Problem 2.19. Use translation invariance to fully justify and express B in terms of k so that 2n?+10 2n7-11 284+5k3+k2+k+1 Σ k=n6-21 = AB k=n6

Answer:

one costs 17 dollars the other costs 55 dollars

Step-by-step explanation:

we have to make 2 equations using variables

x=shirt 1

y= shirt 2

y+x=72

x=3y+4

then substitute 3y+4 for x in the first equation

y+3y+4=72

subtract 4 and add y and 3y

4y=68

divide by 4

y= 17

use this for y in the second equation

x=3(17)+4

x=51+4

x=55  

Let

We know

\(\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}\)

\(\\ \sf\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)\)

\(\\ \sf\longmapsto n(A\cap B)=60+65-100\)

\(\\ \sf\longmapsto n(A\cap B)=125-100\)

\(\\ \sf\longmapsto n(A\cap B)=25\)

The principal amount lent by Kritesh was approximately Rs. 1,050.

We can use the formula for simple interest to solve this problem:

Simple interest = (Principal * Rate * Time) / 100

Here, we are given the rate of interest as 6% p.a. and the time as 146/365 years. We need to find the principal amount.

Let P be the principal amount lent by Kritesh.

Then, using the formula for simple interest, we have:

Simple interest = (P * 6 * 146/365) / 100

10,260 = P + (P * 6 * 146/365) / 100

Multiplying both sides by 100 to remove the fraction, we get:

1,026,000 = 100P + 6P * 146

1,026,000 = 100P + 876P

1,026,000 = 976P

P = 1,026,000 / 976

P ≈ 1,050

Therefore, the principal amount lent by Kritesh was approximately Rs. 1,050.

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Answer:

a = 3 1/4 or 3.25

Step-by-step explanation:

Simplify the right side :

√169 = 13

13 = ∛64a³

Simplify left side :

13 = 4a

Divide both sides by 4 :

13/4 = a

a = 3 1/4 or 3.25

Hope this helped and have a good day

Answer:

1)

1/2 does not belong to the set

All other numbers belong to the Integers (Z).

2)

√7 does not belong to the set.

All other numbers are rational numbers (Q).

Answer:

The parabola is a horizontal parabola and it faces to the right. The vertex is at (3, -3) (*Double check this because I don't have graph paper*) because the vertex is always the same distance from the directrix and the focus.

The MATLAB program uses the fixed-point iteration method to find a real root of the equation 4x + cos(x) - e* = 0. It starts with an initial approximation of xo = 1 and iteratively applies the function g(x) = e* - cos(x) until convergence. The program also calculates the absolute and relative percentage error for the obtained root.

Here is an example MATLAB program that implements the fixed-point iteration method to find the real root of the given equation:

function root = fixedPointIteration()

   e_star = % Enter the desired value for e* here

   xo = 1; % Initial approximation

   % Set the tolerance for convergence

   tolerance = 1e-6;

   % Initialize variables

   x = xo;

   previous_x = xo;

   iteration = 0;

   % Perform the fixed-point iteration

   while true

       iteration = iteration + 1;

       x = e_star - cos(previous_x);

       % Calculate the absolute and relative percentage errors

       abs_error = abs(x - previous_x);

       rel_error = abs_error / abs(x);

       % Check for convergence

       if abs_error < tolerance

           break;

       end

       previous_x = x;

   end

   % Display the results

   disp('Root:')

   disp(x)

   disp('Absolute Error:')

   disp(abs_error)

   disp('Relative Error (%):')

   disp(rel_error * 100)  

   root = x;

end

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Answer:

a=-10

Step-by-step explanation:

y=2x+a ,at x=5

y=2(5)+a

y=10+a

where y=0

10+a=0

a= -10

The rate of change of area is given as 27 π. The time at which radius of circle is increasing is 1.386 sec and change in radius is 3 cm.

What is rate of change?

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

a) Given, radius of circle = 9 cm

rate of change of radius = 3/2

We know area of circle = πr^2

change in area =2πrr'

we get  2×π×9×2/3=27π

B) Given,

g(t) = 12 - 12e^0.5t

derivate it

g'(t) =-12×-1/2e^t/2

g'(t)=3

3= 6e^t/2

t = 1.386

c) f1(t) = t2-4t+4.

Integrate it we get

radius =3.

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Answer:

Approximately normal

Mode: 4

Range:9

Step-by-step explanation:

The data is pretty evenly spread, the data isn’t pushed to the left or right giving the answer of approximately normal.

Mode: The number that occurs the most is the mode. This means that 4 would be the answer because it has the most dots.

Range: To find the range subtract the smallest number from the biggest number. In this case you would get 9-0 (this is because no data is recorded for 10) which equals 9.

I hope this helps! :)

Answer:

C. x - 5y - 30 = 0

Step-by-step explanation:

Y = x/5 - 30

y + 30 = x/5

you multiply both sides by 5

5y + 30 = x

you subtract x from both sides

- x + 5y + 30 = 0

which is the same as

x - 5y - 30 = 0

Answer: you need to add a picture

Step-by-step explanation:

so people know what kinda of problem there trying to figure out

Step-by-step explanation:

what you need to do is find the x values for which f(x) is the same as g(x).

you only need to compare the result values in the table.

what functional result values are the same (in the same line) ?

well, -3 and 0.

-3 is the result when x = 0.

and 0 is the result when x = 2.

so, x = 0 and x = 2 are the two correct answers.

for these 2 x values both functions deliver the same results.

His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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Answer:

If they are parallel then angle b is

A. 51°

Step-by-step explanation:

Therefore, the discount factor for one period with a rate of return of 6 percent is approximately 0.9434.

To calculate the discount factor for one period with a rate of return equal to 6 percent, you can use the formula:

Discount Factor = 1 / (1 + Rate of Return)

Substituting the rate of return of 6 percent (0.06) into the formula:

Discount Factor = 1 / (1 + 0.06) = 1 / 1.06 ≈ 0.9434

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Answer:

B) AGI

Step-by-step explanation:

Definitions

So as Gretchen has subtracted adjustments of student loan interest and IRA contributions from her gross income, the remaining amount is the AGI.

Answer:

The answer is B. y=-3x+4

Step-by-step explanation:

Have a great day :)

The approximate number of students with Scores between 68 and 83 is 98.Answer: a. 98

The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83?

The five-number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The interquartile range is the difference between the third and first quartiles. Interquartile range (IQR) = Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. The 5-number summary for scores on a statistics exam is given below:

Minimum value = 35

First quartile Q1 = 68

Median = 77

Third quartile Q3 = 83

Maximum value = 97

The interval 68–83 is the range between Q1 and Q3.

Thus, it is the interquartile range.

The interquartile range is calculated as follows:IQR = Q3 – Q1 = 83 – 68 = 15

The interquartile range of the scores between 68 and 83 is 15. Therefore, the number of students with scores between 68 and 83 is roughly half of the total number of students. 196/2 = 98.

Thus, the approximate number of students with scores between 68 and 83 is 98.Answer: a. 98

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Answer:

2

Step-by-step explanation:

Answer:

whats the question?

Step-by-step explanation:

Answer:

month us your x, and temp. is your y

type the graph into demos graph calculator.

hope this helps

The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.

To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

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Answer:

the cake that was left is 1 by 15

Step-by-step explanation:

The computation is shown below:

= sale - gave away

\(= \frac{2}{5} - \frac{1}{3}\\\\= \frac{6 - 5}{15} \\\\= \frac{1}{15}\)

Hence, the cake that was left is 1 by 15

So the same is relevant and considered too

Answer:

40

Step-by-step explanation:

A kilometre is 1000 metres.  1000 / 25 = 40.  So forty basketball courts would be approximately 1 km if lined up end to end.

The answer is 40 because 1 kilometer divided by 25 meters would be 40 and each court is 25 meters so that is 40 courts in 1 kilometer.

(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.  Therefore, there are 31 different ways this can happen

To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:

1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).

Therefore, the range of possible values for "x" is 1 to 5.

2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.

To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.

Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.

Therefore, there are 31 different ways this can happen

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In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):

fy(a,b) = lim┬(y→b)⁡〖[f(a,y) - f(a,b)]/(y - b)〗

Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

To see why this is the case, consider the following argument:

Let L be the limit in the expression given above.

Let h = y - b be the change in the y-coordinate from b to y.

Then, we can rewrite the limit as:

fy(a,b) = lim┬(h→0)⁡〖[f(a,b + h) - f(a,b)]/h〗

This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].

As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).

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Answer:

b) m = -2 and b=10 and c) m= 2/5 and b=4

Step-by-step explanation:

For b, we know that the b value (y-intercept) is 10 because it is the y value when x= 0, which is shown on the table as 10.

Next, to find the slope (m-value) we know that 10 gets added to the y value so then x(2) + 10 = 6

subtract 10 from both sides and you get 2x = -4

divide both sides by 2 to get x= -2 or our m-value (slope)
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For c, we know that the graph intercepts the y-axis at 4, so that is our b value.

We know know: y= m(x) + 4

To find the slope, we use the formula: rise/run

When the graph goes up 6 to get to y=10, the x value goes 15 across

Rise = 6 ;  Run = 15

6/15 = 2/5

Therefore, the m value is 2/5