The general solution of the given higher-order differential equation is y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2)).
To find the general solution of the given higher-order differential equation, first, let's rewrite the equation in a more standard form:
16y'''' + 16y'' + 4y = 0
Now, we'll solve this fourth-order linear homogeneous differential equation using the characteristic equation method.
1. Write the characteristic equation:
16r^4 + 16r^2 + 4 = 0
2. Divide the equation by 4 to simplify:
4r^4 + 4r^2 + 1 = 0
3. Apply a substitution: let t = r^2, then the equation becomes:
4t^2 + 4t + 1 = 0
4. Solve the quadratic equation for t using the quadratic formula:
t = (-B ± √(B^2 - 4AC)) / 2A
t = (-4 ± √(4^2 - 4(4)(1))) / (2 * 4)
t = (-4 ± √(16 - 16)) / 8
t = -4/8 = -1/2
5. Substitute back r^2 for t:
r^2 = -1/2
6. Solve for r:
r = ±√(-1/2)
r = ±(1/√2)i
7. Since the roots are complex conjugates, the general solution can be written as:
y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2))
where A and B are arbitrary constants determined by the initial conditions of the problem.
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Please help me with this I have no idea
Answer:
x = 8
Step-by-step explanation:
The two sides equal each other
5x - 13 = x + 19 Subtract x from both sides
5x - x - 13 = x - x + 19
4x - 13 = 19 Add 13 to both sides
4x - 13 + 13 = 19 + 13
4x = 32 Divide both sides by 4
x = 8
Helping in the name of Jesus.
What are the coordinates of each point after quadrilateral ABCD is reflected across the y-axis?
Help please in need this asap
For the given values, the standard deviation for this data set is approximately 3.67 minutes.
What is standard deviation?
In statistics, standard deviation is a measure used to quantify the amount of spread or dispersion of a set of numerical data around the mean. This measure indicates how much the data values vary from the average value of the dataset.
To find the standard deviation, you can follow these steps:
Find the mean (average) of the data set:
mean = (11 + 7 + 14 + 2 + 8 + 13 + 3 + 6 + 10 + 3 + 8 + 4 + 8 + 4 + 7) / 15 = 7.2
Subtract the mean from each data point:
(11 - 7.2), (7 - 7.2), (14 - 7.2), (2 - 7.2), (8 - 7.2), (13 - 7.2), (3 - 7.2), (6 - 7.2), (10 - 7.2), (3 - 7.2), (8 - 7.2), (4 - 7.2), (8 - 7.2), (4 - 7.2), (7 - 7.2)
Simplifying, we get:
3.8, -0.2, 6.8, -5.2, 0.8, 5.8, -4.2, -1.2, 2.8, -4.2, 0.8, -3.2, 0.8, -3.2, -0.2
Square each result:
13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04
Find the mean (average) of the squared results:
(13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04) / 15 = 12.49
Take the square root of the mean:
[tex]\sqrt{(12.49)[/tex] ≈ 3.67
Therefore, the standard deviation for this data set is approximately 3.67 minutes.
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help asap!!!!!!!!!!!!!!!!!
Answer:
126 meters squared
Step-by-step explanation:
To find the surface area
For the top and bottom it will be: l x w x 2(because there's a top and bottom)
3x6x2 = 36
For the sides (left and right) it will be: l x h x 2 (There's left and right)
3x5x2 = 30
For the front and back it will be w x h x 2 (There's the front and the back)
6x5x2 = 60
Added it all together and you get 126
The surface area is 126 meters squared
which type of sampling assumes all the members of a population have an equal chance of being selected for participation in the study?
The type of sampling that assumes all members of a population have an equal chance of being selected for participation in the study is called Simple Random Sampling.
In Simple Random Sampling, each individual in the population has an equal probability of being chosen as a participant, and the selection process is unbiased. This method ensures that the sample is representative of the entire population, thus allowing for valid conclusions to be drawn about the population as a whole.
Here is a step-by-step explanation of how Simple Random Sampling is conducted:
1. Define the population: First, clearly identify the population you want to study.
2. Assign a unique number to each member: To ensure equal chances of selection, assign a unique number to every individual in the population.
3. Determine the sample size: Decide how many participants you need in your study based on factors like required level of accuracy and available resources.
4. Use a random selection method: Use a random selection method such as a random number generator, a lottery system, or a random number table to pick the required number of participants.
5. Collect data from the selected individuals: Once the participants are chosen, collect data from them using appropriate research methods like surveys, interviews, or experiments.
By using Simple Random Sampling, you can obtain a sample that is unbiased and representative of the entire population, which is essential for accurate and reliable research findings.
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Find x of the problem
There is no real solution for X. This means that the given measurements do not form a valid right triangle.
What is the value of X?
Triangle KJL forms a right triangle, with length KL (hypothenuse side) = 10 and JL = X and KL = 24.
We can use the Pythagorean theorem to solve for the missing side, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Therefore, we have:
KL² = KJ² + JL²
Substituting the given values, we get:
10² = 24² + X²
Simplifying and solving for X, we get:
100 = 576 + X²
X² = 100 - 576
X² = -476
Since X² is negative, there is no real solution for X. This means that the given measurements do not form a valid right triangle.
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PLS HELP ASAP !!! What does this mean
Answer:
2 Nd is in order from least to grater
A quarter is about I Inch In
diameter. The word "Liberty"
makes about a 100° angle. How
long is the word in inches?
According to the question the word "Liberty" on the quarter is about 0.872 inches long.
what is diameter?In geometry, a circle's diameter is any straight segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. Either idea can be used to determine a sphere's diameter. The diameter is indeed the length of both the line perpendicular to the two points at each end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.
Since the quarter has a diameter of about 1 inch, we can use its diameter as a reference to estimate the length of the word "Liberty" on the quarter.
If the word "Liberty" makes about a 100° angle, that means it takes up about 100/360 or 5/18 of the circumference of the quarter. The circumference of a circle is given by:
C = 2πr
where C is indeed the circumference, pi (roughly 3.14), is a mathematical constant, and r is the circle's radius. The quarter's approximate 1 inch diameter means that the radius equals 1/2 inch, approximately 0.5 inches.
The circumference of the quarter is therefore:
C = 2π(0.5 inches) = π inches
The length of the word "Liberty" on the quarter is approximately 5/18 of this circumference, which is:
(5/18) × π inches ≈ 0.872 inches
So the word "Liberty" on the quarter is about 0.872 inches long.
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QUICK!!!!
If a universal set is {1, 2, 3, 4, 5, 6, 7} and set C equals {1, 2, 3}, What is the complement of the complement of C?
A) {1, 2, 3}
B) {1, 2, 3, 4, 5, 6, 7}
C) {4, 5, 6, 7}
D) Ø
The concept of a complement of a set is the set of all elements in the universal set that are not in the original set. The answer is B) {1, 2, 3, 4, 5, 6, 7}.
What is a universal set?It is denoted by U. Universal sets are used to define the scope of an expression or equation, as well as to denote sets of all objects, such as the set of real numbers or the set of natural numbers.
The complement of a set is also referred to as its opposite set. In this case, the universal set is {1, 2, 3, 4, 5, 6, 7}, and the set C is {1, 2, 3}.
The complement of C is {4, 5, 6, 7}.
The complement of the complement of C is the set of all elements that are not in the complement of C.
Since the complement of C is {4, 5, 6, 7}, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C, which is {1, 2, 3, 4, 5, 6, 7}.
Therefore, the answer is B) {1, 2, 3, 4, 5, 6, 7}.
To summarize, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C.
In this case, the complement of C is {4, 5, 6, 7}, so the complement of the complement of C is {1, 2, 3, 4, 5, 6, 7}.
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Solve The table shows the costs of a membership and fruit baskets at a discount warehouse club. Item Cost ($) Membership Fee 30 Fruit Basket 15 Mrs. Williams paid a total of $105 for her annual membership fee and several fruit baskets as gifts for her coworkers. Solve the equation 15x+30=105 to find the number of fruit baskets Mrs. Williams purchased.
PLS HELP!!! (AND HURRY)
Answer:
The given equation is:
15x + 30 = 105
Here,
15x represents the total cost of the fruit baskets purchased, and
30 represents the cost of the membership fee.
To find the number of fruit baskets purchased (x), we must isolate the variable on one side of the equation.
Subtracting 30 from both sides, we get:
15x = 105 - 30
15x = 75
Dividing both sides by 15, we get:
x = 5
Therefore, Mrs. Williams purchased 5 fruit baskets for her coworkers.
Amanda Bryan purchased a used car for $12,875 with a 25% down payment. What amount did she finance?
Answer: If Amanda Bryan purchased a used car for $12,875 and made a 25% down payment, then she paid:
25% of $12,875 = 0.25 * $12,875 = $3,218.75
This means that the amount she financed (i.e. borrowed) to purchase the car is the difference between the total cost of the car and the down payment:
Amount financed = Total cost - Down payment
Amount financed = $12,875 - $3,218.75
Amount financed = $9,656.25
Therefore, Amanda Bryan financed $9,656.25 to purchase the used car.
Step-by-step explanation:
Find the area of the Square
1 in
1 in
please explain I'll mark brainlisest
or
The copy machine at the library made a copy of Leslie's 3-page essay in just
1
10
of a minute. What is the speed of the copy machine?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The speed of the copy machine is 30 pages per minute.
What is Fraction ?
A fraction is a way of representing a part of a whole or a division of a quantity into equal parts. It consists of two numbers, one written above the other and separated by a horizontal or diagonal line called a fraction bar. The number written above the fraction bar is called the numerator, and the number written below the fraction bar is called the denominator.
If the copy machine made a copy of Leslie's 3-page essay in just 1/10 of a minute, then it made a copy of one page in 1/10 ÷ 3 = 1/30 of a minute.
To find the speed of the copy machine, we can take the reciprocal of the time it takes to make one copy, which is:
1 ÷ (1/30) = 30
Therefore, the speed of the copy machine is 30 pages per minute.
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GEOMETRY PLS HELP ASAP
Answer:
1) 5
Step-by-step explanation:
Trapezoid Midsegment Theorem:
EF = (DC + AB) / 2
2x + 2 = ((x + 3) +(5x - 9)) / 2
4x + 4 = 6x - 6
-2x = -10
x = 5
in an article in the journal of management, joseph martocchio studied and estimated the costs of employee absences. based on a sample of 176 blue-collar workers, martocchio estimated that the mean amount of paid time lost during a three-month period was 1.3 days per employee with a standard deviation of 1.4 days. martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.1 day per employee with a standard deviation of 1.6 days.
suppose we randomly select a sample of 100 blue-collar workers. based on martocchio
The probability shows that if the mean μ=1, then only 0.0027 is at least as small as the sample mean x=1.5. This also leads to the conclusion that if we believe that μ = 1, we must also believe that there is a 27 in 10,000 chance that our observed sample mean can be described as such.
To achieve the goal of this task, use the mean μ x and the standard deviation σ x.
The task has two conditions, the first is that the standard deviation σ is 1.3 days and the second is that the standard deviation σ is 1.8 days.
If the standard deviation σ is 1.3, then the mean μ is 1.4. And if the standard deviation is σ 1.8, then the mean is μ₁. In this case, the given standard deviation is μ 1.8, so use the second condition to achieve the task goal.
we know that:
μₓ = μ and σₓ = σ/√n
Given that:
μ = 1, σ = 1.8 and n = 100
So, by the formula of standard deviation σₓ,
σₓ = σ/√n = 1.8/√100
= 0.18
Calculate the probability with the mean μ=1, and standard deviation
σₓ =0.18.
P(x > 1.5) = P(z > 0.5/0.18)
= P( z > 2.78)
Looking at the z table, first, find the units and decimals in the first column of the z table. In this case, search for 2.7 first. Then look in which column the 100th value is placed. In this case, 0.08 and follow the number of lines placed 2.7.
Therefore, the value of 2.78 in table z is 0.9973 because z=0.9973, and the right tail area is 0.0027 or (1−0.9973).
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Tonya worked 42.5 hours this week at a rate of 9.75 what is her overtime pay ?
Since overtime is paid at one and one-half, Tonya's overtime pay for this week is $36.56.
What is overtime pay?The overtime pay is the product of the overtime pay rate and the number of overtime hours.
The normal work week is 40 hours. The overtime hours, in this situation, are 2.5 hours.
The total number of hours Tonya worked this week = 42.5 hours
The hourly pay rate = $9.75
Overtime pay rate = $14.625 ($9.75 x 1.5)
Overtime hours worked = 2.5 hours (42.5 - 40)
Overtime pay = $36.56 ($14.625 x 2.5)
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2. The table below shows the lengths of four earthworms found by the lake. Earthworm A B C D Length (cm) 10.2 3 9- 4 9.23 9/²/2 2 Write the lengths in order from shortest to longest.
From shortest to longest, the earthworms measure the following lengths: B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)
how can we describe length ?A physical concept known as length measures the gap between two points or the expanse of an object in one dimension.
Common units used to measure it include metres (m), feet (ft), millimetres (in), centimetres (cm), etc. In several disciplines, including mathematics, engineering, physics, and engineering, length is a crucial concept.
given
From shortest to longest, the earthworms measure the following lengths:
B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)
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what is the length of the missing leg? If necessary, round to the nearest tenth.
Answer:
48 yards
Step-by-step explanation:
Use the Pythagorean theorem:
[tex] {a}^{2} = {52}^{2} - {20}^{2} = 2704 - 400 = 2304[/tex]
[tex]a > 0[/tex]
[tex]a = \sqrt{2304} = 48 \: yd[/tex]
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
For the first question, the measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is IQR, because it is robust to outliers and can provide a better representation of the spread of data for skewed distributions. The option "IQR, because Desert Landing is symmetric" is incorrect because the graph of Desert Landing is not symmetric.
For the second question, we need to compare the measures of center (mean and median) of the two sets of data to determine which shop typically sells the most amount of coffee per hour. To do this, we can calculate the mean and median of each set of data:
For Coffee Ground, the mean is (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.25 gallons and the median is the middle value of the ordered set, which is 5 gallons.
For Wide Awake, the mean is (2.5+10+4+18+4+3+6.5+15+6+5+2.5)/11 = 6.136 gallons and the median is the middle value of the ordered set, which is 4.5 gallons.
Therefore, we can conclude that Wide Awake typically sells the most amount of coffee per hour, with a median value of 4.5 gallons. The option "Wide Awake, with a mean value of about 4.5 gallons" is incorrect because the mean value of Wide Awake is slightly lower than 4.5 gallons. The option "Coffee Ground, with a median value of 5 gallons" is incorrect because the median value of Coffee Ground is lower than the median value of Wide Awake. The option "Coffee Ground, with a mean value of about 5 gallons" is incorrect because the mean value of Coffee Ground is higher than 5 gallons.
Find an angle in each quadrant with a common reference angle with 332°
Answer:
Step-by-step explanation:
In first quadrent, reference angle is equal to 332
in secodn quadrent, 332-180
angle - 180 so 332-180
fouth Quadrent, 360-332
Answer is equal to 28
Answer:
Quadrant 1: 152°
Quadrant 2: 28°
Quadrant 3 (Given): 332°
Quadrant 4: 208°
Step-by-step explanation:
A 332° angle in standard position has its terminal side in quadrant 3 since 332° is between 180° and 360°.
332° - 180° = 152°
The reference angle for 332° is 152°
Quadrant 1: 152°
Quadrant 2: 180° - 152° = 28°
Quadrant 3 (Given): 332°
Quadrant 4: 360° - 152° = 208°
The area of a rectangular field is 80 square meters. If its length is 20 m, how far would you have travelled if you walked the whole way around the field?
Answer: We can start by finding the width of the rectangular field using the formula for area of a rectangle:
Area = length x width
80 = 20 x width
width = 4 meters
Now we can use the formula for perimeter of a rectangle:
Perimeter = 2 x length + 2 x width
Perimeter = 2 x 20 + 2 x 4
Perimeter = 40 + 8
Perimeter = 48 meters
So, you would have traveled 48 meters if you walked the whole way around the field.
Step-by-step explanation:
R=[(a,1),(b,2),(c,3)] is it function or not
Answer:
Yes The set R = [(a,1),(b,2),(c,3)] is a Function.
Step-by-step explanation:
A function ia a relation between two sets ,where each element in domain is associated with only one range.
Some examples of function -
1- x2 (squaring) is a function
2- x3+1 is also a function
3- Sine, Cosine and Tangent are function
in the case the domain {a,b,c} and the range is {1,2,3}
IN R each domain is associated with only one element in range,So R SATISFIES the definiton of Function
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pls solve thisss......
The height of the cone is 15cm.
How to find the radius of the object?From the question;
Height of cylinder = 28cm
Let the radius of the solid object = Rcm
The slant height of the cone = 17cm
Cost of painting = Rs. 140 per 100 sq cm
Cost of painting 1 cm² = 140/100 = RS1.4
The total cost of painting = Rs. 2851.2
Total area of the object = total cost of painting/Cost of painting per sq cm
Total area of the object = 2851.2/1.4 = 2036.57143 cm²
Total surface area of object = CSA of Cylinder + CSA of cone + area of the circle at the bottom
Total surface area of the object = [tex]\pi rh + \pi rl + \pi r^2[/tex]
So, [tex]\frac{2851.2}{1.4}[/tex] = [tex]\pi rh + \pi rl + \pi r^2[/tex]
[tex]\frac{2851.2}{1.4}[/tex] = [tex]2\pi r * 28 + \pi r * 17 + \pi r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1232}{7}r =+\frac{374}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1606}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{2}[/tex]= [tex]1606r + 22r^2[/tex]
[tex]14256 = 1606r + 22r^2[/tex]
[tex]22r^2 + 1606r - 14256 =0[/tex]
Solving the quadratic equation, the possible value of radius are:
r = 8cm
r = -81cm
r = -81cm will be neglected because radius can not be negative.
Therefore, the radius of the object is 8cm
To find the height of the cone, we should know that the relation between radius, height and slant height of the cone is:
[tex]l^2 = r^2 + h^2[/tex]
[tex]h=\sqrt{l^2 - r^2}[/tex]
[tex]h=\sqrt{17^2 - 8^2}[/tex]
[tex]h=\sqrt{225}[/tex]
[tex]h=15cm[/tex]
Therefore, height of cone in the solid object is 15cm
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you flip it twice more and get heads twice more. now what is the conditional probability that the coin you chose is fake?
The conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is higher than the initial probability.
Let A be the event that the coin chosen is fake, and B be the event that the three flips resulted in heads. We are given that the probability of choosing the fake coin is 0.1, i.e. P(A) = 0.1, and the probability of getting heads with the fake coin is 1, i.e. P(B|A) = 1. The probability of getting heads with the fair coin is 0.5, i.e. P(B|A') = 0.5, where A' is the event that the coin chosen is fair. Using Bayes' theorem, we can calculate the conditional probability of A given B:
P(A|B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|A') * P(A'))
Plugging in the given values, we get:
P(A|B) = 1 * 0.1 / (1 * 0.1 + 0.5 * 0.9) = 0.18
Therefore, the conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is 0.18, which is higher than the initial probability of 0.1. This means that the evidence of three consecutive heads increases the likelihood that the coin is fake.
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due tomorrow , please help!!
The surface areas are 756.87 km², 2567.6 in², 853.91 yd², 749.72 cm² and the area to paint is 3268.60 in²
Calculating the surface areasFigure 9
This is calculated as
Area = Base area + 1/2 * Perimeter * Slant height
So, we have
Surface area = (1/4 * 14² * √3) + 1/2 * (14 + 14 + 14) * 32
Surface area = 756.87 km²
Figure 10
This is calculated as
Area = Sum of side areas
So, we have
Surface area = 2 * 1/2 * (35 + 10) * 20.3 + 32 * 17 + 10 * 17 + 20.3 * 17 + 35 * 17
Surface area = 2567.6 in²
Figure 11
Start by calculating the radius using
(2r)² = 19.4² - 14.4²
2r = 13
So, we have
r = 6.5
This area is then calculated as
Area = 2πr(h + r)
So, we have
Area = 2 * 22/7 * 6.5(14.4 + 6.5)
Surface area = 853.91 yd²
Figure 12
This area is calculated as
Area = lw + l√[(w/2)² + h²] + w√[(l/2)² + h²]
So, we have
Area = 15 * 18 + 18√[(15/2)² + 12²] + 15√[(18/2)² + 12²]
Surface area = 749.72 cm²
Area to paintWithout painting the bottom, the area is
Area = 2 * 1/2 * 34 + 42.8 + 36 * √(34² + 42.8²) + 34 * 36
Evaluate
Area = 3268.60 in²
Volume of the coneUnclear dimensions
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the production of a certain polymer fiber follows a normal distribution with a true mean diameter of 20 mm and a standard deviation of 30 mm. compute the probability of a measured value greater than 80 mm. compute the probability of a measured value between 50 and 80 mm.
The probability of a measured value greater than 80 mm in a normal distribution with mean 20 mm and standard deviation 30 mm is (0.0228). The probability of a measured value between 50 and 80 mm is 0.1359.
Probability of a measured value greater than 80 mm:
We can use the standard normal distribution to find this probability, by standardizing the value of 80 mm:
z = (80 - 20) / 30 = 2
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 2 is approximately 0.0228. Therefore, the probability of a measured value of the polymer fiber being greater than 80 mm is approximately 0.0228.
Probability of a measured value between 50 and 80 mm:
Again, we can standardize the values of 50 mm and 80 mm:
z1 = (50 - 20) / 30 = 1
z2 = (80 - 20) / 30 = 2
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between 1 and 2 is approximately 0.1359. Therefore, the probability of a measured value of the polymer fiber being between 50 and 80 mm is approximately 0.1359.
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Miyako hits a jump and follows the path of a parabola.
Her height can be modeled by the equation h = -16t² + 32t + 15,
where his her height in feet after t seconds. Graph the function.
Interpret the key features of the graph in terms of the quantities.
A parabolic function is represented by h = -16T² + 32T + 151.
Describe the parabolic function?A function with the equation f(x) = ax²+ bx + c is said to be parabolic. It is a second-degree quadratic expression in x². A parabola-like form can be seen in the graph of a parabolic function. The range value for the parabolic function is the same for two different domain values. Parabolic motion refers to a variety of motions, such as the motion of a stone thrown under the influence of gravity.
. The function's greatest or minimum value is where the parabola's vertex is located. In this instance, the formula -b/2a,
where a = -16 and b = 321, can be used to get the vertex of the parabola. As a result, this parabola's vertex is located at t = 1 second and h = 31 feet.
The parabola's vertex is located at t = 1 second and h = 31 feet. These are the main characteristics of this graph.
The parabola's axis of symmetry is a vertical line that passes through its vertex.
Because the coefficient of t² is negative, the parabola begins to slope downward.
- The maximum height that Miyako reaches is 31 feet.
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The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3186
grams and a variance of 385,641
. if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be between 3682
and 4552
grams. round your answer to four decimal places.
please need help asap
The probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.
To find the probability that a newborn baby boy's weight Convert the weights to z-scores:
z = (X - μ) / σ, where X is the weight, μ is the mean, and σ is the standard deviation.
First, calculate the standard deviation:
σ = √variance = √385,641 ≈ 621
Now, calculate the z-scores for the given weights:
z1 = (3682 - 3186) / 621 ≈ 0.7986
z2 = (4552 - 3186) / 621 ≈ 2.1965
Use a standard normal table or a calculator with a standard normal probability function to find the probabilities corresponding to these z-scores:
P(Z ≤ 0.7986) ≈ 0.7879
P(Z ≤ 2.1965) ≈ 0.9858
Find the probability that the weight is between the two z-scores:
P(0.7986 ≤ Z ≤ 2.1965) = P(Z ≤ 2.1965) - P(Z ≤ 0.7986) ≈ 0.9858 - 0.7879 ≈ 0.1979
So, the probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.
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Describe the transformation of the graph of f(x) to g(x). f(x) = x^2 g(x) = (x - 2)^2 + 5
The transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.
Explain about the transformation:Think about the function f (x). We measure the movement using the x- and y-axes on a coordinate grid. The following are guidelines for function transformations that could be used with function graphs. All algebraic and graph of transformations are possible.
Transformations can be divided into four categories: translation, rotation, reflection, plus dilation.
Given :
Transformation of the graph of f(x) ---> g(x)
f(x) = x² g(x) = (x - 2)² + 5
There is a shift of 2 units on the left. Subtract 2 from x to get the value (x - 2)
There is a shift of 5 units upward. Add 5 on the function f(x) to get the function g(x).
Thus, the transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.
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What should Andre estimate for the probability of picking out a green block from this bag
The answer using probability are shown:
(A) 43/60 projection is used.
(B) He shouldn't alter the estimate in light of this knowledge.
What is probability?Simply put, the probability is the likelihood that something will occur.
When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.
Statistics is the study of occurrences that follow a probability distribution.
Mathematics' study of random events is known as probability, and there are four major kinds of probability: axiomatic, classical, empirical, and subjective.
So, he would calculate the amount by dividing the overall number of bricks by the proportion of green bricks. The likelihood of choosing a green block out of all 60 bricks would be that.
Then, the probability would be:
= 43/60
Andre shouldn't alter his assessment, in other words.
The explanation is that we do not know whether the bricks he saw were green in color; we are only told that she looked in the bag and found 6 bricks.
The only time Andre needs to adjust his guess is if it turns out that the six bricks Mai saw in the bag were, in fact, green.
The estimate should not be altered until this proof is received.
Therefore, the answer using probability are shown:
(A) 43/60 projection is used.
(B) He shouldn't alter the estimate in light of this knowledge.
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Complete question:
Andre picks a block out of a bag 60 times and notes that 43 of them were green. What should Andre estimate for the probability of picking out a green block from this bag? Mai looks in the bag and sees that there are 6 blocks in the bag. Should Andre change his estimate based on this information? If so, what should the new estimate be? If not, explain your reasoning.