Answer:
If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.
Given,
Annual deposit = $1000
Rate = 8% compounded annually
Time(n) = 10 year
Amount = ?
As we know the formula ,
Amount = P(1+r/100)ⁿ
Amount = 1000(1+8/100)¹⁰
Amount = 1000(1+0.08)¹⁰
Amount =1000(1.08)¹⁰
Amount = 1000 × 2.15892
Amount = $2158.92
Hence, amount in 10year will be $2158.92
ABCD is a trapezium. P is a point along AC such that AP=4PC. DC=1/4AB.
a) express PB in terms of a and b in its simplest form
b) express DP in terms of a and b in its simplest form
c) does DPB form a straight line?
Answer:
a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:
PC = CP = x - b
AP = 4(x - b)
Also, using the fact that DC = (1/4)AB, we have:
AD = x
AB = 4DC = x/4
BC = AB - AD = x/4 - x = -3x/4
Now, consider the similar triangles PBC and ABD:
PB/AB = BC/AD
PB/(x/4) = (-3x/4)/x
PB = -3/4(x/4) = -3x/16
Finally, substituting x = a + b, we have:
PB = -3(a + b)/16
b) Using the same similar triangles as in part (a), we have:
DP/DC = PB/BC
DP/(1/4)AB = PB/(-3x/4)
DP = -3/4(PB)(DC/BC)AB
DP = -3/4(PB)(1/4)/(AB - AD)AB
Substituting the expressions for PB, AB, and AD from part (a), we get:
DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4
DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)
DP = -3/16
So, DP = -3/16(a + b)
c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:
Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16
Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4
Since the slopes are not equal, DPB does not form a straight line.
Factor by substitution: (3y−2)2−(3y−2)−2.
The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²
How to factor Polynomial by substitution?Factoring polynomials simply means separating a polynomial into its component polynomials.
Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.
We have the equation:
(3y - 2)² - (3y - 2)⁻²
Let 3y - 2 be denoted by S and as such we have:
S² - S⁻²
= S² - 1/S²
Using the denominator as factor, we have:
= (S⁴ - 1)/S²
Plugging 3y - 2 for S gives us:
((3y - 2)⁴ - 1)/(3y - 2)²
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88.128 x 0.5 Multiplication question
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
Set up and solve a proportion for the following application problem. If 5 pounds of grass seed cover 355 square feet, how many pounds are needed for 6035 square feet?
Let x be the number of pounds needed for 6035 square feet.
We can set up a proportion between the pounds of grass seed and the square feet covered:
5 pounds / 355 square feet = x pounds / 6035 square feet
To solve for x, we can cross-multiply and simplify:
5 pounds * 6035 square feet = 355 square feet * x pounds
30175 = 355x
x = 30175 / 355
x ≈ 85.07
Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
CAN SOMEONE HELP WITH THIS QUESTION?
Answer:
a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:
A(t) = A0 * (1/2)^(t/8)
where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.
Substituting the given values, we get:
A(t) = 7 * (1/2)^(t/8)
b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:
A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)
Simplifying, we get:
A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)
c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:
A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)
2. Natasha interviewed with 5 companies this week because she is planning on switching companies. Her projected earnings per hour from the companies are written below. 25.13 42 53.5 35.7 47.8 Which inequality represents her earnings, e, from any of the companies she interviewed with? a. e < 53 b. e < 56.7 c. e < 38 d. e< 53.57
the correct option for this question is (a) e < 53.
Why it is?
The inequality that represents Natasha's earnings, e, from any of the companies she interviewed with is:
e < 53.5
This is because her projected earnings per hour range from $25.13 to $53.5, and the maximum value is $53.5. So, her earnings from any of the companies cannot be greater than $53.5 per hour. Therefore, the correct answer is option (a) e < 53.
Earnings are the amount of money that a person earns from their work, business, investments, or other sources of income. This can include salaries, wages, commissions, bonuses, and profits, among others.
Earnings are typically reported as gross income, which is the total amount earned before taxes and other deductions are taken out. It is an important measure of a person's financial well-being and is often used to determine eligibility for credit or loans. Earnings can vary widely depending on a person's job, level of experience, education, and industry, among other factors.
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Thandi is 1,23 m tall and Peter is 0,45 m taller than Thandi.What is Peter's height
Peter is 1.68 meters tall.
What is height?
Height is a measure of the distance between the base and the top of an object, or the distance between the bottom and the top of a vertical structure. It is often used to describe the vertical dimension of an object or structure, such as the height of a building, the height of a person, or the height of a mountain. In mathematics, height can also refer to the vertical distance between two points on a coordinate plane or the vertical dimension of a three-dimensional shape. The height of a triangle, for example, is the perpendicular distance from the base to the highest point of the triangle.
Peter's height is Thandi's height plus the additional 0.45 m. Therefore:
Peter's height = Thandi's height + 0.45 m
Peter's height = 1.23 m + 0.45 m
Peter's height = 1.68 m
Therefore, Peter is 1.68 meters tall.
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Create a real-word mathematical problem as an equation that can be solved using all three properties
Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.
What do you mean by cost?Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.
Solution:
Let x be the quantity of pizzas ordered.
12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.
As a result, the necessary quantity of pizzas is:
[tex]x\geq 3(x-1) \leq x[/tex]
In order to find the best price, we must reduce the total cost, that is determined by:
C(x) = 15x plus 5(x - 1) (x - 1) - 15
Using the cost function's derivative in relation to x, we may calculate:
C'(x) = 20 - 10[tex]/(x-1)^2[/tex]
Finding the critical points by setting the derivative to zero yields the following results:
20 - 10[tex]/(x-1)^2[/tex] = 0
Simplishing, we obtain:
[tex](x-1)^2[/tex]= 2
By solving for x using square root of the both sides, we arrive at:
x = 1 ± √2
The ideal quantity to order is two pizzas because x has to be an integer.
By adding x = 2 to the cost function, we can determine the total cost:
C(2) = 15(2) + 5(2 - 1) - 15 = 22
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Nine friends share 4 sandwiches equally what fraction of a sandwich does each friend get
Answer:
4/9
Step-by-step explanation:
4 sandwiches in between 9 friends
4 sandwiches must be divided in between 9 people
- > [tex]\frac{4 sandwiches}{9 people}[/tex] = [tex]\frac{4}{9}[/tex]
Answer:
Step-by-step explanation:
2/3
Sue deposited $1,500 into two different accounts.
- She deposited $600 into an account that pays 7.5% simple interest.
- She deposited $900 into an account that pays 6% compounded annually.
If Sue does not deposit additional money into the accounts and she doesn't withdraw any
money from the accounts, which is closest to the total balance she will have in the two
accounts at the end of 5 years?
F $2,029.40
G $2,005.68
H $529.40
J $1,995.00
The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:
Balance of the first account with simple interest:
FV = P(1 + rt)
FV = $600(1 + 0.075 x 5)
FV = $825
Balance of the second account with compounded interest:
FV = P(1 + r)^n
FV = $900(1 + 0.06)^5
FV = $1,286.87
Total balance = $825 + $1,286.87
Total balance = $2,111.87
The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.
All I need to know is the answer to this problem so I can compare mine.
Answer:
we will do TanA = perpendicular / Base
A = 35°
Tan 35° = 217 / W
value of Tan 35° is approx = 0.7
0.7 = 217/ W
W = 217 / 0.7
W = 310
Need help pls
geometry
#23
Answer: I think its C
Answer:
Step-by-step explanation:
C is false. [tex]\angle BEC = \angle AED=126[/tex] (vertically opposite).
The rest are correct.
I will mark you brainiest!
The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
The measure of an angle is twice less than that of its supplement angle.
The supplementary angle will be 60°.
What are supplementary angles?
Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.
For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.
Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.
Now,
Let x = measure of the angle.
Then, the supplement angle is 180 - x.
According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:
180 - x = 2x
Solving for x, we get:
180 = 3x
x = 60
Therefore, the angle measures 60 degrees.
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Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?
I will mark you brainiest!
If AB = 35,BC = 15, and EF = 60, then the value of DE IS
A) 140
B) 180
C) 200
D) 210
AB/BC = DE/EF
35/15 = DE/60
DE = 35*60 / 15
DE = 140
answer
A 140
I need this done in 10 mins or less!!!
Answer:
To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:
V = 15 m x 4 m x 8 m x 11 m x 3 m
V = 11,880 cubic meters
Therefore, the total volume of Leah's new planter is 11,880 cubic meters.
Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:
8 x 4 x 2 + x = 212
Simplifying the left side, we get:
64 + x = 212
Subtracting 64 from both sides, we get:
x = 148
Therefore, the volume of the large box is 148 cubic inches.
What is the fourth term of the sequence:
Write the number in the blank only.
a_1 = 5
a_n = 2a_n-1 + 3
The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.
Calculating the fourth term of the sequenceGiven the following definition of functions
a₁ = 5
aₙ = 2aₙ₋₁ + 3
To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:
a₂ = 2a₁ + 3 = 2(5) + 3 = 13
a₃ = 2a₂ + 3 = 2(13) + 3 = 29
a₄ = 2a₃ + 3 = 2(29) + 3 = 61
Therefore, the fourth term of the sequence is 61.
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I need help with a problem on my test.
Write an exponential function to model the situation. Tell what each variable represents. A price of $115 increases 9% each month.
Please help
Answer: 1050$
Step-by-step explanation:
im a math teacher
for each situation, determine taxable income, assuming pretax accounting income is $100 million
Answer:
Temporary Differences Reported First on: The Income Statement The Tax Return Revenue Expense Revenue Expense1) $272) $273) $274) $275) $22 $276) $27 $227) $22 $27 $178) $22 $27 $12 $17Taxable Income assuming pretax accounting income is $100 million1) Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m
Step-by-step explanation:
First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
At age 25 , someone sets up an IRA (individual retirement account) with an APR of 4 %. At the end of each month he deposits $95 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Question content area bottom
Part 1
After retirement the IRA will contain $
enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.
How will you calculate the balance of the IRA?To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:
FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)
Where:
Pmt = $95 (the monthly deposit amount)
r = 4% / 12 = 0.003333 (the monthly interest rate)
n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)
Plugging in these values, we get:
FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)
FV = $98,052.52
Therefore, the IRA will contain $98,052.52 at age 65.
Part 2
To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:
Total Deposits = Pmt * n
Plugging in the values, we get:
Total Deposits = 95 * 480
Total Deposits = $45,600
Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.
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I couldn’t solve this and I was very confused, if anyone can please help me on this I will appreciate it, thank you so much
It is due tomorrow
no 1) what is the square root of 2? it's about 1.5
no 2) pi is 3.14 blah blahblah so just put somewhere around 3
no 3) do square root of 11, it's about 3.3 so put it a tiny bit after no 2.
all of these will be after the 0, not before because theyre positive
hope this helps x
A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.
Answer:
$6235 1
' 1 . ' 8
Answer:
Step-by-step explanation:
I need to find f(g) f(x) please
The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other.
What is inverse?The inverse of a function is a second function that "undoes" the effect of the first function. More specifically, if f is a function that maps elements from a set A to a set B, then its inverse function, denoted as f^(-1), maps elements from B back to A.
According to question:(a) To find f(g(x)), we need to substitute the expression for g(x) into f(x):
f(g(x)) = g(x) / (6 + g(x))
Substituting the expression for g(x) yields:
f(g(x)) = (6x / (1 - x)) / (6 + (6x / (1 - x)))
This equation can be made simpler by first locating a common denominator:
f(g(x)) = (6x / (1 - x)) / ((6(1 - x) / (1 - x)) + (6x / (1 - x)))
f(g(x)) = (6x / (1 - x)) / ((6 - 6x + 6x) / (1 - x))
f(g(x)) = (6x / (1 - x)) / (6 / (1 - x))
f(g(x)) = 6x / 6
f(g(x)) = x
To find g(f(x)), we need to substitute the expression for f(x) into g(x):
g(f(x)) = 6f(x) / (1 - f(x))
Substituting the expression for f(x) yields:
g(f(x)) = 6(x / (6 + x)) / (1 - (x / (6 + x)))
To simplify this expression, we can first find a common denominator:
g(f(x)) = 6(x / (6 + x)) / (((6 + x) / (6 + x)) - (x / (6 + x)))
g(f(x)) = 6(x / (6 + x)) / ((6 + x - x) / (6 + x))
g(f(x)) = 6(x / (6 + x)) / (6 / (6 + x))
g(f(x)) = x
(b) The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other. This means that when we apply one function and then the other, we get back to the original input value. Specifically, if we apply f(x) to x and then apply g(x) to the result, we get x back, and if we apply g(x) to x and then apply f(x) to the result, we also get x back. This is a useful property when analyzing functions and their relationships.
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The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
Mr. Ed earns $15.50 per hour. His regular hours are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay for a week in which he works 45 hours.
Answer:
For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:
40 hours x $15.50 per hour = $620
For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:
5 hours x $15.50 per hour x 1.5 = $116.25
Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:
$620 (regular pay) + $116.25 (overtime pay) = $736.25.
A business analyst wants to determine if the prices of goods at a supermarket have changed significantly since the new owner of the company took over. She looks at the prices of ten items before the new owner took over compared to after the new owner started.
(Chart in photo below)
Based on the data in the table and using a significance level of 0.05, what is the correct P-value and conclusion?
A. With a t statistic of 1.4789 and a P-value of 0.173292, reject the no hypothesis that prices have not changed
B. With a T statistic of 1.4789 and a P value of 0.173292, fail to reject the null hypothesis. The prices have not changed.
C. With a T statistic of 0.7394 and a P value of 0.478505, reject the no hypothesis that prices have not changed.
D. With a T statistic of 0.7394 anda P value of 0.478505, fail to reject the no hypothesis that prices have not changed.
Please answer quickly, 100 points thank you !
Answer: Option A
Step-by-step explanation:
The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:
t = -1.4789
P-value = 0.173292
Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.
With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.
Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.
To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.
Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.
To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:
Mean difference = (0.30 - 0.07) / 10 = 0.023
Standard deviation = 2.967
t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394
The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.
Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:
Thus, the correct option is D.
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To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.