Answers
Answer:
36
Step-by-step explanation:
We have the summation:
\(\displaystyle{\sum_{i=1}^{9} 2i-6\)
Essentially, we want to find the sum of (2i-6) from i=1 to i=9.
First, using summation properties, we can split this to:
\(=\displaystyle{\sum_{i=1}^{9} 2i+\displaystyle{\sum_{i=1}^{9} -6\)
On the right, it will simply be -6 evaluated 9 times. We can also move the constant out from the left:
\(=\displaystyle{2\sum_{i=1}^{9} i+9(-6)\)
For the summation on the left, this will simply be the sum (1+2+3+...+9). This yields 45. Therefore:
\(=2(45)+9(-6)\)
Evaluate:
\(=90-54=36\)
So, our final answer is 36.
Related Questions
The continuous random variable X has a probability density function (pdf) given by f(x) Şi- & for 0 < x < 2 lo otherwise Part(a) Find the median of X, correct to 2 decimal places. 0.59 Part(b) Find P(X >>). Give your answer as a decimal, correct to 2 decimal places. 0.56 Part(c) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one is less than and the other is greater than 2. The order in which we take observations matters. 0.25 Part(d) Find Var(X), correct to 2 decimal places. 0.22 Part(e) Find E(X), correct to 2 decimal places. 0.75 Part(f) Find the value of q such that P(X
Answers
The median of X is 1; P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and the value of q such that P(X < q) = 0.95 is 1.9.
(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.
Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.
For 0 < x < 2, the CDF is:
F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x
Setting (1/2) * x = 0.5 and solving for x:
(1/2) * x = 0.5; x = 1
Therefore, the median of X is 1.
(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.
For x > 2, the PDF is 0, so P(X > x) = 0.
Therefore, P(X > 2) = 0.
(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.
P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)
Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.
Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.
(d) The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:
E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3
To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:
E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Now we can calculate the variance:
Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33
Therefore, Var(X) is approximately 0.33.
(e) The expected value of X, E(X), is given by:
E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Therefore, E(X) is 1.
(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:
∫(0 to q) f(x) dx = 0.95
Since the PDF is constant at 1/2 for 0 < x < 2, we have:
(1/2) * (x) | (0 to q) = 0.95
(1/2) * q = 0.95
q = 0.95 * 2 = 1.9
Therefore, the value of q such that P(X < q) = 0.95 is 1.9.
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A zip line starts on a platform that is 40 meters above the ground. The anchor for the zip line is 198 horizontal meters from the base of the platform. How long is the zip line? *
Answers
Answer:
Solution given:
perpendicular distance =height [p]=40m
base or horizontal distance [b]=198m
Hypotenuse or zip line [h]=?
Now
By using Pythagoras law
h²=p²+b²
h²=40²+198²
h=√40804
h=202m
So the Zip line is 202m long.
1. Shoe B was created by rotating Shoe A counterclockwise about a fixed point. How many degrees was the shoe rotated?
Answers
Answer:
90°
Step-by-step explanation:
Rotation counterclockwise means the rotating an object over a fixed point in the opposite direction of our normal wall clock.
To get exact position of shoe B, shoe A would be rotated in about 90° in the opposite direction of a clock.
Thus, shoe A was rotated 90° about a fixed point to create shoe B.
Prove that if f and g are each uniformly continuous on R, then the composite function
f o g is uniformly continuous on R.
Answers
We have proved that f o g is uniformly continuous on R, as desired.
What is composite function?F(g(x)) or (f g)(x) denotes the combination of the functions f(x) and g(x), where g(x) acts first. It brings together two or more functions to produce a new function.
To prove that the composite function f o g is uniformly continuous on R, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ R,
| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε
We can start by using the uniform continuity of g to choose a δ1 > 0 such that for any x, y ∈ R,
| x - y | < δ1 implies | g(x) - g(y) | < ε
Now, we can use the uniform continuity of f with ε replaced by δ₁ to choose a δ₂ > 0 such that for any u, v ∈ R,
| u - v | < δ₂ implies | f(u) - f(v) | < δ₁
Finally, we can choose δ = δ₂ to show that for any x, y ∈ R,
| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε
To see why this is true, let's assume that | x - y | < δ. Then, by the definition of the composite function,
(f o g)(x) - (f o g)(y) = f(g(x)) - f(g(y))
Now, since | g(x) - g(y) | < δ₁, we know that | f(g(x)) - f(g(y)) | < ε, by the choice of δ₁. And since | x - y | < δ₂ implies | g(x) - g(y) | < δ₁, we have shown that
| x - y | < δ₂ implies | (f o g)(x) - (f o g)(y) | < ε
Therefore, we have proved that f o g is uniformly continuous on R, as desired.
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Do you like me
What is formula
Answers
Answer:
what?
Step-by-step explanation:
Answer:
I am cunfushion
Step-by-step explanation:
In this graph, the number of containers is plotted along the x-axis and the amount of water in the container is along the y-axis
Answers
Answer:
e
Step-by-step explanation:
Identify the sampling technique used to obtain the following sample. the first 35 students leaving the library are asked how much money they spent on textbooks for the semester. Choose the correct sampling technique below. A. Systematic sampling B. Convenience sampling C. Cluster sampling D. Stratified sampling E. Random sampling
Answers
The sampling technique used to obtain the described sample is A. Systematic sampling.
In systematic sampling, the elements of the population are ordered in some way, and then a starting point is randomly selected. From that point, every nth element is selected to be part of the sample.
In the given scenario, the first 35 students leaving the library were selected. This suggests that the students were ordered in some manner, and a systematic approach was used to select every nth student. Therefore, the sampling technique used is systematic sampling.
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x^(1/12) = 49^(1/24), find x
Answers
The calculated value of x in the expression x^(1/12) = 49^(1/24) is 7
Calculating the value of x in the expressionFrom the question, we have the following parameters that can be used in our computation:
x^(1/12) = 49^(1/24)
Express 49 as 7^2
So, we have
x^(1/12) = 7^(2 * 1/24)
Evaluate the products
This gives
x^(1/12) = 7^(1/12)
When both sides of the equations are compared, we have
x = 7
Hence, the value of x in the expression is 7
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Purple paint is made of a ratio of
16 white : 3 blue : 1 red
how much white paint is needed to make one gallon of purple paint?
plz help its important
Answers
there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint (got it from safari)
Please help with this question. Thank you!!!
Answers
Answer:
M(-3, -2.5) and N(3, -1)
Step-by-step explanation:
Given equations:
1st
4y = x - 7make x subject
x = 4y + 7 ___ equation 12nd
x² + xy = 4 + 2y²Substitute equation 1 into 2
x² + xy = 4 + 2y²
\(\sf step : \ x = 4y + 7\)
(4y + 7)² + (4y + 7)y = 4 + 2y²
\(\sf step : \ distribute \ inside \ parenthesis\)
16y² + 56y + 49 + 4y² + 7y = 4 + 2y²
\(\sf step : \ collect \ terms\)
16y² + 4y² -2y² + 56y + 7y + 49 - 4 = 0
\(\sf step : \ simplify\)
18y² + 63y + 45 = 0
\(\sf step : \ middle \ term \ factor\)
18y² + 18y + 45y + 45 = 0
\(\sf step : \ factor \ out\)
18y(y + 1) + 45(y + 1) = 0
\(\sf step : \ collect \ into \ groups\)
(18y + 45)(y + 1) = 0
\(\sf step : \ set \ to \ zero\)
y = -2.5, -1
Now, find value of x
x = 4y + 7
when y = -2.5, x = 4(-2.5) + 7 = -3
when y = -1, x = 4(-1) + 7 = 3
Hence the coordinates are (x, y) = M(-3, -2.5) and N(3, -1).
Answer:
\(M=\left(-3, -\dfrac{5}{2}\right)\)
\(N=(3,-1)\)
Step-by-step explanation:
Given equations:
\(4y=x-7\)
\(x^2+xy=4+2y^2\)
To find the points of intersection, rearrange the linear equation to isolate x:
\(\implies x=4y+7\)
Substitute the found expression for x into the second equation:
\(\implies (4y+7)^2+(4y+7)y=4+2y^2\)
\(\implies 16y^2+56y+49+4y^2+7y=4+2y^2\)
\(\implies 20y^2+63y+49=4+2y^2\)
\(\implies 18y^2+63y+45=0\)
\(\implies 9(2y^2+7y+5)=0\)
\(\implies 2y^2+7y+5=0\)
Factor the quadratic and solve for y:
\(\implies 2y^2+2y+5y+5=0\)
\(\implies 2y(y+1)+5(y+1)=0\)
\(\implies (2y+5)(y+1)=0\)
\(\implies 2y+5=0 \implies y=-\dfrac{5}{2}\)
\(\implies y+1=0 \implies y=-1\)
Substitute the found values of y into the expression for x and solve for x:
\(\begin{aligned}y=-\dfrac{5}{2} \implies x&=4\left(-\dfrac{5}{2}\right)+7\\x&=-10+7\\x&=-3\end{aligned}\)
\(\begin{aligned}y=-1 \implies x&=4\left(-1\right)+7\\x&=-4+7\\x&=3\end{aligned}\)
Therefore, the coordinates of M and N are:
\(M=\left(-3, -\dfrac{5}{2}\right)\)
\(N=(3,-1)\)
Which of these points represent 1/5 on the number line shown below?
Answers
Answer:
Step-by-step explanation:
What is the smallest integer $n$ such that $n\sqrt{2}$ is greater than $20$? (Note: $n\sqrt{2}$ means $n$ times $\sqrt{2}$.)
Answers
Question:
What is the smallest integer \($n$\) such that \($n\sqrt{2}$\) is greater than \($20$\)? (Note: \($n\sqrt{2}$\) means \($n$\) times \($\sqrt{2}$\).)
Solution:
n√2 > 20=> n > 20/√2=> n > 4 x 5/√2=> n > 2 x 2 x 5/√2=> n > √4 x √4 x √25/√2=> n > √2 x √4 x √25=> n > √2 x 4 x 25=> n > 10√2=> n > 14.14 (Rounded)Smallest integer possibility for n is 15.
Hence, the smallest possible integer is 11.
Answer:
15
Step-by-step explanation:
In order to compare $n\sqrt{2}$ to $20$, we can compare the square of $n\sqrt{2}$ to the square of $20.$ We have
\begin{align*}
\left(n\sqrt{2}\right)^2 &= \left(n\sqrt{2}\right)\left(n\sqrt{2}\right) = n^2 \left(\sqrt{2}\right)^2 = n^2\cdot 2= 2n^2,\\
20^2 &= 400.
\end{align*}Therefore, we have $n\sqrt{2} > 20$ whenever $n^2 > 200.$ Since $14^2 = 196$ and $15^2 = 225,$ we know that $\boxed{15}$ is the smallest integer $n$ such that $n\sqrt{2}$ is greater than $20.$
Help!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answers
Answer:
\(Slope (m) = -\frac{2}{3}\)
Step-by-step explanation:
To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.
Thus, on the line, let's pick 2 points as our coordinate pairs at:
When x = -6, y = 5 => (-6, 5), and
When x = 3, y = -1 => (3, -1)
Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)
\( Slope (m) = \frac{y2 - y1}{x2 - x1} \)
\( Slope (m) = \frac{-1 - 5}{3 - (-6)} \)
\( Slope (m) = \frac{-1 - 5}{3 + 6} \)
\( Slope (m) = \frac{-6}{9} \)
\(Slope (m) = -\frac{2}{3}\)
Jose's ball is stuck on the roof of his home, which is 8 feet high. He wants to use a ladder to climb up and get his ball. If he sets the base of the ladder 6 feet away from his home, what is the minimum length that the ladder can be? Explain how you solved this question using context and at least three sentences. Hint: Draw your the scenario and label given values.
Answers
Answer:
10 feet
Step-by-step explanation:
It becomes a right-angled triangle with height of 8feet and base of 6feet.
Using Pythagoras theorem:
a² = b² + c²
a² = 8² + 6²
a² = 64 + 36
a² = 100
a = √100
a = 10
Find the x and y values? I'm not really sure how to get y but I can seem to get the x value.
Answers
They are vertical angles which are congruent.
Because the lines are parallel, the 71 degree angle and the (5x-26) angle when added together need to equal 180 degrees.
SO you have 71 + 5x -26 = 180
Simplify:
5x + 45 = 180
Subtract 45 from both sides:
5x = 135
Divide both sides by 5:
x = 135 / 5
x = 27
Now you have x solve what that angle equals:
5x - 26 = 5(27) - 26 = 135 - 26 = 109 degrees
The angle Y and the angle 5x-26 are vertical angles, which mean they are the same,
so now we know 5x-26 = 109 degrees, so Y also equals 109 degrees.
The answers are:
x = 27
y = 109
A rental company charges $40 a day and 30 cents a mile for renting a truck. Michael rents a truck for 5 days, and his bill comes to $314. How many miles did he drive?
Answers
314 - 200 = 114
114 / 0.3 = 380
So, he drove 380 miles.
Sorry if I misunderstood
Please give brainliest
Have a good day :)
A die is rolled and a coin is flipped simultaneously. the number rolled on the die and whether the coin lands heads or tails is recorded. how many outcomes are in the sample space? 8 6 10 12
Answers
Answer: 12
Step-by-step explanation:
The transitive property of equality states that _____. if a = b, then b = a if a = b, then ac = bc if a = b and b = c, then a = c if a = b and c = c, then a + b = b + c
Answers
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
i got it right on a test
.It makes sense to measure the number of students in a class in partial quantities.
True or False
Answers
can somebody help me with this question 18 divided by (-3)
Answers
Answer:
-6
Step-by-step explanation:
Consider the following data for a dependent variable y and two independent variables, ₁ and 2. x1 22 30 12 45 11 25 18 50 17 41 6 50 19 75 36 12 59 13 76 17 The estimated regression equation for thi
Answers
69.56 + 0.32x₁ - 0.18x₂ is the equation that fits the given data for the dependent variable y and the two independent variables x₁ and x₂.
The given data for a dependent variable y and two independent variables, x₁ and x₂, are as follows:
x₁: 22, 30, 12, 45, 11, 25, 18, 50, 17, 41, 6, 50, 19, 75, 36, 12, 59, 13, 76, 17
y: 50, 90, 50, 80, 60, 80, 50, 70, 60, 70, 50, 70, 90, 80, 70, 60, 80, 50, 70, 60
The estimated regression equation for the given data is given by:
y = 69.56 + 0.32x₁ - 0.18x₂
Here:
y represents the dependent variable.
x₁ and x₂ are the two independent variables.
Therefore, the equation that fits the given data for the dependent variable y and the two independent variables x₁ and x₂ is y = 69.56 + 0.32x₁ - 0.18x₂.
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a ratio of the vertical change to the horizontal change of two points is called:_____.
Answers
Answer:
Step-by-step explanation:
Slope of the line.
Matilda and Lorraine work in the mail room of a large company sorting letters. Matilda has already sorted 50 letters and continues sorting at a rate of 50 letters per hour. Lorraine has already sorted 80 letters and continues sorting at a rate of 40 letters per hour.
Which function can Matilda and Lorraine use to determine the total number of letters they have sorted after x hours? How many letters will they have sorted after 6 hours?
A.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 100x + 120. Thus, they will have sorted 720 letters in 6 hours.
B.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 130. Thus, they will have sorted 670 letters in 6 hours.
C.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 130x + 90. Thus, they will have sorted 870 letters in 6 hours.
D.
The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 30. Thus, they will have sorted 570 letters in 6 hours.
Answers
Answer:
B
Step-by-step explanation:
40x + 80
50x + 50
add them together
????????????????????????????
Answers
Answer:
The answer is in the 4th quadrant
Step-by-step explanation:
I really hope this helped!!! have a great day. :)
Can the following angle measures be the interior angles of a triangle: 29°, 29°, and 29° ? Justify your answer.
Answers
Answer:
No
Step-by-step explanation:
Angle measures of a triangle must add up to 180 and this only adds up to 87
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answers
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A(\(x_1,y_1\)) to B(\(x_2,y_2\)) is given by the formula:
\((x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )\)
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
\(x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2\)
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
\(J = (-6,-2)\)
\(K = (8,-9)\)
The ratio is given as:
\(m : n =2 : 5\)
The x-coordinate is then calculated using:
\(x = (\frac{m}{m + n }) (x_2 - x_1) + x_1\)
So, we have:
\(x = (\frac{2}{2 + 5 }) (8 - -6) -6\)
\(x = (\frac{2}{7}) (14) -6\)
Expand
\(x = (2) (2) -6\)
Open bracket
\(x = 4 -6\)
Subtract 6 from 4
\(x = -2\)
Hence, the x coordinate of the segment is -2
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Which polynomial function has a leading coefficient of 2, root –4 with multiplicity 3, and root 10 with multiplicity 1? f(x) = 2(x – 4)(x – 4)(x – 4)(x 10) f(x) = 2(x 4)(x 4)(x 4)(x – 10) f(x) = 3(x – 4)(x – 4)(x 10) f(x) = 3(x 4)(x 4)(x – 10)
Answers
The equation of the polynomial function is f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)
How to determine the polynomial function?The given parameters are:
Leading coefficient, n = 2Root = -4; Multiplicity = 3Root = 10; Multiplicity = 1The polynomial function is represented as:
f(x) = n * (x - root)^multiplicity
So, we have:
f(x) = 2 *(x + 4)^3 * (x -10)^1
This gives
f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)
Hence, the equation of the polynomial function is f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)
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Answer:
C f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)
Step-by-step explanation:
TRUS. HAVE A GOOD TEST
WXYZ~EFGD.13WXYZ26EFGDWhat is the similarity ratio of WXYZ to EFGD?Simplify your answer and write it as a proper fraction, improper fraction, or whole number
Answers
STEP - BY - STEP SOLUTION
What to find?
The similarity ratio of WXYZ to EFGD.
Given:
The ratio of WXYZ to EFGD can be determine by taking the ratio of any of the simila side of WXYZ to EFGD.
That is;
\(Similarity\text{ ratio=}\frac{WZ}{ED}\)Since EFGD is a rectangle, using the property of the rectangle that state " opposite sides are congruent, we can deduce that ED = EG = 6
Hence,
\(similarity\text{ ratio=}\frac{WZ}{ED}=\frac{3}{6}=\frac{1}{2}\)ANSWER
1/2
the distance between -8 and 6
Answers
Answer:
14 is the number of distance between them if you're asking for
-8-6 it's 2
Answer:
12
Step-by-step explanation:
Get the absolute value of -8 and 6, which is 8 and 6, and add them together.
NEED HELP ASAP solve for x : 3/5 = x-1/8
a.5 b.29/5 c.23/5 d.19/5
Answers
Answer:
\( \boxed{ \sf{ \bold{ \huge{ \boxed{ \frac{29}{5} }}}}}\)Option B is the correct option.
Step-by-step explanation:
\( \sf{ \frac{3}{5} = \frac{x - 1}{8} }\)
Apply cross product property
⇒\( \sf{ 5(x - 1) = 3 \times 8}\)
Distribute 5 through the parentheses
⇒\( \sf{5x - 5 = 3 \times 8}\)
Multiply the numbers
⇒\( \sf{5x - 5 = 24}\)
Move 5 to right hand side and change it's sign
⇒\( \sf{5x = 24 + 5}\)
Add the numbers
⇒\( \sf{5x = 29}\)
Divide both sides of the equation by 5
⇒\( \sf{ \frac{5x}{5} = \frac{29}{5} }\)
⇒\( \sf{x = \frac{29}{5} }\)
Hope I helped!
Best regards!!