The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Substituting the given values, we get:
V = (4/3)π(15)³
V = (4/3)π(3375)
V = 4500π
Therefore, the volume of the sphere is 4500π cubic inches.
Calculate sales tax using the following information:
Taxable amount of the sale: $150
Sales tax percentage: 6.5%
What is the amount of the sales tax?
Round the answer to the nearest cent (hundredths).
The amount of the sales tax is $9.75.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The taxable amount of the sale: $150
Sales tax percentage: 6.5%
To calculate the sales tax, you can multiply the taxable amount of the sale by the sales tax percentage.
Sales Tax = Taxable Amount × Sales Tax Percentage
Sales Tax = $150 × 6.5%
Sales Tax = $150 × 0.065
Apply the multiplication operation, and we get
Sales Tax = $9.75
So, the amount of the sales tax is $9.75.
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Which of the following illustrates the use of the commutative property of addition?
A. (9x + 5y) + 2z = (9x + 5y) + 2z
B. (9x + 5y) + 2z = 9x + (5y + 2z)
C. (9x + 5y) + 2z = (9x + 5y + 2z)
D. (9x + 5y) + 2z = (5y + 9x) + 2z
Answer:
Step-by-step explanation:
The use of the commutative property of addition is illustrated by option D: (9x + 5y) + 2z = (5y + 9x) + 2z.
The commutative property of addition states that the order of addition does not affect the sum. In other words, changing the order of the addends does not change the result. Option D demonstrates this property by showing that adding 9x and 5y to 2z is the same as adding 5y and 9x to 2z. The result is the same regardless of the order in which the addends are combined.
Find the total surface area of a cylinder shown below use 3.14 for pi and provide the answer accurate to two decimal places
Answer:
it is probably 1.884 cm andd it is accurate
Put the following list in order from highest to lowest. Highest 0.19 << < < << Petruta Cioran 13 8% 0.2 27% 4 25
The list in highest tο lowest οrder is as follows :
0.2
27%
25
What is percentage ?Percentage is a way οf expressing a number as a fractiοn of 100. It is often used to cοmpare or describe relative values, such as prοportions, growth rates, or percentages of a whole.
Percentage is calculated by dividing a part of sοmething by the whole and then multiplying by 100. Fοr example, if a class has 25 students and 5 οf them are absent, we can find the percentage οf absent students by dividing the number οf absent students (5) by the tοtal number of students (25) and then multiplying by 100
Accοrding to given information:
The list in οrder from highest to lowest is:
0.2
27%
25
Petruta Ciοran 13
8%
0.19 << < < <<
4
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HELP!!! URGENT!!!
A bank offers all savings accounts 5% interest compounded annually. If one account has a principal of $100 and another
has a principal of $1,000, which account will double first? Explain how you arrived at your answer. Answer in complete sentences
Answer:
$100 account
Step-by-step explanation:
to double, $100 only need to earn 100 in interest, while $1000 account will need earn $1000 in interest. because the interest is the same for both, so the $100 account will double first
One end of a right circular cone has been cut off by a plane parallel to the base of the cone as shown in the figure below.
What is the approximate circumference of the smaller circular base of the remaining section of the cone?
a. 3.03 feet
b.6.06 feet
c. 3.36 feet
d. 5.28 feet
The approximate circumference of the smaller circular base, in the remaining section of the cone, is c. 3.36 feet.
How to find the circumference ?To find the circumference, the formula is :
= π x diameter
So, you need to find the diameter of the smaller circle. If a distance of 14 feet corresponds to 3 feet of diameter , then 5 feet to the smaller circle would be :
= ( 5 x 3 ) / 14
= 1. 0714 feet
The circumference is therefore :
= 3. 14 x 1. 0714
= 3. 36 feet
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Find the volume of a cylinder with a radius of 4cm and a height of 7 cm. Use 3.14 for pi, round your answer to the nearest hundredth, and do not include units.
Answer:
351.68
Step-by-step explanation:
Given:
The radius of the cylinder = r = 4 cm
Height of the cylinder = h = 7 cm
The volume of the cylinder is given by the formula:
V = πr²h
Using π = 3.14
so, the volume of the cylinder will be:
[tex]3.14 X4^{2} X7 = 3.14 X 16 X 7 = 351.68[/tex]
Volume of the cylinder = 351.68
Using the chart, find the equation from
the relation.
input x 10 11 12 13
output y 6 7 8 9
y = x + [?]
Suppose a country has the following balance of payments data. Export of goods 275 Import of goods 325 Service exports 50 Service imports 40 Income receipts from abroad 40 Income payments to foreigners 70 Increase in home country assets abroad 350 Increase in foreign assets in home country 420 (a) Calculate the current account balance. (b) Calculate the financial account balance. (c) Calculate the trade balance. (d) Calculate net factor payments.
A. The current account balance is a deficit of 130
B. The financial account balance is a deficit of 70
C. The trade balance is a deficit of 50.
D. The net factor payments are a deficit of 30.
What is balance of payments?Balance of payments is the method by which countries measure all of the international monetary transactions within a certain period.
(a) The current account balance can be calculated as follows:
Current Account Balance = (Exports of goods + Service exports) - (Imports of goods + Service imports + Income payments to foreigners - Income receipts from abroad)
= (275 + 50) - (325 + 40 + 70 - 40)
= 325 - 455
= -130
So, the current account balance is a deficit of 130.
(b) The financial account balance can be calculated as follows:
Financial Account Balance = Increase in home country assets abroad - Increase in foreign assets in home country
= 350 - 420
= -70
So, the financial account balance is a deficit of 70.
(c) The trade balance can be calculated as follows:
Trade Balance = Exports of goods - Imports of goods
= 275 - 325
= -50
So, the trade balance is a deficit of 50.
(d) The net factor payments can be calculated as follows:
Net Factor Payments = Income receipts from abroad - Income payments to foreigners
= 40 - 70
= -30
So, the net factor payments are a deficit of 30.
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A survey of 1900 commuters in New York City showed that 1130 take the subway, 650 take the bus, and 130 do not take either the bus or the subway.
(a) How many commuters take both the bus and the subway?
Incorrect: Your answer is incorrect.
commuters
(b) How many commuters take only the subway?
commuters
(a) Commuters take both the bus and the subway = 10
(b) commuters take only the subway = 1120
What is a set?
A set is a collection of well-defined objects or elements. A set is represented by capital letter and their elements is represented by small letters.
Let U be the set representing the number of commuters in New york.
⇒n(U) = 1900
Let A be the set representing the commuters take subway
⇒n(A) = 1130
Let B be the set representing the commuters take bus
n(A) = 650
130 commuters do not take either the subway or the bus,
(a) commuters take both the bus and the subway
n(A∪B)=n(A) + n(B) - n(A∩B)
n(A∪B)=n(U)-130⇒1900-130=1770
1770=1130+650-n(A∩B)
⇒n(A∩B) = 10
(b) Commuters take only the subway,
n(A)-n(A∩B) = 1130-10=1120
Hence, commuters take both the bus and the subway is 10
commuters take only the subway is 1120
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Two-lined salamanders have weights that are normally distributed and on average 13.6 grams with a standard deviation of 2.2 grams. A random sample of 8 two-lined salamanders is selected and weighed.
The probability that the sample mean is between 13.6-x and 13.6+x is around 0.68 (more precisely, 0.6827), for some value of x. What is the value of x ?
The value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.
What is Central Limit Theorem ?
Central Limit Theorem states that as the sample size increases the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, for a sample of 8 two-lined salamanders, the standard deviation of the sample means is:
σ = σ/√n = 2.2/√8 = 0.89
We are looking for the value of x such that the probability of the sample mean being between 13.6-x and 13.6+x is 0.6827. This corresponds to the area under the normal curve within x standard deviations of the mean.
We can use a standard normal table or calculator to find the value of x corresponding to 0.6827. The result is approximately x = 0.89.
So, the value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.
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if the demand for apples is highly elastic and the supply is highly inelastic, then a tax imposed on the apples will be paid
The complete statement is -
If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.
What is highly elastic demand?Elastic demand is when the price of a product has a large impact on the quantity purchased.
Given is that the demand for apples is highly elastic and the supply is highly inelastic.
If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.
Therefore, the complete statement is -
If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.
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Solve for x. Round to the nearest tenth, if necessary.
We can use trigonometry to find the length of side SU in triangle TSU. We can use the tangent function, where tangent is equal to the opposite side divided by the adjacent side. In this case, the opposite side is SU and the adjacent side is ST.
What is basic trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the field of mathematics known as "trigonometry." Trigonometric formulas, functions, or identities can consequently be used to determine the missing or unknowable angles or sides of a right triangle.
We know that angle TUS is 37 degrees, so we can use that angle to find the tangent of the angle:
tan(37) = SU / 0.6
Solving for SU:
SU = 0.6 * tan(37)
The exact length of SU can be found by using a calculator or a table of trigonometric values. To a good approximation, the value of SU is approximately 0.73.
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True/Falseif the price of avocados increases by 11% for four consecutive months, then the price of avocados increased by 44% over the four-month period.
The given statement is False because if the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 48.64% over the four-month period.
If the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 44% over the four-month period. The calculation of percentage increase is cumulative, meaning that the increase in price in the second month will be based on the increased price from the first month, and so on.
In this case, if the price starts at $1 and increases by 11% each month, the price after four months will be $1 * 1.11 * 1.11 * 1.11 * 1.11 = $1.4864, which represents an increase of 48.64% over the four-month period, not 44%.
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When calculating the area of a trapezoid, how do you determine which sides are the bases?
A. They're on the top and bottom of the figure
B. They're at the sides of the figure
C. They do not run parallel to each other
D. They run parallel to each other
Answer:
D.
Step-by-step explanation:
The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs of the trapezoid.
Therefore, the answer is D.
Hope it helped!
Rewrite the function in the form of f(t)=a(b)^t to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change.
[tex]f(t) = 4 (1.25)^{t+3} = 4 \cdot (1.25)^{3} \cdot (1.25)^{t}[/tex] using the exponent rule [tex]a^n\cdot a ^m = a^{n+m}[/tex] in reverse. (Using the rule to split apart the exponent.
Continuing to calculate out some values,
[tex]f(t) = 4 \cdot (1.25)^{3} \cdot (1.25)^{t} = 4 \cdot 1.953125 \cdot (1.25)^{t} = 7.8125 \cdot (1.25)^{t}[/tex]
So, [tex]f(t) = 7.8125 \cdot (1.25)^{t}[/tex] or [tex]f(t) = 7.81 \cdot (1.25)^{t}[/tex] rounded to the nearest hundredth.
Since the b-value is greater than 1, this is exponential growth.
The b-value of 1.25 means that for each increase by 1 unit in the t-value, the y-value will become 125% of what it had been. The output will grown by 25%, which is your percent rate of change.
The b-value of your function is always a measurement from 100% or b=1.
If a₁ = 10 and an
=
-4an-1 then find the value of a4.
Answer:
Step-by-step explanation:
[tex]a_{1} =10\\a_{n}=-4a_{n-1}\\put~n=2,3,4\\a_{2}=-4a{1}=-4(10)=-40\\a_{3}=-4a_{2}=-4(-40)=160\\a_{4}=-4a_{3}=-4(160)=-640[/tex]
Heather purchased a sapphire bracelet during the Jewelry Emporium's Semi-Annual Clearance Sale. If Heather paid $149.50 for the bracelet and the original price is $230.00, how much of a discount did she receive?
need answer
Answer:
She received a 35% discount :)).
Step-by-step explanation:
When Fe(s) reacts with Cl_2(g) according to the following reaction, 400 kJ of energy are evolved each mole of Fe (s) that reacts. Complete the for following thermochemical equation.2Fe(s) - 3Cl_2(g) rea 2FeCl_3(s) delta H = kJ
The complete equation is 2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ
Explain Thermochemical Equations?A thermochemical equation is a chemical equation that includes information about the energy change that occurs during a chemical reaction. The energy change is represented by the symbol ΔH (delta H), which stands for the change in enthalpy, or heat energy, of the system. The equation shows the reactants on the left side and the products on the right side, and includes the amount of heat energy evolved or absorbed during the reaction.
For example, consider the reaction:
2H2(g) + O2(g) → 2H2O(l) ΔH = -571 kJ/mol
This equation shows that two molecules of hydrogen gas react with one molecule of oxygen gas to form two molecules of liquid water. The reaction releases 571 kJ of heat energy per mole of hydrogen and oxygen that react.
The complete thermochemical equation for the reaction of Fe(s) with Cl₂(g) to form FeCl₃(s) is:
2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ
This means that the reaction releases 400 kJ of energy for each mole of Fe(s) that reacts. The negative sign indicates that the reaction is exothermic, meaning it releases heat.
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You roll a die 42 times. The table shows the results. Find the experimental probability of rolling each number. Write each probability as a fraction in simplest form. For which number is the experimental probability of rolling the number the same as the theoretical probability?
By applying probability concept, it can be concluded that the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7, P(3) = 1/3, P(4) = 2/21, P(5) = 1/7, and P(6) = 5/42.
Probability is a value used to measure the degree of occurrence of a random event.
P(E) = n(E)/n(S)
n(E) = number of desired events
n(S) = total number of events
We have the following information about a die rolling 42 times:
One Two Three Four Five Six
7 6 14 4 6 5
The theoretical probability of rolling any number on a six-sided die is 7/42 or 1/6.
Now we can calculate the probability of each side by substituting the value in the table into the equation:
P(E) = n(E)/n(S)
P(1) = 7/42
= 1/6
P(2) = 6/42
= 1/7
P(3) = 14/42
= 1/3
P(4) = 4/42
= 2/21
P(5) = 6/42
= 1/7
P(6) = 5/42
Thus, the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7, P(3) = 1/3, P(4) = 2/21, P(5) = 1/7, and P(6) = 5/42.
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(b) Home Hardware is selling locks at $120.00 for four. Rona is selling 6 locks for
$192.00. Which store has the lower cost for one lock? (3 marks)
(i) Aside from the price of the locks in question b, what other factors should you
consider when buying a lock? (2 marks)
Answer: (b) To find the cost per lock, we need to divide the total cost by the number of locks.
For Home Hardware, the cost per lock is 120 / 4 = $30.00.
For Rona, the cost per lock is 192 / 6 = $32.00.
So, Home Hardware has the lower cost per lock at $30.00, compared to Rona's cost of $32.00.
(i) Some other factors to consider when buying a lock include:
Security: The level of security offered by the lock is important to consider, especially for locks that will be used for homes, businesses, or other valuable assets.
Durability: It's important to choose a lock that is durable and resistant to weather and wear-and-tear.
Ease of use: Consider the ease of use of the lock, including how easy it is to install and how user-friendly the lock mechanism is.
Brand reputation: Consider the reputation of the brand, as well as customer reviews and ratings of the product.
Warranty: Look for a lock that comes with a warranty, and consider the length and terms of the warranty.
Step-by-step explanation:
raise the sum of 9 and w to the 7th power
9 + w^7
w^7 + 9
?
The exponential expression is [tex](9 + w)^7[/tex] and the simplified expression is [tex]4782969 + w^7[/tex].
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The integer is given as 7.
The variable is given as w.
The sum of integer and variable needs to be raised to the power of 7.
The sum of integer and variable is -
(9 + w)
This expression needs to be raised to the power of 7.
The exponential expression is -
[tex](9 + w)^7[/tex]
On solving this expression -
[tex]9^7 + w^7\\4782969 + w^7[/tex]
Therefore, the simplified expression is [tex]4782969 + w^7[/tex].
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Find a
polynomial f (x) of degree 4 that has the following zeros.
0, 6 (multiplicity 2), -2
Leave your answer in factored form.
A polynomial f (x) of degree 4 that has the following zeros, 0, 6 (multiplicity 2), -2 is: x (x+2) (x-6)²
What is polynomial?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminate's and coefficients. Nearly all areas of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
given that,
a polynomial f(x) of degree 4 and has the zeros are 0, 6 (multiplicity 2), -2
We know that If a polynomial P(x) is, of degree 4 and has Zeros are a, b, c (multiplicity 2) then polynomial P(x) will be:
P(x) = (x - a)' (x - b)' (x - c)²
P(x) = (x - a)' (x - b)' (x - c)²
So, here polynomial of degree 4 will be:
F(x) = (x- (-2)) [x-6]² (x-0)
F(x) = x (x+2) (x-6)²
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Calculate the distance between the points N=(-2,-1) and L=(3-4) in the coordinate plane. Give an exact answer (not a decimal approximation)
The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.
What is plane?
In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.
A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.
A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.
Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0
Now,
For given two points in (x1,y1),(x2,y2) in coordinate plane
distance between them will be = √((x2-x1)²+(y2-y1)²)
So, distance between N=(-2,-1) and L=(3,-4)=√((3+2)²+(-4+1)²)
=√(25+9)
=√34
hence,
The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.
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6. (a) If a 24 pack of Red Bull costs $40.00, how much is one Red Bull? (
Answer:
about 1.67
Step-by-step explanation:
24x=40
Robert works as a house painter. The number of houses he painted each week for 4 weeks is listed below.
- 4 houses in week 1
- 8 houses in week 2
- 5 houses in week 3
- 9 houses in week 4
Which graph best represents the number of houses Robert painted during the 4 weeks?
A. K
B. L
C. M
D. N
Answer:
Option C. GraphM
Step-by-step explanation:
Only Graph M has all values correct while the other graphs had atleast one or more values wrong
Therefore Graph M is correct
The graph that best explains Roberts' activity during the 4 weeks is C. the graph M
Aidan measure the perimeter of his classroom.He notices the classroom is 1m wider than it is long.Theperimeter of the classroom is between 20 and 35m.The length of each side is a whole number .
what could the dimensions of the room be?find four different possibilities
Answer:
Step-by-step explanation:
The area of Mrs Brown’s classroom is
63 m2
. The area of Mr Black’s
classroom is 64 m2
. Mr Black’s
classroom is bigger.
6. Tony needs a new car while attending college in California for the next three years. The car he would like has an MSRP of $15,000.
Here are two options offered:
1st option (lease); A local dealer can get him a three-year loan with a 7% interest rate if Tony can make a $1,500 down payment.
2nd option (purchase); The same dealer offers the same car for lease with a money factor of 0.00271 and a residual value of 75%.
The lease requires an additional fee of $1,250 to cover Tony's security deposit and the acquisition and documentation fees for the
car.
Tony wants to drive the car home with the smallest monthly payment. Which of the following statements is true?
a. The monthly payment for the loan is lower.
b. The monthly payment for the lease is lower.
PRUP
C. The monthly payments for the lease and loan are the same.
You cannot compare the monthly payments for leases and loans.
d.
A function is represented by the equation y=x(x + 3). Complete the table for the function.
Does the equation represent a linear function? Explain your reasoning.
The outputs for the given inputs are:
Input: -2 -1 0 1
Output: 2 2 0 4
What is a linear function?
A linear function is a mathematical function that has a constant rate of change, or slope, between its input and output variables. In other words, the output of a linear function changes at a constant rate as the input changes.
The given function y = x(x + 3) is not a linear function because it contains a squared term (x^2) and thus has a non-constant rate of change.
To complete the table for the given function, we substitute each input value into the equation and simplify:
Input: -2
Output: (-2)(-2 + 3) = 2
Input: -1
Output: (-1)(-1 + 3) = 2
Input: 0
Output: (0)(0 + 3) = 0
Input: 1
Output: (1)(1 + 3) = 4
Therefore, the outputs for the given inputs are:
Input: -2 -1 0 1
Output: 2 2 0 4
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McCullough Hospital uses a job-order costing system to assign costs to its patients. Its direct materials include a variety of items such as pharmaceutical drugs, heart valves, artificial hips, and pacemakers. Its direct labor costs (e.g., surgeons, anesthesiologists, radiologists, and nurses) associated with specific surgical procedures and tests are traced to individual patients. All other costs, such as depreciation of medical equipment, insurance, utilities, incidental medical supplies, and the labor costs associated with around-the-clock monitoring of patients are treated as overhead costs.
The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.
what is variations ?There is a connection between one set of values about one variable and an other number of values. direct variation With the equations y = mx + b, you have the direct variant function y = mx (often written y = kx). Equations that describe the relation between independent variables in a language also explain how those variables vary between one another. There are various types of variations, including linear, inverse, joint, among combination variations. If y and x are said to be directly connected, then y must equal kx, where k is a number that is every now and again referred to as the perpetual of variation. If y and x have such an inverse connection, then y equals k/x, where k is just the variance constant.
given
1a. Every patient day, the predetermined overhead rate is $970.
compute the combined expected overhead expenses for the ICU and other:
ICU: $3,200,000 plus $236 each patient-day multiplied by 2,000 patient-days equals $3,672,000.
$14,000,000 plus ($96 for each patient day)
(15,728,000 patient-days) divided by 18
Add the anticipated overhead expenses for ICU and Other:
$3,672,000 + $15,728,000 = $19,400,000
19,400,000 divided by 20,000 patient days equals 970 each patient day.
1b. The overall expense allocated to Patients A and B.
The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.
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