Answers
Answer:
8 months
Step-by-step explanation:
[tex]4000=400(\frac{(1+.045)^{n}-1 }{.045})[/tex]
Do what's in parentheses.
[tex]4000=400(\frac{(1.045^{n}-1) }{.045})[/tex]
Multiply 400 by the numerator.
[tex]4000=(\frac{400(1.045^{n})-400 }{.045})[/tex]
Divide both sides by .045.
[tex]180=400(1.045)^{n}-400[/tex]
Add 400 to both sides.
[tex]580=400(1.045)^{n}[/tex]
Divide both sides by 400.
[tex]\frac{29}{20} =1.045^{n}[/tex]
Convert to logarithmic equation.
[tex]log_{1.045}\frac{29}{20}=n[/tex]
8.441=8 months
Hope this helps!!
Related Questions
Classify the triangle with angles measuring 21°, 69°, and 90°
Answers
Answer:
This triangle is a right scalene triangle.
Step-by-step explanation:
Because this triangle has a 90° angle, it is a right triangle. As all the angles are different, we can see that it is a scalene triangle as well.
31. Find the area of the shape below: 15m 3m (a) 87m² (b) 102m2 (c) 152m² (d) 18m² (e) 207m2 4m 6m 6m 3m
Answers
Hello!
see attachment
A1 = green
A2 = yellow
A3 = red
A1 = 15m * 3m = 45m²
A2 = (15m - (6m + 6m)) * 4m = 3m * 4m = 12m²
A3 = 15m * 3m = 45m²
A = A1 + A2 + A3
= 45m² + 12m² + 45m²
= 102m²Answer:
b. 102 m²
Step-by-step explanation:
In order to find the area of shape.
Let's separate it into three rectangle.
We know that
Area of rectangle: Length*breadth
Using this
Area of left rectangle=15*3=45 m²
Area of middle rectangle=4*(15-6-6)=12 m²
Area of right rectangle= 15*3=45m²
Now
Total Area of shape= 45m²+12m²+45m²=102m²
Please hurry!!
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
100
function f(x)= -5
X represents the remaining time in minutes needed to fill the tank. How is the graph of the
parent function (x)-
-
100
transformed to create the graph of the function (x)=
X
O It is a vertical stretch with a factor of 100 and a translation 5 units right.
O It is a vertical stretch with a factor of 95.
O
It is a vertical stretch with a factor of 100 and a translation 5 units down.
It is a vertical stretch with a factor of 500.
-5?
Answers
The function is transformed and it is a vertical stretch with a factor of 100 and a translation 5 units down
Given data ,
Let the transformed function be represented as f' ( x )
Now , The pace of filling a 100-gallon fish tank is x gallons per minute. The tank has been filling for five minutes already.
The parent function's graph is f (x) = x.
Consequently, the function's graph is provided as
f ( x ) = ( 100/x ) - 5
The graph is now 100 times longer vertically, giving us f (x) = 100/x.
By translating by 5 units down, we obtain f (x) = (100/x) - 5.
Hence , it is a translation of 5 units down and a vertical stretch of 100.
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100 Points! Graph the function. State the domain and range of the function. Photo attached. Thank you!
Answers
Answer:
Domain: [tex]x\geq -2[/tex]
Range: [tex]y\geq 0[/tex]
Step-by-step explanation:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
have a great day and thx for your inquiry :)
Fill in tablet for equation y= 600 -6x
Answers
|---|---|
| 0 | 600 |
| 100 | 0 |
| 200 | -600 |
| 300 | -1200 |
| 400 | -1800 |
| 500 | -2400 |
| 600 | -3000 |
Hope this is helpful sorry if it isn’t
Jenny has six blouses, four different skirts, 20 different pairs of socks, and four pairs of shoes in her closet at the end of the week
Part 1: Explain why the methods used in the previous two problems would be inecient in determining the number of different outts Jenny could wear
Part 2: Using the Fundamental Principle of Counting, determine how many outts Jenny could wear. Don’t forget to show your work.
Answers
Part 1: methods did not consider the number of repetitions or combinations of the same item that could be used in different outfits. Part 2: Jenny can wear 1,920 different outfits by choosing one blouse, one skirt, one pair of socks, and one pair of shoes at a time from her closet.
How to answer the aforementioned questionsPart 1:
Because they only considered a limited number of clothing items and did not take into account the fact that different combinations of these items could create a larger number of outfits, the methods used in the previous two problems would be inefficient in determining the number of different outfits Jenny could wear.
Part 2:
Using the Fundamental Principle of Counting, the number of different outfits Jenny could wear can be determined by multiplying the number of choices for each clothing item together. Therefore, the total number of different outfits can be calculated as:
6 blouses x 4 skirts x 20 pairs of socks x 4 pairs of shoes = 1,920 different outfits
Therefore, Jenny can wear 1,920 different outfits by choosing one blouse, one skirt, one pair of socks, and one pair of shoes at a time from her closet.
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x3+y3+z3=k
that the question that i spend along time on and i haven't found an answer but i found this site and tried to solve a couple questions it gave me everything needed so i well try to see if you guys could help me with this
Answers
The cube root of both sides to solve for x variable is
x = (k - y^3 - z^3)^(1/3)
You can solve for y or z in terms of the other variables by rearranging the original equation.
Given the equation: x^3 + y^3 + z^3 = k.
To solve this equation for one of the variables (x, y, or z), you would need additional information or constraints. However, I can provide you with a general method to express one variable in terms of the others. Let's solve for x:
Step 1: Subtract y^3 and z^3 from both sides of the equation.
x^3 = k - y^3 - z^3
Step 2: Take the cube root of both sides to solve for x.
x = (k - y^3 - z^3)^(1/3)
Now, x is expressed in terms of y, z, and k. If you have any specific values for y, z, and k, you can substitute them into this equation to find the corresponding value of x. Similarly, you can solve for y or z in terms of the other variables by rearranging the original equation.
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Use a compass and straightedge to construct an equilateral triangle in which PQ is
one side. Your final answer should be exactly three blue line segments (including the
one already drawn).
Select a tool (compass, segment, ray, line, undo
Answers
Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.
How to explain the triangleThe three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:
1. Draw a line segment PQ.
2. Place the compass at point P and draw a circle with radius PQ.
3. Without changing the radius of the compass, place the compass at point Q and draw another circle.
4. The intersection of the two circles is point R.
Draw line segments PR and QR to form an equilateral triangle.
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Answer:
Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.
How to explain the triangle
The three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:
1. Draw a line segment PQ.
2. Place the compass at point P and draw a circle with radius PQ.
3. Without changing the radius of the compass, place the compass at point Q and draw another circle.
4. The intersection of the two circles is point R.
Draw line segments PR and QR to form an equilateral triangle.
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What’s the answer to n+19=9
Answers
Answer: n= -10
Step-by-step explanation:
n + 19 = 9, so you want to get the variable by itself so you will get rid of the 19, cancelling it by subtracting. So n=9-19 leaving you with -10.
Find and interpret the mean absolute deviation of the data.
1.1,7.5,4.9,0.4,2.2,3.3,5.1
The mean absolute deviation is what
The values differ from the mean by an average of what
Answers
Answer:
step 1: add all you number
Step-by-step explanation:
step 2:divide your answer by the 7.,you have gotten your answer
An economy's consumer price index (CPI) is described by the function f(t)=-0.1t^3+3t^2+500 where t=0 corresponds to the year 1995. Find the point of inflection of the function.
Answers
Explanation: the point of inflection refers to when a function switches concavity (i.e. up or down). If the second derivative of f is positive, the graph is concave up, and if it is negative, the graph is concave down. This means that the graph switches concavity when the second derivative equals zero.
To find the second derivative (f’’(t)), we shall first find f’(t), or the first derivative. Because each term is separated by addition/subtraction, we can take the derivative of each term separately. Using the power rule, ((d/dx)(-0.1t^3)) = -0.1(3)(t)^(3-1)= -0.3t^2. For d/dx of 3t^2, use the power rule again: 3(2)t^(2-1) = 6t. The derivative of 500 is 0 because it is a constant. f’(t) = -0.3t^2 + 6t.
Now we shall do this process again to find the second derivative. For the first term, d/dx of -0.3t^2 = -0.3(2)t^(2-1) = -0.6t. For 6t, d/dx equals 6(1)t^(1-1) = 6. f”(t) = -0.6t + 6
Now that we have the second derivative, we set it equal to zero and solve for t. 0 = -0.6t + 6, -6 = -0.6t, t = 10. Because t = 10 years, the point of inflection occurs in 1995 + 10 = 2005.
Question 4: The length of the diagonal of a square is 6 cm. Find the sides of the square.
Answers
Answer:
The length of each side of the square is approximately 4.24 cm.
Explanation:
We can use the Pythagorean theorem to find the length of each side of the square. Let "s" be the length of each side of the square. The diagonal of the square, which is 6 cm, is the hypotenuse of a right triangle whose legs are two sides of the square. So we have:
[tex]s^2 + s^2 = 6^2[/tex]
Simplifying this equation, we get:
[tex]2s^2 = 36[/tex]
Dividing both sides by 2, we get:
[tex]s^2 = 18[/tex]
Taking the square root of both sides, we get:
s ≈ 4.24
Therefore, the length of each side of the square is approximately 4.24 cm.
Select ALL the correct answers. Which of the following statements are true about the equation below? The graph of the quadratic equation has a maximum value. The extreme value is at the point (7,-3). The graph of the quadratic equation has a minimum value. The solutions are . The extreme value is at the point (3,-7). The solutions are .
Answers
The correct statements regarding the quadratic function x² - 6x + 2 are given as follows:
The graph of the quadratic equation has a minimum value.The solutions are: x = 0.35 and x = 5.64.The extreme value is at the point (3,-7).How to analyze the quadratic function?The quadratic function in the context of this problem is given as follows:
y = x² - 6x + 2.
The coefficients are given as follows:
a = 1, b = -6, c = 2.
As a > 0, the function is a concave up quadratic function, hence it has a minimum value.
Using a calculator with the given coefficients, we have that:
The solutions are: x = 0.35 and x = 5.64.The vertex is: (3, -7).Missing InformationThe function is:
y = x² - 6x + 2.
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Convert the rectangular coordinates to polar coordinates
(1, -9)
Answers
The polar coordinates of (1, -9) are (9.06, -1.47 radians).
To convert from rectangular coordinates to polar coordinates, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:
r = √(1² + (-9)²) = √82 ≈ 9.06
θ = tan⁻¹((-9)/1) ≈ -1.47 radians
Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).
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Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° clockwise.
U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(−4, 0), W′(1, 4)
U′(1, 1), V′(−4, 0), W′(−1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)
Answers
The coordinates of the vertices for the image of the triangle U′V′W′ is
U′(1, 1), V′(−4, 0), W′(−1, 4)
How to find the coordinates after transformationTo rotate a point 90 ° clockwise about the origin, we can apply the transformation (x, y) → (y, -x)
So applying this transformation to each vertex of triangle UVW we get
U(−1, 1) → U' = (1, 1)
V(0, −4) → V' = ( -4, 0)
W(−4, −1) → W' = (-1, 4)
Therefore the coordinates of the vertices for the image triangle U'V'W' are U′(1, 1), V′(−4, 0), W′(−1, 4)
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The spinner will be spun two times.
What is the probability that both spins result in the same color?
Answers
Answer: 11/32
Step-by-step explanation:
The formula for finding this is:
(yellow and yellow) or (pink and pink) or (blue and blue)
First find the probability that both spins will be yellow:
2/8 * 2/8 = 1/16
There are 2 yellow spots out of the 8 total spots.
Because you need to spin yellow and yellow, you multiply the two fractions.
This logic applies to pink and blue.
Next pink:
3/8 * 3/8 = 9/64
Blue:
3/8 * 3/8 = 9/64
Find the probability that you will spin yellow or pink or blue:
1/16 + 9/64 + 9/64 = 11/32
Whenever finding the probability of something or something else, add them.
Assume regular unleaded fuel costs $3.81 per gallon. A Volkswagen Jetta uses unleaded fuel. It gets about 30 miles per gallon.
Imagine that a driver of the Jetta drives 15,000 miles each year. How much money will the driver of the Jetta spend on gas in one year?
Answers
The amount that Jetta spends on gas in one year is $1,905.
Assume regular unleaded fuel costs $3.81 per gallon. A Volkswagen Jetta uses unleaded fuel. It gets about 30 miles per gallon.
The rate is the ratio of the amount of something to the unit.
Imagine that a driver of the Jetta drives 15,000 miles each year.
The amount that Jetta spends on gas in one year is calculated as,
⇒ 15,000 x $3.81 / 30
⇒ $1,905
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Find the areas of the sectors formed by \angle ACB .
A circle is shown. The measure of central angle A C B is 131 degrees. The radius is 3 centimeters. Point D is on the circle but not on arc A B.
Give the exact answers in terms of \pi . Do not approximate the answers.
Area of small sector =
cm2
Area of large sector =
cm2
Answers
To find the area of the large sector, we need to subtract the area of triangle ADB from the area of the circle sector ACB. We can use the Law of Cosines to find the length of segment AD:
AD^2 = AB^2 + BD^2 - 2 * AB * BD * cos(ACB)
AD^2 = 3^2 + 2^2 - 2 * 3 * 2 * cos(131)
AD^2 = 13 - 12cos(131)
AD = sqrt(13 - 12cos(131))
The area of triangle ADB is (1/2) * AB * AD * sin(DAB) = (1/2) * 3 * sqrt(13 - 12cos(131)) * sin(49) = 1.786 cm^2 (rounded to 3 decimal places).
The area of the large sector is pi * 3^2 - 1.786 = 23.556 cm^2 (rounded to 3 decimal places).
Therefore, the area of the small sector is 3.422 cm^2 and the area of the large sector is 23.556 cm^2.
I need the answer and work for these please
Answers
Answer:
Step-by-step explanation:
Hello!
Start With Plugging the numbers in (5) Now use your units to divide and multiply to get your answer
Translate this expression: -3 decreased by the product of 5.1 and a number
Answers
The equivalent value of the expression is A = -3 - ( 5.1 x n ) , where n is the number
Given data ,
Let the expression be represented as A
Now , the value of A is
A = -3 decreased by the product of 5.1 and a number
On simplifying , we get
Let the number be represented as n
A = -3 - ( 5.1 x n )
On further simplification , we get
A = -3 - ( 5.1n )
Hence , the equation is A = -3 - ( 5.1n )
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Which choice is an irrational number?
A 4π/π
B 2 6
C 18
D 21.989
Answers
Answer: The correct option is B) 2√6
explanation:
a number is called irrational if it cannot be written in the form ,p/q where p and q are integers and q ≠0. a number is called rational if it can be written in the form ,p/q where p and q are integers and q ≠0.A) 4π/π = 4 (This simplifies to 4, which is a rational number since it can be expressed as a fraction 4/1.)
B) 2√6 = irrational number (The square root of 6 cannot be simplified to a fraction or whole number, so it is an irrational number.)
C) 18 = rational number (This is a whole number and can be expressed as a fraction 18/1.)
D) 21.989 = rational number (This is a decimal number, but it can be expressed as a fraction, such as 21989/1000.)
Answer:
correct answer BStep-by-step explanation:
because 2 surd 6 will continue to give you an infinite number which is an irrational number
Find the circumference of a circle with diameter, d = 4.13m. Give your answer rounded to 2 DP
Answers
A circle with a diameter of 4.13 meters will have a circumference of 12.97 meters.
Given that:
Diameter, d = 4.13 meters
The circumference is a term used in geometry to describe the boundary or the outer edge of a closed curve, particularly a circle. It refers to the distance around the circle, measured along its outer edge. In simpler terms, the circumference is the total length of the circle.
Let d represent the circle's diameter. The circle's perimeter will be provided as,
C = πd
The formula for calculating a circle's circumference is
C = 3.14 x 4.13
C = 12.9682
C ≈ 12.97 m
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Okay so this is for my portfolio. I have two figures; a rectangular prism (think cereal box) and a cylinder. Is it possible for the cylinder to have a larger VOLUME than the prism, but a smaller measurement of cubic inches?? (Please say yes )
Answers
Step-by-step explanation:
No, it is not possible. Cubic inches are a measurement of volume. If the cylinder has a larger volume, then it also has more cubic inches.
Answer:
no TWT
Step-by-step explanation:
Because these solids have the same height and the same cross-sectional areas at every level, the solids have the same volume due to Cavalieri's principle. The volume of the prism is: V = A B a s e ⋅ h = π r 2 h Therefore, the volume of the cylinder is: V = π r 2 h This should make sense because a cylinder is essentially a circular prism. Also Its cool that we both go to Connexus, i saw it from an old post of yours <3
1) Given a sample of lifetime of the light bulbs X1, X2, X3,. X36) with LX =1800 hours, ›X2-90560 and level of confidence c = 95%. Find the Point Estimate X =
Answers
Step-by-step explanation:
if the length of a Square Garden is 49 feet than what it is area
Which statement about the following equations is correct?
y = 2x + 5
y
O The equations are independent because the lines intersect in one point.
The equations are dependent because the lines are the same line.
O The equations are independent because the equations represent parallel lines.
O The equations are dependent because the lines do not intersect.
= -2x+5
Answers
Answer:
Step-by-step explanation:
The correct statement about the given equations is: "The equations are dependent because the lines are the same line."
In the equation y = 2x + 5, the slope is 2, which means the line has a positive slope and is upward sloping.
The y-intercept is 5, indicating that the line intersects the y-axis at the point (0, 5).
The equation y = -2x + 5 is equivalent to y = 2(-x) + 5, which has the same form as the first equation but with a negative slope.
However, the equations are still dependent because when you simplify the second equation, you obtain the first equation.
These two equations represent the same line with a different slope. Therefore, they are dependent, and any point that satisfies one equation will satisfy the other equation as well.
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Evaluate f(x)=x/3 -15 when x =27
Answers
Answer:f(27)=-6
Step-by-step explanation:
Find two functions defined
implicity by this equation:
Can someone please provide me with both functions? Thank you!
Answers
y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation
The given equation is an equation of an ellipse centered at the origin with a major axis of length 2√7 and a minor axis of length 2√3.
To find two functions defined implicitly by this equation, we can solve for y in terms of x using algebra.
First, we can isolate y²/3 by subtracting x²/7 from both sides:
y²/3 = 1 - x²/7
Multiply by 3 on both sides to eliminate the fraction:
y² = 3 - 3x²/7
y = ±√(3 - 3x²/7)
These are the two functions defined implicitly by the given equation.
The positive square root gives the upper half of the ellipse, while the negative square root gives the lower half.
Hence, y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation
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A $525,000 adjustable-rate mortgage is expected to have the following payments:
Year Interest Rate Monthly Payment
1–5 4% $2,506.43
6–15 6% $3,059.46
16–25 8% $3,464.78
26–30 10% $3,630.65
A fixed-rate mortgage in the same amount is offered with an interest rate of 4.85%.
What is the difference in the total cost between the two mortgages, rounded to the nearest dollar?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$159,134
$153,796
$901,409
$668,123
Answers
The difference in total cost between the two mortgages is $168,852. The Option A is closest.
What is the difference in the total cost?To get total cost of the adjustable-rate mortgage, we have to find total payments for each period and add them up.
Using the monthly payments, we get:
Total payments for years 1-5:
= $2,506.43 x 12 x 5
= $150,385.80
Total payments for years 6-15:
= $3,059.46 x 12 x 10
= $367,135.20
Total payments for years 16-25:
= $3,464.78 x 12 x 10
= $415,773.60
Total payments for years 26-30:
= $3,630.65 x 12 x 5
= $217,839.00
Total cost of adjustable-rate mortgage: $1,151,133.60
The total cost of the fixed-rate mortgage is computed as follows. The Total payments for 30 years is:
= Monthly payment x Number of payments
= $2,728.56 x 12 x 30
= $982,281.60
The difference in total cost is:
= $1,151,133.60 - $982,281.60
= $168,852.00.
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4. Gilbert generated the shape below on a computer. The shape contains an isosceles triangle with a
height of 8 centimeters. Determine the area of the shape to the nearest tenth of a square centimeter.
10 cm
8 cm
12 cm
10 cm
Answers
the area of the shape to the nearest tenth of a square centimeter is 12cm². Opti C
How to determine the value
The formula for calculating the area of a an isosceles triangle is expressed as;
A = 1/2bh
Such that the parameters are expressed as;
A is the area of the triangleb is the base of the triangleh is the height of the triangleFrom the information given, we have that;
base = 3 centimeters
Height = 8 centimeters
Substitute the values, we have;
Area = 1/2 ×8 × 3
Multiply the values, we have;
Area = 24/3
Divide the values
Area = 12 cm²
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solve the equation by completing the square. show your reasoning. 4x^2-28x=-33
Answers
Hello
4x² - 28x = -33
4x² - 28x + 33 = 0
(4x² - 6x) + (-22x + 33) = 0
2x(2x - 3) - 11(2x - 3) = 0
(2x - 11)(2x - 3) = 0
2x - 11 = 0 2x - 3 = 0
2x = 11 2x = 3
x = 11/2 x = 3/2
