Answer:
y=2x−3
⇒−1=2a−3
⇒2a=−1+3=2
∴a=22=1
y=2x−3
b=2×5−3
⇒b=10−3=7
∴b=7
Step-by-step explanation:
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Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication
The function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.
The pseudo code for matrix multiplication may look something like this:
```
MatrixMultiplication(A, B):
n = size of matrix A
C = empty matrix of size n x n
for i = 1 to n do:
for j = 1 to n do:
sum = 0
for k = 1 to n do:
sum = sum + A[i][k] * B[k][j]
C[i][j] = sum
return C
```
Let's break down the number of operations step by step:
1. Assigning the size of matrix A to variable n: 1 operation
2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)
3. Outer loop: for i = 1 to n
- Incrementing i: n operations
- Inner loop: for j = 1 to n
- Incrementing j: n^2 operations (since it is nested inside the outer loop)
- Initializing sum to 0: n^2 operations
- Innermost loop: for k = 1 to n
- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)
- Performing the multiplication and addition: n^3 operations
- Assigning the result to C[i][j]: n^2 operations
- Assigning the value of sum to C[i][j]: n^2 operations
Total operations:
1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1
Therefore, the function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1
To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.
In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
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In right triangle RST, with m∠S = 90°, what is sin T?
The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.
Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:
opposite side / hypotenuse = sin T
We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.
if we know the length of the hypotenuse and the measurement of one acute angle.
thus, we cannot define the value of triangle RST.
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After installing the carpet, Betty decides to install a wood molding around the living room from the last problem. The molding will go around the entire room (15feet long by 15 feet wide). The molding costs $4 per foot. What will the cost of the molding be? hello
please
Answer:
The cost of the molding will be $240-----------------------------------
Find the perimeter of the room:
P = 2(l + w)P = 2(15 + 15) = 2(30) = 60 ftFind the cost of the molding:
60 × 4 = 240Answer:
$240
Step-by-step explanation:
Now we have to,
→ find the cost of molding.
Formula we use,
→ P = 2 × (l + w)
Now the perimeter will be,
→ 2 × (l + w)
→ 2 × (15 + 15)
→ 2 × 30
→ 60 feet
Then the required cost is,
→ P × $4
→ 60 × 4
→ $240
Hence, molding costs $240.
There are 10 circles and 6 squares. What is the simplest ratio of squares to circles
Answer:
3/5
can also be written as 3:5
Step-by-step explanation:
Use:
squares/circles
Fill in the given info.
6/10
simplify (reduce the fraction)
6/10 = 3/5
3/5 is the ratio in simplest form.
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. The ladder makes an angle of 64 ∘with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
31.2 ft
Step-by-step explanation:
sin = opp/hyp
sin64 = 28/hyp
hyp = 28/sin64
use calculator
hyp = 31.15285433330529
Rounded
31.2 ft
The length of the ladder needed to reach an electric box 28 feet up is 31.2 feet.
The ladder, the distance from the wall to the base of the ladder and the distance from the ground to the electric box forms a right angled triangle.
Trigonometric ratios shows the relationship between the sides and angles of a right angled triangle.
Let x represent the length of the ladder, hence:
sin(64) = 28 feet/x
x = 28 feet / sin(64)
x = 31.2 feet
Hence the length of the ladder needed to reach an electric box 28 feet up is 31.2 feet.
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How do you convert grams to moles per gram?
To convert grams to moles per gram, you need to find the molar mass of the substance in grams per mole. Then, divide the number of moles by the given mass to get moles per gram.
To convert grams to moles per gram, you first need to determine the molar mass of the substance you are interested in. The molar mass is the mass of one mole of the substance, expressed in grams. Once you know the molar mass, you can use it to convert grams to moles, and then divide by the total mass to get moles per gram.
Here are the steps to follow:
Determine the molar mass of the substance. This is the sum of the atomic masses of all the atoms in the molecule, expressed in grams per mole. You can find the atomic masses on the periodic table.
Convert the given mass from grams to moles, using the formula:
moles = mass / molar mass
where mass is the given mass in grams, and molar mass is the calculated molar mass in grams per mole.
Divide the number of moles by the given mass, to get the moles per gram. This gives you the number of moles of the substance per gram of the sample.
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h(x) = 18 - 9x + x4, evaluate h(2)
The value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
According to the given question.
We have a function h(x) = 18 - 9x + x^4
Here, we have to find the value of h(2). For this we will substiute x = 2 in the function h(x) = 18 - 9x + x^4.
Therefore, the value of h(2) for the function h(x) = 18 - 9x + x^4 is given by
h(x) = 18 - 9x + x^4
h(2) = 18 - 9(2) + 2^4
h(2) = 18 - 18 + 16
h(2) = 16
Hence, the value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
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Dilate ARST by a scale factor
3
of with the center of dilation
1
4
at the origin.
The dilated figure A'R'S'T' is a larger version of the original figure ARST, with all distances multiplied by a scale factor of 3 and the center of dilation at the origin.
what is triangle?
A triangle is a three-sided polygon, which is a closed two-dimensional figure with straight sides.
Based on the given image, we can follow these steps to dilate the figure ARST by a scale factor of 3 with the center of dilation at the origin:
Plot the coordinates of the original figure ARST: A(2, 2), R(5, 2), S(5, 5), and T(2, 5).
Draw lines from each vertex of the figure to the origin (0, 0).
Measure the distance from the origin to each vertex of the original figure ARST. For example, the distance from the origin to vertex A is:
d(A, 0) = √[(2 - 0)^2 + (2 - 0)^2] = √8
Multiply the distance of each vertex from the origin by the scale factor of 3 to obtain the new distance for the corresponding vertex in the dilated figure. For example, the new distance for vertex A is:
d'(A, 0) = 3 × √8 = 3√8
Draw lines from each vertex of the original figure to the corresponding
Measure the distance along each line For example, the distance along the line from the origin to the dilated point A' is 3√8.
After following these steps, we obtain the coordinates of the dilated figure A'R'S'T' as follows:
A'(3√8, 3√8)
R'(3√20, 3√8)
S'(3√20, 3√20)
T'(3√8, 3√20)
Therefore, the dilated figure A'R'S'T' is a larger version of the original figure ARST, with all distances multiplied by a scale factor of 3 and the center of dilation at the origin.
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slope for (-5,5) (5,-5)
Answer:
Slope(m)=-1
Step-by-step explanation:
A triangle has one side that is `4` centimeters long and one that is `9` centimeters long.
the third side is a whole number of centimeters.
What is the longest possible third side? pls, help.
step-by-step explanation:
remember if you add the given lengths, they must be greater than each other.
4+4=9 so no
9+4 = 13 which is greater than our number. We can make an isosceles triangle.
9+9 is greater than four so it works.
Answer:
probably 14 centimeters
Step-by-step explanation:
I put the new forgis on the jeep
Johnny have 5 Apples in 6 rows how much apples will he have left
It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.
If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.
In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.
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(P+Vˉ2a)(Vˉ−B)=RT Determine (∂∇∂P)T For The Van Der Waal's Gas.
The partial derivative (∂∇∂P)T for the Van der Waals gas is given by
\(\[ \left( \frac{\partial (\frac{\partial P}{\partial V})}{\partial T} \right)_T \]\)
How can we calculate the partial derivative of pressure with respect to volume, with temperature held constant, for the Van der Waals gas?To determine the partial derivative\((\(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\))\) for the Van der Waals gas, we can start by applying the product rule of differentiation. Let's break down the given equation:
\(\((P + \frac{a}{V^2})(V - b) = RT\)\)
Expanding the equation, we have:
\(\(PV - Pb + \frac{a}{V} - \frac{ab}{V^2} = RT\)\)
Rearranging the terms, we get:
\(PV + \frac{a}{V} = RT + Pb + \frac{ab}{V^2}\)
Now, let's differentiate both sides of the equation with respect to volume (\(V\)) while keeping the temperature (\(T\)) constant. Using the chain rule, we obtain:
\(\(\frac{\partial}{\partial V}(PV) + \frac{\partial}{\partial V}(\frac{a}{V}) = \frac{\partial}{\partial V}(RT + Pb + \frac{ab}{V^2})\)\)
Differentiating each term separately:
\(\(P + \frac{-a}{V^2} = 0 + \frac{dP}{dV}b - \frac{2ab}{V^3}\)\)
Simplifying the equation:
\(\(\frac{dP}{dV} = \frac{a}{V^2} + \frac{2ab}{V^3} - \frac{Pb}{V}\)\)
Finally, we need to differentiate the obtained expression for \(\frac{dP}{dV}\) with respect to temperature (\(T\)) while holding volume (\(V\)) constant. This will give us the partial derivative we are looking for:
\(\(\left(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\right)_T = \left(\frac{\partial}{\partial T}\right)_V (\frac{a}{V^2} + \frac{2ab}{V^3} - \frac{Pb}{V})\)\)
Since \(V\) is held constant, the partial derivative of \(\frac{dP}{dV}\) with respect to \(T\) is zero. Therefore, we can conclude that:
\(\(\left(\frac{\partial (\frac{\partial P}{\partial V})}{\partial T}\right)_T = 0\)\)
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What i the equation of a line that i parallel to the line y =2x 7 and pae through the point -2,4
The equation of a line y=2x+8.
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis
Looking at the given line,
y = 2x + 7
Compared with the slope-intercept equation,
Slope, m = 2
If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2
Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes
4 = 2 × - 2 + c
4 = - 4 + c
c = 4 + 4 = 8
The equation becomes y=2x+8.
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A(n) ______________________________ is formed by one side of the triangle and the extension of an adjacent side.
A triangle is a three-sided polygon that consists of three sides and three angles. An extension of a side of a triangle is a line segment that is drawn from one of the endpoints of the side that extends beyond the side.
If we extend one side of the triangle and draw a line that passes through one of the adjacent vertices, the resulting shape is called a triangle's exterior angle. This exterior angle is formed by one side of the triangle and the extension of an adjacent side.
In other words, an exterior angle of a triangle is an angle that is formed by one side of a triangle and the extension of an adjacent side of the triangle.
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Simon does some shopping on the internet. He buys 4 CDs at $8.63 each. How much do the CDs cost altogether?
Answer:
34.52
Step-by-step explanation:
Multiplication plus may i have branlies t
Answer:
the total would be 34.52
Step-by-step explanation:
If we have 4 Cd's that cost 8.63 a piece, all we would need to do is multiply 8.63 by 4, or just add 8.63 4 times.
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What is the simplified form of the square root of 64x16? 8x4 8x8 32x4 32x8
Answer:
8
Step-by-step explanation:
Answer:
8x⁴
Step-by-step explanation:
8x8 = 64
⁴x⁴ = ¹⁶
The width of a rectangle measures (9s+6)(9s+6) centimeters, and its length measures (s+1)(s+1) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
P= ( 18s + 12 ) + ( 2s + 2 ) or just P = 20s + 14
Step-by-step explanation:
9s + 6 is said twice just add both together and it is. 18s + 12.
Same with s + 1 so it would be 2s + 2.
You can add it all together and its 20s + 14.
P = Perimeter.
Looking at the incomes in the piecewise function before Example 2 that are over $74,900 but not over $151,200, the equation is y = 10,312.50 + 0.25(x - 74,900). (a) What does the $10,312 mean? (b) What does the 0.25(x - 74,900) mean? c) Simplify the equation. show work
The simplified equation is y = 10,312.50 + 0.25x - 18,672.50
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
(a) The $10,312.50 represents the fixed amount of income tax owed for the range of incomes between $74,900 and $151,200.
(b) The 0.25(x - 74,900) represents the additional amount of income tax owed based on a tax rate of 0.25 (25%) of the income above $74,900. The x-74,900 term represents the amount of income that is above $74,900, and multiplying by 0.25 calculates the additional tax owed for this portion of the income.
(c) To simplify the equation:
y = 10,312.50 + 0.25(x - 74,900)
y = 10,312.50 + 0.25x - 74,900 * 0.25
y = 10,312.50 + 0.25x - 18,672.50
Hence, the simplified equation is y = 10,312.50 + 0.25x - 18,672.50
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There is a different one like this but it doesn’t have the answer so plz help and this is my 2 try
Answer:
it's c
Step-by-step explanation:
4 times 10 times 6 is 240 and you use volume because its by 3 values.
hope this helped!
Which symbol correctly describes the relationship between these two numbers?
The relationship between these two numbers is 3 > 2.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An expression:
3 is greater than 2.
Here, we will use the inequality symbol.
3 > 2.
Therefore, the expression is 3 > 2.
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The complete question:
Which symbol correctly describes the relationship between these two numbers?
And the expression: 3 is greater than 2.
For a research project, students are asked to study how often students at an online high school look at social
media while doing schoolwork.
1. Sofie decides to develop a survey.
(a) Give an example of a question she could ask on her survey.
(b) How could Sofie select a simple random sample of students to take her survey?
(c) She gives out 80 surveys but receives only 32 completed surveys. What are the sample and
population for Sofie’s research?
(d) Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. If
Sofie uses only the completed surveys, what conclusion could she make about the percent of all high
school students who use social media while doing schoolwork?
(a) Example question: "How often do you look at social media while doing schoolwork?
(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.
(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.
(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.
(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."
(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.
(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.
To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.
Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.
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what is the pattern -8, -2, 4, 10
Answer:
Subtract 8
Add 6
Add 6
Lastly, add 6 again
This is the pattern.
Hope this helps!
The graph of f(x) is shown below of g(x) and f(x) are inverse functions, which graph represents g(x)
Answer:
It's B
Step-by-step explanation:
Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it
The graph of a linear function is shown.
A coordinate plane with a straight line drawn passing through (negative 5, negative 3) and (5, negative 3).
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer:
zero
Step-by-step explanation:
the slope of a function m: y2-y1/x2-x1
m=-3-(-3)/5-(-5)
m=0/10=0
The slope of the line drawn passing through (- 5, - 3) and (5, - 3) is zero, so option C is correct.
What is line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
straight line drawn passing through (- 5, - 3) and (5, - 3)
Calculate the slope of the line as shown below,
\(m = y_2 - y_1 / x_2 - x_1\)
m = slope
m = -3 - (-3) / 5 - (-5)
m = 0 / 10
m = 0
Therefore, the slope of the line drawn passing through (- 5, - 3) and (5, - 3) is zero.
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find the area of the regular polygon
Answer:
433.4
Step-by-step explanation:
Height will be (14/2)/tan36 which is 9.63, then area for one triangle is 1/2*hb which is .5*9.63*7 is 43.34, times 10 you get 433.4
Nat has 2 episodes filmed for her new series. She plans
on filming 6 more episodes per month. Write a linear
equation that could represent this
Which rays are part of line BE?
E
O Ac and E
O AR and
Ac and AB
OAB and A
Rays AB and BE are part of line BE.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
To find the rays which are part of line BE.
Here,, By figure, we have;
Rays AB and BE are part of line BE.
Thus, Rays AB and BE are part of line BE.
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Find the value of r to the nearest tenth
Answer:
29.2m
Step-by-step explanation:
sinB/b = sinC/c
r= sin90×10/sin20
r=29.2
HELP HELP I NEED HELP ASAP PLEASE!!
Find an integer a such that a < √77 < a + 1
PLEASE RIGHT AND EXPLANATION TOO
Answer:
I don't know what z I don't know I don't know
Answer:
Maybe 78 and 76
Step-by-step explanation:
Thats what I got, Idrk how to explain it though-
What is the measure of angle B?
A=50degrees
C=28degrees
Option 1: 78degrees
Option 2: 92degrees
Option 3: 102degrees
Option 4: 282degrees