Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
An insurance company reported that, on average claims for a certain medical procedure are $942. an independent organization constructed a 95% confidence interval of ($930, $950) for the average amount claimed for the particular medical procedure. what conclusion best evaluates the truthfulness of the number reported by the insurance company?
a) with 95% certainty, the average claim for this medical procedure is $942.
b) with 95% certainty, the average claim for this medical procedure is not $942.
c) the confidence interval is consistent with an average claim of $942 for this medical procedure
Solution:
Confidence interval is used to express how confident we are that the population parameter that we are looking for is contained in a range of given values. Looking at the given confident interval, the lower limit is $930 and the upper limit is $950. We can see that the population mean, $942 lies within these values. The correct option would be
c) the confidence interval is consistent with an average claim of $942 for this medical procedure
Tublu buys a cylindrical water tank height 1.4 M and diameter 1.1 M to catch rainwater off his roof.
Complete Question:
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank(not the base). If he uses 250ml to cover 1m2, will he have enough paint to cover the tank with one layer of paint? Take pie as 3.142
Answer:
Yes. It will be enough to cover the tank with 1 layer of paint. The tank requires 1.21 liters of paint.
Step-by-step explanation:
Given:
Height of cylindrical tank (h) = 1.4m
Diameter = 1.1m (radius = ½ of 1.1 = 0.55 m)
Litres of paint available = 2 liters
Rate of usage of paint = 250 ml to 1 m²
π = 3.142
Required:
Determine if the available 2 liters of paint would be enough for the painting
Solution:
Step 1: calculate the curved surface area of the cylindrical tank
Curved surface area (CSA) = 2πrh
= 2*3.142*0.55*1.4
= 4.84 m²
Step 2: Calculate how many liters of paint is required to paint the cylindrical tank having a curved surface area of 4.84 m²
If 1 m² requires 250ml (0.25 liters) of paint,
4.84m² area will require 4.84*0.25 liters
= 1.21 liters of paint.
Since 2 liters of paint is available, it means the paint will be more than enough to cover the tank with 1 layer of paint.
According to a study conducted in one city, 39% of adults in the city have credit card debts of more than $2000. A simple random sample of 100 adults is obtained from the city. Describe the sampling distribution of the sample proportion of adults who have credit card debts of more than $2000.
Answer:
The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean [tex]\mu = 0.39[/tex] and standard deviation [tex]s = 0.0488[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.39, n = 100[/tex]
Then
[tex]s = \sqrt{\frac{0.39*0.61}{100}} = 0.0488[/tex]
By the Central Limit Theorem:
The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean [tex]\mu = 0.39[/tex] and standard deviation [tex]s = 0.0488[/tex]
Problem of the Day
The tortoise and the hare were arguing: who's the fastest? The tortoise boasted he
could swim 220 miles in 10 hours. The hare bragged he could hop 90 miles in 2 hours.
But who is faster? How can you tell?
Answer:
hare
Step-by-step explanation:
Their average rates are ...
tortoise: (220 mi)/(10 h) = 22 mi/h
hare: (90 mi)/(2 h) = 45 mi/h
The hare has a faster speed than the tortoise.
A rectangular box has a base that is 4 times as long as it is wide. The sum of the height and the girth of the box is 200 feet. (a) Express the volume V of the box as a function of its width w. Determine the domain of V (w).
Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.
Step-by-step explanation:
The dimensions of the box are:
L = length
W = width
H = heigth.
We know that:
L = 4*W
And the girth of a box is equal to: G = 2*W + 2*H
then we have:
2*W + 2*H + H = 200ft
2W + 3*H = 200ft
Then we have two equations:
L = 4*W
2W + 3*H = 200ft
We want to find the volume of the box, which is V = W*L*H
and we want in on terms of W.
Then, first we can replace L by 4*W (for the first equation)
and:
2*W + 3*H = 200ft
3*H = 200ft - 2*W
H = (200ft - 2*W)/3.
then the volume is:
V(W) = W*(4*W)*(200ft - 2*W)/3
V(W) = (1/3)*(*W^2*800ft - 8W^3)
The domain of this is the set of W such that the volume is positive, then we must have that:
W^2*800ft > 8W^3
To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)
W^2*800ft = 8W^3
800ft = 8*W
100ft = W.
This means that if W is equal or larger than 100ft, the equation gives a negative volume.
Then the domain is 0 < W < 100ft.
1a. A deep-sea diver is at sea level. He submerges 15 feet per minute,
How many feet below sea level is he after submerging for 10 minutes? First question.
Second question,Then write an integer representing the deep-sea current location.
PLZZZ answer this correctly and i give you a brainliest!!!
Answer:
150, 15x
Step-by-step explanation:
After ten minutes he will be 15 * 10 = 150 feet below sea level.
We can call the number of minutes the diver has been underwater for as x so the integer is 15 * x = 15x.
Can someone help me ? If Tina can type a paper in 5 hours and together she and Tyra can type the paper in 2 hours, how long would it take Tyra to type the same paper alone?
Answer: 3 1/3 hours
Step-by-step explanation:
Tina rate: 1/5 job/hr
Together rate: 1/2 job/hr
Tyra rate: 1/x job/hr
---------
Equation:
rate + rate = together rate
1/5 + 1/x = 1/2
2x + 10 = 5x
3x = 10
x = 3 1/3 hrs (time for Tyra to do the job alone)
Answer:
3 1/3 hours
Step-by-step explanation:
Find the missing length indicated. x=
Answer: x = 120
Step-by-step explanation:
Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.
Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)
Cos(A) = 64/Z
Cos(A) = Z/(64 +225)
We can take the quotient of those two equations and get:
[tex]1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}[/tex]
Then:
Z = √(18,496) = 136.
now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.
Then, using the Pythagorean theorem:
64^2 + x^2 = 136^2
x = √(136^2 - 64^2) = 120
There is a triangle with a perimeter of 63 cm, one side of which is 21 cm. Also, one of the medians is perpendicular to one of the angle bisectors. Then what you've got to do is find the side lengths of the triangle
Answer:
21cm; 28cm; 14cm
Step-by-step explanation:
There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.
Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.
Let O is AK and BM cross point.
Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)
=> triangle ABM is isosceles => AB=AM (1)
1. Let AC=21 So AM=21/2=10.5 cm
So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm
Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)
2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.
3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm
We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB
=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.
Let check if this triangle exists ( if the triangle's inequality fulfills).
BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.
This variant is the only possible solution of the given problem.
Given that Justin is collecting data on reaction time, what type of data is he working with?
a. qualitative
b. discrete quantitative
c. continuous quantitative
d. none of the above
Answer:
The correct option is (c)
Justin is working with continuous quantitative type of data.
Step-by-step explanation:
We are given that Justin is collecting data on reaction time.
The reaction time is obtained through measurements and it can take any value within a range therefore, it falls in the category of continuous data.
Moreover, since reaction time can be measured thus have numerical value therefore, it is a quantitative type of data.
Therefore, we can conclude that Justin is working with continuous quantitative type of data.
Other examples of continuous quantitative type of data are
measuring height
measuring temperature
Colton makes the claim to his classmates that less than 50% of newborn babies born this year in his state are boys. To prove this claim, he selects a random sample of 344 birth records in his state from this year. Colton found that 176 of the newborns are boys. What are the null and alternative hypotheses for this hypothesis test
Answer:
Null hypothesis:[tex]p \leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]
Step-by-step explanation:
Information given
n=344 represent the random sample taken
X=176 represent the anumber of boys babies
[tex]\hat p=\frac{176}{344}=0.512[/tex] estimated proportion of boys babies
[tex]p_o=0.5[/tex] is the value that we want to check
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotheis to verify
We want to check if the true proportion of boys is less than 50% then the system of hypothesis are .:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]
Answer:
p= 0.5
p>0.5
Step-by-step explanation:
Which ordered pair is a solution of this equation?
-2x + 9y = -26
(-4,-4)
(4,4)
(-4,-5)
(-5,-4)
State sales tax is 3%. How much would you pay on a $246 pair of shoes?
Round your answer to the nearest cent.
Answer:
Step-by-step explanation:
246(.03)= 7.38
246+7.38= $253.38
Select the proper reason if this
statement is provided as a fact at the
beginning of a proof.
Bargains Galore marked down a $82 cappuccino machine to $72. Calculate the following (if necessary, round your answer for markdown percent to the nearest hundredth percent):
Answer:
12.2%
Step-by-step explanation:
82 · [tex]\frac{100-x}{100}[/tex] = 72 When multiplied by a certain percent we get 72
82(100-x) = 7200
100(A whole as you may say) - *a percent* = the markdown
8200-82x=7200
82x = 1000
x ≈ 12.2
Tell me if you need further explanation
Answer:
12.20%
Step-by-step explanation:
$82 went down to $72.
$82 - $72 = $10
The price went down $10.
Now we find the percent that $10 is of $82.
percent = part/whole * 100%
percent = 10/82 + 100% = 12.195%
Answer: 12.20%
3(x + 2) = 12 solve for x
Answer:
x = 2.
Step-by-step explanation:
3(x + 2) = 12
3x + 6 = 12
3x = 6
x = 2
Hope this helps!
Answer:
4
Step-by-step explanation:
Which digit has the greatest value in the number 1567?
Answer: The 1 because it’s value is The Thousands place.
Each Value Broken down and then Added together:
1000 + 500 + 60 + 7 = 1567
As you can visually see here the 1 is the greatest value number.
Answer:1
Step-by-step explanation: 1 takes place in the thousands place which is greater than 5 (hundreds) , 6 (tenths) , and 7 (ones)
Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about
the origin?
Answer:
A. (x, y) ⇒ (-x, -y)
Step-by-step explanation:
Rotation 180° in either direction is equivalent to reflection across the origin, and/or reflection across both axes (in either order). It negates both coordinates.
(x, y) ⇒ (-x, -y) . . . . rotation 180°
Suppose you live in a town with a population of 25,000 where the municipal waste is sent to its own local landfill. If each resident generates 3 lbs. of trash per day, how many pounds of waste are sent to the landfill each day
Answer:
75000lb
Step-by-step explanation:
There are 25000 residents. Times it by the 3lb of waste per person and that's how much waste is made from 25000 residents.
Answer:
Step-by-step explanation:
A state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement. You choose 4 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.Is the experiment binomial?A. Yes, there are a fixed number of trials and the trials are independent of each other.B. No, there are more than two outcomes for each trial.C. Yes, the probability of success is the same for each trial.D. No, because the probability of success is different for each trial.
Answer:
A) Yes, there are a fixed number of trials and the trials are independent of each other.
Sample size 'n' = 37
probability of success p = 0.1081
q = 0.8919
Step-by-step explanation:
Explanation:-
Given data we will observe that
There are a fixed number of trials and the trials are independent of each other.
Given a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Given size 'n' = 37
The probability that a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.
Proportion
[tex]p = \frac{x}{n} = \frac{4}{37} = 0.1081[/tex]
q = 1 - p = 1 - 0.1081 = 0.8919
Final answer:-
Sample size 'n' = 37
p = 0.1081
q = 0.8919
Coin B is going to be thrown 4000 times.
Work out an estimate for the number of times
coin B will land on Heads.
Answer:
The probability of "heads" is ½ and the probability of "tails" is ½.
This means that if we flip this coin several times, we expect it to land on "heads" for half of the time.
If we flip the coin 4000 times, we would expect it to land on "heads" 2000 times, because ½ × 4000 = 2000
A bank loaned out $20,000, part of it at the rate of 6 % per year and the rest at 16 % per year. If the interest received in one year totaled $1500, how much was loaned at 6 %?
Answer:
$1,020
Step-by-step explanation:
0.06x + 0.16(20,000 - x) = 1500
Given f(x)=3x and g(x)=1/x+3 which value is in the domain of f(g)
Answer:
8 lies in the domain of f(g)
Please answer this correctly
Answer:
25%
Step-by-step explanation:
Total cards = 4
The number 4 = 1
p(4) = 1/4
In %age:
=> 25%
Answer:
25%
Step-by-step explanation:
There is only 1 four card from the 4 cards.
1 card out of 4 cards.
1/4 = 0.25
P(4) = 25%
If 12 5 )tan( = x and π
Answer:
[tex]sinx=-\dfrac{12}{13}[/tex]
[tex]cosx=-\dfrac{5}{13}[/tex]
[tex]cotx=\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given that:
[tex]\dfrac{12}{5} = tan(x)[/tex]
[tex]\pi <x < 3\pi/2[/tex]
i.e. x is in 3rd quadrant. So tan is positive.
To find:
sin(x), cos(x), and cot(x).
Solution:
Given that:
[tex]\dfrac{12}{5} = tan(x)[/tex]
We know by trigonometric identities that:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
Comparing with the given values:
[tex]\theta=x[/tex]
Perpendicular = 12 units
Base = 5 units
Using pythagorean theorem, we can find out hypotenuse:
According to pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
[tex]\Rightarrow Hypotenuse=\sqrt{12^2+5^2}\\\Rightarrow Hypotenuse=\sqrt{169} = 13 units[/tex]
We can easily find out the values of:
[tex]sinx, cos x\ and\ cot x[/tex]
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinx =\dfrac{12}{13}[/tex]
Given that x is in 3rd quadrant, sinx will be negative.
[tex]\therefore sinx =-\dfrac{12}{13}[/tex]
[tex]sin\theta =\dfrac{Base}{Hypotenuse}[/tex]
[tex]cosx =\dfrac{5}{13}[/tex]
Given that x is in 3rd quadrant, cosx will be negative.
[tex]\therefore cosx =-\dfrac{5}{13}[/tex]
[tex]cot\theta = \dfrac{1}{tan\theta}[/tex]
Given that x is in 3rd quadrant, cotx will be positive.
[tex]cotx = \dfrac{1}{\dfrac{12}{5}} = \dfrac{5}{12}[/tex]
Suppose that a tunnel is dug through the center of the earth. You stand on a tower 100 m tall and drop a 3-kg rock into the tunnel. What is the frequency of the resulting harmonic motion?
Answer:
The frequency of the resulting harmonic motion is 0.000219 Hz
Step-by-step explanation:
We are going to calculate the time it takes for one single wave ocillation.
Frequency and the time taken to finish a single wave oscillation are inversely proportional. The formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T
In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.
I consider the initial speed to be zero, because it is of no significance compared with the free fall into the earth, through the earth and back again.
Given from Wikipedia:
The diameter of the earth is 1.2742 * 10⁴ km which is 1.27 * 10⁷ m
2 times the radius = diameter, so the radius of the earth = (1.27 * 10⁷ m) /2 = 6.4 * 10⁶ m
radius earth = r
r = 6.4 * 10⁶ m
Now imagine the tunnel and the free fall.
1. Initially the rock has no speed.
2. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.
3. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed and it has travelled the distance r !
4. After this moment, the Rock will be slowed down because of the negative accelleration...
After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely, and again passing the distance r.
5. Now at the other end of the earth there is the same initial situation as described at point 1, only the Rock has travelled the distance equal to the diameter of the earth, (exactly 2 times r).
So basically, the samething happens once more, only this time it starts exactly from the other end of the earth...
6. Initially the rock has no speed.
7. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.
8. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed.
9. By now the Rock will be slowed down because of the negative accelleration... It is moving towards the initial starting point...
After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely.
10. Now finally the Rock is exactly at the starting position.
In reality there will have been some loss of speed due to friction, so the Rock will be slightly lower then the 100 m above the ground.
let's calculate the time it takes to free fall for the distance r.
initial speed =0 and after 6.4 * 10⁶ m it's speed will be maximum. We need to find out how much time passes before that distance is passed.
r = v*t + 0.5*a*t²
r = 0 + 0.5*a*t²
0.5*a*t² = r
t² = r / ( 0.5 * a )
t² = 6.4 *10⁶ / ( 0.5 * 9.8 )
t² = 1.306 * 10 ⁶
t = 1142.86 s
Now please confirm that in order for the Rock to move back to the initial starting point it has to travel 4 times as much time. It has to travel r to centre of the earth then another r to travel to to the other side of the earth, and back again. So indeed 4 times r.
The time it will take must be the same as 4 * 1142.86 s
now this is the time of one single wave ocillation.
Since T = 4571.43 s
f = 1 / 4571.43
f = 0.00021874993164 Hz
The frequency of the resulting harmonic motion is 2.19 *10-4
The frequency of the resulting harmonic motion is 0.000219 Hz
the line through (5, 7) and (1, - 5)
Answer:
Hey there!
Slope of the line: [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope of the line: [tex]\frac{12}{4}[/tex], which is equal to 3.
Point slope form: y2-y1=m(x2-x1)
Point slope form: y-7=3(x-5)
Y intercept form: y-7=3x-15
Y intercept form: y=3x-8
Let me know if this helps :)
A normally distributed population of package weights has a mean of 63.5 g and a standard deviation of 12.2 g. XN(63.5,12.2) a. What percentage of this population weighs 66 g or more
Answer:
The percentage is %z [tex]= 41.9[/tex]%
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 63.5 \ g[/tex]
The standard deviation is [tex]\sigma = 12.2 \ g[/tex]
The random number is x = 66 g
Given the the population is normally distributed
The probability is mathematically represented as
[tex]P(X > 66 ) = P(\frac{X - \mu }{\sigma} > \frac{x - \mu }{\sigma } )[/tex]
Generally the z-score for this population is mathematically represented as
[tex]Z = \frac{ X - \mu}{ \sigma}[/tex]
So
[tex]P(X > 66 ) = P(Z > \frac{66 - 63.5 }{12.2 } )[/tex]
[tex]P(X > 66 ) = P(Z > 0.2049 )[/tex]
Now the z-value for 0.2049 from the standardized normal distribution table is
[tex]z = 0.41883[/tex]
=> [tex]P(X > 66 ) = 0.41883[/tex]
The percentage is
% z [tex]= 0.41883 * 100[/tex]
%z [tex]= 41.9[/tex]%
Not sure how I would solve this
Answer:
me too
Step-by-step explanation:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 1 + 0.5 + 0.25 + 0.125 + ...
Answer:
Convergent. The sum is 2.
Step-by-step explanation:
First let's find the rate of the series. We can find it by dividing one term by the term before:
[tex]0.5 / 1 = 0.5[/tex]
[tex]0.25 / 0.5 = 0.5[/tex]
[tex]0.125 / 0.25 = 0.5[/tex]
So the rate of the series is 0.5. The series is convergent if the rate is between 0 and 1, so this series is convergent.
We can find its sum with the following equation:
[tex]S = a_1 / (1 - r)[/tex]
Where a_1 is the first term and r is the rate.
So we have that:
[tex]S = 1/ (1 - 0.5)[/tex]
[tex]S = 2[/tex]
The sum of the series is 2.
Aphrodite took out a 30-year loan from her bank for $170,000 at an APR of
7.2%, compounded monthly. If her bank charges a prepayment fee of 6
months' interest on 80% of the balance, what prepaymeant fee would
Aphrodite be charged for paying off her loan 12 years early?
A. $3246.74
B. $4078.20
C. $4895.83
D. $4921.46
Answer:
A. $3246.74
Step-by-step explanation:
The monthly payment can be found from the amortization formula.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the principal amount, r is the annual rate compounded n times per year for t years.
Filling in the values, we compute the monthly payment to be ...
A = $170,000(.072/12)/(1 -(1 +.072/12)^(-12·30)) = $1153.94
__
The remaining balance after t years will be ...
B = P(1 +r/n)^(nt) -A((1 +r/n)^(nt) -1)/(r/n)
For the given initial principal and the computed payment, after 18 years, the balance will be ...
B = $170000(1 +.072/12)^(12·18) -$1153.94((1 +.072/12)^(12·18) -1)/(.072/12)
B = $111,054.71
The prepayment penalty appears to be ...
(r/2)(0.80B) = (.072/2)(0.80)($111,054.71) = $3,198.38
The closest listed answer choice is ...
A. $3246.74
_____
Please ask your teacher how to get the answer, since none of the offered choices appear to be correct.