Answer:
a) $3125.76
b) $225.76
Step-by-step explanation:
(a) A = P(1 + r/n)^(nt)
In this case, P = $2900, r = 0.0115 (1.15% expressed as a decimal), n = 12 (since the interest is compounded monthly), and t = 2.
A = $2900(1 + 0.0115/12)^(12*2) = $3125.76
(b) Interest = A - P
Interest = $3125.76 - $2900 = $225.76
Help please!! Please!!
Answer: Range = 22 IQR = 13
Step-by-step explanation:
To find the range of a data set, subtract the largest value of the data set from the smallest value. 45 is the largest value and 23 is the smallest, and 45-23 is 22, so the range is 22. To find the IQR, you must subtract the upper quartile and the lower quartile. We can find this after finding the mean by re-arranging all the values in order from lowest to greatest, and finding the middle value. Once we do so, we get 33.5. Then, we find the median of all the numbers below and after the median to get the lower and upper quartiles. Then, we subtract them to get the IQR 13.
a boy walks 1260 m on a bearing of 120° how far south is he from his starting point
[tex]\sf D = 1260 \ m[120 \ o] \ CW \ from +y-axis.[/tex]
[tex]\sf Y = 1260\times Cos \ (120) = -630 = 630 \ m. \ South.[/tex]
Therefore, 630 m far south is he from his starting point.
Simplify.
38 x 33 ÷ 3² = 3[?]
Using order of operations, we can simply solve this problem left to right.
When two numbers having the same base and also having exponents are multiplied, we add the exponents.
3^8 x 3^3 = 3^11
When two numbers having the same base and also having exponents are divided, we subtract the exponents.
3^11 / 3^2 = 3^9
Answer: 3^9
Hope this helps!
Hello
3⁸ x 3³ ÷ 3²
= 3⁸⁺³ ÷ 3²
= 3¹¹ ÷ 3²
= 3¹¹⁻²
= 3⁹
. Francois has 8 feet of trim. He is
making 3 picture frames. Write a
fraction that represents the number of
feet of trim that can be used for each
picture frame. Fill in the bubble before
each number that is correct.
Pls help it’s a grade
Answer:
[tex]\displaystyle \frac{8}{3} \;\text{feet per picture frame}[/tex]
Step-by-step explanation:
We will divide the total amount of trim that Francois has, 8 feet, by the number of picture frames, 3. This will give us a fraction that represents how many feet of trim can be used for each picture frame.
[tex]\displaystyle \frac{\text{8\;\;feet}}{\text{3 picture frames}} =\frac{8}{3} \;\text{feet per picture frame}[/tex]
can you guys help me with this
Answer:
The correct equation is D. 13x - 2y = 40
13(2) - 2(-7) = 26 + 14 = 40
13(4) - 2(6) = 52 - 12 = 40
PLS HELP RN
The rectangle has sides measuring 2 cm and 4 cm, and the arcs of two circles are
drawn in the rectangle as shown. Find the area of the shaded region.
The area of the shaded region is 4 cm².
What is the area of the shaded region?The area of the shaded region is calculated by applying Cavalieri's principle.
Cavalieri's principle states that if two three-dimensional objects have the same cross-sectional area along a height and the same height, then the figures have the same volume.
The area of the shaded figure is calculate as follows;
from the diagram the width of the shaded region = 2 cm
The height of the shaded region = 2 cm
Area = 2 cm x 2 cm = 4 cm²
Thus, the area of the shaded region is determined by considering Cavalieri's principle.
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3. A test has a maximum possible score of 200. The results achieved by a class of 20 stu * dentsarelisted / 168, 152, 112, 88, 95, 123, 177, 166, 145, 104, 112, 156, 110, 141 , 177, 166, 134, 190, 111, and 120. Calculate the percentile rank of a score of 141, to the nearest percentile. (4 marks)
The percentile rank of a score of 141, to the nearest percentile, is 53.
What is the percentile rank?The percentile rank describes the percentage of scores in the frequency distribution that are equal to or lower than the achieved score.
To calculate the percentile rank of a score of 141, we can proceed as follows:
Firstly, the scores are arranged in ascending order: 88, 95, 104, 110, 111, 112, 112, 120, 123, 134, 141, 145, 152, 156, 166, 166, 168, 177, 177, 190.
The number of scores below 141 = 10
The number of scores equal to 141 = 1
The following percentile rank formula can be used to determine the percentile rank of a score of 141:
Percentile Rank = [(M + (0.5 * R)) / Y] x 100, where:
M = Number of Ranks below x
R = Number of Ranks equals x
Y = Total Number of Ranks
Percentile Rank = [(10 + (0.5 * 1)) / 20] x 100
= 52.5
Percentile Rank = 53
Thus, the percentile rank of a score of 141 in a test with a maximum possible score of 200 is 53.
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find the general solution of the given second-order differential equation. y'' − 6y' + 10y = 0
The general solution of the differential equation is: y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t), where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.
The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. Its characteristic equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:
r^2 e^(rt) - 6r e^(rt) + 10 e^(rt) = 0
Dividing both sides by e^(rt) (which is non-zero), we get:
r^2 - 6r + 10 = 0
Solving for r using the quadratic formula, we get:
r = (6 ± sqrt(6^2 - 4(1)(10))) / 2
r = 3 ± i
Therefore, the general solution of the differential equation is:
y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t)
where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.
This solution consists of a linear combination of two functions: the exponential function e^(3t) and the periodic function cos(t) or sin(t), which oscillates between -1 and 1. The exponential function represents the growth or decay of the system, while the periodic function represents the oscillations or vibrations of the system. The constants c1 and c2 determine the amplitude and phase of the oscillations, respectively. The behavior of the system depends on the signs and magnitudes of the real and imaginary parts of the roots, which determine whether the solutions are overdamped, critically damped, or underdamped.
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Cho sells kakigori, a Japanese frozen dessert flavored with sweet syrup, at a street stand.
The scatter plot shows the daily high temperature and the number of servings of kakigori
Cho sells each day for 12 days. Based on a line of best fit for the data, about how many
servings of kakigori will Cho sell on a day when the high temperature is 29° Celsius?
Number of Servings Sold
115
110
105
100
95
90
85
80
75
70
65
60
55
50
0
18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)
94
101
88
111
We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.
From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.
By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.
Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
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What is tan A? use a slash for the fraction.
Remember - SOH CAH TOA
cos(A) = adjacent / hypotenuse
adjacent = 5
sin(A) = opposite / hypotenuse
opposite = 12
hypotenuse = 13
tan(A) = opposite / adjacent
tan(A) = 12 / 5
Answer: tan(A) = 12/5
Hope this helps!
this graph shows how fast the international space station travels in orbit around the earth. what is the meaning of the point x-coordinate of 3
The X-Coordinate of 3 only represents a specific moment in time during the orbit and not necessarily the speed of the ISS at all times.
Since the graph is showing how fast the International Space Station (ISS) is traveling in orbit around the Earth, the x-coordinate of 3 likely represents a specific point in time or duration of the orbit.
To find out what the x-coordinate of 3 represents, we need to know the units of time on the x-axis. If the units are in minutes, then a value of 3 would represent 3 minutes. Similarly, if the units are in hours, then a value of 3 would represent 3 hours.
Assuming the units on the x-axis are in minutes, the point with an x-coordinate of 3 represents the speed of the ISS 3 minutes into its orbit. This means that at that point in time, the ISS was traveling at a speed of approximately 27,500 kilometers per hour.
It's important to note that the speed of the ISS can vary throughout its orbit, depending on factors such as altitude, atmospheric conditions, and changes in the orbit itself. Therefore, the x-coordinate of 3 only represents a specific moment in time during the orbit and not necessarily the speed of the ISS at all times.
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Note the full question is
Representing Proportional Relationships
This graph shows how fast the International Space Station travels in orbit around Earth.
What is the meaning of the point with an x-coordinate of 3?
pls help me im begging
The surface area of the triangular prism in square meters is:
549.15 m²
How to find the surface area of triangular prism?The total surface area of the given prism would be the sum of the areas of the individual faces that make up the prism.
The formula for area of a triangle is:
Area = ¹/₂ * base * height
The formula for area of a rectangle is:
Area = Length * width
Thus:
Total surface area of prism is:
TSA = (15 * 13) + (15.81 * 15) + 2(¹/₂ * 9 * 13)
TSA = 549.15 m²
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(b)
Factorise the following:
4x²-4
(2) 8y2 - 2
5n²-20
(6)
12x²y-27y³ (10)
3p²q-48q³
(14)
-x² +16
(18)
-3n³+3n
(22)
(5)
(9)
(13)
(17)
(21)
8y²-2
100m² - 25
75a²-126²
2ax * - 50a
-9x² +1
-8b +32b
Answer:
not possible
Step-by-step explanation:
error
a merchant has coffee worth $20 a pound that she wishes to mix with 80 pounds of coffee worth $80 a pound to get a mixture that can be sold for $60 a pound. how many pounds of the $20 coffee should be used
To obtain a mixture of coffee that can be sold for $60 a pound, the merchant must mix the $20 coffee with the $80 coffee in such a way that the resulting mixture is worth $60 per pound.
To determine how many pounds of the $20 coffee should be used, we can set up a system of equations using the weights of each type of coffee and their corresponding values per pound.
Let x be the number of pounds of the $20 coffee to be used. Then, the total weight of the mixture is 80 + x pounds. The value of the $20 coffee is $20 per pound, and the value of the $80 coffee is $80 per pound. The value of the mixture must be $60 per pound. Therefore, we can write the following equation:
$20x + 80(80) = 60(80 + x)$
Simplifying and solving for x, we get:
$x = 200$
Therefore, the merchant should use 200 pounds of the $20 coffee and mix it with 80 pounds of the $80 coffee to obtain a mixture that can be sold for $60 a pound.
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How do I solve this?
Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown below.
Given that;
Expression is,
⇒ tan² θ - sin² θ = tan² θ × sin² θ
Now, We can simplify as;
⇒ tan² θ - sin² θ
⇒ sin² θ / cos² θ - sin²θ
⇒ sin² θ (1 / cos² θ - 1)
⇒ sin² θ (sec² θ - 1)
⇒ sin² θ × tan² θ
Thus, Prove of expression tan² θ - sin² θ = tan² θ × sin² θ is shown.
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an answering service staffed with one operator takes phone calls from patients for a clinic after hours. patient phone calls arrive at a rate of lambda equals 15 per hour. the interarrival time of the arrival process can be approximated with an exponential distribution. patient phone calls can be processed at a rate of mu equals 25 per hour. the processing time for the patient phone calls can also be approximated with an exponential distribution. determine the utilization factor.
The utilization factor can be calculated as the ratio of the arrival rate to the service rate. In this case, the arrival rate (lambda) is 15 per hour, and the service rate (mu) is 25 per hour. Therefore, it is important for the clinic to monitor the utilization factor and adjust staffing levels as needed to ensure efficient and effective patient communication.
So the utilization factor is:
Utilization factor = lambda / mu
Utilization factor = 15 / 25
Utilization factor = 0.6
This means that on average, the operator is utilized 60% of the time. In other words, there is a 40% idle time during which no phone calls are being processed. This is a relatively low utilization factor, which suggests that there is some capacity to handle more phone calls if necessary. However, it is important to note that if the arrival rate were to increase, the utilization factor would increase as well, which could lead to longer wait times for patients and potential bottlenecks in the phone system.
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y varies jointly as the square of x, the square of z, and when x = 3 and
z = 4, then y = 72
What’s the equation?
The equation will be y = kx²z², where k is the proportionality constant.
Given that y varies jointly as the square of x, the square of z,
And when x = 3 and z = 4, then y = 72,
So, we can write,
y ∝ x²z²
or,
y = kx²z² [k = proportionality constant]
Now, given x = 3 and z = 4, then y = 72,
Therefore,
72 = 3²·4²·k
72 = 9·16 k
k = 72 / 144
k = 0.5
Therefore, the value of proportionality constant k is 0.5.
Hence the equation will be y = kx²z², where k is the proportionality constant.
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Help me please I don’t understand this at all
The equation of the line represented by the points on the graph is (5x+16)/6.
What is a line?line is a straight one-dimensional figure that does not have a thickness, and it extends endlessly in both directions.
To calculate the equation of the line represented by the points on the graph, we use the formula below
Formula:
(y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁)....................... Equation 1From the points in the graph,
Given:
y₁ = 1y₂ = 6x₁ = -2x₂ = 4Substitute these values into equation 1
[y-1]/[x-(-2)] = (6-1)/[4-(-2)]y-1/x+2 = 5/66(y-1) = 5(x+2)6y-6 = 5x+106y = 5x+10+66y = 5x+16y = (5x+16)/6Learn more about lines here: https://brainly.com/question/29044610
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Solve:
3(x - 2) - 2x < 18 PLSS HELP
[tex]3(x - 2) - 2x < 18\\3x-6-2x < 18\\x < 24[/tex]
Evaluate the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) st tan(2x + 9)dx
Answer:
1/2 ㏑(sec (2x + 9)) + c ........ absolute sec (2x +9)
Step-by-step explanation:
∫tan (2x + 9) dx
let u = 2x + 9
du/dx = 2
dx = du/2 = (1/2) du
now we have ∫tan u (1/2 du)
= 1/2 ∫tan u du
= 1/2 ㏑ (sec u) ...... absolute
=1/2 ㏑(sec (2x + 9)) + c ........ absolute
A golfer played 7 rounds of golf with the following scores: 1 round at 3 over par, 2 rounds with 1 over par, 3 rounds with 3 under par, and the last round at 1 under par. How did she finish with respect to par?
Answer:
To determine how the golfer ended in terms of par, tally up all of her scores and deduct them from the total par for the seven rounds.
The total par for seven rounds multiply by eighteen is 126 (assuming the course is a regular par 72).
The golfer's score in relation to par for each round is:
1 round at 3 over par = 75 (72 + 3)
2 rounds with 1 over par = 73 (72 + 1) x 2 = 146
3 rounds with 3 under par = 69 (72 - 3) x 3 = 207
1 round at 1 under par = 71 (72 - 1)
you add all the pars working above, which is
75 + 146 + 207 + 71 = 499
Her score of 499 is 27 below par (126 - 499 = -373), meaning she ended significantly below par.
Find the volume of a right circular cone that has a height of 15.4 m and a base with a circumference of 18 m. Round your answer to the nearest tenth of a cubic meter.
The volume of the right circular cone with a height of 15.4 m and a base circumference of 18 m is 15.68 cubic meters.
To find the volume of a right circular cone, we can use the formula:
Volume = (1/3) × π × r² × h,
where π is the mathematical constant pi, r is the radius of the base, and h is the height of the cone.
Given that the base has a circumference of 18 m, we can calculate the radius using the formula:
Circumference = 2 × π × r
18 = 2 × π × r
r = 18 / (2 × π) = 2.864 m.
Now we can substitute the values into the volume formula:
Volume = (1/3) × π × (2.864 m)² × 15.4 m,
Volume = 15.68 m³
Therefore, the volume of the right circular cone with a height of 15.4 m and a base circumference of 18 m is 15.68 cubic meters.
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Tommy and his friends are planning a trip to the Mega Vault trampoline park. The employee
Tommy spoke to on the phone said the total cost for all 5 of them would be $85. This includes
a $3 fee added to each entrance ticket to cover the cost of a pair of grip socks.
Which equation can you use to find c, the cost of an entrance ticket?
5(c + 3) = 85
5c + 3 - 85
3c+5 85
3(c+5)= 85
The equation to find the entrance cost is 5(c + 3) = 85.
Given that 5 five friends made plan for trip, which will cost them a total of $85,
This includes a $3 fee added to each entrance ticket to cover the cost of a pair of grip socks.
We need to establish an equation to find c, the cost of an entrance ticket,
So,
The total cost of one entrance ticket = c + 3,
So, for 5 people = 5(c+3)
Now, this is equal to 85.
So the equation is = 5(c + 3) = 85.
Hence the equation to find the entrance cost is 5(c + 3) = 85.
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(c) Write
3"
9-1
as a power of 3
Let's first start by rewriting the denominator to have a base of 3.
9 = 3^2
9^(n - 1) = 3^2(n - 1)
Now that we have two terms with the same base, we can subtract the exponents.
3^n / 3^2(n - 1) = 3^[n - 2(n - 1)]
3^[n - 2n + 2]
3^[-n + 2]
3^-(n - 2)
Answer: 3^(-n + 2) OR 3^-(n - 2)
Hope this helps!
Which improper fraction is equal to the decimal 2.8?
Answer: 14/5
Step-by-step explanation:
2.8 = 28/10
this can be simplified to 14/5
Answer:
14/5
Step-by-step explanation:
Segments DE, EF and DF are all tangent to the circle. Find the perimeter of Triangle DEF.
*
73
26.5
37.8
84
The perimeter of the triangle is 73 unit.
We know that tangents drawn from external point are equal in length.
So, HE = EI = 16 unit
IF = GF = 9.5 unit
DG = DH = 11 unit
So, the length of sides are
DE = 16 + 11 = 27
EF = 9.5 + 16 = 25.5
FD = 11 + 9.5 = 20.5
Now, the perimeter of Triangle DEF is
= DE + EF + FD
= 27 + 25.5 + 20.5
= 73 unit
Therefore, the perimeter of the triangle is 73 unit.
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(x - 2)/(x + 2) - (x + 2)/(x - 2)
Answer:
[tex]-\cfrac{8x}{x^2-4}[/tex]
----------------------------------
Simplify in below steps:
[tex]\cfrac{x-2}{x+2} -\cfrac{x+2}{x-2} =[/tex] Bring to common denominator
[tex]\cfrac{(x-2)^2}{(x+2)(x-2)} -\cfrac{(x+2)^2}{(x+2)(x-2)}=[/tex] Multiply both fractions by x +2 or x - 2
[tex]\cfrac{(x-2)^2-(x+2)^2}{(x+2)(x-2)}=[/tex] Make a single fraction
[tex]\cfrac{(x-2+x+2)(x-2-x-2)}{(x+2)(x-2)}=[/tex] Factorize the numerator
[tex]\cfrac{2x(-4)}{(x+2)(x-2)}=[/tex] Simplify the numerator
[tex]-\cfrac{8x}{x^2-4}[/tex] Answer
Used identity:
[tex](a+b)(a-b)=a^2-b^2[/tex]please help me do this question!
Answer: (a): 162 (b):
Step-by-step explanation: Since Mr.Siva had 54 cups sold which is 3/9 all we have to do is multiply 3/9 to the point where its a whole so 3/9 x 3 is 1, whatever we do with this fraction we do with the cups he sold, so 54 x 3 is 162. Since we know that he had a total of 162 cups, all we have to do is subtract how many cups he sold in the morning which was 54. So 162 - 54 is 108. Hope this help! :)
Find the volume of liquid needed to fill a sphere of radius R to height R/5.
To find the volume of liquid needed to fill a sphere of radius R to a height of R/5, we can consider the spherical cap formed by the liquid.
The volume of a spherical cap can be calculated using the formula:
V = (1/3)πh²(3R - h)
Where V is the volume, h is the height of the cap, and R is the radius of the sphere.
In this case, the height of the cap is R/5 and the radius of the sphere is R. Substituting these values into the formula, we get:
V = (1/3)π(R/5)²(3R - R/5)
= (1/3)π(R²/25)(15R - R/5)
= (1/3)π(R²/25)(74R/5)
= (74/75)πR³
So, the volume of liquid needed to fill the sphere to a height of R/5 is (74/75)πR³.
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the number of ants in a colony doubles every month. which type of function best models this relationship?
The relationship described, where the number of ants in a colony doubles every month, can be modeled by an exponential function.
An exponential function is of the form y = ab^x, where 'a' is the initial value or starting point, 'b' is the growth factor, and 'x' represents the time or number of months in this case.
In the given scenario, the initial number of ants is multiplied by a growth factor of 2 every month. This corresponds to the base 'b' of the exponential function being equal to 2. The exponent 'x' represents the number of months elapsed.
Therefore, the exponential function y = 2^x best models the relationship between the number of ants in the colony and the time, as it reflects the doubling pattern observed in the colony's population over time.
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