Choose the mapping statement that represents each rotation.

the standard matrix of the linear transformation T: ℝ² → ℝ², which first reflects points through the line x₂ = -x₁ and then reflects points through the origin, is:

[ -1  0 ]

[  0  1 ]

To find the standard matrix of the linear transformation T: ℝ² → ℝ², we can determine how the basis vectors of ℝ² transform under the given transformation.

The standard basis vectors of ℝ² are:

e₁ = (1, 0) (corresponding to the x-axis)

e₂ = (0, 1) (corresponding to the y-axis)

First, let's apply the reflection through the line x₂ = -x₁:

For e₁ = (1, 0), the reflection through the line x₂ = -x₁ maps it to (-1, 0).

For e₂ = (0, 1), the reflection through the line x₂ = -x₁ maps it to (0, 1).

Next, let's apply the reflection through the origin:

For (-1, 0), the reflection through the origin keeps it the same (-1, 0).

For (0, 1), the reflection through the origin keeps it the same (0, 1).

Now, we have the transformed basis vectors:

T(e₁) = (-1, 0)

T(e₂) = (0, 1)

The standard matrix of the linear transformation T is constructed by placing the transformed basis vectors as columns:

[ -1  0 ]

[  0  1 ]

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Answer:

\(50^{o}\)

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Add 40 degrees to the 90 degrees and that will become 130 and all triangles add up to 180 so subtract 130 from 180 and you'll be left with 50

Adam should start cooking the turkey at 12:55 in order for it to be ready to carve at 17:15.

Based on the cooking instructions provided, since the turkey weighs 7kg, it falls into the category of "over 4kg." Therefore, the cooking time will be 20 minutes per kg, plus 90 minutes. Thus, the cooking time for the turkey would be:

(7 kg x 20 minutes per kg) + 90 minutes = 140 minutes + 90 minutes = 230 minutes.

So the turkey needs to cook for 230 minutes.

If Adam plans to carve the turkey at 17:15, then he needs to account for the resting time of 30 minutes before carving. Therefore, the turkey needs to finish cooking 30 minutes before 17:15, which is at 16:45.

Subtracting 230 minutes from 16:45 gives us the time when the turkey needs to be put in the oven, which is:

16:45 - 230 minutes = 12:55.

Therefore, Adam should start cooking the turkey at 12:55 in order for it to be ready to carve at 17:15, assuming he follows the cooking instructions provided.

The complete question is:-

Adam buys a bigger turkey than he needs the turkey he buys weighs 7kg the cooking instructions are:

less than 4kg-allow 20 minutes per kg, plus 70 minutes

over 4kg allow 20 minutes per kg, plus 90 minutes

always leave the turkey to rest for 30 minutes before carving to retain moisture.

he plans to carve the turkey at 17:15.

what time should he start cooking the turkey?

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To solve this problem, we need to use the Laplace transform and the recursive relation (7) as follows:

(a) We know that T(1/2) = r2. Using the recursive relation (7), we can express T(s) in terms of T(s-1/2) as:

T(s) = sT(s-1/2)

Substituting s = 1 in the above equation, we get:
T(1) = 1 * T(1/2)
T(1) = T(1/2) = r2

Now, taking the Laplace transform of both sides of the recursive relation (7), we get:
L{tT(s)} = L{xT(s-1/2)}

Using the property of Laplace transform that L{t^n} = n!/s^(n+1), we can rewrite the left-hand side as:
L{tT(s)} = -d/ds L{T(s)}

Similarly, using the property of Laplace transform that L{x^n} = n!/s^(n+1), we can rewrite the right-hand side as:
L{xT(s-1/2)} = -d/ds L{T(s-1/2)}

Substituting these expressions in the Laplace transform equation, we get:
-d/ds L{T(s)} = -d/ds L{T(s-1/2)}

Simplifying the above equation, we get:
L{T(s)} = L{T(s-1/2)}

Now, using the initial condition T(1/2) = r2, we can rewrite the above equation as:
L{T(s)} = L{T(s-1/2)} = r2/s

Taking the Laplace transform of t-1/2, we get:
L{t-1/2} = 1/s^(3/2)

Multiplying this expression by L{T(s)} = r2/s, we get:
L{t-1/2} L{T(s)} = r2/s^(5/2)

The answer to part (a) is L{t-1/2} = r2/s^(5/2).

(b) To determine L{x7/2}, we can use the fact that L{x^n} = n!/s^(n+1). Thus, we have:
L{x7/2} = (7/2)!/s^(7/2+1)

Simplifying the above expression, we get:
L{x7/2} = 7!/2^7 s^(1/2)

Now, multiplying this expression by L{T(s)} = r2/s, we get:
L{x7/2} L{T(s)} = 7!/2^7 r2 s^(-3/2)

The answer to part (b) is L{x7/2} = 7!/2^7 r2 s^(-3/2).

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The special marks that are used to show that segments are congruent is a double bar with an equals sign on top. "≅"

Congruent is used when two objects or segment have same size or shape. It's is often used in the field of geometry in which two given figures have similar shape or size.

When two angles or segment are the same in size, they're said to be congruent.

Congruent can be illustrated thus, if segment AB is congruent to segment CD, this would be written as

AB ≅ CD

Therefore, when this symbol "≅" is used, it indicates that the two segments have the same length and are therefore congruent.

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X = 40c + 39 = 40(4) + 39 = 199 is the required smallest positive integer.

The smallest positive integer which when divided by 4, 5, 8 and 9 leaves remainder 3, 4, 7 and 8, respectively is 539.

The given equation isx ≡ 3 (mod 4)x ≡ 4 (mod 5)x ≡ 7 (mod 8)x ≡ 8 (mod 9)

By the first condition,x = 4a + 3

where a is any positive integer.

Substituting in the second condition,4a + 3 ≡ 4 (mod 5)⇒ 4a ≡ 1 (mod 5)⇒ a ≡ 4 (mod 5)

Let a = 5b + 4 (where b is any positive integer)

Substituting this in x = 4a + 3, we get

x = 4(5b + 4) + 3 ⇒ x = 20b + 19

Now, substituting this in the third condition,20b + 19 ≡ 7 (mod 8)⇒ 4b ≡ 4 (mod 8)⇒ b ≡ 1 (mod 2)Let b = 2c + 1

Substituting this in x = 20b + 19,x = 20(2c + 1) + 19 ⇒ x = 40c + 39

Finally, substituting this in the fourth condition,40c + 39 ≡ 8 (mod 9)⇒ 4c ≡ 5 (mod 9)

We know that the modular inverse of 4 modulo 9 is 7.

Multiplying both sides by 7,7(4c) ≡ 7(5) (mod 9)⇒ 28c ≡ 35 (mod 9)⇒ c ≡ 4 (mod 9)

Hence,x = 40c + 39 = 40(4) + 39 = 199 is the required smallest positive integer.

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Folding a piece of paper to reach the moon would require an impractical number of folds, far exceeding the physical limits of paper.

The distance from Earth to the moon is approximately 384,400 kilometers. Let's assume we have a standard sheet of paper that is 0.1 millimeters thick. Each time we fold the paper, its thickness doubles. After one fold, the thickness would be 0.2 millimeters, after two folds it would be 0.4 millimeters, and so on. If we continue this doubling process, after 42 folds, the paper's thickness would reach about 439.8 kilometers.

However, even after reaching this astonishing thickness, the folded paper would still be nowhere near the distance required to reach the moon. To put it into perspective, after 42 folds, the paper would only be approximately 0.0001% of the distance to the moon. Folding the paper enough times to bridge the remaining distance is impossible due to the physical constraints of paper and the enormity of the distance involved.

In conclusion, folding a piece of paper to reach the moon would require an impractical number of folds, making it unfeasible in reality. The enormity of the distance between Earth and the moon, combined with the limited thickness of paper, prevents us from achieving this feat.

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Answer:

A=6

Step-by-step explanation:

M=3A

M+6=2(A+6)     M+6=2A+12      M=2A+6

System of equations:

M=3A            Subtract

M=2A+6

0=A-6

A=6

The length of the hypotenuse is 4√3 units.

Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,

16x² = x² + (3√5)²

15x² = 45

x² = 3

x = ±√3

Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.

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Given, P, denote the statement that5+9+13+17+.....+(4n+1) = n(2n+3)We are to use the principle of mathematical induction to show that the statement is true for all natural numbers.

Step 1: Verify the statement for n = 1

Put n = 1 in the given statement, we get

LHS: 5+9+13+17+....+(4n+1) = 5+1 = 6

RHS: n(2n+3) = 1(2 + 3) = 5As

LHS = RHS, the given statement is true for n = 1.

Step 2: Assume that the statement is true for n = k, i.e.,P(k) : 5+9+13+17+....+(4k+1) = k(2k+3)

Step 3: To prove that the statement is true for

n = k+1, i.e.,

P(k+1) : 5+9+13+17+....+[4(k+1)+1] = (k+1)(2k+5)Add (4(k+1)+1) to both sides of P(k), we get

LHS of P(k+1): 5+9+13+17+....+[4(k+1)+1] = [5+9+13+17+....+(4k+1)] + [4(k+1)+1]LHS of P(k+1):

5+9+13+17+....+[4(k+1)+1] = [k(2k+3)] + [4(k+1)+1]

{Using P(k)}LHS of P(k+1): 5+9+13+17+....+[4(k+1)+1] = 2k² + 7k + 5 + 4k + 5

LHS of P(k+1): 5+9+13+17+....+[4(k+1)+1] = 2k² + 11k + 10LHS of P(k+1): 5+9+13+17+....+[4(k+1)+1] = (k+1)(2k+5)RHS of P(k+1): (k+1)(2k+5) = 2k² + 7k + 5 + 4k + 5

RHS of P(k+1): (k+1)(2k+5) = 2k² + 11k + 10RHS of P(k+1): (k+1)(2k+5) = LHS of P(k+1)As

LHS = RHS, we can say that the given statement is true for all natural numbers.

Therefore, we have proved that the given statement holds for all natural numbers by the principle of mathematical induction.

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Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of B

To find the value of B we use cosine

That's

cos∅ = adjacent / hypotenuse

From the question

adjacent = 4

hypotenuse = 5

We have

\( \cos(B) = \frac{4}{5} \\ B = { \cos }^{ - 1} ( \frac{4}{5}) \\ = 36.869897645...\)

We have the final answer as

Hope this helps you

Answer:

The vertex is ( -2, -4)

Step-by-step explanation:

The vertex form is

y = a( x-h) ^2 +k

where ( h,k) is the vertex

f(x) = (x + 2)^2 – 4

Rewriting

f(x) = (x -  -2)^2 – 4

The vertex is ( -2, -4)

Answer:

68°F is 20°C

Step-by-step explanation:

C = (5/9)(F - 32)

C = (5/9)(68 - 32)

C = (5/9)(36)

C = 5 * 4

C = 20

Answer: 68°F is 20°C

The expense function consists of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula: P = (r(PV)) / (1 - (1+r)^(-n)) = $1,062.66 per month. The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months).

A depreciation function is a mathematical model that explains how the worth of an object decreases over time. It denotes the pace at which the worth of an asset depreciates over time.

In the given question,

a. The expense function will consist of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula:

\(P = (r(PV)) / (1 - (1+r)^(-n))\)

where P is the monthly payment, r is the monthly interest rate (4.875%/12 = 0.40625%), PV is the present value of the loan (54,000 - 8,000 = 46,000), and n is the total number of payments (4 years x 12 months per year = 48). Plugging these values into the formula, we get:

\(P = (0.0040625(46000)) / (1 - (1 + 0.0040625)^(-48)) = $1,062.66 per month\)

The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months), so the monthly depreciation can be calculated as:

d = (54000 - 0) / 120 = $450 per month

Therefore, the expense function E(x) and depreciation function D(x) are:

E(x) = 1062.66 + 450x

D(x) = 450x

where x is the number of months since the car was purchased.

b. The graph of the expense function and depreciation function on the same axes is attached.

c. At the intersection point (around 66 months), the monthly loan payment becomes greater than the monthly depreciation cost, meaning that Winnie is paying more each month than the car is depreciating. After 66 months, the expense function is increasing faster than the depreciation function, so the total value of the car is decreasing rapidly. By the end of 120 months, the car will have depreciated to a value of $0 and Winnie will have paid a total of $62,719.20 in loan payments.

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Answer:

-2.2

-2.5

-2.8

cuz uhhhhhhhhhhhhhhh

Answer:

2.1

2.3

2.7

Step-by-step explanation:

Yes

Answer:

1/4

Step-by-step explanation:

0.25

25/100

25 ÷ 25 = 1

100 ÷ 25 = 4

1/4

Answer: 80%

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

70% to 0.70

60*0.70= 42

Using division operation, if Amanda and her two friends split the total cost of renting a truck equally, Amanda will pay $47.50.

The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves the dividend (the total cost) divided by the divisor (3 friends), which results in a quotient.

Fixed cost for renting a truck = $120

The variable cost per mile = $0.50

The total miles Amanda and her two friends drove = 45 miles

The variable cost for 45 miles = $22.50 ($0.50 x 45)

The total costs = Fixed + Variable Costs

= $142.50

Cost paid by Amanda = $47.50 ($142.50/3)

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The fixed cost for renting a truck is $120 with a variable cost per mile of $0.50.

Answer:

Step-by-step explanation:

Circumference = π × diameter

3.14 = π

3,14 × 12 = 37.68 cm

Answer:

x=59

Step-by-step explanation:

x+12+x+x-9=180

3x+3=180

  -3       -3

3x=177/3

x=59

The total area of the two lawns is 30000m²

james mows two lawns

.the first lawn is 1000 meters long and 100 meters wide

Area of a rectangular lawn is calculated by the formula

area = l x w

Where l stands for the length of the lawn and w stands for the width of the lawn

Here, length is 1000m and width is 100m

area = 1000 x 100 = 100000

the second lawn is thee same length, and a width that is 2 times as much as the first one.

Area = l x w

Here Here, length is 1000m and width is 2 x 100m = 200

area = 1000 x 200 = 200000

The total area of the two lawns is equal to summatiom of area of 1st lawn and 2nd lawn

total area = 100000 + 200000 = 30000m²

Therefore,  the total area of the two lawns that is of area of 1st lawn and 2nd lawn is 30000m²

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The appropriate inference procedure is a one-sample z-test for p.

A one-sample z-test for the percentage would be the proper inference method in this case.

This is due to the fact that we only have one sample of coin flips and wish to determine whether the population's genuine percentage of heads (p), which represents the proportion of heads in the population, differs substantially from 0.5 (our null hypothesis).

In a one-sample z-test for the percentage, the sample proportion (p-hat) is calculated, and the standard error formula is used to get a z-statistic, which is then compared to a normal distribution to provide a p-value.

If the p-value is less than the significance level, which is typically 0.05, the null hypothesis is rejected.

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Answer:

The answer is 12 units

Step-by-step explanation:

The length of the radius is 12 units

The radius of a circle is a line drawn from the center of the circle to its circumference

The length (L) of the arc is given as:

\(L = 10\pi\)

The length of an arc is:

\(L = r\theta\)

So, we have:

\(r\theta =10\pi\)

The angle at the center of the circle is \(\frac{5\pi}{6}\)

So, we have:

\(r* \frac{5\pi}{6}=10\pi\)

Multiply both sides by 6

\(r* 5\pi=60\pi\)

Divide both sides by 5pi

\(r = 12\)

Hence, the length of the radius is 12 units

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35

Step-by-step explanation:

200-60 =140

140/4 which is the bonus

you should get 35

Answer:

it should be 35

Step-by-step explanation:

if the combined total of both prizes is 200, and we know the first one is 60, the second prize must be 140. now because the second prize had a bonus of 4 times the original prize amount, we divide 140 by 4 and get 35.

35*4=140+60=200

200-60=140÷4=35

hope this helped

1.129 + 8 = 9.129

1.129*8 = 9.032