Answer: $91017.17865 / 12 = $7585.5987
Step-by-step explanation:
To solve this problem, we need to first determine the total interest that will be earned on the account over the 5-year period. We can do this by using the formula for compound interest, which is:
A = P (1 + r/n) ^ nt
where A is the total amount of money in the account after the interest has been compounded, P is the initial deposit, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is deposited.
In this case, the initial deposit is $10,000, the interest rate is 2.05%, the number of times the interest is compounded per year is 12 (because the interest is compounded monthly), and the number of years the money is deposited is 5. Plugging these values into the formula, we get:
A = 10000 (1 + 0.0205 / 12) ^ (12 * 5)
A = 10000 (1.001708333) ^ 60
A = 10000 (1.101717865)
A = 101017.17865
Therefore, the total amount of money in the account after 5 years will be $101017.17865.
Since Monica wants to save up $10,000, we can subtract this amount from the total amount in the account to find out how much she needs to deposit each month in order to reach her goal:
101017.17865 - 10000 = 91017.17865
Therefore, Monica needs to deposit $91017.17865 each month in order to save up $10,000 in 5 years. This means that she will need to deposit $91017.17865 / 12 = $7585.5987 per month in order to reach her goal.
Select all of the following that are quadratic equations. x2 + 3 x -5 = 0 x2 - x = 3 x + 7 5 x - 7 = 0 7 x2 + 14 x = 0 x3 - 3 x2 + 1 = 0 x - 5 = 9 x + 7
Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0 are quadratic equation.
What exactly is a math equation?Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.
Here,
Given:
[tex]x^{2}[/tex] + 3 x -5 = 0
[tex]x^{2}[/tex] - x =0
3 x + 7 .5 x - 7 = 0
7 [tex]x^{2}[/tex] + 14 x = 0
[tex]x^{3}[/tex]- 3 x2 + 1 = 0
x - 5 = 9 x + 7
The [tex]x^{2}[/tex] is present in equation which are quadratic
thus,
[tex]x^{2}[/tex] + 3 x -5 = 0
[tex]x^{2}[/tex] - x =0
7 [tex]x^{2}[/tex] + 14 x = 0
these following above equations are quadratic equation .
Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0 are quadratic equation.
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Two positive numbers have a sum of 8 and a product of 13. Algebraically determine the value of the larger of the two numbers to the nearest hundredth
The value of the larger of the two numbers is 5.73.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Two numbers = M and N
M + N = 8 _____(1)
M = 8 - N _____(2)
MN = 13 _____(3)
Putting (2) in (3) we get,
(8 - N)N = 13
8N - N² = 13
N² - 8N + 13 = 0
This is in the form of ax² + bx + c = 0
a = 1, b = -8 and c = 13
Using the determinant we have,
N = -b ± √(b² - 4ac) / 2a
N = 8 ± √(64 - 52) / 2
N = 8 ± √12 / 2
N = 8 ± 2√3 / 2
N = 4 ± √3
N = 4 + √3 and N = 4 - √3
[√3 = 1.73]
N = 5.73
N = 2.27
Now,
When N = 5.73, M = 8 - 5.73 = 2.27
When N = 2.27, M = 8 - 2.27 = 5.73
Now,
The two numbers are 5.73 and 2.27
Thus,
The larger of the two numbers is 5.73.
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In what ratio is the line joining the points (- 5 1 and 2 3?
The ratio is 7:4 for the line joining the points (- 5 1) and (2 3)
In mathematics, a ratio shows how many times one number is represented by another. TA ratio can have quantities of any kind, such as counts of persons or objects, measurements of lengths, weights, or times, etc. Both numbers must be positive in the vast majority of situations.
We can calculate the ratio by subtracting the x-values and y-values of the given points:
(2 + 5) : (3 - 1)
= 7 : 4
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constructing cones a right triangle whose hypotenuse is 23 m long is revolved about one of its legs to generate a right circular cone. find the radius, height, and volume of the cone of greatest volume that can be made this way.
constructing cones a right triangle whose hypotenuse is 23 m long is revolved about one of its legs to generate a right circular cone. radius: 11.5 m height: 23 m volume: 1650.6 m³
The hypotenuse of the triangle is 23 m. This means that the two sides are 11.5 m and 11.5 m. This gives us the radius of the cone.
The height of the cone is the same as the hypotenuse, so the height is 23 m.
The volume of a right circular cone can be calculated using the following formula: V = (πr²h)/3. In this case, the radius is 11.5 m, the height is 23 m, and π = 3.14. Plugging these values into the formula, we get a volume of 1650.6 m³.
V = (πr²h)/3
V = (3.14 × 11.5² × 23)/3
V = 1650.6 m³
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On Saturday, 3 child tickets were sold for every 2 adult tickets sold. The ratio of child tickets sold to adult tickets sold is?
Answer: 3:2
Step-by-step explanation:
We know that every 3 child tickets were sold for every 2 adults tickets sold
So the ratio is 3:2
A double slit is illuminated simultaneously with light of wavelength 700 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe.
The unknown wavelength of a light with m= 4 bright fring overlaps m = 3 bright orange fringe and used in a double slit is 450 nm.
Double Slit experiment:
In modern physics, the double-slit experiment shows that light and matter can exhibit properties of both classically defined waves and particles.
Furthermore, it demonstrates the fundamental stochastic nature of quantum mechanical phenomena.
Formula ,
λ = x.d/n.L
where , λ = wavelength of light used (nm)
x = distance from central fringe (m)
d = distance between the slits (m)
n = the order of the fringe
L = length from slits to the viewing screen (m)
thus, taking ratios for the two waves: let w = unknown wavelength
600/w = 4/3 (as other factors are same for both)
thus, w = 450 nm
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Complete questions :
A double slit is illuminated simultaneously with light of wavelength 700 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe What is the unknown wavelength? Express your answer to three significant figures and include the appropriate units.
A line passes through the points (0, -6) and (7, 4). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of the line passing through the points (0, -6) and (7, 4) in slope-intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.
What is Slope?Slope of a line is defined as the tangent of the angle that the line makes with X axis.
Slope, usually denoted by 'm' of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,
m = (y₂ - y₁) / (x₂ - x₁)
The equation of a line in slope-intercept form is y = mx + b, where b is y intercept and m is the slope.
Here, we have two points (0, -6) and (7, 4).
m = (4 - -6) / (7 - 0) = 10/7
y intercept is the y coordinate of the point where the line touches with the Y axis. x coordinate will be zero there.
We already have such point (0, -6).
So b = -6
Substituting these in slope-intercept form,
y = [tex]\frac{10}{7}[/tex]x - 6
Hence, the equation of the given line in slope intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.
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HEELPG HLOHEHEO HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer: A
Step-by-step explanation:
adding two circles to the left side would result in square triangle circle circle and if you add a square to the right it would be circle circle triangle square thus balancing it
A line segment with a length of 16 units is reflected across the y-axis, then translated 5 units down on a coordinate plane, resulting in a new segment.
What is the length of this new line segment? ________________ units
The solution is 16 units
The length of the line segment is 16 units
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the length of the line segment be = A
Now , the initial length of the line segment = 16 units
The line is reflected across the y-axis
So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)
And , the resulting line is translated 5 units down
But , the line segment does not change in dimension at all
So , the reflection and a translation does not affect the length of the line segment
Hence , the length of the line segment is 16 units
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1 4/5 × 3 1/2 please help me
Answer:6 3/10
Step-by-step explanation:
use Desmos calculator
The price of a home (in thousands of dollars) is associated with the number of square feet in a home. Home prices in Smavile can be modeled using the equation p = 150 + 0.041a where p is the price of the home in thousands of dollars and a is the area of the house in square feet Home prices in Fancyville can be modeled using the equation p = 250 + 0.198a Ngoc saw a real estate advertisement for a 2800 square foot home that was selling for $280,000. Which city should she predict that the home is in?
Ngoc should predict that the home is located in Smavile based on the real estate advertisement
How to determine the city she should predict that the home is in?From the question, we have the following parameters that can be used in our computation:
Function 1: p = 150 + 0.041a (Smavile)
Function 2: p = 250 + 0.198a (Fancyville )
Where
a = area
p = price
From the question, we have
a = area = 2800
p = price = 280000
Using the above as a guide, we have the following:
So, we have
Function 1: p = 150 + 0.041 * 2800 (Smavile)
Evaluate the expression
p = 264.8 -- false
Function 2: p = 250 + 0.198 * 2800 (Fancyville )
Evaluate the expression
p = 804.4 --- false
264.8 is closer to 280 than 804.4
Hence, the home is in Smavile
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PLEASE HELP ME I WILL GIVE BRAINLIEST!!
Which row of Pascal's Triangle should you use to expand the binomial (a + b)^4?
Answer:
Step-by-step explanation:
a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1
so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6
given a = d and b = -5y
∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +
Help with doing Literal Equations
solve for A
h=2a/b1+b2
Answer:
a = −1 / 2 b^3 + 1 / 2 bh
Step-by-step explanation:
1 )
h = 2a / b^1 + b^2
2 ) Multiply both sides by b.
bh = b^3 + 2a
3 ) Flip the equation.
b^3 + 2a = bh
4 ) Add -b^3 to both sides.
b^3 + 2a + −b^3 = bh + −b^3
2a = −b^3 + bh
5 ) Divide both sides by 2.
2a / 2 = −b^3 + bh / 2
a = −1 / 2 b^3 + 1 / 2 bh
Hope this helps! :)
help please:
solve for x
The value x from given triangle FGH of x is 11.
What is an exterior angle theorem?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
From the given figure, ∠G=2x+8, ∠H=65° and ∠JFG=9x-4.
Here, ∠JFG=∠G+∠H
⇒ 9x-4=2x+8+65
⇒ 9x-2x=73+4
⇒ 7x=77
⇒ x=11
Hence, the value of x is 11.
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(a) what is the coefficient of x3y4 in (-3x 4y)7? (b) what is the coefficient of x2y7 in (5x - y)9?
a) The co-efficient of x⁴y³ = -241920
b) The coefficient of x²y⁷ = 900
What Does an Expression Coefficient Mean?
A coefficient is an integer that is either multiplied by the variable it is associated with or written alongside the variable. A coefficient is, in other words, the numerical factor of a term that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.The expansion is given by the following formula:
(a + b)ⁿ = Σⁿₓ=₀(ⁿₓ) aⁿ⁻ˣ bˣ, where
(ⁿₓ) = n! / (n-x)! k! and n! = 1.2..3.....n.
a) (-3x+4y)⁷ = ⁷C₀ (-3x)⁷(4y)⁰ + ⁷C₁ (-3x)⁶(4y)¹ + ⁷C₂ (-3x)⁵(4y)¹ + ⁷C₃ (-3x)⁴(4y)³ + ⁷C₄ (-3x)³(4y)⁴ + ⁷C₅ (-3x)²(4y)⁵ + ⁷C₆ (-3x)¹(4y)⁶ + ⁷C₇ (-3x)⁰(4y)⁷
The co-efficient of x⁴y³ = 35x - 27x³ * 256y⁴
= -241920x³y⁴
Hence, the coefficient of x⁴y³ = -241920.
b) (5x - y)⁹ = ⁹C₀(5x)⁹(-y)⁰ + ⁹C₁(5x)⁸(-y)¹ + ⁹C₂(5x)⁷(-y)² + ⁹C₃(5x)⁶(-y)³ + ⁹C₄(5x)⁵(-y)⁴ + ⁹C₅(5x)⁴(-y)⁵ + ⁹C₆(5x)³(-y)⁶ + ⁹C₇(5x)²(-y)⁷ + ⁹C₈(5x)(-y)⁸ + ⁹C₉(5x)⁰(-y)⁹
The coefficient of x²y⁷ = 36 * 25x² * y⁷
= 900x²y⁷
Hence, the coefficient of x²y⁷ = 900.
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What is 2.03 x 1011 written in standard notation?
A. 20,300,000,000
B. 203,000,000,000
C. 2,030,000,000,000
D. 20,300,000,000,000
PLEASE HELP ME WITH THIS!!11111111
The perimeter of a rectangle is 96 inches. The length of the rectangle is 12 less than twice the width. Find the dimensions of the rectangle.
The Length is _____ inches
The width is ______ inches
The dimensions of the rectangle are length is 108 inches and width is 60 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
The perimeter of a rectangle is 96 inches.
The length of the rectangle is 12 less than twice the width.
Length L=2W-12
Width=W
Perimeter=2(Length+Width)
=2(2W-12+W)
96=2(W-12)
Divide both sides by 2
48=W-12
Add 12 on both sides
60=W
Now length=2(60)-12
=120-12=108
Hence, the dimensions of the rectangle are length is 108 inches and width is 60 inches.
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4
y A duck's mass at birth was 0.05 kilogram. The duck gained approximately 0.042
kilogram each week. After how many weeks is the duck's mass 0.890 kilogram?
Ο Α. 10
O B. 17
OC. 20
D. 21
Answer: C. 20
Step-by-step explanation:
Ley y be the duck mass, and x be the number of weeks
Our equation will be
y = 0.042x + 0.05
Then we plug 0.89 in the y
0.89 = 0.042x + 0.05
0.84 = 0.042x
x = 20 Weeks
So the answer is C. 20 weeks
what is the best approximation for the area of this circle? use 3.14 to approximate pi.
The best approximation for the area of this circle with a radius of 8in is 201.0 in².
A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The area, a circle occupies in a two-dimensional plane is known as the area of the circle. Therefore, the area that a circle with radius r encloses is πr².
Given the radius r of the circle is 8 in. Then, the area is,
A = 3.14×(8 in)² =200.96 in²=201.0 in²
The answer is 201.0 in² and the correct option is option c.
The complete question is -
What is the best approximation for the area of this circle? Circle with radius labeled 8 in. Use 3.14 to approximate pi. a) 25.1 in² b) 50.2 in² c) 201.0 in² d) 803.8 in²
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Solve the system of equations by the substitution method.
x +9y = 24
2x + 3y = 3
Answer:
x= 24 − 9y
x= 3/2 − 3y/2
Step-by-step explanation:
Which phrase best describes a scatterplot in which the variables has a correlation coefficient of r=0.86
Answer:
A strong positive association
Step-by-step explanation:
A perfect fit for a positive line would be 1. A perfect fit for a negative line would be -1.
The scale goes from 1 tp -1.
.86 is pretty close to 1.
What is 11C9?
O A. 66
OB. 55
OC. 45
OD. 36
How do you dilate a rectangle by 2?
To dilate a rectangle by 2 , multiplied by the scale factor with every coordinates of rectangle
Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.
Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)
We have to dilate by scale factor 2, then every coordinate point of the original triangle will multiplied by the scale factor
Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4, -4)
Therefore, When we dilate a rectangle by scale factor 2 ,
The dilated triangle will be A’B’C’D’ and the coordinate points obtained are A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4, -4)
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What is the median of the data set?
41,14,28,34,93,45,10,16,19,54,67
A. 41
B. 34
C.38
D.45
Answer: 34
Step-by-step explanation:
PLEASE HELP QUICK :)) PLEASE AND TY
Answer:
option 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0-(-2)}{4-0}[/tex] = [tex]\frac{0+2}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = [tex]\frac{1}{2}[/tex] x - 2
the lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1.5 hour. there are four batteries in a package. what lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?
Therefore lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours
What is standard deviation ?In statistics, the standard deviation measures how widely distributed or how much a bunch of values can vary. While a big standard deviation shows that values are scattered throughout a wider range, a low standard deviation suggests that values are frequently close to the set's mean.
Here,
given that the lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour.
Sample size=n =9
Sample mean =X' N is(13,1/3)
If c is the lifetime value, then only 5% of all packages will have a total battery lifetime that is longer than that amount.
Then we have P(X>c) =0.05
Convert into Z score to get
P(x-13/(1/3) > z) = 0.05
z =1.645 from std normal distribution table
Hence x = 13 + 1.645/3
x=13.548
Therefore lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours.
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a chess club meets every week and has 6 members. each member of the club plays one opponent each week. how many weeks will it take for every member to play each of the other members of the club?
It will take 5 weeks for every member to play each of the other members of the club.
What are the arrangements?
A strategy or preparation for something, especially for it to occur in a certain way: Two days a week, she had the plan to work from home. The motel was filled, so we had to find another place to stay.
Here, we have
A chess club meets every week and has 6 members.
Each member of the club plays one opponent each week.
We have to find out how many weeks will it take for every member to play each of the other members of the club.
Total number of matches played = (6×5)/2 = 15
Games per week = 3
Every member is to play each of the other members of the club = 15÷3= 5.
Hence, it will take 5 weeks for every member to play each of the other members of the club.
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What percentage of women in the united states work and have a child under 6 years of age?
In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force
What is Percent ?Percentages are fundamentally fractions with 100 as the denominator. To show that a number is a percentage, the percent symbol (%) is placed next to it. For instance, if you answered 45 out of 100 questions on a test accurately (45/100), you would have gotten a 45% mark.
According to the given information
In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force compared with 75.5 percent of mothers whose youngest child was age 6 to 17.
In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force
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Mekala has an mp3 player called the jumble. The jumble randomly selects a song for the user to listen to. Mekala's jumble has 444 techno songs, 222 country songs, and 333 jazz songs on it. Mekala plans to listen to 270270270 songs. Complete the following statement with the best prediction. Mekala will listen to.
The statement that "close to 60 country songs" but probably not exactly 60 country songs is, best prediction to complete the given statement .
So, the correct option is option (B).
Mekala has MP3 player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.
firstly, we represent this songs in ratio format :
Now, the ratio of techno songs to country songs to jazz songs = 4 : 2 : 3
Let the total number of songs which is unknowns be" x". So,
Total number of techno songs = 4x
Total number of country songs = 2x
Total number of jazz songs = 3x
Total number of songs that Mekala plans to Listen = 270
Then, 4 x + 2 x + 3 x = 270
=> 9 x = 270
Dividing both sides by 9, we get
=> x = 30
So, Number of techno songs = 4 × 30
= 120
Number of country songs = 2×30 = 60
Number of jazz songs = 3 × 30 = 90
but all this is based on prediction only.
Hence, the total country songs are close to 60 but not exactly 60.
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Complete question:
Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 techno songs, 2 country songs, and3 jazz songs on it. Mekala plans to listen to 270 songs.
Complete the following statement with the best prediction.
Mekala will listen to...
Please choose from one of the following options.
a) Exactly 60 country songs
b) Close to 60 country songs but probably not exactly 60country songs
c)Exactly 210 country songs
d)Close to 210 country songs but probably not exactly 210 country songs