(a) The mean of Y is 100 meters, and the standard deviation of W is approximately 0.7348 meters.
(b) The mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
a) To find the mean and standard deviation of Y, where Y = (X₁ + X₂) / 2, we use the properties of the mean and variance of a sum of independent random variables.
Mean of Y:
The mean of Y is simply the average of the means of X₁ and X₂, as the measurements are independent and have the same true height of 100 meters.
Mean(Y) = (Mean(X₁) + Mean(X₂)) / 2 = (100 + 100) / 2 = 100 meters
The standard deviation of Y:
When adding or subtracting independent random variables, the variances add up. Since the measurements are independent, we can use the formula:
Var(Y) = Var((X₁ + X₂) / 2) = (Var(X₁) + Var(X₂)) / 4
Now, calculate the variance of Y:
Var(Y) = (1.2² + 0.85²) / 4 ≈ 0.54
Standard deviation(Y) = √Var(Y)
≈ √0.54
≈ 0.7348 feet
b) Now, let's find the mean and standard deviation of W, where W = (1/3)X₁ + (2/3)X₂.
Mean of W:
Mean(W) = (1/3) * Mean(X₁) + (2/3) * Mean(X₂)
= (1/3) * 100 + (2/3) * 100
= 100 meters
The standard deviation of W:
To calculate the standard deviation of W, we need to find the variance of W and then take its square root.
Var(W) = (1/3)² * Var(X₁) + (2/3)² * Var(X₂)
= (1/9) * 1.2² + (4/9) * 0.85²
Now, calculate the variance of W:
Var(W) = 0.0181 + 0.1956 =0.481
Standard deviation(W) = √Var(W)
≈ √0.481
≈ 0.6935 meters
So, the mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
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For each value of u, determine whether it is a solution to 9u-7≥65.
Find the coordinate using the subtraction method
-2x+9y=-9
-3x+5y=12
The co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
How to co-ordinate using subtraction method?
The technique of subtracting one vector's coordinates from another vector's coordinates is known as vector subtraction.Addition is represented by travelling up the -axis and to the right on the -axis. Subtraction is represented by going left and down the -axis. Since we are travelling below, we can deduct from our coordinate point, and since we are heading rightward, we can add to it.So, the given equations are
-2x+9y=-9 ⇒ (i)
-3x+5y=12 ⇒ (ii)
(i) * 5 ⇒ -10x + 45y = -45
(ii) * 9 ⇒ -27x + 45y = 108
⇒ 17x = 153
x = 9
Now, substitute x=9 in equation (i)
-2(9) + 9y = -9
-18 + 9y = -9
9y = -9 + 18
y = 9/9
y = 1
Hence, the co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
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Quick!
The chart shows the results of 24 spins that Suzanne made with a spinner.
Based on these results, what is the probability that Suzanne's spinner will land on France the next time?
Answer:
I was going to answer but there is no attachment.
Step-by-step explanation:
I NEED URGENT HELP.⚠️
Find the intercepts of the line
y+1=3(x-4)
Answer:
x=13/3
Step-by-step explanation:
what is 1-1/3 pls help me
Answer:
2/3
Step-by-step explanation:
1-1/3 is the same that 3/3 - 1/3
3/3 - 1/3 = 2/3
a restaurant wants to gather data about a new dish by giving out free samples and asking for feedback. who should the restaurant give samples to? 1 point all diners diners who are willing to pay for the samples 80% of diners diners who spend the most money on their meal
The correct option regarding who should the restaurant give samples to generate a representative sample is given as follows:
All diners diners who are willing to pay for the samples.
What is sampling?Sampling is a technique for when a group of elements from a population is taken to represent the entire population.
This group of elements has to be representative of the entire population, as to lead to correct conclusions.
In this problem, all the dinners who are willing to pay for the samples should be sampled, as if they are willing to pay, it means that they are interested in the new dish, hence their opinions should be considered as it would improve the restaurant's revenue with the new dish.
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HELP ME ASAP!!!!!!!!
Answer:
The lie is #3
Step-by-step explanation:
The only way to solve this is by testing each equation to see if it's true. Remember that dividing powers with the same base, in this case b, means you're just subtracting the exponents.
Substituting 5 for y in #1 gives us the equation [tex]\frac{b^9}{b^5}=b^4[/tex]. This is the same as saying [tex]b^9^-^5=b^4[/tex], which is true.
Substituting 7 for z and 2 for x in #2 gives us [tex]\frac{b^7}{b^2}=b^5[/tex]. Like we did for the first one, this is the same as [tex]b^7^-^2=b^5[/tex], which is also true.
That means that #3 is a lie, but substituting 2 for x anyway gives us [tex]\frac{b^8}{b^2}=b^8[/tex], or [tex]b^8^-^2=b^8[/tex]. This is not a true statement, and x would have to equal 0 for this to be true.
Omar is constructing equilateral triangle ABC. Using a compass and a straightedge, he need to copy AB to
form the other two sides of the triangle. He sets the compass width to AB and draws two arcs from A as shown.
Points A and B with identical construction marks as parts of a circle with center point A.
After plotting point C, he will draw three line segments to connect points A, B, and C. What steps should he follow to plot point C?
Without changing the compass width, draw an arc from B to intersect the other arc, and plot point C.
Without changing the compass width, draw an arc from B, and plot point C on the new arc.
Increase the compass width, draw an arc from B to intersect the other arc, and plot point C.
Increase the compass width, draw an arc from B, and plot point C on the new arc.
An equilateral triangle is a triangle that has three equal-length sides, commonly referred to as a "regular" triangle.
What is the equilateral triangle?When all three sides of a triangle are equal, the triangle is said to be equilateral. The third side is likewise equal in this unique instance of an isosceles triangle. A triangle with the sides AB, BC, and CA is equilateral.An equilateral triangle is a triangle whose three sides are all the same length, also referred to as a "regular" triangle. An isosceles triangle with three equal sides is called an equilateral triangle. It is a special case of an isosceles triangle.An equilateral triangle in geometry is a triangle whose sides are all of the same length. Since the three sides are equal, the three angles that are opposite the equal sides are also equal.Find the attachment answer
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find the equation of a line passing through points (-9,8) (-18,12)
Answer: -4/9
Step-by-step explanation:
12 - 8 / -18 - (-9)
4 / -18 + 9
4 / -9
- 4/9
I need help with this question been stuck on it for a while
The correct options are B and C, or 3x-21 and -3x21, since the inequality sign must be "flipped," or reversed, whenever you multiply or divide both sides of the inequality.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.
x≤-7
3x≥-21
-3x≤21
The correct options are B and C that is 3x≥-21 and -3x≤21 because anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.
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Alex made a $4000 down payment on a car. The total cost of the car was $11000. He made 40 equal monthly payments to pay the car in full. How much did Alex pay per month? Define a variable, write an equation, and solve.
Answer: Alex Paid $175 for 40 months
Step-by-step explanation:
$4000 = y-int or b
$11000 = y
40 months = x
Slope - intercept form : Y=mx+b
We are solving for m which is the slope (How much Alex Paid per month)
11000=m(40)+4000
11000=40m+4000
7000=40m
7000/40
m=175
In art, what is the difference between symmetry and balance?
This should probably go in the ART section of Brainly, it may be confusing to people like me, who only have math on here :]
Balance is the use of even elements in a work of art, while symmetry is a type of balance, where parts of the image are mirrored.
Hope this helps,
:]
In triangle TSP, TS=SP=10 cm, TP= 12 cm. Find three heights of triangle TSP
pls answer quickly I will give brainliest to fastest answer
Answer:
Plot each graph on the same coordinate system.
TSP
TP=12cm
T
Step-by-step explanation:
What is the equation of this line? Graph of a line passing through the origin and the point begin ordered pair 4 comma negative 1 end ordered pair
Answer:
y = - [tex]\frac{1}{4}[/tex] x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line
m = [tex]\frac{-1-0}{4-0}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x ← equation of line
The figure shows two parallel lines cut by a transversal what is the value of x
The value of.x will be 20 and the angles will each have a value of 90 degrees.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
Hence, The value of.x will be 20 and the angles will each have a value of 90 degrees.
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--------------------
Answer:
-------------------
Step-by-step explanation:
Please say the transformations it would take to get ABCD TO A’B’C’D’
The sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
What is Graph transformation?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Given is a quadrilateral ABCD and its transformed form.
The following transformations are done to obtain the transformed image -
The quadrilateral ABCD is reflected across the y - axis.The following transformation → (x - 2, y - 0) is applied to the image.Then, the image is reduced by a scale factor of [k] which is less than one.Therefore, the sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
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A box has length of 6 feet width of 7 feet and a height of 4 inches
Answer: 168in^3
Step-by-step explanation:
6 x 7 x 4 = 168
In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
The score of the netball team in 5th game is 26.
What is average?A number that is calculated by adding quantities together and then dividing the total by the number of quantities is called average.
Given that, a team scored average 31 points in first four game, and then 30 points average in first five game.
Score in 4 games = 4x31 = 124
Score in 5 games = 5x30 = 150
Score in 5th game = 150-124 = 26
Hence, The score of the netball team in the 5th game is 26.
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The point (2, 90) represents the value that after 2 weeks, Paul's math average is a 90. The
point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to a 50
because he doesn't do homework and doesn't know how to log into Quizlet. What equation
represents the line of Paul's grade downfall? (5 Points)
y = -0.10x + 130
y=20x-100
y = 20x- 130
y=0.10x+90
y=-20x+90
y=-20x+130
Answer:
The equation that represents the line of Paul's grade downfall is:
y = (-20)x + 130
This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul's math average) decreases by 20.
Step-by-step explanation:
To find the equation that represents the line of Paul's grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul's math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to 50. We can plot these two points on the coordinate plane as follows:
(2, 90)
(4, 50)
To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points, we get:
m = (50 - 90) / (4 - 2)
= -40 / 2
= -20
To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:
y = mx + b
Substituting the coordinates of the point (2, 90) and the slope of -20, we get:
90 = (-20)(2) + b
= -40 + b
= b - 40
Solving for b, we get:
b = 90 + 40
= 130
Below are two parallel lines with a third line intersecting them.
x =
136
Solve this problem and explain how you did it. Hurry, it's due by Sunday at 11:59 pm!
Answer: m<a 57 degrees
Step-by-step explanation:
All of the angles are the same and equal, so all angles are 57 degrees. Including m<a
which exspression shows 50+30 written as a product of two ffactors
Hey, sorry if I mixed up some words I had just broke my wrist yesterday...
Now, 50 Can be written as five, multiplied by 30 can be written as three multiplied by 10. So 50 unless 30 that's equal to five, multiplied by 10 plus three, multiplied by 10. here 10 is a common factor. So this equals 10 multiplied by the sum of five and three.
Adam and Eric went hiking at different times. Adam is currently 73 feet above sea level while Eric is just starting at 24 feet below sea level. What is the difference in their elevations?
Answer: The answer is 97
Step-by-step explanation:
Since Adam is above sea level, the number 73 is positive. The number 24 would be negative since it's below sea level.
73 - ( -24) = 97
To check to make sure it's right we can do this:
-24 + 97 = 73
73 - 97 = -24
i need help pls and explain how it would help alot thjanks
Answer:
neither are functions
Step-by-step explanation:
For a relation to be a function each value of the input x must map to exactly one unique value in the output y
(1)
This relation is not a function since
7 → 2 and 5 → 2
Two different values of x have the same output , thus not a function
(2)
This relation is not a function since
3 → 10 and 3 → 8
Two different values of x have the same output, thus not a function
Answer:
Step-by-step explanation:
neither are functions
Express the radical using the imaginary unit, i.
Express your answer in simplified form.
+√-16 = ±
What is the range of the function f(x) = -2(x+1)-2, when the domain is {-5, 0, 5}?
A {-5,0,5}
B {-11,-1,9}
C {-14,-4,6}
D {-10, 0, 10}
Answer: D
Step-by-step explanation:
To find the range, substitute each element in the domain into the function.
[tex]f(-5)=-2(-5+1)-2=-10\\\\f(0)=-2(0+1)-2=0\\\\f(5)=-2(5+1)-2=10[/tex]
Which line is parallel to the line given below? y=-4/3x+1
The line which is parallel to the given line y=-4/3x+1 is y = -4/3x + 2
What is the equation of the line?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that the equation of the line is:
y = -4/3x + 1 ..........(1)
To find the equation of the line is parallel to the given line equation.
We know that the given equation is in the slope-intercept form
y = mx+c, where m is the slope and c, is the intercept.
Compare with given equation(1) we get
m = -4/3 and c=1
Now change the y-intercept c=1 to an intercept of c= 2
Therefore (1) becomes
y = -4/3x + 2
Hence, The equation of line y = -4/3x + 2 is the parallel line to the given equation of the line.
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Which is g(x)? In this question
The equation of the transformed function is (c) g(x) = 4(1/3x)²
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
g(x) = horizontally shrunk of f(x) by a factor 1/3 and vertical stretch by a factor of 4
The above equations implies that, we have the transformation to be:
Horizontally shrunk of f(x)Vertical stretch by a factor of 4Mathematically, this can be represented as
g(x) = 4f(1/3x)
Substitute the known values in the above equation, so, we have the following representation
g(x) = 4(1/3x)²
Hence, the transformed function si g(x) = 4(1/3x)²
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23 ✓24 In a recent year, 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
The Total number of registered doctors will be 246753.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Let the total number of doctors be x.
Since 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year. This will be:
23.1% × x = 55700
0.231x = 55700
Divide
x = 57000 / 0.231
x =246753
The doctors are =246753.
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