Answer:
Step-by-step explanation:
To find the frequency for which the particular solution to the differential equation has the largest amplitude, we first need to know the differential equation we are working with. However, since you didn't provide the specific differential equation, let's work with a general example: a forced harmonic oscillator. The equation for a forced harmonic oscillator can be written as:
m * d²x/dt² + c * dx/dt + k * x = F0 * cos(ωt)
where:
m is the mass of the oscillator
x is the displacement of the oscillator
c is the damping coefficient
k is the spring constant
F0 is the amplitude of the external force
ω is the angular frequency of the external force
For this type of equation, we can find the particular solution in the form:
x_p(t) = X * cos(ωt - δ)
where:
X is the amplitude of the particular solution
δ is the phase angle
We can rewrite the differential equation in the frequency domain by substituting x(t) = X * cos(ωt - δ) and its derivatives into the original equation, then applying the trigonometric identities. After simplifying, we can find the expression for X, the amplitude of the particular solution:
X = F0 / sqrt((k - mω²)² + (cω)²)
To find the frequency for which the particular solution has the largest amplitude, we need to maximize X with respect to ω. To do this, we can find the critical points by differentiating X with respect to ω and setting the result to zero:
dX/dω = 0
To simplify the problem, we can define the damping ratio ζ = c / (2 * sqrt(m * k)) and the undamped natural frequency ω_n = sqrt(k / m). The expression for X becomes:
X = F0 / sqrt((ω_n² - ω²)² + (2 * ζ * ω_n * ω)²)
Now, we differentiate X with respect to ω and set it to zero. Solving for ω, we get:
ω = ω_n * sqrt(1 - 2ζ²)
This is the frequency for which the particular solution to the differential equation has the largest amplitude, assuming a positive frequency and that the damping ratio ζ is less than 1 / sqrt(2). Otherwise, the system will be overdamped, and there will be no resonant frequency.
the frequency for which the particular solution to the differential equation has the largest amplitude is:
ω = √(γ/2 - β^2)
To find the frequency for which the particular solution to the differential equation has the largest amplitude, we can assume that the particular solution is of the form:
y(t) = A*cos(ωt + φ)
where A is the amplitude, ω is the frequency, and φ is the phase angle.
Substituting this form of y(t) into the differential equation gives:
-ω^2Acos(ωt + φ) - 2βωAsin(ωt + φ) + γA*cos(ωt + φ) = f(t)
Simplifying this equation gives:
(A/|D|)[γcos(ωt + φ) - ω^2cos(ωt + φ) - 2βω*sin(ωt + φ)] = f(t)
where |D| is the modulus of the denominator of A*cos(ωt + φ) and is given by:
|D| = √[ (γ - ω^2)^2 + (2βω)^2 ]
To find the frequency for which the amplitude of the particular solution is largest, we need to minimize the modulus of the denominator |D| over all frequencies ω. We can do this by finding the critical points of |D| with respect to ω and then checking which of these critical points correspond to a minimum.
Differentiating |D| with respect to ω gives:
d|D|/dω = [2ω(γ - ω^2) - 4β^2ω]/|D|
Setting this equal to zero and solving for ω gives:
ω = ±√(γ/2 - β^2)
We can see that there are two critical points for |D|, one positive and one negative. To check which of these corresponds to a minimum, we can use the second derivative test:
d^2|D|/dω^2 = (2γ - 6ω^2)/|D|^3
Substituting ω = ±√(γ/2 - β^2) into this expression gives:
d^2|D|/dω^2 = ±4√2β^3/γ^(3/2)
Since β and γ are both positive, the second derivative is negative for both critical points, which means that they both correspond to maxima of |D|. The positive critical point corresponds to the frequency for which the amplitude of the particular solution is largest.
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(b) a hospital wants to select a minimum temperature for requiring further medical tests. what should that temperature be, if we want only 2 % of healty people to exceed it?
The temperature should be 99.471° F. If we want only 2.0% of healthy people.
Given that:
μ = 98.20
σ = 0.62
Determine the z-score in the normal probability table in the appendix that corresponds with a probability of:
1 − 0.02 =0.98
It is calculated by subtracting the population mean from the individual raw scores and dividing the difference by the population standard deviation. The process of converting raw scores to standardized scores is called standardization or normalization (although "normalization" can refer to different types of comparisons; see Normalization for more information).
The standardized score is the value x decreased by the mean and then divided by the standard deviation:
Z = X - μ / σ
⇒ x = μ+ zσ
= 98.20+ (2.05)(0.62) = 99.471
Therefore, Only 2% of the healthy people exceed 99.471° F.
Complete Question:
Assume that human body temperatures are normally distributed with a mean of 98.20 F and a standard deviation of 0.62∘F. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)
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Find the solution(s) to 2x² + 5x-3 = 0. Check all that apply.
A. x = -3
B. x = 1/2
C. x = -1/2
D. X = 2
E. x = 3
Answer:
A and B
Step-by-step explanation:
Let's factor this the "old fashioned" way. The standard form of a quadratic is
[tex]y=ax^2+bx+c[/tex]
If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.
We need to find the product of our a and c. Our a = 2 and our c = -3. So that gives us a -6. Now we have to find the factors of 6 (the negative right now doesn't matter so much). The factors of 6 are 1, 6 and 2, 3. Both of those possibilities will work to give us a +5, which is the linear term. Putting in the 2, 3 first:
[tex]0=2x^2+3x+2x-3[/tex]
Now group the terms together into groups of 2:
[tex]0=(2x^2+3x)+(2x-3)[/tex]
The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same. In the first term we can factor out a common x, and in the second term, the only thing common is a 1. So that looks like this:
[tex]x(2x+3)+1(2x-3)[/tex]
What's inside those parenthesis are not actually identical, so 2 and 3 won't work. Lets try 1 and 6. For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative. So let's try that:
[tex](2x^2+6x)+(-x-3)[/tex]
In the first term we can factor out the common 2x and in the second term we can factor out the common -1:
[tex]2x(x + 3) - 1(x + 3)[/tex]
Now what's common is [tex](x + 3)[/tex], so we can factor THAT out and what is left over is [tex]2x - 1[/tex]:
[tex](x + 3)(2x - 1) = 0[/tex]
If [tex]x + 3 = 0[/tex], then [tex]\bold{x = -3}[/tex]
and if [tex]2x - 1 = 0[/tex], then [tex]2x = 1[/tex] and [tex]\bold{x = \frac{1}{2} }[/tex]
What is the y-coordinate of the point that divides the
directed line segment from J to K into a ratio of 5:1?
v = (m²+ n )(V₂ - V₁) + V₁
-8
O-5
00
06
o
The point with the y-coordinate of 0 splits the directed line segment from J to K into a 5:1 ratio.
What is x and y-coordinate?An X coordinate value denotes a location that is relative to a point of reference to the east or west. A Y coordinate value denotes a location that is relative to a point of reference to the north or south.
Considering J (1, -10) and K (7, 2)
In this case, let's suppose that point L divides the directed line segment from J to K into a 5:1 ratio.
We know that from coordinate geometry's inherent characteristics.
The point's coordinates are (x1, y1), (x2, y2) where they meet in the ratio of m:n.
[tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]
Now putting the respective values,
= ([tex](\frac{(5 .1)(1 .1) }{5 +1} , \frac{(5 . 2)(1 . (-10))}{5+1}[/tex]
= (6, 0)
Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
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Pleaseeeeee Helppppp Meeeeeeeeeeeeeee-
(Subject: Highschool, Algebra)
Answer:
I have graphed it in the explanation part.
Step-by-step explanation:
First, we have to rewrite the two equations in the form y = mx + b.
2x - y = 4
-y = -2x + 4
y = 2x - 4
x - y = -2
-y = -x - 2
y = x + 2
As we see from the graph, the intersect point is at (6, 8)
rovide an example of when you might want to take a systematic random sample instead of a simple random sample, and explain what the advantages of a systematic random sample might be
A stratified random sample is preferred when the population is heterogeneous, ensuring a proportional representation of each subgroup, and allowing for more accurate comparisons and reliable inferences about the population.
When the community under study is heterogeneous, which means it can be broken down into different divisions or sectors, a stratified random sample is usually favored over a basic random sample.
In this situation, a stratified random sample makes it possible for each stratum to be proportionally reflected in the sample, guaranteeing that each subset is properly represented. When analyzing the differences or parallels between various subgroups, this method can be especially helpful.
For instance, a business might want to poll to find out how satisfied customers are with its offerings. They might choose to select a stratified random sample based on customer demographic categories or regions as opposed to a straightforward random sample.
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The question is -
Provide an example of when you might want to take a stratified random sample instead of a simple random sample and explain what the advantages of a stratified random sample might be.
17. reflection
centered
in y = 1 followed by a dilation
at B' with a scale factor of 2
y
O
A
A
C
B
X
89
Answer:
See below
Step-by-step explanation:
Helping in the name of Jesus.
Answer the question Good Luck
Answer:
96
Step-by-step explanation:
Because it is
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 10 feet. Container B has a diameter of 8 feet and a height of 17 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Answer:
the height of the water in Container B is 22.48 feet.
Step-by-step explanation:
you were asked to find the p-value for the test statistic, given the following information: a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 423 gram setting. it is believed that the machine is underfilling the bags. a 26 bag sample had a mean of 415 grams with a variance of 256 . assume the population is normally distributed. a level of significance of 0.02 will be used. find the p-value of the test statistic.
Answer:
A.
Step-by-step explanation:
IM GUEssing that thi sis it
Thabang used 1/5 of his money to buy a CD. Calculate how much the CD cost
Answer: divide 1/5 by the price of the CD
Formula: A = P(1+r/n)(nt)
Step-by-step explanation: , if you have a $1,000 CD with a term of three years and an APY of 5%, you can multiply $1,000 by 5% to find the interest
Answer:
20% of his money
Step-by-step explanation:
it's 1/5 of 100% of his money
If a varies jointly as b and c, find a when b= 4 and c= −3
a= 24 when b= 8 and c= 12
In the proportion , a=-3 when b=4 and c=-3.
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here the given is a directly proportional to b and c . then,
=> a ∝ bc
Now converting into equation add constant then
=> a = kbc [ where k is constant]
Now a= 24 when b= 8 and c= 12 then,
=>24=k(8*12)
=> k = 24/(8*12) = 2/8 = 1/4
Then the equation is [tex]a=\frac{1}{4}bc[/tex]
Now b=4 and c=-3 then,
=> a= (1/4)*4*-3 = -3.
Hence a=-3 when b=4 and c=-3.
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Answer:
a = -3
Step-by-step explanation:
Calculate the length of AC
The calculated length of AC from the right triangles is 320 units
Calculating the length of ACfrom the question, we have the following parameters that can be used in our computation:
The right triangle
The length of the segment AC is calculated as
sin(30) = 160/AC
Make AC the subject
So, we have
AC = 160/sin(30)
When evaluated, we get
AC = 320
Hence the length of AC is 320 units
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i need to know the length of side EF and side FG
The lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.
What are the lengths?
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.
Let's start by finding the measure of ∠G, using the fact that the sum of the angles in a triangle is 180 degrees:
m∠G = 180° - m∠E - m∠F = 180° - 39° - 86° = 55 °
Now we can use the Law of Sines to find the lengths of EF and FG:
EF/sin(F) = EG/sin(G)
EF/sin(86) = 7.9/sin(55)
EF = sin(86)*7.9/sin(55) ≈ 10.2
Similarly,
FG/sin(E) = EG/sin(G)
FG/sin(39) = 7.9/sin(55)
FG = sin(39)*7.9/sin(55) ≈ 5.8
Therefore, the lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.
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Complete question is: The lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.
Pleaseeee help me find this answerrrrrrrr
The function is linear because as the x-value increases, the y-values increases.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the y-intercept or initial number.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 3)/(0 - 1)
Slope (m) = -2/-1
Slope (m) = 2
Based on the information provided above at point (0, 9), an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 5x + 9
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Does anyone have the answer for this ??? Giving brainliest
ANSWERS:
A. 6 old printers would produce the batch of magazines in less time than 2 new printers
B. Using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers
EXPLANATIONS:
a) To determine which option would produce a batch of magazines in less time, we need to compare the printing rates of each option.
The old printers can produce a batch of magazines in 30 minutes, which means their printing rate is:
5 printers / 30 minutes = 1/6 printers per minute
The new printers can produce the same batch of magazines in 16 minutes, which means their printing rate is:
4 printers / 16 minutes = 1/4 printers per minute
If we use 6 old printers, their printing rate would be:
6 printers / 30 minutes = 1/5 printers per minute
If we use 2 new printers, their printing rate would be:
2 printers / 16 minutes = 1/8 printers per minute
Therefore, 6 old printers would produce the batch of magazines in less time than 2 new printers.
b) To determine how much less time it would take to produce the batch of magazines with 6 old printers, we can set up a proportion:
1/5 printers per minute = 1/x minutes
Solving for x, we get:
x = 5 minutes
Therefore, using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers.
If AABC is a triangle with mzC = 90°, which of the
following must be true about angles A and B?
OA.
1
sin A
O C.
=
O B. cos A = 1
tan A +
O D. sin A
sin B
=
1
tan B
cos B
cos B
=
1
Answer:
C. cos A = 1 and sin B = 1.
Step-by-step explanation:
The angles in a triangle must add up to 180°. Since angle C is 90°, angles A and B must add up to 90°. Therefore, the sine of angle A and the sine of angle B must both equal 1. Since the sine of an angle is equal to the cosine of its complement, cos A = 1 and sin B = 1.
x^3 = -216/343
Round to the nearest tenth. Put the negative sign in the numerator.
Putting the negative sign to the numerator, we have the value of x = -6/7.
What is Algebraic expression?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
The given equation is:
x³ = -216/343
To solve for x, we can take the cube root of both sides of the equation:
∛(x³) = -∛(216/343)
x = -∛(216/343)
Solving for numerator:
216 = 6 × 6 × 6
∛216 = 6
Solving for denominator:
343 = 7 × 7 × 7
∛343 = 7
Therefore,
x = -∛(216/343)
x = -(6/7)
x = -6/7
Putting the negative sign to the numerator, we have the value of x = -6/7.
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Mary is 3 times as old as her son. In 12 years Mary will ve twice as old as her son. How old are each of them now
Answer:
Mary is 36 years old
Her son is 12 years old
Step-by-step explanation:
Let's assume, that Mary's son is x years old and Mary is 3x years old
Let's write 2 equations according to the given information:
x = 3x (Mary is 3 times older than her son)
3x + 12 = 2(x + 12) (after 12 years, she will be 2 times older than her son)
3x + 12 = 2x + 24
3x - 2x = 24 - 12
x = 12
That means, Mary's son is 12 years old
Mary is 3 × 12 = 36 years old
Centerville is 7 miles due north of the airport, and Newberry is due east of the airport. If the distance between Centerville and Newberry is 10 miles, how far is Newberry from the airport? If necessary, round to the nearest tenth.
Answer:
12.2 miles
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Here, A represents the airport, C represents Centerville, and N represents Newberry. We want to find the distance x between N and A.
Since Centerville is 7 miles due north of the airport, the distance AC is 7 miles. Since the distance between Centerville and Newberry is 10 miles, we can use the Pythagorean theorem to find the distance AN. So the distance between Newberry and the airport is approximately 12.2 miles.
(x + 4) (2x - a) = 0 In the given equation, a is a constant. If the equation has the solutions X = 4 and x = -4, what is the value of a?
Since we know that the equation has the solutions [tex]x = 4[/tex] and [tex]x = -4[/tex] the value of a could be either [tex]8[/tex] or [tex]-8[/tex] .
What is the product of two factors?We know that the product of two factors is equal to zero only when at least one of the factors is zero.
[tex](x + 4) \ (2x - a) = 0[/tex]
This equation has two factors: [tex](x + 4)[/tex] and [tex](2x - a)[/tex] . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.
Setting [tex](x + 4)[/tex] equal to zero, we get:
[tex]x + 4 = 0[/tex]
[tex]x = -4[/tex]
This means that [tex]-4[/tex] is one of the solutions of the equation.
Setting [tex](2x - a)[/tex] equal to zero, we get:
[tex]2x - a = 0[/tex]
[tex]2x = a[/tex]
[tex]x = a/2[/tex]
This means that [tex]a/2[/tex] is another solution of the equation.
Since we know that the equation has the solutions [tex]x = 4[/tex] and [tex]x = -4[/tex] , we can substitute these values into the expression we found for x in terms of a to get:
[tex]a/2 = 4[/tex] or [tex]a/2 = -4[/tex]
Solving for a in each case, we get:
[tex]a = 8[/tex] or [tex]a = -8[/tex]
Therefore, the value of a could be either [tex]8[/tex] or [tex]-8[/tex] .
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write an equation of the line passing through (-1,3) and (2,4). give the answer in standard form.
the equation of the line in standard form is
Answer:
Step-by-step explanation:
Hello : let A(-1,3) B(2,4)
the slope is : (YB - YA)/(XB -XA)
(4-3)/(2+1) = 1/3
an equation is : y=ax+b a is a slope
y = 1/3x +b
the line through point B (2,4) : 4 = (1/3)(2)+b
b =10/3 the equation is : y =1/3x+10/3
20/23 as a decimal rounded
Answer:
≈ 0,9
Step-by-step explanation:
To the nearest tenth:
[tex] \frac{20}{23} ≈0.9[/tex]
why might a repeated-measures study require half the number of subjects compared to a similar matched-subjects study with the same number of scores?
The repeated measures studies require fewer subjects than matched subjects studies with the same number of outcomes is that repeated measures designs reduce intersubject variability.
In repeated measures studies, each participant is measured multiple times under different conditions or treatments.
Whereas, In a matched-subjects study, each participant in the treatment group is compared to participants in the control group.
Intersubject variability can be large, and differences between treatment and control groups may be attributed to differences in these individual characteristics.
However, in a repeated-measures design, each participant served as its own control, reducing inter-subject variability.
This makes it easier to recognize differences in treatment conditions and can increase effect sizes.
Therefore, a repeated measures study may require fewer subjects to achieve the same statistical power as a matched subjects study with the same number of outcomes.
However, it is important to note that repeated measures designs may have their own limitations: Potential Order Effect or Practice Effect.
These limitations should be carefully considered when designing a study, and an appropriate design should be chosen based on the research question and the nature of the data.
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4
Triangle ABC is shown. Use the graph to answer the question.
Determine the coordinates of the image if triangle ABC is translated 5 units down
OA(-4,-2), B(4,-2). C'(0, 2)
OA(1, -7), 8(9,-7). C'(5,-3)
OA(1, 3), B(9, 3), C'(5, 7)
Please help me, its homeowkr
Determine the proper prism's base. The base takes the form of the prism's base. Calculate the base's area. The appropriate prism's height should be measured. Multiply the base's area by the prism's height.
What is prism in geometry?A prism is a three-dimensional geometric object with two parallel, congruent bases and rectangular sides connecting the bases. The prism's name is derived from the design of its base. For instance, the bases of a triangular prism, rectangular prism, and so on, are all triangular. The distance between the two parallel bases of a prism determines its height. The formula V = Bh, where B is the area of the base and h is the height of the prism, can be used to determine the volume of a prism.
The formula V = Bh can be explained as follows:
Determine the proper prism's base. The base takes the form of the prism's base. The base, for instance, might be a triangle, square, rectangle, or any other polygon.
Calculate the base's area. The formula's B stands in for this.
The appropriate prism's height should be measured.
To get the volume, multiply the base's area by the prism's height.
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help asapp!!!!!!!!!!!!
HELPPPPPPPPP PLEASE HURRY !!!!!!!!!!!!!!!!! GIVING 40 POINTS!!!!!!!!!!!!!!!!!!
HELPPPPPPPPPPPPP
This is used to calculate the height of the object at any time t during its flight.
The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.
The acceleration due to gravity is taken to be -9.8 m/[tex]s^2[/tex] (negative since it acts downward), and the formula for the height is derived from the equation of motion:
h(t) = -1/2 [tex]gt^2[/tex] + vt + hi
Where:
g = 9.8 m/[tex]s^2[/tex] (acceleration due to gravity)
t = time (in seconds)
v = initial velocity (in meters per second)
hi = initial height (in meters)
The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).
This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/[tex]s^2[/tex] until it reaches the maximum height and then starts to fall back down.
So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.
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In a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 50 kids
Yes, there could be total number 50 kids in the group. If there are 50 kids in the group, then more than half of them would be boys, which means there would be at least 26 boys in the group.
Let B be the number of boys and G be the total number of kids in the group.
Given that more than 1/2 are boys, we have B > G/2. Also, given that the boys are less than 2/3 of the group, we have B < 2G/3.
If there are 50 kids in the group, then we have:B > 50/2
B > 25B < 50(2/3)
B < 33.33
B ≤ 33 (since B is an integer)
Therefore, the number of boys in the group can be any integer between 26 and 33, inclusive.
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a medical devices company wants to know the number of hours its mri machines are used per day. a previous study found a standard deviation of four hours. how many mri machines must the company find data for in order to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval?
The medical devices company must find data for at least 543 MRI machines.
How to calculate the number MRI machines?To calculate the number of MRI machines needed for a 98% confidence interval with a margin of error of 0.20 hour, we need to use the formula:
n = [(z*σ)/E]²
where:
n is the sample sizez is the z-score for the desired confidence level (98% = 2.33)σ is the standard deviation (4 hours)E is the margin of error (0.20 hour)Substituting the values:
n = [(2.33*4)/0.20]²
n = 542.89
Rounding up to the nearest whole number, the medical devices company must find data for at least 543 MRI machines to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval.
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a group contains 5 men and 5 women. how many ways are there to arrange these people in a row if the men and women alternate?
The number of ways are there to arrange these people in a row if the men and women alternate is 2880.
The concepts of counting are permutation and combination, and they are used in a variety of contexts. A permutation is a list of the many configurations that may be created from the given set of items. Details are crucial in permutation because the order or sequence is crucial.
The techniques used to count the number of outcomes that can occur under different circumstances are permutation and combination. Combinations and permutations are also referred to as arrangements and choices, respectively. The sum rules and product rules may be used to conveniently apply counting according to the basic idea of counting.
5 men and 5 women sit around a table so that they all seat alternately
Formula used:
n! = n x (n - 1) x (n-2) x....... (n-n1)
According to the question,
5 Men sit alternate in 5! ways
5 women can be seated around the circle in (5 - 1)!
⇒ 5! × 4!
⇒ 5 × 4 × 3 × 2 × 1 × 4 × 3 × 2 × 1
⇒ 120 × 24
⇒ 2880
:. The number of ways is 2880.
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