Let [tex]X(s)[/tex] and [tex]Y(s)[/tex] denote the Laplace transforms of [tex]x(t)[/tex] and [tex]y(t)[/tex].
Taking the Laplace transform of both sides of both equations, we have
[tex]\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s[/tex]
[tex]\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}[/tex]
Eliminating [tex]Y(s)[/tex], we get
[tex]\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)[/tex]
Take the inverse transform of both sides to solve for [tex]x(t)[/tex].
[tex]\boxed{x(t) = \dfrac14 (1 - e^t)}[/tex]
Solve for [tex]Y(s)[/tex].
[tex](s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}[/tex]
Taking the inverse transform of both sides, we get
[tex]\boxed{y(t) = e^t - 1 + \dfrac14 t}[/tex]
Paul teaches math to five classes in sixth grade. he wants to measure the variation in the performances of students of each class. which measures will help him?
The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.
What are the measures of variation?
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1)
First quartile = 1/4 x (n + 1)
The mean absolute deviation is the average of the distance of a data set from its mean.
Mean absolute deviation = ∑ l x - m(x) l
Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.
Here are the options:
Mean absolute deviation
mean
interquartile range
median
mode
To learn more about interquartile range, please check: https://brainly.com/question/3966385
#SPJ1
mean absolute deviation
mean
median
interquartile range
mode
A pencil at a stationery store costs $1, and a pen costs $1.50. stella spent $21 at the store. she bought a total of 18 items. which system of equations can be used to find the number of pencils (x) and pens (y) she bought? x 18y = 21 x = 1.5y 18x y = 21 x = 1.5y x 1.5y = 21 x y = 18 1.5x y = 21 x = 18y
Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
The correct option is C.
What is liner equation?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
According to the given information:Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.
Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:
x + y = 18
We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,
1x + 1.5y = 21
Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:
X+1.5Y = 21, and X+Y = 18
equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
To know more about liner equation visit:
https://brainly.com/question/1347950
#SPJ4
answer????? with steps
Find the area of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal. 6
The area of the given semicircle is 56.574 sq. units. Half of the area of the circle is the area of the semicircle.
What is the area of the semicircle?The area of the semicircle is
A = [tex]\frac{1}{2}[/tex] πr² sq. units
Where r - radius
A semicircle is nothing but half part of the circle. So, its area is also half of the circle's area.
Calculation:It is given that,
The radius of the semicircle is
r = 6
So, its area in terms of π is
A = [tex]\frac{1}{2}[/tex] πr²
= [tex]\frac{1}{2}[/tex] × π × 6²
= 18π sq. units
On substituting π = 3.143, we get
A = 18 × 3.143 = 56.574 sq. units
Thus, the area of the given semicircle in terms of π is 18π or in terms of π =3.143 is 56.574 sq. units.
Learn more about semicircle here:
https://brainly.com/question/15656472
#SPJ1
An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are shaded.
An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the area of the shaded regions.
Shaded area = area of the
– area of the + area of the – area of the
Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.
Find the expression for the area of the shaded regions:From the question we can say that the Hexagon has three shapes inside it,
PentagonSquareTriangleAlso it is given that,
An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.
From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.
A pentagon is shown inside a regular hexagon.
Area of first shaded region = Area of the hexagon - Area of pentagonAn equilateral triangle is shown inside a square.
Area of second shaded region = Area of the square - Area of equilateral triangleThe expression for total shaded region would be written as,
Shaded area = Area of first shaded region + Area of second shaded region
Hence,
⇒ Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle.
Learn more about area of a shape here:
brainly.com/question/16501078
#SPJ1
Answer:
Regular Hexagon
Regular Pentagon
Square
Equilateral Triangle
Step-by-step explanation:
E2020 Geometry B!! :3
Elsa went to Malacca with three friends. The total amount spent by them is RMx. If Elsa spent RM 145, and the amount spent by each of her three friends did not exceed RM 110 per person, which of the following cannot be the value of x.
The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x
InequalityTotal amount spent = RMxAmount spent by Elsa = RM 145Amount spent by each of her three friends = RM 110Elsa + 3(her friends) ≤ Total
145 + 3(110) ≤ x
145 + 330 < x
475 ≤ x
Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x
Learn more about inequality:
https://brainly.com/question/11613554
#SPJ1
Word Problem On Division
1. a cup can hold 2/9 ( fraction) litres of water. how many cups of water can be filled with 3 litre bottle?
Applying the knowledge of fractions, the number of cups of water that will fill a bottle of 3 liters is calculated as: 13.5 cups.
What are Fractions?Fractions are numbers that indicate a part of whole numbers. For example, 2/9 of a liter means 2/9 of a part of 1 liter.
What is a Proportion?In math, a proportion is simply and equation that sets to ratios equal to each other.
To solve the problem given, create a proportion then use cross product to find the wanted value, which is the number of cups of water that can be filled into a 3-liter bottle.
Let x represent the cups of water we are looking for.
1 cup = 2/9 liter
x = 3 liters
We would have:
(1)(3) = (2/9)(x)
3 = 2x/9
(3)(9) = 2x
27/2 = x
x = 13.5
The number of cups of water to fill a 3-liter bottle is: 13.5.
Learn more about fractions on:
https://brainly.com/question/78672
#SPJ1
Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?
Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3
The question has to do with line division
What is line division?This is the division of a line into a given ratio.
How to find the coordinate of Q?
Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.
Let
x₁ = coordinate of P = -3, x₂ = coordinate of R = -3 and x₃= coordinate of Q.Since R divides PQ in the ratio, 1:3, we have that
PR/RQ = 1/3
(x₂ - x₁)/(x₃ - x₂) = 1/3
Substituting the values of the variables into the equation, we have
(x₂ - x₁)/(x₃ - x₂) = 1/3
(-1 - (-3))/(x₃ - (-3)) = 1/3
(-1 + 3)/(x₃ + 3) = 1/3
2/(x₃ + 3) = 1/3
x₃ + 3 = 2 × 3
x₃ + 3 = 6
x₃ = 6 - 3
x₃ = 3
So, the x-coordinate of Q is 3
Learn more about line division here:
https://brainly.com/question/13018136
#SPJ1
If the infinite curve y = e^−2x, x ≥ 0, is rotated about the x-axis. Find the area of the resulting surface.
The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
Learn more about area of infinite curve here
https://brainly.com/question/3139455
#SPJ4
hey can you help me with this one ?
Answer:
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
Step-by-step explanation:
[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]
[tex]3a^{2} -10a-112=0[/tex]
[tex](3a+14)(a-8)=0[/tex]
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]
So, required values of " a " are :
[tex]\qquad \sf \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]
what is a real world example of a rational function, and how could you graph it and put it in a table?
An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.
What is a rational function?This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.
The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.
How to graph a real world situationFirst you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.
Read more on the rational function here: https://brainly.com/question/12434659
#SPJ1
Dario is the kicker for his high school football team. The path of the football when kicked can be
represented by the quadratic function y = -16x²
-16x2 +85x, where x is the horizontal distance (in
feet) and y is the height (in feet). How far does Dario kick the football? Express your answer as a
decimal rounded to the nearest hundredth.
Answer:
Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession. He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point. It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.
Step-by-step explanation:
We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods. The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.
Differentiate
y = -16x² +85x
The first derivative produces an equation that gives us the slope of the line at any point x. At the ball's top height, it stops and reverses direction, a point at which the slope is zero.
y = -16x² +85x
d(y)/d(x) = -32x + 85
0 = -32x + 85
32x = 85
x = 2.66 feet horizontal distance when the ball reaches its peak.
At x = 2.66, y is 112.9 feet high
When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.
Graph:
See attached plot of the function.
Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.
After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.
Trigonometry Question:
Find all solutions on the interval [0,2π)
12sin^2(x)+cos(x)-6=0
Recall the Pythagorean identity,
[tex]\sin^2(x) + \cos^2(x) = 1[/tex]
Use it to rewrite the equation in terms of cos only.
[tex]12 (1 - \cos^2(x)) + \cos(x) - 6 = 0[/tex]
[tex]-12 \cos^2(x) + \cos(x) + 6 = 0[/tex]
Factorize the left side.
[tex]-(3\cos(x) + 2) (4\cos(x) - 3) = 0[/tex]
Solve the two cases for [tex]\cos(x)[/tex].
[tex]3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0[/tex]
[tex]\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34[/tex]
From the first equation, we get one family of solutions:
[tex]\cos(x) = -\dfrac23[/tex]
[tex]x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi[/tex]
From the second equation, we get another family:
[tex]\cos(x) = \dfrac34[/tex]
[tex]x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi[/tex]
where [tex]n[/tex] is an integer.
We get solutions in the given domain for
[tex]n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}[/tex]
[tex]n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}[/tex]
PLEASE HELP!!!!!! I CAN’T UNDERSTAND!!!! How to do this one
The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
What is binomial expansion?Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.
What is Pascal's triangle?Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.
What is the coefficient of t²s⁵ in the expansion of (2t + s)⁷?
The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.
So, each term is ⁿCₓaˣbⁿ⁻ˣ.
Comparing (a + b)ⁿ with (2t + s)⁷,
a = 2t, b = s and n = 7.So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ
= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ
So, the coefficient term is ⁷Cₓ(2)ˣ
Now for the term t²s⁵, x = 2.
So, the coeficient term is ⁷Cₓ(2)ˣ = ⁷C₂(2)²
= 7!/2!(7 - 2)! × 4
= 7!/2!5! × 4
= 7 × 6 × 5!/(2! × 5!) × 4
= 7 × 6/2 × 4
= 7 × 3 × 4
= 84
So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
Learn more about binomial expansion here:
https://brainly.com/question/25086608
#SPJ1
A sample of n = 64 scores is selected from a population with µ = 80 with σ = 24. On average, how much error is expected between the sample mean and the population mean?
The expected error between the sample mean and the population mean is 3.
In this problem, we have been given :
population mean (μ) = 80,
standard deviation (σ) = 24,
sample size (n) = 64
We know that,
The Central Limit Theorem states that, for a normally distributed random variable X, with mean μ and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation, which is also called standard error [tex]s=\frac{\sigma}{\sqrt{n} }[/tex]
We need to find the error between the sample mean and the population mean.
standard error
= σ /√n
= 24 /√64
= 24 / 8
= 3
Therefore, the expected error between the sample mean and the population mean = 3
Learn more about the Central Limit Theorem here:
https://brainly.com/question/15404124
#SPJ4
Point P is on line segment \overline{OQ}
OQ
. Given PQ=x+7,PQ=x+7, OP=4x-10,OP=4x−10, and OQ=4x,OQ=4x, determine the numerical length of \overline{OQ}.
OQ
.
Answer:
Step-by-step explanation:
4x - 10 + x + 7 = 4x
5x - 3 = 4x
-3 = -x
x = 3
4(3) - 10 = 12 - 10 = 2
3 + 7 = 10
10+2 = 12
4(3)= 12
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y=60x+30
y=60x+30 represents what Health Club B charges. Health Club A charges a $50 sign-up fee and $27 per month.
Answer is Healthclub A costs $33 less in monthly fees than Healthclub B
The number next to the “x” is your rate.
So Healthclub A charges $33 less than B
A charges 27 monthly fee
B charges 60 monthly fee
60-27=33
Identify the slope type of the graph shown above.
Question 15 options:
A)
Undefined
B)
Zero
C)
Positive
D)
Negative
Answer:
Zero
Step-by-step explanation:
which is equivalent to (-2x^3y^5)^2
Answer:
[tex]4x^{6} y^{10}[/tex] A.
If "a", "b" and "c" vectors are in cyclic order then:
If a, b and c vectors are in cyclic order , the scalar product is equals to zero which makes Option C to be correct.
What are scaler and vector quantities?A vector can be regarded as quantities that posses both magnitude and a direction this is the opposite to scalar quantity which posses just the magnitude without any direction.
Geometrically, the vector can be described as the line segment, having its length as the magnitude with the arrow over it showing direction.
The scalar product can be gotten with the multiplication of the magnitudes of vectors .
Hence, If a, b and c vectors are in cyclic order , the scalar product is equals to zero .
Learn more about vectors at:
https://brainly.com/question/15519257
#SPJ1
CHECK THE COMPLETE QUESTION IN THE ATTACHMENT
Solve for the value of x in the diagram below. Show your work and explain the steps you used to solve.
Answer: x = 2
Step-by-Step Solution:
Given:
OH = WO = LW
OH = 2x + 1
WO = 3x - 1
LW = 5
To Find:
The value of 'x'
Solution:
We know, OH = WO = LW
So, equate any two of the values given :-
2x + 1 = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2
Hence, x = 2.
what is the solution to this equation 7x-3(x-6)=30
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
⨠ use the distributive property
[tex]\sf{7x-3(x-6)=30}[/tex]
[tex]\sf{7x-3x+18=30}[/tex]
⨠ combine like terms
[tex]\sf{4x+18=30}[/tex]
⨠ subtract both sides by 18
[tex]\sf{4x=30-18}[/tex]
[tex]\sf{4x=12}[/tex]
⨠ divide both sides by 4
[tex]\boxed{\sf x=3}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Profit is the difference between revenue and cost. the revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 30x – 130. the cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. the variable x represents the number of skateboards sold.
Profit function in terms of x = 33x + 390.
What is a profit in business?
In its simplest form, it's the amount left after subtracting your total expenses from your total revenue. The money remaining, your profits, can either be kept in the business and re-invested to finance future growth, or distributed as a draw or dividends to stakeholders.Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial
[tex]2x^{3} + 30x - 130[/tex]
The cost, in dollars, of producing the skateboards can be modeled by
[tex]2x^{3} -3x - 520[/tex]
Profit function = Revenue - cost
= [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]
= 33x + 390
Therefore, profit function in terms of x = 33x + 390
Learn more about profit
brainly.com/question/13538701
#SPJ4
How do you construct a frequency distribution table using sturge’s approximation
The steps to use to construct a frequency distribution table using sturge’s approximation is as below.
How to construct a frequency distribution table?The steps to construct a frequency distribution table using Sturge's approximation are as follows;
Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.
Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;
K = 1 + 3.322logN
where;
K= Number of classes
logN = Logarithm of the total number of observations.
Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size
Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.
Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.
Step 6; Distribute the data into respective classes:
Read more about frequency distribution table at; https://brainly.com/question/27820465
#SPJ1
Select true or false to tell whether the following conditional p q is true or false. Use the truth table if needed.
If 3 + 2 = 5, Then 5 + 5 = 10
The given condition on the basis of truth table is true.
According to the statement
we have given that the some condition p and q. and we have to find that the given condition is true or false on the basis of the truth table.
So, The given conditions are:
If 3 + 2 = 5, Then 5 + 5 = 10
Now,
The Truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered.
So, the given conditions are properly verified with the truth table. So, it is true.
So, The given condition on the basis of truth table is true.
Learn more about Truth table here
https://brainly.com/question/18575348
#SPJ1
Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party. If Mr. McConnell divides the pizza evenly among his 4 students, how much pizza will each student get?
If Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.
How much pizza will each student get?Given the data in the question;
Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party.McConnell divides the pizza evenly among his 4 students.First we convert the mixed fraction into an improper fraction.
6 2/3 = ( 6×3 + 2 )/3 = 20/3
Since McConnell divides the pizza evenly among his 4 students.
We will divide 20/3 by 4
20/3 ÷ 4
20/3 × 1/4
(20 × 1) / (3 × 4 )
20/12
5/3
Therefore, if Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.
Learn more about fractions here: brainly.com/question/10354322
#SPJ1
What is the perimeter of the given triangle?
10 units
16 units
17.2 units
19.2 units
Answer:
17.2 units
Step-by-step explanation:
You would use the Pythagorean Theorem to solve. The height (a) is 4 units. The base (b) is 6 units.
4^2 + 6^2 = sqrt(52)
This would mean that the hypotenuse is 7.211102550927979 units or 7.2 units (the square root of 4^2 + 6^2).
Now you would need to just add all three sides.
6 + 4 + 7.2 = 17.2 units
Hope that helps! Please mark me brainliest!
The volume occupied by 34 grams of brass is 4.0 cubic centimeters. the density of the brass is...
Answer:
8.5 g/cm^3
Step-by-step explanation:
Density = mass/volume
= 34 g / 4 cm^3 = 8.5 g/cm^3
Answer:
8.5 grams per cubic centimeter.
Step-by-step explanation:
Density = mass / volume
= 34 / 4
= 8.5 grams / cubic centimeter.
A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five times the age of the son. Six years from now the son’s age will be?
Answer:
20
Step-by-step explanation:
To solve this you have to make a system of equations.
Since the father and son's age sum up to 60, the first equation will be:
f + s = 60
Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:
6 - (5s) = f
Now, you have to solve the first equation to let it equal to s
f + s = 60
f = 60 - s
Plug in
6 - 5s = 60 - s
+s +s
6 - 4s = 60
-6 -6
---------------------
-4s = 54
----- -----
-4 -4
s ≅ 14
14 + 6 = 20
Answer:
20.
Step-by-step explanation:
x = father's age and y = son's age,
x + y = 60
x - 6 = 5(y - 6)
x - 5y = -24
Subtract this from first equation:
6y = 84
y = 14
So the son's age is 14.
Six years time son will be 20.
What will be the length of the diagonal of a rectangle of sides 6 m and 8 m?
Answer:
The length of the diagonal of a rectangle is 10m
Step-by-step explanation:
There is a visual below,
The diagonal of a rectangle has formed 2 right triangles.
This diagonal is called hypotenuse side length of a triangle
To find the hypotenuse, we can use the Pythagorean Theorem
a² + b² = c²
we are given the length of a and b, where a = 6 and b = 8
(6)² + (8)² = c²
36 + 64 = c²
100 = c²
√100 = c
10 = c
Learn more about the Pythagorean Theorem here: https://brainly.com/question/343682