TRAVEL Roscoe is exchanging $121 for Euros for his upcoming trip to Germany. If $2 can be exchanged for 1.78 Euros, how many Euros will Roscoe have?

The dimensions of the package of maximum volume that can be sent are 20 inches by 40 inches.

Let us represent the length of the square cross-section of the postal package with x, and the width of the package with y.

So, the perimeter is given by the equation -

y + 4x = 120

y = 120-4x    -----------(1)

the volume will be

V = \(x^{2} y\)        -----------(2)

Now, substitute (1) in (2), and we get,

V = \(x^{2}\) (120-4x)

V = 120\(x^{2}\) - 4\(x^{3}\)

Differentiating with respect to x, we get,

V' = 240x - 12\(x^{2}\)

V'=0

hence, 240x - 12\(x^{2}\) = 0

12\(x^{2}\) = 240x

dividing by 120x on both sides,

hence, x=20

Now, we know that,

y = 120 - 4x

y = 120-4(20)

y = 120-80

y=40

Hence, the dimensions that maximize the volume of the package are 20 inches by 40 inches.

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A polynomial with roots A, B, and C can be written as it follows:

Because every time a complex number is the root of a polynomial, it's conjugated also is, let the roots A, B, and C stands for -2i, +2i, and 3, respectively. So, we can write the polynomial as follows:

Now, we just need to make the calculation needed to reach the expanded form:

The answer to the present question is the following polynomial:

The function y=tanx is not defined is B) x = 4π.

The function y = tanx is not defined for __E) x = 0__.Explanation:A trigonometric function is defined as a function that relates angles of a triangle to the ratio of its sides. The sine (sin), cosine (cos), and tangent (tan) functions are examples of trigonometric functions. y = tan x is one of the many types of trigonometric functions, where the ratio of opposite side and adjacent side is tan x. In a tan x function, it is said to be undefined when the cosine value of the given angle is zero.

Hence, we can find the undefined values in a tan x function by finding out the angles where cos x = 0. Let's solve the given question. 

We are given y = tan x function is not defined for what values of x. 

From the unit circle, we know the values of sin, cos, and tan for different angles in radians. So, cos x is zero at two angles, which are x = π/2 and x = 3π/2. Hence, tan x is undefined for these two angles as tan x = sin x/cos x. When cos x is zero, then it's impossible to divide by zero. Therefore, the function is undefined when x = π/2 and x = 3π/2. Answer: B) x = 4π.

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Answer:

-6

Step-by-step explanation:

y=-6x + 3

This is in the form y = mx+b where m is the slope and b is the y intercept

The slope is -6 and the y intercept is 3

Answer:

yes

Step-by-step explanation:

Answer:

it is irrational

Step-by-step explanation:

The number to be added to the blank should be 9.

According to the statement

we have to find the number which is missing from the given expression.

So, For this purpose, We know that the

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given function is f(x) = 4(x² − 6x + ____) + 20. To complete the expression, complete the square of the one inside the parentheses. This is done by dividing the coefficient of x with 2 and then raising it to two.

-6/2 = -3

(-3)² = 9

Therefore, the number to be added to the blank should be 9.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

In the function f(x) = 4(x^2 − 6x + ____) + 20, what number belongs in the blank to complete the square?

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Answer:

\(x = 2 \: or \: x = \frac{1}{2} \\ (x - 2)(2x - 1) = 0 \\ {2x}^{2} - x - 4x + 2 \\ {2x}^{2} - 5x + 2\)

Step-by-step explanation:

Events A and B are mutually exclusive and the probability of either event A or event B occurring is 1/4.

Gien that,

Two standard-number cubes are being tossed.

We need to determine if the events A and B are mutually exclusive.

Event A means that the sum of the two numbers rolled is 12.

Event B means that both dice show an odd number.

Determine if events A and B are mutually exclusive,

Since event A requires the sum of the two numbers to be 12, that means we need to roll a 6 on both dice.

However, rolling a 6 on both dice means that both numbers are even, so events A and B cannot occur at the same time.

Therefore, events A and B are mutually exclusive.

To find P(A or B),

Calculate the probability of either event A or event B occurring.

Adding the probability of event A to the probability of event B, and then subtracting the probability of both events occurring at the same time (since they are mutually exclusive).

The probability of rolling a 6 on one die is 1/6,

So the probability of rolling a 6 on both dice is,

(1/6) x (1/6) = 1/36.

Therefore, P(A and B) = 1/36.

The probability of rolling an odd number on one die is 1/2,

So the probability of rolling an odd number on both dice is,

(1/2) x (1/2) = 1/4.

To find P(A or B),

Add the probability of event A (1/36) to the probability of event B (1/4), and then subtract the probability of both events occurring (1/36).

P(A or B) = (1/36) + (1/4) - (1/36)

              = 1/4

So the probability of either event A or event B occurring is 1/4.

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Answer:

Step-by-step explanation:

area of field=1/2(a+b)h

a=12

b=20

h=?

h=pythagoras theorem

a²+b²=c²

a²+8²=17²

a²+64=289

a²=289-64

a²=221

a=√221

a=14.9

area of field=1/2(12+20)14.9

area=238.4m²

£19.75×3=£59.25

Any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.

Given quadratic equation is:

\(x^{2} +bx+5=0\)

Any equation of the form \(ax^{2} +bx+c=0\) is called a quadratic equation where a≠0.

To have two real number solutions the discriminant of a quadratic equation should be greater than or equal to zero.

\(D\geq 0\)

\(b^{2} -4(1)(5)\geq 0\)

\(b^{2}-20 \geq 0\)

\(b^{2} -(2\sqrt{5}) ^{2}\geq 0\)

\((b+2\sqrt{5} )(b-2\sqrt{5} )\geq 0\)

b∈\((-\infty,-2\sqrt{5}]\)∪\([2\sqrt{5},\infty)\)

Hence, any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.

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Answer:

Step-by-step explanation:

Answer:

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Class 11

>>Physics

>>Units and Measurement

>>Errors in Measurement

>>You measure two quantities ...

Question

Bookmark

You measure two quantities as A=1.0m±0.2m, B=2.0m±0.2m. We should report correct value for

AB

as

Medium

Solution

verified

Verified by Toppr

Correct option is

D

1.4m±0.2m

Here, A=1.0m±0.2m, B=2.0m±0.2m

AB=(1.0m)(2.0m)=2.0m

2

AB

=

2.0m

=1.414m

Rounding off to two significant figures, we get

AB

=1.4m

AB

ΔAB

=

2

1

(

A

ΔA

+

B

ΔB

)=

2

1

(

1.0

0.2

+

2.0

0.2

)=

2

0.3

Δ

AB

=

2

0.3

×

AB

=

2

0.3

×1.414=0.212m

Rounding off to one significant figure, we get

Δ

AB

=0.2m

The correct value for

AB

is 1.4m±0.2m

Answer:

i believe its 1200

Step-by-step explanation:

The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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The area of the circle to the nearest tenth is approximately 283.5 cm², and the circumference of the circle to the nearest tenth is approximately 59.7 cm.

What is the circumference of a circle?​

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole. A geodesic, the shortest distance between any two points on a sphere,

The area of a circle with radius r is given by the formula A = πr², and the circumference of a circle with radius r is given by the formula C = 2πr.

Substituting r = 9.5 cm, we have:

A = π(9.5 cm)² ≈ 283.53 cm² (rounded to the nearest tenth)

C = 2π(9.5 cm) ≈ 59.69 cm (rounded to the nearest tenth)

Therefore, the area of the circle to the nearest tenth is approximately 283.5 cm², and the circumference of the circle to the nearest tenth is approximately 59.7 cm.

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A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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Answer:

56 tiles

Step-by-step explanation:

\(\dfrac{252}{4\frac{1}{2}}= \\\\\\\dfrac{252}{\frac{9}{2}}= \\\\\\252\times \dfrac{2}{9}= \\\\\\\boxed{56}\)

Hope this helps!

Same with the other question we did, we are given the area of each tile which is 4 1/2in^2.

All we need to do it divide.

252 / 4.5 = 56

So, she would need 56 tiles in total.

Best of Luck!

In order to determine the optimal number of bedrooms and bathrooms for Doreen to rent, we need to consider her utility function and the budget constraint. Doreen's utility function is U(x,y) = min(x, 2y), where x represents the number of bedrooms and y represents the number of bathrooms. The rental price per bedroom is £400 and per bathroom is £200.

Let's assume Doreen rents x bedrooms and y bathrooms. The total cost of renting can be calculated as follows:

Rent = (x * £400) + (y * £200)

Doreen's budget constraint is £1000 per month, so we have:

(x * £400) + (y * £200) ≤ £1000

To optimize Doreen's utility within her budget, we can substitute the utility function into the budget constraint:

min(x, 2y) ≤ £1000 - (y * £200)

min(x, 2y) ≤ £1000 - £200y

min(x, 2y) ≤ £1000 - £200y

Now we need to analyze the possible combinations of x and y that satisfy the budget constraint. Since the utility function U(x,y) = min(x, 2y), Doreen will choose the combination of x and y that maximizes the minimum value between x and 2y while still satisfying the budget constraint.

To find the optimal solution, we can substitute different values of y into the inequality and determine the corresponding x that satisfies the budget constraint. We start with y = 0 and gradually increase y until the budget constraint is reached. The optimal solution occurs when the maximum utility is achieved within the budget constraint.

b. In this case, Doreen has a budget of £500 to spend on both furniture and clothing. The cost of furniture per unit is £50, and the cost of clothing per unit is £20. Her utility function is U(f,c) = 10.3c^0.7, where f represents furniture and c represents clothing.

To determine how much Doreen spends on furniture and clothing, we need to maximize her utility within the budget constraint. Let's assume Doreen spends £x on furniture and £y on clothing.

We have the following budget constraint:

£50x + £20y ≤ £500

To optimize Doreen's utility, we substitute the utility function into the budget constraint:

10.3c^0.7 ≤ £500 - (£50x + £20y)

Similarly to part a, we need to analyze different combinations of x and y that satisfy the budget constraint. By substituting different values of x and y, we can determine the optimal solution that maximizes Doreen's utility within her budget.

c. If the local furniture shop offers a 50% discount on all prices, the cost of furniture per unit is reduced by half (£50/2 = £25 per unit). However, the price of clothing remains the same at £20 per unit.

To calculate how much Doreen spends on furniture and clothing after the discount, we use the same budget constraint as in part b:

£50x + £20y ≤ £500

Since the price of furniture per unit is now £25, we replace £50x in the budget constraint with £25x:

£25x + £20y ≤ £500

By substituting different values of x and y into the modified budget constraint, we can determine the new optimal solution that maximizes Doreen's utility within her budget.

d. The utility function for Doreen's preferences over pizza and vegan burgers is given as U(p, v) = 2p + v.

To calculate the marginal utility from pizza

, we differentiate the utility function with respect to p:

∂U(p, v)/∂p = 2

The marginal utility from pizza is a constant value of 2.

To calculate the marginal utility from vegan burgers, we differentiate the utility function with respect to v:

∂U(p, v)/∂v = 1

The marginal utility from vegan burgers is a constant value of 1.

Diminishing marginal utility occurs when the marginal utility of consuming an additional unit of a good decreases as the quantity of that good increases. In this utility function, the marginal utility of pizza remains constant at 2, while the marginal utility of vegan burgers also remains constant at 1. Therefore, this utility function does not exhibit diminishing marginal utility for either pizza or vegan burgers.

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Answer:

117.16

Step-by-step explanation

16% and add it to 100% then convert it to its decimal place so you have 1.16

1.16 X 101 = £117.16

The values of (x - 1/x) = √32 and  x² + 1/x² = 34.

Algebraic identities are mathematical equations or expressions that hold true for all values of the variables involved.

Using some algebraic identities we can solve the given problem. Here are some commonly used algebraic identities:

=> (a + b)² = a² + b² + 2ab

=> (a - b)² = a² + b² - 2ab

Here we have

=> x+1/x = 6  

Do squaring on both sides

=> (x + 1/x)² = 36

As we know (a + b)² = a² + b² + 2ab

=> x² + 1/x² + 2x (1/x)  = 36  

=> x² + 1/x² + 2 = 36  

=> x² + 1/x²  = 36 - 2

=>  x² + 1/x² = 34  ---- (1)

As we know (a - b)² = a² + b² - 2ab

=> (x - 1/x)² = x² + 1/x² - 2 x(1/x)

=> (x - 1/x)² = x² + 1/x² - 2  

=> (x - 1/x)² = 34 - 2     [ From  (1) ]

=> (x - 1/x) = √32

Therefore,

The values of (x - 1/x) = √32 and  x² + 1/x² = 34.

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The compound inequality to determine the Fahrenheit temperature range is given by  \(-40 < \frac{5}{9}(F-32) < 125\) .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

Inequality is represented by:

A compound inequality is of the form : a < x < b implies that the value of x lies between the values of a and b.

According to the question if temperature is denoted in Celsius the inequality can be written as : -40° < °C < 125°

Now we know that the relation between C and F can be written as

\(C=\frac{5}{9}(F-32)\)

Therefore the required inequality will be of the form:

\(-40 < \frac{5}{9}(F-32) < 125\)

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The general solution to the differential equation y' - 2y + 3e^t = 0 is: y = Ce^(2t) - e^t.  As t approaches infinity, the solution approaches infinity because the dominant term in the solution is e^(2t).

The given differential equation is:

y' - 2y + 3e^t = 0

We can first find the homogeneous solution by setting the right-hand side equal to zero:

y' - 2y = 0

This is a separable differential equation that can be solved by separating variables:

dy/y = 2dt

Integrating both sides, we get:

ln|y| = 2t + C

where C is an arbitrary constant. Solving for y, we get:

y = Ce^(2t)

This is the general solution to the homogeneous equation.

Now, we need to find a particular solution to the non-homogeneous equation. Since the non-homogeneous term is a constant times e^t, we can guess a particular solution of the form:

y_p = Ae^t

where A is a constant. Substituting this into the original equation, we get:

Ae^t - 2Ae^t + 3e^t = 0

Simplifying, we get:

A = -1

Therefore, the particular solution is:

y_p = -e^t

The general solution to the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:

y = Ce^(2t) - e^t

To determine how solutions behave as t approaches infinity, we can analyze the behavior of the exponential terms. Since e^(2t) grows much faster than e^t, the dominant term as t approaches infinity is e^(2t). Therefore, the solution approaches infinity as t approaches infinity.

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Answer:

40.0707

Step-by-step explanation:

because you multiply -0.0035 (-20.2) + 40= 40.0707

The probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable is 0.3823

In this question, we have been given  the horses in a large stable have a mean weight of 1124lbs, and a standard deviation of 150lbs.

We need to find the probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable.

μ = 1124 lbs, σ = 150 lbs, n = 41,

s = 150/(√41)

  = 23.43

pvalue of Z when X = 1124 + 7 = 1131 subtracted by the pvalue of Z when X = 1124 - 7 = 1117

So by the Central Limit Theorem,

Z = (1131 - 1124)/23.43

Z = 0.2987  has a pvalue of 0.7651

for X = 1117,

Z = (1117- 1124)/23.43

Z = -0.2988 has a pvalue of 0.3828

0.7651 -  0.3828 = 0.3823

Therefore, the probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable is 0.3823

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The transformation needed to the graph f (x) = | x + 2 | + 3 from  the graph of y = | x | is 2 units to the right and 3 units to the down.

The equation of the original graph is given by:

y = | x |

Now, the transformed graph is given as:

f (x) = | x + 2 | + 3

y = | x + 2 | + 3

This can also be written as:

y - 3 = | x + 2 |

So, we can see the transformation as:

the function will be transformed 2 units to the right and it will be transformed 3 units down.

Therefore, the transformation needed to the graph f (x) = | x + 2 | + 3 from  the graph of y = | x | is 2 units to the right and 3 units to the down.

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Answer:

D. 13

Step-by-step explanation:

Answer:

I'd pick 13

Step-by-step explanation:

Let M (-12,5) be the given point and O (0,0) be the origin.

Answer:

wasn't sure of what you wanted.

Step-by-step explanation:

Answer:

i believe its $48.75

Step-by-step explanation:

I didn't know if each pair of jean was 30.50 each. I just did 30.50 + 20.75 to get 51. 25. Then i subtracted that from 100, 100- 51.25, to get 48.75

To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.

This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.

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