Answer:
1. Clockwise rotation by π/2 radians
: D
2. Reflection about the x-axis
: E
3. Counterclockwise rotation by π/2 radians
: F
4. The projection onto the x-axis given by T(x,y) = (x,0)
: C
5. Reflection about the y-axis : A
6. Reflection about the line y = x : B
Step-by-step explanation:
Given a linear transformation [tex]T:\mathbb{R}^2\to\mathbb{R}^2[/tex], one matrix representation of T is obtained by stacking the vectors T(1,0) and T(0,1) in columns.
a) A counter clockwise rotation of [tex]\pi/2[/tex] radians sends (1,0) to (0,-1) and it sends (0,1) to (1,0), so the matrix representation is
[tex]\left[\begin{matrix} 0& 1 \\ -1 & 0 \end{matrix}\right][/tex] which corresponds to matrix D.
From now on, I will provide the values of T(1,0) and T(0,1)
b) Reflection about the x-axis T(1,0) = (1,0) and T(0,1) = (0,-1), which corresponds to matrix E.
c) Counterclockwise rotation by π/2 radians T(1,0) = (0,1), T(0,1) = (-1,0). Matrix F
d) The projection onto the x-axis given by T(x,y) = (x,0). T(1,0) = (1,0) T(0,1) = (0,0). Matrix C
e) Reflection about the y-axis T(1,0) = (-1,0) T(0,1) = (0,1). Matrix A
f) Reflection about the line y = x. This transformation corresponds to interchanging the values of x and y. That is, send (x,y) to (y,x). So, in this case
T(1,0) = (0,1) T(0,1) = (1,0). Matrix B
Select the correct answer.
Four-thirds times the sum of a number and 8 is 24. What is the number?
A.
40
B.
26
O c.
24
OD.
10
Answer: D. 10
Step-by-step explanation:
4/3 (x + 8) = 24
Multiply both sides by 3/4....
x + 8 = 18
x = 10
Rectangle is 5ft in length and 3 ft in height. What is the area of the rectangle
Answer: 15
Step-by-step explanation:
to find the area multiply the length by height
in this case it’s 5ft and 3ft
5 • 3 = 15
A=15
There are three highways in the county. The number of daily accidents that occur on these highways are Poisson random variables with respective parameters 0.3, 0.5, and 0.7.
Required:
Find the expected number of accidents that will happen on any of these highways today.
Answer:
50% Chance
Step-by-step explanation:
So Pr(0.3, 0.5, and 0.7) = (30% + 50% + 70%) / 300
= 1/2
A box containing 15 DVDs is selling for $156.00. The box contains some
DVDs worth $11.00 each and some DVDs worth $9.00 each. Which system of
equations can be used to determine x, the number of $11.00 DVDs, and y, the
number of $9.00 DVDs?
Answer:
Step-by-step explanation:
x + y = 15
11x + 9y = 156
Look at this expression.
Can you put it in the simplest form?
The denominator contains negative exponents. Using the negative exponent rule, multiply the denominator by -1 and then reverse the fraction and multiply.
The denominator becomes x^3y^4
The problem then becomes -3x^6y^4 times x^3y^2
When multiplying exponents add them together:
The final answer is -3x^9y^6
Can someone please help me?
Answer:
''0 is neither a rational number nor an irrational number.''
Step-by-step explanation:
Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.
To solve the system given below using substitution, it is best to start by
solving the second equation for y.
5x + 2y = 33
6y + x = 3
true or false
Answer:
False, it is easier to isolate x.
Step-by-step explanation:
6y+x=3
x=3-6y
could you help me with this problem
Answer:
For x
We use cosine
cos 45° = 2/x
After solving
x = 2√2
Since we have the value of x we use it to get the value of y
we use cosine
cos 60° = 2√2/y
y =2√2/cos 60
y = 4√2
We use Pythagoras theorem to find z
(4√2)² = (2√2)² + z²
z² = 32 - 8
z² = 24
z = √24
z = 2√6
Therefore x = 2√2
y = 4√2
z = 2√6
Hope this helps.
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
Please answer this correctly
Answer:
Skateboard:
Scooter:
Bike:
Step-by-step explanation:
19 + 14 + 17 = 50 (there were 50 customers)
19 out of 50 = 38%
14 out of 50 = 28%
17 out of 50 = 34%
Hope this helps!
A game require rolling a six sided die numbered fro 1 to 6. What is the probability of rolling a 1 or a 2?
Answer:
1/3
Step-by-step explanation:
hello,
probability of 1 = 1/6
probability of 2 = 1/6
probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0
so the answer is 2/6=1/3
Which best describes her prediction?
Verify the identity. Please explain step by step.
Step-by-step explanation:
sin²α − sin⁴α
Factor out sin²α.
sin²α (1 − sin²α)
Use Pythagorean theorem.
(1 − cos²α) cos²α
Distribute.
cos²α − cos⁴α
A contractor is considering whether he should take on a project that promises a profit of $8800 with a probability of 0.83 or a loss (due to bad weather, strikes, etc.) of $2900 with a probability of 0.17. What is the expected profit for the contractor
Answer: 6811
Step-by-step explanation:
in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17
--
so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811
2 Points
If f(x) = x + 8 and g(x) = -4x - 3, find (f+ g)(x).
O A. (f+ g)(x) = -3x + 5
O B. (f+ g)(x) = 5x + 11
O C. (f+g)(x) = -5x - 11
O D. (f+ g)(x) = 3x - 5
SUBMI
Answer: A
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Since we are given f(x) and g(x), we cna add them together.
x+8+(-4x-3)
x+8-4x-3
-3x+5
Calculate the length of the
circumference of a circle with
radius of 1.6m
Answer:
C = 10.05
Step-by-step explanation:
Formula: C = 2[tex]\pi[/tex]r
circumference = ?
Solution:
C = 2[tex]\pi[/tex](1.6 m) (multiply)
C = 3.2[tex]\pi[/tex]m
C = 3.2(3.14) m (multiply)
C = 10.048
Rounded off (If needed): 10.05
When 3 times a number is subtracted from 10, the result is the sum of the number and 22
Answer:
x = -6
Step-by-step explanation:
Let the number be x
Condition:
=> 10-3x = x+22
Let's Solve it:
=> -3x-x = 22-10
=> -2x = 12
Dividing both sides by -2
=> x = -6
Answer:
x=6
Step-by-step explanation:
At a department store, Kendra has a debt greater than $25.00. Which could be Kendra’s balance? A.Negative 32 dollars B.Negative 22 dollars C.Negative 19 dollars D.Negative 11 dollars
Answer:
A. Negative 32 dollars
Step-by-step explanation:
Kendra has a debt. Doubt means that the balance is Negative.
If the debt is greater than 25 USD . Kendra's debt has to be more negative than 25 . Amoung all other numbers only debt 32 is more negative than 25.
Answer:
I think it would be 32
Step-by-step explanation:
So she can pay the debt off
find the value of ∛27
Answer:
3
Step-by-step explanation:
3^3 = 27
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?
Answer:
[tex]j^4k[/tex]
Step-by-step explanation:
[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]
Answer:
4
Step-by-step explanation:
give me brainliest
in a classroom 5/8 of the students are wearing blue shirts and 1/4 for wearing white shirts there are 24 students in the classroom how many are wearing shirts other than blue shirts and
Answer:
3
Step-by-step explanation:
Those wearing a shirt of another color are ...
1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8
of the total number of students in the classroom
(1/8)×(24 students) = 3 students . . . . wearing another color
_____
Alternate solution
With the given information, you know ...
(5/8)(24) = 15 . . . students wear blue
(1/4)(24) = 6 . . . . students wear white
24 -15 -6 = 3 . . . students wear another color
The computer hardware company requires all of its chips purchased from its supplier of computer chips to meet specifications of 1.2 cm with the margins of error of plus and minus 0.1 cm. Based on the computer chip supplied last month, the mean length of a computer chip was 0.9 cm. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications
Answer:
Step-by-step explanation:
The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm
This means that the required length of computer chips is between 1.1cm - 1.3cm
Where 1.1cm = [1.2 - 0.1]
1.3cm = [1.2 + 0.1]
Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.
The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:
- The length of the chips.
The length of the chips his production team produces should be tailored to meet the length specification of his client.
Which of the following equations describes the line shown below? Check all
that apply.
(-6,4)
(3,1)
Answer:
y-4=-1/3(x+6)
y-1=1/3(x-3)
Step-by-step explanation:
4-1/-6-3
3/-9
-1/3
y-4=-1/3(x+6)
y-1=1/3(x-3)
A taxi company charges based on the function rule P(t) = 0.5t + 2.5, where t is the
time taken for a trip (in minutes) and P(t) is the amount in dollars. If a trip takes 30 minutes, how much will it cost the client?
Answer:
$17.5
Step-by-step explanation:
hello,
we need to compute P(30)
P(30) = 0.5*30 + 2.5 = 15 + 2.5 = 17.5
hope this helps
Solve the system of equations. \begin{aligned} & -10x+3y = 5 \\\\ & x=y-4 \end{aligned} −10x+3y=5 x=y−4
Answer:
x = 1
y = 5
Step-by-step explanation:
You can use either substitution or elimination for this problem. I will use substitution.
Step 1: Replace x in the 1st equation
-10(y-4) + 3y = 5
-10y + 40 + 3y = 5
-7y = -35
y = 5
Step 2: Plug y into an original equation to find x
x = 5 - 4
x = 1
And you have your final answers!
Answer:
x = 1
Step-by-step explanation:
y = 5
Find the product
2y2(3x + 5z)
Answer:
6xy^2+10y^2z is the answer
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
in a bag there are 2 red, 3 yellow, 4 green, 6 blue marbles.
what is the probability of p (blue)?
Answer:
2/5
Step-by-step explanation:
2 red, 3 yellow, 4 green, 6 blue marbles. = 15 marbles
P( blue) = blue / total
=6/15
=2/5
In which set does -15/2 belong? Answer choices: Rational numbers
Integers
Whole numbers
All of the above
Answer:
Rational numbersStep-by-step explanation:
When an integers or a whole number is divided by another integer or whole number the result is a whole number.
Hence [tex]\frac{-15}{2}[/tex] is a rational number
This is because both -15 and 2 are integer numbers
Answer:
rational
Step-by-step explanation:
5. The equations are written in point-slope form. Which equation represents a line through points (-8, 3) and (-2, -3)?
O y-3 =-1(x+8)
Oy - 3=3(x+8)
O y-3 =-3(x+8)
Oy-3 = 1(x+8)
Answer:
y-3 =-1(x+8)
Step-by-step explanation:
The equation of a line is passing through two points is given by
(Y-y1)/(x-x1)= (y2-y1)/(x2-x1)
The points are (-8, 3) and (-2, -3)?
Y1= 3
Y2 = -3
X1= -8
X2 = -2
(Y-y1)/(x-x1)= (y2-y1)/(x2-x1)
(Y-3)/(x-(-8)) = (-3-3)/(-2-(-8))
(Y-3)/(x+8)= (-6)/(6)
(Y-3)/(x+8)= -1
Y-3= -1(x+8)