Compute the orthogonal projection of [-2 2] onto the line through [ -1 5] and the origin. The orthogonal projection is [ __ __ ]
Answers
the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75] using unit vector.
First, we need to calculate the unit vector of the line. This can be done by subtracting the two given points and dividing the result by the magnitude of the vector:
[-1 5] - [0 0]
= [-1 5]
|[-1 5]| = sqrt(1^2 + 5^2) = sqrt(26) = 5.1
Unit vector = [-1/5.1 5/5.1] = [-0.196 0.980]
Next, we need to calculate the dot product of the vector [-2 2] and the unit vector [-0.196 0.980]. This will give us the scalar projection.
(-2)(-0.196) + (2)(0.980) = -0.392 + 1.960 = 1.568
Finally, we can calculate the orthogonal projection by multiplying the scalar projection by the unit vector.
[-0.196 0.980] (1.568) = [-0.301 1.527]
Rounding to two decimal places, the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75].
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Related Questions
any jus want to help with this? i attached the picture
Answers
1. The difference in the distance of Jupiter from the sun than Mercury will be 4.816.
2. The difference in the distance of Neptune from the sun than Mars will be
3. The greatest distance between Earth and Uranus is Uranus.
4. The greatest distance between Venus and Saturn is Saturn
How to calculate the distance?From the information, the average distance from the sun to each planets have been given. The difference in the distance of Jupiter from the sun than Mercury will be:
= 5.203 - 0.387
= 4.816
The difference in the distance of Jupiter from the sun than Mars will be:
= 30.07 - 1.524
= 28.546
The greatest distance between Earth and Uranus is Uranus and the greatest distance between Venus and Saturn is that of Saturn.
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Suppose X,Y and Z are three different random variables. Let X obey a Bernoulli Distribution. The probability distribution function is. c is a constant here.
Let Y obey the Standard Normal (Gaussian) Distribution, which can be written as Y N(0,1). X and Y are independent. Meanwhile, let Z = XY.
Calculate the covariance of Y and Z (Cov(Y, Z)) and determine whether values of c would affect the correlation.
Answers
The value of c does not affect the covariance of Y and Z.
How did we arrive at this assertion?The covariance of Y and Z can be calculated as Cov(Y, Z) = E[YZ] - E[Y]E[Z]. Since X is Bernoulli with parameter p and E[X] = p, we have E[Z] = pE[Y]. Hence,
Cov(Y, Z) = E[YZ] - E[Y]E[Z]
= E[YXY] - pE[Y]^2
= pE[Y^2 X] - pE[Y]^2
= p(E[Y^2]E[X] + Var[Y]p) - pE[Y]^2
= p(1 * p + 1 * p^2) - p^2
= p - p^2
It can be seen that the value of c does not affect the covariance of Y and Z.
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the table represents a function.
x
-6
-2
0
3
f(x)
3
1
4
-2
Answers
The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
Function is defined as an expression that defines a relationship between one variable and another variable .
In the question ,
it is given that ,
the value of the function f(x) at different values of x is given ,
we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .
from the table , we see that when x \(=\) -2 , the value of f(x) is \(=\) 1 ,
that means f(-2) \(=\) 1 .
Therefore , The value of the function f(x) at x = -2 is , f(-2) = 1 , the correct option is (c) .
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What is the answer pleaseee
Answers
Answer: 803.84cm3
Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.
To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.
4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.
Now, we have the area of the circle. 50.24cm squared!
The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,
16cm x 50.24cm squared = 803.84cm cubed.
The volume of the can of soup is 803.84cm cubed.
▀▄▀▄What is the LCM and GCF of 25 and 75? ▄▀▄▀
Answers
Answer:
LCM = 75
GCF = 25
Step-by-step explanation:
25 = 5 x 5
75 = 3 x 5 x 5
LCM = 3 x 5 x 5 = 75
GCF = 5 x 5 = 25
Hope that helps!
Answer: The LCM of 25 & 75 is 75, and the GCF of them is 25
Step-by-step explanation: hope it helps :)
John had a baseball cards until he gave x cards away. How many cards does he have now?
Answers
Answer:
I don’t think the question makes sense
If x = 2, y = 3 and z = -5, find the value of square root of x + y squared + z squared
Answers
The value of square root of x + y squared + z squared is 30
How to solve algebra?x = 2, y = 3 and z = -5
\(( \sqrt{x + y} )^{2} + z ^{2} \)
substitute the value of x, y and z
\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)
simplify the square root and square
\( = (2 + 3) + 25\)
\( = 5 + 25\)
\( = 30\)
Ultimately, x + y squared + z squared is 30
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One cylinder has a volume that is 8 Centimeters cubed less than StartFraction 7 over 8 EndFraction of the volume of a second cylinder. If the first cylinder’s volume is 216 Centimeters cubed, what is the correct equation and value of x, the volume of the second cylinder?
StartFraction 7 over 8 EndFraction x + 8 = 216; x = 182 centimeters cubed
StartFraction 7 over 8 EndFraction x minus 8 = 216; x = 196 centimeters cubed
StartFraction 7 over 8 EndFraction x + 8 = 216; x = 238 centimeters cubed
StartFraction 7 over 8 EndFraction x minus 8 = 216; x = 256 centimeters cubed
Answers
Answer:
7/8X-8=216
x=256
7/8x-8=216
+8 +8
7/8x=224
7/8 7/8
x=256
Step-by-step explanation:
Fill in the blanks to follow the steps in solving the equation:
5x − 12 − 6x = −10x + 7 − 1
Answers
Answer:
see explanation
Step-by-step explanation:
5x - 12 - 6x = - 10x + 7 - 1
step 1 : combine like terms
- x - 12 = - 10x + 6
step 2 : collect x- terms on the left side of the equation
add 10x to both sides
9x - 12 = 6
step 3 : collect constants on the right side of the equation
add 12 to both sides
9x = 18
step 4 : isolate x by dividing both sides by 9
x = 2
To solve the equation 5x - 12 - 6x = -10x + 7 - 1, combine like terms and isolate the x term and we get x=2
Explanation:To solve the equation 5x - 12 - 6x = -10x + 7 - 1, we need to combine like terms on both sides of the equation. Let's start by combining the x terms on the left side:
(5x - 6x) - 12 = -10x + 7 - 1
Simplifying further:
-x - 12 = -10x + 6
Next, we want to get all the x terms on one side of the equation. We can do this by adding 10x to both sides:
-x - 12 + 10x = -10x + 6 + 10x
Simplifying further:
9x - 12 = 6
Now, we want to isolate the x term. Let's add 12 to both sides:
9x - 12 + 12 = 6 + 12
Simplifying further:
9x = 18
Finally, divide both sides of the equation by 9 to solve for x:
x = 2
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the dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. the dynamic equation shows the mathematical conversion to z-scores in real-time. drag the vertical line to see the corresponding z-score for each possible class size.
Answers
The Z-Score associated on moving one standard devations to the right is equals to the 1.0, i.e., Z = 1.00. So, correct answer is option (c).
We have, The number of classes, n = 5
Mean of size of five classes,µ = 44
Standard deviations for five classes,σ = 8
The dynamic equation for conversion to z-scores in real-time is, Z = (Xᵢ - µ )/standard deviations (s)
Z-Score : A Z-Score is a metric that represents that how closely a value relates to mean of set of values. If Z score value is zero that means data point's scores are same as mean score.
Formula for Z- Score is Z = (X - µ)/σ
where, X ---> data values
µ --> mean of values
σ --> standard deviation
For 32, Z = (X - µ)/σ = (32 - 44)/8 = -1.50
For 42 , Z= (X- µ)/σ = (42 - 44)/8 = -0.25
For 48, Z = ( 48 - 44)/8 = 0.5
For 52, Z = ( 52 - 44)/8 = 1.0
For 54, Z = (54 - 44)/8 = 1.25
When we move One standard deviations to right , that means X = 44 + 8 = 52 , So the Z-Score for 52 is Z = 1.0. Hence, required value is 1.0.
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Complete question:
The dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. The dynamic equation shows the mathematical conversion to z-scores in real-time. Drag the vertical line to see the corresponding z-score for each possible class size,
Z =( Xᵢ - X)/s Created by Gary M. McClelland, Professor Emeritus | University of Colorado Boulder Cengage Learning. All Rights Reserved. 1. Make sure the green line is on the mean value of x= 44. Next, move the green line one standard deviation to the right. What Z-score is associated with this value?
a. ) Z-0.75
b) Z= 0.80
c) Z = 1.00
d) Z = 0.5
The number of visits to public libraries increased from 1.5 billion in 1991 to 1.7 billion in 1996. Find the average rate of change in the numb
of public library visits from 1991 to 1996.
The average rate of change between 1991 and 1996 was
(Simplify your answer. Type an integer or a decimal.)
Save
billion
Answers
The average rate of change between 1991 and 1996 is 40 million
How to determine the average rate of change between 1991 and 1996?The given parameters are:
Population in 1991 = 1.5 billion
Population in 1996 = 1.7 billion
The average rate of change between 1991 and 1996 is calculated as:
Rate = (1.7 billion -1.5 billion)/(1996 - 1991)
Evaluate
Rate = 40 million
Hence, the average rate of change between 1991 and 1996 is 40 million
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Joelle can read 3 pages in 4 minutes, 4.5 pages in 6 minutes, and 6 pages in 8 minutes. What is the unit rate
Answers
Joelle can read 3 pages in 4 minutes, than means 3/4 = 0.75 pages per minute
4.5 pages in 6 minutes = 4.5/6 = 0.75 pages per minute
6 pages in 8 minutes = 6/8 = 0.75 pages per minute
The rate is contant and is equal to 0.75 pages per minute
Answer:
0.75 pages per minute
What is the solution to the equation x/4 = 6/12?x = 1x = 2x = 8x = 4
Answers
The equation given is,
\(\frac{x}{4}=\frac{6}{12}\)Multiply both sides by 4
\(4\times\frac{x}{4}=4\times\frac{6}{12}\)Simplify
\(x=2\)Hence, x = 2.
PLS LOOK AT PHOTO
HELPPP ASAP!!!
[6 11 -47
1
-5
6 8 -5
3 -9 6
Match each value to the correct entry in matrix AB.
[5 7
54
A = 4 -1
27
23
and B= 2
Answers
The matrix is 3 × 3 square matrix . Its values are:
\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)
Given,
Matrix A and Matrix B
Now,
According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.
So,
Apply multiplication rule,
\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)
Thus the values of the matrix can be calculated.
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Which equation can be used to solve for x xx in the following diagram? Choose 1 answer: (Choice A) A ( 5 x + 30 ) − 5 x = 90 (5x+30)−5x=90left parenthesis, 5, x, plus, 30, right parenthesis, minus, 5, x, equals, 90 (Choice B) B ( 5 x + 30 ) + 5 x = 180 (5x+30)+5x=180left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 180 (Choice C) C ( 5 x + 30 ) + 5 x = 90 (5x+30)+5x=90left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 90 (Choice D) D 5 x = ( 5 x + 30 ) 5x=(5x+30)
Answers
Answer: answer is C
Step-by-step explanation:
for find x
(5x+30)+5x=90
5x+30+5x=90 add like terms
after,
10x+30=90
10x+30-30=90-30
10x/10=60/10
x = 6
to obtain answer as C
it mean
(5x+30)+5x=90
(5(6)+30)+5(6)=90 we know x=6 so add 6 to x and multiply and obtain answer is correct!
30+30+30=90
Solve by using subitution
Please explain your steps and explain why it's no solution thanks :)
2x-y=2. Y=2x+1
Answers
Y=2x+1
2x-y=2
2x-(2x+1)=2
-1=2
-1+1=2+1
0=3
No solution
Answer:
No Solutions
Step-by-step explanation:
1. Substitute the 2x + 1 in for the y in the first equation. Rewrite it as 2x - (2x + 1) = 2.
2. Add the opposite and change the equation to 2x + -1(2x + 1) = 2.
3. Use the distributive to make the equation look like this: 2x + -2x + -1 = 2
4. Combine like terms and add 2x and -2x. They cancel each other out.
5. You will end up with -1 ≠ 2. Since -1 and 2 are not equal, there are no solutions.
An elevator goes up to seven floor it travels down five floors from there it goes up three floors write a sum of integers that could be used to determine the location of the elevator get the last four in which the elevator stops
Answers
The elevator is on level five
Model the problem with algebra tiles. Then use the model to write an algebraic expression that represents the situation. Enrique decreased his weight by four pounds for the wrestling tournament. How can you model this situation? The situation can be modeled with algebra tiles as and . The situation can be represented as the algebraic expression .
Answers
Answer:
Model the problem with algebra tiles. Then use the model to write an algebraic expression that represents the situation.
Enrique decreased his weight by four pounds for the wrestling tournament.
How can you model this situation?
The situation can be modeled with algebra tiles as
✔ one orange x tile
and
✔ four blue – tiles
.
The situation can be represented as the algebraic expression
✔ x – 4
.
Step-by-step explanation:
Answer:
one orange x tile four blue - tiles x-4
Step-by-step explanation:
hope u have a great day also a good quote u were born to stand out not blend in
Question 11(Multiple Choice Worth 5 points)
(One-Step Inequalities MC)
Which graph represents the solution to the inequality -0.25 is greater than or equal to the product of a number and -0.5?
Answers
A graph which represents the solution to the given inequality (-0.25 ≥ -0.5n) is: graph .
What is an inequality?An inequality is to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).Translating the word problem into an inequality, we have:
-0.25 ≥ -0.5 × n
Next, we would find the solution to this given inequality in order to determine its graph:
-0.25 ≥ -0.5n
Dividing both sides by -0.5, we have:
n ≥ -0.25/-0.5
n ≥ 0.5
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2x + 4 < 10 I really need help on this
Answers
Answer:
x < 3
Step-by-step explanation:
Answer:
x < 3
Step-by-step explanation:
treat the sign as if it was an equal sign
then you would solve for x
2x < 6
x < 3
however, there are some cases where the sign would switch directions, you can search up "inequalities algebra" to see more examples
what is −4/5+40/75+100%=
Answers
-0.8+1.875+100%
1.05+100%
0.1
Before Buddy the Elf goes crazy pushing all of the buttons on the elevator, only 4 buttons are lit up out of 79 floors. About what percent is this?
Can anyone help a girl out?
Answers
Answer:
5%
Step-by-step explanation:
DIvide 4 by 79
Andrew has a Frisbee™ with a radius of 5 cm. What is the approximate circumference of the Frisbee™?
Answers
Answer:
the circumference of the dics is 62.8cm
Step-by-step explanation:
i need help last question
Answers
Answer:
whatever u got form p and n just add it and that will be your asnwer i think
Step-by-step explanation:
Help please it’s important
Answers
Answer:
C
Step-by-step explanation:
plz i need the answer today
Answers
sorry
i dont know
i wish i could help
Answer:
Step-by-step explanation:
Oreana's 150 g bag of trail mix is x% raisins. Brandon's 250 g bag of trail mix is y% raisins. They combine the two mixes together in one bowl.
Write an expression which shows how many grams of raisins are in the bowl
Answers
The expression which shows how many grams of raisins are in the bowl will be
(0.01x) * 150 + (0.01y) * 250
What is the expression that shows the raisin?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The expression which shows how many grams of raisins are in the bowl will be:
= (x% × 150) + (y% × 250)
= (0.01x) * 150 + (0.01y) * 250
This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.
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in a population of grasshoppers, the ratio of grasshoppers with a white marking to those without a white marking is 2:3. An entomologist captures and photographs 290 grasshoppers. How many photographs are likely to show grasshoppers with a white marking?
A. 193
B. 58
C. 112
D. 116
Answers
Answer:
D. 116
Step-by-step explanation:
Let the grasshoppers with a white marking be 2x.
Let the grasshoppers without a white marking be 3x.
2x + 3x = 290
5x = 290
x = 290 / 5
x = 58
The grasshoppers with a white marking
= 2x
= 2 ( 58 )
= 116
A plane descends 1000 ft while flying
2.7 mi. What is the angle of descent?
Answers
Answer:
4.02°
Step-by-step explanation:
The angle of descent can be obtained using trigonometry ;
Since we have a right angled triangle ;
Let's use the relation:
Sin θ = opposite / hypotenus
Hypotenus = 2.7 miles
1 mile = 5280 feets
2.7 miles = (2.7 * 5280) = 14256 feets
Sin θ = 1000 / 14256
Sin θ = 0.0701459
θ = sin^-1(0.0701459)
θ = 4.0223674
Brody runs a farm stand that sells strawberries and grapes. Each pound of strawberries sells for $2.50 and each pound of grapes sells for $2. Brody made $160 from selling a total of 72 pounds of strawberries and grapes. Graphically solve a system of equations in order to determine the number of pounds of strawberries sold, x,x, and the number of pounds of grapes sold, yy.
Answers
The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given that the selling price of strawberries each pound = $2.50,
The selling price of grapes each pound = $2
The total earning = $160
Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,
x = y + 12 and 2.50x + 2y= 160
Solve the equation by substitution method;
x = 32 and y = 20
Therefore, the number of pounds of strawberries sold is 32
the number of pounds of grapes sold is 20.
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