what is the mean of this data set? 12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18. answers: 13.50, 14.00, 14.75, and 15.75
Answers
Answer:
14.75
Step-by-step explanation:
Add them all up, divide by 12
Related Questions
1.1.3 Quiz: Exponents
Question 2 of 10
Simplify (6^7)³.
Answers
Answer:6^21
Step-by-step explanation:
work out the area of the circle
take pi to be 3.142 give your answer to 1 decimal place
radius 8
Answers
The area of the circle with the given radius is 201.088 square units.
What is area of a circle?The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.
Given that, the radius of a circle is 8 units.
Here, area of a circle
= 3.142×8²
= 3.142×64
= 201.088 square units
Therefore, the area of the circle is 201.088 square units.
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Which statement describes how to determine if a relation given in a table is a function?
If none of the output values are repeated, the relation is a function.
If none of the input values are repeated, the relation is a function.
If any of the input values are equal to the output values, the relation is a function.
If all the output values are paired with the same input value, the relation is a function.
Answers
Answer:
If none of the input values are repeated, the relation is a function.
Step-by-step explanation:
When all outputs have a different input, its a function.
Answer:
B
Step-by-step explanation:
Did it on edge 100%
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Round your answers to two decimal places (e.g. 98.76).
Answers
Answer:
a) 0.6730 = 67.30% probability that no samples are mutated.
b) 0.9436 = 94.36% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either it is mutated, or it is not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases.
This means that \(p = 0.03\)
13 samples are studied
This means that \(n = 13\)
(a) No samples are mutated.
This is P(X = 0). So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730\)
0.6730 = 67.30% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
\(P(X \leq 1) = P(X = 0) + P(X = 1)\)
So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730\)
\(P(X = 1) = C_{13,1}.(0.03)^{1}.(0.97)^{12} = 0.2706\)
Then
\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.6730 + 0.2706 = 0.9436\)
0.9436 = 94.36% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
\(P(X > 6.5) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)\)
Then
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 7) = C_{13,7}.(0.03)^{7}.(0.97)^{6} \approx 0\)
Using two decimal digits precision, all will be 0. So
0% probability that more than half the samples are mutated.
Please help! What is the surface area of the cylinder with height 4 m and radius 8 m? Round your answer to the nearest thousandth.
Make sure to round please.
Answers
The surface area of the cylinder is 948m²
What is surface area of cylinder?The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;
SA = 2πr(r+h)
Where r is the radius of the base and h is the height of the cylinder.
r =8m
h = 4m
SA = 2 × 3.14 × 8 (8+4)
SA = 78.96 × 12
SA = 947.52 m²
to the nearest whole number
SA = 948 m²
therefore the surface area of the cylinder is 948 m²
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Please help me!!!
Sharon factored the polynomial
x^2 + 81 as (x+9)(x-9)
using the difference of 2 squares method. Her teacher marked her andar wrong. Do you agree or disagree. Write a 1 sentence explaining why you agree or disagree with her teacher. You must write a sentence to earn a full credit.
Answers
Answer:
I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.
Step-by-step explanation:
The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.
Which of the following represents 20 = 5 x 4
A. 5 is 4 times as many as 20
B. 20 is 2 times as many as 10
C. 4 is 5 times as many as 20
D. 20 is 5 times as many as 4
Answers
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
the answer is d because
20 is "=" 5 times "×" as 4
so the formula derived is
20= 5x4
is represents =
times represents ×
hope you get it
1. A therapeutic drug has the side effect of raising a patient's heart rate. The relationship between ,
the amount of the drug in the patient's body (in milligrams), and r, the patient's heart rate (in beats
per minute) is given by r(Q) = 60+ 0.2Q. Over time the level of the drug in the patient's
bloodstream changes. The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)".
a. What is the heart rate of this patient 5 minutes after the drug was administered? 8 minutes?
10 minutes? 13 minutes?
Answers
Complete question :
A therapeutic drug has the side effect of raising a patient's heart rate. The relationship between ,
the amount of the drug in the patient's body (in milligrams), and r, the patient's heart rate (in beats
per minute) is given by r(Q) = 60+ 0.2Q. Over time the level of the drug in the patient's
bloodstream changes. The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)^t.
a. What is the heart rate of this patient 5 minutes after the drug was administered? 8 minutes?
10 minutes? 13 minutes?
Answer:
76.384 ;
68.389 ;
65.369;
62.749
Step-by-step explanation:
Given function:
r(Q) = 60+ 0.2Q ; amount of drug on patient's body, Q and heart rate (r)
The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)^t
a. What is the heart rate of this patient
5 minutes after the drug was administered?
t = 5 ; quantity of drug on patient's body ;
Q(5) = 250(0.8)^5 = 81.92
Q = 81.92
Heart rate (r)
r(81.92) = 60+ 0.2(81.92) = 76.384
t = 8 minutes?
Q(8) = 250(0.8)^8 = 41.94304
Q = 41.94304
Heart rate (r)
r(41.94304) = 60+ 0.2(41.94304) = 68.389
t = 10 minutes
Q(10) = 250(0.8)^10 = 26.8435456
Q = 26.8435456
Heart rate (r)
r(26.8435456) = 60+ 0.2(26.8435456) = 65.369
t = 13 minutes
Q(13) = 250(0.8)^13 = 13.7438953472
Q = 13.7438953472
Heart rate (r)
r(13.7438953472) = 60+ 0.2(13.7438953472) = 62.749
Dwight is making accessories for the soccer team. He uses 727.32 inches of fabric on headbands for 34 players and 4 coaches. He also uses 293.42 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
Total fabric used per player is 312.56 inches.
What is the total fabric used per player?To get the quantity of fabric used accessories per player, we need to add the fabric used for headbands and wristbands and divide by total number of players.
The total fabric used for headbands for players and coaches is 727.32 inches.
The total players and coaches is:
= 34 + 4
= 38
Length of fabric used for them is:
= 727.32 / 38
= 19.14 inches
The fabric used for wristbands per player is 293.42 inches
So, the total fabric used per player is:
= 19.14 + 293.42
= 312.56 inches.
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In a recent year, a hospital had 4588 births. Find the mean number of births per day, then use that result and the Poisson distribution to find the probability that in a day there are 16 births.
Answers
Answer:
4221 birhs
Step-by-step explanation:
. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births.
6. Journalise the following transactions
1. Bricks for Rs 60,000 and timber for Rs 35,000 purchased for
the construction of building. The payment was made by cheque.
2. Placed in fixed deposit account at bank by transfer from current
account Rs 13,000.
3. Appointed Mr. S.N. Rao as Accountant at Rs 300 p.m. and
Received Rs 1000 as security Deposit at 5% p.a. interest.
4. Sold goods to shruti for Rs 80,000 at 15% trade discount and
4% cash discount. Received 75% amount immediately through a
cheque.
5. Purchased goods from Richa for Rs 60,000 at 10% trade
discount and 5% cash discount. 60% amount paid by cheque
immediately.
6.
On 18th jan,Sold goods to shilpa at the list price of Rs 50,000
20% trade discount and 4% cash discount if the payment is made
within 7 days. 75% payment is received by cheque on Jan 23rd.
7. On 25th jan, sold goods to garima for Rs 1,00,000 allowed her
20% trade discount and 5% cash discount if the payment is made
within 15 days. She paid 1/4th of the amount by cheque on Feb 5th
and 60% of the remainder on 15th in cash.
8. Purchased land for Rs 2,00,000 and paid 1% as brokerage and
Rs 15,000 as registration charges on it. Entire payment is made by
cheque.
9. Goods worth Rs 25,000 and cash Rs 40,000 were taken away
by the proprietor for his personal use.
10. Sold goods costing Rs 1,20,000 to charu at a profit of 33% 3 %
on cost less 15% trade discount.
9
11. Paid rent of building Rs 60,000 by cheque. Half the building is
used by the proprietor for residential purpose.
12. Sold goods costing Rs 20,000 to sunil at a profit of 20% on
sales less 20% trade discount .
13. Purchased goods for Rs 1000 from nanda and supplied it to
helen for Rs 1300. Helen returned goods worth Rs 390, which in
turn were returned to nanda.
14. Received invoice at 10% trade discount from rohit and sons
and supplied these goods to madan, listed at Rs 3000.
Answers
1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)
2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)
3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)
4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)
5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)
6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)
7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)
8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)
9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)
10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)
11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)
12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)
13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)
14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)
Here are the journal entries for the given transactions:
1. Bricks and timber purchased for construction:
Debit: Bricks (Asset) - Rs 60,000
Debit: Timber (Asset) - Rs 35,000
Credit: Bank (Liability) - Rs 95,000
2. Transfer to fixed deposit account:
Debit: Fixed Deposit (Asset) - Rs 13,000
Credit: Current Account (Asset) - Rs 13,000
3. Appointment of Mr. S.N. Rao as Accountant:
Debit: Salary Expense (Expense) - Rs 300
Debit: Security Deposit (Asset) - Rs 1,000
Credit: Accountant (Liability) - Rs 300
4. Goods sold to Shruti:
Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000
Credit: Sales (Income) - Rs 80,000
5. Goods purchased from Richa:
Debit: Purchases (Expense) - Rs 60,000
Credit: Accounts Payable - Richa (Liability) - Rs 60,000
6. Goods sold to Shilpa:
Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000
Credit: Sales (Income) - Rs 50,000
7. Goods sold to Garima:
Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000
Credit: Sales (Income) - Rs 1,00,000
8.Purchase of land:
Debit: Land (Asset) - Rs 2,00,000
Debit: Brokerage Expense (Expense) - Rs 2,000
Debit: Registration Charges (Expense) - Rs 15,000
Credit: Bank (Liability) - Rs 2,17,000
9. Goods and cash taken away by proprietor:
Debit: Proprietor's Drawings (Equity) - Rs 65,000
Credit: Goods (Asset) - Rs 25,000
Credit: Cash (Asset) - Rs 40,000
10. Goods sold to Charu:
Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000
Credit: Sales (Income) - Rs 1,20,000
Credit: Cost of Goods Sold (Expense) - Rs 80,000
Credit: Profit on Sales (Income) - Rs 40,000
11. Rent paid for the building:
Debit: Rent Expense (Expense) - Rs 60,000
Credit: Bank (Liability) - Rs 60,000
12. Goods sold to Sunil:
Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000
Credit: Sales (Income) - Rs 24,000
Credit: Cost of Goods Sold (Expense) - Rs 20,000
Credit: Profit on Sales (Income) - Rs 4,000
13. Goods purchased from Nanda and supplied to Helen:
Debit: Purchases (Expense) - Rs 1,000
Debit: Accounts Payable - Nanda (Liability) - Rs 1,000
Credit: Accounts Receivable - Helen (Asset) - Rs 1,300
Credit: Sales (Income) - Rs 1,300
14. Goods received from Rohit and Sons and supplied to Madan:
Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)
Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700
Debit: Accounts Receivable - Madan (Asset) - Rs 3,000
Credit: Sales (Income) - Rs 3,000
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a certain number of yams is sufficient to feed 20 students for 12 days for how many days would the same number of yams feed 15 students
Answers
Step-by-step explanation:
no of days = (15×12)/20= 9 days
I hope this helps
15 students consume it in = (20×12)÷15
= 16 days
determine the range of the following graph
Answers
The range of the graphed function in this problem is given as follows:
[-9, 9].
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.The values of y in this function are between -9 and 9, inclusive, hence the range of the function is given as follows:
[-9, 9].
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A farmer planted 3,060 tomato plants in his garden. Due to a severe drought, the number of tomato plants is decreasing according to the following function.
Which expression represents the number of months, x, it will take for the number of tomato plants in his crop to reach 51?
A.
B.
C.
D.
Answers
The number of months to reach 51 can be illustrated as 3060 - 100x = 51.
What is an expression?The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.
The farmer planted 3,060 tomato plants in his garden.
Let's assume there's a decrease of 100 monthly.
The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c
This will be:
3060 - 100x = 51.
This illustrates the equation for the number of months.
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AB= 10 & AC=25 find the length of BC.
Answers
Answer:
15
Step-by-step explanation:
We can imagine this like a number line.
A------------B--------------------C
The distance from A to B is 10.
The distance from A to C is 25.
This means that the distance from B to C will be \(25-10=15\).
Hope this helped!
What is the value of the constant in the equation that relates the height and
width of this rectangle?
Answers
Answer:
10 over=5
i asked this quetion
Answer:50
Step-by-step explanation:
Will the following side lengths form a right triangle? 14, 21, 25
Answers
Answer:
They will not.
Step-by-step explanation:
\( {14}^{2} + {21}^{2} = 196 + 441 = 637\)
\( {25}^{2} = 625\)
Mrs. Becker drives past the Route 50 drawbridge light every morning on the way to
work. Eight out of 10 times, the traffic light is red. There are only 25 days of school le
how many of those days should she expect to get stopped at that light?
Answers
Answer:
20 days
Step-by-step explanation:
1) \(\frac{8}{10}\) must be written as a fraction where the denominator is 25 since there are 25 days of school.
\(\frac{8}{10} = \frac{x}{25}\)
2) Cross multiply them.
\(10(x) = 25(8)\)
\(10x = 200\)
3) Solve for \(x\).
\(x = \frac{200}{10}\)
\(x = 20\)
solve the equation n - 9/10 = - 109/10
Answers
to solve this question, we need to simplify
step 1
write out the equation and collect like terms
\(\begin{gathered} n-\frac{9}{10}=-\frac{109}{10} \\ n=-\frac{109}{10}+\frac{9}{10} \end{gathered}\)step 2
take the LCM and solve the fraction
the LCM here is 10
\(\begin{gathered} n=-\frac{109}{10}+\frac{9}{10} \\ n=\frac{-109+9}{10} \\ n=-\frac{100}{10} \\ n=-10 \end{gathered}\)Identify the terminal point for a 30° angle in a unit circle.
O A (1,
O R. (4,4)
O c. (9.12)
OD. (1,7)
SUBMIT
Answers
Answer:
The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).
Step-by-step explanation:
12 of the students of the school band likes to play the drums. These 12 students make up 24% of the band. How many student are in the band?
Answers
Answer: 50
Step-by-step explanation:
You'll need to find one percent first:
12 ÷ 24= 0.5
0.5= 1% of the band
Now multiply one percent by 100:
0.5x100= 50
There are 50 students in the school band
What is the represent a function?
Answers
We can represent a function in four ways: Algebraically, Numerically, Graphically, Visually.
In the given question we have to explain how we represent a function.
A function is a relationship between two sets of variables in which one variable depends on another. Different techniques can be used to portray various sorts of functions. Typically, functions are represented by diagrams or formulas. The four approaches for representing a function are as follows:
Algebraically
Numerically
Graphically
Visually
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1 peso = $ .075. How many pesos (whole number) do you get for $100 ?
Answers
Answer:
133
Step-by-step explanation:
100/.75 = 133.33 = 133
[f-g] (3) for f(x)=4x+3 and g(x)=8/x+2 step by step!
Answers
Answer:
10.4
Step-by-step explanation:
x=3⇒f(3)= 4×3+3=15
x=3⇒g(3)=8/3+2≈4.6
f(3)-g(3)=15-4.6=10.4
what does 1\4 divided by 1 3/5 equal and how do i work it out
Answers
Answer:
slimer 16 goofy butt fart gamer setup
Step-by-step explanation:
Dominic is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over t months is given by the equation C=45t+100. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
Answers
The slope intercept form is y=mx+b, and b represents the y-intercept. In the given equation C=45t+100, 100 is the y-intercept. It represents the one-time fee to join the gym membership.
Answer:
y intercept is 100
which represents the one-time joining fee
Step-by-step explanation:
Type < or > to make this statement true -a___-b
Answers
The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 19. 17 < 23 20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)
To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.
To indicate that the first value is less than the second value, write <.
Alternatively, to indicate that the first value is greater than the second value, write >.
Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36
To determine the direction of inequality, we need to compare the values.
We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.
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The correct question would be as
Write > or < to make each statement true.
11. -5 0
12. 9 -8
13. -7 7
14. 55 -75
15. -32 -24
16. 89 73
17. -58 -51
18. -32 4
19. 17 23
20. 18 -36
How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)
Now just equate this to a time 0 payment at the same rate
\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
Corey spent 18 minutes coloring. She spent 6 times as many minutes reading
Answers
Answer:
18 x 6 =108. she spent 108 minutes reading.
Step-by-step explanation:
Evaluate the expression when =c24 and =d25. +dc4
Answers
The expression given is 3c + 5d and the expression when c = 24 and d =25 will be 197.
How to illustrate the expression?It should be noted that an expression is simply used to illustrate the relationship between the variables.
In this case, the expression given is 3c + 5d.
Therefore, the expression given is 3c + 5d and the expression when c = 24 and d =25 will be:
= 3c + 5d
= 3(24) + 5(25)
= 72 + 125
= 197
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Complete question:
The expression given is 3c + 5d. Evaluate the expression when c = 24 and d =25.