It should be noted that to prove that arc AB is equal to arc CD, we can use the fact that vertical angles are equal. Specifically, the angles formed by radii OA and OB are vertical angles with angles formed by radii OC and OD.
How to explain the proofingLet's call the angle formed by radii OA and OB angle x, and the angle formed by radii OC and OD angle y. Since ZAOB is a central angle of circle O, we know that arc AB is equal to twice angle x. Similarly, since COD is a central angle of circle O, we know that arc CD is equal to twice angle y.
Now, since angles x and y are vertical angles, they are equal. Therefore, arc AB is equal to twice angle x, which is equal to twice angle y, which in turn is equal to arc CD.
Therefore, we have proven that arc AB is equal to arc CD.
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Assuming line ABCD is a diameter. The proof is not valid in general for any chord.
What is circle theorem?To prove AB = CD, we show triangles ABO and DCO are congruent.
1. OB=OC radius of inner circle
2. OA=OD radius of outer circle
3. angle ABO = angle DCO
4. SSA = SSA indicates congruent triangles
Therefore AB = CD
Angles ABC and DCB are straight angles.
Angles OBC and OCB are congruent triangle OBC is isosceles with OB=OC
Therefore angle ABO = ABC - OBC = DCB - OCB = DCO
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Find the surface area of the sphere. Use 3.14 for pi.
sphere is 7 yd
Figure LMNO is a reflection of HIJK. Which angle is congruent to ZH?
The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.
When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.
In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.
Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
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A brick has a mass of 2,022.75 grams and a volume of 1,064.5 cubic centimeters.
What is the density of the brick, in grams per cubic centimeter (³) ²¹
g
cm
3
Round your answer to the nearest tenth.
Answer:
To find the density of the brick, we need to divide its mass by its volume:
density = mass / volume
Plugging in the values given in the problem, we get:
density = 2,022.75 g / 1,064.5 cm³
Simplifying the division, we get:
density = 1.8996 g/cm³
Rounding to the nearest tenth, we get:
density ≈ 1.9 g/cm³
Therefore, the density of the brick is approximately 1.9 grams per cubic centimeter (g/cm³).
URGENT!! Will give brainliest :)
What is the equation for the line of best fit for the following data? Round the slope and -intercept of the line to three decimal places.
A. y=-0.580×+ 10.671
B. y=-10.671 x+ 0.580
C. y= 10.671 x-0.580
D. y= 0.580x - 10.671
To find the equation for the line of best fit, we can use linear regression. Based on the given data:
x: 2, 5, 7, 12, 16
y: 9, 10, 5, 3, 2
The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.
Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.
The result is:
Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)
So, the correct answer is:
A. y = -0.580x + 10.671
of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
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please help and explain and show your work on how you got the answer. I WILL MARK YOU BRAINLIEST
Answer:
Step-by-step explanation:
it is -2
Answer: -2
Step-by-step explanation:
So this is asking for the cube root of -8.
This is the same as asking what is multiplied by itself 3 times to get -8.
-2 * -2 *-2 = -8
You can also use a calculator.
Another way to solve it is to write -8^(1/3).
Hope this helps!!!
A scale drawing of a famous statue uses a scale factor of 230:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
191.7 feet
228.2 feet
231.2 feet
276 feet
The actual height of the statue is option C 231.2 feet.
What is scale factor?A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.
In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.
Given that the scale factor is 230:1.
Thus,
actual height of statue / 230 = height of drawing / 1.2 feet
Now,
actual height of statue = (1.2 feet / 1.2 feet) * 230
actual height of statue = 230 feet
Hence, the actual height of the statue is option C 231.2 feet.
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1.what is the surface area of a cone with a radius of 5m and a slant height of 8m?
2.a box has a side of 9cm what is its surface area?
3.compute for the surface area of a cube with a side of 8cm
4.an aquarium has a length of 6m width of 10m and a height of 7m what is its surface area?
5.find the surface area of a rectangular prism with a length of 5cm width of 8cm and a height of 6cm
6.what is the surface area of a square pyramid with a side of 9cm and a height of 7cm.
the school picnic is a two-day weekend event. it has been scheduled for may. the area routinely gets 16 rainy days in may. what is the probability that the weekend will be dry?
The probability of the weekend being dry for the school picnic is approximately 23.4%.
First, let's define some terms:
1. Probability: The likelihood of a specific event happening
2. Picnic: The school event that is scheduled for a two-day weekend in May
3. Rainy: Refers to days with rain
Now, let's calculate the probability that the weekend will be dry:
There are 16 rainy days in May, and May has 31 days. So, there are (31 - 16) = 15 dry days in May.
Each weekend has two days. Since May has 31 days, there are (31 / 7) = approximately 4.43 weeks in May. To account for the remaining days, we round down to 4 weeks and add the remaining 2 days as another weekend, resulting in 5 weekends.
Now, we'll determine the probability of having a dry day on any given day in May:
Dry day probability = (number of dry days) / (total days in May) = 15 / 31 ≈ 0.484
Since we want the probability of having two consecutive dry days (the whole weekend), we'll multiply the probabilities of each day being dry:
Weekend probability of being dry = (dry day probability) * (dry day probability) ≈ 0.484 * 0.484 ≈ 0.234
So, the probability of the weekend being dry for the school picnic is approximately 23.4%.
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A curved ladder that children can climb on can be modeled by the equation y=-1/20x^2+x where x and y are measured in feet. Make a table of values that shows the height of the ladder for x = 0, 5, 10 , 15, and 20 feet from the left end
The values of x and y of a curved ladder in feet given by the equation y=-1/20x^2+x are as follows in tabular form,
Values of x (in feet) Values of y (in feet)
0 0
5 3.75
10 5
15 3.75
20 0
A curved ladder that children can climb on is modeled by the system of equations as,
y=-(1/20)x^2+x
where, x and y are measured in feet.
Putting x= 0 in the above equation y=-(1/20)x^2+x , we get,
y = - (1/20) (0^2) + (0) = 0
Putting x= 5 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(5^2)+(5) = -5/4 + 5 = 15/4 = 3.75
Putting x= 10 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(10^2)+(10) =-5 +10 = 5
Putting x= 15 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(15^2)+(15) = -45/4 +15= 3.75
Putting x= 20 in the above equation y=-(1/20)x^2+x , we get,
y= - (1/20)(20^2)+(20) = -20 +20 = 0
Hence, when x= 0 feet, y = 0 feet ; x= 5 feet, y = 3.75 feet ; x = 10 feet, y = 5 feet ; x =15 feet , y =03.75 feet ;and x = 20feet, y = 0 feet from the solving the given equation.
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true or false? use cases can help with developing quantitative and measurable usability tests. group of answer choices
The given statement about developing quantitative and measurable usability tests is true.
Explain about how this given statement is true?Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.
By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.
This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.
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An 18 gram sample of a substance that's used to detect explosives has a k-value of 0.215.
Find the substance's half-life in days. Round your answer to the nearest tenth.
The substance's half-life in days is 3 days.
What is exponential decay?
If a quantity declines at a pace proportionate to its current value, exponential decay may be present. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time.
Here, we have
Given: An 18-gram sample of a substance that's a by-product of fireworks has a k-value of 0.215.
We have to find the substance's half-life in days.
Using the formula for the exponential decay that is N = N₀e⁻ⁿˣ,
we have N = 18/2, N₀ = 18, and n = 0.215.
N = N₀e⁻ⁿˣ
9 = 18e⁻⁰°²¹⁵ˣ
9/18 = e⁻⁰°²¹⁵ˣ
1/2 = e⁻⁰°²¹⁵ˣ
Taking logs on both sides, we get
㏑(1/2) = -0.215x
x = ㏑(1/2)/(-0.215)
x = -0.6931/(-0.215)
x = 3.22
Hence, the substance's half-life in days is 3 days.
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What is the total surface area of the figure shown?
The total surface area of the given figure is 619.2 in², which is not listed in the provided options.
Give a brief account on total surface area.The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.
The triangular face of the given figure represent an equilateral triangle of sides 12 in.
Area of the triangle = (√3/4) × a²
Area of the triangular face:
= (√3/4) × 12²
= (√3/4) × 144
= 57.6 in²
Area of the rectangle = Length × width
Area of the rectangular face:
= 12 × 14
= 168 in²
Area of the given figure:
= (2 × 57.6) + (3 × 168)
= 115.2 + 504
= 619.2 in²
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please someone help and give answers !!!
16.) Mean average deviation= option C
17.) Range of a data set = option E.
18.) First quartile = opinion AB
19.) Second quartile = option B
20.) Third quartile = option A
21.) Interquartile range = option D
How to determine the measures of the spread?
To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:
16.) Mean average deviation: The average deviation of data from the mean.
17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.
18.) First quartile: The median in the lower half.
19.) Second quartile: The median value in a data set.
20.) Third quartile: The median in the upper half.
21.) Interquartile range: The distance between the first and the third quartile.
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What is the value of x in this triangle?
x=47°
The degree of a triangle is equal to 180°.
Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.
180-102-31=47°
Therefore the answer would be x=47°
a production process is designed to fill 100 soda cans per minute with with 6.8 ounces of soda, on average. overfilling is costly and under-filling risks a large fine. you are the production chief and instruct your staff to take regular random samples to test the process. what is the correct way to set up the hypotheses test?
Answer:
6.8 ounces
To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.
We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.
If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.
I hope this helps! Let me know if you have any other questions.
The distance between two cities on a map is 17 centimeters. The scale on the map relates 5 centimeters on the map as 30 miles on the road. What is the actual distance, in miles, between the two cities?
Answer: 102 miles.
Step-by-step explanation:
You divide 17 by 5 and then multiply by 30.
4y = -x - 32 (Show work)
Answer: the solution for y in terms of x is y = (-1/4)x - 8.
Step-by-step explanation: In order to obtain a solution for y in the given equation of 4y = -x - 32, it is imperative to achieve the isolation of y on a singular side of the equation. To accomplish this task, it is possible to perform division on both sides of the equation by a factor of 4:
The given equation 4y/4 = (-x - 32)/4 can be expressed in an academic manner as follows: The given equation reveals that the quotient of 4y divided by 4 is equivalent to the quotient of the opposite of x added to negative 32, also divided by 4.
Upon performing simplification, the expression on the right-hand side yields:
The equation y = (-1/4)x - 8 can be expressed in an academic manner as follows: The dependent variable y is equivalent to the product of the constant (-1/4) and the independent variable x, with an additional decrement of eight.
Find a degrees. a 12 13 5
In the given triangle, α is equal to 67.36°.
What is a triangle's definition?
A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).
Now,
Using Trigonometric functions
We can use the sine function
So,
Sin α=Perpendicular/Hypotenuse
Sin α = 12/13
α=67.36°
Hence,
The value of α will be 67.36°.
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Mack's Toy Shop made 600 trains yesterday and found that 30 were defective. They
plan to make 4,500 trains this week.
Using the information given, how many trains are expected to be defective?
225 trains
6,000 trains
15 trains
500 trains
Answer:
225 trains
Step-by-step explanation:
since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :
600 / 30 = 20/1
one out of 20 is defect.
so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :
4500 / 20 = 225
I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?
Explain what values must be known to write the explicit formula for both an arithmetic and geometric sequence?
PLEATHE!!
The explicit formula for an arithmetic sequence is:
an = a1 + (n-1)d
The explicit formula for a geometric sequence is:
an = a1 * [tex]r^{(n-1)}[/tex]
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
To write the explicit formula for both an arithmetic and geometric sequence, the following values must be known:
For an Arithmetic Sequence:
The first term (a1) of the sequence.
The common difference (d) between consecutive terms in the sequence.
The explicit formula for an arithmetic sequence is:
an = a1 + (n-1)d
Where:
an is the nth term of the sequence.
a1 is the first term of the sequence.
d is the common difference between consecutive terms.
n is the position of the term in the sequence.
For a Geometric Sequence:
The first term (a1) of the sequence.
The common ratio (r) between consecutive terms in the sequence.
The explicit formula for a geometric sequence is:
an = a1 * r^(n-1)
Where:
an is the nth term of the sequence.
a1 is the first term of the sequence.
r is the common ratio between consecutive terms.
n is the position of the term in the sequence.
Therefore, The explicit formula for an arithmetic sequence is:
an = a1 + (n-1)d
The explicit formula for a geometric sequence is:
an = a1 * [tex]r^{(n-1)}[/tex]
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PLS HELP ME ON THIS
WHAT COULD BE THE LARGEST WHOLE NUMBER?
Step-by-step explanation:
7 + x = 2x, so x = 7
In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 3.5 inches. What is the probability that a randomly selected student will be taller than 63 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.
A local doctor’s office logged the number of patients seen in one day by the doctor for ten days. Find the mean, median, range, and midrange of the number of patients seen in ten days.
27, 31, 27, 35, 35, 25, 28, 35, 33, 24
Calculate the mean, median, range, and midrange of the number of patients seen in ten days.
Answer:
Step-by-step explanation:
Medium is 28
Mean is 29
Range is 11
Midrange is 29.5
how would you define the actual score and theoretical score on an exam, and how would you calcutre the percent success
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
We define the actual score, theoretical score, and explain how to calculate the percent success on an exam.
Actual score:
The actual score refers to the number of points a student has earned on an exam.
It represents the student's performance on the test, taking into account the correct and incorrect answers.
Theoretical score:
The theoretical score is the maximum number of points a student can earn on an exam.
This represents a perfect performance, where the student answers all questions correctly.
Calculating percent success:
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
a. Divide the actual score by the theoretical score: (actual score) / (theoretical score)
b. Multiply the result by 100: (result from step a) * 100
c. The final value is the percent success.
For example, if a student has an actual score of 80 and the theoretical score is 100, the percent success would be calculated as follows:
a. 80 / 100 = 0.8
b. 0.8 * 100 = 80
c. The percent success is 80%.
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What is the range of f? A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
Choose 1 answer:
(Choice A) The f(x)-values -6, -3, 0, 2, and 5
(Choice B) The f(x)-values -5, -2, 0, 2, and 5
(Choice C) -6 ≤ f(x) ≤ 5
(Choice D) − 5 ≤ f(x) ≤ 5
The range of f include the following: D. -5 ≤ f(x) ≤ 5.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-6, 5} or -6 ≤ x ≤ 5.
Range = {-5, 5} or -5 ≤ f(x) ≤ 5.
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how can the power series method be used to solve the nonhomogeneous equation, about the ordinary point ? carry out your idea by solving the equation. you can either attach your work or type in your work.
The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.
The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.
Assuming that the nonhomogeneous differential equation has the form
y''(x) + p(x)y'(x) + q(x)y(x) = f(x)
where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation
y''(x) + p(x)y'(x) + q(x)y(x) = 0
Using the power series method, we can assume a solution of the form:
y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...
where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.
Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.
After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:
y(x) = u(x) + v(x)
where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.
Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.
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In ΔUVW, w = 1. 4 cm, m m∠W=63° and m m∠U=29°. Find the length of v, to the nearet 10th of a centimeter
The length of v, to the nearest 10th of a centimeter is 2.2.
To find the length of side v in triangle UVW, 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 sides and angles in the triangle.
Using this formula, we have,
v/sin(m∠V) = w/sin(m∠W)
We know that w = 1.4 cm and m∠W = 63°. To find sin(m∠W), we can use a calculator,
sin(63°) ≈ 0.89
Substituting the values we know into the formula, we get,
v/sin(m∠V) = 1.4/0.89
To solve for v, we need to find sin(m∠V). We know that the sum of the angles in a triangle is 180°, so we can find m∠V by subtracting the measures of the other two angles from 180°,
m∠V = 180° - m∠U - m∠W
m∠V = 180° - 29° - 63°
m∠V = 88°
Now, we can substitute the value of sin(m∠V) into the equation and solve for v,
v/ sin(88°) = 1.4/0.89
v ≈ 2.2 cm
Therefore, the length of side v in triangle UVW is approximately 2.2 cm to the nearest tenth of a centimeter.
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Answer:
1.6
Step-by-step explanation: This is answer on DeltaMath
a researcher has collected the following sample data. the mean of the sample is 5. 3 5 12 3 2 the coefficient of variation is . a. 81.24% b. 72.66% c. 330% d. 264%
The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is 91%. Option A is the correct answer.
To calculate the coefficient of variation, first, we need to calculate the standard deviation and mean of the sample.
The mean of the sample is (3 + 5 + 12 + 3 + 2)/5 = 5.
To find the standard deviation, we first need to calculate the variance. The variance can be found by taking the sum of the squared differences between each data point and the mean, dividing by the sample size minus one, and then taking the square root.
The variance is ((3-5)² + (5-5)² + (12-5)² + (3-5)² + (2-5)²)/4 = 20.5.
The standard deviation is the square root of the variance, which is approximately 4.53.
Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100%.
Coefficient of variation = (4.53/5) x 100% = 90.6%.
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The question is -
A researcher has collected the following sample data. The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is?
a. 91%
b. 72.66%
c. 330%
d. 264%
An electronic book device had a value of t dollars before a holiday. The value decreased by 15% after the holiday. Which expressions show the value of the electronic book device after the holiday? Select all the expressions that apply.
A. 1.15
B. 0.85
C. −0.15
D. 1−0.15
E. −0.85
F. (1−0.15)
The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
Which expressions show the value of the electronic book device after the holiday?The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.
Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.
In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).
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