Answers
0² = 0 ( zero to the power of any no. equals to zero )
0-² = 1/0² = 1/0 ( numerator can't be zero , it's undefined )
0⁰ is undefined
Skills
a) P² × P⁵ = P⁷
b)P¹²÷P⁴ = P³
c) (P³)⁷ = P²¹
d) P⁰× q³ = 1 × q³ = q³
e) 3P⁴×5P² = 15P⁶
f) 6Pq³×2P⁹q² = 12P¹⁰q⁵
g)P⁷/P² = P⁵
h)8P¹¹/2P⁹ = 4P²
i) (2P⁴)³=2³×P¹² = 8P¹²
j) (8q²×3q⁷)/6q⁸ = 24q⁹/6q⁸ = 4q
Stretch
a) 2²⁰÷4¹⁰= 1048576÷1048576 = 1
b) (2⁶)²÷4⁵ = 2¹²÷4⁵ = 4096 ÷ 1024 = 4
c) 3⁷ ÷ 9³ = 2187 ÷ 729 = 3
d) 27⁵ ÷ 3¹² = 14348907 ÷ 531441 = 27
Please give brainliest
\(\textsf {Skills :}\)
\(\mathsf {a) p^{2} \times p^{5} = p^{7}}\)
\(\mathsf {b) p^{12} \div p^{4} = p^{8}}\)
\(\mathsf {c) (p^{3})^{7} = p^{21}}\)
\(\mathsf {d) p^{0} \times q^{3} = q^{3}}\)
\(\mathsf {e) 3p^{4} \times 5p^{2} = 15p^{6}}\)
\(\mathsf {f) 6pq^{3} \times 2p^{9}q^{2} = 12p^{10}q^{5}}\)
\(\mathsf {g)\frac{p^{7}}{p^{2}} = p^{5}}\)
\(\mathsf {h) \frac{8p^{11}}{2p^{9}}=4p^{2}}\)
\(\mathsf {i) (2p^{4})^{3} = 8p^{12}}\)
\(\mathsf {j) \frac{8q^{2} \times 3q^{7}}{6q^{8}} = 4q}\)
\(\textsf {Stretch :}\)
\(\mathsf {a) 2^{20} \div 4^{10} = 2^{20} \div 2^{20} = 1}\)
\(\mathsf {b) (2^{6})^{2} \div 4^{5} = 2^{12} \div 2^{10} = 2^{2} = 4}\)
\(\mathsf {c) 3^{7} \div 9^{3} = 3^{7} \div 3^{6} = 3}\)
\(\mathsf {d) 27^{5} \div 3^{12} = 3^{15} \div 3^{12} = 3^{3} = 27}\)
Related Questions
8. Label the following statements as being true or false. Assume that the udnerlying inner product spaces are finite-dimensional. Justify or provide counterexample (a) Every self-adjoint operator is normal. (b) Operators and their adjoints have the same eigenvectors. (c) If T is an operator on an inner product space V, then T is normal if and only if [T]g is normal, where B is an ordered basis for V. (d) A matrix A is normal if and only if TA is normal. Here, TA is the linear mapping associated to A. (e) The eigenvalues of a self-adjoint operator must all be real. (f) The identity and zero operators are self-adjoint. (g) Every normal operator is diagonalizable. (h) Every self-adjoint operator is diagonalizable.
Answers
Every self-adjoint operator can be diagonalized with respect to an orthonormal basis of eigenvectors. v* is an eigenvector of A* with eigenvalue λ*.
(a) False. Every self-adjoint operator is indeed normal. This can be justified by the fact that self-adjoint operators satisfy the condition A* = A, where A* denotes the adjoint of A. For any self-adjoint operator A, we have AA = AA, which implies that AA = AA. Therefore, self-adjoint operators are normal.
(b) True. Operators and their adjoints have the same eigenvectors. This can be justified by the fact that if v is an eigenvector of an operator A with eigenvalue λ, then Av = λv. Taking the adjoint of both sides gives (Av)* = (λv), which simplifies to A v* = λ* v*. Hence, v* is an eigenvector of A* with eigenvalue λ*.
(c) False. The statement is not true in general. The normality of an operator T depends on the properties of the operator itself and not on the choice of basis. The matrix [T]g represents the operator T with respect to the ordered basis B, but its normality does not guarantee the normality of T.
(d) True. A matrix A is normal if and only if its associated linear mapping TA is normal. This can be justified by the fact that if A is a normal matrix, then AA = AA. Multiplying both sides by T on the left, we have (TA)(TA) = T(AA) = (TA)(TA)*, which shows that TA is also normal.
(e) True. The eigenvalues of a self-adjoint operator must all be real. This is a fundamental property of self-adjoint operators, and it can be proven using the spectral theorem for self-adjoint operators.
(f) True. The identity and zero operators are indeed self-adjoint. The identity operator preserves the inner product, and its adjoint is itself. Similarly, the zero operator has a trivial adjoint, which is also the zero operator.
(g) True. Every normal operator is diagonalizable. This is a consequence of the spectral theorem for normal operators, which states that every normal operator can be diagonalized with respect to an orthonormal basis of eigenvectors.
(h) True. Every self-adjoint operator is diagonalizable. This is a special case of the more general result that normal operators are diagonalizable, and self-adjoint operators are a subset of normal operators. Therefore, every self-adjoint operator can be diagonalized with respect to an orthonormal basis of eigenvectors.
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help me..........................
Answers
Answer:
d.90l
Step-by-step explanation:
26: 128:: 91: 200: 63: 162 :: 39:?
options 298, 280, 288, 244
Answers
The given series is: 26: 128:: 91: 200: 63: 162 :: 39:? Let's break down the given series:- The first pair, 26: 128, is obtained by squaring the first number and subtracting 2. So, 26²- 2 = 128.
- The second pair, 91: 200, is obtained by cubing the first number and adding 2. So, 91³ + 2 = 200.
- The third pair, 63: 162, is obtained by squaring the first number and subtracting 3. So, 63² - 3 = 162.
Now, let's find the missing number in the series:
- To find the missing number, 39: ?, we can follow the same pattern. By cubing 39 and adding 3,
we get 39³ + 3 = 59319 + 3 = 59322.
So, the missing number in the series is 59322.
The missing number in the series 26: 128:: 91: 200: 63: 162 :: 39:? is 59322.
The pattern in the given series involves alternating between squaring and cubing the first number, followed by adding or subtracting a constant. By applying this pattern to the missing number, we find that it is 59322.
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convert 900 cm/hour into cm per min
Answers
Answer: 15 cm/min
Step-by-step explanation:
900÷60
60=hour
1 hour is 60 minutes.
900 cm/hr = 900 cm per 60 minutes.
To find cm per minute, divide total cm by 60 minutes:
900 / 60 = 15 cm/min.
What is the value of the expression 1 2 3 4 5?
Answers
The value of the given and completed expression in this problem is
-1
What are combined operations?Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.
In this case we have an arithmetic polynomial.
We complete the expression as follows:
1 + 2 - 3 + 4 - 5
We group the positive terms on one side and negative terms on the other:
(1 + 2 + 4) - (3 + 5)7 - (8)-1The value of the expression (1 + 2 - 3 + 4 - 5) is -1
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sam is building a model or an egyptian pyramid out of cardboard. he plans to make asquare base with an edge of 16 inches. The height of each triangular face is 9 inches . Determine the total amount of cardboard he will use for all the surfaces in square inches
Answers
Answer:
544
Step-by-step explanation:
Luke invests £34000 into an account that pays 3. 4% compound interest per
annum for the first two years, and 2. 3% thereafter.
COMPLETION
34%
Given that the interest is paid into his account monthly (and calculated
monthly), work out how much money Luke will have in his account after 6
years and 3 months.
Answers
Luke will have amount of £43,292.17 in his account after 6 years and 3 months.
To solve this problem, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount of money in the account
P = the initial amount of money invested
r = the annual interest rate (as a decimal)
n = the number of times per year the interest is compounded
t = the number of years
For the first two years, the interest rate is 3.4% per annum, compounded monthly. So we have:
P = £34,000
r = 0.034/12 = 0.0028333 (monthly interest rate)
n = 12 (monthly compounding)
t = 2 (years)
Using the formula, we can calculate the amount of money in the account after two years:
A1 = £34,000(1 + 0.0028333/12)^(12*2) ≈ £37,144.14
After the first two years, the interest rate is 2.3% per annum, compounded monthly. So we have:
P = £37,144.14
r = 0.023/12 = 0.0019167 (monthly interest rate)
n = 12 (monthly compounding)
t = 4.25 (years)
Note that we need to use 4.25 years for the remaining time because 6 years and 3 months is equivalent to 6.25 years, and we have already accounted for the first 2 years.
Using the formula, we can calculate the amount of money in the account after the remaining 4.25 years:
A2 = £37,144.14(1 + 0.0019167/12)^(12*4.25) ≈ £43,292.17
Therefore, the total amount of money in the account after 6 years and 3 months is approximately £43,292.17.
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Dylan's hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 168 hikers.
Answers
Answer:
you would need 12 rooms
Step-by-step explanation:
168/12=11.2 so you would have 11 full rooms and then a room for the leftover two
Answer:
11.2 or just 11
Step-by-step explanation:
Okay, so, I apologize if this is an idiot answer, but if you take your 168 hikers and divide them by each room which can hold 15 hikers, you'll get 11.2. NOW MAYBE THE .2 OF THE HIKERS CAN SLEEP ON THE FLOOR I DON'T KNOW SORRY IF THIS IS A TERRIBLE ANSWER.
10. (1 point) Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y
2
−Y
1
is 0.
A>
B<
C=
D incomparable with 11. ( 1 point) The inflation gap π
2
−π
1
is 0.
A>
B<
C=
D incomparable with
12. (1 point) Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long long-run equilibrium, output gap Y
3
−Y
1
0.
A>
B<
C=
D incomparable with 13. (1 point) The inflation gap π
3
−π
1
is 0.
A>
B<
C=
D incomparable with
14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. A monetary easing B monetary tightening C raise the
r
ˉ
D lower the
r
ˉ
15. (1 point) After the Fed achieve its goal, the output gap Y
3
−Y
1
is 0. A > B< C= D incomparable with
Answers
Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y2−Y1 is: B< (less than)As the output gap measures the difference between the actual output (Y2) and potential output (Y1), when the output gap is less than zero, that is, the actual output is below potential output.
The inflation gap π2−π1 is 0. C= (equal)When the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.12. Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long-run equilibrium, output gap Y3−Y1 is 0. C= (equal). As the long run equilibrium represents the potential output of the economy, when the actual output is equal to the potential output, the output gap is zero.13.
The inflation gap π3−π1 is 0. C= (equal) Again, when the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. B monetary tightening When the central bank takes price stability as its primary mandate, it aims to keep the inflation rate low and stable. In the case of a positive shock, which can lead to higher inflation rates, the central bank may implement a monetary tightening policy to control the inflation.
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A square of side 6cm has the same area as a rectanglevof length 9cm. Find the breadth of the rectangle
Answers
Answer:
4
Step-by-step explanation:
Since the area of a square is the side length squared, we get the area of the square as 6 * 6 = 36. Since this is also the area of the rectangle, we need to divide 36 by the length to get the width. 36 / 9 = 4
Answer:
4 cm.
Step-by-step explanation:
9 * b = 6*6 where b = the breadth of the rectangle
b = 36/9 = 4.
Find the zeros of the following quadratic function by completing the square. What are the x-intercepts of the graph of the function? g(x)=x² -3/4x-7/64 Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. The zeros and the x-intercepts are different. The zeros are the x-intercepts are
Answers
The correct choice is: A. The zeros and the x-intercepts are different. The zeros are the x-intercepts are not applicable.
To find the zeros of the quadratic function g(x) = x² - (3/4)x - (7/64), we can complete the square. The quadratic function can be rewritten as:
g(x) = (x² - (3/4)x) - (7/64)
To complete the square, we need to add and subtract the square of half the coefficient of the x-term. The coefficient of the x-term is -3/4, so half of it is -3/8. Adding and subtracting (-3/8)² to the equation:
g(x) = (x² - (3/4)x + (-3/8)²) - (-3/8)² - (7/64)
Simplifying:
g(x) = (x - 3/8)² - 9/64 - 7/64
g(x) = (x - 3/8)² - 16/64
g(x) = (x - 3/8)² - 1/4
Now, we can see that the equation is in the form (x - h)² - k, where the vertex is at (h, k). In this case, the vertex is (3/8, -1/4).
Since the vertex is the lowest point on the graph, it means that the parabola opens upwards, and there are no x-intercepts. Therefore, the zeros and x-intercepts of the graph are different.
Therefore, the correct choice is:
A. The zeros and the x-intercepts are different. The zeros are the x-intercepts are not applicable.
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what do symbols represent in algebra?
Answers
Answer:
One of the most common algebraic symbols is the use of x, y or another letter of the alphabet to indicate a variable or unknown quantity. Common symbols used in algebra also include those related to equality, inequality, factorials and organization, like braces, brackets and parentheses.
Give brainiest please ;-;
Answer:
different variables represent unknown numbers.
Step-by-step explanation:
For example the equation 5x = 15
X is a variable that represents an unknown number. To get the unknown number in the example you need to divide 15 by 5 and 5 by 5 to get X alone and then X will equal 3.
So 5×3=15
I hope this helps
AcellusFind the centroid of AABC ifA - (3, 3), B = (1,0), and C - (2,9).([?], [ 1)Hint: Centroid (MAInter
![AcellusFind the centroid of AABC ifA - (3, 3), B = (1,0), and C - (2,9).([?], [ 1)Hint: Centroid (MAInter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/B8c1LL8XKHwvNEhIeCqjqLvxIHara5SO.jpeg)
Answers
we need to find the centroid of these three points, to do this we will use the equation the image says:
\(x_{centroid}=(\frac{x_1+x_2+x_3^{}}{3})\)and
\(y_{centroid}=(\frac{y_1+y_2+y^{}_3}{3})\)so, to identify x1, x2, and x3, remember that the points always are written in this order= (x,y) so, we have the points:
A - (3, 3), x1=3 y1=3
B = (1,0), x2=1 y2=0
C - (2,9). x3=2 y3=9
and now replace it on the equation:
\(x_{centroid}=(\frac{3+1+2}{3})=2\)\(y_{centroid}=(\frac{3+0+9}{3})=4\)so the answer is:
the centroid is on the point: (2,4)
the set of all elements of interest in a study is . a. a sample b. set notation c. a set of interest
Answers
The statement describes a set of interest in a study, which is the set of all elements being investigated or under consideration. It is not a sample, which refers to a subset of the population being studied.
The set of all elements of interest in a study is called the population. It refers to the entire group of individuals, objects, or measurements that are being studied and from which data can be collected. The population can be finite or infinite and can include people, animals, plants, materials, or any other object or concept of interest. In statistical analysis, researchers use samples of the population to make inferences or draw conclusions about the entire population. By selecting a representative sample, researchers can reduce the cost and time required for data collection and analysis while still obtaining valid and reliable results.
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a fair bet is a: wager entered into with honesty and concern for the welfare of the other party. gamble that provides net gains to all participants so there is no loser. wager entered into when the rules are clear to all participants. gamble that, on average, will leave a person with the same amount of money.
Answers
Answer:gamble that,on average,will leave a person with the same amount of money.
Step-by-step explanation:
If the mpc increases in value, what will happen to the slope of the consumption function?
Answers
If the mpc increases in value, the consumption function will become steeper.
What is MPC ?
MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.
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The sum of two numbers is 2490. Find the numbers if 8.5% of the first is equal to 6.5% of the second.
Answers
Thus the numbers are 1411 and 1079 respectively.
Please help me!!!! I have been stuck on this question for like a half an hour now.
Answers
You can simplify by taking out the GCF for each term which is 3. So divide each term by 3, which leaves you with
3(3x^2+7x+2)
Simplify & factor and you get
3(3x+1)(x+2)
I got 6 and 7 I just need 8 and 9.
Answers
Answer:
8) 92°
9) 44°
Step-by-step explanation:
8) 92°
9) 44°
the length of the garden to be x-2 feet and the width to be x+3 feet
standard form:
function form:
what is the y intercept of the function
Answers
Step-by-step explanation:
\((x - 2)(x + 3) = \\ {x}^{2} + x - 6\)
standard form
\( {x}^{2} + x - 6 = 0\)
function form
\(f(x) = {x}^{2} + x - 6\)
y-intercept = -6
There are 1,000 meters in 1 kilometer. Convert 5,000 meters to kilometers.
A) 0.5 km
Eliminate
B) 5 km
C) 50 km
D) 500 km
Answers
Answer:
B) 5 km
Step-by-step explanation:
There are 1,000 m in 1 km, so x km=5000m
Set up a proportion:
\(\frac{1000m}{1km}=\frac{5000m}{x km}\)
Cross multiply and solve for "x":
(1000 m)(x km)=(5000 m)(1 km)
1000x=5000
(1000x/1000)=5000/1000
x=5 km
Consider the simple linear regression model: yi = β0 + β1xi + εi Show that minimizing the sum of squared residuals lead to the following least squares coefficient estimates: βˆ 0 = ¯y − βˆ 1x, ¯ βˆ 1 = Pn i=1(xi − x¯)(yi − y¯) Pn i=1(xi − x¯) 2 , where y¯ = 1 n Pn i=1 yi and x¯ = 1 n Pn i=1 xi .
Answers
The simple linear regression model is given by yi = β0 + β1xi + εi, where β0 is the intercept, β1 is the slope, xi is the predictor variable, yi is the response variable, and εi is the error term. These are the least squares coefficient estimates for the simple linear regression model.
The goal of least squares regression is to find the values of β0 and β1 that minimize the sum of the squared residuals.
To find the least squares coefficient estimates, we need to minimize the sum of the squared residuals. The residual is the difference between the observed value of yi and the predicted value of yi. The predicted value of yi is given by β0 + β1xi. Therefore, the residual can be written as yi - (β0 + β1xi).
The sum of squared residuals is given by:
Σi=1n (yi - β0 - β1xi)²
To find the values of β0 and β1 that minimize this sum, we take the partial derivatives with respect to β0 and β1 and set them equal to zero:
∂/∂β0 Σi=1n (yi - β0 - β1xi)² = 0
∂/∂β1 Σi=1n (yi - β0 - β1xi)² = 0
Solving these equations yields:
βˆ 0 = ¯y − βˆ 1x
and
βˆ 1 = Pn i=1(xi − x¯)(yi − y¯) / Pn i=1(xi − x¯)²
where y¯ = 1 n Pn i=1 yi and x¯ = 1 n Pn i=1 xi. These are the least squares coefficient estimates for the simple linear regression model.
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What is the vertex of the graph of the quadratic function f(c) = x2 + 8x + 10?
Answers
Vertex is at (4,−6)and the axis of symmetry is x=4
what is 9/2 x 1/4 ??
Answers
Answer:
1.125
Step-by-step explanation:
Answer:1 1/8
Step-by-step explanation:Multiply it and then change to mixed numbers.
look at pic below.
A hardware salesman measures the mass of a box containing 1000 washers. The mass is 1.2314 kg. What is the mass of a single washer in milligrams? Wr your answer as a decimal,
Answers
The mass of a single washer can be calculated by dividing the total mass of the box (1.2314 kg) by the number of washers (1000). The mass of a single washer is expressed in milligrams.
To calculate the mass of a single washer, we divide the total mass of the box (1.2314 kg) by the number of washers (1000).
1.2314 kg divided by 1000 washers equals 0.0012314 kg per washer.
To convert the mass from kilograms to milligrams, we need to multiply by the appropriate conversion factor.
1 kg is equal to 1,000,000 milligrams (mg).
So, multiplying 0.0012314 kg by 1,000,000 gives us 1231.4 mg.
Therefore, the mass of a single washer is 1231.4 milligrams (mg).
Note: In scientific notation, this would be written as 1.2314 x 10^3 mg, where the exponent of 3 represents the milli prefix.
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W is less than 8 but greater than -3.
Answers
Answer:
W= a number greater then -3= -2,-1,0,1,2,3,4,5,6,7,8,9,10...
Step-by-step explanation:
Answer: It can be a number from -2 to 7;):
Step-by-step explanation: Look
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Please help :)
Chloe is an acrobat in a local circus. Her job is to move across a tightrope from point A to point B while blindfolded! She can only move using the distances that you tell her to move in your instructions. Chloe may go past the ladder. However, if she does, make sure she turns around and goes back toward the ladder.
Use the link: Link
Your Task: Work with your partner to find different combinations of the lengths given in parts (a) through (d) below that will allow Chloe to move from point A and end at point B (the end of the tightrope). You may use each length as many times as you like. .
1. For each crossing, look for at least three different ways to get the acrobat across. *Draw a diagram on your paper that shows the solution with the least amount of steps. *For the neither 2 write a number sentence/equation.
Answers
Explanation:
We'll let you draw the diagram. Here are some possible equations. We have listed the shortest sequence first.
(a) 24 = (10 + 10 + 4) = (8 + 8 + 8) = (10 + 8 + 4 + 2)
(b) 17 = (10 + 3 + 2 + 2) = (10 + 3 + 3 + 3 - 2) = (3 + 3 + 3 + 3 + 3 + 2)
(c) 15 = (11 + 4) = (6 + 6 + 3) = (4 + 4 + 4 + 3)
(d) 27 = (19 + 8) = (19 + 12 - 4) = (19 + 12 + 4 - 8)
Fill in the blanks with the missing numbers from the table of values for the equation y=−5x+1
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
For the values of x , the corresponding values of y are :
x = -1 and y = 6x = 0 and y = 1 x = 1 and y = -4 x = 2 and y = -9(2x + 4- 6x=24,5)
Find x
Answers
Answer:
x= −241 /4
Step-by-step explanation:
a basket contains $7$ green marbles and $5$ red marbles. a marble is taken from the basket at random; its color is recorded, then the marble is returned to the basket. a second marble is then taken from the basket at random, and its color is recorded. what is the probability that the same color is recorded both times?
Answers
35/864 is the probability that the same color is recorded both times .
How does probability explain work?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.7/12*1/2 = 7/24
red marbles = 5/12*1/3 ⇒ 5/36
the probability = 7/24*5/36 ⇒ 35/864
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