The first digit of the whole- number quotient will be in the hundred place.
To determine which place will the first digit of the whole- number quotient be placed after taking the quotient of 572 and 4, we will follow the steps below;
Round up 572 to 1 significant figure. The value expressed as one significant figure is 600.Since the divisor is a unit value, we will not be rounding it up.Take the quotient of 600 and 4.[tex]\frac{600}{4}=\frac{150\times 4}{4 \times 1} =150[/tex]
From the result, we can see that the first digit of the whole- number quotient is to the nearest hundred (100)
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40.185 + 0.01
Round your answer to the nearest
hundredth.
Answer:
40
Step-by-step explanation:
Answer:
40.20 luv:)
Step-by-step explanation:
10. Which statement about this flgure is true?
A. it has reflectional symmetry.
B. It has no rotational symmetry.
C. It has rotational symmetry with an angle of rotation of 180 deg.
D. It has point symmetry.
HURRYYYY PLEASEEE
You can wash a car 1.5 times as fast as your friend. Working together, the two of you can wash 1 car in 6 minutes. How long does it take each of you to wash the car when working alone? Leave your answer as a fraction!
If the two of you can wash 1 car in 6 minutes:
It will take you 10 minutes to wash the car alone
take your friend 15 minutes to wash the car alone
Let the duration you can work be represented by y
Let the duration your friend can work be represented by x
You can wash a car 1.5 times as fast as your friend
That is, y = 1.5x
Working together, the two of you can wash 1 car in 6 minutes
This can be represented by the equation
[tex]\frac{1}{x}+\frac{1}{y} = \frac{1}{6}[/tex]
Substitute x = 1.5y into the equation above
[tex]\frac{1}{1.5y}+\frac{1}{y} = \frac{1}{6}\\\\\frac{1+1.5}{1.5y} = \frac{1}{6}\\\\\frac{2.5}{1.5y} = \frac{1}{6}\\\\1.5y=2.5(6)\\\\1.5y=15\\\\y=\frac{15}{1.5} \\\\y=10[/tex]
It will take you 10 minutes to wash the car alone
Substitute y = 10 into x = 1.5y
x = 1.5(10)
x = 15 minutes
It will take your friend 15 minutes to wash the car alone
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Let A be a given matrix below. First, find the eigenvalues and their corresponding eigenspaces for the following matrices. Then, find an invertible matrix P and a diagonal matrix such that A = PDPâ’1.
(a) [ 3 2 2 3 ]
(b) [ 1 â 1 2 â 1 ]
(c) [1 2 3 0 2 3 0 0 3]
(d) [3 1 1 1 3 1 1 1 3]
It looks like given matrices are supposed to be
[tex]\begin{array}{ccccccc}\begin{bmatrix}3&2\\2&3\end{bmatrix} & & \begin{bmatrix}1&-1\\2&-1\end{bmatrix} & & \begin{bmatrix}1&2&3\\0&2&3\\0&0&3\end{bmatrix} & & \begin{bmatrix}3&1&1\\1&3&1\\1&1&3\end{bmatrix}\end{array}[/tex]
You can find the eigenvalues of matrix A by solving for λ in the equation det(A - λI) = 0, where I is the identity matrix. We also have the following facts about eigenvalues:
• tr(A) = trace of A = sum of diagonal entries = sum of eigenvalues
• det(A) = determinant of A = product of eigenvalues
(a) The eigenvalues are λ₁ = 1 and λ₂ = 5, since
[tex]\mathrm{tr}\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3 + 3 = 6[/tex]
[tex]\det\begin{bmatrix}3&2\\2&3\end{bmatrix} = 3^2-2^2 = 5[/tex]
and
λ₁ + λ₂ = 6 ⇒ λ₁ λ₂ = λ₁ (6 - λ₁) = 5
⇒ 6 λ₁ - λ₁² = 5
⇒ λ₁² - 6 λ₁ + 5 = 0
⇒ (λ₁ - 5) (λ₁ - 1) = 0
⇒ λ₁ = 5 or λ₁ = 1
To find the corresponding eigenvectors, we solve for the vector v in Av = λv, or equivalently (A - λI) v = 0.
• For λ = 1, we have
[tex]\begin{bmatrix}3-1&2\\2&3-1\end{bmatrix}v = \begin{bmatrix}2&2\\2&2\end{bmatrix}v = 0[/tex]
With v = (v₁, v₂)ᵀ, this equation tells us that
2 v₁ + 2 v₂ = 0
so that if we choose v₁ = -1, then v₂ = 1. So Av = v for the eigenvector v = (-1, 1)ᵀ.
• For λ = 5, we would end up with
[tex]\begin{bmatrix}-2&2\\2&-2\end{bmatrix}v = 0[/tex]
and this tells us
-2 v₁ + 2 v₂ = 0
and it follows that v = (1, 1)ᵀ.
Then the decomposition of A into PDP⁻¹ is obtained with
[tex]P = \begin{bmatrix}-1 & 1 \\ 1 & 1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1 & 0 \\ 0 & 5\end{bmatrix}[/tex]
where the n-th column of P is the eigenvector associated with the eigenvalue in the n-th row/column of D.
(b) Consult part (a) for specific details. You would find that the eigenvalues are i and -i, as in i = √(-1). The corresponding eigenvectors are (1 + i, 2)ᵀ and (1 - i, 2)ᵀ, so that A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1+i & 1-i\\2&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}i&0\\0&i\end{bmatrix}[/tex]
(c) For a 3×3 matrix, I'm not aware of any shortcuts like above, so we proceed as usual:
[tex]\det(A-\lambda I) = \det\begin{bmatrix}1-\lambda & 2 & 3 \\ 0 & 2-\lambda & 3 \\ 0 & 0 & 3-\lambda\end{bmatrix} = 0[/tex]
Since A - λI is upper-triangular, the determinant is exactly the product the entries on the diagonal:
det(A - λI) = (1 - λ) (2 - λ) (3 - λ) = 0
and it follows that the eigenvalues are λ₁ = 1, λ₂ = 2, and λ₃ = 3. Now solve for v = (v₁, v₂, v₃)ᵀ such that (A - λI) v = 0.
• For λ = 1,
[tex]\begin{bmatrix}0&2&3\\0&1&3\\0&0&2\end{bmatrix}v = 0[/tex]
tells us we can freely choose v₁ = 1, while the other components must be v₂ = v₃ = 0. Then v = (1, 0, 0)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}-1&2&3\\0&0&3\\0&0&1\end{bmatrix}v = 0[/tex]
tells us we need to fix v₃ = 0. Then -v₁ + 2 v₂ = 0, so we can choose, say, v₂ = 1 and v₁ = 2. Then v = (2, 1, 0)ᵀ.
• For λ = 3,
[tex]\begin{bmatrix}-2&2&3\\0&-1&3\\0&0&0\end{bmatrix}v = 0[/tex]
tells us if we choose v₃ = 1, then it follows that v₂ = 3 and v₁ = 9/2. To make things neater, let's scale these components by a factor of 2, so that v = (9, 6, 2)ᵀ.
Then we have A = PDP⁻¹ for
[tex]P = \begin{bmatrix}1&2&9\\0&1&6\\0&0&2\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}1&0&0\\0&2&0\\0&0&3\end{bmatrix}[/tex]
(d) Consult part (c) for all the details. Or, we can observe that λ₁ = 2 is an eigenvalue, since subtracting 2I from A gives a matrix of only 1s and det(A - 2I) = 0. Then using the eigen-facts,
• tr(A) = 3 + 3 + 3 = 9 = 2 + λ₂ + λ₃ ⇒ λ₂ + λ₃ = 7
• det(A) = 20 = 2 λ₂ λ₃ ⇒ λ₂ λ₃ = 10
and we find λ₂ = 2 and λ₃ = 5.
I'll omit the details for finding the eigenvector associated with λ = 5; I ended up with v = (1, 1, 1)ᵀ.
• For λ = 2,
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}v = 0[/tex]
tells us that if we fix v₃ = 0, then v₁ + v₂ = 0, so that we can pick v₁ = 1 and v₂ = -1. So v = (1, -1, 0)ᵀ.
• For the repeated eigenvalue λ = 2, we find the generalized eigenvector such that (A - 2I)² v = 0.
[tex]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}^2 v = \begin{bmatrix}3&3&3\\3&3&3\\3&3&3\end{bmatrix}v = 0[/tex]
This time we fix v₂ = 0, so that 3 v₁ + 3 v₃ = 0, and we can pick v₁ = 1 and v₃ = -1. So v = (1, 0, -1)ᵀ.
Then A = PDP⁻¹ if
[tex]P = \begin{bmatrix}1 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1\end{bmatrix}[/tex]
[tex]D = \begin{bmatrix}5&0&0\\0&2&0\\0&2&2\end{bmatrix}[/tex]
A taxi service charges an initial fee plus $1.80
per mile. How far can you travel for $12
?
What information do you need in order to be able to solve the problem?
Answer:
You would need the intial fee in dollars/cents
Expression:
c=initial fee
x=amount of miles
[tex]1.80x+c=12[/tex]
Step-by-step explanation:
You would need the intial fee in dollars/cents
Expression:
c=initial fee
x=amount of miles
[tex]1.80x+c=12[/tex]
Need help plotting x and y intercept heres a better explanation of what I need to do
Need Asap pls
Find the excluded value of the Following. Make sure to show the solution.
1. - 4/b + 6
2. x - 1 / (x - 3) (x + 4)
help me with this guys
Let y = cos⁻¹(x), so that cos(y) = x.
For some angle y between 0 and π, cos(y) takes on some value between -1 and 1.
For the y in this range, we have cos(y) = -1/2 exactly when y = 2π/3.
Then
tan(cos⁻¹(-1/2)) = tan(2π/3) = sin(2π/3)/cos(2π/3) = (√3/2)/(-1/2) = -√3
Help would be well appreciated!!!!!!
How would you rewrite -5 - (-8) as an addition problem?
Answer:
if there are 2 negatives by each other it would become a postive so -5+8
Step-by-step explanation:
Answer:
-5+8
Step-by-step explanation:
minus a negative is equivalent to plus a positive
$75 to $25 show your work
Answer:
decrease
Step-by-step explanation:
the percent change measures FROM the first value. A change from 50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50). A change from 75 to 50 is a change of -33.3% (25 is still the difference between the two. 25 is 33.3% of 75
What’s the next 3 terms of the sequence -2,8,-32?
Answer:
Step-by-step explanation:
This is a geometric series.
First term = - 2
Ratio = second term ÷ first term = 8 ÷ (-2) = -4
Next three terms are:
-32 *(-4) = 128
128*(-4) = - 512
-512*(-4) = 2048
Answer:
The next 3 terms would be 128, -512, 2048
Step-by-step explanation:
Since we are dealing with a Geometric Sequence we use this formula [tex]a_{n}=a_{1} *r^{n-1}[/tex]
Since the first term([tex]a_{1}[/tex]) is -2 and for us to find R we have to divide 8 by -2 = -4
So we would rewrite the equations to find the next three terms as
[tex]a_{4}=-2*-4^{4-1}=-2*-4^3=128[/tex]
[tex]a_{5}=-2*-4^{5-1}=-2*-4^4=-512[/tex]
[tex]a_{6}=-2*-4^{6-1}=-2*-4^5=2048[/tex]
A leaky pipe drips 2 fluid ounces of water per hour. How many cups of water does it leak in 2 days? Remember that 8 fluid ounces = 1 cup
Answer:
12 cups
Step-by-step explanation:
There are 48 hours in two days.
48 · 2 = 96 ( 2 being fluid ounces per hour )
96 ÷ 8 = 12 ( 8 being fl oz in each cup )
I hope that this helped!!!
How do I find x in this problem, x/5-2/3=3/2
Answer:
x = 38/6
Step-by-step explanation:
x/5 - 2/3 = 3/2
3x - 2x5/3x2 = 3/2
3x-10/6 = 3/2
2(3x-10) = 3x6
6x-20 = 18
6x = 18+20
6x =38
x =38/6 or x = 6.33
The question is written on the image
Answer:
I have attached the answer below.
Step-by-step explanation:
The diagram which has red ink cannot take a perfect feeding path.
Hopefully this helps.
in a certain game, a fair die is rolled and a player gains 20 points if the die shows a 6. if the die does not show a 6, the player loses 3 points. if the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
The expected gain or loss is an illustration of mean and expected values.
The expected total gain is 83 points
The given parameters are:
Addition of 20 points for rolling a 6Removal of 3 points for not rolling a 6The probability of rolling a 6 in a fair die is 1/6.
The probability of not rolling a 6 in a fair die is 5/6.
So, the expected gain in each game is:
[tex]\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}[/tex]
[tex]\mathbf{E(x) = \frac{20}6 - \frac{15}6}[/tex]
Take LCM
[tex]\mathbf{E(x) = \frac{5}6}[/tex]
[tex]\mathbf{E(x) = 0.83}[/tex]
The number of games is 100.
So, the expected gain is:
[tex]\mathbf{Gain = 100 \times 0.83}[/tex]
[tex]\mathbf{Gain = 83}[/tex]
Hence, the expected total gain is 83 points
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plzzzz help me!!!
Plz don't steal my points or add a link
Answer: What do you mean? if you till me i can help you
Step-by-step explanation:
What is the measure of ZPRQ?
P
O
A. 172°
1020
B. 70°
70"
s
C. 86°
D. 1020
Answer: should be 86°, not sure.
Step-by-step explanation:
STATION 5 ! GIVING BRAINLIEST TO WHOEVER ANSWER W AN GREAT EXPLNATION<3
Answer:
a.
Step-by-step explanation:
Answer:
A, B, E
Step-by-step explanation:
I just put the number of fiction books over the number of nonfiction books. Then I plugged it into a calculator and if the answer was the same as 15/22, then it was right!
2385/3498=15/22
3945/5786=15/22
2340/3588≠15/22
2480/3410≠15/22
4650/6820≠15/22
2310/3696=15/22
Determine if the table represents a linear function, quadratic function, or exponential function.
Answer:
Quadratic
Step-by-step explanation:
Formula: ax^2+bx+c
Two parallel chords PQ and MN are 3 cm apart on the same side of a circle where PQ = 7 cm
and MN = 14 cm. Calculate the radius of the circle.
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.407869.html
There is currently 9 inches of snow on the ground.
With the thunderstorms today the snow will melt at
a rate of 1.5 inches per hour.
1. Write an equation to represent this situation
2. What do the slave and y-intercept mean
3. After how many hours would all the snow be melted
4. Make a table of this situation to show when all the snow would be melted
Answer:cold weather pose, there are armies that have and can conduct large-scale, ... to one inch (2.5 centimeters) per hour accumulates.
Step-by-step explanation:
Answer:
1.5 × ? = 9
9÷1.5 = 6
so the answer would be 6 hours
Transform y = cot(x) to get the graph of. Which type of transformation is not performed? vertical shift horizontal shift vertical stretch horizontal stretch.
Transformation involves changing the form of the function
The transformation that is not performed is (a) vertical shift
The function is given as:
[tex]\mathbf{y = cot(x)}[/tex]
From the complete question, the transformed function is:
[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]
On y = cot(x); start by translating the function 2 units left.
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (x +2,y)}[/tex]
So, we have:
[tex]\mathbf{y = cot(x + 2)}[/tex]
Next, stretch the function horizontally by a factor of 1/5
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (\frac 15x,y)}[/tex]
So, we have:
[tex]\mathbf{y=cot[\frac 15(x+2)]}[/tex]
Lastly, stretch the function vertically by a factor of 3
The rule of this transformation is:
[tex]\mathbf{(x,y) \to (x,3y)}[/tex]
So, we have:
[tex]\mathbf{y=3cot[\frac 15(x+2)]}[/tex]
From the above transformations, we have:
Horizontal shift Vertical stretch Horizontal stretchHence, the transformation that is not performed is (a) vertical shift
Read more about transformations at:
https://brainly.com/question/13801312
Answer:
vertical shift
Step-by-step explanation:
edge
Need help with this one too plzzz
Answer:
0.83
Step-by-step explanation:
volume = length*height*width
1500=L*30*60
1500=1800L
1500/1800 = 0.83
length = 0.83
Evaluate.
3.23
+52
- 18 ÷6 A.25 B.31 C.40 D.46
Answer:
d
Step-by-step explanation:
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
I need the answer please and thank you
Answer: First do 145 - 25, which is 120. Then do 120 ÷ 15 = 8. Therefore the slope intercept is y ÷ 15 = x. Their voyage will last 8 days.
Explanation: Brainliest please
What is 13% of 50% of 329,500,000
Answer:
21417500
Step-by-step explanation:
Calculate 50% of the given amount then 13% of result
50% of 329500000
= [tex]\frac{50}{100}[/tex] × 329500000
= 0.5 × 329500000
= 164750000
Then
13% of 164750000
= [tex]\frac{13}{100}[/tex] × 164750000
= 0.13 × 164750000
= 21417500
2x=x-4
solve for x
step by step please
2x = x - 4
2x - x = - 4
x = - 4
________
Hope it helps ⚜
Answer:
x=-4
Step-by-step explanation:
2x=x-4
2x-x=-4
x=-4
Proof
2*(-4)=-4-4
-8=-8
write an equation of the line slope intercept form that is parallel to Y= 1/2 X +3 and through the point (2, -1)
Answer:
y=1/2x
Step-by-step explanation:
I first did point-slope form which is
y+1=1/2(x-2)
Then, I converted it into slope-intercept form which is
y=1/2x
