The required exact value of tan(5π/12) is (2 + √3) / 3.
We can use the half-angle identity for a tangent:
tan(x/2) = [1 - cos(x)] / sin(x)
to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.
First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:
sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2
cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2
Now we can use the half-angle identity for a tangent with x=5π/6:
tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)
= [1 - (-√3/2)] / (1/2)
= (2 + √3) / 3
Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.
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Suppose we wish to factor 13b2 + 23b - 8 by grouping. What is the key number, ac?
The key number, ac, is -104.
What is key number ?
Key number is the product of the coefficients of the first and last terms. The right binomial factors for a quadratic expression can be determined with its assistance.
We must multiply the coefficient of the quadratic term by the constant term to obtain the key value, ac, which results in:
ac = 13(-8) = -104
Therefore, The key number, ac, is -104.
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Hurry up please
State the domain and range and tell if the graph is a function yes or no
What’s the domain and range?
The graph is a function: yes
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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Answers for these test question, thank you
The missing lengths of the following two triangles:
Case 1: x = 50 km
Case 2: x = 40 km
Case 3: Obtuse
Case 4: Acute
Case 5: Right
Case 6: m = 16, n = 8√3
Case 7: x = 3√2, y = 3
How to find the length of missing sides in a triangle
In this problem we must determine all missing lenghts in a triangle, this can be done by law of cosine:
x² = a² + b² - 2 · a · b · cos X
Where X is the angle opposite to side x.
Now we proceed to determine the missing lengths of the following two triangles:
Case 1
x = √[(14 km)² + (48 km)² - 2 · (14 km) · (48 km) · cos 90°]
x = 50 km
Case 2
x = √[(24 km)² + (32 km)² - 2 · (24 km) · (32 km) · cos 90°]
x = 40 km
In addition, we can determine if any triangle is acute, obtuse and right also by law of cosine:
cos X = - (x² - a² - b²) / (2 · a · b)
Case 3
cos X = - [(18 in)² - (12 in)² - (9 in)²] / [2 · (12 in) · (9 in)]
cos X = - 0.458 (Obtuse)
Case 4
cos X = - [(15 ft)² - (12 in)² - (14 in)²] / [2 · (12 in) · (14 in)]
cos X = 0.342 (Acute)
Case 5
cos X = - [(5 ft)² - (3 in)² - (4 in)²] / [2 · (3 in) · (4 in)]
cos X = 0 (Right)
Finaly, we determine the missing lengths of two right triangles by trigonometric functions:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Now we find the missing lengths:
Case 6
m = 8 / cos 60°
m = 16
n = 8 · tan 60°
n = 8√3
Case 7
x = 3 / sin 45°
x = 3√2
y = 3 / tan 45°
y = 3
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Peter has won the lottery. He will receive Kenya Shillings 87325 per month for the next 21 years, a total of Kenya Shillings 22.01
million.
What single deposit (in millions) should the lottery commission make now to fund Peter's annuity. Assume 10.7%
annual interest, compounded monthly
The requried lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.
To calculate the present value of Peter's annuity,
[tex]PV = PMT * (1 - (1 + r)^{-n}) / r[/tex]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
In this case, PMT = 87325, r = 0.107/12 = 0.008917, and n = 21*12 = 252.
Substitute the value in the formula given above:
[tex]PV = 87325 * (1 - (1 + 0.008917)^{-252} / 0.008917[/tex]
PV = 8747531.78
Thus, the lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.
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Round to the nearest tenth, then find the sum. 35.26 + 8.32 + 6.78 i will give 12 points pleas help me in in a test
Answer:
Step-by-step explanation:
35.26 rounded to 35.3
8.32 rounded to 8.3
6.78 rounded to 6.8
35.3 + 8.3 = 43.6
43.6 + 6.8 = 50.4
The answer is 50.4.
39.26 rounds to 35.3
8.32 rounds to 8.3
6.78 rounds to 6.8
When you add them together, you get 50.4.
when its comes to interest,most CDs will allow which of the following options?
a. Unlimited withdraws of interest
b. Periodic interest payout
c. loans against principal
d. Withdrawal of principal
When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.
A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.
However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.
While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.
Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.
So, correct option is B.
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if $5700 is invested in a savings account for which interest is compounded annually, and if the $5700 turns into $6100 in 12 years, what is the interest rate of the savings account?
Answer:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the ending amount, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = $5700, A = $6100, n = 1 (since the interest is compounded annually), and t = 12. We can solve for r:
$6100 = $5700(1 + r/1)^(1*12)
$6100/$5700 = (1 + r)^12
1.0702 = (1 + r)^12
log(1.0702) = log[(1 + r)^12]
0.0291 = 12log(1 + r)
0.00243 = log(1 + r)
10^(0.00243) = 1 + r
r = 0.0059 or 0.59%
Therefore, the interest rate of the savings account is 0.59%.
Pls tell me just the answer
The domain of the function g(x) is given as follows:
B. All values of x such that x ≥ 0.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
The function for this problem is defined as follows:
[tex]g(x) = \sqrt{8x}[/tex]
The square root function assumes values that are greater than or equals to zero, hence the domain of the function is obtained as follows:
8x ≥ 0.
x ≥ 0.
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Manuel bought a car for 65% of the original price of $7,000. How much did he pay for the car
Manuel bought a car for 65% (percentage) of the original price of $7,000, he must have paid $4,550 for the car.
What is the percentage?The percentage is a number or ratio that represents a fraction of a whole number or the sum of ratios.
The percentage is computed by dividing one number by another and multiplying the result by 100.
The original price of the car = $7,000
The discount factor = 65% (1 - 35%) or 0.65
The discounted price = $4,550 ($7,000 x 0.65)
Thus, by implication, for receiving a discount of 35% (100% - 65%), Manuel paid $4,550 for the car.
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X
-2
-1
01
2
3
-2
0
7
What is the rate of change for the interval between 0
and 2 for the quadratic equation as f(x)=2x²+x-3
represented in the table?
O
5
10
The rate of change for the interval between 0 and 2 for the quadratic equation is 10.
What is the change in interval of the quadratic equation?
A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms that are raised to the power of two.
The general form is;
ax² + bx + c = 0
Where;
x is the variablea, b, and c are constantsThe rate of change for the interval between 0 and 2 for the quadratic equation is calculated as;
f(2) - f(0) = 7 - (-3)
= 7 + 3
= 10
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The volume of a sphere is 33.51032164 cubic meters. What is the radius of the sphere?
The radius of the sphere that has a volume of 33.51032164 cubic meters is approximately 2 meters.
What is the Radius of a Sphere?The radius of a sphere is the distance from the center of the sphere to any point around the circumference. The radius is half of the length of the diameter of a sphere.
The volume of a sphere = 4/3 * π * r³
Given that:
Volume ≈ 33.5 cubic meters
Use the formula to find the radius of the sphere:
33.5 = 4/3 * π * r³
33.5 = 4π/3 * r³
3 * 33.5 = 4π * r³
100.5/4π = r³
r³ = 7.998
r = ∛7.998
r ≈ 2 meters.
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Solve for a.
60°
a
60°
a = [? ]°
The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].
Explanation:
To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:
60°a / 60° = [? ]° / 60°
This simplifies to:
a = [? ]° / 60°
Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:
a = [? ] / 60
Therefore, the value of a is dependent on the value of [? ].
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La empresa clarisse dedicada al rubro de telefónica, está ampliando su cobertura, debido a esto está colocando postes, donde la séptima parte de un poste está enterrada, y sobresale del suelo 25 metros. Calcular la altura del poste aproximado a los centímetros.
The approximate height of the pole in centimeters is 17,500 centimeters.
We have,
Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.
We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.
25 = L/7
where L is the total length of the pole.
We can solve for L by multiplying both sides of the equation by 7:
L = 7 x 25
= 175 meters
Now we need to convert this length to centimeters.
Since 1 meter is equal to 100 centimeters,
175 meters x 100
= 17,500 centimeters
Therefore,
The approximate height of the pole in centimeters is 17,500 centimeters.
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The complete question.
The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.
Fill in the blanks using the available answers
I believe the first part is 2.2. But lost on the fill in the blanks. Help please.
Note that the estimated population mean is 2.2
The mean absolute deviation is 1
The average distance each data value is from the mean is 1 hours per night
The distribution has _Low_ variability
How did we reach the above conclusions?Where the data graphed is:
Hours Per Night Students
0.5 0
1 2
1.5 3
2 4
2.5 2
3 2
3.5 1
4 1
The estimate of the population mean is
0.5 (0 ) + 1 ( 2) + 1.5( 3) + 2(4) + 2.5(2) + 3( 2 ) + 3.5( 1) + 4( 1) =3 3
⇒ 33 / 15
population Mean = 2.2
To find the Mean Absolute Deviation:
0.5 - 2.2 = - 1.7
1 - 2.2 = -1 .2
1.5 - 2.2 = - 0.7
2 - 2.2 = - 0.2
2.5 - 2.2 =0.3
3 - 2.2 = 0.8
3.5 - 2.2 = 1.3
4 - 2.2 = 1.8
The absolute deviations from the sample mean are
1.7 , 1.2, 0.7, 0.2 , 0.3, 0.8 , 1.3,1.8
Thus
(1.7 + 1.2 + 0.7 + 0.2+0.3 + 0.8 + 1.3 +1.8) / 8 = 8/8 = 1
Therefore, the M.A. D is 1 hours per nigh
For average distance each data value is from the mean...
|(-1.7)| + |( -1.2) | + | ( -0.7)| + |( -0.2 | + | 0.3| + | 0.8| + | 1.3 | + | 1.8 | = 8
8/ 8 = 1
So average distance of each data value form the mean is 1 hours per night.
We discovered that the M.A. D in this scenario is 1hr/ night. We may claim that the distribution has low variability because this number is quite tiny.
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Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+3cos(θ)+7=0
Select all that apply:
1.77
0.48
1.4
3.77
2.99
2.51
Answer:3.77
2.51 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
-7u^2 + 3u + 7 = 0
Multiplying both sides by -1, we get:
7u^2 - 3u - 7 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 7, b = -3, and c = -7. Substituting these values, we get:
u = (3 ± sqrt(9 + 196)) / 14
u = (3 ± 5sqrt(5)) / 14
Therefore, either:
What is the x of a 68⁰? I’m in 8th grade learning about angels and basically adding them .
The complement and the supplement of an angle of 68º are given as follows:
Complement: 22º.Supplement: 112º.How to obtain the complement of an angle?When two angles are complementary, the sum of the measures of the angles is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.When two angles are supplementary, the sum of the measures of the angles is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.Hence the complement and the supplement of an angle of 68º are obtained as follows:
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José has a wedge-shaped piece of wood as shown in the diagram. José plans to paint the piece
needs.
3 in.
4 in.
5 in.
8 in.
Answer:
E. 108 in.²
Step-by-step explanation:
The piece of wood has the shape of a triangular prism.
SA = lateral area + area of the bases
SA = perimeter × height + 2 × bh/2
SA = (5 + 3 + 4) in. × 8 in. + 3 in. × 4 in.
SA = 108 in.²
e desea estimar el gasto promedio mensual en dolares de una familia de cierta ciudad del pais gasta en embutidos.
a) Determine cuantas familias se debe tomar como muestra con una confianza del 95% y un error de 2 dolares . Un especialista a estimado una desviacion estandar de 9 dolares.
b) Haga el calculo para una nueva urbanizacion con 850 familias con un 99% de confianza y un error de 1.5 dolares considerando la desviacion estandar con un valor de 9 dolares.
Answer:
a) Utilizando la fórmula para el tamaño de muestra, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).
Sustituyendo los valores, obtenemos:
n = (1.96 * 9 / 2)^2 ≈ 77
Por lo tanto, se debe tomar una muestra de al menos 77 familias.
b) De manera similar, tenemos:
n = (Z * σ / E)^2
donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).
Sustituyendo los valores, obtenemos:
n = (2.58 * 9 / 1.5)^2 ≈ 261
Por lo tanto, se debe tomar una muestra de al menos 261 familias.
Step-by-step explanation:
The length of a picture frame is 7 inches more than the width. For what values of x is the perimeter of the picture frame greater than 150 inches?
Help me please please please
Answer:
C you are so welcome I hope it helped you
Which of the following scatterplots shows a correlation affected by an influential point?
Answer:
The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.
Step-by-step explanation:
Please give the brainliest, really appreciated. Thank you
The chief physician at a hospital wants to analyze the amount of time it takes two doctors to complete a particular surgical procedure. A sample of 35 of these procedures performed by Dr. McCoy were completed in a mean time of 60.3 minutes with a standard deviation of 4.3 minutes. A sample of 41 these procedures performed by Dr. Turk were completed in a mean time of 61.2 minutes with a standard deviation of 4.7 minutes. A claim is made that the mean time for Dr. McCoy (
ц1) is less than the mean time for Dr. Turk ц2
).
For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.
(a) Calculate the value of the test statistic used in this test.
Test statistic's value =
(b) Use your calculator to find the P-value of this test.
P-value =
Submit QuestionQuestion 9
The value of the test statistic used in this test is t = -2.168 and the P-value of this test is P-value is 0.034
To test whether the mean time for Dr. McCoy is different from the mean time for Dr. Turk, we can use a two-sample t-test with unequal variances. The test statistic for this test is given by:
t = (X₁ - X₂) / √(s₁²/n₁ + s₂²/n₂)
where X₁ and X₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.
Plugging in the given values, we get:
t = (78 - 78.7) / √(2.3²/38 + 4.1²/33)
= -2.168
Therefore, the value of the test statistic used in this test is t = -2.168.
b) To find the P-value of this test, we need to use a t-distribution with degrees of freedom given by:
df = (s₁²/n₁+ s₂²/n₂)² / [ (s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1) ]
Plugging in the given values, we get:
df = (2.3²/38 + 4.1²/33)² / [ (2.3²/38)²/37 + (4.1²/33)²/32 ] ≈ 65.385
Using a t-distribution table or a calculator with t-distribution function, we find that the P-value for a two-tailed test with t = -2.168 and df = 65.385 is approximately 0.034.
Therefore, the P-value of this test is P-value = 0.034
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Which type of relationship is indicated by the residual plot? Non-linear relationship. Linear relationship Exponential relationship
The type of relationship that is indicated by the residual plot is given as follows:
Non-linear relationship.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.
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The annual profits for a company are given in the following table, where x represents the number of years since 2012, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected profit (in thousands of dollars) for 2022, rounded to the nearest thousand dollars.
The linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
How to calculate the valueReplacing the means, the intercept a is given by:
108.8 = 22.6(2.5) + a.
a = 108.8 - 22.6(2.5)
a = 52.33
Therefore, the linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
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Answer:
Step-by-step explanation:
a principal data about the distance, in miles that his teachers and bus drivers live from the school, the box plots below show these data. based on the box plots, which statement is true?
Option C is the true statement from the data that has been gathered and shown in the image
How to get the true statementThe interquartile range exemplifies the "dispersion" or width of a set [1] by determining the difference between the top quartile (the 25% highest) and lower quartile (the 25% lowest). In reference to the provided picture:
- The bus drivers' interquartile range is 10, represented by subtracting their distance's lowest point (10) from the highest (20).
20 - 10 = 20
- Similarly, the teachers' interquartile range is 15, which stems from finding the difference between their lowest distance (15) and highest distance (30).
30 - 15 = 15
Therefore, comparing both ranges reflects that the bus drivers have an interquartile range of distances that is 5 miles smaller than the one for the teachers. Consequently, we opt for option C.
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A line has a slope of 3 and y-intercept of -4. Write its equation in slope- intercept form.
Answer:
y=mx + b
Step-by-step explanation:
y=3x-4
3 is the slope and -4 is the y intercept
Draw a net to represent the following 3d shape.
Don't forget your lebel where the 6cm and 4cm are on the net.
Answer: Discover how a 3D solid shape can be made up from a 2D net. Understand how nets are formed with examples of common 3D polygons and prisms.
Step-by-step explanation:
Alma makes `5` cups of her favorite shade of purple paint by mixing `3` cups of blue paint, `1 & 1/2 cups of red paint, and 1/2 a cup of white paint.
Alma has `2` cups of white paint.
How much blue paint and red paint will Alma need to use with the `2` cups of white paint?
Alma need to use 6 cups of blue paint and 4 cups of red paint with the 2 cups of white paint.
Here, Alma makes 5 cups of her favorite shade of purple paint by mixing
3 cups of blue paint,
1 1/2 cups of red paint,
and 1/2 a cup of white paint.
Alma has 2 cups of white paint.
The ratio of blue to the white paint is:
3 : (1/2)
so, for 2 cups of white paint,
3 : (1/2) = x : 2
x = 6 cups of blue paint
The ratio of red to the white paint is,
3: (1 1/2)
3 : (3/2)
So, for 2 cups of white paint,
3 : (3/2) = y : 2
y = 4 cups of red paint
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Two forces act at a point in the plane. the angles between the two forces are given. fidn the magnitude of the resultant force
The resultant between the two vectors is 21.17 lb
What is parallelogram law of vectors?Parallelogram law of vectors says that if two vectors acts on a point, the resultant of this vectors can be represented by the diagonal from the point of intersection.
R² = x²+y2+2xycos (tetha)
where x and y are the vectors
When x = 20.6 and y = 17.4
R² = 20.6²+17.4²+2(20.6)(17.4)cos 112.9
R² = 727.12+716.88cos 112.9
R² = 727.12 -278.95
R² = 448.17
R = √448.17
R = 21.17 lb
Therefore the resultant is 21.17lb
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Help please 3rd times a charm
The amount that you would save in annual fuel expenses would be $9, 333. 32
The amount that you would have saved over the five years would be $52, 854.63
How to find the fuel savings ?The amount saved in fuel when using the hybrid is:
= Fuel usage by SUV - Fuel usage by Hybrid
= ( 30, 000 / 9 x 4 ) - ( 30, 000 / 30 x 4 )
= $9, 333.32
If you saved this amount as an annuity, it would come out to:
= ( 9, 333.32 / 12 ) x [ ( 1 + 0. 004333 ) ^ ( 12 x 5 ) - 1 ] / 0. 004333
= 777. 78 x 0. 2957 / 0. 004333
= $ 52, 854.63
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