The age of the oldest student is 13 years.
Let the age of the oldest student be x years.
The sum of ages of all 21 students is (21 × 14 years 3 months)
= (21 × 14) + (21 × 3/12) years
= 297 years
When the oldest student is not counted, the sum of ages is (20 × 14 years 2 months)
= (20 × 14) + (20 × 2/12) years
= 284 years
we have the equation:
297 - x = 284
Solving for x, we get:
x = 13 years
Therefore, the age of the oldest student is 13 years.
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In the diagram above, L1 is parallel to both L2 and L3; AC is perpendicular to L3. Find x, y, and z.
Check the picture below.
After the president of the United States is sworn into office, the Presidential Inaugural Parade travels a straight path west from the U. S. Capitol (B) to the White House (A) down Pennsylvania Avenue. How is this path defined?
The path of the Presidential Inaugural Parade is defined as a straight line that runs west from the U.S. Capitol Building, located at the eastern end of the National Mall in Washington D.C., to the White House, located just a few blocks to the north.
The parade typically follows Pennsylvania Avenue, which is the main ceremonial route used for many official processions in the nation's capital. The path is lined with grandstands for spectators and is closed to vehicle traffic during the parade. The parade route is flanked by some of Washington D.C.'s most important landmarks, including the National Archives Building, the Department of Justice, the Old Post Office Pavilion, and the Trump International Hotel. The Presidential Inaugural Parade has been a tradition in the United States for over 200 years and is a key part of the Inauguration Day ceremonies, which mark the peaceful transfer of power from one presidential administration to the next.
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the interest is component is annually
The equation P (1 + r/100)n, wherein P = the principal, r = yearly rate of interest, and n = the number of years and time periods, yields the amount of money when interest is made worse annually.
Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. For an amount, compound interest is computed using either the principal and accrued interest. This is the primary distinction among compound and simple interest. The formula P (1 + r/100)n, where P = principal, r = yearly rate of interest, and n = the number of years or time periods, yields the amount if interest is compounded annually.
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Evaluate the surface integral. ∫∫s z^2 ds, S is the part of the paraboloid x = y^2 + z^2 given vy ≤ x ≤ 4
according to question the surface integral is (32π - 192)/15.
To evaluate the surface integral, we need to parameterize the surface and find the surface element ds.
Let's consider the parameterization:
x = y^2 + z^2
y = y
z = z
The surface element can be found as:
ds = √(1 + (dx/dy)^2 + (dx/dz)^2) dy dz
ds = √(1 + 4y^2) dy dz
Now, we can rewrite the integral as:
∫∫s z^2 ds = ∫∫R (y^2 + z^2)^2 √(1 + 4y^2) dy dz
where R is the projection of the surface S onto the yz-plane, which is the region 0 ≤ y ≤ 2, -√(4 - y^2) ≤ z ≤ √(4 - y^2).
Let's evaluate the integral:
∫∫s z^2 ds = ∫0^2 ∫-√(4-y^2)^√(4-y^2) (y^2 + z^2)^2 √(1 + 4y^2) dz dy
Using cylindrical coordinates, we can rewrite the integral as:
∫0^2 ∫0^π/2 ∫0^2r (r^2 cos^2θ + r^2 sin^2θ)^2 r √(1 + 4r^2 sin^2θ) dr dθ dy
Simplifying and solving the integral, we get:
∫∫s z^2 ds = (32π - 192)/15
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find the general solution of the given differential equation. (x2 − 4) dy dx + 4y = (x + 2)2
the general solution of the given differential equation is:
y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|
To find the general solution of the given differential equation:
(x^2 - 4) dy/dx + 4y = (x + 2)^2
We can rearrange the equation to isolate the derivative term:
dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)
First, let's simplify the numerator:
[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y
= x^2 + 4x + 4 - 4y
= x^2 + 4x - 4y + 4
Now, substitute this simplified expression back into the differential equation:
dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)
This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.
First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)
dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)
The integrating factor is given by the exponential of the integral of P(x):
μ(x) = exp ∫ (4x / (x^2 - 4)) dx
To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:
μ(x) = exp ∫ (2x dx) / (x^2 - 4)
= exp ∫ (du / u)
= exp(ln|u|)
= |u|
Substituting back u = x^2 - 4:
μ(x) = |x^2 - 4|
Now, multiply the entire differential equation by the integrating factor:
|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)
The left side can be simplified using the product rule for differentiation:
d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)
Now, integrate both sides with respect to x:
∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx
Integrating the left side gives:
|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx
= (1/3) x^3 + 2x^2 + 4x + C1
where C1 is the constant of integration.
Finally, divide both sides by |x^2 - 4| to solve for y:
y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|
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Of the 400 freshmen at Westview High School, 92 students are in band, 60 students are in chorus, and 20 students are in both band and chorus. If a student is chosen at random, Find each probability as a fraction (in simplest form), decimal, and percent.
Answer:
Step-by-step explanation:
As an estimation we are told £3 is €4.
Convert €90.50 to pounds.
Give your answer rounded to 2 DP.
Answer: £67.875
Step-by-step explanation:
€90.50 x 3/4 = £67.875
Calculate the average number of employees per dealership if 1. 5% of the total number of employees worked at the head office in August 2020
To calculate the average number of employees per dealership, we need to first find the total number of employees working in both the dealerships and the head office. Let's assume that the total number of employees in August 2020 was 1000.
If 1.5% of the total number of employees worked at the head office, then the number of employees working in the head office would be 0.015 x 1000 = 15. To find the number of employees working in dealerships, we can subtract the number of employees working in the head office from the total number of employees, which is 1000 - 15 = 985.
Next, we need to calculate the average number of employees per dealership. To do this, we can divide the number of employees working in dealerships by the number of dealerships. Let's assume there are 10 dealerships in total. Therefore, the average number of employees per dealership would be 985/10 = 98.5.
So, on average, each dealership would have approximately 98.5 employees in August 2020.
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What is the area of a regular pentagon with a side of five? Round the answer to the nearest 10th. Type the number only or your answer will be marked wrong.
Find the area of the triangle below to the nearest
tenth.
56°
78°
7.2 cm
Please help me solve
Answer:
0.09 l
Step-by-step explanation:
Given:
900 ml ⇒ 10s
Required:
Liters per second
Analyze:
Let the unknown amount be x.
900 ml ⇒ 10s
x ⇒ 1s
Solve:
Use cross multiplication
900 × 1 = 10 × x
900 = 10x
Divide both sides by 10.
90 ml = x
To covert the answer into liters divide it by 1000.
0.09 l = x
Paraphrase:
We breathe 0.09 liters of air per second
Of the 400 freshmen at Westview High School, 92 students are in band, 60 students are in chorus, and 20 students are in both band and chorus. If a student is chosen at random, Find each probability as a fraction (in simplest form), decimal, and percent.
question .1 student in chorus and in band
question 2 student (not in band | in chorus)
question 3 student (in band | not in chorus)
Solve the inequality:
[tex]x^2 - 3x - 4 \ \textless \ = 4[/tex]
Answer:
[tex]\Large \textsf{$\boxed{\boxed{-1.702\leq x\leq4.702}}$}[/tex]
Step-by-step explanation:
The inequality required to solve:
[tex]\Large \textsf{$\Rightarrow$\ } \boxed{\Large \textsf{$x^2-3x-4\leq 4$}}[/tex]
[tex]\large \textsf{First, subtract 4 from both sides:}\\ \\\large \textsf{$\Rightarrow x^2-3x-8\leq 0$}\\\\\large \textsf{This is in the form of a quadratic equation, where $ax^2+bx+c=0$}\\\large \textsf{We need to consider the LHS as an equation, and solve for $x$:}\\\\\large \textsf{Using the quadratic formula:}\\\\\large \textsf{$\boxed{x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$} \large \textsf{ , where $ax^2+bx+c=0$}\\\\[/tex]
[tex]\large \textsf{$x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}$}\\\\\large \textsf{$\therefore x=-1.702, 4.702$}[/tex]
Now, this is not the solution of the inequality yet. These are the x-intercepts (roots) of the graph of y = x² - 3x - 8. From the graph, we can apply the inequality sign, and solve for values below or equal to y = 0.
[see attached diagram of graph]
[tex]\large \textsf{From the graph, we can conclude that:}\\\\\Large \textsf{$\boxed{\boxed{-1.702\leq x\leq4.702}}$}[/tex]
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Explain step by step
Answer:
(a) $ 7000
(b) $ 5600
Step-by-step explanation:
discount = 20%
20% = $1400
1% = 1400/20
original price = 100%
= 1400/20 × 100
= $7000
sale price = 80%
= 1400/20 × 80
= $5600
In a population of 1,500 students that was wrongly recorded as 900, find the percentage error.
The Percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.
To find the percentage error, we need to calculate the difference between the recorded value and the true value, then divide that difference by the true value and multiply by 100 to get a percentage.
True value = 1,500
Recorded value = 900
Difference = True value - Recorded value
Difference = 1,500 - 900
Difference = 600
Percentage error = (Difference / True value) x 100
Percentage error = (600 / 1,500) x 100
Percentage error = 40
Therefore, the percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.
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1.2-14 at the end of a semester, 29 students in a statistics class rated their instructor on a five-point scale (i.e., evalu- ating him/her as very poor, poor, fair, good, and excellent). how many different ratings combinations are possible?
To determine the number of different ratings combinations possible, we can use the combination formula. Since there are five possible ratings (very poor, poor, fair, good, and excellent) and 29 students in the class. Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
The formula we can use is:
nCr = n! / r!(n-r)!
where n is the total number of items (in this case, the number of ratings), and r is the number of items we are choosing (in this case, the number of students).
Using this formula, we can find the number of different ratings combinations possible by plugging in the values:
nCr = 5! / 29!(5-29)!
nCr = 5! / 29!(-24)!
nCr = 5 x 4 x 3 x 2 x 1 / (29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
nCr = 657,800
Therefore, there are 657,800 different ratings combinations possible for the 29 students in the statistics class.
In this scenario, there are 29 students and a 5-point scale for rating their instructor. To determine the number of different rating combinations possible, we will use the concept of combinations with repetitions allowed.
In this case, the formula for combinations with repetitions is given by:
C(n+r-1, r) = C(n+r-1, n-1), where n is the number of ratings (5) and r is the number of students (29).
Using the formula, we get:
C(5+29-1, 29) = C(33, 29) = 33! / (29! * 4!)
Calculating the factorials and simplifying the expression, we get:
C(33, 29) = 46,376
Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
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There are 5 red marbles and 3 blue marbles in a jar. What is the probability you selected a blue marble, do not replace it, and then select another blue marble?
Answer:
3/28
Step-by-step explanation:
5 + 3 = marbles in total.
P(first blue) = 3/8
P(second blue) = (3-1) / (8-1) = 2/7
P(selecting 2 blue) = (3/8) X (2/7) = 6/56 = 3/28
Which of the following sets of data provides the clearest difference between the two samples?
a) One sample has M = 20 with s2 = 5 and the other has M = 30 with s2 = 5.
b) One sample has M = 20 with s2 = 5 and the other has M = 25 with s2 = 5.
c) One sample has M = 20 with s2 = 10 and the other has M = 30 with s2 = 10.
d) One sample has M = 20 with s2 = 10 and the other has M = 25 with s2 = 10.
The set of data that provides the clearest difference between the two samples is option (c): One sample has M = 20 with s2 = 10 and the other has M = 30 with s2 = 10. The reason is that the standard deviation is higher in both samples compared to the other options, and the means of the two samples are also relatively far apart, making the difference between the two samples clearer. I
n options (a) and (b), the means are not far enough apart to provide a clear difference, and in option (d), while the means are farther apart than in option (b), the standard deviation is the same, which makes the difference less clear.
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what is the image of point p(-2 3 5) after a reflection about the xy-plane
When a point is reflected about the xy-plane, its z-coordinate is negated while its x and y-coordinates remain the same. the image of the point P(-2, 3, 5) after a reflection about the xy-plane is the point P'(-2, 3, -5).
what is coordinates ?
Coordinates are values used to indicate the position of a point in a coordinate system. A coordinate system is a system that uses one or more numbers, called coordinates, to determine the position of a point or object. For example, in a two-dimensional Cartesian coordinate system, a point is located by its distance from two perpendicular lines, the x-axis and the y-axis, which intersect at a point called the origin. The coordinates of a point are usually represented by an ordered pair (x, y) in this system. In a three-dimensional coordinate system, a point is located by its distance from three perpendicular planes, and its coordinates are usually represented by an ordered triple (x, y, z).
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Find the volume of the or
Answer:
400
Step-by-step explanation:
V= [tex]\frac{1}{3}[/tex]Bh
the base is a square, so B= [tex]10^{2}[/tex] or 100
h= 12
B= 100
Bh= 1200
[tex]\frac{1200}{3}[/tex] = 400
V=400
Enter the value for x that makes the equation 13x+22=x-34+5x true
Answer: -8
Step-by-step explanation:
13x+22=x-34+5x
13x+22=6x-34 (combine like terms)
13x-6x+22=6x-6x-34 (subtract 6x on each side)
7x+22=-34
7x-22+22=-34-22 (subtract 22 on each side)
7x=-56
7x/7x = -56/7 (divide 7 on each side)
x=-8
2, 5; 7, 11 WHAT IS THE GENERAL RULE OF THIS SEQUENCE ?
There is no general rule for the sequence as this is neither an arithmetic sequence nor a quadratic sequence.
How to find the general rule ?If this is an arithmetic sequence, then there would be a constant difference between the consecutive terms.
Difference between term 2 and term 1 : 5 - 2 = 3
Difference between term 3 and term 2 : 7 - 5 = 2
Difference between term 4 and term 3 : 11 - 7 = 4
This is therefore not an arithmetic sequence.
We can check to see if it is quadratic with the second difference :
Difference between the second and first differences: 2 - 3 = -1
Difference between the third and second differences: 4 - 2 = 2
These are still not constant which means that there is no general rule given the terms.
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Here’s the picture i’m not sure what to do if someone could help me that would be awesome
The true statement from the graph is this: D. The girls have a higher interquartile range but a lower mean than the boys.
What is the true statement?The interquartile range of the girls' resting heart rate spans from 80 to 88 while the interquartile range of the boys spans from 84 to 90. So, the interquartile range for the girls is higher than that of the boys. Also, the mean of the girls is lower than that of the boys.
The mean of the girls is the sum of the rates divided by 8 = 11/8 = 1.375
The mean for the boys is the sum of the rates divided by 6 = 11/6 = 1.833
Som the mean of the girls is lower than that of the boys.
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18. a population has a mean of 300 and a standard deviation of 12. a sample of 64 observations will be taken. the probability that the sample mean will be between 295 to 305 is
The probability that the sample mean will be between 295 and 305 can be determined using the Central Limit Theorem and the properties of the normal distribution.
According to the Central Limit Theorem, for a large sample size (n ≥ 30), the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. In this case, since the sample size is 64, we can assume that the sample mean will follow a normal distribution.
To find the probability that the sample mean will be between 295 and 305, we need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the given range (295 to 305), μ is the population mean (300), σ is the population standard deviation (12), and n is the sample size (64).
By calculating the z-scores for the lower and upper limits of the range and referring to the standard normal distribution table, we can find the corresponding probabilities. The probability can be calculated by subtracting the cumulative probability corresponding to the lower limit from the cumulative probability corresponding to the upper limit.
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A particle moves along the curve defined by the equation y = x^3 â 3x. The x-coordinate of the particle, x(t), satisfies the equation dx/dt = 1/Vt+1, for t > 3 with the initial condition x(3) = -1. . Vt+1 (A) Find x(t) in terms of t. (B) Find dy/dt in terms of t. (C) Find the location and speed of the particle at time t = 8.
(A) x(t) = ln(t+1) + C, where C is a constant.
(B) dy/dt = 3x^2 - 3.
(C) At t = 8, the particle is located at x = ln(9) - 1 and has a speed of |3(3ln(9) - 3)^2 - 3|.
(A) To find x(t) in terms of t, we integrate dx/dt with respect to t. Integrating 1/(t+1) gives us ln(t+1) + C, where C is a constant. Since x(3) = -1, we can substitute t = 3 and x = -1 into the equation to solve for C. We get -1 = ln(3+1) + C, which gives us C = -1 - ln(4). Therefore, x(t) = ln(t+1) - ln(4) - 1.
(B) To find dy/dt in terms of t, we differentiate y = x^3 - 3x with respect to t using the chain rule. We have dy/dt = (dy/dx) * (dx/dt) = (3x^2 - 3) * (dx/dt). Substituting dx/dt = 1/(t+1), we get dy/dt = (3x^2 - 3)/(t+1).
(C) At t = 8, we can substitute t = 8 into x(t) to find the x-coordinate of the particle. We have x(8) = ln(8+1) - ln(4) - 1 = ln(9) - ln(4) - 1. To find the y-coordinate, we substitute this value of x into y = x^3 - 3x, giving us y(8) = (ln(9) - ln(4) - 1)^3 - 3(ln(9) - ln(4) - 1). To find the speed, we substitute x = ln(9) - ln(4) - 1 into dy/dt = (3x^2 - 3)/(t+1) and take the absolute value.
Therefore, at t = 8, the particle is located at the point (ln(9) - ln(4) - 1, (ln(9) - ln(4) - 1)^3 - 3(ln(9) - ln(4) - 1)), and its speed is given by |3((ln(9) - ln(4) - 1)^2 - 1)/(8+1)|.
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Which graph represents the solution of y ≥ x2 + 2?
Find the sector area for the following:
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (6)^2}{360} \\\\\\ A=\cfrac{9\pi }{2}\implies A=\cfrac{9(3.14) }{2}\implies A=14.13~yd^2[/tex]
Find scale factor of the dilation.
Answer:
Scale factor is 2
Step-by-step explanation:
Not sure how to explain, just count the number of points the dilated figure is from the point of dillations compared to the original figure. 2/1=2.
When you graph a graph a quadratic function, its shape is called a ____
A. triangle
B. square
C. parabola
D. line
E. circle
When you graph a quadratic function, its shape is called a parabola.
Option C is the correct answer.
We have,
A parabola is a curve that is formed when graphing a quadratic function.
It is a U-shaped curve that can open upwards or downwards, depending on the coefficients of the quadratic equation.
A quadratic function is a polynomial function of degree 2, which can be expressed in the form y = ax² + bx + c, where a, b, and c are constants and x represents the variable.
The coefficient a determines whether the parabola opens upwards or downwards.
If coefficient a is positive, the parabola opens upwards, and if coefficient a is negative, the parabola opens downwards.
The vertex of the parabola is the highest or lowest point on the curve, depending on the orientation.
Thus,
A parabola is a specific shape that is formed when graphing a quadratic function, characterized by its U-shape.
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The diameter of the circle is 27 ft what is the area of the circle rounded to the nearest hundreth?
