The volume of a right rectangular prism can be calculated by multiplying the length, width, and height together. Therefore, the volume of the jewelry box will depend on the specific measurements of the box.
To calculate the volume of the wooden jewelry box, we need to know its length, width, and height. Once we have those measurements, we can multiply them together to determine the volume of the box.
For example, if the length of the box is 5 inches, the width is 3 inches, and the height is 2 inches, then the volume of the box would be 5 x 3 x 2 = 30 cubic inches.
Learn more about volume: https://brainly.com/question/463363
#SPJ4
In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 18 feet and a height of 50 feet and makes 5 revolutions. Assuming the spiral staircase is centered about the z-axis, find a vector parametric equation for the helical path you take from the point (28,0,0) to the point (28,0,40) that makes 4 revolutions during the time interval 0≤t≤1
The vector parametric equations that describe the helical path you take from the point (28, 0, 0) to the point (28, 0, 40) as you make 4 revolutions during the time interval 0 ≤ t ≤ 1 are:
x(t) = 28 + 18 cos(πt / 15)
y(t) = 18 sin(πt / 15)
z(t) = 50t
To find a vector parametric equation for the helical path, we need to describe the position of a point on the spiral staircase as it moves from (28, 0, 0) to (28, 0, 40) while making 4 revolutions during the time interval 0 ≤ t ≤ 1.
Let's define the following parameters:
R: Radius of the spiral staircase = 18 feet
H: Height of the spiral staircase = 50 feet
N: Number of revolutions during the time interval = 4
T: Total time taken to complete N revolutions = 1 hour (or 60 minutes)
The parametric equations for the helical path can be given as follows:
x(t) = 28 + R × cos(2πNt/T)
y(t) = R × sin(2πNt/T)
z(t) = H × t
Where:
x(t), y(t), z(t) are the coordinates of the point on the helical path at time t.
R × cos(2πNt/T) and R × sin(2πNt/T) describe the circular motion of the point in the xy-plane as it makes N revolutions over the time interval.
H × t describes the linear motion of the point along the z-axis.
Now, let's plug in the given values:
R = 18 feet
H = 50 feet
N = 4
T = 60 minutes
And simplify the equations:
x(t) = 28 + 18 × cos(2π × 4t / 60)
y(t) = 18 × sin(2π × 4t / 60)
z(t) = 50 × t
Simplifying further:
x(t) = 28 + 18 × cos(π × t / 15)
y(t) = 18 × sin(π × t / 15)
z(t) = 50 × t
These equations describe the helical path you take from the point (28, 0, 0) to the point (28, 0, 40) as you make 4 revolutions during the time interval 0 ≤ t ≤ 1.
Learn more about vector parametric equation click;
https://brainly.com/question/32591934
#SPJ4
How do you solve a 3x3 augmented matrix?
To solve a 3×3 augmented matrix use the method of elementary row operations.
What is a matrix?
A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.
An augmented matrix for a system of equations is a matrix of numbers where each column contains all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).
The system of equations are - x - 2y + 3z = 7, 2x + y + z = 4, -3x + 2y -2z = -10
Here is the augmented matrix for this system.
[tex]\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right][/tex]
This matrix can be solved using the method of elementary row operations.
Interchange Two Rows. With this operation interchange all the entries in row i and row j. The notation used here is Ri ↔ Rj.
[tex]\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \stackrel{R_1 \leftrightarrow R_3}{\rightarrow}\left[\begin{array}{rrr|r}-3 & 2 & -2 & -10 \\2 & 1 & 1 & 4 \\1 & -2 & 3 & 7\end{array}\right][/tex]
Multiply a Row by a Constant. In this operation multiply row i by a constant c and the notation will be cRi.
[tex]\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \stackrel{-4 R_3}{\rightarrow}\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\12 & -8 & 8 & 40\end{array}\right][/tex]
Add a Multiple of a Row to Another Row.
Row i will be replaced in this procedure with row i times a constant c plus row j. Ri + cRi → Rj is the notation for this operation. This procedure involves taking an input from row i multiplying it by c, adding the equivalent value from row j, and then returning the result to row i.
[tex]\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \begin{gathered}R_3-4 R_1 \rightarrow R_3 \\\rightarrow\end{gathered}\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-7 & 10 & -14 & -38\end{array}\right][/tex]
Let’s go through the individual computation to make sure you followed this.
-3 - 4(1) = -7
2 - 4(-2) = 10
-2 - 4(3) = -14
-10 - 4(7) = -38
Therefore, the matrix is solved using row operations.
To learn more about matrix from the given link
https://brainly.com/question/1279486
#SPJ4
(a) (5 pts) prove the following identity: n 1 log n = 2
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
Proof:
Let S(n) = n + 1 log n
We will prove S(n) = 2 by induction.
Base Case:
Let n = 1. Then S(1) = 1 + 1(log 1) = 1 + 0 = 1 = 2.
Inductive Step:
Assume S(k) = 2 for some arbitrary integer k ≥ 1. We must show that S(k + 1) = 2.
S(k + 1) = (k + 1) + 1(log(k + 1))
= k + 1 + 1(log k + log 1)
= k + 1 + 1(log k + 0)
= k + 1 + 1(log k)
= k + 1 + log k
= 2 + log k
= 2 (by induction hypothesis)
Therefore, S(n) = 2 for all positive integers n.
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
Learn more about integer here
https://brainly.com/question/15276410
#SPJ4
The maximum acceleration attained on the interval 0≤t≤3 by the particle whose velocity is given by v(t) = t3 -3t2 +12t +4 is? a.9
b.12
c.14
d.21
e.40
For the velocity function v(t) = t³ - 3t² + 12t + 4, with interval 0 ≤ t ≤ 3, the maximum acceleration is option D: 21 m/s².
What is velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
The velocity function is v(t) = t³ - 3t² + 12t + 4.
The interval is given as - [0,3]
Maximize the function to obtain the value of t.
v'(t) = a(t) = 3t² - 6t + 12
Maximize it again -
a'(t) = 6t - 6 = 0
6t = 0 + 6
t = 6/6
t = 1
Now there are three critical points for t = {0,1,3}
1 and 3 are endpoints of the interval [0,3].
To get the maximum acceleration, plug in the values of t in the equation .
First substitute the value t = 0 -
a(0) = 3t² - 6t + 12
a(0) = 3(0)² - 6(0) + 12
a(0) = 12
Now substitute the value t = 1 -
a(1) = 3t² - 6t + 12
a(1) = 3(1)² - 6(1) + 12
a(1) = 3 - 6 + 12
a(1) = 15 - 6
a(1) = 9
Now substitute the value t = 3 -
a(3) = 3t² - 6t + 12
a(3) = 3(3)² - 6(3) + 12
a(3) = 27 - 18 + 12
a(3) = 39 - 18
a(3) = 21
So, the maximum acceleration is 21 m/s² when t =3.
Therefore, the maximum acceleration is 21 m/s².
To learn more about velocity from the given link
brainly.com/question/24445340
#SPJ4
PLEASE HELP TIME LIMIT - 100 POINTS
Use Graph For Reference
The line of best fit gives a general outlook on the data while the correlation is the exact points showcased to calculate or show for a data set or table.
How to explain the informationIt should be noted that between the two variables it is a positive correlation because they both increase in the same direction.
Positive correlation is a relationship between two variables in which both variables move in tandem that is, in the same direction.
In order to find the residual one would subtract the predicted value from the measured value.
The diagram is attached.
Learn more about line of best fit on:
https://brainly.com/question/17261411
#SPJ1
rewrite the equation in exponential form ln(m)=n
The equation would be written in exponential form as follows: [tex]$$\ln(m) = n \Rightarrow m = e^n$$[/tex]
The equation ln(m)=n can be rewritten in exponential form as m=e^n. This can be seen by taking the natural logarithm (ln) of both sides of the equation. The natural logarithm of m is equal to n, so we have ln(m)=n. Applying the exponential function, e^x, to both sides of the equation gives us m=e^n. This can be further understood by calculating the exponential of both sides.
For example, if n = 1, then ln(m)=1, so m=e^1. Applying the exponential function, e^x, to both sides of the equation, we have m=e^1. Calculating e^1 gives us m=e^1=2.718. Thus, ln(m)=1 can be rewritten in exponential form as m=2.718.
The equation in Latex would be written as follows: [tex]$$\ln(m) = n \Rightarrow m = e^n$$[/tex]
Learn more about exponential form here:
https://brainly.com/question/28970280
#SPJ4
Considera una caja de zapatos tradicional y dibujala. En dicho dibujo denota o nombra lo siguiente
With the identification of plans, angles, Rectangles, and segments, you can find the shoe box in the attachment.
Every point on a Plano has the same level because it is a space with only two dimensions.
The ángulos are a component of a plan that is created from two recitals with a common vertex. In the case of our shoe box, all angles are right-angled, despite the perspective appearing to be greater or smaller than 90 degrees.
Semirrectas are rectus with a known beginning but no known end. We can extend two segments in the shoe box so that they become semi-rectangles.
The segments are straight lines with clearly defined beginnings and end. All of the lines that form in the shoe box are segments.
The following is identified in the drawing.
2 color Morado plans4 blue angular shapes2 semi-rectangular black lines are divided into four segments, each of which is redKnow more about rectangles
https://brainly.com/question/30385039
#SPJ4
The Full question:
Consider a traditional and illustrated shoe box. This illustration indicates or names the following.
using the squeeze theorem to find the limit of (xy^4)/(x^4 y^4)
The limit of (xy⁴)/(x⁴y⁴) is 0.
The limit squeeze theorem (also known as sandwich theorem) states that if a function f(x) lies between two functions g(x) and h(x) and the limits of each of g(x) and h(x) at a particular point are equal (to L), then the limit of f(x) at that point is also equal to L. This looks something like what we know already in algebra. If a ≤ b ≤ c and a = c then b is also equal to c. The squeeze theorem says that this rule applies to limits as well. We define the squeeze theorem mathematically as follows:
"Let f(x), g(x), and h(x) are three functions that are defined over an interval I such that g(x) ≤ f(x) ≤ h(x) and suppose lim ₓ → ₐ g(x) = lim ₓ → ₐ h(x) = L, then lim ₓ → ₐ f(x) = L".
Here:
The function f lies between g and h and hence they are lower and upper bounds of f respectively.
'a' doesn't necessarily need to be within I.
We have to find the limit of (xy⁴)/(x⁴y⁴).
After applying the limit squeeze theorem, we get
[tex]\lim_{x \to \infty} \frac{xy^{4} }{x^{4}y^{4} }\\ = \lim_{x \to \infty} \frac{1}{x^{3} } \\= 0[/tex]
Thus, the limit of (xy⁴)/(x⁴y⁴) is 0.
To learn more about limits, visit brainly.com/question/8533149
#SPJ4
A recent poll of 750 randomly selected smartphone users found that 176 of the respondents admitted to walking into something or someone while texting on their cell phone. Construct and interpret a 95% confidence interval for the proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone
Based on the sample data, there is a 95% chance that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.
A 95% confidence interval for the proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone can be calculated as follows:
Let p be the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone. Based on the sample of 750 respondents, the point estimate of p is 176/750 = 0.235.
Using the normal approximation to the binomial distribution, the standard error of the point estimate is estimated as [tex]\sqrt{ (p(1-p)/n)}[/tex], where n = 750. This gives us a standard error of [tex]\sqrt{(0.235 * 0.765/750)}[/tex] = 0.018.
A 95% confidence interval for the true proportion p is then given by the point estimate plus or minus 1.96 times the standard error. This gives us the following interval:
0.235 - 1.96 * 0.018 <= p <= 0.235 + 1.96 * 0.018
0.199 <= p <= 0.271
So, we are 95% confident that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.
Interpretation: Based on the sample data, there is a 95% chance that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.
Here you can learn more about confidence interval
brainly.com/question/30329435
#SPJ4
Geometry
A box contains ten $1 bills, ten $5 bills, and three $10 bills. What is the probability of selecting a $10 dollar bill or a $5 dollar bill? Please make sure you use the equation. Please express your answer as a fraction, decimal and a percent.
The probability of selecting a $10 dollar bill or a $5 dollar bill would be = 13/23
What is probability?Probability is defined as the expression that can be used to represent the possible outcome of an event which may likely occur or not.
The quantity of $1 bill = 10
The quantity of $5 bill = 10
The quantity of $10 bill = 3
The sum total of bills in the box = 23
The probability of choosing a 5 or 10 bills;
= 10+3/23
= 13/23
Learn more about probability here:
https://brainly.com/question/25870256
#SPJ1
What does x equal?
5x+10=2x+16
Answer:
X = 2
Step-by-step explanation:
5x + 10 = 2x + 16
3x + 10 = 16
3x = 6
x = 2
Hope this helps! Pls give brainliest!
Five more people are ahead of me in line than are behind me. There are 3 times as many people in line as there are people behind me. How many people are in line?
A. 15
B. 17
C. 18
D. 20
15
There's 5 people behind me and 10 people in front of me.
Let P and Q be equivalent propositional forms. Explain why P ↔ Q is a tautology. Hint: it might be helpful to consider truth tables for a simple example like P = (~ R) VT and Q = ~ (R^(~T)). However you must argue in general, not just for a specific example. =N
P ↔ Q is a tautology because if P and Q are equivalent propositional forms, they have the same truth value in every possible interpretation, making the bi-conditional proposition P ↔ Q always true.
A tautology is a proposition that is always true, regardless of the truth values of its component propositions.
When two propositions, P and Q, are equivalent, it means that they have the same truth value in every possible interpretation. That is, P and Q are logically equivalent.
Therefore, if P and Q are equivalent propositional forms, then P ↔ Q, the bi-conditional proposition, is a tautology. This is because the truth value of P ↔ Q will always be true, as both P and Q have the same truth value in every possible interpretation.
This can be shown through the truth table for P ↔ Q. The bi-conditional proposition is true if and only if both P and Q have the same truth value. If P and Q are equivalent, then they will always have the same truth value, and so P ↔ Q will always be true.
In general, for any equivalent propositions P and Q, P ↔ Q will always be a tautology.
To learn more about the equivalent propositional, visit:
brainly.com/question/14811926
#SPJ4
unrise, a bed-and-breakfast hotel, charges a one-time deposit of $25 plus $95 per night. Another bed-and-breakfast hotel called Bright Eyes charges a flat rate of $110 per night. Amanda wants to book a hotel for 5 nights. Which hotel costs less to stay for 5 nights? How much less?
Bright Eyes; $35
Sunrise; $50
Bright Eyes; $50
Sunrise; $35
Answer:
Sunrise; $35
Step-by-step explanation:
Hope it helps! =D
2. Ken is paying P2,500 every 3 mothy For the amount he bowowed at an
interest vate 8% compounded quarterly. How much did he borrowed
It haguel Hiat loan will be paid in 2 years and a months ?
Ken borrowed P8,077.84 from Haguel for a period of 2 years and a month.
To calculate the amount Ken borrowed,
We need to use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A is the amount after t years
P is the principal amount (the amount borrowed)
r is the annual interest rate (8% in this case)
n is the number of times the interest is compounded in a year (4 times in this case, since the interest is compounded quarterly)
t is the number of years
We know the amount after 2 years and 1 month,
So we can use that information to solve for the principal amount P.
First, we need to convert the number of years and months into a single value in terms of years:
2 years and 1 month = 2 + 1/12 = 2.0833 years
Next, we can plug in the values into the formula:
A = P * (1 + r/n)^(nt)
A = P * (1 + 0.08/4)^(4 * 2.0833)
A = P * (1.02)^(8.3333)
A = P * 1.2288
We also know that Ken is paying P2,500 every 3 months,
So we can multiply that by 4 (since there are 4 quarters in a year) to find the annual payment:
P2,500 * 4 = P10,000
And we know that A = P * 1.2288,
So we can substitute in the values we have:
P10,000 = P * 1.2288
Now we can solve for P:
P = P10,000 / 1.2288
P = 8077.84
For more questions on compound interest
https://brainly.com/question/29502697
#SPJ4
a projectile is launched with speed v0 and at angle θ0 with respect to the horizontal. which gives the horizontal component of the launch velocity?
Average velocity = 0 gives the horizontal component of the launch velocity .
What does average velocity mean?
The difference between the change in position or displacement (x) and the time periods (t) during which the displacement happens is known as average velocity.
Depending on how the displacement is displaced, the average velocity may be positive or negative. Meters per second (m/s or ms-1) is the standard international unit for average velocity.
Typical flight of a projectile is as shown in the picture above.
In the problem it is given that initial velocity V₀ at an angle θ
above the horizontal. As such inn the picture U= V₀
This velocity can be resolved into its x and y components.
Component along x axis, and
Component along y axis = V₀ Sin θ
Let t be time of flight.
Average velocity = Displacement/time of flight
It is given that "It lands at the same level from which it was launched", means that displacement in the y axis is = 0
Average velocity = 0/t = 0 ............1
cos θ component.
Average velocity = V₀ cos θ ............ 2
Average velocity we need to add both vectors along x and y directions
. In this instant it is simple as one of the vectors is
Average velocity = 0
Learn more about Average velocity
brainly.com/question/862972
#SPJ4
Can someone tell me the answers to these? (Sorry the picture looks weird
So x/1 + y/-2 = 1 and x/1 + y/-2 = 1 are the slope intercept forms of graphs 1, respectively.
what is slope intercept form ?The optimal angle in geometry is where the line's incline contacts the y-axis. a point where a line or curve's y-axis crosses it. This is demonstrated using the equation and for straight line, Y = shifting from traditional, where m denotes the slope and c the en la. The line's slope (m) as well as y-intercept (b) are highlighted in the analytic form of the equation. The slope is feet and the y-intercept is b when an equation has to have the intercept form (y=mx+b). It is also reasonable to rewrite some equations so that they appear to be slope intercepts. For example, the inclination and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0.
given
The slope intercept form = x/a + y /b = 1
1) for graph 1
The intercept form is x/1 + y/-2 = 1
2) for graph 2
The intercept form is x /-1 + y /1 = 1
So x/1 + y/-2 = 1 and x/1 + y/-2 = 1 are the slope intercept forms of graphs 1, respectively.
To know more about slope intercept visit:
https://brainly.com/question/19824331
#SPJ1
Determining class width. Below are some pieces of information you may need to help you compute a class width. Using the formula introduced in class, please find the class width. EXPLAIN how you arrived at your answer, and write your answer below.
Number of desired classes: 5
Largest value in the dataset: 273
Smallest number in the dataset: 17
Number of data in the data set: 84
Ji-Yoon loaded 84 Trucks in 14 hours. Find her loading speed in Trucks Per Hour.
Ji-Yoon's loading speed is 6 trucks per hour.
How to determine the speed of loading the truckFrom the question, we have the following parameters that can be used in our computation:
Ji-Yoon loaded 84 Trucks in 14 hours
Ji-Yoon's loading speed an be calculated by dividing the total number of trucks loaded (84) by the number of hours it took to load them (14):
This is repesented as
84/14 = 6
Hence, the speed is 6 trucks per hour
Read more about speed at
https://brainly.com/question/3518342
#SPJ1
from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.
There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.
Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.
So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
To learn more about the number, visit:
brainly.com/question/17429689
#SPJ4
The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.
There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.
Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.
So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.
To learn more about Number
brainly.com/question/17429689
#SPJ4
in fall 2020, the department has a cohort of 100 mds juniors. students in the class are enrolled in various classes including stor 435 (undergraduate probability), math 547 (linear algebra for applications) and comp 401 (foundations of programming). to simplify notation below i will denote these as prob., la and comp. assume the classes are not taught at the same time so there can be students who are taking all 3 courses. further there can also be students who are taking none of these 3 courses. 65 of these students are in prob, 45 in la and 40 in comp. there are 25 students that are in both prob. and comp, 20 that are in both la and comp, and 30 that are in both prob. and la. in addition, there are 10 students taking all 3 classes. how many students are taking none of the classes? (you can use venn diagrams for this problem.)
30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
To learn more about intersection visit: brainly.com/question/28337869
#SPJ4
30 students are taking none of the classes.
We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.
In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.
So, we can apply PIE as follows:
students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)
Using the given information, we have:
students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)
students taking none of the classes = 100 - (95 - 25)
students taking none of the classes = 100 - 70
students taking none of the classes = 30
Hence, 30 students are taking none of the classes.
To learn more about Intersection
brainly.com/question/28337869
#SPJ4
David's school is more than 8. 5 miles from his house. Let x represent the distance between David's house and school
The distance between David's house and school is definitely greater than 8.5miles as his school is more than 8.5 miles.
The answer must not be 8 , because as David stays 8.5 miles distance more from his school. An Inequality for a is a>8.5.
The illustration of two expressions by inequal symbol is known as inequality mathematical statement in algebra. It has non equal expressions on both sides. The inequality shows the values on the left side should be bigger or smaller than the expression on the right. The relationships between two algebraic expressions that are expressed using inequality symbols are literal inequalities. An algebraic expression is an expression built up from constant algebraic variables, numbers and the operators.
So the distance between David's house and school must be the value greater than 8.5
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ4
There are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks are there?
Answer:
There are 5 ducks
Step-by-step explanation:
2 ducks behind
1 duck in the middle
2 ducks infront
Dennis is 55 5/6 inches tall. Dwight is 1 1/3 inches shorter than Dennis and Jane is 1 1/4 inches shorter than Dwight. How tall is Jane?
Answer:
53 1/4
Step-by-step explanation:
55 5/6 - 1 1/3 - 1 1/4 Rewrite with a common denominator
55 10/12 - 1 4/12 - 1 3/12
55 10/12 - 1 4/12 = 54 6/12
54 6/12 - 1 3/12
53 3/12
53 1/4
How much fencing does she need?
Answer: 24 feet
Step-by-step explanation:
Perimeter: 2(length+width)
2(7+5)
14+10=24
an $m \times n \times p$ rectangular box has half the volume of an $(m 2) \times (n 2) \times (p 2)$ rectangular box, where $m, n$, and $p$ are integers, and $m \le n \le p$. what is the largest possible value of $p$?
The largest possible value of p can be determined by analysing the ratio of the volumes of the two rectangular boxes.
The volume of the first box is V1 = m*p*n and the volume of the second box is [tex]$V2 = (m2)\cdot (n2)\cdot (p2)$[/tex]. Therefore, we can set up the following equation to solve for p:
[tex]$\frac{V1}{V2} = \frac{mnp}{(m2)(n2)(p2)} = \frac{1}{2}$[/tex]
Solving for p gives us the following:
[tex]$p = \sqrt[3]{\frac{2(m2)(n2)}{mn}}$[/tex]
Since m, n, and p must all be integers, the largest possible value of p is the largest integer such that
[tex]$p \le \sqrt[3]{\frac{2(m2)(n2)}{mn}}$.[/tex]
Learn more about Volume:
https://brainly.com/question/463363
#SPJ4
if l is parallel to m find x
The correct answer fort parallel angles is x = 33° and y = 10°.
What is an example of a similar angle?The angles created when a transversal intersects two parallel lines are known as corresponding angles. Opening and shutting a lunchbox, completing a Rubik's cube, and an infinite stretch of parallel train lines are common examples of identical angles.
Angle 3y + 20° and angle 5y are parallel angles.
3y + 20° = 5y
2y = 20°
y = 10°
Angles 2x - 16° and 3y + 20° are in direct opposition to one another.
3y + 20° = 2x - 16°
Put the value of angle y in the equation.
3(10) + 20 = 2x - 16
30 + 20 = 2x - 16
50 = 2x - 16
2x = 66
x = 33
As a result, the angles are 33° for x and 10° for y.
To know more about parallel angles visit:-
https://brainly.com/question/7849620
#SPJ1
Question:
Find the value of x for which l is parallel to m. The diagram is not to scale. Lines l and m are parallel.
A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40kph. What is its average speed for the whole journey?
The average speed of the whole journey is 24 kilometres per hour.
How to find the average speed of the journey?The average speed is the total distance travelled by the object in a particular time interval.
A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40km/h.
Therefore, the average speed for the whole journey can be calculated as follows:
The total distance travelled is 120 km.
Hence,
total time = 120 / 60 + 120 / 40
total time = 2 + 3 = 5 hours
Therefore,
average speed = total distance / total time taken
average speed = 120 / 5
average speed = 24 km/hr
learn more on average speed here: https://brainly.com/question/29798030
#SPJ1
Use common logarithms to approximate log9 72 to four decimal places. (Show your common
log and your answer).
log9 72 to four decimal places is 2.8594
To approximate log9 72 using common logarithms, we can use logarithmic properties and logarithmic tables.
First, we can rewrite 72 as [tex]9^3[/tex] to find the exponent that gives us 72:
log9 72 = log9 ([tex]9^3[/tex]) = 3
Now, we can use logarithmic tables or a calculator to find the common logarithm of 9, which is 0.954243:
log10 9 = 0.954243
Finally, we can divide the result by the common logarithm of 10 to find the logarithm to base 9:
log9 72 = (1/log10 9) * log10 72 = 0.954243 * log10 72 ≈ 2.859437
log9 72 to four decimal places is 2.8594.
To learn more about logarithmic properties:
https://brainly.com/question/30339791
#SPJ4
What is a fundamental solution in differential equations?
The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.
What is the differential equations?
A differential equation is an equation that relates an unknown function to its derivatives. It describes the behavior of a physical, biological, or engineering system in terms of changes in variables over time.
A fundamental solution in differential equations is a particular solution to a differential equation that contains arbitrary constants. It is called "fundamental" because it is a building block for constructing more general solutions to the equation. The general solution to a differential equation can be found by adding a linear combination of several fundamental solutions. The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.
To learn more about differential equations, Visit
https://brainly.com/question/1164377
#SPJ4