The alternative hypothesis for this problem b. HA: µD>0
What is meant by hypothesis?
In math, A hypothesis is an assumption made based on some evidence.
Here we have given that systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system.
And we need to find the alternative hypothesis for this problem
While we looking into the given question we have identified the following values,
Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25
New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25
Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25
Basically, while written the hypothesis, we have to follow the order of the following,
=> (Old-New, Larger-Smaller>)
Therefore, the correct option is (B).
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Score on last attempt: 2.5 out of 3 Score in gradebook 2.5 out of 3 For each of the following accounts, determine the growth factor and percent change for the account value over one compounding period a Account A has a 5% APR compounded monthly (12 times per year). Determine the account value's growth factor and percent change per compounding period Preview 1. Monthly Growth Factor: 1.0041667 ii. Monthly Percent Change: (1.0041667-1)-100 % Preview b. Account B has a 6.9% APR compounded quarterly (4 times per year). Determine the account value's growth factor and percent change per compounding period. i. Quarterly Growth Factor: 14(0.069/4) Preview 11. Quarterly Percent Change: (1.01725-1)*100 % Preview c. Account Chas a 3.4% APR compounded daily (365 times per year). Determine the account value's growth factor and percent change per compounding period i. Daily Growth Factor: 1+(0.034/100) Preview 11. Daily Percent Change: (1.00034.1) 100 N% Preview Submit
given rate r = 5% compounded monthly r = 0.05/12 = 0.0041667
(1) monthly growth factor = 1.0041667 (2) monthly percent change = (1.0041667-1)*100%= 0.0041667*100% monthly percent change = 0.41667%
(B) given rate r = 6.9% compounded quarterly
r = 0.069/4 = 0.01725
(1) Quarterly growth factor = 1.01725
(2) Quarterly percent change = (1.01725-1)*100%= 0.01725*100% monthly percent change =1.725%
(C) given rate r = 3.4% compounded quarterly
r = 0.034/365 = 9.315 * 10 ^ - 5
(1) daily growth factor = 1 + 9.315 * 10 ^ - 5 = 1.00009315
(2) daily percent change = (1.00009315-1)*100%= 0.00009315*100% monthly percent change =0.009315%
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At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was _______mg
At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.
A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.
The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:
r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr
If we integrate both sides of this equation with respect to t, we get:
A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt
This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:
A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt
The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:
A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt
The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:
A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)
Combining constants and simplifying gives:
A(t) = 25e^-0.1 t - 25e^-0.3 t
We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.
Taking the limit as t approaches 0 gives:
A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]
This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.
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The ABC Corporation is considering opening an office in a new market area that
would allow it to increase its annual sales by $2.6 million. The cost of goods sold is
estimated to be 40 percent of sales, and corporate overhead would increase by
$306,500, not including the cost of either acquiring or leasing office space. The
corporation will have to invest $2.6 million in office furniture, office equipment, and
other up-front costs associated with opening the new office before considering the
costs of owning or leasing the office space.
A small office building could be purchased for sole use by the corporation at a total
price of $5.8 million, of which $900,000 of the purchase price would represent land
value, and $4.9 million would represent building value. The cost of the building would
be depreciated over 39 years. The corporation is in a 21 percent tax bracket. An
investor is willing to purchase the same building and lease it to the corporation for
$645,000 per year for a term of 15 years, with the corporation paying all real estate
operating expenses (absolute net lease). Real estate operating expenses are
estimated to be 50 percent of the lease payments. Estimates are that the property
value will increase over the 15-year lease term for a sale price of $6.3 million at the
end of the 15 years. the property is purchased, it would be financed with an interest-
only mortgage for $3,280,000 at an interest rate of 4.5 percent with a balloon
payment due after 15 years.
Required:
a. What is the return from opening the office building under the assumption that it is
leased?
b. What is the return from opening the office building under the assumption that it is
owned?
c. What is the return on the incremental cash flow from owning versus leasing?
A:
The return from opening the office building under the assumption that it is leased would be the difference between the net income generated by the increase in sales and the expenses associated with opening the new office, including the cost of leasing the office space.
To calculate the net income generated by the increase in sales, we first need to calculate the total cost of goods sold. Since the cost of goods sold is estimated to be 40 percent of sales, the cost of goods sold for the new office would be 40 percent x $2.6 million = $<<40*.01*2.6=1.04>>1.04 million.
Subtracting the cost of goods sold from the increase in sales, we find that the net income generated by the increase in sales would be $2.6 million - $1.04 million = $<<2.6-1.04=1.56>>1.56 million.
Next, we need to calculate the expenses associated with opening the new office, including the cost of leasing the office space. Since the corporate overhead would increase by $306,500, the total up-front costs associated with opening the new office would be $306,500 + $2.6 million = $<<306.5+2.6=2.906>>2.906 million.
To calculate the cost of leasing the office space, we need to multiply the annual lease payment by the number of years in the lease term. Since the annual lease payment is $645,000 and the lease term is 15 years, the total cost of leasing the office space would be $645,000 x 15 years = $<<645000*15=9675000>>9.675 million.
Subtracting the total up-front costs and the cost of leasing the office space from the net income generated by the increase in sales, we find that the return from opening the office building under the assumption that it is leased would be $1.56 million - $2.906 million - $9.675 million = $<<1.56-2.906-9.675=-9.020>>-9.020 million. This means that the corporation would incur a loss of $9.020 million by opening the new office and leasing the office space.
B:
C:
To calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space.
First, let's calculate the cash flow from leasing the office space. We already know that the total cost of leasing the office space would be $9.675 million. To calculate the cash flow from leasing the office space, we need to subtract the real estate operating expenses from the total cost of leasing the office space. Since the real estate operating expenses are estimated to be 50 percent of the lease payments, the real estate operating expenses would be 50 percent x $645,000 = $<<50*.01645=322500>>322,500 per year. Since the lease term is 15 years, the total real estate operating expenses would be $322,500 x 15 years = $<<322.515=4837.5>>4,837,500. Subtracting the real estate operating expenses from the total cost of leasing the office space, we find that the cash flow from leasing the office space would be $9.675 million - $4.837.5 million = $<<9.675-4.837.5=4.837.5>>4,837,500.
Next, let's calculate the cash flow from owning the office space. We already know that the total up-front costs associated with opening the new office would be $2.906 million. To calculate the cash flow from owning the office space, we need to subtract the total annual operating expenses from the net income generated by the increase in sales. Since the net income generated by the increase in sales is $1.56 million and the total annual operating expenses are $217,774.36, the cash flow from owning the office space would be $1.56 million - $217,774.36 = $<<1.56-217774.36=1.34222564>>1,342,225.64.
Finally, to calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space. Therefore, the return on the incremental cash flow from owning versus leasing would be $1,342,225.64 - $4,837,500 = $<<1.34222564-4.837.5=-3.495.5>>-3,495,500. This means that the corporation would incur a loss of $3.495.5 million by choosing to own the office space instead of leasing it.
Which equation has no solution?
0 14x-21=-6
012-x1=9
O 13x + 61 = 6
O 1-2x+81 = 0
Step-by-step explanation:
1 , 14x=-6+21
14x=15 , divide both sides by q4 to get the value of x
x=15/14
2 , x1=x
-x=9-12
-x=-3 , divide both side by -1
x=3
3, 13x=6_61
13x= 55 , divide both sides by 13
x=55/13
4, 1-2x+81=1+81_2x
82_2x=0
-2x=-82 , divide both sides by -2
x=41
So, all of them have a solution
Jeff has two pieces of rope.the first piece of rope is 5/10 meter long. The second piece of rope is 52/100 meter long. The length of the third piece of rope is between the lengths of the first and second pieces of rope
Answer: 51/100
Step-by-step explanation:
I'm assuming that the numerator is supposed to be a whole number, because there is an infinite number of answers if it is not a whole number. 5/10 can be rewritten as 50/100 by multiplying the numerator and denominator by 10. The only fraction with a whole number numerator between 50/100 and 52/100 is 51/100. Hope this helped!
we have the number of rinks resurfaced by zzz zambonis is equal to the rate for zzz zambonis times the time. we want the time for 1\,\text{rink}1rink1, start text, r, i, n, k, end text , and we want that time to be less than or equal to 5\,\text{minutes}5minutes5, start text, m, i, n, u, t, e, s, end text. therefore: 1\,\text{rink}
we want that time to be less than equation or equal to 5 minutes start text, m, i, n, u, t, e, s, end text. therefore: 1[tex]5minutes[/tex]
Rate for ZZZ Zambonis × Time ≤ 5 minutes
Time ≤ 5 minutes/Rate for ZZZ Zambonis
To solve for the time needed to resurface one rink, we first need to set up an equation. We know that the number of rinks resurfaced by ZZZ Zambonis is equal to the rate for ZZZ Zambonis multiplied by the time. We want the time for 1 rink to be less than or equal to 5 minutes, so we need to solve for time in the equation. We can do this by dividing both sides of the equation by the rate for ZZZ Zambonis, resulting in the equation Time ≤ 5 minutes/Rate for ZZZ Zambonis. This equation gives us the maximum time needed to resurface one rink.
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an assembly consists of two mechanical components. suppose that the probabilities that the firt and second components meet specfications are 0.81 and 0.84 respectfully. assume that the components are independent. x denotes the number of components in the assembly that meet specifications. obtain the cumulative distribution function (cdf)
The probability of the cumulative distribution function to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,
P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
As given in the question,
Let probability of the first component to meet the specification be P (M)
= 0.81
And probability of the second component to meet the specification be P (N)
= 0.84
Probability of the first component do not meet the specification be P ( M' )
= 1 - 0.81
= 0.19
Probability of second component do not meet the specification be P(N' )
= 1 - 0.84
= 0.16
X defined the number of components to the meet the specifications
Here X = 0, 1, 2
P( X = 0 ) represents components do not meet any specifications
= P( M' ∩ N' )
= P(M') P(N') ( Independent )
= 0.19 × 0.16
= 0.0304
P( X= 1) represents components meet only one specification
= P( M∩N') ∪ P( M'∩N)
= P( M∩N') + P( M'∩N)
= P(M) P(N') + P(M') P(N)
= 0.81(0.16) + (0.19)(0.84)
= 0.1296 + 0.1596
= 0.2892
P( X=2) represents components meet both the specification
= P( M ∩ N )
= P(M) P(N)
= 0.81(0.84)
= 0.6804
Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.
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Which of the following sets of numbers could not represent the three sides of a right
triangle?
O {48, 55, 73}
O {39, 80, 89}
O {42, 56, 70}
O {10, 23, 26}
Submit Answer
{48, 55, 73} and {10, 23, 26} do not represent a right angle triangle.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
Now,
48² + 53² = 73².
2304 + 2809 = 5329.
5113 ≠ 5329 so do not represents a right-angle triangle.
Similarly,
39² + 80² = 89² represents a right-angle triangle.
42² + 56² = 70² represents a right-angle triangle.
10² + 23² ≠ 26²so do not represent a right-angle triangle.
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Here is the preference schedule for a recent election among four candidates:
Number of voters 7 1 11 5 2 19 9
1st choice A X D A X A G
2nd choice X G G G A D X
3rd choice D D A X G X D
4th choice G A X D D G A
How many voters voted in this election?
How many first place votes are needed for a majority?
Which candidate/choice had the most first-place votes?
Which candidate/choice has the least first-place votes?
Which candidate/choice had the most last-place votes?
Which candidate/choice has the least last-place votes?
Answer:
There were a total of 7 + 1 + 11 + 5 + 2 + 19 + 9 = 44 voters in this election.
To get a majority, a candidate would need at least 44 / 2 + 1 = 23 first place votes.
The candidate with the most first-place votes is A, with a total of 7 + 1 + 5 = 13 first-place votes.
The candidate with the least first-place votes is X, with a total of 1 first-place vote.
The candidate with the most last-place votes is G, with a total of 9 + 2 + 9 = 20 last-place votes.
The candidate with the least last-place votes is X, with a total of 0 last-place votes.
Step-by-step explanation:
HELP QUICK!! Which set of side measurements could be used to form a right triangle?
Answer:
3, 4, 5
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
differentiate of the following w.r.t.x
i mark u branlist if u give me right answer
The differentiation of y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x is cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
How to differentiate y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x?In mathematics, differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how the function changes as its input (or independent variable) change
Given: y = logx - cosecx + 5ˣ + 3/(x^(3/2))
Thus, the derivative will be:
d/dx [logx - cosecx + 5ˣ + 3/(x^(3/2))]
= d/dx [logx] - d/dx [logx] + d/dx [5ˣ] + 3d/dx[(x^(3/2))]
= 1/x - (-cotx)cosecx + log(5).5ˣ + 3(-3/2)x^((3/2) -1)
= cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))
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46. The table shows the temperature (in degrees) for eight consecutive days as well as the
respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature 68 77 83 85 89 94 96 99
Number of Cones 403 447 457 465 489 503 543 576
About how many ice cream cones would you expect the shop to sell if the temperature one day
is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
0579 cones
0585 cones
O 602 cones
(617 cones
A line of best fit for this problem is y = 5.08x + 46.59. The number of ice cream cones that you would expect the shop to sell if the temperature one day is 106 degrees is; 585 cones
How to find the line of best fit?A graph of the scatter plot and line of best fit is as shown in the attached file.
The temperature in this problem is the independent variable, or x. This is due to the fact that we are assuming that the particular number of ice cream cones sold will depend on the temperature. Therefore, we can say that the number of ice cream cones will be the dependent variable, or y.
Therefore in our graphing calculator, we will enter temperature in the first list and then the number of cones in the second.
Sequel to drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax + b:
a = 5.08
b = 46.59
Therefore, the equation is;
y = 5.08x + 46.59.
Entering our temperature of 106 degrees, for x gives;
y = 5.08(106) + 46.59
= 585.07
≈ 585
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(easy) Jinsoul had 2 apples and Chaeyoung had 3 apples. Chaeyoung suggest they share, Jinsoul agrees. Together it makes 5 apples. BUT The apple tree they picked from has 20? 5+20=?
Answer:
Step-by-step explanation:
5+ 20= 25
Because when you set them up and add them properly you get 25
(Not sure if that was the question you wanted us to answer..)
leg-leg (ll) congruence theorem if the legs of a right triangle are congruent to the legs of a second right triangle, then the triangles are congruent.
The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.
We know that two triangles are congruent if and only if they have three pairs of equal sides.
In the case of the LL congruence theorem,
the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).
Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.
Alternatively
If the legs are of equal length then
Their squares would be equal to
Hence, the sum of these squares too would be equal.
Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.
Hence, by SSS congruence criteria
the triangles would be congruent.
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If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')) OR ((w OR y') AND (x OR Y)') ? A) TRUE B) Not enough information.C) FALSE D) NULL
After solving the logical operations it can be determined that the correct answer is C) FALSE.
What are logical operations?Logical operations are phrases that connect expressions to test if they are true or not.
What does the complement sign mean?The complement (') sign means that the opposite value of the variable is needed. For example if y is false, y' means true.
Let False = 0 and True = 1
= ((0 OR 0') AND (1' AND 0')) OR ((0 OR 0') AND (1 OR 0)')
= ((0 OR 1) AND (0 AND 1)) OR ((0 OR 1) AND (1)')
= (1 AND 0) OR (1 AND 0)
= 0 OR 0
= 0
Hence, the answer is C) FALSE
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Ariel earns $8.00 per hour. Her benefits package is equal to 15% of her hourly wages.
Ariel works 40 hours each work week. How much does Ariel earn in a week WITH
benefits?
Answer:
$368 per week
Step-by-step explanation:
[tex]8 \times 40 \times 1.15 = 368[/tex]
4 kilometer from house to the nearest mailbox. how far is it in meter?
Answer:
4 kilometers is equal to 4000 meters.
Step-by-step explanation:
1 kilometer is equal to 1000 meters, so 4 kilometers is equal to 4 x 1000 = 4000 meters. This is because the prefix "kilo" means 1000, so 1 kilometer is equivalent to 1000 meters.
how to solve probability of distribution
Answer:
Step-by-step explanation:
How to find the mean of the probability distribution: Steps
Step 1: Convert all the percentages to decimal probabilities. For example: ...
Step 2: Construct a probability distribution table. ...
Step 3: Multiply the values in each column. ...
Step 4: Add the results from step 3 together.
consider a pair of integers (a b) the following operations can be performed on (a,b) in any order, zero or more times
If we consider a pair of integers (a b) and the given operations, then the java program that depicts it is as written below.
How to carry out programming in Java?The program that carries out the required operations on the pair of integers is;
static LinkedList<Pair<Integer,Integer>> pairs = new LinkedList<Pair<Integer, Integer>>();
public static String isItPossible(Integer a, Integer b, Integer c, Integer d){
pairs.addLast(new Pair<Integer, Integer>(a,b));
while (!pairs.isEmpty()){
Pair<Integer,Integer> pair = pairs.poll();
Integer key = pair.getKey();
Integer value = pair.getValue();
if(key.equals(a) &&
value.equals(b)){
return "YES";
}
int sum=key+value;
if (sum<=c){
pairs.addLast(new Pair<Integer, Integer>(sum,value));
}
if (sum<=d){
pairs.addLast(new Pair<Integer, Integer>(key,sum));
}
}
return "NO";
}
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Complete question is;
Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times:
• (a, b)(a + b, b)
• (a, b) → (a, a + b)
Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example
(a, b) = (1, 1)
(c,d) = (5,2)
Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on.
Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000
What improvement can we make?
In general, the improvements that we can make refer to optimizations that can be applied in a context.
¿What are the improvements?In a particular process or context, the best are optimizations that are done to make something more efficient or to improve the quality of an element.
For example, some improvements that we could make in our community are:
Establish more efficient containers to better collect garbage.Optimize public lighting. Improve solid waste management.¡Hope this helped!
Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. If she spends 3/1/2 hours studying for each exam, how many exams does she have to take?
The number of exams that Gretchen has to take is 4 exams.
How many exams does Gretchen have to take?From the information illustrated, Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. The total hours that she used will be:
= 5.1 + 3 3/5 + 5 3/10
= 5.1 + 3.6 + 5.3
= 14 hours.
Since she spends 3/1/2 hours studying for each exam, the number of exams that she has to take will be:
= Number of hours / Hours used for each exam
= 14 / 3 1/2
= 4 exams
The number of exams are 4.
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Round 13.689 to the nearest hundredth
a clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $55, while 8000 shirts can be sold at a price of $47. give a linear equation in the form p
The linear relationship between the number of shirts, n ,it can sell and the price, p is p = (-1/250)x + 79
The linear equation is
y = mx + b
Where m is the slope of the line
b is the y intercept
Here p is the total price
n is the number of shirts
The equation will be
p = mn + b
The price of 6000 shirts = $55
The price of 8000 shirts = $47
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line = (47-55) / (8000-6000)
= -8/2000
= - 1/250
Substitute the point (6000, 55) in the equation
55 = (-1/250)(6000) + b
55 = -24 + b
b = 55 + 24
b = 79
Substitute the values in the equation
p = (-1/250)x + 79
Therefore, the linear relation in the form of p is p = (-1/250)x + 79
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If a line is tangent to a circle, then it is ___________ to the radius drawn to the point of tangency.
If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.
Given that the radius is drawn to the point of tangency of a tangent line.
We are required to fill the blank with the appropriate word.
Radius is basically the line segment which joins the center to any point on the circumference of the circle.
Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.
When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.
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which phrase describes the variable expression 7 ÷ s?
a) 7 decreased by s
b) the product of 7 and s
c) 7 increased by s
d) the quotient of 7 and s
The phrase describes the variable expression 7 ÷ s is the quotient of 7 and s.
The correct option is (d).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 7 ÷ s
We know that the division results to quotient.
So, the expression shows the 7 is divided by s to give the quotient.
Hence, the answer is the quotient of 7 and s.
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evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are a1
The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
1. The integral is given as an area under a graph.
2. The graph has labeled regions.
3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.
4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.
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Use the given information to prove that ΔRST ≅ ΔVUT.
Given: ST ≅ UT
∠SRT ≅ ∠UVT
Prove: ΔRST ≅ ΔVUT
Based on the given information , the proof of triangle RST ≅ triangle VUT is shown below .
In the question ,
two triangles are given where ;
it is given that side ST ≅ UT
and ∠SRT ≅ ∠UVT .
we have to prove that ΔRST congruent ΔVUT .
In triangle RST and triangle VUT .
side ST = side UT .....given that ST ≅ UT ;
angle SRT = angle UVT ....given that ∠SRT ≅ ∠UVT ;
angle RTS = angle VTU .....because they are vertically opposite angles .
Hence by ASA congruence , triangle RST ≅ triangle VUT .
Therefore , it is proved that triangle RST ≅ triangle VUT .
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In triangle, HIJ, N is the centroid. If
HK = 10, find KI.
Answer:
4k because is right is the best answer
Rewrite the set U by listing its elements. Make sure to use the appropriate set
notation.
U= {x|x is an integer and -4
U =
The set U can be rewritten by listing its elements as follows:
U = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}
In this notation, the "..." symbol indicates that the set continues in both the negative and positive direction, and that all integers from negative infinity to positive infinity are included in the set. This notation is commonly used to represent sets of integers or other infinite sets in mathematics.
Cast Iron Grills, Incorporated, manufactures premium gas barbecue grills. The
company reports inventory and cost of goods sold based on calculations from a LIFO
periodic inventory system. Cast Iron's December 31, 2024, fiscal year-end inventory
consisted of the following (listed in chronological order of acquisition):
Units. Unit cost
6,800. 600
4,900. 700
7,800. 800
The replacement cost of the grills throughout 2025 was $900. Cast Iron sold 36,000
grills during 2025. The company's selling price is set at 200% of the current
replacement cost.
Required:
1. & 2. Compute the gross profit (sales minus cost of goods sold) and the gross profit
ratio for 2025 under two different assumptions. First, that Cast Iron purchased 37,000
units and, second, that Cast Iron purchased 19,500 units during the year.
4. Compute the gross profit (sales minus cost of goods sold) and the gross profit ratio
for 2025 assuming that Cast Iron purchased 37,000 units (as per the first assumption)
and 19,500 units (as per the second assumption) during the year and uses the FIFO
inventory cost method rather than the LIFO method.
Answer:
a) ending inventory: 11,850,000
cost of goods sold: 25,200,000
gross profit 25,200,000
b)
ending inventory: 1,800,000
cost of goods sold: 23,100,000
gross profit 50,400,000 - 23,100,000 = 27,300,000
5,200 at $600
4,100 at $700
6,200 at $800
purchase 29,000 at $900
-sold 28,000 grills
As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account
ending inventory
5,200 at $ 600
4,100 at $ 700
6,200 at $ 800
1,000 at $ 900
Total $ 11,850,000
cost of good sold:
28,000 x $900 = $25,200,000
sales revenue
28,000 x 900 x 200% = $50,400,000
gross profit sales revenue less COGS
b) 5,200 at $600
4,100 at $700
6,200 at $800
purchase 15,500 at $900
-sold 28,000 grills
we check how many layer deep we go:
28,000 - 15,500 at 900= 12,500
12,500 - 6,200 at 800= 6,300
6,300 - 4,100 at 700 = 2,200 at 600
Ending Inventory
3,000 at $600 = $ 1,800,000
COGS:
15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000
Step-by-step explanation: