therefore, the median number of books read by Mr. Johnson's students is 5.
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what are the answers to these questions?
a) dV/dt=?
b) dV/dt=?
c) dV/dt=?
The value of differentiation A) dV/dt = 2πrh(dr/dt) ,B) dV/dt = π(r²(dh/dt) , C) π(2rh(dr/dt) + r²(dh/dt))
What is a differentiation?A mathematical procedure called differentiation is used to determine the derivative of a function with respect to a variable. The rate at which one quantity changes in relation to another is determined using this method.
If we have a function f(x) = x2, for instance, its derivative f'(x) = 2x tells us how quickly the function changes in relation to x.
The following formula determines the volume V of a right circular cylinder with radius r and height h:
V = πr²h
The cylinder's radius is r in this instance, and its height is h.
When we change the formula's specified values, we obtain:
V = πr²h
= (12)(2) = 2 cubic metres.
As a result, the right circular cylinder has a 2 cubic unit volume.
Let's now think about how dv/dt and dr/dt relate when h is constant and r varies over time.
When we take into account time t and differentiate both sides of the formula V =πr²h, we obtain:
dV/dt = d(r²h)/dt
(r²)(dr/dt)(dh/dt) = dV/dt
h is a constant, hence dh/dt = 0.
Therefore,
dV/dt= ((2r)(dr/dt)(dh/dt)
= 2rh(dr/dt)
B)
Let's now think about how dv/dt and dh/dt relate when r is constant and h varies over time.
When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:
dV/dt equals d(r²h)/dt
r²(dh/dt) = dV/dt
As r is constant, dr/dt is equal to 0.
Therefore,
r2(dh/dt) = dV/dt
C)
Given that r and h are time-varying, let's look at the relationship between dv/dt, dh/dt, and dr/dt.
When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:
dV/dt equals d(r²h)/dt
dV/dt is equal to (r²)(dh/dt) + (r²)(dr/dt)
Therefore,
((2rh(dr/dt) + r2(dh/dt))
= dV/dt)
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5. 56 oz = ____lb ____oz
A. 2 lb 1 oz
B. 2 lb 3 oz
C. 2 lb 6 oz
D. 3 lb 8 oz
56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.
What is pound?Pound is a unit of measurement for mass or weight commonly used in the United States and the United Kingdom. The symbol for pound is "lb".
According to question:In the English system of measurement, there are 16 ounces in one pound. To convert a weight in ounces to pounds, we need to divide the number of ounces by 16.
In this case, we have 56 ounces. So, by dividing 56 by 16, we obtain:
56 / 16 = 3 with a remainder of 8
This means that 56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.
In the US customary system, one pound is equal to 16 ounces, while in the imperial system used in the UK, one pound is equal to 14 ounces.
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Convert 56 ounces(oz) into pounds(Ib)
56 oz = ____lb ____oz
A. 2 lb 1 oz
B. 2 lb 3 oz
C. 2 lb 6 oz
D. 3 lb 8 oz
The figure below shows a satellite orbiting Earth. The satellite passes directly over two tracking stations A and B, which are 68 miles apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 83.9 degrees and 86.2 degrees respectively. How far is the satellite from station
A and how high is the satellite above the ground? Round answers to the nearest whole mile.
Step-by-step explanation:
let the third vertex=C
180-86.2=93.8°
angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°
angles of triangle are 83.9°,93.8°,2.3°
by sine formula
[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]
what's the linear relationship for this im stuck
Answer:
slope = 15
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table
m = [tex]\frac{21-6}{2-1}[/tex] = [tex]\frac{15}{1}[/tex] = 15
the linear relationship is then of the form
y = mx + c ( m is the slope and c the y- intercept )
from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9
y = 15x - 9 ← linear relationship
Given that the probability of a student taking a physics class is 23, and the probability of a student taking a math class given that the student takes a physics class is 710, what is the probability of a student taking a math class and a physics class? Enter your answer as a fraction in simplest form.
The probability of a student taking a math class and a physics class is [tex]\frac{7}{15}[/tex].
What is probability?
To determine the possibility of an event, one might utilise probability as a technique. Only the probability of an event occurring can be determined using it. A scale where 1 denotes a specific occurrence and 0 signifies impossibility.
We are given that the probability of the student taking a physics class is [tex]\frac{2}{3}[/tex].
Also, it is given that the probability of a student taking a math class given that the student takes a physics class is [tex]\frac{7}{10}[/tex].
So, probability of a student taking a math class and a physics class is:
⇒ Probability = [tex]\frac{2}{3}[/tex] * [tex]\frac{7}{10}[/tex]
⇒ Probability = [tex]\frac{14}{30}[/tex]
⇒ Probability = [tex]\frac{7}{15}[/tex]
Hence, the probability of a student taking a math class and a physics class is [tex]\frac{7}{15}[/tex].
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Determine the union of j and k.
j = {7, 14, 21, 28, 35,42}
k = {14,28, 42, 56, 70}
The union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70} . Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.
What is a set ?
In mathematics, a set is a collection of distinct objects, called elements or members of the set. Sets are often denoted by curly braces {} enclosing the list of elements, separated by commas. For example, the set of natural numbers less than 5 can be written as {0, 1, 2, 3,
The union of two sets J and K, denoted by J ∪ K, is the set that contains all the elements that are in J or K, or in both.
In this case, J = {7, 14, 21, 28, 35, 42} and K = {14, 28, 42, 56, 70}. To find the union of J and K, we simply combine all the elements in both sets, removing any duplicates.
Therefore, the union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70}
Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.
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HELP ASAP 25 PONITS PLEASE
Answer:
The Markdown amount: $9.45
Sale price: $13.05
Step-by-step explanation:
Convert 42% to decimal, which is 0.42
a = p(w). (formula)
a=22.5(0.42). or 22.5 x 0.42
a = 9.45
22.50 - 9.45 = 13.05
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5 cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangle be?
The sides of the right triangle are 15 cm, 20 cm, and 25 cm.
What is triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
Let x be the length of the shorter leg of the right triangle.
Then, according to the problem statement, the longer leg is 5 cm more than the shorter leg, which means its length is x + 5 cm.
The hypotenuse is 10 cm more than the shorter leg, so its length is x + 10 cm.
By the Pythagorean theorem, we have:
x² + (x+5)² = (x+10)²
Expanding the squares and simplifying, we get:
x² + x² + 10x + 25 = x² + 20x + 100
Subtracting x² and simplifying further, we get:
x² - 10x - 75 = 0
Factorizing the left-hand side, we get:
(x - 15)(x + 5) = 0
Therefore, the possible solutions are x = 15 and x = -5, but x cannot be negative in this context, so we take x = 15 cm.
Then, the longer leg is x + 5 = 20 cm, and the hypotenuse is x + 10 = 25 cm.
Therefore, the sides of the right triangle are 15 cm, 20 cm, and 25 cm.
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Need help for this question.
The measure of the angle x is 41.41° in the given triangle.
What is a triangle?Triangle is a clοsed twο-dimensiοnal shape. It is a three-sided pοlygοn. All sides are made οf straight lines. The pοint where twο straight lines jοin is the vertex. Hence, the triangle has three vertices. Each vertex fοrms an angle.
Given that cos θ = side adjacent to angle x/hypotensive
Here, side adjacent to angle x = 6
hypotensive = 8
cos x = 6/8
x = arccos 6/8
x = 41.41°
Thus, the measure of the angle x is 41.41° in the given triangle.
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Emily is selling t-shirts for $7 each. If she earns a total of $126, how many t-shirts did she sell? Write and solve an equation to solve this problem. (Hint. You need to identify a variable AND embed it in the equation.)
Answer:
7x = 126 is the equation
She sold 18 t-shirts.
Step-by-step explanation:
Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.
126/7 = 18.
The equation would be:
7x = 126.
please help with this
Option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
What is a polynomial?A pοlynοmial is a mathematical expressiοn cοnsisting οf variables, cοefficients, and the οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents.
Pοlynοmials are an impοrtant part οf the "language" οf mathematics and algebra. They are used in nearly every field οf mathematics tο express numbers as a result οf mathematical οperatiοns. Pοlynοmials are alsο "building blοcks" in οther types οf mathematical expressiοns, such as ratiοnal expressiοns.
We have:
6x² − 8x
= 2(3x² −4x)
Then,
6x² - 3x + 8x -4
= 6x² +8x−3x−4
= 2x(3x+4) −3x −4
= 2x(3x+4)−(3x+4)
= (2x−1)(3x+4)
Thus, option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
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Find the area of the shape below. Use NUMBERS ONLY in the blank. NO units.
30 ft
60 ft
60 ft
60 ft
60 ft
30 ft
The shape is like a plus sign
The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².
How to find the area ?You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.
The area of the composite shapes would therefore be :
= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )
= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )
= 1, 800 + 1, 800 + 4, 500
= 8, 100 ft ²
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What is the average cost per unit?
Using calculations based on a perpetual inventory system, the inventory balance that Altira Corporation would report in its August 31, 2024, balance sheet and the cost of goods sold it would report in the income statement, using the Average Cost Method are as follows:
Ending inventory = $39,860Cost of Goods Sold = $71,540.What is the average cost method under the perpetual inventory system?The average cost method or the weighted-average cost method under the perpetual inventory system adds up all the cost of goods available for sale at each sales point and divides by the number of units available for sale in determining the average cost to be applied to the cost of goods sold.
Principally, the perpetual inventory system ensures that each inventory movement is separately recognized and the cost of goods sold determined, unlike the periodic inventory system.
Cost of Goods Sold:August 14 for Sales of 6,000 units:
Average cost per unit = $5.46 ($54,600 ÷ 10,000)
Cost of goods sold = $32,760 ($5.46 x 6,000)
August 25 for Sales of 7,000 units:
Average cost per unit = $5.54 ($21,840 + $33,600 ÷ 10,000)
Cost of goods sold = $38,780 ($5.54 x 7,000)
Total cost of goods sold = $71,540 ($32,760 + $38,780)
Total cost of goods available for sale = $111,400 ($10,600 + $44,000 + $33,600 + $23,200)
Ending Inventory = $39,860 ($111,400 - $71,540)
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Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Step-by-step explanation:
Mona had = 32 math problems.
Let math problems shw completed be x.
Before dinner: 3/4x maths.
remaining maths = x- 3/4x
= 4x-3x/4 = 1/3x.
stick of butter weight a quarter of a pound how much do 13 sticks of butter weight