find the algebraic Inverse: f (x) 1/4x - 2
Answers
Answer:
inverse function f⁻(x) = 1 / (4x + 8)
Mark it as brainlist answer
Step-by-step explanation:
Related Questions
4s4 17s2 14s 2 = (2s3 3s2-4s 1)(x)
Answers
The required difference of the polynomial functions is -9s^2 + 4s - 2
Given the following difference of polynomial expressed as:
(–6s2 + 12s – 8) – (3s2 + 8s – 6)
We are to find the difference
(–6s2 + 12s – 8) – (3s2 + 8s – 6)
Expand
–6s^2 + 12s – 8 - 3s^2 - 8s + 6
Collect the like terms
–6s^2- 3s^2 + 12s - 8s - 8 + 6
-9s^2 + 4s - 2
Hence the required difference of the polynomial functions is -9s^2 + 4s - 2
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complete question
Find each difference.
(–6s2 + 12s – 8) – (3s2 + 8s – 6) =
–9s2 + 4s – 14
–9s2 + 4s – 2
–9s2 + 20s – 14
–9s2 + 20s – 2
Solve the equation graphically
x³ +256 = 0
Answers
The equation x³ + 256 = 0 has a value of x = -6.35
How to solve the equation?The equation is given as
x³ + 256 = 0
To determine the solution graphically, we simply enter the equation in a graphing calculator
And then, we write out where the equation intercepts the x-axis
Using the above as a guide, we have
x³ + 256 = 0
Plot the graph (see attachment)
From the graph, we have
x = -6.35 (approximately)
Hence, the solution to the equation is x = -6.35
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6x-7y=7andx-7y=-8 find valve of x and y
Answers
Answer:
x = 3, y = 11/7.
Step-by-step explanation:
6x - 7y = 7
x - 7y = -8 Subtract:
5x = 15
x = 3
3 - 7y = -8
-7y = -11
y = 11/7.
Answer: x = 3 and y = 11/7
Step-by-step explanation: 6x-7y+(-6x) = 7+(-6x) -7y/-7 = -6x+7/-7 y = 6/7x-1 x-7 (6/7 (x) -1) = -8 -5x+7+(-7) = -8+(-7) -5x/-5 = -15/-5 x = 3 y = 6/7x-1 y = (6/7) (3) -1 y = 18/7-1 18/7-1/1 18/7-7/7 y= 11/7 x = 3 and y = 11/7
A small tree is 80 cm tall.
A few years later, the tree is 1.2 m tall.
Find the percentage increase.
Answers
amount of increase = 120-80 = 40 centimeters
40 ÷ 80 = 0.5 = 50%
There was a 50% increase.
Consider a random sample of size 32 from a distribution with mean 40 and variance 8. find the (approximate) probability that the sample mean is between 39.75 and 41.25.
Answers
The probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
The probability that the sample mean is between 39.75 and 41.25 can be calculated using the Central Limit Theorem. This theorem states that the distribution of the sample means will be normally distributed with a mean equal to the population mean (μ = 40) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ = 8/√32).
Using this information, we can calculate the probability that the sample mean is between 39.75 and 41.25, which will be the area under the normal curve between those two points. This area can be calculated using the z-score formula, which is (x-μ)/σ = (41.25-40)/(8/√32). This gives us a z-score of 0.25. The probability can then be calculated using a z-table, which is approximately 0.5987. Therefore, the probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
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a dvd rental company charges $10 per month plus $0.75 per rental. Andy wants to spend no more than 25.00 per month on DVD rentals. Select the inequality that represents how many DVDs Andy can rent in one month that satisfies this condition. The number of rentals in a month is represented by n. A. 10.75n < 25
Answers
The answer of the question based on the inequality the answer is Andy can rent up to 20 DVDs in a month and spend no more than $25.
What is Inequality equations?An inequality equation is mathematical statement that compares the two values or expressions using inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
The total cost, C, for renting n DVDs in a month is given by:
C = 10 + 0.75n
The question tells us that Andy wants to spend no more than $25 per month on DVD rentals. Therefore, we can write an inequality:
C ≤ 25
Substituting the expression for C from above, we get:
10 + 0.75n ≤ 25
Simplifying the inequality, we can subtract 10 from both sides:
0.75n ≤ 15
Finally, we can divide both sides by 0.75:
n ≤ 20
Therefore, the inequality that represents how many DVDs Andy can rent in one month that satisfies the condition of spending no more than $25 per month is:
n ≤ 20
So, Andy can rent up to 20 DVDs in a month and spend no more than $25.
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How many pints and in a cup??
Answers
Answer:
.5
Step-by-step explanation:
because a pint is 2 cups so divide by 4 because you multiply that 2 by another 2 is 4 so once you do that its .5
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer: A
Step-by-step explanation:
There is 3 ticks until it hits the whole number 1. it is on the first tick. 1/3
Answer:
b i really hope im right
Step-by-step explanation:
!Urgent Help To Whoever Is Willing!
Answers
The average rate of variance of wind chill over each of these 3 intervals is 0.638, 0.523, and 0.332, respectively.
How to calculate the valueLet's select three respective intervals of wind speed and calculate the mean rates of variance in wind chill inside those ranges.
Interval 1: 3 ≤ w ≤ 10
Average rate of variance runs at: (wind chill at w=10 - wind chill at w=3) / (10 - 3)
= (-17.191 - (-20.475)) / (10 - 3)
= 0.638
Interval 2: 10 ≤ w ≤ 20
Average rate of variance stands at: (wind chill at w=20 - wind chill at w=10) / (20 - 10)
= (-12.958 - (-17.191)) / (20 - 10)
= 0.523
Interval 3: 20 ≤ w ≤ 30
Average rate of variance boils down to: (wind chill at w=30 - wind chill at w=20) / (30 - 20)
= (-9.635 - (-12.958)) / (30 - 20)
= 0.332
Hence, the average rate of variance of wind chill over each of these 3 intervals is:
0.638, 0.523, and 0.332, respectively.
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what is 90% of 760 . what is the answer
Answers
Answer:
684
Step-by-step explanation:
Since 90% = 0.9
0.9 x 760
Which equals 684
Please mark as brainliest
Answer:
=684
Step-by-step explanation:
90% of 760
90/100 x 760
=684
I will give 100 points to anyone who can answer my question.
Answers
Answer:
A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.
Answer:
The answers are (-10, -4) and (0, 1)
Step-by-step explanation:
The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.
Hope this helps!
In the answer box below, type an exact answer only (i.e. no decimals). You do not need to fully simplify/reduce fractions and radical expressions. If \( \tan \alpha=-\frac{19}{180} \) with α in quadrant II, then find tan(2α). tan(2α)=
Answers
When tan(α) is -19/180 and α is in second quadrant tan2α will be -6840/32039 .
Given,
tan(α) = -19/180
α is in quadrant || .
Now
tan(2α) = 2tanα /1 - tan²α
Substitute the values of tanα in tan(2α) .
So,
tan(2α) = 2*(-19/180) / 1 - (-19/180)²
tan(2α) = -6840/32039 .
Thus when tan(α) is -19/180 and α is in second quadrant tan2α will be -6840/32039 .
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find an equation of a parabola that has curvature 4 at the origin. (assume the parabola has its vertex at the origin, and opens upward.) y(x) =
Answers
The equation of the parabola that has curvature 4 at the origin and opens upward is:
y(x) = 2x^2
k = |(y''(x))/(1 + (y'(x))^2)^(3/2)|
where y''(x) represents the second derivative of the function and y'(x) represents the first derivative of the function.
Since the vertex of the parabola is at the origin, we know that the equation of the parabola can be written as:
y(x) = ax^2
where a is a constant. Now, we can find the second derivative of this equation:
y''(x) = 2a
Next, we can find the first derivative of the equation:
y'(x) = 2ax
Using these values, we can plug them into the formula for curvature:
k = |(2a)/(1 + (2ax)^2)^(3/2)| We know that the curvature at the origin is 4, so we can set k equal to 4 and solve for a:
4 = |(2a)/(1 + (2*0)^2)^(3/2)|
4 = 2a
a = 2 Therefore, the equation of the parabola that has curvature 4 at the origin and opens upward is: y(x) = 2x^2
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Please help I’m running out of time!!!
After which event did General Douglas MacArthur take command of the US Army in the Pacific?
The Japanese invaded the Philippines.
O The US won the battle of Midway Island.
O The US and Japan fought for Guadalcanal.
O The Japanese almost won the battle of Iwo Jima.
Answers
Answer:
The answer is Battle of Midway
Step-by-step explanation:
in a hospital, a sample of 8 weeks was selected, and it was found that an average of 438 patients were treated in the emergency room each week. the standard deviation was 16. find the 99% confidence interval of the true mean. assume the variable is normally distributed
Answers
Sure, here is the solution to your problem, The formula for the confidence interval is CI = X + (Zα/2 * σ/√n) where X is the sample mean, Zα/2 is the z-score for the desired confidence level (99% in this case), σ is the population standard deviation, and n is the sample size.
Plugging in the values given, we get:
CI = 438 + (2.878 * 16/√8)
Using a z-score table, we find that Zα/2 = 2.878 for a 99% confidence level.
Simplifying the expression, we get:
CI = 438 + 16.192
Therefore, the 99% confidence interval for the true mean number of patients treated in the emergency room per week is (421.808, 454.192).
Note that since the sample size is small (n=8), we cannot assume that the variable is exactly normally distributed. However, the central limit theorem suggests that for large enough samples (usually n>30), the distribution of the sample mean will be approximately normal regardless of the shape of the population distribution.
To find the 99% confidence interval for the true mean of patients treated in the emergency room each week, we'll use the formula:
CI = X + (Z * (s / √n))
where CI is the confidence interval, X is the sample mean, Z is the Z-score for the desired confidence level, s is the standard deviation, and n is the sample size.
Here, X = 438, s = 16, and n = 8. To find the Z-score for a 99% confidence level, refer to a standard Z-score table, which gives us Z = 2.576.
So, the 99% confidence interval for the true mean is approximately 423.43 to 452.57 patients treated in the emergency room each week, assuming the variable is normally distributed.
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School administrators asked a group of students and teachers which of two
school logo ideas, logo A or logo B, they prefer. This table shows the results,
Which statement is true?
Logo A
Logo B
Total
Students
14
86
100
Teachers
14
11
25
Total
28
97
125
A. There is no difference between the preferences of students and
teachers.
B. Logo B is more popular with both teachers and students.
C. Logo A is equally popular with students and teachers.
D. Logo A is more popular with teachers, but logo B is more popular
with students,
Answers
Answer:
D
Step-by-step explanation:
Teachers favor logo A by a vote of 14 to 11 while students heavily favor logo b with a vote of 86 to 14.
Logo A is more popular with teachers, but logo B is more popular
with students so option (D) will be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
A frequency table is a table in which we have some data and their frequency.
Given,
Number of students = 100
Out of 100 students 86 preferred logo B.
Number of teachers = 25
Out of 25 teachers, 14 teachers preferred logo A.
Hence Logo A is more popular with teachers, but logo B is more popular with students.
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if the partial sum with three terms is used to approximate the value of the convergent series ∑n=3[infinity](−1)n 1n2n, what is the alternating series error bound?
Answers
The alternating series error bound for the partial sum with three terms is 1/24
The alternating series error bound is given by the formula:
En = |Rn| <= |an+1|
where Rn is the remainder after n terms and an+1 is the absolute value of the (n+1)th term of the series.
The nth term of the series is:
an = (-1)^n * 1/(n*2^n)
The (n+1)th term of the series is:
a(n+1) = (-1)^(n+1) * 1/[(n+1)*2^(n+1)]
Taking the absolute value of the (n+1)th term, we get:
|a(n+1)| = 1/[(n+1)*2^(n+1)]
To find the alternating series error bound for the partial sum with three terms, we set n=2 (since we have three terms in the partial sum), and substitute the values into the formula:
En = |Rn| <= |an+1|
E2 = |R2| <= |a3|
E2 = |(-1)^3 * 1/(3*2^3)| = 1/24
Therefore, the alternating series error bound for the partial sum with three terms is 1/24
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one of the following steps is not required as a step to test for the null hypothesis: compute the p-value. compute the standard error of the slope estimate compute the t-statistic. test for the errors to be normally distributed.
Answers
One of the following steps is not required as a step to test for the null hypothesis is Compute the standard error of the slope estimate.
What is hypothesis testing?Hypothesis testing is a statistical method for testing the validity of a hypothesis made about a parameter in a population. This method may be used to assess the truth of a hypothesis made about a population parameter.
A hypothesis testing problem involves determining whether there is enough evidence in a sample data to support the hypothesis about the population.
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Calculate the number of kilowatt-hours (kW-hrs) consumed in a week by an 850 -Watt window air conditioner that is left on all day. 0.168 kW−hrs 142.8 kW−hrs 5.95 kW-hrs 20.4 kW-hrs
Answers
The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.
To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.
Power of the air conditioner = 850 Watts
Duration of usage per day = 24 hours (left on all day)
Number of days in a week = 7 days
To calculate the energy consumption, we can use the formula:
Energy (kW-hrs) = Power (kW) * Time (hours)
First, let's convert the power from Watts to kilowatts by dividing it by 1000:
Power (kW) = 850 Watts / 1000 = 0.85 kW
Now we can calculate the energy consumption in a week:
Energy (kW-hrs) = Power (kW) * Time (hours)
Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days
Energy (kW-hrs) = 14.28 kW-hrs
Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen, and King only)?
A. 1/13
B. 1/4
C. 9/52
D. 3/13
Answers
Answer:
D, 3/13 simplified from 12/52
Step-by-step explanation:
the reason that it would be 3/13 is because its simplified from 12/52, which is 12 of the possibly of face cards over 52 the amount of cards in the deck, so the possibility was 12/52, but simplified would be 3/13 ! love you !
BE SAFE !!!! HOPE THIS HELPS!!!!
<3 <3 <3 <3 <3
The probability that the card drawn is a face card is 3/13.
Option D is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
There are 3 face cards.
Number of jack = 4
Number of queen = 4
Number of king = 4
Total number of cards = 52
The probability that the card drawn is Jack.
= 4/52
The probability that the card drawn is Queen.
= 4/52
The probability that the card drawn is King.
= 4/52
The probability that the card drawn is a face card.
= 4/52 + 4/52 + 4/52
= 3 x 4/52
= 3 x 1/13
= 3/13
Thus,
The probability that the card drawn is a face card is 3/13.
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SOMEONE PLEASE HELP!! thank you :)
Answers
Answer:
This is an arithmetic sequence with a common difference d of -9
Step-by-step explanation:
When you find out d, you realize the difference between the numbers to be -9. Since it is d and not common ratio r, it is an arithmetic sequence.
Groups have a common identity but not shared expectations.truefalse
Answers
Answer:
false
Step-by-step explanation:
A set of people who interact on the basis of shared expectations and who possess some degree of common identity. A small group of people who interact over a relatively long period of time on a direct and personal basis will share expectations.
A plan for a house is drawn on a 1:40 scale. If the length of the living room on the plan measures 4.5 inches, what is the actual length of the built living room? 45 feet 25 feet 15 feet 12 feet
Answers
Answer:
actual length = 15 feet
Step-by-step explanation:
using the conversion
12 inches = 1 foot
the actual length = 40 × scale length = 40 × 4.5 = 180 inches = 180 ÷ 12 = 15 feet
The four corners of a rectangular city block are located at (-5, -2).(-5,9), (9,9), and(9, -2) on the coordinate grid below. Randy walks all the way around the block and stopswhen he gets back to where he started. Each unit on the grid represents 10 meters. Howmany meters does Randy walk? Type the answer in the box below.ol987654321--10-9-8-7-6-5-4-3-2-1-1 2 3 4 567 8 9 10-34-5-6-7-8-9-10meters
Answers
Plot the four vertices of the rectangle using the given coordinates:
Find the perimeter of the rectangle by adding the length of each side.
The sides of that rectangle have lengths of 14, 11, 14 and 11 units. Then, the perimeter of the rectangle is:
\(14+11+14+11=50\)Since each unit on the grid represents 10 meters, multiply that result by 10 to find the real distance that Randy walked, measured in meters:
\(50\times10m=500m\)Therefore, the answer is:
\(500\text{ meters}\)
∠A and ∠B are complementary angles. If m∠A = (2x - 13) and m∠B = (4x - 5), then find the measure of ∠B
Answers
Hey there! I'm happy to help!
If angles are complementary, they add up 90 degrees.
This means that 2x-13+4x-5=90
Let's solve this equation now.
2x-13+4x-5=90
We combine like terms.
6x-18=90
We add 18 to both sides.
6x=108
x=18
Now we plug this x value into the value for angle B.
4(18)-5
72-5
67
Therefore, the measure of angle B is 67 degrees.
Have a wonderful day!
Find the partial sum sn of the geometric sequence that satisfies the given conditions. a3 = 36, a6 = 288, n = 5
Answers
The value of the partial sum of geometric sequence with terms a3 = 36 and a6 = 288 is given by 297. This is obtained by using the concept of partial sum of a geometric progression.
What is geometric progression?
Geometric progression is defined as a series of numbers having a fixed ratio between each term and its preceding term. It is also known as a geometric sequence or G.P., and is exemplified as a1, a2, a3, ….., an
Here, the first term is denoted by a1 and its common ratio is shown by r, which is calculated using the formula a2 by a1. The partial sum of a G.P. is given by a1 ( rn - 1 ) / ( r - 1 ), when r > 1 and a1 ( 1 - rn ) / ( 1 - r ), when r < 1
Calculation of the partial sum of the geometric sequence that satisfies the given conditions. a3 = 36, a6 = 288, n = 5
Given:
Value of a3 = 36
Value of a6 = 288
n = 5
a3 = ar2 — 1
a6 = ar5
Now, a6 / a3 = ar5 / ar2 = 288 / 36
r3 = 8
Taking cube root both sides, we get,
r = 2
Putting the value of r in equation 1,
a3 = a(2)2
36 = 4a
a = 9
As r > 1, using the formula for Sn as a(rn - 1) / (r - 1)
Sn = 9(2n - 1) / (2 - 1)
Sn = 9(2n - 1)
Using n = 5, we have,
Sn = 9[(2)5 - 1]
Sn = 9(32 - 1)
Sn = 9 × 33
Sn = 297
Hence, the value of the partial sum of a G.P. is 297
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find the slope of the curve y=x2−4x−5 at the point p(3,−8) by finding the limit of the secant slopes through point p
Answers
To find the slope of the curve \(y=x^2-4x-5\) at the point P(3,-8) using the limit of the secant slopes, we need to calculate the slope between P and nearby point on curve as distance between points approaches zero.
The slope of a curve at a specific point can be approximated by calculating the slope of a secant line that passes through that point and a nearby point on the curve. In this case, we are interested in finding the slope at point P(3,-8). Let's choose another point on the curve, Q, with coordinates (x, y). The slope of the secant line passing through points P and Q is given by (y - (-8))/(x - 3). To find the slope of the curve at point P, we need to calculate the limit of this expression as the point Q approaches P.
To do this, we substitute the equation of the curve, \(y=x^2-4x-5\), into the expression for the slope of the secant line. We have (x^2-4x-5 - (-8))/(x - 3). Simplifying this expression gives \((x^2-4x+3)/(x-3)\). Taking the limit of this expression as x approaches 3, we get \((3^2-4(3)+3)/(3-3)\), which becomes (9-12+3)/0. Since we have a 0 in the denominator, we cannot directly evaluate the limit. However, this form suggests that we have a factor of (x-3) in both the numerator and denominator. Factoring the numerator further gives ((x-3)(x-1))/(x-3). Canceling out the common factor (x-3), we are left with (x-1). Substituting x=3 into this expression gives the slope of the curve at point P as (3-1), which is equal to 2.
Therefore, the slope of the curve \(y=x^2-4x-5\) at point P(3,-8) is 2.
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a canoe rental service charges a $30 transportation fee and $55 dollars an hour to rent a canoe. what is the cost of renting the canoe for 6 hours?
Answers
Answer:
Cost for 6 hour canoe rental = $360.00
Step-by-step explanation:
We can model the situation using the slope-intercept form of line, whose general equation is given by:
y = mx + b, where
m is the slope (change in the dependent variable / change in the independent variable),and b is the y-intercept.We see that cost depends on the amount of hours a canoe is rented as cost only increases as hours increase.
Thus, we can use the equation:
C(h) = mh + b, where
C(h) is the cost in dollars per hours of the canoe rental,m is the marginal cost (i.e., the increase in cost per hours passed,and b is the initial cost (i.e., the cost even when 0 hours have passed)Since the transportation fee is $30, it's our b value as the customer pays $30 even when 0 hours have passed.
Since the customer pays $55 an hour, it's our marginal cost.
Thus, our equation (with 55 substituted for m and 30 substituted for b) is:
C(h) = 55h + 30
Now we can plug in 6 for h to find the cost of renting the canoe for 6 hours:
C(6) = 55(6) + 30
C(6) = 330 + 30
C(6) = 360
Thus, the cost of renting the canoe for 6 hours is $360.
¬∀x¬p(x) not all people run 1 hour every weekday someone runs 1 hour every weekday not everyone runs every hour every weekday no one runs 1 hour every weekday all people do not run 1 hour every weekday not all people run during the week
Answers
It can be determined that not all people run for 1 hour every weekday, but the exact proportion or number of individuals who do engage in this activity is not specified.
Based on the given statements, it can be concluded that not all people run for 1 hour every weekday. This means that there are individuals who do not engage in this activity.
However, it does not specify the exact number or percentage of people who do run for 1 hour every weekday. Additionally, it is mentioned that someone does run for 1 hour every weekday, which implies that there is at least one individual who follows this routine. Furthermore, it is stated that not everyone runs every hour every weekday.
This suggests that some individuals may run for less than 1 hour or may not run at all on certain weekdays. It is also mentioned that no one runs for 1 hour every weekday, which contradicts the earlier statement that someone does engage in this activity.
Therefore, the given statements are inconsistent.
In conclusion, based on the given statements, it can be determined that not all people run for 1 hour every weekday, but the exact proportion or number of individuals who do engage in this activity is not specified.
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At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is
100
°
100°100, degree Celsius. This causes the iron to cool and the temperature difference drops by
60
%
60%60, percent every second.
Answers
It takes approximately 4.8 seconds for the temperature difference between the hot iron rod and the freezing water to drop from 100 °C to 10 °C.
What is the freezing point?The freezing point is the temperature at which a liquid changes into a solid state at a given pressure. For pure water, the freezing point is 0 °C (32 °F) at a pressure of 1 atmosphere (atm). This means that when the temperature of the water is reduced to 0 °C under normal atmospheric pressure, it will freeze and turn into ice.
According to the given informationLet's denote the initial temperature difference between the hot iron rod and the freezing water as ΔT₀ = 100 °C.
According to the problem statement, the temperature difference drops by 60% every second, which means that at time x seconds after the rod is plunged into the water, the temperature difference is:
ΔT(t) = ΔT₀ * 0.4ˣ
We can use this equation to find the time it takes for the temperature difference to reach a certain value. For example, if we want to find the time it takes for the temperature difference to drop to 10 °C, we can solve the following equation for x:
10 = 100 * 0.4ˣ
0.4ˣ = 0.1
x = log(0.1)/log(0.4) ≈ 4.8 seconds
Therefore, it takes approximately 4.8 seconds for the temperature difference between the hot iron rod and the freezing water to drop from 100 °C to 10 °C.
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