Determine the steady-state current in the RLC circuit to be 0.68 A.
The equation for Lq′′ + Rq′ + 1/C q = E is used to find the steady-state current in each RLC circuit. The circuit parameters are L = 0.1 H, C = 0.01 F, R = 3 Ω, and E(t) = 5cos10t - 5sin10t.Lq′′ + Rq′ + 1/C q = E can be written as Ld²q/dt² + Rdq/dt + 1/C q = E(t)The current flowing through the circuit can be determined using this formula. To calculate the current, we can use E(t) = 5cos10t - 5sin10t.The current can be found using the equation q(t) = Q cos(wt - φ), where Q = I/Z, Z = √(R² + (wL - 1/wC)²), w = 2πf, and φ = tan⁻¹((wL - 1/wC)/R). Z, w, and φ can be calculated from the parameters of the circuit.Using the above formulas, the following is obtained.I = 5/√(3² + (10π x 0.1 - 1/(10π x 0.01))²) = 0.68 ADetermine the steady-state current in the RLC circuit to be 0.68 A.
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A sample of 10 widgets has a mean of 32.500 and standard
deviation of 6.050. At 90% confidence, the lower limit with 3
decimal places is
The lower limit with 3 decimal places at 90% confidence is 29.266.
To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.
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What is the perimeter of triangle jeg? 60 units 65 units 70 units 75 units
The perimeter of the triangle jeg is 60 units where the sides of the triangle are given.
What is perimeter?Perimeter is the total distance around the outer boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
According to question:EK = x + 5
KJ = x +5
FG = 2x
GH = 3x - 5
Assuming that the triangle is equilateral:
equate GH = FG
3x - 5 = 2x
solve for x
x = 5
therefore, one side of the triangle is
(x + 5) + (x + 5) = 20
and the equilateral triangle's perimeter is
3×one side = 3 ×20 units
Thus, Perimeter = 60 units.
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The complete question is What is the perimeter of triangle JEG?
60 units
65 units
70 units
75 units
Increase 402€ by 23%
The value of 402€ after increasing by 23% is 494.46€. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four basic operations, often known as "arithmetic operations," are said to be able to adequately explain all the real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given a value as 402€ which is to be increased by 23%.
So, by using the addition operation, we get the value as,
⇒ 402€ + 23%
⇒ 402€ + 92.46€
⇒ 494.46€
Hence, the value of 402€ after increasing by 23% is 494.46€.
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Question: Find the value of 402€ when increased by 23%.
the solution shown for the equation is incorrect. What is the correct solution? what is the error -7(2-r) = 28 -14-7r=28 -7r=42 r=-6
CEREAL The volume of a box of cereal in square inches can be represented by
the expression 2x² + 30x + 108. Factor the expression.
Answer:
2(x+6)(x+9)
Step-by-step explanation:
Factor out a 2.
The result is 2(x^2+15x+54).
From here, many ways are possible, but for simplicity, we’ll go for a guess and check method. Assuming you know how it works, 2 numbers (we’ll call them a and b) satisfy a+b=15 and ab=54. After a bit of guessing, we can derive that the 2 numbers are 6 and 9. Our factored expression resembles 2(x+a)(x+b), so our factored expression is
2(x+6)(x+9)
Two similar polygons have areas of 128 in2 and 98 in2. If the smaller polygon has a perimeter of 42 in, what is the perimeter of the larger polygon?
In response to the query, we can state that Hence, the bigger polygon's equation circumference measures around 54.86 inches.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
Area of a smaller polygon is equal to (k * side of a smaller polygon)2.
bigger polygon's area is equal to (k * side of larger polygon)2.
Area of bigger polygon / area of smaller polygon = (k * side of larger polygon) / (k * side of smaller polygon) /
[tex]\sqrt(128/98) k * 42 = (48 / side of smaller polygon) * 42 = 48 * (42 / side of smaller polygon) = (k * side of bigger polygon) / (k * 42)[/tex]
Greater polygon's perimeter is equal to 48 * (42 / smaller polygon's side) [tex]= 48 * (42 / (42k)) = 48 * (1/k).[/tex]
We may utilize the fact that the ratio of the two polygons' surface areas is to calculate k:
bigger polygon's area divided by smaller polygon's area equals 128/98, or 64/49.
the ratio of the sides of the two polygons is 8/7.
K thus equals 7/8.
Hence, the bigger polygon's circumference measures around 54.86 inches.
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helpppp again please
Answer: Volume = 23816.41
the tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (esp). a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. the experiment was repeated seven times, and x, the number of decisions, was recorded. (assume that the seven trials are independent.) a. if the psychic is guessing (i.e., if the psychic does not possess esp), what is the value of p, the probability of a correct decision on each trial? b. if the psychic is guessing, what is the expected number of correct decisions in seven trials? c. if the psychic is guessing, what is the probability of no correct decisions in seven trials? d. now suppose the psychic has esp and p
a. The probability of a correct decision on each trial is 0.1.
b. The expected number of correct decisions in seven trials is 0.7.
c. The probability of no correct decisions in seven trials is approximately 0.478.
d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.
Therefore, the probability of a correct decision on each trial is -
p = 1/10 = 0.1
b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -
E(X) = np = 7 × 0.1 = 0.7
Therefore, the number of correct decisions is 0.7.
c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -
[tex]P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}[/tex]
In this case, n = 7, x = 0, and p = 0.1.
Substituting these values into the formula, we get -
[tex]P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478[/tex]
Therefore, the probability value is 0.478.
d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -
q = 1 - p
q = 1 - 0.5
q = 0.5
The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -
[tex]P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}[/tex]
In this case, n = 7, x = 7, p = 0.5, and q = 0.5.
Substituting these values into the equation, we get -
[tex]P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078[/tex]
Therefore, the probability value is 0.0078.
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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)
a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?
b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?
c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?
d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.
Fill in the blank with the correct term or number to complete the sentence.
A _____ expression like (3+5) x (4-1) is a combination of numbers and at least one operation
An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.
What is the answer for the 'angles of polygons' question?
Answer:
18 bc there a 9 angles and below is is another angle so u do 9 + 9 or 9(2) and u will get 18
One of the acute angles of a right triangle is 36 then the other acute angle is
Answer:
54
Step-by-step explanation:
So a right angle has one right angle and each angle is equal to ninety degrees. So you have 90+36=126. Sum of angles in a triangle is 180 so subtract 126 from it to get 54.
Have a wonderful day and feel free to ask me again. Peace
The two-way frequency table below shows data on playing a sport and playing a musical instrument for students in a class.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
Plays sports Does not play sports
Plays a musical instrument 666 777
Does not play a musical instrument 888 333
Plays a sport Does not play a sport Row total
Plays a musical instrument
1.001.001, point, 00
Does not play a musical instrument
1.001.001, point, 00
The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.
What is frequency?Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.
Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.
This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.
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Please ASAP Help
Will mark brainlest due at 12:00
The midpoint of the line segment with the endpoints is (-2, 5).
option B.
What is the coordinates of the midpoint of a line segment?To find the coordinates of the midpoint of a line segment with endpoints K(-9, 3) and H(5, 7), we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Where;
(x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.Plugging in the coordinates of K and H, we get:
Midpoint = [(-9 + 5)/2, (3 + 7)/2]
= [-2, 5]
Therefore, the midpoint of the line segment with endpoints K(-9, 3) and H(5, 7) is (-2, 5).
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The model shows that 3 and one fifth divided by four fifths equal 4 what would happen if you divide by 8/5 instead of 4/5
Dividing by a larger fraction (8/5) instead of 4/5 results in a smaller answer (2), because we are dividing the same amount (16/5) into more parts (8) compared to dividing by 4/5.
If you divide 3 and one fifth by four fifths, you can first convert the mixed number to an improper fraction:
3 and 1/5 = (3 x 5 + 1) / 5 = 16/5
Then, you can perform the division as follows:
(16/5) / (4/5) = (16/5) x (5/4) = 4
So, we get an answer of 4.
If we divide by 8/5 instead of 4/5, we can use the same process but with the new fraction:
(16/5) / (8/5) = (16/5) x (5/8) = 2
So, the answer would be 2.
This is because when we divide by a smaller fraction, we are dividing the same amount into fewer parts, which results in a larger answer.
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Select the correct answer. The product of two integers is 72. One number is two less than five times the other. Which of the following equations could be used to find one of the numbers?
A. 2x2 − 5x = 72
B. 5x2 − 2x = 72
C. 2x2 − 5 = 72
D. 5x2 − 2 = 72
Answer:
Option B.
Step-by-step explanation:
Convert the word problem into an equation.
[tex](x)(5x-2) = 72[/tex]
Simplify this to get
[tex]5x^2-2x=72[/tex]
Option B.
Use the given point and slope to write an equation in slope intercept form.
(3, 0); slope 5
An equation of this line in slope-intercept form is y = 5x - 15.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At data point (3, 0) and a slope of 5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 5(x - 3)
y - 0 = 5x - 15
y = 5x - 15
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Which answer choice is the correct solution set for the function, f(x)=-2x^(2)-2x+4?
Answer:
Step-by-step explanation:
Hello please help, the table is attached Task 1.B
The average speed of the bus between Bradbury Place and Broomhills Park is 31 km/hl. Work out how many kilometres the bus travels between these two stops. If your answer is a decimal, give it to 1 d.p.
Answer:
7.8 km
Step-by-step explanation:
You want the distance between two points when the travel time is 15 minutes at an average speed of 31 km/h.
DistanceThe relation between time, speed, and distance is ...
distance = speed × time
Here, the time is the difference between 14:50 and 14:35, which is 50-35 = 15 minutes. In terms of hours, that is 15/60 = 1/4 hours.
The speed is given as 31 km/h, so the distance is ...
(31 km/h)×(1/4 h) = 31/4 km = 7.75 km ≈ 7.8 km
The distance between the two bus stops is about 7.8 km.
Answer:7.75 km so approximately 7.8 km
Step-by-step explanation:
i am not sure but i think the answer is 7.8 km
14:50 - 14:35= 15 minutes
because in every hour the bus travel 31 km/h so,
31 km/h divided by 60
multiply the answer by 15 = 7.75 km
G
3
X
You are traveling by car to New York City. The map you will use for your journey is
below.
Seattle
• San Jose
• Los Angeles
1 unit
1 unit = 557 miles
Denver
El Paso
Chicago
Houston
a) What is the scale factor on the map? (1 point)
Memphis
New York
Jacksonville
grup
The scale factor on the map is 1 unit = 557 miles. This means that for every 1 unit on the map, it corresponds to 557 miles in the real world.
What is a map?A map is a visual representation of an area. It shows physical features such as landforms, bodies of water, and other geographical features. It can also represent political boundaries, transportation networks, and population density. Maps are useful tools for navigation, planning, and communication. They are also used for research, education, and leisure activities.
For example, if Seattle to San Jose on the map is 1 unit, then it is equivalent to 557 miles in the real world. Similarly, if Denver to El Paso is 2 units, then it would be equivalent to 1114 miles in the real world.
This scale factor is important when planning a journey because it helps travelers to accurately calculate the distance they need to travel. Knowing the exact distance can help travelers plan their stops along the way, choose the most efficient route, and estimate the amount of time it will take to get to their destination. Additionally, it can help travelers to plan their budget accordingly, since they will have an idea of how much gas they need to buy and how much accommodation costs they need to cover.
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Do what the picture says.Right answer gets brainilest!!!!
Answer:
142.5 ft^2
Step-by-step explanation:
You need to calculate each figure separately
area of the first rectangle = 5 x 4 = 20
area of the second rectangle = (5+6)x(4) = 44
area of 1/4 circle = 1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5
area of figure: 78.5 + 20 + 44 = 142.5
Answer:
To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.
Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:
Area = (b1 + b2) / 2 * h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
Plugging in the values, we get:
Area = (6ft + 10ft) / 2 * 5ft
Area = 8ft * 5ft
Area = 40 sq ft
Area ≈ 3.73 sq m (rounded to two decimal places)
Therefore, the area of this figure is approximately 3.73 square meters.
(If it wasn't in decimals, it would be 40 square feet.)
Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
How many cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inches?
125 cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inch.
What is a cube?A cube is a 3-dimensional solid shape with six square faces that are all congruent, and with all edges of equal length.
The volume of a cube is calculated by cubing the length of one of its edges.
To find the number of cubes with an edge length of 1/5 inch that are needed to build a cube with an edge length of 1 inch, we need to calculate the ratio of the volumes of the two cubes.
The volume of the larger cube with an edge length of 1 inch is:
V_large = (1 inch)^3 = 1 cubic inch
The volume of the smaller cube with an edge length of 1/5 inch is:
V_small = (1/5 inch)^3 = 1/125 cubic inches
To find the number of small cubes, we need to divide the volume of the larger cube by the volume of the smaller cube:
Number of small cubes = V_large / V_small = 1 cubic inch / (1/125 cubic inches) = 125
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I'm having a hard time understanding how
x2+3x=0
then x(x+3)=0
breaks down to x=-3,0
The solution to the equation x² + 3x = 0 when solved for variable x are x = -3 and 0
What are equations?Equations are statements with equal values
Calculating the solution for xGiven the following equation
x² + 3x = 0
Factor out x from the equation
So, the equation becomes
x(x + 3) = 0
The above equation means that
x = 0
Also, it means that
x + 3 = 0
When the equation is evaluated, we have
x = 0 and x = -3
Now that we have the values of x, we can conclude that the solutions are x = 0 and x = -3
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I’m really bad at these problems can someone please help!?
The value of x, y, z are 14√2, 4√7, 2√21
What is trigonometric ratio?Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Tan (45) = 14√2/x
1 = 14√2/x
x =14 √2
the third side(hypotenuse) = √14√2)²+14√2)²
= √56+56
= √112
= 4√7
sin(30) = y/4√7
1/2 = y/4√7
2y = 4√7
y = 2√7
cos 30 = z/4√7
√3/2 = z/4√7
2z = 4√21
z = 2√21
therefore the value of x , y , z are 14√2, 4√7, 2√21
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A net for a cube has a total surface area of 150 in.2. what is the length of one side of a square face?
a. 4 in.
b. 5 in.
c. 16 in.
d. 25 in.
The length of one side of a square face is 5 inches
The surface area of a cube is given by 6s^2, where s is the length of one side of a square face. If the net for a cube has a total surface area of 150 in^2, we can set up an equation:
6s^2 = 150
Dividing both sides by 6, we get:
s^2 = 25
Taking the square root of both sides, we get:
s = 5
Therefore, the length of one side of a square face is 5 inches.
So, the answer is (b) 5 in.
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m=-475+2650
which number of hours and minuets is closest to the amount of time that the jet has been flying if the jet is 1,500 miles from los angeles
Answer: 11550
Step-by-step explanation:
First you add 475+2650=11550
PLEASE ANSWER!!! WILL GIVE BRAINLIEST!!!
Question 3: A rectangle has sides measuring (7x - 1) units and (2x + 3) units.
Part A:
Create an expression that represents the area of the rectangle:
Calculate the area. SHOW ALL WORK:
Write the expression in standard form:
Part B: Identify the following by using the expression below. 4x^2 + 3y - 6x^4y + 4
Degree:__
#Terms:__
Drag & Drop, write the expression in standard form.
A) -6x^4 + 4x^2 + 3y + 4
B) 4x^2 + 3y - 6x^4 + 4
C) -6x^4 + 3y + 4x^2 + 4
D) 4x^2 - 6x^4 + 3y + 4
Part C: Choose the term that makes the statement true.
Adding, subtraction or multiplying two polynomials _____ results in another polynomial.
A) Always
B) Sometimes
C) Never
Answer:
Part A:
The expression that represents the area of the rectangle is:
Area = length × width
Area = (7x - 1)(2x + 3)
Area = 14x^2 + 19x - 3
To calculate the area, we multiplied the length (7x - 1) by the width (2x + 3).
To write the expression in standard form, we rearrange the terms in descending order of degree:
Area = -3 + 19x + 14x^2
Part B:
The expression in standard form is:
-6x^4 + 4x^2 + 3y + 4
Degree: 4
Terms: 4
Part C:
Adding, subtracting, and multiplying two polynomials always results in another polynomial. Therefore, the term that makes the statement true is A) Always.
Step-by-step explanation:
Use the relative frequency table shown to the right to calculate the number of the 300
measurements falling into each of the measurement classes. Then graph a frequency histogram for these data.
Measurement Class Relative Frequency
00.5-2.50 0.15
02.5-4.50 0.1
04.5-6.50 0.1
06.5-8.50 0.05
08.5-10.5 0.1
10.5-12.5 0.2
12.5-14.5 0.2
14.5-16.5 0.1
Calculate the number of measurements that fall into each class.
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
What is relative frequency ?
Relative frequency is a measure used to calculate the proportion or percentage of occurrences of an event in relation to the total number of events or observations. It is calculated by dividing the frequency of an event by the total number of observations in a dataset. The relative frequency is expressed as a decimal, fraction, or percentage. It is useful for comparing the occurrence of events in different datasets or for comparing the distribution of events in a single dataset.
According to the question:
To calculate the number of measurements that fall into each class, we need to multiply the relative frequency of each class by the total number of measurements, which is 300.
For the 00.5-2.50 class: 0.15 x 300 = 45
For the 02.5-4.50 class: 0.1 x 300 = 30
For the 04.5-6.50 class: 0.1 x 300 = 30
For the 06.5-8.50 class: 0.05 x 300 = 15
For the 08.5-10.5 class: 0.1 x 300 = 30
For the 10.5-12.5 class: 0.2 x 300 = 60
For the 12.5-14.5 class: 0.2 x 300 = 60
For the 14.5-16.5 class: 0.1 x 300 = 30
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
To graph a frequency histogram for these data, we can plot the number of measurements in each class on the vertical axis and the measurement classes on the horizontal axis, with the bars for each class touching each other. The resulting histogram should have eight bars of varying heights, with the tallest bars representing the classes with the most measurements.
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A cubic die is biased, so that for each integer n,1≤n≤6 , the probability of the event {n} is p({n})=2p if n=3 or n=4 and p({n})=p , otherwise a) What is the expected number of times the die comes up 6 , when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?
Hence, the answers are a) 9.14 and b) 7.
a) What is the expected number of times the die comes up 6, when it is rolled 32 times?b) What is the expected number of times the die must be rolled until the first 6 comes up?Solutions:Part a) Let X be the number of times the die comes up 6 when it is rolled 32 times.To find the expected number of times the die comes up 6, we'll apply the formula E(X) = np, where n is the number of trials and p is the probability of success on any given trial.If we look at the bias in this particular cubic die, we see that when the event is {6}, then p({6}) = p = 2p/4. This implies that p = 2/7, therefore: E(X) = np = 32*2/7 = 9.14285714286 = 9.14Part b) Let Y be the number of times the die must be rolled until the first 6 comes up.Let's use the geometric distribution to calculate the expected number of rolls E(Y).Since the event "6" has a probability of 1/7, then p = 1/7. Thus, the expected number of times the die must be rolled until the first 6 comes up is given by E(Y) = 1/p, which is 7 rolls.Hence, the answers are a) 9.14 and b) 7.
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Given the function
` f(x)= {( -6, x<0), ( sqrt(7 x^2 + 9), x\geq 0):}`
Calculate the following values:
`f(-6)= ` `f(0)= ` `f(6)= `
Answer:
f(-6) = -6 (since -6 is less than 0)
f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)
f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)
Step-by-step explanation:
To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.
For x less than 0:
f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)
For x greater than or equal to 0:
f(x) = sqrt(7x^2 + 9)
Therefore:
f(-6) = -6 (since -6 is less than 0)
f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)
f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)
The diagonals of parallelogram ABCD intersect at E. If AE=2x+ 4., EB=6+3y,EC=15-y and ED =x+4 then, find the lengths of diagonals AC and BD.
The length of the diagonals AC and BD are 28 and 18 units respectively.
How to find the diagonal of a parallelogram?A parallelogram is a quadrilateral that has opposite sides equal to each other and opposite sides parallel to each other. The diagonal of a parallelogram are not equal but they bisect each other.
Therefore,
AE = EC
EB = ED
Hence,
2x + 4 = 15 - y
2x + y = 11
6 + 3y = x + 4
x - 3y = 2
Combine the equation
2x + y = 11
x - 3y = 2
multiply equation(ii) by 2
2x + y = 11
2x - 6y = 4
7y = 7
y = 7 / 7
y = 1
Let's find x
x = 2 + 3y
x = 2 + 3(1)
x = 2 + 3
x = 5
Therefore,
x = 5 and y = 1
AE = EC = 2(5) + 4 = 14
AC = 14(2) = 28 units
EB = ED = 6 + 3(1) = 9
BD = 9(2) = 18 units
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