The area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is given by
Area = ∬R dA where R is the region we're trying to find the area of.
We can find the area of the region by subtracting the area of the smaller circle from the area of the larger circle.
The area of the larger circle is:
Area = ∬R dA = ∬((x − 2)^2 + y^2 <= 4) dA = π*4 = 4π
The area of the smaller circle is:
Area = ∬((x^2 + y^2) <= 4) dA = π*4 = 4π
Therefore, the area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is
Area = 4π - 4π = 0
The area of the region is 0 square units.
Answer:
I agree with kiddobreeze08
Prove that the two lines represented by the following equations are perpendicular to each other.
a)6x²-5xy-6y² = 0
b) x²-y²+x+y=0
c) x² - y² = 0
Two lines represented by the following equations are perpendicular to each other. Explanation is given below.
What is a perpendicular line?Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.
We have the equations:
a)6x²-5xy-6y² = 0
b) x²-y²+x+y=0
c) x² - y² = 0
The above lines are the product of two separate lines.
To prove that the two lines represented by the following equations are perpendicular to each other:
We have drawn the graphs of all the three equations.
The attached images are equation 1, equation 2, equation 3 are in the order of a, b and c.
And we can clearly see that the lines are perpendicular.
The general formula of the equation,
ah²+ 2hk + bk² = 0.
When a+b = 0,
Then the lines are perpendicular.
The sum of the coefficients of order 2 variable is zero.
a). 6 - 6 = 0
b). 1-1 = 0
c). 1-1 = 0
Therefore, the proof is given above.
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How do you find the ratio of a line segment?
P=(m+nmx2+nx1,m+nmy2+ny1). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
What is the segment ratio formula?
P=(m+nmx2+nx1,m+nmy2+ny1). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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what is the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise?
The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).
What is rotation?
The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.
Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then
=> (x , y) = (-8,0)
Now 270 degrees counter clockwise rotation then,
=> (y,-x) = (0,-(-8))
=> (y,-x)=(0,8)
Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).
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Express
2x² + 8x + 3
in the form 2(x + p)² + q
Answer:
2x^2 + 8x + 3 in 2( x + 2 )^2 + q form is 2( x + 2 )^2 - 5
managers must make a number of important decisions about the use of control charts. what are they? multiple select question. what size samples to take how often samples should be taken how many control charts to use to monitor the process what type of control chart to use what tools to use to take measurements at what points in the process to use control charts
Managers must make all the given vital decisions from the options, hence, d) All of the above is the correct answer.
Managers must make a number of important decisions about the use of control charts, some of which include:
What size samples to takeHow often samples should be takenHow many control charts to use to monitor the processWhat type of control chart to use (e.g. X-bar chart, R chart, etc.)What tools to use to take measurementsAt what points in the process to use control charts.These are all important decisions that managers need to make when using control charts to monitor and improve processes in an organization. The right decisions can help ensure that control charts are effective in detecting and addressing issues with processes, while the wrong decisions can lead to control charts being ineffective or even counterproductive.
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The complete question is -
Managers must make a number of important decisions about the use of control charts. what are they?
multiple select questions.
a) what size samples to take and how often samples should be taken.
b) how many control charts to use to monitor the process.
c) what type of control chart to use.
d) what tools to use to take measurements at what points in the process to use control charts.
e) All of the above.
Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
1. how many cups of water should he use with 6 scoops of fruit mix?
2. Rate needed
3. What is the unit rate?
4. Interpretation of unit rate?
12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup
What is the unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.
Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1
∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.
Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3
=0.5 scoops/cup of water
The unit rate means the number of scoops that are required to be mixed with a cup of water.
Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup
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jessie uses a graph to record deposits into her savings account. her account starts with $80 deposits. she adds $25 per week to the account
Camera search
Answer: y=25x+80
Step-by-step explanation:
a car rental company charges an initial fee of $42 and a daily fee of $12. a customer pays a total of $138. how many days did the customer rent the car?
The customer rented the car for 8 days.
The total amount paid by the customer, $138, is made up of the initial fee and the daily fee multiplied by the number of days the car was rented.
We can set up the equation as:
138 = 42 + 12x (where x is the number of days the car was rented)
To find the number of days, we can subtract the initial fee from both sides of the equation:
138 - 42 = 12x
96 = 12x
Then we can divide both sides by 12 to solve for x:
x = 8
So the customer rented the car for 8 days.
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From the parent function, how has the equation y = (x+3)² been shifted?
Up 3
Down 3
Right 3
Left 3
The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.
How has the equation been shifted?For a general function y = f(x), we define a horizontal translation of N units as:
g(x) = f(x + N)
if N > 0, the shift is to the left.if N < 0, the shift is to the right.Here the original function is y = x² and the translated one is:
y = (x + 3)²
So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.
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For each data set below determine the: a) order of each reactant b) rate law expression c) overall order of the reaction d) value of the rate constant with proper units 1981
The explanation of each of the term are defined below.
The order of each reactant is known as the reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations.
The term rate law expression in math is defined as the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power in which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.
The term overall order of the reaction is known as the sum of orders for each reactant.
Finally value of the rate constant means the rate constant is temperature dependent.
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you need to find the height of the cylinder
TSA = 2πrh + πr² (r = 40/2 = 20)
4715 = 40πh + 400π
4715/(40π) = h + 10
≈ 37.5 = h + 10
h = 27.5 cm
Hope this helped.
Answer:-
h = 17.52cm
Step-by-step explanation:
To find the height, we'll use the formula for a surface area of a cylinder.
[tex]\boxed{\sf SA=2\pi rh+2\pi r^2}[/tex]
Since the diameter is 40 cm, than the radius is :-
[tex]\sf r=\cfrac{d}{2}[/tex][tex]\sf r=\cfrac{40\;cm}{2}[/tex][tex]\sf r=20cm[/tex]Now, let's substitute the values to the SA formula:-
[tex]\sf 4715\;cm^2=2\pi (20cm)h+2\pi (20cm)^2[/tex]
[tex]\sf 4715cm^2=40\pi cmh+800cm^2\pi[/tex]
[tex]\sf \cfrac{4715cm^2-800cm^2\pi }{40\pi cm} =\cfrac{40\pi cm(h)}{40\pi cm}[/tex]
[tex]\sf h=\cfrac{2,201.725877cm^2}{40\pi cm}[/tex]
[tex]\sf h=17.52\; cm[/tex]
____________________
Hope this helps!
Have a great day!
and 49 are complementary . If m angle3=3x-7 and m angle9=4x-1 , find m angle3 .
Answer: m angle3 = 3x - 7 = 3(14) - 7 = 37 degrees
Step-by-step explanation:
Since angles 3 and 9 are complementary, their measures add up to 90 degrees. So, we can set up the equation:
m angle3 + m angle9 = 90
We can substitute in the given values for the measures of each angle:
(3x - 7) + (4x - 1) = 90
Solving for x:
7x - 8 = 90
7x = 98
x = 14
In Exercises 1-4, find the exact values of the six trigono-
metric functions of the angle shown in the figure. (Use the
Pythagorean Theorem to find the third side of the triangle.)
1.
2.
0
8
6
0
13
5
Only number 1 and 2
Answer:
1. 10
2. 12
Step-by-step explanation:
1. 8² + 6² = y² (Taking the unknown side as y)
64 + 36 = 100
y² = 100
y = 10
2. 5² + x² = 13² (Taking the unknown side as x)
x² = 13² - 5²
= 169 - 25
= 144
x² = 144
x = 12
If a road map has a scale of 3 in: 100 mi, find the following distances
How far is it between Cardwell and Claremont if they are 4.5 inches apart on the map?
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
If a road map has a scale of 3 inches to 100 miles.
Then the scale factor is given as,
Sclar factor = 100 / 3
Sclar factor = 33.33 miles per inch
Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,
Distance = 33.33 x 4.5
Distance = 150 miles
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
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The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90. What is the
value of the third quartile for this data set?
OA. 85
OB. 90
OC 92.5
OD. 95
The answer reads "40," is the correct response to the earlier question.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.
There are data of 9 students and we need to arrange them in ascending order to find our answer.
So, the arrangement looks like the following:
⇒ 25, 35, 45, 50, 60, 80, 90, 95, 100
We are aware that
In all cases, the middle value is the median.
Therefore, it is safe to say that the Median of the aforementioned arrangement is 60.
Hence, Median of the numbers on the left of the median is 60=35+45/2 = 40
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what is the x value of the solution to this system of equations? 2x-3y=8 4x+5y=2
Answer: y=18
Step-by-step explanation:
Communication Explain how to use algebra to find two numbers whose difference is 8 and whose product is a minimum.
The two numbers are 4 and -4, and their product is 4 * -4 = -16, which is the minimum value.
What is algebra?Generally, To find two numbers whose difference is 8 and whose product is a minimum, we can use algebra. Let's call the two numbers x and y. We know that:
x - y = 8 (the difference between the two numbers is 8)
To find the product of the two numbers, we can multiply x and y:
xy = x(x - 8) = x^2 - 8x
To find the minimum value of the product, we can take the derivative of this expression with respect to x and set it equal to 0:
d(xy)/dx = 2x - 8 = 0
Solving for x, we find that x = 4.
Therefore, one of the numbers is 4. We can use the equation x - y = 8 to find the other number:
4 - y = 8
y = -4
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what is the value of
HURRY UP PLEASE WILL GIVE brainliest and 50 pts.
Answer:
Step-by-step explanation:
Anything raised to the power of 0 equals 1, so we have 1 raised to the power of -3. That's the same thing as
[tex]\frac{1}{1^3}[/tex] which is just 1. The answer is 1.
Is it possible to form a triangle whose sides are 6cm 5 cm and 9 cm?
Yes, it is possible to construct a triangle with the given sides 6cm 5 cm and 9 cm.
As given in the question,
Let the triangle with the given side length be ΔABC.
Measure of the side length is equal to :
Side Length 1 ( AB ) = 6cm
Side Length 2 ( BC ) = 5cm
Side Length 3 ( CA ) = 9cm
To construct a triangle following property should satisfied:
Sum of the two side length is always greater than the third side.
AB + BC
= 6cm + 5cm
= 11cm > 9cm
BC + CA
= 5cm + 9cm
= 14cm > 6cm
CA + AB
= 9cm + 6cm
= 15cm > 5cm
Here the required condition to construct a triangle is satisfied.
Therefore, yes it is possible to construct a triangle with the given sides measure .
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given this information, in order to use her 4 hours of time spent studying to get the highest possible test score, how many hours should she have spent solving multiple choice problems, and how many hours should she have spent reviewing lecture notes? 0 hours working on problems, 4 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.
The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.
So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
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Find the equation of a circle with centre c(3,2) and locus of point p(1,1)
The equation of the circle with center (3, 2) and point (1, 1) is:
(x - 3)² + (y - 2)² = 5.
The equation of a circle with center (h, k) and radius r is given by the equation: (x - h)² + (y - k)² = r²
To find the equation of the circle with center (3, 2) and a point on the circle (1, 1), we first need to find the radius of the circle. We can use the distance formula to find the distance between the center and the point on the circle:
r = √((1 - 3)² + (1 - 2)²) = √((-2)² + (-1)²) = √5
So the radius of the circle is √5
Now we can substitute the center and radius into the equation of a circle:
(x - 3)² + (y - 2)² = (√5)²
Simplifying, we get:
(x - 3)² + (y - 2)² = 5
So the equation of the circle with center (3, 2) and point (1, 1) is:
(x - 3)² + (y - 2)² = 5.
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Rewrite the following equations in the form ax + by = c, where A is a positive integer.
y = x + 9
y = -6x - 5
y = 2/3x + 1
Answer:
y = x + 9 ==> x + (-y) = -9
y = -6x - 5 ==> 6x + y = -5
y = 2/3x + 1 ==> 2x/3 + (-y) = -1
Step-by-step explanation:
y = x + 9 ==> isolate the constant 9
**Don't subtract x on both sides as x has to be positive**
y - 9 = x ==> keep x positive by subtracting 9 on both sides
-9 = x - y ==> subtract y on both sides to isolate the constant
x + (-y) = -9 ==> make the equation in the form of ax + by = c
y = -6x - 5 ==> isolate the constant -5
y + 6x = -5 ==> isolate -5 by adding 6x on both sides, making x positive
6x + y = -5 ==> make the equation in the form of ax + by = c
y = 2x/3 + 1 ==> isolate the constant 9
**Don't subtract 2x/3 on both sides as x has to be positive**
y - 1 = 2x/3 ==> keep x positive by subtracting 1 on both sides
-1 = 2x/3 - y ==> subtract y on both sides to isolate the constant
2x/3 + (-y) = -1 ==> make the equation in the form of ax + by = c
A line segment can be drawn from each vertex of a polygon to every other vertex, forming the sides and diagonals of the polygon. A square, for example, has 4 sides and 2 diagonals. Using combinations, write an expression that would give you the total number of sides and diagonals for a polygon with n sides.
The total number of sides and diagonals for a polygon with n sides is given by the equation n(n - 3)/2.
What is polygon?In geometry, a polygon is a two-dimensional closed object with straight sides that is flat or planar. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the spots where two sides meet.
Here,
A square has 4 sides and 2 diagonals.
Now, a pentagon will have 5 sides and 5 diagonals
A hexagonal when drawn will have 6 sides and 9 diagonals
Thus, we see that;
When n = 4, d = 2
When n = 5, d = 5
When n = 6, d = 9
Using combination, we will find number of pairs of 2 vertices that can possibly be formed from n-vertices. Thereafter we will subtract n from that since it's neighboring vertices can't combine with the current one.
Thus, we have;
C(n, 2) - n
This gives s;
(n(n-1)/2) - n
Simplifying this gives;
(n(n - 1) - 2n)/2
(n² - n - 2n)/2
(n² - 3n)/2
n(n - 3)/2
The expression that would give you the total number of sides and diagonals for a polygon with n sides is n(n - 3)/2.
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the area of a trapezium is 1440 cm². if the lengths of its parallel sides are 54.6 cm and 35.4 cm, find the distance between them
Answer:
h = 32 cm
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the distance between the parallel sides b₁ and b₂
given A = 1440 , b₁ = 54.6 , b₂ = 35.4 , then
[tex]\frac{1}{2}[/tex] h (54.6 + 35.4) = 1440 ( multiply both sides by 2 to clear the fraction )
h × 90 = 2880 ( divide both sides by 90 )
h = 32
the distance between the parallel sides is 32 cm
what is the end behavior:
[tex]0.5\sqrt[3]{x-4}-5[/tex]
Step-by-step explanation:
f(x) = 0.5 ∛(x − 4) − 5
As x approaches ∞:
f(∞) = 0.5 ∛(∞ − 4) − 5
f(∞) = 0.5 ∛(∞) − 5
f(∞) = 0.5 (∞) − 5
f(∞) = ∞ − 5
f(∞) = ∞
As x approaches -∞
f(-∞) = 0.5 ∛(-∞ − 4) − 5
f(-∞) = 0.5 ∛(-∞) − 5
f(-∞) = 0.5 (-∞) − 5
f(-∞) = -∞ − 5
f(-∞) = -∞
A mall independent movie company determine the profit, P, for producing n DVD copie of a recent releae i P=-0. 02n^23. 4n-16. P i the profit in thouand of dollar and n i in thouand of unit
The equation P = -0.02n^2 + 3.4n - 16 represents the profit, P, in thousands of dollars for a small independent movie company as a function of the number of DVD copies produced, n, in thousands.
The equation is a quadratic equation, which means it is a polynomial equation of degree 2. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants and x is the variable. In this case, the equation can be written as P = -0.02n^2 + 3.4n - 16, where P is the variable, and -0.02, 3.4, and -16 are the constants.
The first term in the equation is -0.02n^2, which represents the cost of producing the DVD copies. As n increases, the cost of production also increases, and the coefficient -0.02 represents that the cost of production is directly proportional to n^2. The negative sign in front of the term indicates that as the number of copies increases, the cost of production also increases and thus the profit decreases.
The second term in the equation is 3.4n, which represents the revenue generated by the sale of the DVD copies. As n increases, the revenue generated also increases, and the coefficient 3.4 represents that the revenue is directly proportional to n. The positive sign in front of the term indicates that as the number of copies increases, the revenue generated also increases and thus the profit increases.
The last term in the equation, -16, represents the fixed costs associated with producing the DVD copies, such as overhead costs, marketing and distribution costs, etc. These costs are not directly related to the number of copies produced and are constant regardless of how many copies are produced.
In summary, the equation P = -0.02n^2 + 3.4n - 16 represents the profit for a small independent movie company as a function of the number of DVD copies produced. The profit is affected by the cost of production, revenue generated from sales, and fixed costs. As the number of copies increases, the cost of production increases, the revenue generated increases, and the fixed costs remain constant. The profit is the difference between the revenue generated and the costs incurred.
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The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.
The length of the median of the trapezoid is 12.
The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.
So, we can write the equation as follows:
(1/2) * 5 * (b1 + b2) = 60
To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.
So, the length of the median is (b1 + b2) / 2.
We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.
(1/2) * 5 * (b1 + b2) = 60
(1/2) * 5 * (b1 + b2) = 60
b1 + b2 = 24
b1 = b2 + 4
b2 = 24 - b1
b1 = (24 - b1) + 4
b1 = 24 - b1 + 4
b1 = 28 - b1
b1 = 28 - (24 - b1)
b1 = 4 + b1
b1 = b2 + 4
b1 = b1
So, the lengths of the bases are equal to 14 and 10.
Length of median = (14 + 10) / 2 = 12.
Therefore, The length of the median of the trapezoid is 12.
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a collector offers to buy state quarters for $2000\%$ of their face value. the face value of each quarter is $25$ cents. at that rate how many dollars will bryden get for his four state quarters?
A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.
In the given question, a collector offers to buy state quarters for 2000% of their face value.
The face value of each quarter is 25 cents.
We have to find at that rate how many dollars Bryden will get for his four state quarters.
As given that,
Collector buy state quarters = 2000% of their face value
We can write 2000% as 20×100%.
It means that state quarters is 20 times of their face value.
As we know that, 4 quarter is equal to the one dollar. So,
Bryden get for his four state quarters = 20×1 dollars
Bryden get for his four state quarters = 20 dollars
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The expected value of a discrete random variable (a) is the outcome that is most likely to occur (b) can be found by determining the 50% value in the c.d.f. (c) equals the population median. (d) is computed as a weighted average of the possible outcome of that r able, where the weights are the probabilities of that outcome.
Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
Variable : What is it ?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.
Here,
Given :
A discrete random variable's anticipated value
So, in order to determine the expected value of a discrete random variable,
we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,
where weights are the probability of that outcome.
Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
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a therapist wanted to determine if yoga or meditation is better for relieving stress. the therapist recruited 100 of her high-stress patients. fifty of them were randomly assigned to take weekly yoga classes and the other 50 were assigned weekly meditation classes. after one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. the therapist wants to construct a 95% confidence interval for the difference in proportions of patients experiencing stress relief after yoga and after meditation. are the conditions for inference met?
The required Confidence interval for the given data is CI = 0.6 - 0.7 ± 1.96[tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex].
What is hypothesis test?Hypothesis testing is a methodical process for determining whether research study findings are consistent with a specific idea that pertains to a population. To evaluate a hypothesis about a population, hypothesis testing uses sample data.
According to question:We have,
x1 = 30, x2 = 35
n1 = 50, n2 = 50
p1 = x1/n1 = 30/50 = 0.6
p2 = x2/n2 = 35/50 = 0.7
Then,
at α= 0.05, the critical value taken by table of z
Zc = 1.96
CI =[tex]P_{1}-P_{2}[/tex] ±[tex]\sqrt{\frac{P_{1}(1-P_{1})}{n_{1}}+\frac{P_{2}((1-P_{2})}{n_{2}} }[/tex]
CI = 0.6 - 0.7 ± 1.96 [tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex]
This is our needed answer,So option (D) is correct.
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