Note: In the following problem, it is important to show all the steps used to get your answers.
Suppose an imaginary closed economy is characterized by the following:
C = c0 + c1 (Y − T)
T = 300 I = 400 G = 400
C is consumption, Y and YD are, respectively, income and disposable income, T is the level
of taxes, I and G, are, respectively, private investment, and government spending.
c0 and c1 are, respectively, autonomous consumption and the marginal propensity to con-
sume; their values are unknown. However, the expression for private saving, S, is as specified
below.
S = 0.5Y − 500
1. Find the equilibrium values of GDP, consumption, disposable income, and private saving.
(5 points)
2. Find the expression of the investment multiplier in terms of c0 and/or c1. (3 points)
3. Find the values of c0 and c1 and the value of the investment multiplier (Hint: you’ll prob-
ably find c0 is equal to an even number, which is multiple of 2). (5 points)
4. From this question on, you must use when needed the values of c0 and c1 found in the pre-
vious question. Suppose now that the government tax revenue, T, has both autonomous
and endogenous components, in the sense that the tax level depends on the level of in-
come.
T = t0 + t1Y
t0 is the autonomous tax level, and t1 is the marginal tax rate.
Given the values of private investment and government spending mentioned above, find
the expression for the equilibrium GDP in terms of c0, c1, t0 and t1. (4 points)
5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same
level of equilibrium GDP as the one obtained (1). (4 points)
6. Find the expression for the investment multiplier in terms of c1and t1 and possibly c0, and
t0. (4 points)
7. Assume now that private investment, I, increases by 50. Find the change in GDP, ∆Y,
induced by the change in investment, ∆I = 50. (4 points)
8. The government does not like the change in GDP induced by the increase in private in-
vestment. It wants to bring it back to the level found in Question (1). For that purpose, it
has the options to change its spending or to change taxes.
(a) If the government changes its spending alone, find the level of ∆G required to coun-
teract the effect on GDP of the fall in investment. (4 points)
(b) If the government changes instead the level of its autonomous taxes alone, find the
level of ∆t0 required to counteract the effect on GDP of the fall in investment. Explain
what happened. (4 points)
(c) How does ∆G compare to ∆t0? Explain the difference, if there is any. (4 points)
(d) In which direction should the government change its marginal tax rate, t1 (increase
or decrease), if it uses it as the sole policy instrument to counteract the effect of the
change in investment? Explain intuitively your answer. (4 points)
Only need to answer 5-8 questions!!!!
Answers
5. Assuming that t0 = 200 find the value of the marginal tax rate that will yield the same level of equilibrium GDP as the one obtained
(1). Solution: Given, T = t0 + t1Y and T = 300
Substituting the given values, we get300 = 200 + t1YGDP, Y = C + I + G + X - M
where, Y = GDP; C = consumption; I = private investment; G = government spending; X = exports; M = imports
We know, C = c0 + c1 (Y − T) Disposable income, YD = Y − T
So, C = c0 + c1 (Y − T) = c0 + c1YD
From the question, S = 0.5Y − 500
We know that, private saving, S = Y − C − T
So, Y − C − T = 0.5Y − 500 ⇒ 0.5Y = C + T + 500
Putting the values,
0.5Y = (c0 + c1YD) + T + 500 ⇒ 0.5Y = (c0 + c1(Y - T)) + T + 500 ⇒ 0.5Y = c0 + c1Y - c1T + T + 500
Solving the above expression, we get
0.5Y - c1Y = c0 - 0.5T + 500 ⇒ 0.5(1-c1)Y = c0 - 0.5T + 500
Hence, Y = (c0 - 0.5T + 500) / (0.5 - c1)
Again, from the question, Y = C + I + G + X - M
Substituting the values we get,
(c0 + c1(Y − T)) + 400 = I + 400 + Y - 500 + X - X0.5Y − 500 + 400 = I + 300 + X − G ⇒ 0.5Y + I = 1200 + G + X
Assuming equilibrium GDP Y = Y*, private investment I = I*, government spending G = G* and net exports X = X*, so0.5Y* + I* = 1200 + G* + X*
Now, from the given information of S, we have S = Y* − C* − T.
Substituting for C* from the equation above, we get S = Y* − (c0 + c1(Y* − T)) − T ⇒ S = Y* − c0 − c1Y* + c1T − T
Substituting for Y* from above, we have S = ((c0 - 0.5T + 500) / (0.5 - c1)) - c0 - c1[((c0 - 0.5T + 500) / (0.5 - c1))] + c1T - T
Now, we need to find the value of t1 when t0 = 200. For this, we need to substitute the value of t0 and Y* in T = t0 + t1YSo, 300 = 200 + t1Y* ⇒ t1 = (300 - 200) / Y* ⇒ t1 = 0.1
Therefore, the value of the marginal tax rate t1 is 0.1.
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Related Questions
please help me. Please no one answer if you don’t know I’m really struggling and I can’t get this
Answers
Answer:
Right, Wrong, Right, Wrong, Right.
Step-by-step explanation:
Can the sides of a triangle have lengths 3.5, 10.9, and 14.4?
Answers
Answer:
No
Step-by-step explanation:
A triangle can NOT have those lengths because any side of a triangle has to have a length greater than the sum of the other two sides. In this case, 14.4, one of the sides, is not greater than the sum of the other two sides (which is also 14.4).
Hope this helps :)
to graph an exponential, you need to plot a few points, and then connect the dots and draw the graph. where do you come up with the values to use in the graph
Answers
When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.
The T-chart employs positive real numbers since this is the most typical form of exponential function.
Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.
The exponential function can be represented by the following equation:
\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.
When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.
The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.
Therefore, the correct answer is option A.
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The fill volume of an automated filling machine used for filling cans of carbonated beverages is normally distributed, with a mean of 370 cc and a standard deviation of 4 cc. a) What is the probability that a fill volume is less than 363 cc? b) If all cans less than 365 cc or greater than 375 cc are scrapped, what proportion of the cans is scrapped? c) Determine specifications that are symmetric about the mean that include 96% of all cans. d) Spose that mean of the filling operation can be adjusted but the standard deviation remains at 4 cc. At what value should the mean be set so that 99% of all cans exceed 365 cc.
Answers
a. the probability that a fill volume is less than 363 cc is approximately 0.0401. b. the proportion of cans that are scrapped is approximately 0.2112. c. the mean that include 96% of all cans are approximately 361.784 cc to 378.216 cc. d. the mean should be set at approximately **355.
a) The probability that a fill volume is less than 363 cc can be determined using the properties of a normal distribution. By calculating the Z-score and using a standard normal distribution table, we can find the corresponding probability.
The Z-score is calculated as:
Z = (X - μ) / σ
where X is the fill volume, μ is the mean, and σ is the standard deviation.
Substituting the given values into the formula:
Z = (363 - 370) / 4 = -1.75
Using a standard normal distribution table, we can find the probability associated with a Z-score of -1.75, which is approximately 0.0401.
Therefore, the probability that a fill volume is less than 363 cc is approximately 0.0401.
b) To determine the proportion of cans that are scrapped, we need to find the area under the normal distribution curve for values less than 365 cc and greater than 375 cc.
First, we calculate the Z-score for each value:
Z1 = (365 - 370) / 4 = -1.25
Z2 = (375 - 370) / 4 = 1.25
Using the standard normal distribution table, we can find the probability associated with Z1 and Z2.
The proportion of cans scrapped is the sum of the probabilities for Z-scores less than Z1 and greater than Z2. Let's denote this as P_scrapped.
P_scrapped = P(Z < Z1) + P(Z > Z2)
Using the table, we find P(Z < -1.25) ≈ 0.1056 and P(Z > 1.25) ≈ 0.1056.
P_scrapped = 0.1056 + 0.1056 = 0.2112
Therefore, the proportion of cans that are scrapped is approximately 0.2112.
c) To determine specifications symmetric about the mean that include 96% of all cans, we need to find the Z-scores corresponding to the cutoff points. Since the distribution is symmetric, we can split the 96% equally on both tails.
The cutoff point for each tail can be calculated as:
Z = ±invNorm((1 - 0.96) / 2) = ±invNorm(0.02 / 2)
Using the inverse normal distribution function, we find Z ≈ ±2.054.
Now we can calculate the actual specifications:
Lower specification = μ - (Z * σ) = 370 - (2.054 * 4) = 361.784
Upper specification = μ + (Z * σ) = 370 + (2.054 * 4) = 378.216
Therefore, specifications symmetric about the mean that include 96% of all cans are approximately 361.784 cc to 378.216 cc.
d) To find the mean value at which 99% of all cans exceed 365 cc, we need to calculate the Z-score corresponding to the desired probability and solve for the mean.
The Z-score can be calculated as:
Z = (X - μ) / σ
We are given that Z ≈ 2.33 (corresponding to the 99th percentile in a standard normal distribution).
Substituting the given values into the formula:
2.33 = (365 - μ) / 4
Solving for μ:
365 - μ = 2.33 * 4
μ = 365 - (2.33 * 4) ≈ 355.68
Therefore, the mean should be set at approximately **355.
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Determine whether each pair of expressions is equivalent. Explain your reasoning.
Answers
The answer is:
\(\large\textbf{They aren't equivalent.}}\)
In-depth explanation:
To determine the answer to this problem, we will use one of the exponent properties:
\(\sf{x^{-m}=\dfrac{1}{x^m}}\)
And
\(\sf{\dfrac{1}{x^{-m}}=x^m}\)
Now we apply this to the problem.
What is 4⁻³ equal to? Well according to the property, it's equal to:
\(\sf{4^{-3}=\dfrac{1}{4^3}}\)
And this question asks us if 4⁻³ is the same as 1/4⁻3.
Well according to the calculations performed above, they're not equivalent.
A group of friends wants to go to the amusement park. They have $116 to spend on parking and admission. Parking is $10.25, and tickets cost $35.25 per person, including tax. Which equation could be used to determine "p", the number of people who can go to the amusement park?
A. 35.25(10.25+p) = 116
B. 116-10.25/35.25 = p
C. p = 10.25-116/35.25
D. 10.25p = 116 - 35.25
Answers
The equation is:
p = ($116 - $10.25)/$35.25
Which is the equation we can see in option B, so we conclude that the correct option is B.
Which equation could be used to determine "p", the number of people who can go to the amusement park?
We know that the group of friends has a total of $116, and we know that the parking costs $10.25 and each ticket costs $35.25.
So if p friends pay for the ticket, then the total cost is:
C(p) = $10.25 + $35.25*p
Then the maximum number of friends that can go to the park with the $116 is given by the equation:
$10.25 + $35.25*p = $116
Solving that for p, we get:
p = ($116 - $10.25)/$35.25
Which is the equation we can see in option B, so we conclude that the correct option is B.
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simplify
rewrite the expression in the form a^n
Answers
Ic=(6.6N-m everal students perform an experiment using 0.150 kg pendulum bob attached to string and obtain the following data: C Length of the string (m) 1.40 1.20 Time for 50.0 vibrations (s) 119 110 99.9 95. 0.90 0.70 0.50 70.9 They want to determine an experimental value for the acceleration due to the gravitational force in the classroom using information from the slope of the line: To do this, they should plot the data using which of the graphs shown below? (A) (B) II MII (D) IV Fana 4-k mylra
Answers
The graph they should use is (B) with T^2 on the y-axis and L on the x-axis.
To determine the experimental value for the acceleration due to gravity, the students need to plot the period squared (T^2) versus the length of the string (L) and find the slope of the line. This is because the period of a pendulum is given by T = 2π√(L/g), where g is the acceleration due to gravity. Rearranging this equation, we get T^2 = (4π^2/g)L, which is the equation of a straight line with slope (4π^2/g) and y-intercept 0. Therefore, the graph they should use is (B) with T^2 on the y-axis and L on the x-axis.
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1) Consider the two functions. Which statement is true?A) The rate of change for function A and function B are the same.B) The slope of function B is negative and the slope of function A is positive.C) The rate of change for function A is greater than the rate of change for function B.D) The rate of change for function B is greater than the rate of change for function A
Answers
Answer:
B.
Step-by-step explanation:
WILL MARK BRAINLIEST !!! HELP !!! determine the value of x and y that would make a parallelogram 3x-1
Answers
Answer:
x=4, y=3.
Step-by-step explanation:
Solving for x,
⟿ 3x-1=11
⟿ 3x=11+1
⟿ 3x=12
⟿ x=12/3
⟿ x=4.
Solving for y,
⟿ 5y=15
⟿ y=15/5
⟿ y=3.
Therefore, x=4 and y=3.
An aquarium is designing a new exhibit to showcase clownfish and queen angelfish. The exhibit will hold a rectangular tank with length twice the size of the width, height is equal to 4 feet and total volume will equal to 500 cubic feet. What is a reasonable width of the tank to the nearest tenth of a foot?
Answers
Answer:
The width of the tank is approximately 7.9 feet.
Step-by-step explanation:
The pool is a rectangular prism with the following dimensions:
length = 2*x feet
width = x feet
height = 4 feet
With volume equal to 500 cubic feet, therefore:
volume = length*width*height = 500
(2*x)*(x)*(4) = 500
8*x² = 500
x = sqrt(500 / 8)
x = sqrt(62.5)
x = 7.90569 feet
The width of the tank is 7.9 feet.
You buy 1 shirt and 2 pair of pants for $31 Your friend buys 3 shirts and 1 pair of pants for $38
Answers
Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.
What is System of Linear EquationA system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.
A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.
In this problem, we need to define our variables and the solve the equations.
Let;
x = cost of shirty = cost of pantx + 2y = 31 ...eq(i)
3x + y = 38 ...eq(ii)
Solving both equations
x = 9, y = 11
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STT 1.3 Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement. Her final position
A is postive
B Is negative
C Could be either positive or negative
Answers
Sarah's final position would be negative. Therefore, option B is the correct answer.
Given that, Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement.
A negative displacement means that Sarah has moved backward along the x-axis, so her final position would be negative.
Therefore, option B is the correct answer.
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Easy.
Find the area of the figure.
Answers
Answer:
i DONT KNOW
Step-by-step explanation:
The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3/8 of the items barbecued or veggie burgers, and 1/3 of the items barbecued or corn cobs, what fraction of barbecued items are mushroom caps?
Answers
Answer:
7/24
Step-by-step explanation:
Let
total items barbequed = 1
Veggie burgers = 3/8
Corn cobs =1/3
Mushroom caps = x
Veggie burgers + corn cobs + x = 1
3/8 + 1/3 + x = 1
9+8 /24 + x = 1
17/24 + x = 1
x= 1 - 17/24
=24-17 /24
= 7/24
x = 7/24
Fraction of barbequed items that are mushroom's is 7/24
Answer:7/24
Step-by-step explanation:
what level of confidence would you need to have so that the value of the true population mean of training time was between 49.01 and 53.99 days?
Answers
1) Option B, which states that the confidence interval size shrank from 0.99 to 0.90, is the right answer.
2) Option D is the best decision. Confidence interval: 0.88
1) Confidence intervals are ranges of estimates for unknown parameters in frequentist statistics. Confidence intervals are given a confidence level. The most common level is 95%, but other levels, such as 90% or 99%, may be used as well.
Therefore, option B is the correct choice, which states that the confidence interval size decreased from 0.99 to 0.90
2) Probability is another word for confidence in statistics. An estimate that falls between the upper and lower values of a confidence interval, such as one constructed with a 95% level of confidence, is 95 out of 100 times likely to be accurate.
It can be calculated as:
df=n-1=19
t critical value 0.12 (two tail) = 1.62797
M = 51.5
sM = √(6.842 / 20) = 1.53
μ = M ± Z (sM)
μ = 51.5 ± 1.62797 * 1.53
μ = 51.5 ± 2.49
therefore, CI { 49.01 and 53.99 }
The correct choice is option D. 0.88 confidence interval.
Question:
. move the slider all the way to the right to a confidence coefficient of 0.99. now move the slider to a confidence coefficient of 0.90. what happened to the size of the confidence interval during the move from 0.99 to 0.90? from 0.99 to 0.90 the confidence interval size became larger from 0.99 to 0.90 the confidence interval size became smaller from 0.99 to 0.90 the confidence interval size remained constant -select- 2. what level of confidence would you need have so that the value of the true population mean of training time was between 49.01 and 53.99 days? 0.93 0.97 0.85 0.88
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For the following population of N = 9 scores: 4, 2, 0, 5, 3, 2, 1, 7, 3a. Sketch a histogram showing the populationdistribution.
Answers
Given:
The population of N = 9 scores is 4, 2, 0, 5, 3, 2, 1, 7, 3
Required:
Sketch a histogram showing the population distribution.
Explanation:
Make a frequency table for the given data as:M
A) Translation: 1 unit left and 1 unit down
B) Translation: 1 unit right and 1 unit up
C) Translation: 3 unit right
D) Translation: 4 unit right and 1 unit up
Answers
In translations, points like X become X’ and Z becomes Z’, W becomes W’ and so on.
So let’s focus on point X of the original shape. To get from X to X’ , we just shift one point to the right and one point up. Therefore we know the whole shape was translated one unit right and one unit up.
is (x+1) a factor of polynomial x^3+2x^2-19x-20
Answers
Answer:
Step-by-step explanation:
3
3|-d + 2| + 1 if d = 4
Answers
Answer:
7
Step-by-step explanation:
reminder that the absolute value function always gives a positive result.
3 | - d + 2 | + 1 ( substitute d = 4 )
3 | - 4 + 2 | + 1
= 3 | - 2 | + 1
= 3 × 2 + 1
= 6 + 1
= 7
Earth has a diameter of 7,926 miles. What is its diameter in kilometers? (1 mile = 1.6 kilometers)
A. 49,553 km
B. 120,586 km
C. 1,392,650 km
D. 12,682 km
Answers
The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.
Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:
Diameter in kilometers = Diameter in miles × Conversion factor
Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile
Diameter in kilometers = 12,681.6 kilometers
Rounding this value to the nearest whole number, we get 12,682 kilometers.
Therefore, the correct answer is option D: 12,682 km.
Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.
Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.
Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.
In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.
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Kristina owns a local bakery and sells boxes of cannolis. Each box contains 9 cannolis. If she sells 6 boxes of cannolis by closing time on Friday, how many cannolis did she make to fill all the boxes that she sold?
Answers
Answer:
63 cupcakes
Step-by-step explanation:
let f be a differentiable function suchf(1)=pi that and f'x=root x^3=6. what is the value of f(5)?
Answers
The correct option is (A) 55.8093 (approximately). i.e The value of f(5) = 55.8093
Given that a differentiable function f(1) = π, and f'x = √(x³) = 6.
To find the value of f(5).
As we know, If f(x) is differentiable at x = a, then f(x) is continuous at x = a.
And, f'(x) = (dy/dx) is the derivative of f(x) at x = a.
Then we have to integrate f'(x) to get f(x).
So we have,f'(x) = √(x³) ------(1)
Integrating both sides with respect to x, we get,
f(x) = ∫ f'(x) dx
= ∫√(x³) dx
= ∫ x⁽³/²⁾ dx
=(2/5) x⁽⁵/²⁾ + C, where C is a constant of integration.
Using the given condition f(1) = π, we get,
π = f(1) = (2/5) * 1^(5/2) + C or
C = π - (2/5).
Therefore, f(x) = (2/5) x⁽⁵/²⁾ + π - (2/5) = (2/5) (x⁽⁵/²⁾ - 1) + π.
Now putting the value of x = 5, we get,
f(5) = (2/5) (5⁽⁵/²⁾) - 1) + π= 55.8093 (approximately).
Hence, the value of f(5) is 55.8093 (approximately).
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Choose the correct answers for amount financed and the finance charge in dollars for the following problem. Curtis Hindle purchased a mountain bike for $650. 00 with 75% down. He will make 12 payments of $24. 38 each. What is the total amount paid (including down payment) and finance charge in dollars? The total paid (including down payment) is $. The finance charge in dollars is $.
Answers
In this case, the amount financed is 25% of $650.00. We will calculate the amount of financing below: Amount financed = 0.25 x $650.00Amount financed = $162.50Curtis will make 12 payments of $24.38 each.
The total payments for 12 months will be $292.56, as shown below: Total payments = 12 x $24.38Total payments = $292.56The total amount that Curtis paid (including down payment) is calculated below: Total paid = $650.00 + $292.56Total paid = $942.56The finance charge in dollars is calculated below: Finance charge = Total paid - Amount financed Finance charge = $942.56 - $162.50Finance charge = $780.06Therefore, the total paid (including down payment) is $942.56 and the finance charge in dollars is $780.06.
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Under his cell phone plan, Brayden pays a flat cost of $66. 50 per month and $4 per gigabyte, or part of a gigabyte. (For example, if he used 2. 3 gigabytes, he would have to pay for 3 whole gigabytes. ) He wants to keep his bill under $85 per month. What is the maximum whole number of gigabytes of data he can use while staying within his budget?
Answers
In linear equation, 4 is the maximum whole number of gigabytes of data he can use while staying within his budget.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Let the number of gigabyte so f data she can use while staying within her budget then,
we can write the cost equation as following
4x + 66.50 ) ≤ 85
85 - 66.50 ≤ 4x
18.5 ≤ 4x
x ≤ 18.5/4
x ≤ 4. 625
Xmax = 4
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What is the square of 1 to 100?.
Answers
We get the squares of the number as 1 , 4 , 9 , 16.......as given below, hence we get square of any number by product with itself.
What is square of the number?The outcome of multiplying an integer by itself is referred to as the resultant number's square. In essence, a square number is a result of multiplying two identical numbers. The best illustration of a square number in geometry is the area of a square with side lengths of "n" (where n is an integer).
As an illustration, (-7)² = -7 -7 = 49 (two negative signs multiplied by each other result in a positive sign). The value of multiplying -7 and -7 is 49, which is a positive square number.
Below are the squares of 1 to 100.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
21² = 441
22² = 484
23² = 529
24² = 576
25² = 625
26² = 676
27² = 729
28² = 784
29² = 841
30² = 900
31² = 961
32² = 1024
33² = 1089
34² = 1156
35² = 1225
36² = 1296
37² = 1369
38² = 1444
39² = 1521
40² = 1600
41² = 1681
42² = 1764
43² = 1849
44² = 1936
45² = 2025
46² = 2116
47² = 2209
4²2 = 2304
49² = 2401
50² = 2500
51² = 2601
52² = 2704
53² = 2809
54² = 2916
55² = 3025
56² = 3136
57² = 3249
58² = 3364
59² = 3481
60² = 3600
61² = 3721
62² = 3844
63² = 3969
64² = 4096
65² = 4225
66² = 4356
67² = 4489
68² = 4624
69² = 4761
70² = 4900
71² = 5041
72² = 5184
73² = 5329
74² = 5476
75² = 5625
76² = 5776
77² = 5929
78² = 6084
79² = 6241
80² = 6400
81² = 6561
82² = 6724
83² = 6889
84² = 7056
85² = 7225
86² = 7396
87² = 7569
88² = 7744
89² = 7921
90² = 8100
91² = 8281
92² = 8464
93² = 8649
94² = 8836
95² = 9025
96² = 9216
97² = 9409
98² = 9604
99² = 9801
100² = 10000
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(PLS HURRY!) On Melissa's 6th birthday, she gets a 2000$ CD that earns 6% interest, compounded. If the CD matures on her 14th birthday, how much money will be available?
Answers
Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -
\(A = P(1 + r/n)^(nt)\)
Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).
It is not given how many times per year the interest is compounded, so assume it is compounded annually.
Using these values in the formula -
\(A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69\)
Therefore, the value is obtained as $3187.69.
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For what value of x is the equation 3(2x + 4) - x = 47 true? *
Answers
Answer:
x = 7
Step-by-step explanation:
3(2x + 4) - x = 47
Multiply out the brackets: 6x + 12 - x = 47
Collect like terms: 6x - x + 12 = 47
Combine like terms: 5x + 12 = 47
Subtract 12 from both sides: 5x = 35
Divide both sides by 5: x = 7
Step-by-step explanation:
Open the bracket by using the number outside the bracket to multiply the ones inside.
Opening the bracket, we have that; 6x+12 - x =47
6x-x+12=47
5x+12=47
Collect like terms,
5x=47-12
5x=35
d.b.s by 5 to make x the subject
5x/5=35/5
x=7
when you take the scholastic assessment test (sat), your score is recorded as a percentile score. if you scored in the 92nd percentile, it means that you scored better than approximately 92% of those who took the test. (a) if lisa's score was 84 and that score was the 26th score from the top in a class of 250 scores, what is lisa's percentile rank? (round your answer to the nearest whole number.)
Answers
Lisa's percentile rank will be 89%.
What is percentile?
The k-th percentile is the score at or below which a given percentage falls, or the score below which a particular percentage of the scores in the frequency distribution falls.
The percentile rank is utilized to compare a score to the rest of the scores in a set of scores. It tells us the percentage of scores equal or below a particular scores.
\(P = \frac{R}{N+1} (100)\)
where, R is the rank and N is the score.
Here,
Lisa's rank = 250 - 26 = 224, N = 250
So, her percentile rank will be,
\(P = \frac{224}{250+1}(100) = 89.24\\ P = 89%\)
P = 89%
Therefore, the Lisa's percentile rank will be 89%.
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What type of fire extinguisher can be used for fire caused by
flammable liquids?
Select one:
A.
Water extinguisher
B.
Dry powder extinguisher
C.
Foam extinguisher
D.
Carbon dioxide extinguisher
E.
A a
Answers
The type of fire extinguisher that can be used for fires caused by flammable liquids is the foam extinguisher.
A foam extinguisher is designed to extinguish fires involving flammable liquids, such as gasoline, oil, or paint. It works by forming a blanket of foam over the fuel, cutting off the oxygen supply and smothering the flames.
Here is a step-by-step explanation of how a foam extinguisher works:
1. When a fire caused by flammable liquids occurs, grab the foam extinguisher and remove the safety pin.
2. Aim the nozzle at the base of the fire, where the flammable liquid is burning.
3. Squeeze the handle to release the foam. The foam will expand and cover the fuel, preventing the fire from spreading and extinguishing it.
4. Continue applying the foam until the fire is completely out. Make sure to cover the entire area affected by the fire to ensure it does not reignite.
Therefore , the correct answer is option c : foam extinguisher .
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