With compound interest of 3.8% compounded annually it will take 7 years for the value of the account to reach $6,880.
What is Compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
Formula to find compound interest:
A=P(1+r/n)^nt
Where,
A = amount
P = principal
r = rate of interest
n = number of times interest is compounded per year
t = time (in years)
Alternatively, we can write the formula as given below:
CI = A – P
Where CI=Compound Interest
Now,
As given
A=$6880
P=$5300
r=3.8%
n=1
t=?
Therefore,
The time it would take to become $6880 will be
6880=5300(1+3.8/100)^t
From here t=7 years
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an engine with a 12- gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour. the tank was full when the engine began running, and there are now 9.3 gallons left in the tank. create and solve an equation to find the number of hours x the engine has been running.
If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3" .
the total capacity of the tank is = 12 gallon ;
the constant use rate of engine is = 0.6 gallons per hour ;
the amount of fuel left in the tank is = 9.3 gallons ;
let the number of hours the engine is running is = x hours ;
the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 9.3 = 0.6x ;
⇒ 0.6x = 2.7 ;
⇒ x = 2.7/0.6 ;
⇒ x = 4.5 hours
Therefore , the engine has been running for 4.5 hours .
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If EF=8, FD=10, ED=11, IG=24, and HG=26.4, find the perimeter of GHI. Round your answer to the nearest tenth if necessary. Figures are not easily drawn to scale.
The perimeter of the given figure is 79.4 units.
What is perimeter:The perimeter of a polygon is defined as the length of the boundary around the sides of the polygon. The perimeter of a polygon can be calculated by calculating the sum of the lengths of the sides of the polygon.
Perimeter of polygon = Sum of sidesHere we have
EF = 8, FD = 10, ED = 11, IG = 24, and HG = 26.4
As we know,
Perimeter = Sum of all sides
The perimeter of GHI = (EF + FD + ED + IG + HG)
= 8 + 10 + 11 + 24 + 26.4
= 79.4 units
Therefore,
The perimeter of the given figure is 79.4 units.
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Write a formula in the form
f (t) = A cos Bt+ k that models the surface temperature of the
lake.
Answer:
The formula is going to be 17 hrs
The average tuition for a full-time under-
graduate student in a public college in 2002 was $4,790. In
2012 it was $8,240. Using the linear function model, estimate
the cost of tuition in 2018.
The estimated cost of tuition in 2018 using this linear function model is $726,430
What is the linear function?
A linear function is a mathematical function that describes a straight line. The general form of a linear function is:
y = f(x) = mx + b
To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.
Substituting the values, we get:
m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345
Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:
y = mx + b
4,790 = 345 * 2002 + b
b = 4,790 - 345 * 2002 = -1,015,290
So, the equation of the line is y = 345x - 1,015,290
To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:
y = 345(2018) - 1,015,290 = 726,430
Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430
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If point R has coordinates (x,y) and point S has coordinates (x + 1, y + 1), what is the distance between R and S?
The distance between the two points R and S is √2.
The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.
The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:
d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.
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Determine whether the underlined value is a parameter or a statistic_ The average score for a class of 28 students taking a calculus midterm exam was 72% Is the value a parameter or a statistic? A. The value is a statistic because the class of 28 students is a sample. b. The value is a parameter because the class of 28 students is a sample c. The value is a parameter because the class of 28 students is a population. d. The value is a statistic because the class of 28 students is a population.
The value is a parameter because the class of 28 students is a population.
A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.
The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.
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Solve using substitution.
y = -10
2x + y = −18
Answer:
try your best
Step-by-step explanation:
u can do it!!
fire station is to be located along a road of length a, where a is a fixed positive real number. if fires will occur at points uniformly chosen on (0,a), where should the station be located so as to minimize the expected distance from the fire?
The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.
The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.
The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.
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Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Answer:
18 miles
Step-by-step explanation:
m = # of miles
$4.60 + ($0.50/mi)m = $13.60
($0.50/mi)m = $13.60 - $4.60 = $9.00
m = ($9.00) / ($0.50/mi) = 18 miles
how to find a vector perpendicular to another vector
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):
AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.
The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).
A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.
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Can anyone help me with this problem
Answer:
-7
Step-by-step explanation:
angles in a triangle add up to 180⁰
90⁰+30⁰+(x+67)=180⁰
187+x=180⁰
x=180⁰-187⁰
x=-7
Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.
7cos(9x)−1=1
Answer:
To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:
7cos(9x) = 2
To find the solutions of the equation, we can divide both sides by 7:
cos(9x) = 2/7
Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.
x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....
we can also express the solution in degrees by multiplying the radian measure with 180/Pi.
x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....
or
x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....
where k is an integer.
So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.
I need help solving
Answer: 189 degrees
Step-by-step explanation:
Since 17x + 2 = 16x + 9, we can solve for x:
17x + 2 = 16x + 9
Subtract 16x from both sides:
x + 2 = 9
Subtract 2 from both sides:
x = 11
The angle indicated in bold is 17x + 2, so we just substitute 11 into x and get 17 * 11 + 2, = 187 + 2 = 189 degrees :>
Copy the problem and write a statement/reason proof
Answer:
..........................
i need an answer for this please
Answer:
-1
Step-by-step explanation:
top: -20/(-4) = 5
bottom: -49+44 = -5
5/(-5) =-1
Please help me with this geometry question
Please help me i have a horrible grade in this class
If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
It is given that triangle ABC is similar to triangle DEF.
It can be seen in the image that ΔDEF is a dilated version of ΔABC.
In ΔABC the measurement of side AB = 23 units
In ΔABC the measurement of side BC = 11 units
In ΔDEF the measurement of side EF = 52 units
In ΔDEF the measurement of side DE = x units
Apply the formula for indirect measurement to find the measurement of side DE.
AB/DE = BC/EF
Substitute the values in the equation -
23/x = 11/52
23 × 52 = 11x
x = (23 × 52)/11
x = 1196/11
x = 108.72
Therefore, the measurement of DE is 108.72 units.
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is y=2.2x proportional
Answer:
yes
Step-by-step explanation:
A proportional relation has an equation of the form
y = kx,
where k is a real number.
y = 2.2x is an equation of the form y = kx with k = 2.2, so y = 2.2x is proportional.
Answer: yes
Graph the solution to this inequality on the number line.
−4x≥12
Answer:
Solution set for x is x ≤ -3
First option
Step-by-step explanation:
We have the equation
- 4x ≥ 12
Divide both sides by 4:
- x ≥ 12/4
-x ≥ 3
Multiply by -1 to make x positive. When we multiply an inequality by a negative number the inequality sign changes: ≥ becomes ≤
Therefore we get
x ≤ 3
On the number line this is represented by the first choice
Note that the 3rd and 4th choices are easily eliminate since they represent ≥ -3 and > -3
Choice #2 has an unfilled circle at -3. This represents a < inequality
A filled circle represents a ≤ inequality
Answer
Solution set for x is x ≤ -3
First option
A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B.
(And please hurry.)
What objective function can be used to maximize the profit?
P = _a + _b
Let a = units of A produced
Let b = units of B produced
At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.
Therefore
a ≥ 30
b ≥ 10
a + b ≤ 80
Product A yields a profit of $15 and product B yields a profit of $8.
Therefore the objectve profit function is
P(a,b) = 15a + 8b
Answer:
The objective function is
P(a,b) = 15a + 8b, subject to
a >= 30; b>= 10; a+b <= 80
Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.
The maximum profit occurs when a=70 and b=10.
Answer:
P= 15a + 8b
Step-by-step explanation:
Find the 12th term of the geometric sequence 7, -21, 63, …
The 12th term of the geometric sequence 7, -21, 63 is -1240029, this is determined using the Geometric progression formula.
What is geometric progression?When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.
The geometric progression is given by the formula:
aₙ = arⁿ⁻¹
a = first term = 7
r = common ratio = - 21 / 7 = - 3
n = number of terms = 12
Therefore, substituting the values in the GP:
a₁₂ = 7 × -3¹²⁻¹
a₁₂ = 7 × -3¹¹
a₁₂ = 7 × -177147
a₁₂ = -1240029
Therefore, the 12th term of the geometric progression is -1240029.
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find the length of the diagnol with work shown please
The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]
How can calculate a diagonal's length?If you know the width and height of a rectangle, you can find its diagonal. The diagonal is equal to the sum of the square roots of the width and height.If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w. Given a diagonal (d) and a width (w), its length is given by h = (d2w2). The diagonal is the line that passes across the centre of a square or rectangle and connects one corner to the other. Any square with two diagonals has sides that are both the same length.The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]7[tex]n^{2}[/tex] + 7[tex]n^{2}[/tex] = [tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]To learn more about diagnol refer to:
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Are these triangles similar? If so why?
In the given image the triangle POR and triangle FGH are not equal or similar to each other.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
In ΔPQR, the line segment PQ measures 35 units.
In ΔPQR, the line segment PR measures 49 units.
In ΔPQR, the line segment QR measures 63 units.
In ΔFGH, the line segment FG measures 69 units.
In ΔFGH, the line segment GH measures 38 units.
In ΔFGH, the line segment HF measures 67 units.
These two triangles are not similar to each other.
Both these triangles have different measurements of line segments.
Both these triangles have no data available for their angles.
The only way the two triangles are similar is that they both are scalene triangles as they both have different measuring sides.
Therefore, the two triangles are not similar.
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His former car was able to travel 20. 28 miles per gallon. Is Xavier getting better gas
mileage in his new car? Explain.
Xavier is not getting better mileage with his new car.
it is given that
distance traveled by Xavier's new car in 20.28 gallons = 472miles
the mileage can be calculated using the formula = (distance traveled)/( gallons of fuel used).
So, the mileage of the new car = 472/20 = 23.06 miles per gallon, and the mileage of Xavier's former car = 20.28 miles per gallon.
From the above data, we can see that the mileage of the former car is greater than the new car.
Therefore, Xavier is not getting better mileage with his new car.
The given question is incomplete, the complete question is
Xavier's new car uses 25 gallons for 472 miles, His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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A rectangle has a height of x+4x+4 and a width of x^2+3x+2
The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
Explain the term area of the rectangle?Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth. In other words, a rectangle's area is equal to the sum of its width and length.So, from the definition of the area of the rectangle.
Area = length x width
Given:
length/height = x+4x+4 = 5x + 4width = x^2+3x+2Thus,
Area = (5x + 4)(x^2+3x+2)
Simplifying,
Area = 5x(x^2+3x+2) + 4(x^2+3x+2)
Area = 5x³ + 19x² + 22x + 18
Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.
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The complete question is-
A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.
Answer? Please help.
Answer:
answer is no
Step-by-step explanation:
Peter expected to earn $425 in a week. In fact he earned $500. What was the percent of error?
The percent of error is 17.65% .
The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.
So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.
In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.
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HURRY 60 POINTS Question Consider the two-way table. Group 1 Group 2 Category A 36 20 Category B 12 35 Complete the table below to show the relative frequencies of the data in the first column. Enter numbers in the boxes as decimals to the hundredth place. Group 1 Category A Category B
Answer:
Category A 0.75
Category B 0.25
Hope it helps !!
The hertz (Hz) is a unit of frequency that represents the number of complete cycles per second. It is used to measure repeating events, both scientific and general. For instance, a clock ticks at 1 Hz. One scientific application is the electromagnetic spectrum, or the range of all possible frequencies of electromagnetic waves. The spectrum includes frequencies from everyday contexts, such as radio and TV signals, microwaves, light (infrared, visible, and ultraviolet), and X-raysThe hertz (Hz) is a unit of frequency that represents.
For each question, use powers to write a mathematical expression. Then evaluate each expression.
Express your answer as a power.
a. How many hertz are in 1 gigahertz? 1 terahertz?
b. A television channel has a frequency of 60 megahertz. What is the channel’s frequency in hertz?
c. The frequency of a microwave is 30 gigahertz. What is the microwave’s frequency in hertz?
d. The frequency of a visible ray of light is 1000 terahertz. A radio station has a frequency of
100 megahertz. How many times greater is the frequency of the light than the frequency of the
radio station?
a. There are 10⁹ hertz in 1 giga hertz and 10^12 hertz in one terahertz
b. The channels frequency in hertz 6×10⁷hertz
c. The frequency of a microwave in hertz is 3× 10^10 hertz
d. The frequency of light is 10⁵ times greater than the frequency of the radio station
What is frequency?Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is is 1/2 second, the frequency is 2 per second. If it takes 1/100 of an hour, the frequency is 100 per hour.
The S.I unit of frequency is hertz and it has other bigger unit stated as follows:
1 kilohertz = 10³hertz
1megahertz = 10⁶ hertz
1 gigahertz = 10⁹ hertz
1 tera hertz = 10^12 hertz
Therefore 60mega hertz = 60× 10⁶ = 6×10⁷
30 gigahertz = 30 × 10⁹ = 3 × 10^10
if the frequency of light is 1000 tera hertz and 100 mega hertz is the frequency of a radio station , then the frequency of light will be 1000×10^12 ÷ 100× 10⁶ = 10⁵ greater than the frequency of the radio station.
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A sphere has a radius of 2 mm. What is the difference between the volume of the sphere and an approximation using a left sum with 16 intervals? Round to the nearest hundredth
The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.
The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we know that the sphere has a radius of 2 mm.
Then the volume of the sphere is calculated by using the formula,
=> V = 4/3πr³
Here we know that the value of r = 2.
Then the volume is calculated as,
=> V = 4/3 x π x 2³
When we simplify this one then we get,
=> V = 10.67π = 33.51
Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is
=> 33.51 - 16
=> 17.51
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