Giselle spent 7/10 of her money on a book and 10/100 of her money on food. What fraction of her money did she spend altogether?

The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

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The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

hope this helps, this is the fastest I could do

Answer:

( x + 2)(2x + 3)

Step-by-step explanation:

\(2 {x}^{2} + 7x + 6 \\ \\ = 2 {x}^{2} + 4x + 3x + 6 \\ \\ = 2x(x + 2) + 3(x + 2) \\ \\ = ( x + 2)(2x + 3)\)

Answer:

-2.964

Step-by-step explanation:

Answer:

y = x + 2

Step-by-step explanation:

Slope Intercept form is:

y = mx+b

m = slope

b = y-intercept

Divide both sides by 5:

y - 2 = x

Rewrite in Slope Intercept form:

y = x + 2

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

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Given that the area is bounded by y² = x and x - y = 2 and we have to use horizontal slicing to find the area.

Below is the figure of the given curve, To find the area we will use integration.

Consider a horizontal slice of thickness 'dy' at a distance y from the x-axis, let its length be x.

\(Now, the equation of the parabola is given by y² = x ...(1)\)

And the line is given by x - y = 2Putting the value of x from Given that the area is bounded by y² = x and x - y = 2 and we have to use horizontal slicing to find the area. (1) into equation (2),

\(we get,y² - y - 2 = 0y² - 2y + y - 2 = 0y(y - 2) + 1(y - 2) = 0(y - 2)(y + 1) = 0y = -1, 2\)

\(Now, the area is given by the integral of the horizontal slices which is as follows, A = ∫(y = -1 to y = 2) x dy\)\(Where x = y², and x = 2 + ySo, A = ∫(y = -1 to y = 2) (2 + y - y²) dyA = [(2y + (y²/2) - (y³/3))] (-1 to 2)A = [(2(2) + (2²/2) - (2³/3)) - (2(-1) + ((-1)²/2) - ((-1)³/3))]A = [4 + 2 - (8/3)] - [-2 - (1/2) + (1/3)]A = 5 1/6\)

\(Therefore, the area bounded by y² = x and x - y = 2 using horizontal slicing is 5 1/6 square units.-------------------------------------------------------------------------------------------------------------------------------Given that the region bounded by y = x, y = x², x = 1, and x = 2 is rotated about the line x = 2.\)

To find the volume, we will use the Washer method.

Consider a washer or a ring of thickness 'dx' at a distance x from the line x = 2.

\(Let its inner radius be 'r' and the outer radius be 'R'.

Now, the curves are y = x, y = x², x = 1, and x = 2.\)

\(These curves intersect at (1,1) and (2,2) points.\)

\(The inner radius of the washer is given by the distance between the line x = 2 and y = x which is 2 - x\)

\(And, the outer radius of the washer is given by the distance between the line x = 2 and y = x² which is 2 - x²\)

\(Therefore, the volume of the solid is given by the integral of the washers which is as follows, V = π ∫(x = 1 to x = 2) [R² - r²] dxWhere R = 2 - x² and r = 2 - x\)

\(So, V = π ∫(x = 1 to x = 2) [(2 - x²)² - (2 - x)²] dxV = π ∫(x = 1 to x = 2) [4 - 4x² + x⁴ - 4 + 4x - x²] dxV = π ∫(x = 1 to x\)= \(2) [x⁴ - 4x² + 4x] dxV = π [(x⁵/5) - (4x³/3) + 2x²] (1 to 2)V\)=\(π [(2⁵/5) - (4(2³)/3) + 2(2²)] - [(1⁵/5) - (4(1³)/3) + 2(1²)]V\) =\(π [(32/5) - (32/3) + 8] - [(1/5) - (4/3) + 2]V = (94π/15) cubic units\)

Therefore, the volume of the solid generated by rotating the region bounded by y = x, y = x², x = 1, and x = 2 about the line x = 2 is (94π/15) cubic units.

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Finding the area bounded by (y^2 = x) and (x - y = 2) using horizontal slicing:

To find the area using horizontal slicing, we integrate the difference in the y-values of the two curves over the interval where they intersect.

First, let's find the points of intersection between the two curves:

(y^2 = x) and (x - y = 2).

Substituting the second equation into the first equation:

((x - 2)^2 = x).

Expanding and rearranging the equation:

(x^2 - 4x + 4 = x).

Bringing all terms to one side:

(x^2 - 5x + 4 = 0).

Factoring the quadratic equation:

((x - 1)(x - 4) = 0).

So, the points of intersection are (x = 1) and (x = 4).

Now, let's integrate the difference in the y-values of the two curves over the interval from (x = 1) to (x = 4):

The curve (y^2 = x) gives us \(\(y = \sqrt{x}\)\).

The line (x - y = 2) can be rearranged to (y = x - 2).

The difference in y-values is (y_2 - y_1 = (x - 2) - \(\sqrt{x} = x - 2 - \sqrt{x}\)\).

The area is given by the integral:

\(\(\int_{1}^{4} (x - 2 - \sqrt{x}) \, dx\)\).

Evaluating this integral:

\(\(\int_{1}^{4} (x - 2 - \sqrt{x}) \, dx = \left[\frac{x^2}{2} - 2x - \frac{2}{3}x^{\frac{3}{2}}\right]_{1}^{4}\).\)

Simplifying:

\(\(\left[\frac{x^2}{2} - 2x - \frac{2}{3}x^{\frac{3}{2}}\right]_{1}^{4} = \left[\frac{16}{2} - 8 - \frac{2}{3}(4)^{\frac{3}{2}}\right] - \left[\frac{1}{2} - 2 - \frac{2}{3}(1)^{\frac{3}{2}}\right]\)\)

Calculating the values:

\(\(\left[8 - 8 - \frac{2}{3}(4)^{\frac{3}{2}}\right] - \left[\frac{1}{2} - 2 - \frac{2}{3}\right]\)\)

Simplifying further:

\(\(-\frac{2}{3}(4)^{\frac{3}{2}} + \frac{3}{2} - \frac{5}{6}\)\)

Finally, evaluating the expression:

\(\(-\frac{2}{3}(4)^{\frac{3}{2}} + \frac{3}{2} - \frac{5}{6} \approx -3.301\)\)

Therefore, the area bounded by (y^2 = x) and (x - y = 2) using horizontal slicing is approximately -3.301 square units.

(2) Finding the volume of the region bounded by (y = x), (y = x^2), (x = 1), and (x = 2) when rotated about the line (x = 2):

To find the volume, we can use the method

of cylindrical shells.

The radius of each cylindrical shell will be the distance between the line (x = 2) and the curve (y = x), which is (r = 2 - x).

The height of each cylindrical shell will be the difference between the curves (y = x) and (y = x^2), which is (h = x - x^2).

The differential volume element of each cylindrical shell is given by

\(\(dV = 2\pi rh \, dx = 2\pi (2 - x)(x - x^2) \, dx\)\)

To find the total volume, we integrate this expression from

(x = 1) to (x = 2):

\(\(V = \int_{1}^{2} 2\pi (2 - x)(x - x^2) \, dx\)\)

Evaluating this integral:

\(\(V = \left[\pi (2x - \frac{x^2}{2} - \frac{x^3}{3})\right]_{1}^{2}\)\)

Simplifying:

\(\(V = \left[\pi (4 - 2 - \frac{8}{3} - 2 + \frac{1}{2} + \frac{1}{3})\right] - \left[\pi (2 - \frac{1}{2} - \frac{1}{3})\right]\)\)

Calculating the values:

\(\(V = \left[\pi (-\frac{1}{6})\right] - \left[\pi (\frac{11}{6})\right]\)\)

Simplifying further:

\(\(V = -\frac{\pi}{6} - \frac{11\pi}{6} = -\frac{12\pi}{6} = -2\pi\)\)

Therefore, the volume of the region bounded by (y = x), (y = x^2), (x = 1), and (x = 2) when rotated about the line (x = 2) is -2π cubic units.

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Answer:

Step-by-step explanation:

F

Answer:

the correct answer is $269

Step-by-step explanation:

Answer:

$269

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

The solution to the optimal control problem involves finding the optimal control input u(t) = x₂(t) - c1/2, determining the constants c₁ and c₂ using the boundary conditions, and finding the value of x₃_unspecified using the integral of x₂.

To solve the given optimal control problem, we need to minimize the cost function J(u) = ∫(x₁² + x₂² + u²) dt over the time interval t ∈ [0,1], subject to the given dynamics and initial and final conditions.

Let's denote the unknown function 21(t) as x₃(t).

The given dynamics are:

dx₁/dt = x₂

dx₂/dt = u

dx₃/dt = x₂

We can use the Euler-Lagrange equations to find the optimal control u(t) that minimizes the cost function.

The Euler-Lagrange equation is given by:

d/dt (∂L/∂u_dot) - ∂L/∂u = 0

Where L is the Lagrangian defined as L = x₁² + x₂² + u².

Let's compute the partial derivatives of L:

∂L/∂u = 2u

∂L/∂x₁_dot = 0 (since x₁ does not explicitly depend on time)

∂L/∂x₂_dot = 2x₂

∂L/∂x₃_dot = 0 (since x₃ does not explicitly depend on time)

Now, substitute these derivatives into the Euler-Lagrange equation:

d/dt (2x₂) - 2u = 0

This simplifies to:

2(d/dt)(x₂) - 2u = 0

Integrating both sides with respect to time, we get:

2x₂ - 2u = c1

Rearranging the equation, we have:

u = x₂ - c1/2

Since we need to minimize the cost function, we set the control input u(t) to its optimal value. Thus, u(t) = x₂(t) - c1/2.

Now, let's consider the boundary conditions:

x₁(0) = 0, x₂(0) = 1, x₁(1) and x₃(1) are unspecified.

Using the given dynamics, we can solve for x₁ and x₂:

dx₁/dt = x₂

dx₂/dt = u = x₂ - c1/2

Integrating the first equation, we get:

x₁(t) = ∫(x₂(t)) dt

Integrating the second equation, we get:

x₂(t) - (c1/2)t + c₂ = x₂(t)

Using the initial condition x₂(0) = 1, we can find c₂ = 1.

Therefore, x₂(t) - (c1/2)t + 1 = x₂(t)

Substituting this expression for x₂ into the equation for x₁, we get:

x₁(t) = ∫(x₂(t) - (c1/2)t + 1) dt

Now, using the boundary condition x₁(0) = 0, we can determine c₁.

Finally, we need to find the unspecified value of x₃(1). For this, we can use the equation dx₃/dt = x₂ and integrate it:

x₃(t) = ∫(x₂(t)) dt

Using the boundary condition x₃(1) = 21(1) = x₃_unspecified, we can determine the value of x₃_unspecified.

To summarize, the solution to the optimal control problem involves finding the optimal control input u(t) = x₂(t) - c1/2.

Note that the exact values of c₁, c₂, and x₃_unspecified will depend on the specific values of x₁, x₂, and the integral of x₂ obtained by solving the differential equations and integrating.

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Answer:

I think its A

The data is symmetric and shows that half of the assignments contained 15 problems or fewer.

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

65.974 Square-miles

Step-by-step explanation:

We do 3.14*2^2=12.566

We then do 3.14*5^2=78.54

78.54-12.566=65.974

The change in the area of the circular oil spill is given by the equation

A = 65.973 miles²

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the change in area of circular oil spill be A

Now , the equation will be

The initial radius of the circular oil spill r = 2 miles

The increased radius of the circular oil spill R = r + 3

R = 5 miles

Now , the initial area of the circular oil spill = πr²

Substituting the values in the equation , we get

The initial area of the circular oil spill = 4π miles²

Now ,

The increased area of the circular oil spill = πR²

Substituting the values in the equation , we get

The increased area of the circular oil spill = 25π miles²

And , change in area of circular oil spill A = 25π miles² - 4π miles²

On simplifying the equation , we get

The change in area of circular oil spill A = 21π miles²

The change in area of circular oil spill A = 65.973 miles²

Therefore , the value of A is 65.973 miles²

Hence , the change in circular area is 65.973 miles²

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to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.

"""

Python version: 3.6

Python program to calculate the total price for car wash services

"""

# dictionary containing the services as keys and their price as values

services = {'Air freshener' : 1, 'Rain repellent' : 2, 'Tire shine' : 2, 'Wax' : 3, 'Vacuum' : 5}

# variable to store the base car wash price

base_wash = 10

# variable to store the total price

total = 0

# read the 2 services

service_choice1 = input()

service_choice2 = input()

print("ZyCar Wash")

# display the base wash price

print("Base car wash -- ${}".format(base_wash))

total += base_wash # add base_wash to total

# first service read is in services dictionary

if service_choice1 in services:

   total += services[service_choice1] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice1, services[service_choice1]))

# second service read is in services dictionary    

if service_choice2 in services:

   total += services[service_choice2] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice2, services[service_choice2]))

# display the total price  

print("----")

print("Total price: ${}".format(total))    

# end of program

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Answer:

 1, 2, 3, 4, 6, 9, 12, 18, and 36

Answer:

1. 12 square kilometers

2.18 square inches

Step-by-step explanation:

To find the area of a square you multiply the base and the height. Then you divide it by 2. 8 times 3 divided by 2 is 12. 4 times 9 divided by 2 is 18. Hope this helps!

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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Answer:d

Step-by-step explanation:

Answer:

336 ways

Step-by-step explanation:

The digits are 1, 2, 2, 4, 5, 5, 6, and 2 that is total eight digits.

The number 654-5222 contains 7 digits.

So, we have find The number of permutations for choosing 7 digits from 8 digits given above.

This can be done in following ways

\(\frac{8!}{3!\times2!}\) = \(\frac{40320}{6\times2}\)

= 336 ways

Answer:

1.1???????

Step-by-step explanation:

Answer:Its most likely to be D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

All you need to know is that the square root of 81 is 9. Then you can eliminate all the graphs that don´t have C plotted at 9.

Answer:

7 weeks.

Step-by-step explanation:

It took Emmy six weeks of vocal lesson to learn twelve pieces. If you divide 12÷6 it equals 2 or if you multiply 6×2 it equals 12, just like that if you divide (14÷7=2) or multiply (7×2) you will get the answer. you can also divide first and then multiply to check the answer/vice-versa.

Answer:

positive

Step-by-step explanation:

for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)

y = -1/2x+3 = Line A

y = 2x+3 = PERPENDICULAR to Line A

The missing prime factor of 270 is 5. To find the prime factorization of 270, we divide the number by prime factors starting from 2

Dividing 270 by 2 gives us 135, which is not divisible by 2 anymore. Next, we divide 135 by 3, which gives us 45. Dividing 45 by 3 again gives us 15.

Continuing this process, we find that 15 can be divided by 3 one more time to give us 5. At this point, 5 is a prime number and cannot be divided further. Therefore, the prime factorization of 270 is \(2^1.3^3.5^1\).

The given list of prime factors, 2, 3, 3, 3, is correct except for the missing prime factor 5. The exponent of 5 in the prime factorization is 1, indicating that 270 can be expressed as the product of 2 raised to the power of 1, 3 raised to the power of 3, and 5 raised to the power of 1.

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The correct Numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Evaluate the subtraction inside the parentheses:

3 − 2 = 1

Step 2: Rewrite the expression with the simplified value:

9 x 4 + 1

Step 3: Perform the multiplication:

9 x 4 = 36

Step 4: Add the products:

36 + 1 = 37

Therefore, the correct numerical expression for "9 times 4 added to the difference of 3 and 2" is 37.

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The rate constant K is 0.0015.

Zero-order reaction of reactant a is found to have [a]0=0.25 m and

if [a]=0.10 m at t=100s, then we need to find the rate constant k.

The rate constant, k, is a proportionality constant that indicates the relationship between the molar concentration of reactants and the rate of a chemical reaction

k=([a]0-[a])/t

where k is rate constant,

By the given data we have [a]0=0.25 m

[a]=0.10 m

t=100s

k=?

The rate constant, is a proportionality constant that indicates the relationship between the molar concentration of reactants and the rate of a chemical reaction.

The rate constant is denoted by k.

k=([a]0-[a])/t

Subtract 0.10 from 0.25 and divide it by 100

=(0.25-0.10)/100

=0.15/100

=0.0015

Therefore 0.0015 is the rate constant when a zero-order reaction of reactant a is found to have [a]0=0.25 m and [a]=0.10 m at t=100.

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Answer:

Ms. Cohen can buy 12 poxes of crayons.

Step-by-step explanation:

Ms. Cohen can buy 12 boxes of crayons with the rest of her money. In the question it states she only wants to buy 1 poster not more than one so if she buys 1 poster that's

30-5-25

and than you can just count up by 2 till you get the closest to 25

25-24=1$

24/2 = 12

Hope this helps.

The number of boxes of crayons that can be bought is needed.

The number of boxes that can be bought at most is 12.

Let \(x\) be the number of boxes of crayons

Total amount of money = $30

Cost of one box = $2

Cost of poster = $5

The linear inequality will be

\(2x+5\leq 30\\\Rightarrow x\leq\dfrac{30-5}{2}\\\Rightarrow x\leq 12.5\)

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To calculate the weighted average grade, we need to multiply each grade by its corresponding weight, add up these products, and then divide by the total weight. Let's do this for the student's grades:

Weighted grade for unit tests = 86% x 0.25 = 21.5%

Weighted grade for final test = 85% x 0.4 = 34%

Weighted grade for class project = 90% x 0.15 = 13.5%

Weighted grade for homework submissions = 92% x 0.2 = 18.4%

Total weight = 0.25 + 0.4 + 0.15 + 0.2 = 1

Weighted average grade = (21.5% + 34% + 13.5% + 18.4%) / 1 = 87.4%

Therefore, the student's weighted average grade is 87.4%.

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