Through hypothesis testing, we cannot reject the null hypothesis at the 1% level of significance. Thus, there is no strong evidence to suggest that the mean nicotine content is greater than what is advertised.
Explanation:The subject here is statistics, specifically hypothesis testing. For this problem, we are asked to test the null hypothesis H0: m = 1.5 against the alternative hypothesis Ha: m > 1.5 at 1% level of significance.
Using the given data, we calculate the test statistic (z) using the formula: z = (x - µ) / (s/√n), where x is the sample mean, µ is the population mean, s is the standard deviation, and n is the sample size. Substituting the given values, we get z = (1.52 - 1.5) / (0.1/√400) = 2.
The z-score at 0.01 level of significance is -2.33 on the left and 2.33 on the right. As our test statistic (2) falls within this range, we fail to reject the null hypothesis (H0: m = 1.5). This suggests that there's no strong evidence to support that the mean nicotine content is greater than advertised.
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Hasan plans to choose a book from a section of the store where everything is 25% 25 % off. He writes the expression d?0.25d d - 0 . 25 d to find the sale price of the book if the original price is d d dollars. Bella correctly writes another expression, 0.75d 0 . 75 d , that will also find the sale price of the book if the original price is d dollars. Use the drop-down menus to explain what each part of Hasan's and Bella's expressions mean.
Answer:
Both are correct. See below.
Step-by-step explanation:
Hasan's expression 0.25d will find the amount of the discount in $$$ for a 25% discount. By writing d-0.25d he will also find the sale price by subtracting the original by the discount in $$$.
Bella's expression 0.75d finds the sale price for a 25% discount. If you receive 25% off then you pay 75%. Bella also wrote d-0.75d which gives the amount in dollars of the discount. By subtracting the sale price from the original, we find the deduction the sale gives.
Answer:
Step-by-step explanation:
Suppose the band sells erasers for $2 per package and pencils for $5 per package. The band sells 220 packages in all and earns a total of $695. Write a system of equations to find the number of teacher type of package sold
(98 x2) + (69 x52) =
4 + (34 x 19) + 987 =
Question
(98 x2) + (69 x52) =
4 + (34 x 19) + 987 =
Answer:
37841637Step-by-step explanation:
(98 x2) + (69 x52) =
196 + 3588 =
3784
---------------
4 + (34 x 19) + 987 =
4 + 646 + 987 =
1637
I WILL MARK YOU BRAINLYEST if you answer all of my problems !!!!!!!!!!!
1# how many candy bars can you buy with $5.10 if one candy bar cost $0.85?
2# a number n minus 3 is greater than or equal to 12
solve for the variable
7# x-7=12
8# y/8=7
9# 10-4x=6x
A ladder that is 20 ft. Long is leaning against the side of a building. If the angle formed between the ladder and the ground is 75, how far is the bottom of the ladder from the base of the building?
Answer:
The ladder from the base of the building is 5.18 ft (Approx)
Step-by-step explanation:
As given
A ladder that is 20 ft. Long is leaning against the side of a building.
If the angle formed between the ladder and the ground is 75.
Now using the trignometric property .
[tex]cos\theta = \frac{Base}{Hypotenuse}[/tex]
As shown in the figure.
[tex]\theta = 75^{\circ}[/tex]
Base = CB
Hypotenuse = AC = 20 ft.
Put in the trignometric identity .
[tex]cos75^{\circ} = \frac{CB}{AC}[/tex]
[tex]cos75^{\circ} = \frac{CB}{20}[/tex]
[tex]cos\ 75^{\circ} = 0.259[/tex]
Put in the above
[tex] 0.259= \frac{CB}{20}[/tex]
[tex]0.259 = \frac{CB}{20}[/tex]
CB = 0.259 × 20
CB = 5.18 ft (Approx)
Therefore the ladder from the base of the building is 5.18 ft (Approx) .
Mitchell is a big coffee fan, so he always takes care of coffee brewing at the office. Normally he uses 100100 grams of Robusta coffee to prepare 1010 cups of coffee. His friend brings him a packet of Arabica coffee and tells him that he should use 20\%20% more than usual when brewing Arabica coffee. How many grams of coffee should he use to make a 1515-cup pot of Arabica coffee?
Answer:
180 grams
Step-by-step explanation:
Mitchell has to use more coffee than usual for two reasons: First, he's making a larger pot than usual (15(15left parenthesis, 15 cups rather than 10)10)10, right parenthesis. And second, he's using the Arabica coffee, which requires 20\%20%20, percent more coffee for the same strength.
2
Instead of brewing \blue{10}10start color blue, 10, end color blue cups, Mitchell wants to brew \red{15}15start color red, 15, end color red cups, which means he has to use \dfrac{\red{15}}{\blue{10}}=\purple{1.5}
=1.5start fraction, start color red, 15, end color red, divided by, start color blue, 10, end color blue, end fraction, equals, start color purple, 1, point, 5, end color purple times more coffee.
3
As his friend said, Mitchell also has to use \pink{20\%}20%start color pink, 20, percent, end color pink more coffee than usual, so he'll have to multiply the amount of coffee by \green{1.2}1.2start color green, 1, point, 2, end color green, or \green{120\%}120%start color green, 120, percent, end color green.
4
The total amount of coffee he has to use is 100100100 grams \times×times \purple{1.5} \times \green{1.2} = 1801.5×1.2=180start color purple, 1, point, 5, end color purple, times, start color green, 1, point, 2, end color green, equals, 180 grams.
Annabelle apanhou o Polar Express até o Pólo Norte! O Polar Express tem 100 metros de comprimento e leva 30 segundos para atravessar a ponte de gelo de 400 metros do Papai Noel. Qual a velocidade do trem?
Answer:
Speed of train = 16.67 m/s
Step-by-step explanation:
The translated question is
Annabelle took the Polar Express to the North Pole! The Polar Express is 100 meters long and takes 30 seconds to cross the Santa Fe 400 meter ice bridge. How fast is the train?
Total distance traveled by train to cross the bridge = Length of bridge + Length of train
Total distance traveled by train to cross the bridge = 400 + 100 = 500 meter.
Time taken for this = 30 seconds.
Speed = Distance / Time = 500/30=16.67 m/s
Answer:
Speed of train = 16.67 m/s
Step-by-step explanation:
Please give Brainliest
What is the probability that a red or green marble will be selected from a bag containing 9 red marbles, 6 blue marbles, 7 green marbles, and 11 yellow marbles if one is selected randomly?
Answer: [tex]\bold{\dfrac{16}{33} = 48\%}[/tex]
Step-by-step explanation:
Red or Green
[tex]=\dfrac{red}{total}+\dfrac{green}{total}[/tex]
[tex]=\dfrac{9}{33}+\dfrac{7}{33}[/tex]
[tex]=\dfrac{16}{33}[/tex]
≈ 48%
Suppose that, based on a sample, the 99.7% confidence interval for the mean of a population is (59,95). What is the mean of the sample?
Answer:
mean = 77
Step-by-step explanation:
We have a confidence interval of (59, 95) with a confidence of 99.7 percent
99.7 is 6 standard deviations from the mean, 3 on each side of the mean
mean - 3 sigma = 59
mean + 3 sigma = 95
We can use elimination to eliminate sigma. Add these equations together
mean - 3 sigma = 59
mean + 3 sigma = 95
---------------------------------
2 * mean = 154
Divide each side by 2
2 * mean/2 = 154/2
mean = 77
Based on a sample where the 99.7% confidence interval for the mean of a population is (59,95), 77 is the mean
Name FIVE x-values for which the cosine function equals 0.
Answer:
You didn't input the function, but the cosine of 90 degrees is zero.
Cosine values of zero also occur when an angle equals
270 degrees 450 degrees 630 degrees and 810 degrees.
Step-by-step explanation:
Answer:
That would be 0, 180, 360, 540, and 720.
Step-by-step explanation:
If the value of sine is 0. Add 180 five times and we get the five numbers for the answer.
An object is launched at 20 m/s from a height of 65 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.9t? + 20t + 65. What is the object's maximum height? The numeric answer only, rounded to the nearest meter.
Answer: 85 meters
Step-by-step explanation:
The maximum height is the y-value of the vertex.
h(t) = -4.9t² + 20t + 65
a=-4.9 b=20 c=65
[tex]t=\dfrac{-b}{2a} = \dfrac{-(20)}{2(-4.9)} =\dfrac{-20}{-9.8}=2[/tex]
h(2) = -4.9(2)² + 20(2) + 65
= -19.6 + 40 + 65
= 85.4
The function h(t)=-4.87t^2+18.75t is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. Rounded to the nearest hundredth, what are the domain and range of the function h(t)?
Answer:
A
Step-by-step explanation:
Trust the spam
Let $f(x) = x^{10}-8x^8-8x^3+12x^2-5x-5$. Without using long division (which would be horribly nasty!), find the remainder when $f(x)$ is divided by $x^2-1$.
To find the remainder when dividing the polynomial f(x) = x^10-8x^8-8x^3+12x^2-5x-5 by x^2-1, we can use synthetic division. Carrying out the synthetic division process, the remainder is -10x + 7.
Explanation:To find the remainder when dividing the polynomial f(x) = x^{10}-8x^8-8x^3+12x^2-5x-5 by x^2-1, we can use polynomial long division. However, since we want to avoid this method, we can use synthetic division instead.
Write the divisor in its factored form: x^2 - 1 = (x-1)(x+1).Perform synthetic division using the factored form of the divisor. Start by writing the coefficients of the dividend in descending order: 1, 0, -8, 0, -8, 12, -5, 0, 0, -5.Carry out the synthetic division process, dividing by the 1st factor (x-1), then by the 2nd factor (x+1). The final remainder is the result of the division.After performing synthetic division, we find that the remainder is -10x + 7. Therefore, the remainder when dividing f(x) by x^2 - 1 is -10x + 7.
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If a → b is true, then ~a → b is also true.
Answer:
False
Step-by-step explanation:
To determine whether the statemaent "If [tex]a\Rightarrow b[/tex] is true, then [tex]\neg a\Rightarrow b[/tex] is also true" holds, you can form the truth table:
[tex]\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}[/tex]
When the result of the column [tex]a\Rightarrow b[/tex] takes value 1 (true), the result of the column [tex]\neg a\Rightarrow b[/tex] is not always 1, then the statement is false.
The lengths of two sides of a triangle are 3 inches in 8 inches find the range of possible links for the third side S
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
1. a ≤ 3 ≤ 8 then a + 3 > 8 → a > 8 - 3 → a > 5 FALSE, because a ≤ 3.
2. 3 ≤ a ≤ 8 then 3 + a > 8 → a > 5 therefore 5 < a ≤ 8
3. 3 ≤ 8 ≤ a then 3 + 8 > a → 11 > a → a < 11 therefore 8 ≤ a < 11.
Answer: 5 < a < 11 → S = (5, 11)Given the parametric equations, x = 2t + 5 and y = 3t^2 - 1, find the point on the graph at time, t = 4.
Please explain how you got your answer.
Answer: (13, 47)
The expression t = 4 means that 4 units of time have come off the clock (possibly 4 seconds). Plug this value into each equation given for x and y
x = 2*t + 5 = 2*4 + 5 = 8 + 5 = 13
y = 3*t^2 - 1 = 3*4^2 - 1 = 3*16 - 1 = 48 - 1 = 47
In short, if t = 4 then it leads to x = 13 and y = 47 at the same time. These x and y values pair up to get the final answer (13,47)
--------------
Here's an update:
If t = 2, then,
x = 2t+5 = 2*2+5 = 4+5 = 9y = 3t^2-1 = 3*2^2-1 = 3*4-1 = 12-1 = 11In short, if t = 2, then x = 9 and y = 11
The point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].
To find the point on the graph at time [tex]\(t = 4\)[/tex] given the parametric equations [tex]\(x = 2t + 5\)[/tex] and [tex]\(y = 3t^2 - 1\)[/tex], substitute [tex]\(t = 4\)[/tex] into both equations.
1. For [tex]\(x\)[/tex]:
[tex]x = 2t + 5[/tex]
[tex]x = 2(4) + 5[/tex]
[tex]x = 8 + 5[/tex]
[tex]x = 13[/tex]
So, at [tex]\(t = 4\), \(x = 13\)[/tex].
2. For [tex]\(y\)[/tex]:
[tex]y = 3t^2 - 1[/tex]
[tex]y = 3(4)^2 - 1[/tex]
[tex]y = 3(16) - 1[/tex]
[tex]y = 48 - 1[/tex]
[tex]y = 47[/tex]
So, at [tex]\(t = 4\), \(y = 47\)[/tex].
Therefore, the point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
The graph of the function f(x) = x^3 – 7x – 6 intersects the x-axis at the points (–2, 0), (–1, 0), and (3, 0) as shown.
Which expression is equivalent to x^3 – 7x – 6?
Answer: D
Step-by-step explanation:
The x-intercepts of the graph are: x = -2 , x = -1, and x = 3
--> x + 2 = 0, x + 1 = 0, and x - 3 = 0
--> (x + 2) (x + 1) (x - 3)
Please help!!!!!!!!!!!
Answer:u got to multiply
Step-by-step explanation:
What is the result of division?
Answer:
2x² +4x +11 +20/(x-2)
Step-by-step explanation:
The synthetic division is in the attachment. It shows the above quotient is the result of the division.
Brandon buys a radio for 43.99 in a state where sales tax is 7%.What is the total brandon pays for the radio
Answer:
$3.08
Step-by-step explanation:
Please help me
thanks
Problem 1
Answer: choice D) 84% of the wage earners earn less than $14,000 each
------------
The empirical rule states that 95% of the area under a normal curve is within 2 standard deviations (approximately), so 100-95 = 5% is found in the two tails combined, leaving 5/2 = 2.5% in each tail. Because the top 2.5% earns $18000 or more, this means 18000 is roughly 2 standard deviations above the mean, so z = 2
If z = 2 corresponds to with x = 18000, with mean mu = 10000, then the standard deviation sigma is...
z = (x-mu)/sigma
2 = (18000 - 10000)/sigma
2 = 8000/sigma
2sigma = 8000
sigma = 8000/2
sigma = 4000
So mu+sigma = 10000+4000 = 14000 is the cutoff mark for the earners 1 standard deviation above the mean.
Check out the attached image figue 1 for the diagram for the empirical rule. Add up the values that are to the left of z = 1, so 2.35+13.5+34+34 = 83.85 which rounds to 84
===============================================
Problem 2
Answer: choice D) 2.5%
-----------
x = 250, mu = 190 and sigma = 30
z = (x-mu)/sigma
z = (250-190)/30
z = 60/30
z = 2
According to the emprical rule, roughly 95% of the distribution is within 2 standard deviations. So 100-95 = 5% is in the combined tails leaving 5/2 = 2.5% is in the upper tail.
===============================================
Problem 3
Answer: Choice D) 4,4,4,5,5,6,7,7,8,8,8
------------
Plot each of the values on a dot plot. See the attached image figure 2 for each dotplot. Notice how plot D is bimodal with two hill features, so this distribution is non-normal. Normal distributions only have one mode (one hill).
You may use a calculator to complete this test. if 1 egg and 1/3 cup of oil are needed for each bag of brownie mix, how many bags of brownie mix do you need if you want to use up all 3 eggs and 1 cup of oil?
If G(x) = 3x + 1, then G -1(1) is
4
1/3
0
Answer:
0
Step-by-step explanation:
[tex]g(x) = 3x + 1 \\\ y = 3x + 1[/tex]
Changing x to y and y to x:
[tex]x = 3y + 1 \\\ 3y = x - 1 \\\ y = \frac{x - 1}{3} \\\ g^{-1}(x) = \frac{x - 1}{3} \\\ g^{- 1} (1) = \frac{1 - 1}{3} \\\ g^{- 1} (1) = 0[/tex]
I hope I helped you.
Answer:
0
Step-by-step explanation:
Hope this helps.
The ratio of students that ride the bus as compared to those that walk on 10:1. Does this school have more students that ride the bus or walk? How do you know.
Answer: Yes they do.
Step-by-step explanation:
This because the ratio 10:1 means that for every 10 students that ride the bus only one walks. So if you had 30 students riding he bus you would only have 3 students that walked. So no matter what you will have more kids riding the bus.
what is the solution to the system of equations?
2x-3y+z=-19
5x+y-z=-7
-x+6y-z=35
A. (2,-6,-11)
B. (-2,6,3)
C. (6,2,-25)
D. (-2,6,9)
that answer is B because first u have to solve for Z in 2x-3y+Z=19
Z will be Z=-19-2x+3y
Answer:
B. (-2,6,3)
Step-by-step explanation:
First we will cancel the z-variable in the first two equations. We will do this by adding the second equation to the first:
[tex]\left \{ {{2x-3y+z=-19} \atop {+(5x+y-z=-7)}} \right. \\\\7x-2y=-26[/tex]
Next we cancel the z-variable in the bottom two equations. We will do this by subtracting the bottom equation from the middle one:
[tex]\left \{ {{5x+y-z=-7} \atop {-(-x+6y-z=35)}} \right. \\\\6x-5y=-42[/tex]
We can now take these equations without z as a system:
[tex]\left \{ {{7x-2y=-26} \atop {6x-5y=-42}} \right.[/tex]
We will make the coefficients of y the same by multiplying the top equation by 5 and the bottom by 2:
[tex]\left \{ {{5(7x-2y=-26)} \atop {2(6x-5y=-42)}} \right. \\\\\left \{ {{35x-10y=-130} \atop {12x-10y=-84}} \right.[/tex]
Next we subtract the bottom equation from the top:
[tex]\left \{ {{35x-10y=-130} \atop {-(12x-10y=-84)}} \right. \\\\23x=-46[/tex]
Divide both sides by 23:
23x/23 = -46/23
x = -2
Substitute this into the first equation without z:
7(-2)-2y = -26
-14-2y = -26
Add 14 to each side:
-14-2y+14 = -26+14
-2y = -12
Divide both sides by -2:
-2y/-2 = -12/-2
y = 6
Substitute both x and y into our first original equation:
2(-2)-3(6)+z = -19
-4-18+z = -19
-22+z = -19
Add 22 to each side:
-22+z+22 = -19+22
z = 3
Given sin(−θ)=1/5 and tanθ=√6/12 .
What is the value of cosθ ?
A). √6/60
B). −2√6/5
C). −√6/60
D). 2√6/5
Answer:
B). −2√6/5
Step-by-step explanation:
tan theta = sin theta/ cos theta
Multiply each side by cos theta
tan theta * cos theta = sin theta
Divide each side by tan theta
cos theta = sin theta/ tan theta
We know that the sin (- theta) = - sin theta since sin is and odd function
sin theta = - ( sin (-theta))
Putting this into the above equation,
cos theta = - ( sin (-theta)) / tan theta
cos theta = - 1/5 / (sqrt(6)/12)
Remember when dividing fractions, we use copy dot flip
cos theta = -1/5 * 12/ sqrt(6)
cos theta = -12/ (5 sqrt(6))
We cannot leave a sqrt in the denominator, so multiply the top and bottom by sqrt(6)/sqrt(6)
cos theta = -12/ (5 sqrt(6)) * sqrt(6)/sqrt(6)
cos theta = -12 sqrt(6) / 5*6
Simplify the fraction.
cos theta = -2 sqrt(60/5
Given sin(−θ)=1/5, we know sin(θ)=−1/5, and tan(θ)=√6/12 is positive, indicating that cos(θ) must be positive in the fourth quadrant. Using the Pythagorean identity, we find that cos(θ)=2√6/5, which corresponds to option (D).
Explanation:The question asks for the value of cos(θ) given sin(−θ) = 1/5 and tan(θ) = √6/12.
First, recognize that sin(−θ) = −sin(θ), which means that sin(θ) = −1/5. Then, use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find cos(θ).
sin^2(θ) = (1/5)^2 = 1/25
cos^2(θ) = 1 − (1/25) = 24/25
cos(θ) = ±√(24/25)
Since tan(θ) = √6/12 is positive, and tangent is the ratio of sine to cosine, and we know sine is negative (sin(θ) = −1/5), then cosine must be positive for the tangent to be positive. So, cos(θ) is the positive root.
cos(θ) = √(24/25) = 2√6/5. This matches with option D).
1 _____ 2
Choose the relationship symbol to make a true statement.
<
=
>
Answer: <
Step-by-step explanation: The top triangle (1) has a smaller area than triangle 2.
Answer:
Angle 1 < Angle 2
Step-by-step explanation:
This is a short answer, but I promise that its 100% correct.
Hope it helps.
Anna, Irina, Avel, and Vlad are going on a road trip. The following table shows an incomplete probability model for who will be driving during any given kilometer.
Anna: 1/8
Irina: 3/8
Avel: ?
Vlad: 1/8
If the road trip involves 640km of driving, which of the following is the best prediction for the number of kilometers that Avel will drive?
A. 80
B. 160
C. 240
D. 320
Answer:
1. [tex]\dfrac{3}{8}[/tex]
2. 240 km
Step-by-step explanation:
Anna drives [tex]\dfrac{1}{8},[/tex] Irina drives [tex]\dfrac{3}{8},[/tex] Vlad drives [tex]\dfrac{1}{8},[/tex] then Avel drives
[tex]1-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8}{8}-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8-1-3-1}{8}=\dfrac{3}{8}.[/tex]
If the road trip involves 640 km of driving, then Avel drives
[tex]640\cdot \dfrac{3}{8}=80\cdot 3=240\ km.[/tex]
Football State University $150 for 7 games University of Football $200 for 8 games Gridiron University $175 for 6 games Sports University $125 for 4 games The chart shows the cost of buying season football tickets and how many games are included in the cost. Which university gives the best deal on football tickets? A) Football State University B) University of Football C) Gridiron University D) Sports University
Answer:
A
Step-by-step explanation:
We can find the cost per game to see which is the lowest. The lowest cost will be the best deal on football tickets.
Football State - $150/7= $21.43
University of Football - $200/8= $25
Gridiron - $175/6= $29.17
Sports - $125/4= $31.25
Football State University is the best deal.
By calculating the cost per game for each university, Football State University appears to provide the best deal since it has the lowest cost per game among the options.
Explanation:This is a mathematical problem and relates to the concept of unit price in economics. To answer, you must calculate the cost per game for each university, and the one with the lowest cost per game provides the best deal. For Football State University, you'd do $150 divided by 7, resulting to approximately $21.43. University of Football, $200 divided by 8, which equals to $25. Gridiron University, $175 divided by 6 equals approximately $29.17. Lastly, Sports University $125 divided by 4 gives us $31.25. Therefore, according to these calculations,
Football State University
offers the best deal on football tickets since its price per game is the least.
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Gil borrows $8,000 for college expenses. He will pay a total of $10,280 after 6 years. Gil says the interest rate is at least 5%. Is he correct?
Answer:
Gil is not correct.
Step-by-step explanation:
We have been given that Gil borrows $8,000 for college expenses. He will pay a total of $10,280 after 6 years. Gil says the interest rate is at least 5%.
We will use simple interest formula to check whether Gil is right or not.
[tex]A=P*(1+r*t)[/tex], where
A= Final amount after t years.
P= Principal amount.
r= Interest rate in decimal form.
Let us substitute our given values in above formula to find the interest rate.
[tex]10280=8000*(1+r*6)[/tex]
[tex]10280=8000+48000*r[/tex]
[tex]2280=48000*r[/tex]
[tex]r=\frac{2280}{48000}[/tex]
[tex]r=0.0475[/tex]
Since r is in decimal form, so let us convert interest rate in percent by multiplying by 100.
[tex]0.0475*100=4.75[/tex]
Therefore, the original interest rate is 4.75% which is less than 5%, so Gil is not correct.
Answer:
The answer is gill is incorrect he will pay 2280 interest, which corresponds to an interest rate of 4.75
Step-by-step explanation: